export const description = ` Floating Point unit tests. `; import { makeTestGroup } from '../common/framework/test_group.js'; import { objectEquals, unreachable } from '../common/util/util.js'; import { kValue } from '../webgpu/util/constants.js'; import { FP, FPInterval, FPIntervalParam, IntervalEndpoints, } from '../webgpu/util/floating_point.js'; import { map2DArray, oneULPF32, oneULPF16, oneULPF64 } from '../webgpu/util/math.js'; import { reinterpretU16AsF16, reinterpretU32AsF32, reinterpretU64AsF64, } from '../webgpu/util/reinterpret.js'; import { UnitTest } from './unit_test.js'; export const g = makeTestGroup(UnitTest); const kFPTraitForULP = { f32: 'f32', f16: 'f16', } as const; /** Endpoints indicating an expectation of unbounded error */ const kUnboundedEndpoints: IntervalEndpoints = [Number.NEGATIVE_INFINITY, Number.POSITIVE_INFINITY]; /** Interval from kUnboundedEndpoints */ const kUnboundedInterval = { f32: FP.f32.toParam(kUnboundedEndpoints), f16: FP.f16.toParam(kUnboundedEndpoints), abstract: FP.abstract.toParam(kUnboundedEndpoints), }; /** @returns a number N * ULP greater than the provided number */ const kPlusNULPFunctions = { f32: (x: number, n: number) => { return x + n * oneULPF32(x); }, f16: (x: number, n: number) => { return x + n * oneULPF16(x); }, abstract: (x: number, n: number) => { return x + n * oneULPF64(x); }, }; /** @returns a number one ULP greater than the provided number */ const kPlusOneULPFunctions = { f32: (x: number): number => { return kPlusNULPFunctions['f32'](x, 1); }, f16: (x: number): number => { return kPlusNULPFunctions['f16'](x, 1); }, abstract: (x: number): number => { return kPlusNULPFunctions['abstract'](x, 1); }, }; /** @returns a number N * ULP less than the provided number */ const kMinusNULPFunctions = { f32: (x: number, n: number) => { return x - n * oneULPF32(x); }, f16: (x: number, n: number) => { return x - n * oneULPF16(x); }, abstract: (x: number, n: number) => { return x - n * oneULPF64(x); }, }; /** @returns a number one ULP less than the provided number */ const kMinusOneULPFunctions = { f32: (x: number): number => { return kMinusNULPFunctions['f32'](x, 1); }, f16: (x: number): number => { return kMinusNULPFunctions['f16'](x, 1); }, abstract: (x: number): number => { return kMinusNULPFunctions['abstract'](x, 1); }, }; /** @returns the expected IntervalEndpoints adjusted by the given error function * * @param expected the endpoints to be adjusted * @param error error function to adjust the endpoints via */ function applyError( expected: number | IntervalEndpoints, error: (n: number) => number ): IntervalEndpoints { // Avoiding going through FPInterval to avoid tying this to a specific kind const unpack = (n: number | IntervalEndpoints): [number, number] => { if (expected instanceof Array) { switch (expected.length) { case 1: return [expected[0], expected[0]]; case 2: return [expected[0], expected[1]]; } unreachable(`Tried to unpack an IntervalEndpoints with length other than 1 or 2`); } else { // TS doesn't narrow this to number automatically return [n as number, n as number]; } }; let [begin, end] = unpack(expected); begin -= error(begin); end += error(end); if (begin === end) { return [begin]; } return [begin, end]; } // FPInterval interface ConstructorCase { input: IntervalEndpoints; expected: IntervalEndpoints; } g.test('constructor') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore const cases: ConstructorCase[] = [ // Common cases { input: [0, 10], expected: [0, 10] }, { input: [-5, 0], expected: [-5, 0] }, { input: [-5, 10], expected: [-5, 10] }, { input: [0], expected: [0] }, { input: [10], expected: [10] }, { input: [-5], expected: [-5] }, { input: [2.5], expected: [2.5] }, { input: [-1.375], expected: [-1.375] }, { input: [-1.375, 2.5], expected: [-1.375, 2.5] }, // Edges { input: [0, constants.positive.max], expected: [0, constants.positive.max] }, { input: [constants.negative.min, 0], expected: [constants.negative.min, 0] }, { input: [constants.negative.min, constants.positive.max], expected: [constants.negative.min, constants.positive.max] }, // Infinities { input: [0, constants.positive.infinity], expected: [0, Number.POSITIVE_INFINITY] }, { input: [constants.negative.infinity, 0], expected: [Number.NEGATIVE_INFINITY, 0] }, { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, ]; // Note: Out of range values are limited to infinities for abstract float, due to abstract // float and 'number' both being f64. So there are no separate OOR tests for abstract float, // otherwise the testing framework will consider them duplicated. if (p.trait !== 'abstract') { // prettier-ignore cases.push(...[ // Out of range { input: [0, 2 * constants.positive.max], expected: [0, 2 * constants.positive.max] }, { input: [2 * constants.negative.min, 0], expected: [2 * constants.negative.min, 0] }, { input: [2 * constants.negative.min, 2 * constants.positive.max], expected: [2 * constants.negative.min, 2 * constants.positive.max] }, ] as ConstructorCase[]); } return cases; }) ) .fn(t => { const i = new FPInterval(t.params.trait, ...t.params.input); t.expect( objectEquals(i.endpoints(), t.params.expected), `new FPInterval('${t.params.trait}', [${t.params.input}]) returned ${i}. Expected [${t.params.expected}]` ); }); interface ContainsNumberCase { endpoints: number | IntervalEndpoints; value: number; expected: boolean; } g.test('contains_number') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore const cases: ContainsNumberCase[] = [ // Common usage { endpoints: [0, 10], value: 0, expected: true }, { endpoints: [0, 10], value: 10, expected: true }, { endpoints: [0, 10], value: 5, expected: true }, { endpoints: [0, 10], value: -5, expected: false }, { endpoints: [0, 10], value: 50, expected: false }, { endpoints: [0, 10], value: Number.NaN, expected: false }, { endpoints: [-5, 10], value: 0, expected: true }, { endpoints: [-5, 10], value: 10, expected: true }, { endpoints: [-5, 10], value: 5, expected: true }, { endpoints: [-5, 10], value: -5, expected: true }, { endpoints: [-5, 10], value: -6, expected: false }, { endpoints: [-5, 10], value: 50, expected: false }, { endpoints: [-5, 10], value: -10, expected: false }, { endpoints: [-1.375, 2.5], value: -10, expected: false }, { endpoints: [-1.375, 2.5], value: 0.5, expected: true }, { endpoints: [-1.375, 2.5], value: 10, expected: false }, // Point { endpoints: 0, value: 0, expected: true }, { endpoints: 0, value: 10, expected: false }, { endpoints: 0, value: -1000, expected: false }, { endpoints: 10, value: 10, expected: true }, { endpoints: 10, value: 0, expected: false }, { endpoints: 10, value: -10, expected: false }, { endpoints: 10, value: 11, expected: false }, // Upper infinity { endpoints: [0, constants.positive.infinity], value: constants.positive.min, expected: true }, { endpoints: [0, constants.positive.infinity], value: constants.positive.max, expected: true }, { endpoints: [0, constants.positive.infinity], value: constants.positive.infinity, expected: true }, { endpoints: [0, constants.positive.infinity], value: constants.negative.min, expected: false }, { endpoints: [0, constants.positive.infinity], value: constants.negative.max, expected: false }, { endpoints: [0, constants.positive.infinity], value: constants.negative.infinity, expected: false }, // Lower infinity { endpoints: [constants.negative.infinity, 0], value: constants.positive.min, expected: false }, { endpoints: [constants.negative.infinity, 0], value: constants.positive.max, expected: false }, { endpoints: [constants.negative.infinity, 0], value: constants.positive.infinity, expected: false }, { endpoints: [constants.negative.infinity, 0], value: constants.negative.min, expected: true }, { endpoints: [constants.negative.infinity, 0], value: constants.negative.max, expected: true }, { endpoints: [constants.negative.infinity, 0], value: constants.negative.infinity, expected: true }, // Full infinity { endpoints: [constants.negative.infinity, constants.positive.infinity], value: constants.positive.min, expected: true }, { endpoints: [constants.negative.infinity, constants.positive.infinity], value: constants.positive.max, expected: true }, { endpoints: [constants.negative.infinity, constants.positive.infinity], value: constants.positive.infinity, expected: true }, { endpoints: [constants.negative.infinity, constants.positive.infinity], value: constants.negative.min, expected: true }, { endpoints: [constants.negative.infinity, constants.positive.infinity], value: constants.negative.max, expected: true }, { endpoints: [constants.negative.infinity, constants.positive.infinity], value: constants.negative.infinity, expected: true }, { endpoints: [constants.negative.infinity, constants.positive.infinity], value: Number.NaN, expected: true }, // Maximum f32 boundary { endpoints: [0, constants.positive.max], value: constants.positive.min, expected: true }, { endpoints: [0, constants.positive.max], value: constants.positive.max, expected: true }, { endpoints: [0, constants.positive.max], value: constants.positive.infinity, expected: false }, { endpoints: [0, constants.positive.max], value: constants.negative.min, expected: false }, { endpoints: [0, constants.positive.max], value: constants.negative.max, expected: false }, { endpoints: [0, constants.positive.max], value: constants.negative.infinity, expected: false }, // Minimum f32 boundary { endpoints: [constants.negative.min, 0], value: constants.positive.min, expected: false }, { endpoints: [constants.negative.min, 0], value: constants.positive.max, expected: false }, { endpoints: [constants.negative.min, 0], value: constants.positive.infinity, expected: false }, { endpoints: [constants.negative.min, 0], value: constants.negative.min, expected: true }, { endpoints: [constants.negative.min, 0], value: constants.negative.max, expected: true }, { endpoints: [constants.negative.min, 0], value: constants.negative.infinity, expected: false }, // Subnormals { endpoints: [0, constants.positive.min], value: constants.positive.subnormal.min, expected: true }, { endpoints: [0, constants.positive.min], value: constants.positive.subnormal.max, expected: true }, { endpoints: [0, constants.positive.min], value: constants.negative.subnormal.min, expected: false }, { endpoints: [0, constants.positive.min], value: constants.negative.subnormal.max, expected: false }, { endpoints: [constants.negative.max, 0], value: constants.positive.subnormal.min, expected: false }, { endpoints: [constants.negative.max, 0], value: constants.positive.subnormal.max, expected: false }, { endpoints: [constants.negative.max, 0], value: constants.negative.subnormal.min, expected: true }, { endpoints: [constants.negative.max, 0], value: constants.negative.subnormal.max, expected: true }, { endpoints: [0, constants.positive.subnormal.min], value: constants.positive.subnormal.min, expected: true }, { endpoints: [0, constants.positive.subnormal.min], value: constants.positive.subnormal.max, expected: false }, { endpoints: [0, constants.positive.subnormal.min], value: constants.negative.subnormal.min, expected: false }, { endpoints: [0, constants.positive.subnormal.min], value: constants.negative.subnormal.max, expected: false }, { endpoints: [constants.negative.subnormal.max, 0], value: constants.positive.subnormal.min, expected: false }, { endpoints: [constants.negative.subnormal.max, 0], value: constants.positive.subnormal.max, expected: false }, { endpoints: [constants.negative.subnormal.max, 0], value: constants.negative.subnormal.min, expected: false }, { endpoints: [constants.negative.subnormal.max, 0], value: constants.negative.subnormal.max, expected: true }, ]; // Note: Out of range values are limited to infinities for abstract float, due to abstract // float and 'number' both being f64. So there are no separate OOR tests for abstract float, // otherwise the testing framework will consider them duplicated. if (p.trait !== 'abstract') { // prettier-ignore cases.push(...[ // Out of range high { endpoints: [0, 2 * constants.positive.max], value: constants.positive.min, expected: true }, { endpoints: [0, 2 * constants.positive.max], value: constants.positive.max, expected: true }, { endpoints: [0, 2 * constants.positive.max], value: constants.positive.infinity, expected: false }, { endpoints: [0, 2 * constants.positive.max], value: constants.negative.min, expected: false }, { endpoints: [0, 2 * constants.positive.max], value: constants.negative.max, expected: false }, { endpoints: [0, 2 * constants.positive.max], value: constants.negative.infinity, expected: false }, // Out of range low { endpoints: [2 * constants.negative.min, 0], value: constants.positive.min, expected: false }, { endpoints: [2 * constants.negative.min, 0], value: constants.positive.max, expected: false }, { endpoints: [2 * constants.negative.min, 0], value: constants.positive.infinity, expected: false }, { endpoints: [2 * constants.negative.min, 0], value: constants.negative.min, expected: true }, { endpoints: [2 * constants.negative.min, 0], value: constants.negative.max, expected: true }, { endpoints: [2 * constants.negative.min, 0], value: constants.negative.infinity, expected: false }, ] as ContainsNumberCase[]); } return cases; }) ) .fn(t => { const trait = FP[t.params.trait]; const i = trait.toInterval(t.params.endpoints); const value = t.params.value; const expected = t.params.expected; const got = i.contains(value); t.expect(expected === got, `${i}.contains(${value}) returned ${got}. Expected ${expected}`); }); interface ContainsIntervalCase { lhs: number | IntervalEndpoints; rhs: number | IntervalEndpoints; expected: boolean; } g.test('contains_interval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore const cases: ContainsIntervalCase[] = [ // Common usage { lhs: [-10, 10], rhs: 0, expected: true }, { lhs: [-10, 10], rhs: [-1, 0], expected: true }, { lhs: [-10, 10], rhs: [0, 2], expected: true }, { lhs: [-10, 10], rhs: [-1, 2], expected: true }, { lhs: [-10, 10], rhs: [0, 10], expected: true }, { lhs: [-10, 10], rhs: [-10, 2], expected: true }, { lhs: [-10, 10], rhs: [-10, 10], expected: true }, { lhs: [-10, 10], rhs: [-100, 10], expected: false }, // Upper infinity { lhs: [0, constants.positive.infinity], rhs: 0, expected: true }, { lhs: [0, constants.positive.infinity], rhs: [-1, 0], expected: false }, { lhs: [0, constants.positive.infinity], rhs: [0, 1], expected: true }, { lhs: [0, constants.positive.infinity], rhs: [0, constants.positive.max], expected: true }, { lhs: [0, constants.positive.infinity], rhs: [0, constants.positive.infinity], expected: true }, { lhs: [0, constants.positive.infinity], rhs: [100, constants.positive.infinity], expected: true }, { lhs: [0, constants.positive.infinity], rhs: [Number.NEGATIVE_INFINITY, constants.positive.infinity], expected: false }, // Lower infinity { lhs: [constants.negative.infinity, 0], rhs: 0, expected: true }, { lhs: [constants.negative.infinity, 0], rhs: [-1, 0], expected: true }, { lhs: [constants.negative.infinity, 0], rhs: [constants.negative.min, 0], expected: true }, { lhs: [constants.negative.infinity, 0], rhs: [0, 1], expected: false }, { lhs: [constants.negative.infinity, 0], rhs: [constants.negative.infinity, 0], expected: true }, { lhs: [constants.negative.infinity, 0], rhs: [constants.negative.infinity, -100 ], expected: true }, { lhs: [constants.negative.infinity, 0], rhs: [constants.negative.infinity, constants.positive.infinity], expected: false }, // Full infinity { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: 0, expected: true }, { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: [-1, 0], expected: true }, { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: [0, 1], expected: true }, { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: [0, constants.positive.infinity], expected: true }, { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: [100, constants.positive.infinity], expected: true }, { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: [constants.negative.infinity, 0], expected: true }, { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: [constants.negative.infinity, -100 ], expected: true }, { lhs: [constants.negative.infinity, constants.positive.infinity], rhs: [constants.negative.infinity, constants.positive.infinity], expected: true }, // Maximum boundary { lhs: [0, constants.positive.max], rhs: 0, expected: true }, { lhs: [0, constants.positive.max], rhs: [-1, 0], expected: false }, { lhs: [0, constants.positive.max], rhs: [0, 1], expected: true }, { lhs: [0, constants.positive.max], rhs: [0, constants.positive.max], expected: true }, { lhs: [0, constants.positive.max], rhs: [0, constants.positive.infinity], expected: false }, { lhs: [0, constants.positive.max], rhs: [100, constants.positive.infinity], expected: false }, { lhs: [0, constants.positive.max], rhs: [constants.negative.infinity, constants.positive.infinity], expected: false }, // Minimum boundary { lhs: [constants.negative.min, 0], rhs: [0, 0], expected: true }, { lhs: [constants.negative.min, 0], rhs: [-1, 0], expected: true }, { lhs: [constants.negative.min, 0], rhs: [constants.negative.min, 0], expected: true }, { lhs: [constants.negative.min, 0], rhs: [0, 1], expected: false }, { lhs: [constants.negative.min, 0], rhs: [constants.negative.infinity, 0], expected: false }, { lhs: [constants.negative.min, 0], rhs: [constants.negative.infinity, -100 ], expected: false }, { lhs: [constants.negative.min, 0], rhs: [constants.negative.infinity, constants.positive.infinity], expected: false }, ]; // Note: Out of range values are limited to infinities for abstract float, due to abstract // float and 'number' both being f64. So there are no separate OOR tests for abstract float, // otherwise the testing framework will consider them duplicated. if (p.trait !== 'abstract') { // prettier-ignore cases.push(...[ // Out of range high { lhs: [0, 2 * constants.positive.max], rhs: 0, expected: true }, { lhs: [0, 2 * constants.positive.max], rhs: [-1, 0], expected: false }, { lhs: [0, 2 * constants.positive.max], rhs: [0, 1], expected: true }, { lhs: [0, 2 * constants.positive.max], rhs: [0, constants.positive.max], expected: true }, { lhs: [0, 2 * constants.positive.max], rhs: [0, constants.positive.infinity], expected: false }, { lhs: [0, 2 * constants.positive.max], rhs: [100, constants.positive.infinity], expected: false }, { lhs: [0, 2 * constants.positive.max], rhs: [constants.negative.infinity, constants.positive.infinity], expected: false }, // Out of range low { lhs: [2 * constants.negative.min, 0], rhs: 0, expected: true }, { lhs: [2 * constants.negative.min, 0], rhs: [-1, 0], expected: true }, { lhs: [2 * constants.negative.min, 0], rhs: [constants.negative.min, 0], expected: true }, { lhs: [2 * constants.negative.min, 0], rhs: [0, 1], expected: false }, { lhs: [2 * constants.negative.min, 0], rhs: [constants.negative.infinity, 0], expected: false }, { lhs: [2 * constants.negative.min, 0], rhs: [constants.negative.infinity, -100 ], expected: false }, { lhs: [2 * constants.negative.min, 0], rhs: [constants.negative.infinity, constants.positive.infinity], expected: false }, ] as ContainsIntervalCase[]); } return cases; }) ) .fn(t => { const trait = FP[t.params.trait]; const lhs = trait.toInterval(t.params.lhs); const rhs = trait.toInterval(t.params.rhs); const expected = t.params.expected; const got = lhs.contains(rhs); t.expect(expected === got, `${lhs}.contains(${rhs}) returned ${got}. Expected ${expected}`); }); // Utilities interface SpanIntervalsCase { intervals: (number | IntervalEndpoints)[]; expected: number | IntervalEndpoints; } g.test('spanIntervals') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore return [ // Single Intervals { intervals: [[0, 10]], expected: [0, 10] }, { intervals: [[0, constants.positive.max]], expected: [0, constants.positive.max] }, { intervals: [[0, constants.positive.nearest_max]], expected: [0, constants.positive.nearest_max] }, { intervals: [[0, constants.positive.infinity]], expected: [0, Number.POSITIVE_INFINITY] }, { intervals: [[constants.negative.min, 0]], expected: [constants.negative.min, 0] }, { intervals: [[constants.negative.nearest_min, 0]], expected: [constants.negative.nearest_min, 0] }, { intervals: [[constants.negative.infinity, 0]], expected: [Number.NEGATIVE_INFINITY, 0] }, // Double Intervals { intervals: [[0, 1], [2, 5]], expected: [0, 5] }, { intervals: [[2, 5], [0, 1]], expected: [0, 5] }, { intervals: [[0, 2], [1, 5]], expected: [0, 5] }, { intervals: [[0, 5], [1, 2]], expected: [0, 5] }, { intervals: [[constants.negative.infinity, 0], [0, constants.positive.infinity]], expected: kUnboundedEndpoints }, // Multiple Intervals { intervals: [[0, 1], [2, 3], [4, 5]], expected: [0, 5] }, { intervals: [[0, 1], [4, 5], [2, 3]], expected: [0, 5] }, { intervals: [[0, 1], [0, 1], [0, 1]], expected: [0, 1] }, // Point Intervals { intervals: [1], expected: 1 }, { intervals: [1, 2], expected: [1, 2] }, { intervals: [-10, 2], expected: [-10, 2] }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const intervals = t.params.intervals.map(i => trait.toInterval(i)); const expected = trait.toInterval(t.params.expected); const got = trait.spanIntervals(...intervals); t.expect( objectEquals(got, expected), `${t.params.trait}.span({${intervals}}) returned ${got}. Expected ${expected}` ); }); interface isVectorCase { input: (number | IntervalEndpoints | FPIntervalParam)[]; expected: boolean; } g.test('isVector') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; return [ // numbers { input: [1, 2], expected: false }, { input: [1, 2, 3], expected: false }, { input: [1, 2, 3, 4], expected: false }, // IntervalEndpoints { input: [[1], [2]], expected: false }, { input: [[1], [2], [3]], expected: false }, { input: [[1], [2], [3], [4]], expected: false }, { input: [ [1, 2], [2, 3], ], expected: false, }, { input: [ [1, 2], [2, 3], [3, 4], ], expected: false, }, { input: [ [1, 2], [2, 3], [3, 4], [4, 5], ], expected: false, }, // FPInterval, valid dimensions { input: [trait.toParam([1]), trait.toParam([2])], expected: true }, { input: [trait.toParam([1, 2]), trait.toParam([2, 3])], expected: true }, { input: [trait.toParam([1]), trait.toParam([2]), trait.toParam([3])], expected: true, }, { input: [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], expected: true, }, { input: [trait.toParam([1]), trait.toParam([2]), trait.toParam([3]), trait.toParam([4])], expected: true, }, { input: [ trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4]), trait.toParam([4, 5]), ], expected: true, }, // FPInterval, invalid dimensions { input: [trait.toParam([1])], expected: false }, { input: [ trait.toParam([1]), trait.toParam([2]), trait.toParam([3]), trait.toParam([4]), trait.toParam([5]), ], expected: false, }, // Mixed { input: [1, [2]], expected: false }, { input: [1, [2], trait.toParam([3])], expected: false }, { input: [1, trait.toParam([2]), [3], 4], expected: false }, { input: [trait.toParam(1), 2], expected: false }, { input: [trait.toParam(1), [2]], expected: false }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const input = t.params.input.map(e => trait.fromParam(e)); const expected = t.params.expected; const got = trait.isVector(input); t.expect( got === expected, `${t.params.trait}.isVector([${input}]) returned ${got}. Expected ${expected}` ); }); interface toVectorCase { input: (number | IntervalEndpoints | FPIntervalParam)[]; expected: (number | IntervalEndpoints)[]; } g.test('toVector') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; return [ // numbers { input: [1, 2], expected: [1, 2] }, { input: [1, 2, 3], expected: [1, 2, 3] }, { input: [1, 2, 3, 4], expected: [1, 2, 3, 4] }, // IntervalEndpoints { input: [[1], [2]], expected: [1, 2] }, { input: [[1], [2], [3]], expected: [1, 2, 3] }, { input: [[1], [2], [3], [4]], expected: [1, 2, 3, 4] }, { input: [ [1, 2], [2, 3], ], expected: [ [1, 2], [2, 3], ], }, { input: [ [1, 2], [2, 3], [3, 4], ], expected: [ [1, 2], [2, 3], [3, 4], ], }, { input: [ [1, 2], [2, 3], [3, 4], [4, 5], ], expected: [ [1, 2], [2, 3], [3, 4], [4, 5], ], }, // FPInterval { input: [trait.toParam([1]), trait.toParam([2])], expected: [1, 2] }, { input: [trait.toParam([1, 2]), trait.toParam([2, 3])], expected: [ [1, 2], [2, 3], ], }, { input: [trait.toParam([1]), trait.toParam([2]), trait.toParam([3])], expected: [1, 2, 3], }, { input: [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], expected: [ [1, 2], [2, 3], [3, 4], ], }, { input: [trait.toParam([1]), trait.toParam([2]), trait.toParam([3]), trait.toParam([4])], expected: [1, 2, 3, 4], }, { input: [ trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4]), trait.toParam([4, 5]), ], expected: [ [1, 2], [2, 3], [3, 4], [4, 5], ], }, // Mixed { input: [1, [2]], expected: [1, 2] }, { input: [1, [2], trait.toParam([3])], expected: [1, 2, 3] }, { input: [1, trait.toParam([2]), [3], 4], expected: [1, 2, 3, 4] }, { input: [1, [2], [2, 3], kUnboundedInterval[p.trait]], expected: [1, 2, [2, 3], kUnboundedEndpoints], }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const input = t.params.input.map(e => trait.fromParam(e)); const expected = t.params.expected.map(e => trait.toInterval(e)); const got = trait.toVector(input); t.expect( objectEquals(got, expected), `${t.params.trait}.toVector([${input}]) returned [${got}]. Expected [${expected}]` ); }); interface isMatrixCase { input: (number | IntervalEndpoints | FPIntervalParam)[][]; expected: boolean; } g.test('isMatrix') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; return [ // numbers { input: [ [1, 2], [3, 4], ], expected: false, }, { input: [ [1, 2], [3, 4], [5, 6], ], expected: false, }, { input: [ [1, 2], [3, 4], [5, 6], [7, 8], ], expected: false, }, { input: [ [1, 2, 3], [4, 5, 6], ], expected: false, }, { input: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], ], expected: false, }, { input: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], ], expected: false, }, { input: [ [1, 2, 3, 4], [5, 6, 7, 8], ], expected: false, }, { input: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], ], expected: false, }, { input: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], ], expected: false, }, // IntervalEndpoints { input: [ [[1], [2]], [[3], [4]], ], expected: false, }, { input: [ [[1], [2]], [[3], [4]], [[5], [6]], ], expected: false, }, { input: [ [[1], [2]], [[3], [4]], [[5], [6]], [[7], [8]], ], expected: false, }, { input: [ [[1], [2], [3]], [[4], [5], [6]], ], expected: false, }, { input: [ [[1], [2], [3]], [[4], [5], [6]], [[7], [8], [9]], ], expected: false, }, { input: [ [[1], [2], [3]], [[4], [5], [6]], [[7], [8], [9]], [[10], [11], [12]], ], expected: false, }, { input: [ [[1], [2], [3], [4]], [[5], [6], [7], [8]], ], expected: false, }, { input: [ [[1], [2], [3], [4]], [[5], [6], [7], [8]], [[9], [10], [11], [12]], ], expected: false, }, { input: [ [[1], [2], [3], [4]], [[5], [6], [7], [8]], [[9], [10], [11], [12]], [[13], [14], [15], [16]], ], expected: false, }, // FPInterval, valid dimensions { input: [ [trait.toParam(1), trait.toParam(2)], [trait.toParam(3), trait.toParam(4)], ], expected: true, }, { input: [ [trait.toParam(1), trait.toParam(2)], [trait.toParam(3), trait.toParam(4)], [trait.toParam(5), trait.toParam(6)], ], expected: true, }, { input: [ [trait.toParam(1), trait.toParam(2)], [trait.toParam(3), trait.toParam(4)], [trait.toParam(5), trait.toParam(6)], [trait.toParam(7), trait.toParam(8)], ], expected: true, }, { input: [ [trait.toParam(1), trait.toParam(2), trait.toParam(3)], [trait.toParam(4), trait.toParam(5), trait.toParam(6)], ], expected: true, }, { input: [ [trait.toParam(1), trait.toParam(2), trait.toParam(3)], [trait.toParam(4), trait.toParam(5), trait.toParam(6)], [trait.toParam(7), trait.toParam(8), trait.toParam(9)], ], expected: true, }, { input: [ [trait.toParam(1), trait.toParam(2), trait.toParam(3)], [trait.toParam(4), trait.toParam(5), trait.toParam(6)], [trait.toParam(7), trait.toParam(8), trait.toParam(9)], [trait.toParam(10), trait.toParam(11), trait.toParam(12)], ], expected: true, }, { input: [ [trait.toParam(1), trait.toParam(2), trait.toParam(3), trait.toParam(4)], [trait.toParam(5), trait.toParam(6), trait.toParam(7), trait.toParam(8)], ], expected: true, }, { input: [ [trait.toParam(1), trait.toParam(2), trait.toParam(3), trait.toParam(4)], [trait.toParam(5), trait.toParam(6), trait.toParam(7), trait.toParam(8)], [trait.toParam(9), trait.toParam(10), trait.toParam(11), trait.toParam(12)], ], expected: true, }, { input: [ [trait.toParam(1), trait.toParam(2), trait.toParam(3), trait.toParam(4)], [trait.toParam(5), trait.toParam(6), trait.toParam(7), trait.toParam(8)], [trait.toParam(9), trait.toParam(10), trait.toParam(11), trait.toParam(12)], [trait.toParam(13), trait.toParam(14), trait.toParam(15), trait.toParam(16)], ], expected: true, }, { input: [ [trait.toParam([1, 2]), trait.toParam([2, 3])], [trait.toParam([3, 4]), trait.toParam([4, 5])], ], expected: true, }, { input: [ [trait.toParam([1, 2]), trait.toParam([2, 3])], [trait.toParam([3, 4]), trait.toParam([4, 5])], [trait.toParam([5, 6]), trait.toParam([6, 7])], ], expected: true, }, { input: [ [trait.toParam([1, 2]), trait.toParam([2, 3])], [trait.toParam([3, 4]), trait.toParam([4, 5])], [trait.toParam([5, 6]), trait.toParam([6, 7])], [trait.toParam([7, 8]), trait.toParam([8, 9])], ], expected: true, }, { input: [ [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], [trait.toParam([4, 5]), trait.toParam([5, 6]), trait.toParam([6, 7])], ], expected: true, }, { input: [ [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], [trait.toParam([4, 5]), trait.toParam([5, 6]), trait.toParam([6, 7])], [trait.toParam([7, 8]), trait.toParam([8, 9]), trait.toParam([9, 10])], ], expected: true, }, { input: [ [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], [trait.toParam([4, 5]), trait.toParam([5, 6]), trait.toParam([6, 7])], [trait.toParam([7, 8]), trait.toParam([8, 9]), trait.toParam([9, 10])], [trait.toParam([10, 11]), trait.toParam([11, 12]), trait.toParam([12, 13])], ], expected: true, }, { input: [ [ trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4]), trait.toParam([4, 5]), ], [ trait.toParam([5, 6]), trait.toParam([6, 7]), trait.toParam([7, 8]), trait.toParam([8, 9]), ], ], expected: true, }, { input: [ [ trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4]), trait.toParam([4, 5]), ], [ trait.toParam([5, 6]), trait.toParam([6, 7]), trait.toParam([7, 8]), trait.toParam([8, 9]), ], [ trait.toParam([9, 10]), trait.toParam([10, 11]), trait.toParam([11, 12]), trait.toParam([12, 13]), ], ], expected: true, }, { input: [ [ trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4]), trait.toParam([4, 5]), ], [ trait.toParam([5, 6]), trait.toParam([6, 7]), trait.toParam([7, 8]), trait.toParam([8, 9]), ], [ trait.toParam([9, 10]), trait.toParam([10, 11]), trait.toParam([11, 12]), trait.toParam([12, 13]), ], [ trait.toParam([13, 14]), trait.toParam([14, 15]), trait.toParam([15, 16]), trait.toParam([16, 17]), ], ], expected: true, }, // FPInterval, invalid dimensions { input: [[trait.toParam(1)]], expected: false }, { input: [[trait.toParam(1)], [trait.toParam(3), trait.toParam(4)]], expected: false, }, { input: [ [trait.toParam(1), trait.toParam(2)], [trait.toParam(3), trait.toParam(4), trait.toParam(5)], ], expected: false, }, { input: [ [trait.toParam(1), trait.toParam(2)], [trait.toParam(3), trait.toParam(4)], [trait.toParam(5)], ], expected: false, }, { input: [ [trait.toParam(1), trait.toParam(2)], [trait.toParam(3), trait.toParam(4)], [trait.toParam(5), trait.toParam(6)], [trait.toParam(7), trait.toParam(8)], [trait.toParam(9), trait.toParam(10)], ], expected: false, }, // Mixed { input: [ [1, [2]], [3, 4], ], expected: false, }, { input: [ [[1], [2]], [[3], 4], ], expected: false, }, { input: [ [1, 2], [trait.toParam([3]), 4], ], expected: false, }, { input: [ [[1], trait.toParam([2])], [trait.toParam([3]), trait.toParam([4])], ], expected: false, }, { input: [ [trait.toParam(1), [2]], [3, 4], ], expected: false, }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const input = t.params.input.map(a => a.map(e => trait.fromParam(e))); const expected = t.params.expected; const got = trait.isMatrix(input); t.expect( got === expected, `${t.params.trait}.isMatrix([${input}]) returned ${got}. Expected ${expected}` ); }); interface toMatrixCase { input: (number | IntervalEndpoints | FPIntervalParam)[][]; expected: (number | IntervalEndpoints)[][]; } g.test('toMatrix') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; return [ // numbers { input: [ [1, 2], [3, 4], ], expected: [ [1, 2], [3, 4], ], }, { input: [ [1, 2], [3, 4], [5, 6], ], expected: [ [1, 2], [3, 4], [5, 6], ], }, { input: [ [1, 2], [3, 4], [5, 6], [7, 8], ], expected: [ [1, 2], [3, 4], [5, 6], [7, 8], ], }, { input: [ [1, 2, 3], [4, 5, 6], ], expected: [ [1, 2, 3], [4, 5, 6], ], }, { input: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], ], expected: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], ], }, { input: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], ], expected: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], ], }, { input: [ [1, 2, 3, 4], [5, 6, 7, 8], ], expected: [ [1, 2, 3, 4], [5, 6, 7, 8], ], }, { input: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], ], expected: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], ], }, { input: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], ], expected: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], ], }, // IntervalEndpoints { input: [ [[1], [2]], [[3], [4]], ], expected: [ [1, 2], [3, 4], ], }, { input: [ [[1], [2]], [[3], [4]], [[5], [6]], ], expected: [ [1, 2], [3, 4], [5, 6], ], }, { input: [ [[1], [2]], [[3], [4]], [[5], [6]], [[7], [8]], ], expected: [ [1, 2], [3, 4], [5, 6], [7, 8], ], }, { input: [ [[1], [2], [3]], [[4], [5], [6]], ], expected: [ [1, 2, 3], [4, 5, 6], ], }, { input: [ [[1], [2], [3]], [[4], [5], [6]], [[7], [8], [9]], ], expected: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], ], }, { input: [ [[1], [2], [3]], [[4], [5], [6]], [[7], [8], [9]], [[10], [11], [12]], ], expected: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], ], }, { input: [ [[1], [2], [3], [4]], [[5], [6], [7], [8]], ], expected: [ [1, 2, 3, 4], [5, 6, 7, 8], ], }, { input: [ [[1], [2], [3], [4]], [[5], [6], [7], [8]], [[9], [10], [11], [12]], ], expected: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], ], }, { input: [ [[1], [2], [3], [4]], [[5], [6], [7], [8]], [[9], [10], [11], [12]], [[13], [14], [15], [16]], ], expected: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], ], }, // FPInterval { input: [ [trait.toParam(1), trait.toParam(2)], [trait.toParam(3), trait.toParam(4)], ], expected: [ [1, 2], [3, 4], ], }, { input: [ [trait.toParam(1), trait.toParam(2)], [trait.toParam(3), trait.toParam(4)], [trait.toParam(5), trait.toParam(6)], ], expected: [ [1, 2], [3, 4], [5, 6], ], }, { input: [ [trait.toParam(1), trait.toParam(2)], [trait.toParam(3), trait.toParam(4)], [trait.toParam(5), trait.toParam(6)], [trait.toParam(7), trait.toParam(8)], ], expected: [ [1, 2], [3, 4], [5, 6], [7, 8], ], }, { input: [ [trait.toParam(1), trait.toParam(2), trait.toParam(3)], [trait.toParam(4), trait.toParam(5), trait.toParam(6)], ], expected: [ [1, 2, 3], [4, 5, 6], ], }, { input: [ [trait.toParam(1), trait.toParam(2), trait.toParam(3)], [trait.toParam(4), trait.toParam(5), trait.toParam(6)], [trait.toParam(7), trait.toParam(8), trait.toParam(9)], ], expected: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], ], }, { input: [ [trait.toParam(1), trait.toParam(2), trait.toParam(3)], [trait.toParam(4), trait.toParam(5), trait.toParam(6)], [trait.toParam(7), trait.toParam(8), trait.toParam(9)], [trait.toParam(10), trait.toParam(11), trait.toParam(12)], ], expected: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], ], }, { input: [ [trait.toParam(1), trait.toParam(2), trait.toParam(3), trait.toParam(4)], [trait.toParam(5), trait.toParam(6), trait.toParam(7), trait.toParam(8)], ], expected: [ [1, 2, 3, 4], [5, 6, 7, 8], ], }, { input: [ [trait.toParam(1), trait.toParam(2), trait.toParam(3), trait.toParam(4)], [trait.toParam(5), trait.toParam(6), trait.toParam(7), trait.toParam(8)], [trait.toParam(9), trait.toParam(10), trait.toParam(11), trait.toParam(12)], ], expected: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], ], }, { input: [ [trait.toParam(1), trait.toParam(2), trait.toParam(3), trait.toParam(4)], [trait.toParam(5), trait.toParam(6), trait.toParam(7), trait.toParam(8)], [trait.toParam(9), trait.toParam(10), trait.toParam(11), trait.toParam(12)], [trait.toParam(13), trait.toParam(14), trait.toParam(15), trait.toParam(16)], ], expected: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], ], }, { input: [ [trait.toParam([1, 2]), trait.toParam([2, 3])], [trait.toParam([3, 4]), trait.toParam([4, 5])], ], expected: [ [ [1, 2], [2, 3], ], [ [3, 4], [4, 5], ], ], }, { input: [ [trait.toParam([1, 2]), trait.toParam([2, 3])], [trait.toParam([3, 4]), trait.toParam([4, 5])], [trait.toParam([5, 6]), trait.toParam([6, 7])], ], expected: [ [ [1, 2], [2, 3], ], [ [3, 4], [4, 5], ], [ [5, 6], [6, 7], ], ], }, { input: [ [trait.toParam([1, 2]), trait.toParam([2, 3])], [trait.toParam([3, 4]), trait.toParam([4, 5])], [trait.toParam([5, 6]), trait.toParam([6, 7])], [trait.toParam([7, 8]), trait.toParam([8, 9])], ], expected: [ [ [1, 2], [2, 3], ], [ [3, 4], [4, 5], ], [ [5, 6], [6, 7], ], [ [7, 8], [8, 9], ], ], }, { input: [ [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], [trait.toParam([4, 5]), trait.toParam([5, 6]), trait.toParam([6, 7])], ], expected: [ [ [1, 2], [2, 3], [3, 4], ], [ [4, 5], [5, 6], [6, 7], ], ], }, { input: [ [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], [trait.toParam([4, 5]), trait.toParam([5, 6]), trait.toParam([6, 7])], [trait.toParam([7, 8]), trait.toParam([8, 9]), trait.toParam([9, 10])], ], expected: [ [ [1, 2], [2, 3], [3, 4], ], [ [4, 5], [5, 6], [6, 7], ], [ [7, 8], [8, 9], [9, 10], ], ], }, { input: [ [trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4])], [trait.toParam([4, 5]), trait.toParam([5, 6]), trait.toParam([6, 7])], [trait.toParam([7, 8]), trait.toParam([8, 9]), trait.toParam([9, 10])], [trait.toParam([10, 11]), trait.toParam([11, 12]), trait.toParam([12, 13])], ], expected: [ [ [1, 2], [2, 3], [3, 4], ], [ [4, 5], [5, 6], [6, 7], ], [ [7, 8], [8, 9], [9, 10], ], [ [10, 11], [11, 12], [12, 13], ], ], }, { input: [ [ trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4]), trait.toParam([4, 5]), ], [ trait.toParam([5, 6]), trait.toParam([6, 7]), trait.toParam([7, 8]), trait.toParam([8, 9]), ], ], expected: [ [ [1, 2], [2, 3], [3, 4], [4, 5], ], [ [5, 6], [6, 7], [7, 8], [8, 9], ], ], }, { input: [ [ trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4]), trait.toParam([4, 5]), ], [ trait.toParam([5, 6]), trait.toParam([6, 7]), trait.toParam([7, 8]), trait.toParam([8, 9]), ], [ trait.toParam([9, 10]), trait.toParam([10, 11]), trait.toParam([11, 12]), trait.toParam([12, 13]), ], ], expected: [ [ [1, 2], [2, 3], [3, 4], [4, 5], ], [ [5, 6], [6, 7], [7, 8], [8, 9], ], [ [9, 10], [10, 11], [11, 12], [12, 13], ], ], }, { input: [ [ trait.toParam([1, 2]), trait.toParam([2, 3]), trait.toParam([3, 4]), trait.toParam([4, 5]), ], [ trait.toParam([5, 6]), trait.toParam([6, 7]), trait.toParam([7, 8]), trait.toParam([8, 9]), ], [ trait.toParam([9, 10]), trait.toParam([10, 11]), trait.toParam([11, 12]), trait.toParam([12, 13]), ], [ trait.toParam([13, 14]), trait.toParam([14, 15]), trait.toParam([15, 16]), trait.toParam([16, 17]), ], ], expected: [ [ [1, 2], [2, 3], [3, 4], [4, 5], ], [ [5, 6], [6, 7], [7, 8], [8, 9], ], [ [9, 10], [10, 11], [11, 12], [12, 13], ], [ [13, 14], [14, 15], [15, 16], [16, 17], ], ], }, // Mixed { input: [ [1, [2]], [3, 4], ], expected: [ [1, 2], [3, 4], ], }, { input: [ [[1], [2]], [[3], 4], ], expected: [ [1, 2], [3, 4], ], }, { input: [ [1, 2], [trait.toParam([3]), 4], ], expected: [ [1, 2], [3, 4], ], }, { input: [ [[1], trait.toParam([2])], [trait.toParam([3]), trait.toParam([4])], ], expected: [ [1, 2], [3, 4], ], }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const input = map2DArray(t.params.input, e => trait.fromParam(e)); const expected = map2DArray(t.params.expected, e => trait.toInterval(e)); const got = trait.toMatrix(input); t.expect( objectEquals(got, expected), `${t.params.trait}.toMatrix([${input}]) returned [${got}]. Expected [${expected}]` ); }); // API - Fundamental Error Intervals interface AbsoluteErrorCase { value: number; error: number; expected: number | IntervalEndpoints; } // Special values used for testing absolute error interval // A small absolute error value is a representable value x that much smaller than 1.0, // but 1.0 +/- x is still exactly representable. const kSmallAbsoluteErrorValue = { f32: 2 ** -11, // Builtin cos and sin has a absolute error 2**-11 for f32 f16: 2 ** -7, // Builtin cos and sin has a absolute error 2**-7 for f16 } as const; // A large absolute error value is a representable value x that much smaller than maximum // positive, but positive.max - x is still exactly representable. const kLargeAbsoluteErrorValue = { f32: 2 ** 110, // f32.positive.max - 2**110 = 3.4028104e+38 = 0x7f7fffbf in f32 f16: 2 ** 10, // f16.positive.max - 2**10 = 64480 = 0x7bdf in f16 } as const; // A subnormal absolute error value is a subnormal representable value x of kind, which ensures // that positive.subnormal.min +/- x is still exactly representable. const kSubnormalAbsoluteErrorValue = { f32: 2 ** -140, // f32 0x00000200 f16: 2 ** -20, // f16 0x0010 } as const; g.test('absoluteErrorInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); const smallErr = kSmallAbsoluteErrorValue[p.trait]; const largeErr = kLargeAbsoluteErrorValue[p.trait]; const subnormalErr = kSubnormalAbsoluteErrorValue[p.trait]; // prettier-ignore return [ // Edge Cases // 1. Interval around infinity would be kUnboundedEndpoints { value: constants.positive.infinity, error: 0, expected: kUnboundedEndpoints }, { value: constants.positive.infinity, error: largeErr, expected: kUnboundedEndpoints }, { value: constants.positive.infinity, error: 1, expected: kUnboundedEndpoints }, { value: constants.negative.infinity, error: 0, expected: kUnboundedEndpoints }, { value: constants.negative.infinity, error: largeErr, expected: kUnboundedEndpoints }, { value: constants.negative.infinity, error: 1, expected: kUnboundedEndpoints }, // 2. Interval around largest finite positive/negative { value: constants.positive.max, error: 0, expected: constants.positive.max }, { value: constants.positive.max, error: largeErr, expected: kUnboundedEndpoints}, { value: constants.positive.max, error: constants.positive.max, expected: kUnboundedEndpoints}, { value: constants.negative.min, error: 0, expected: constants.negative.min }, { value: constants.negative.min, error: largeErr, expected: kUnboundedEndpoints}, { value: constants.negative.min, error: constants.positive.max, expected: kUnboundedEndpoints}, // 3. Interval around small but normal center, center should not get flushed. { value: constants.positive.min, error: 0, expected: constants.positive.min }, { value: constants.positive.min, error: smallErr, expected: [constants.positive.min - smallErr, constants.positive.min + smallErr]}, { value: constants.positive.min, error: 1, expected: [constants.positive.min - 1, constants.positive.min + 1]}, { value: constants.negative.max, error: 0, expected: constants.negative.max }, { value: constants.negative.max, error: smallErr, expected: [constants.negative.max - smallErr, constants.negative.max + smallErr]}, { value: constants.negative.max, error: 1, expected: [constants.negative.max - 1, constants.negative.max + 1] }, // 4. Subnormals, center can be flushed to 0.0 { value: constants.positive.subnormal.max, error: 0, expected: [0, constants.positive.subnormal.max] }, { value: constants.positive.subnormal.max, error: subnormalErr, expected: [-subnormalErr, constants.positive.subnormal.max + subnormalErr]}, { value: constants.positive.subnormal.max, error: smallErr, expected: [-smallErr, constants.positive.subnormal.max + smallErr]}, { value: constants.positive.subnormal.max, error: 1, expected: [-1, constants.positive.subnormal.max + 1]}, { value: constants.positive.subnormal.min, error: 0, expected: [0, constants.positive.subnormal.min] }, { value: constants.positive.subnormal.min, error: subnormalErr, expected: [-subnormalErr, constants.positive.subnormal.min + subnormalErr]}, { value: constants.positive.subnormal.min, error: smallErr, expected: [-smallErr, constants.positive.subnormal.min + smallErr]}, { value: constants.positive.subnormal.min, error: 1, expected: [-1, constants.positive.subnormal.min + 1] }, { value: constants.negative.subnormal.min, error: 0, expected: [constants.negative.subnormal.min, 0] }, { value: constants.negative.subnormal.min, error: subnormalErr, expected: [constants.negative.subnormal.min - subnormalErr, subnormalErr] }, { value: constants.negative.subnormal.min, error: smallErr, expected: [constants.negative.subnormal.min - smallErr, smallErr] }, { value: constants.negative.subnormal.min, error: 1, expected: [constants.negative.subnormal.min - 1, 1] }, { value: constants.negative.subnormal.max, error: 0, expected: [constants.negative.subnormal.max, 0] }, { value: constants.negative.subnormal.max, error: subnormalErr, expected: [constants.negative.subnormal.max - subnormalErr, subnormalErr] }, { value: constants.negative.subnormal.max, error: smallErr, expected: [constants.negative.subnormal.max - smallErr, smallErr] }, { value: constants.negative.subnormal.max, error: 1, expected: [constants.negative.subnormal.max - 1, 1] }, // Zero { value: 0, error: 0, expected: 0 }, { value: 0, error: smallErr, expected: [-smallErr, smallErr] }, { value: 0, error: 1, expected: [-1, 1] }, // Two { value: 2, error: 0, expected: 2 }, { value: 2, error: smallErr, expected: [2 - smallErr, 2 + smallErr] }, { value: 2, error: 1, expected: [1, 3] }, { value: -2, error: 0, expected: -2 }, { value: -2, error: smallErr, expected: [-2 - smallErr, -2 + smallErr] }, { value: -2, error: 1, expected: [-3, -1] }, // 64-bit subnormals, expected to be treated as 0.0 or smallest subnormal of kind. { value: reinterpretU64AsF64(0x0000_0000_0000_0001n), error: 0, expected: [0, constants.positive.subnormal.min] }, { value: reinterpretU64AsF64(0x0000_0000_0000_0001n), error: subnormalErr, expected: [-subnormalErr, constants.positive.subnormal.min + subnormalErr] }, // Note that f32 minimum subnormal is so smaller than 1.0, adding them together may result in the f64 results 1.0. { value: reinterpretU64AsF64(0x0000_0000_0000_0001n), error: 1, expected: [-1, constants.positive.subnormal.min + 1] }, { value: reinterpretU64AsF64(0x0000_0000_0000_0002n), error: 0, expected: [0, constants.positive.subnormal.min] }, { value: reinterpretU64AsF64(0x0000_0000_0000_0002n), error: subnormalErr, expected: [-subnormalErr, constants.positive.subnormal.min + subnormalErr] }, { value: reinterpretU64AsF64(0x0000_0000_0000_0002n), error: 1, expected: [-1, constants.positive.subnormal.min + 1] }, { value: reinterpretU64AsF64(0x800f_ffff_ffff_ffffn), error: 0, expected: [constants.negative.subnormal.max, 0] }, { value: reinterpretU64AsF64(0x800f_ffff_ffff_ffffn), error: subnormalErr, expected: [constants.negative.subnormal.max - subnormalErr, subnormalErr] }, { value: reinterpretU64AsF64(0x800f_ffff_ffff_ffffn), error: 1, expected: [constants.negative.subnormal.max - 1, 1] }, { value: reinterpretU64AsF64(0x800f_ffff_ffff_fffen), error: 0, expected: [constants.negative.subnormal.max, 0] }, { value: reinterpretU64AsF64(0x800f_ffff_ffff_fffen), error: subnormalErr, expected: [constants.negative.subnormal.max - subnormalErr, subnormalErr] }, { value: reinterpretU64AsF64(0x800f_ffff_ffff_fffen), error: 1, expected: [constants.negative.subnormal.max - 1, 1] }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.absoluteErrorInterval(t.params.value, t.params.error); t.expect( objectEquals(expected, got), `${t.params.trait}.absoluteErrorInterval(${t.params.value}, ${ t.params.error }) returned ${got} (${got.begin.toExponential()}, ${got.end.toExponential()}). Expected ${expected}` ); }); interface CorrectlyRoundedCase { value: number; expected: number | IntervalEndpoints; } // Correctly rounded cases that input values are exactly representable normal values of target type // prettier-ignore const kCorrectlyRoundedNormalCases = { f32: [ { value: 0, expected: [0, 0] }, { value: reinterpretU32AsF32(0x03800000), expected: reinterpretU32AsF32(0x03800000) }, { value: reinterpretU32AsF32(0x03800001), expected: reinterpretU32AsF32(0x03800001) }, { value: reinterpretU32AsF32(0x83800000), expected: reinterpretU32AsF32(0x83800000) }, { value: reinterpretU32AsF32(0x83800001), expected: reinterpretU32AsF32(0x83800001) }, ] as CorrectlyRoundedCase[], f16: [ { value: 0, expected: [0, 0] }, { value: reinterpretU16AsF16(0x0c00), expected: reinterpretU16AsF16(0x0c00) }, { value: reinterpretU16AsF16(0x0c01), expected: reinterpretU16AsF16(0x0c01) }, { value: reinterpretU16AsF16(0x8c00), expected: reinterpretU16AsF16(0x8c00) }, { value: reinterpretU16AsF16(0x8c01), expected: reinterpretU16AsF16(0x8c01) }, ] as CorrectlyRoundedCase[], } as const; // 64-bit normals that fall between two conjunction normal values in target type const kCorrectlyRoundedF64NormalCases = [ { value: reinterpretU64AsF64(0x3ff0_0000_0000_0001n), expected: { f32: [reinterpretU32AsF32(0x3f800000), reinterpretU32AsF32(0x3f800001)], f16: [reinterpretU16AsF16(0x3c00), reinterpretU16AsF16(0x3c01)], }, }, { value: reinterpretU64AsF64(0x3ff0_0000_0000_0002n), expected: { f32: [reinterpretU32AsF32(0x3f800000), reinterpretU32AsF32(0x3f800001)], f16: [reinterpretU16AsF16(0x3c00), reinterpretU16AsF16(0x3c01)], }, }, { value: reinterpretU64AsF64(0x3ff0_0800_0000_0010n), expected: { f32: [reinterpretU32AsF32(0x3f804000), reinterpretU32AsF32(0x3f804001)], f16: [reinterpretU16AsF16(0x3c02), reinterpretU16AsF16(0x3c03)], }, }, { value: reinterpretU64AsF64(0x3ff0_1000_0000_0020n), expected: { f32: [reinterpretU32AsF32(0x3f808000), reinterpretU32AsF32(0x3f808001)], f16: [reinterpretU16AsF16(0x3c04), reinterpretU16AsF16(0x3c05)], }, }, { value: reinterpretU64AsF64(0xbff0_0000_0000_0001n), expected: { f32: [reinterpretU32AsF32(0xbf800001), reinterpretU32AsF32(0xbf800000)], f16: [reinterpretU16AsF16(0xbc01), reinterpretU16AsF16(0xbc00)], }, }, { value: reinterpretU64AsF64(0xbff0_0000_0000_0002n), expected: { f32: [reinterpretU32AsF32(0xbf800001), reinterpretU32AsF32(0xbf800000)], f16: [reinterpretU16AsF16(0xbc01), reinterpretU16AsF16(0xbc00)], }, }, { value: reinterpretU64AsF64(0xbff0_0800_0000_0010n), expected: { f32: [reinterpretU32AsF32(0xbf804001), reinterpretU32AsF32(0xbf804000)], f16: [reinterpretU16AsF16(0xbc03), reinterpretU16AsF16(0xbc02)], }, }, { value: reinterpretU64AsF64(0xbff0_1000_0000_0020n), expected: { f32: [reinterpretU32AsF32(0xbf808001), reinterpretU32AsF32(0xbf808000)], f16: [reinterpretU16AsF16(0xbc05), reinterpretU16AsF16(0xbc04)], }, }, ] as const; g.test('correctlyRoundedInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore return [ // Edge Cases { value: constants.positive.infinity, expected: kUnboundedEndpoints }, { value: constants.negative.infinity, expected: kUnboundedEndpoints }, { value: constants.positive.max, expected: constants.positive.max }, { value: constants.negative.min, expected: constants.negative.min }, { value: constants.positive.min, expected: constants.positive.min }, { value: constants.negative.max, expected: constants.negative.max }, // Subnormals { value: constants.positive.subnormal.min, expected: [0, constants.positive.subnormal.min] }, { value: constants.positive.subnormal.max, expected: [0, constants.positive.subnormal.max] }, { value: constants.negative.subnormal.min, expected: [constants.negative.subnormal.min, 0] }, { value: constants.negative.subnormal.max, expected: [constants.negative.subnormal.max, 0] }, // 64-bit subnormals should be rounded down to 0 or up to smallest subnormal { value: reinterpretU64AsF64(0x0000_0000_0000_0001n), expected: [0, constants.positive.subnormal.min] }, { value: reinterpretU64AsF64(0x0000_0000_0000_0002n), expected: [0, constants.positive.subnormal.min] }, { value: reinterpretU64AsF64(0x800f_ffff_ffff_ffffn), expected: [constants.negative.subnormal.max, 0] }, { value: reinterpretU64AsF64(0x800f_ffff_ffff_fffen), expected: [constants.negative.subnormal.max, 0] }, // Normals ...kCorrectlyRoundedNormalCases[p.trait], // 64-bit normals that fall between two conjunction normal values in target type ...kCorrectlyRoundedF64NormalCases.map(t => { return {value: t.value, expected: t.expected[p.trait]} as CorrectlyRoundedCase;}), ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.correctlyRoundedInterval(t.params.value); t.expect( objectEquals(expected, got), `${t.params.trait}.correctlyRoundedInterval(${t.params.value}) returned ${got}. Expected ${expected}` ); }); interface ULPCase { value: number; num_ulp: number; expected: number | IntervalEndpoints; } // Special values used for testing ULP error interval const kULPErrorValue = { f32: 4096, // 4096 ULP is required for atan accuracy on f32 f16: 5, // 5 ULP is required for atan accuracy on f16 }; g.test('ulpInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = kFPTraitForULP[p.trait]; const constants = FP[trait].constants(); const ULPValue = kULPErrorValue[trait]; const plusOneULP = kPlusOneULPFunctions[trait]; const plusNULP = kPlusNULPFunctions[trait]; const minusOneULP = kMinusOneULPFunctions[trait]; const minusNULP = kMinusNULPFunctions[trait]; // prettier-ignore return [ // Edge Cases { value: constants.positive.infinity, num_ulp: 0, expected: kUnboundedEndpoints }, { value: constants.positive.infinity, num_ulp: 1, expected: kUnboundedEndpoints }, { value: constants.positive.infinity, num_ulp: ULPValue, expected: kUnboundedEndpoints }, { value: constants.negative.infinity, num_ulp: 0, expected: kUnboundedEndpoints }, { value: constants.negative.infinity, num_ulp: 1, expected: kUnboundedEndpoints }, { value: constants.negative.infinity, num_ulp: ULPValue, expected: kUnboundedEndpoints }, { value: constants.positive.max, num_ulp: 0, expected: constants.positive.max }, { value: constants.positive.max, num_ulp: 1, expected: kUnboundedEndpoints }, { value: constants.positive.max, num_ulp: ULPValue, expected: kUnboundedEndpoints }, { value: constants.positive.min, num_ulp: 0, expected: constants.positive.min }, { value: constants.positive.min, num_ulp: 1, expected: [0, plusOneULP(constants.positive.min)] }, { value: constants.positive.min, num_ulp: ULPValue, expected: [0, plusNULP(constants.positive.min, ULPValue)] }, { value: constants.negative.min, num_ulp: 0, expected: constants.negative.min }, { value: constants.negative.min, num_ulp: 1, expected: kUnboundedEndpoints }, { value: constants.negative.min, num_ulp: ULPValue, expected: kUnboundedEndpoints }, { value: constants.negative.max, num_ulp: 0, expected: constants.negative.max }, { value: constants.negative.max, num_ulp: 1, expected: [minusOneULP(constants.negative.max), 0] }, { value: constants.negative.max, num_ulp: ULPValue, expected: [minusNULP(constants.negative.max, ULPValue), 0] }, // Subnormals { value: constants.positive.subnormal.max, num_ulp: 0, expected: [0, constants.positive.subnormal.max] }, { value: constants.positive.subnormal.max, num_ulp: 1, expected: [minusOneULP(0), plusOneULP(constants.positive.subnormal.max)] }, { value: constants.positive.subnormal.max, num_ulp: ULPValue, expected: [minusNULP(0, ULPValue), plusNULP(constants.positive.subnormal.max, ULPValue)] }, { value: constants.positive.subnormal.min, num_ulp: 0, expected: [0, constants.positive.subnormal.min] }, { value: constants.positive.subnormal.min, num_ulp: 1, expected: [minusOneULP(0), plusOneULP(constants.positive.subnormal.min)] }, { value: constants.positive.subnormal.min, num_ulp: ULPValue, expected: [minusNULP(0, ULPValue), plusNULP(constants.positive.subnormal.min, ULPValue)] }, { value: constants.negative.subnormal.min, num_ulp: 0, expected: [constants.negative.subnormal.min, 0] }, { value: constants.negative.subnormal.min, num_ulp: 1, expected: [minusOneULP(constants.negative.subnormal.min), plusOneULP(0)] }, { value: constants.negative.subnormal.min, num_ulp: ULPValue, expected: [minusNULP(constants.negative.subnormal.min, ULPValue), plusNULP(0, ULPValue)] }, { value: constants.negative.subnormal.max, num_ulp: 0, expected: [constants.negative.subnormal.max, 0] }, { value: constants.negative.subnormal.max, num_ulp: 1, expected: [minusOneULP(constants.negative.subnormal.max), plusOneULP(0)] }, { value: constants.negative.subnormal.max, num_ulp: ULPValue, expected: [minusNULP(constants.negative.subnormal.max, ULPValue), plusNULP(0, ULPValue)] }, // 64-bit subnormals { value: reinterpretU64AsF64(0x0000_0000_0000_0001n), num_ulp: 0, expected: [0, constants.positive.subnormal.min] }, { value: reinterpretU64AsF64(0x0000_0000_0000_0001n), num_ulp: 1, expected: [minusOneULP(0), plusOneULP(constants.positive.subnormal.min)] }, { value: reinterpretU64AsF64(0x0000_0000_0000_0001n), num_ulp: ULPValue, expected: [minusNULP(0, ULPValue), plusNULP(constants.positive.subnormal.min, ULPValue)] }, { value: reinterpretU64AsF64(0x0000_0000_0000_0002n), num_ulp: 0, expected: [0, constants.positive.subnormal.min] }, { value: reinterpretU64AsF64(0x0000_0000_0000_0002n), num_ulp: 1, expected: [minusOneULP(0), plusOneULP(constants.positive.subnormal.min)] }, { value: reinterpretU64AsF64(0x0000_0000_0000_0002n), num_ulp: ULPValue, expected: [minusNULP(0, ULPValue), plusNULP(constants.positive.subnormal.min, ULPValue)] }, { value: reinterpretU64AsF64(0x800f_ffff_ffff_ffffn), num_ulp: 0, expected: [constants.negative.subnormal.max, 0] }, { value: reinterpretU64AsF64(0x800f_ffff_ffff_ffffn), num_ulp: 1, expected: [minusOneULP(constants.negative.subnormal.max), plusOneULP(0)] }, { value: reinterpretU64AsF64(0x800f_ffff_ffff_ffffn), num_ulp: ULPValue, expected: [minusNULP(constants.negative.subnormal.max, ULPValue), plusNULP(0, ULPValue)] }, { value: reinterpretU64AsF64(0x800f_ffff_ffff_fffen), num_ulp: 0, expected: [constants.negative.subnormal.max, 0] }, { value: reinterpretU64AsF64(0x800f_ffff_ffff_fffen), num_ulp: 1, expected: [minusOneULP(constants.negative.subnormal.max), plusOneULP(0)] }, { value: reinterpretU64AsF64(0x800f_ffff_ffff_fffen), num_ulp: ULPValue, expected: [minusNULP(constants.negative.subnormal.max, ULPValue), plusNULP(0, ULPValue)] }, // Zero { value: 0, num_ulp: 0, expected: 0 }, { value: 0, num_ulp: 1, expected: [minusOneULP(0), plusOneULP(0)] }, { value: 0, num_ulp: ULPValue, expected: [minusNULP(0, ULPValue), plusNULP(0, ULPValue)] }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.ulpInterval(t.params.value, t.params.num_ulp); t.expect( objectEquals(expected, got), `${t.params.trait}.ulpInterval(${t.params.value}, ${t.params.num_ulp}) returned ${got}. Expected ${expected}` ); }); // API - Acceptance Intervals // List of frequently used JS number in test cases, which are not exactly representable in f32 or f16. type ConstantNumberFrequentlyUsedInCases = '0.1' | '-0.1' | '1.9' | '-1.9'; // Correctly rounded expectation of frequently used JS Number value in test cases const kConstantCorrectlyRoundedExpectation = { f32: { // 0.1 falls between f32 0x3DCCCCCC and 0x3DCCCCCD '0.1': [reinterpretU32AsF32(0x3dcccccc), reinterpretU32AsF32(0x3dcccccd)], // -0.1 falls between f32 0xBDCCCCCD and 0xBDCCCCCC '-0.1': [reinterpretU32AsF32(0xbdcccccd), reinterpretU32AsF32(0xbdcccccc)], // 1.9 falls between f32 0x3FF33333 and 0x3FF33334 '1.9': [reinterpretU32AsF32(0x3ff33333), reinterpretU32AsF32(0x3ff33334)], // -1.9 falls between f32 0xBFF33334 and 0xBFF33333 '-1.9': [reinterpretU32AsF32(0xbff33334), reinterpretU32AsF32(0xbff33333)], } as { [value in ConstantNumberFrequentlyUsedInCases]: IntervalEndpoints }, f16: { // 0.1 falls between f16 0x2E66 and 0x2E67 '0.1': [reinterpretU16AsF16(0x2e66), reinterpretU16AsF16(0x2e67)], // -0.1 falls between f16 0xAE67 and 0xAE66 '-0.1': [reinterpretU16AsF16(0xae67), reinterpretU16AsF16(0xae66)], // 1.9 falls between f16 0x3F99 and 0x3F9A '1.9': [reinterpretU16AsF16(0x3f99), reinterpretU16AsF16(0x3f9a)], // 1.9 falls between f16 0xBF9A and 0xBF99 '-1.9': [reinterpretU16AsF16(0xbf9a), reinterpretU16AsF16(0xbf99)], } as { [value in ConstantNumberFrequentlyUsedInCases]: IntervalEndpoints }, // Since abstract is actually f64 and JS number is also f64, the JS number value will map to // identical abstracty value without rounded. abstract: { '0.1': 0.1, '-0.1': -0.1, '1.9': 1.9, '-1.9': -1.9, } as { [value in ConstantNumberFrequentlyUsedInCases]: number }, } as const; interface ScalarToIntervalCase { input: number; expected: number | IntervalEndpoints; } g.test('absInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore return [ // Common usages { input: 1, expected: 1 }, { input: -1, expected: 1 }, // abs(+/-0.1) is correctly rounded interval of 0.1 { input: 0.1, expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1']}, { input: -0.1, expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1']}, // abs(+/-1.9) is correctly rounded interval of 1.9 { input: 1.9, expected: kConstantCorrectlyRoundedExpectation[p.trait]['1.9']}, { input: -1.9, expected: kConstantCorrectlyRoundedExpectation[p.trait]['1.9']}, // Edge cases { input: constants.positive.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: constants.positive.max }, { input: constants.positive.min, expected: constants.positive.min }, { input: constants.negative.min, expected: constants.positive.max }, { input: constants.negative.max, expected: constants.positive.min }, // Subnormals { input: constants.positive.subnormal.max, expected: [0, constants.positive.subnormal.max] }, { input: constants.positive.subnormal.min, expected: [0, constants.positive.subnormal.min] }, { input: constants.negative.subnormal.min, expected: [0, constants.positive.subnormal.max] }, { input: constants.negative.subnormal.max, expected: [0, constants.positive.subnormal.min] }, // Zero { input: 0, expected: 0 }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.absInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.absInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // Acos expectation intervals are bounded by both inherited atan2(sqrt(1.0 - x*x), x) and absolute error. // Atan2 introduce 4096ULP for f32 and 5ULP for f16, and sqrt inherited from 1.0/inverseSqrt. // prettier-ignore const kAcosIntervalCases = { f32: [ { input: kPlusOneULPFunctions['f32'](-1), expected: [reinterpretU32AsF32(0x4048fa32), reinterpretU32AsF32(0x40491bdb)] }, // ~π { input: -1/2, expected: [reinterpretU32AsF32(0x4005fa90), reinterpretU32AsF32(0x40061a93)] }, // ~2π/3 { input: 1/2, expected: [reinterpretU32AsF32(0x3f85fa8f), reinterpretU32AsF32(0x3f861a94)] }, // ~π/3 // Input case to get smallest well-defined expected result, the expectation interval is bounded // by ULP (lower boundary) and absolute error (upper boundary). // f32 1.0-1ULP=0x3F7FFFFF=0.9999999403953552, // acos(0.9999999403953552)=3.4526698478747995220159699019994e-4 rounded to f32 0x39B504F3 or 0x39B504F4, // absolute error interval upper boundary 0x39B504F4+6.77e-5=0.00041296700619608164 i.e. f64 0x3F3B_106F_C933_4FB9. { input: kMinusOneULPFunctions['f32'](1), expected: [reinterpretU64AsF64(0x3f2f_fdff_6000_0000n), reinterpretU64AsF64(0x3f3b_106f_c933_4fb9n)] }, // ~0.0003 ] as ScalarToIntervalCase[], f16: [ { input: kPlusOneULPFunctions['f16'](-1), expected: [reinterpretU16AsF16(0x4233), reinterpretU16AsF16(0x4243)] }, // ~π { input: -1/2, expected: [reinterpretU16AsF16(0x402a), reinterpretU16AsF16(0x4037)] }, // ~2π/3 { input: 1/2, expected: [reinterpretU16AsF16(0x3c29), reinterpretU16AsF16(0x3c38)] }, // ~π/3 // Input case to get smallest well-defined expected result, the expectation interval is bounded // by ULP (lower boundary) and absolute error (upper boundary). // f16 1.0-1ULP=0x3BFF=0.99951171875, // acos(0.99951171875)=0.03125127170547389912035676677648 rounded to f16 0x2800 or 0x2801, // absolute error interval upper boundary 0x2801+3.91e-3=0.035190517578125 i.e. f64 0x3FA2_047D_D441_3554. { input: kMinusOneULPFunctions['f16'](1), expected: [reinterpretU16AsF16(0x259d), reinterpretU64AsF64(0x3fa2_047d_d441_3554n)] }, // ~0.03 ] as ScalarToIntervalCase[], } as const; g.test('acosInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // The acceptance interval @ x = -1 and 1 is kUnboundedEndpoints, // because sqrt(1 - x*x) = sqrt(0), and sqrt is defined in terms of // inverseqrt. // The acceptance interval @ x = 0 is kUnboundedEndpoints, because atan2 // is not well-defined/implemented at 0. { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: kUnboundedEndpoints }, { input: -1, expected: kUnboundedEndpoints }, { input: 0, expected: kUnboundedEndpoints }, { input: 1, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, // Cases that bounded by absolute error and inherited from atan2(sqrt(1-x*x), x). Note that // even x is very close to 1.0 and the expected result is close to 0.0, the expected // interval is still bounded by ULP as well as absolute error, specifically lower boundary // comes from ULP error and upper boundary comes from absolute error in those cases. ...kAcosIntervalCases[p.trait], ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.acosInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.acosInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // Some of these are hard coded, since the error intervals are difficult to express in a closed // human-readable form due to the inherited nature of the errors. // prettier-ignore const kAcoshAlternativeIntervalCases = { f32: [ { input: 1.1, expected: [reinterpretU64AsF64(0x3fdc_6368_8000_0000n), reinterpretU64AsF64(0x3fdc_636f_2000_0000n)] }, // ~0.443..., differs from the primary in the later digits { input: 10, expected: [reinterpretU64AsF64(0x4007_f21e_4000_0000n), reinterpretU64AsF64(0x4007_f21f_6000_0000n)] }, // ~2.993... ] as ScalarToIntervalCase[], f16: [ { input: 1.1, expected: [reinterpretU64AsF64(0x3fdb_bc00_0000_0000n), reinterpretU64AsF64(0x3fdd_1000_0000_0000n)] }, // ~0.443..., differs from the primary in the later digits { input: 10, expected: [reinterpretU64AsF64(0x4007_e000_0000_0000n), reinterpretU64AsF64(0x4008_0400_0000_0000n)] }, // ~2.993... ] as ScalarToIntervalCase[], } as const; g.test('acoshAlternativeInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ ...kAcoshAlternativeIntervalCases[p.trait], { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: kUnboundedEndpoints }, { input: -1, expected: kUnboundedEndpoints }, { input: 0, expected: kUnboundedEndpoints }, { input: 1, expected: kUnboundedEndpoints }, // 1/0 occurs in inverseSqrt in this formulation { input: constants.positive.max, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.acoshAlternativeInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.acoshAlternativeInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // Some of these are hard coded, since the error intervals are difficult to express in a closed // human-readable form due to the inherited nature of the errors. // prettier-ignore const kAcoshPrimaryIntervalCases = { f32: [ { input: 1.1, expected: [reinterpretU64AsF64(0x3fdc_6368_2000_0000n), reinterpretU64AsF64(0x3fdc_636f_8000_0000n)] }, // ~0.443..., differs from the alternative in the later digits { input: 10, expected: [reinterpretU64AsF64(0x4007_f21e_4000_0000n), reinterpretU64AsF64(0x4007_f21f_6000_0000n)] }, // ~2.993... ] as ScalarToIntervalCase[], f16: [ { input: 1.1, expected: [reinterpretU64AsF64(0x3fdb_bc00_0000_0000n), reinterpretU64AsF64(0x3fdd_1c00_0000_0000n)] }, // ~0.443..., differs from the primary in the later digits { input: 10, expected: [reinterpretU64AsF64(0x4007_e000_0000_0000n), reinterpretU64AsF64(0x4008_0400_0000_0000n)] }, // ~2.993... ] as ScalarToIntervalCase[], } as const; g.test('acoshPrimaryInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ ...kAcoshPrimaryIntervalCases[p.trait], { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: kUnboundedEndpoints }, { input: -1, expected: kUnboundedEndpoints }, { input: 0, expected: kUnboundedEndpoints }, { input: 1, expected: kUnboundedEndpoints }, // 1/0 occurs in inverseSqrt in this formulation { input: constants.positive.max, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.acoshPrimaryInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.acoshPrimaryInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // Asin cases that bounded by inherited atan2(x, sqrt(1.0 - x*x)) rather than absolute error. // Atan2 introduce 4096ULP for f32 and 5ULP for f16, and sqrt inherited from 1.0/inverseSqrt. // prettier-ignore const kAsinIntervalInheritedCases = { f32: [ { input: -1/2, expected: [reinterpretU32AsF32(0xbf061a96), reinterpretU32AsF32(0xbf05fa8e)] }, // ~-π/6 { input: 1/2, expected: [reinterpretU32AsF32(0x3f05fa8e), reinterpretU32AsF32(0x3f061a96)] }, // ~π/6 ] as ScalarToIntervalCase[], f16: [ { input: -1/2, expected: [reinterpretU16AsF16(0xb83a), reinterpretU16AsF16(0xb827)] }, // ~-π/6 { input: 1/2, expected: [reinterpretU16AsF16(0x3827), reinterpretU16AsF16(0x383a)] }, // ~π/6 ] as ScalarToIntervalCase[], } as const; g.test('asinInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); const abs_error = p.trait === 'f32' ? 6.81e-5 : 3.91e-3; // prettier-ignore return [ // The acceptance interval @ x = -1 and 1 is kUnboundedEndpoints, // because sqrt(1 - x*x) = sqrt(0), and sqrt is defined in terms of // inversqrt. // The acceptance interval @ x = 0 is kUnboundedEndpoints, because // atan2 is not well-defined/implemented at 0. { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: kUnboundedEndpoints }, { input: -1, expected: kUnboundedEndpoints }, // Subnormal input may get flushed to 0, and result in kUnboundedEndpoints. { input: constants.negative.subnormal.min, expected: kUnboundedEndpoints }, { input: 0, expected: kUnboundedEndpoints }, { input: constants.positive.subnormal.max, expected: kUnboundedEndpoints }, { input: 1, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, // When input near 0, the expected result is bounded by absolute error rather than ULP // error. Away from 0 the atan2 inherited error should be larger. { input: constants.negative.max, expected: trait.absoluteErrorInterval(Math.asin(constants.negative.max), abs_error).endpoints() }, // ~0 { input: constants.positive.min, expected: trait.absoluteErrorInterval(Math.asin(constants.positive.min), abs_error).endpoints() }, // ~0 // Cases that inherited from atan2(x, sqrt(1-x*x)) ...kAsinIntervalInheritedCases[p.trait], ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.asinInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.asinInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // Some of these are hard coded, since the error intervals are difficult to express in a closed // human-readable form due to the inherited nature of the errors. // prettier-ignore const kAsinhIntervalCases = { f32: [ { input: -1, expected: [reinterpretU64AsF64(0xbfec_343a_8000_0000n), reinterpretU64AsF64(0xbfec_3432_8000_0000n)] }, // ~-0.88137... { input: 0, expected: [reinterpretU64AsF64(0xbeaa_0000_2000_0000n), reinterpretU64AsF64(0x3eb1_ffff_d000_0000n)] }, // ~0 { input: 1, expected: [reinterpretU64AsF64(0x3fec_3435_4000_0000n), reinterpretU64AsF64(0x3fec_3437_8000_0000n)] }, // ~0.88137... ] as ScalarToIntervalCase[], f16: [ { input: -1, expected: [reinterpretU64AsF64(0xbfec_b800_0000_0000n), reinterpretU64AsF64(0xbfeb_b800_0000_0000n)] }, // ~-0.88137... { input: 0, expected: [reinterpretU64AsF64(0xbf85_0200_0000_0000n), reinterpretU64AsF64(0x3f89_fa00_0000_0000n)] }, // ~0 { input: 1, expected: [reinterpretU64AsF64(0x3fec_1000_0000_0000n), reinterpretU64AsF64(0x3fec_5400_0000_0000n)] }, // ~0.88137... ] as ScalarToIntervalCase[], } as const; g.test('asinhInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ ...kAsinhIntervalCases[p.trait], { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.asinhInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.asinhInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kAtanIntervalCases = { f32: [ // x=-√3=-1.7320508... quantized to f32 0xBFDDB3D7, // atan(0xBFDDB3D7)=-1.0471975434247854181546378047331 ~ -pi/3 rounded to f32 0xBF860A92 or 0xBF860A91, // kValue.f32.negative.pi.third is 0xBF860A92. { input: reinterpretU32AsF32(0xbfddb3d7), expected: [kValue.f32.negative.pi.third, kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.third)] }, // atan(-1)=-0.78539816339744830961566084581988 ~ -pi/4 rounded to f32 0xBF490FDB or 0xBF490FDA, // kValue.f32.negative.pi.quarter is 0xBF490FDB. { input: -1, expected: [kValue.f32.negative.pi.quarter, kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.quarter)] }, // x=-1/√3=-0.577350269... quantized to f32 0xBF13CD3A, // atan(0xBF13CD3A)=-0.52359876782648663982267459646249 ~ -pi/6 rounded to f32 0xBF060A92 or 0xBF060A91, // kValue.f32.negative.pi.sixth is 0xBF060A92. { input: reinterpretU32AsF32(0xbf13cd3a), expected: [kValue.f32.negative.pi.sixth, kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.sixth)] }, // x=1/√3=0.577350269... quantized to f32 0x3F13CD3A. { input: reinterpretU32AsF32(0x3f13cd3a), expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.sixth), kValue.f32.positive.pi.sixth] }, { input: 1, expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.quarter), kValue.f32.positive.pi.quarter] }, // x=√3=1.7320508... quantized to f32 0x3FDDB3D7. { input: reinterpretU32AsF32(0x3fddb3d7), expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.third), kValue.f32.positive.pi.third] }, ] as ScalarToIntervalCase[], f16: [ // x=-√3=-1.7320508... quantized to f16 0xBEED, // atan(0xBEED)=-1.0470461377318847079113932677171 ~ -pi/3 rounded to f16 0xBC31 or 0xBC30, // kValue.f16.negative.pi.third is 0xBC30. { input: reinterpretU16AsF16(0xbeed), expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.third), kValue.f16.negative.pi.third] }, // atan(-1)=-0.78539816339744830961566084581988 ~ -pi/4 rounded to f16 0xBA49 or 0xBA48. // kValue.f16.negative.pi.quarter is 0xBA48. { input: -1, expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.quarter), kValue.f16.negative.pi.quarter] }, // x=-1/√3=-0.577350269... quantized to f16 0xB89E, // atan(0xB89E)=-0.52344738860166563645762619364966 ~ -pi/6 rounded to f16 0xB831 or 0xB830, // kValue.f16.negative.pi.sixth is 0xB830. { input: reinterpretU16AsF16(0xb89e), expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.sixth), kValue.f16.negative.pi.sixth] }, // x=1/√3=0.577350269... quantized to f16 0x389E { input: reinterpretU16AsF16(0x389e), expected: [kValue.f16.positive.pi.sixth, kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.sixth)] }, { input: 1, expected: [kValue.f16.positive.pi.quarter, kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.quarter)] }, // x=√3=1.7320508... quantized to f16 0x3EED { input: reinterpretU16AsF16(0x3eed), expected: [kValue.f16.positive.pi.third, kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.third)] }, ] as ScalarToIntervalCase[], } as const; g.test('atanInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore return [ { input: 0, expected: 0 }, ...kAtanIntervalCases[p.trait], { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const ulp_error = t.params.trait === 'f32' ? 4096 : 5; const error = (n: number): number => { return ulp_error * trait.oneULP(n); }; const expected = trait.toInterval(applyError(t.params.expected, error)); const got = trait.atanInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.atanInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // Some of these are hard coded, since the error intervals are difficult to express in a closed // human-readable form due to the inherited nature of the errors. // prettier-ignore const kAtanhIntervalCases = { f32: [ { input: -0.1, expected: [reinterpretU64AsF64(0xbfb9_af9a_6000_0000n), reinterpretU64AsF64(0xbfb9_af8c_c000_0000n)] }, // ~-0.1003... { input: 0, expected: [reinterpretU64AsF64(0xbe96_0000_2000_0000n), reinterpretU64AsF64(0x3e98_0000_0000_0000n)] }, // ~0 { input: 0.1, expected: [reinterpretU64AsF64(0x3fb9_af8b_8000_0000n), reinterpretU64AsF64(0x3fb9_af9b_0000_0000n)] }, // ~0.1003... ] as ScalarToIntervalCase[], f16: [ { input: -0.1, expected: [reinterpretU64AsF64(0xbfbb_0c00_0000_0000n), reinterpretU64AsF64(0xbfb8_5800_0000_0000n)] }, // ~-0.1003... { input: 0, expected: [reinterpretU64AsF64(0xbf73_0400_0000_0000n), reinterpretU64AsF64(0x3f74_0000_0000_0000n)] }, // ~0 { input: 0.1, expected: [reinterpretU64AsF64(0x3fb8_3800_0000_0000n), reinterpretU64AsF64(0x3fbb_2400_0000_0000n)] }, // ~0.1003... ] as ScalarToIntervalCase[], } as const; g.test('atanhInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ ...kAtanhIntervalCases[p.trait], { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: kUnboundedEndpoints }, { input: -1, expected: kUnboundedEndpoints }, { input: 1, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.atanhInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.atanhInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // Large but still representable integer const kCeilIntervalCases = { f32: [ { input: 2 ** 30, expected: 2 ** 30 }, { input: -(2 ** 30), expected: -(2 ** 30) }, { input: 0x80000000, expected: 0x80000000 }, // https://github.com/gpuweb/cts/issues/2766 ], f16: [ { input: 2 ** 14, expected: 2 ** 14 }, { input: -(2 ** 14), expected: -(2 ** 14) }, { input: 0x8000, expected: 0x8000 }, // https://github.com/gpuweb/cts/issues/2766 ], abstract: [ { input: 2 ** 52, expected: 2 ** 52 }, { input: -(2 ** 52), expected: -(2 ** 52) }, { input: 0x8000000000000000, expected: 0x8000000000000000 }, // https://github.com/gpuweb/cts/issues/2766 ], } as const; g.test('ceilInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore return [ { input: 0, expected: 0 }, { input: 0.1, expected: 1 }, { input: 0.9, expected: 1 }, { input: 1.0, expected: 1 }, { input: 1.1, expected: 2 }, { input: 1.9, expected: 2 }, { input: -0.1, expected: 0 }, { input: -0.9, expected: 0 }, { input: -1.0, expected: -1 }, { input: -1.1, expected: -1 }, { input: -1.9, expected: -1 }, // Edge cases { input: constants.positive.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: constants.positive.max }, { input: constants.positive.min, expected: 1 }, { input: constants.negative.min, expected: constants.negative.min }, { input: constants.negative.max, expected: 0 }, ...kCeilIntervalCases[p.trait], // Subnormals { input: constants.positive.subnormal.max, expected: [0, 1] }, { input: constants.positive.subnormal.min, expected: [0, 1] }, { input: constants.negative.subnormal.min, expected: 0 }, { input: constants.negative.subnormal.max, expected: 0 }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.ceilInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.ceilInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // Cos interval cases on x=π/3, the result of f32 and f16 is different because π/3 quantized to // different direction for two types. const kCosIntervalThirdPiCases = { // prettier-ignore f32: [ // cos(-1.0471975803375244) = 0.499999974763 { input: kValue.f32.negative.pi.third, expected: [kMinusOneULPFunctions['f32'](1/2), 1/2] }, // cos(1.0471975803375244) = 0.499999974763 { input: kValue.f32.positive.pi.third, expected: [kMinusOneULPFunctions['f32'](1/2), 1/2] }, ], f16: [ // cos(-1.046875) = 0.50027931 { input: kValue.f16.negative.pi.third, expected: FP['f16'].correctlyRoundedInterval(0.50027931).endpoints(), }, // cos(1.046875) = 0.50027931 { input: kValue.f16.positive.pi.third, expected: FP['f16'].correctlyRoundedInterval(0.50027931).endpoints(), }, ], }; g.test('cosInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // This test does not include some common cases. i.e. f(x = π/2) = 0, // because the difference between true x and x as a f32 is sufficiently // large, such that the high slope of f @ x causes the results to be // substantially different, so instead of getting 0 you get a value on the // order of 10^-8 away from 0, thus difficult to express in a // human-readable manner. { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: kUnboundedEndpoints }, { input: constants.negative.pi.whole, expected: [-1, kPlusOneULPFunctions[p.trait](-1)] }, { input: 0, expected: [1, 1] }, { input: constants.positive.pi.whole, expected: [-1, kPlusOneULPFunctions[p.trait](-1)] }, { input: constants.positive.max, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, ...(kCosIntervalThirdPiCases[p.trait] as ScalarToIntervalCase[]), ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const error = (_: number): number => { return t.params.trait === 'f32' ? 2 ** -11 : 2 ** -7; }; const expected = trait.toInterval(applyError(t.params.expected, error)); const got = trait.cosInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.cosInterval(${t.params.input}) returned ${got}. Expected ${expected}, ===${t.params.expected}===` ); }); // Some of these are hard coded, since the error intervals are difficult to express in a closed // human-readable form due to the inherited nature of the errors. // prettier-ignore const kCoshIntervalCases = { f32: [ { input: -1, expected: [reinterpretU32AsF32(0x3fc583a4), reinterpretU32AsF32(0x3fc583b1)] }, // ~1.1543... { input: 0, expected: [reinterpretU32AsF32(0x3f7ffffd), reinterpretU32AsF32(0x3f800002)] }, // ~1 { input: 1, expected: [reinterpretU32AsF32(0x3fc583a4), reinterpretU32AsF32(0x3fc583b1)] }, // ~1.1543... ] as ScalarToIntervalCase[], f16: [ { input: -1, expected: [reinterpretU16AsF16(0x3e27), reinterpretU16AsF16(0x3e30)] }, // ~1.1543... { input: 0, expected: [reinterpretU16AsF16(0x3bff), reinterpretU16AsF16(0x3c01)] }, // ~1 { input: 1, expected: [reinterpretU16AsF16(0x3e27), reinterpretU16AsF16(0x3e30)] }, // ~1.1543... ] as ScalarToIntervalCase[], } as const; g.test('coshInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ ...kCoshIntervalCases[p.trait], { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.coshInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.coshInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kDegreesIntervalCases = { f32: [ { input: kValue.f32.negative.pi.whole, expected: [kMinusOneULPFunctions['f32'](-180), kPlusOneULPFunctions['f32'](-180)] }, { input: kValue.f32.negative.pi.three_quarters, expected: [kMinusOneULPFunctions['f32'](-135), kPlusOneULPFunctions['f32'](-135)] }, { input: kValue.f32.negative.pi.half, expected: [kMinusOneULPFunctions['f32'](-90), kPlusOneULPFunctions['f32'](-90)] }, { input: kValue.f32.negative.pi.third, expected: [kMinusOneULPFunctions['f32'](-60), kPlusOneULPFunctions['f32'](-60)] }, { input: kValue.f32.negative.pi.quarter, expected: [kMinusOneULPFunctions['f32'](-45), kPlusOneULPFunctions['f32'](-45)] }, { input: kValue.f32.negative.pi.sixth, expected: [kMinusOneULPFunctions['f32'](-30), kPlusOneULPFunctions['f32'](-30)] }, { input: kValue.f32.positive.pi.sixth, expected: [kMinusOneULPFunctions['f32'](30), kPlusOneULPFunctions['f32'](30)] }, { input: kValue.f32.positive.pi.quarter, expected: [kMinusOneULPFunctions['f32'](45), kPlusOneULPFunctions['f32'](45)] }, { input: kValue.f32.positive.pi.third, expected: [kMinusOneULPFunctions['f32'](60), kPlusOneULPFunctions['f32'](60)] }, { input: kValue.f32.positive.pi.half, expected: [kMinusOneULPFunctions['f32'](90), kPlusOneULPFunctions['f32'](90)] }, { input: kValue.f32.positive.pi.three_quarters, expected: [kMinusOneULPFunctions['f32'](135), kPlusOneULPFunctions['f32'](135)] }, { input: kValue.f32.positive.pi.whole, expected: [kMinusOneULPFunctions['f32'](180), kPlusOneULPFunctions['f32'](180)] }, ] as ScalarToIntervalCase[], f16: [ { input: kValue.f16.negative.pi.whole, expected: [-180, kPlusOneULPFunctions['f16'](-180)] }, { input: kValue.f16.negative.pi.three_quarters, expected: [-135, kPlusOneULPFunctions['f16'](-135)] }, { input: kValue.f16.negative.pi.half, expected: [-90, kPlusOneULPFunctions['f16'](-90)] }, { input: kValue.f16.negative.pi.third, expected: [-60, kPlusNULPFunctions['f16'](-60, 2)] }, { input: kValue.f16.negative.pi.quarter, expected: [-45, kPlusOneULPFunctions['f16'](-45)] }, { input: kValue.f16.negative.pi.sixth, expected: [-30, kPlusNULPFunctions['f16'](-30, 2)] }, { input: kValue.f16.positive.pi.sixth, expected: [kMinusNULPFunctions['f16'](30, 2), 30] }, { input: kValue.f16.positive.pi.quarter, expected: [kMinusOneULPFunctions['f16'](45), 45] }, { input: kValue.f16.positive.pi.third, expected: [kMinusNULPFunctions['f16'](60, 2), 60] }, { input: kValue.f16.positive.pi.half, expected: [kMinusOneULPFunctions['f16'](90), 90] }, { input: kValue.f16.positive.pi.three_quarters, expected: [kMinusOneULPFunctions['f16'](135), 135] }, { input: kValue.f16.positive.pi.whole, expected: [kMinusOneULPFunctions['f16'](180), 180] }, ] as ScalarToIntervalCase[], } as const; g.test('degreesInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = p.trait; const constants = FP[trait].constants(); // prettier-ignore return [ { input: constants.positive.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: kUnboundedEndpoints }, { input: 0, expected: 0 }, { input: constants.positive.max, expected: kUnboundedEndpoints }, { input: constants.negative.infinity, expected: kUnboundedEndpoints }, ...kDegreesIntervalCases[trait] ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.degreesInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.degreesInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kExpIntervalCases = { f32: [ { input: 1, expected: [kValue.f32.positive.e, kPlusOneULPFunctions['f32'](kValue.f32.positive.e)] }, // exp(88) = 1.6516362549940018555283297962649e+38 = 0x7ef882b6/7. { input: 88, expected: [reinterpretU32AsF32(0x7ef882b6), reinterpretU32AsF32(0x7ef882b7)] }, // exp(89) overflow f32. { input: 89, expected: kUnboundedEndpoints }, ] as ScalarToIntervalCase[], f16: [ { input: 1, expected: [kValue.f16.positive.e, kPlusOneULPFunctions['f16'](kValue.f16.positive.e)] }, // exp(11) = 59874.141715197818455326485792258 = 0x7b4f/0x7b50. { input: 11, expected: [reinterpretU16AsF16(0x7b4f), reinterpretU16AsF16(0x7b50)] }, // exp(12) = 162754.79141900392080800520489849 overflow f16. { input: 12, expected: kUnboundedEndpoints }, ] as ScalarToIntervalCase[], } as const; g.test('expInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = p.trait; const constants = FP[trait].constants(); // prettier-ignore return [ { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: 0, expected: 1 }, ...kExpIntervalCases[trait], ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const error = (x: number): number => { let ulp_error; switch (t.params.trait) { case 'f32': { ulp_error = 3 + 2 * Math.abs(t.params.input); break; } case 'f16': { ulp_error = 1 + 2 * Math.abs(t.params.input); break; } } return ulp_error * trait.oneULP(x); }; const expected = trait.toInterval(applyError(t.params.expected, error)); const got = trait.expInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.expInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kExp2IntervalCases = { f32: [ // exp2(127) = 1.7014118346046923173168730371588e+38 = 0x7f000000, 3 + 2 * 127 = 258 ulps. { input: 127, expected: reinterpretU32AsF32(0x7f000000) }, // exp2(128) overflow f32. { input: 128, expected: kUnboundedEndpoints }, ] as ScalarToIntervalCase[], f16: [ // exp2(15) = 32768 = 0x7800, 1 + 2 * 15 = 31 ulps { input: 15, expected: reinterpretU16AsF16(0x7800) }, // exp2(16) = 65536 overflow f16. { input: 16, expected: kUnboundedEndpoints }, ] as ScalarToIntervalCase[], } as const; g.test('exp2Interval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = p.trait; const constants = FP[trait].constants(); // prettier-ignore return [ { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: 0, expected: 1 }, { input: 1, expected: 2 }, ...kExp2IntervalCases[trait], ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const error = (x: number): number => { let ulp_error; switch (t.params.trait) { case 'f32': { ulp_error = 3 + 2 * Math.abs(t.params.input); break; } case 'f16': { ulp_error = 1 + 2 * Math.abs(t.params.input); break; } } return ulp_error * trait.oneULP(x); }; const expected = trait.toInterval(applyError(t.params.expected, error)); const got = trait.exp2Interval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.exp2Interval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // Large but still representable integer const kFloorIntervalCases = { f32: [ { input: 2 ** 30, expected: 2 ** 30 }, { input: -(2 ** 30), expected: -(2 ** 30) }, { input: 0x80000000, expected: 0x80000000 }, // https://github.com/gpuweb/cts/issues/2766 ], f16: [ { input: 2 ** 14, expected: 2 ** 14 }, { input: -(2 ** 14), expected: -(2 ** 14) }, { input: 0x8000, expected: 0x8000 }, // https://github.com/gpuweb/cts/issues/2766 ], abstract: [ { input: 2 ** 62, expected: 2 ** 62 }, { input: -(2 ** 62), expected: -(2 ** 62) }, { input: 0x8000_0000_0000_0000, expected: 0x8000_0000_0000_0000, }, // https://github.com/gpuweb/cts/issues/2766 ], } as const; g.test('floorInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore return [ { input: 0, expected: 0 }, { input: 0.1, expected: 0 }, { input: 0.9, expected: 0 }, { input: 1.0, expected: 1 }, { input: 1.1, expected: 1 }, { input: 1.9, expected: 1 }, { input: -0.1, expected: -1 }, { input: -0.9, expected: -1 }, { input: -1.0, expected: -1 }, { input: -1.1, expected: -2 }, { input: -1.9, expected: -2 }, // Edge cases { input: constants.positive.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: constants.positive.max }, { input: constants.positive.min, expected: 0 }, { input: constants.negative.min, expected: constants.negative.min }, { input: constants.negative.max, expected: -1 }, ...kFloorIntervalCases[p.trait], // Subnormals { input: constants.positive.subnormal.max, expected: 0 }, { input: constants.positive.subnormal.min, expected: 0 }, { input: constants.negative.subnormal.min, expected: [-1, 0] }, { input: constants.negative.subnormal.max, expected: [-1, 0] }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.floorInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.floorInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kFractIntervalCases = { f32: [ { input: 0.1, expected: [kMinusOneULPFunctions['f32'](reinterpretU32AsF32(0x3dcccccd)), reinterpretU32AsF32(0x3dcccccd)] }, // ~0.1 { input: 0.9, expected: [reinterpretU32AsF32(0x3f666666), kPlusOneULPFunctions['f32'](reinterpretU32AsF32(0x3f666666))] }, // ~0.9 { input: 1.1, expected: [reinterpretU32AsF32(0x3dccccc0), reinterpretU32AsF32(0x3dccccd0)] }, // ~0.1 { input: -0.1, expected: [reinterpretU32AsF32(0x3f666666), kPlusOneULPFunctions['f32'](reinterpretU32AsF32(0x3f666666))] }, // ~0.9 { input: -0.9, expected: [reinterpretU32AsF32(0x3dccccc8), reinterpretU32AsF32(0x3dccccd0)] }, // ~0.1 { input: -1.1, expected: [reinterpretU32AsF32(0x3f666666), reinterpretU32AsF32(0x3f666668)] }, // ~0.9 // https://github.com/gpuweb/cts/issues/2766 { input: 0x80000000, expected: 0 }, ] as ScalarToIntervalCase[], f16: [ { input: 0.1, expected: [reinterpretU16AsF16(0x2e66), reinterpretU16AsF16(0x2e67)] }, // ~0.1 { input: 0.9, expected: [reinterpretU16AsF16(0x3b33), reinterpretU16AsF16(0x3b34)] }, // ~0.9 { input: 1.1, expected: [reinterpretU16AsF16(0x2e60), reinterpretU16AsF16(0x2e70)] }, // ~0.1 { input: -0.1, expected: [reinterpretU16AsF16(0x3b33), reinterpretU16AsF16(0x3b34)] }, // ~0.9 { input: -0.9, expected: [reinterpretU16AsF16(0x2e60), reinterpretU16AsF16(0x2e68)] }, // ~0.1 { input: -1.1, expected: [reinterpretU16AsF16(0x3b32), reinterpretU16AsF16(0x3b34)] }, // ~0.9 { input: 658.5, expected: 0.5 }, ] as ScalarToIntervalCase[], abstract: [ { input: 0.1, expected: reinterpretU64AsF64(0x3fb999999999999an) }, { input: 0.9, expected: reinterpretU64AsF64(0x3feccccccccccccdn) }, { input: 1.1, expected: reinterpretU64AsF64(0x3fb99999999999a0n) }, { input: -0.1, expected: reinterpretU64AsF64(0x3feccccccccccccdn) }, { input: -0.9, expected: reinterpretU64AsF64(0x3fb9999999999998n) }, { input: -1.1, expected: reinterpretU64AsF64(0x3fecccccccccccccn) }, // https://github.com/gpuweb/cts/issues/2766 { input: 0x80000000, expected: 0 }, // https://github.com/gpuweb/gpuweb/issues/4523 { input: 3937509.87755102, expected: [0, 0.75] }, ] as ScalarToIntervalCase[], } as const; g.test('fractInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore return [ { input: 0, expected: 0 }, { input: 1.0, expected: 0 }, { input: -1.0, expected: 0 }, ...kFractIntervalCases[p.trait], // Edge cases { input: constants.positive.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: 0 }, { input: constants.positive.min, expected: constants.positive.min }, { input: constants.negative.min, expected: 0 }, { input: constants.negative.max, expected: [constants.positive.less_than_one, 1.0] }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.fractInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.fractInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kInverseSqrtIntervalCases = { f32: [ // 0.04 rounded to f32 0x3D23D70A or 0x3D23D70B, // 1/sqrt(0x3D23D70B)=4.9999998230487200185270893769213 rounded to f32 0x409FFFFF or 0x40A00000, // 1/sqrt(0x3D23D70A)=5.0000000558793553117506910583908 rounded to f32 0x40A00000 or 0x40A00001. { input: 0.04, expected: [reinterpretU32AsF32(0x409FFFFF), reinterpretU32AsF32(0x40A00001)] }, // ~5.0 // Maximum f32 0x7F7FFFFF = 3.4028234663852886e+38, // 1/sqrt(0x7F7FFFFF)=5.4210110239862427800382690921791e-20 rounded to f32 0x1F800000 or 0x1F800001 { input: kValue.f32.positive.max, expected: [reinterpretU32AsF32(0x1f800000), reinterpretU32AsF32(0x1f800001)] }, // ~5.421...e-20 ] as ScalarToIntervalCase[], f16: [ // 0.04 rounded to f16 0x291E or 0x291F, // 1/sqrt(0x291F)=4.9994660279328446295684795818427 rounded to f16 0x44FF or 0x4500, // 1/sqrt(0x291E)=5.001373857053206453045376503367 rounded to f16 0x4500 or 0x4501. { input: 0.04, expected: [reinterpretU16AsF16(0x44FF), reinterpretU16AsF16(0x4501)] }, // ~5.0 // Maximum f16 0x7BFF = 65504, // 1/sqrt(0x7BFF)=0.00390720402370454101997160826062 rounded to f16 0x1C00 or 0x1C01 { input: kValue.f16.positive.max, expected: [reinterpretU16AsF16(0x1c00), reinterpretU16AsF16(0x1c01)] }, // ~3.9072...e-3 ] as ScalarToIntervalCase[], } as const; g.test('inverseSqrtInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // Note that the 2 ULP error is not included here. // prettier-ignore return [ // Exactly representable cases { input: 1, expected: 1 }, { input: 0.25, expected: 2 }, { input: 64, expected: 0.125 }, // Cases that input and/or result not exactly representable ...kInverseSqrtIntervalCases[p.trait], // 1/sqrt(100.0)=0.1, rounded to corresponding trait { input: 100, expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 // Out of definition domain { input: -1, expected: kUnboundedEndpoints }, { input: 0, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const error = (n: number): number => { return 2 * trait.oneULP(n); }; const expected = trait.toInterval(applyError(t.params.expected, error)); const got = trait.inverseSqrtInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.inverseSqrtInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // Expectation interval of 1/inverseSqrt(sum(x[i]^2)) on some special values array x for certain // float traits, used as expectation for `length` and `distance`. // These cases are hard coded, since the error intervals are difficult to express in a closed // human-readable form due to the inherited nature of the errors. // prettier-ignore const kRootSumSquareExpectationInterval = { f32: { '[0.1]': [reinterpretU64AsF64(0x3fb9_9998_9000_0000n), reinterpretU64AsF64(0x3fb9_999a_7000_0000n)], // ~0.1 '[1.0]' : [reinterpretU64AsF64(0x3fef_ffff_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_9000_0000n)], // ~1.0 '[10]' : [reinterpretU64AsF64(0x4023_ffff_7000_0000n), reinterpretU64AsF64(0x4024_0000_b000_0000n)], // ~10 '[1.0, 1.0]' : [reinterpretU64AsF64(0x3ff6_a09d_b000_0000n), reinterpretU64AsF64(0x3ff6_a09f_1000_0000n)], // ~√2 '[1.0, 1.0, 1.0]' : [reinterpretU64AsF64(0x3ffb_b67a_1000_0000n), reinterpretU64AsF64(0x3ffb_b67b_b000_0000n)], // ~√3 '[1.0, 1.0, 1.0, 1.0]' : [reinterpretU64AsF64(0x3fff_ffff_7000_0000n), reinterpretU64AsF64(0x4000_0000_9000_0000n)], // ~2 } as {[s: string]: IntervalEndpoints}, f16: { '[0.1]': [reinterpretU64AsF64(0x3fb9_7e00_0000_0000n), reinterpretU64AsF64(0x3fb9_b600_0000_0000n)], // ~0.1 '[1.0]' : [reinterpretU64AsF64(0x3fef_ee00_0000_0000n), reinterpretU64AsF64(0x3ff0_1200_0000_0000n)], // ~1.0 '[10]' : [reinterpretU64AsF64(0x4023_ea00_0000_0000n), reinterpretU64AsF64(0x4024_1200_0000_0000n)], // ~10 '[1.0, 1.0]' : [reinterpretU64AsF64(0x3ff6_8a00_0000_0000n), reinterpretU64AsF64(0x3ff6_b600_0000_0000n)], // ~√2 '[1.0, 1.0, 1.0]' : [reinterpretU64AsF64(0x3ffb_9a00_0000_0000n), reinterpretU64AsF64(0x3ffb_d200_0000_0000n)], // ~√3 '[1.0, 1.0, 1.0, 1.0]' : [reinterpretU64AsF64(0x3fff_ee00_0000_0000n), reinterpretU64AsF64(0x4000_1200_0000_0000n)], // ~2 } as {[s: string]: IntervalEndpoints}, } as const; g.test('lengthIntervalScalar') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ {input: 1.0, expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 {input: -1.0, expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 {input: 0.1, expected: kRootSumSquareExpectationInterval[p.trait]['[0.1]'] }, // ~0.1 {input: -0.1, expected: kRootSumSquareExpectationInterval[p.trait]['[0.1]'] }, // ~0.1 {input: 10.0, expected: kRootSumSquareExpectationInterval[p.trait]['[10]'] }, // ~10 {input: -10.0, expected: kRootSumSquareExpectationInterval[p.trait]['[10]'] }, // ~10 // length(0) = kUnboundedEndpoints, because length uses sqrt, which is defined as 1/inversesqrt {input: 0, expected: kUnboundedEndpoints }, // Subnormal Cases { input: constants.negative.subnormal.min, expected: kUnboundedEndpoints }, { input: constants.negative.subnormal.max, expected: kUnboundedEndpoints }, { input: constants.positive.subnormal.min, expected: kUnboundedEndpoints }, { input: constants.positive.subnormal.max, expected: kUnboundedEndpoints }, // Edge cases { input: constants.positive.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: kUnboundedEndpoints }, { input: constants.negative.max, expected: kUnboundedEndpoints }, { input: constants.positive.min, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.lengthInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.lengthInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kLogIntervalCases = { f32: [ // kValue.f32.positive.e is 0x402DF854 = 2.7182817459106445, // log(0x402DF854) = 0.99999996963214000677592342891704 rounded to f32 0x3F7FFFFF or 0x3F800000 = 1.0 { input: kValue.f32.positive.e, expected: [kMinusOneULPFunctions['f32'](1.0), 1.0] }, // kValue.f32.positive.max is 0x7F7FFFFF = 3.4028234663852886e+38, // log(0x7F7FFFFF) = 88.72283905206835305421152826479 rounded to f32 0x42B17217 or 0x42B17218. { input: kValue.f32.positive.max, expected: [kMinusOneULPFunctions['f32'](reinterpretU32AsF32(0x42b17218)), reinterpretU32AsF32(0x42b17218)] }, ] as ScalarToIntervalCase[], f16: [ // kValue.f16.positive.e is 0x416F = 2.716796875, // log(0x416F) = 0.99945356688393512460279716546501 rounded to f16 0x3BFE or 0x3BFF. { input: kValue.f16.positive.e, expected: [reinterpretU16AsF16(0x3bfe), reinterpretU16AsF16(0x3bff)] }, // kValue.f16.positive.max is 0x7BFF = 65504, // log(0x7BFF) = 11.089866488461016076210728979771 rounded to f16 0x498B or 0x498C. { input: kValue.f16.positive.max, expected: [reinterpretU16AsF16(0x498b), reinterpretU16AsF16(0x498c)] }, ] as ScalarToIntervalCase[], } as const; g.test('logInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { // prettier-ignore return [ { input: -1, expected: kUnboundedEndpoints }, { input: 0, expected: kUnboundedEndpoints }, { input: 1, expected: 0 }, ...kLogIntervalCases[p.trait], ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const abs_error = t.params.trait === 'f32' ? 2 ** -21 : 2 ** -7; const error = (n: number): number => { if (t.params.input >= 0.5 && t.params.input <= 2.0) { return abs_error; } return 3 * trait.oneULP(n); }; const expected = trait.toInterval(applyError(t.params.expected, error)); const got = trait.logInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.logInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kLog2IntervalCases = { f32: [ // kValue.f32.positive.max is 0x7F7FFFFF = 3.4028234663852886e+38, // log2(0x7F7FFFFF) = 127.99999991400867200665269600978 rounded to f32 0x42FFFFFF or 0x43000000 = 128.0 { input: kValue.f32.positive.max, expected: [kMinusOneULPFunctions['f32'](128.0), 128.0] }, ] as ScalarToIntervalCase[], f16: [ // kValue.f16.positive.max is 0x7BFF = 65504, // log2(0x7BFF) = 15.999295387023410627258428389903 rounded to f16 0x4BFF or 0x4C00 = 16.0 { input: kValue.f16.positive.max, expected: [kMinusOneULPFunctions['f16'](16.0), 16.0] }, ] as ScalarToIntervalCase[], } as const; g.test('log2Interval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { // prettier-ignore return [ { input: -1, expected: kUnboundedEndpoints }, { input: 0, expected: kUnboundedEndpoints }, { input: 1, expected: 0 }, { input: 2, expected: 1 }, { input: 16, expected: 4 }, ...kLog2IntervalCases[p.trait], ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const abs_error = t.params.trait === 'f32' ? 2 ** -21 : 2 ** -7; const error = (n: number): number => { if (t.params.input >= 0.5 && t.params.input <= 2.0) { return abs_error; } return 3 * trait.oneULP(n); }; const expected = trait.toInterval(applyError(t.params.expected, error)); const got = trait.log2Interval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.log2Interval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); g.test('negationInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // Edge cases { input: constants.positive.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: constants.negative.min }, { input: constants.positive.min, expected: constants.negative.max }, { input: constants.negative.min, expected: constants.positive.max }, { input: constants.negative.max, expected: constants.positive.min }, // Normals { input: 0, expected: 0 }, { input: 1.0, expected: -1.0 }, { input: -1.0, expected: 1 }, { input: 0.1, expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // ~-0.1 { input: 1.9, expected: kConstantCorrectlyRoundedExpectation[p.trait]['-1.9'] }, // ~-1.9 { input: -0.1, expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 { input: -1.9, expected: kConstantCorrectlyRoundedExpectation[p.trait]['1.9'] }, // ~1.9 // Subnormals { input: constants.positive.subnormal.max, expected: [constants.negative.subnormal.min, 0] }, { input: constants.positive.subnormal.min, expected: [constants.negative.subnormal.max, 0] }, { input: constants.negative.subnormal.min, expected: [0, constants.positive.subnormal.max] }, { input: constants.negative.subnormal.max, expected: [0, constants.positive.subnormal.min] }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.negationInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.negationInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); g.test('quantizeToF16Interval') .paramsSubcasesOnly( // prettier-ignore [ { input: kValue.f32.negative.infinity, expected: kUnboundedEndpoints }, { input: kValue.f32.negative.min, expected: kUnboundedEndpoints }, { input: kValue.f16.negative.min, expected: kValue.f16.negative.min }, { input: -1.9, expected: kConstantCorrectlyRoundedExpectation['f16']['-1.9'] }, // ~-1.9 { input: -1, expected: -1 }, { input: -0.1, expected: kConstantCorrectlyRoundedExpectation['f16']['-0.1'] }, // ~-0.1 { input: kValue.f16.negative.max, expected: kValue.f16.negative.max }, { input: kValue.f16.negative.subnormal.min, expected: [kValue.f16.negative.subnormal.min, 0] }, { input: kValue.f16.negative.subnormal.max, expected: [kValue.f16.negative.subnormal.max, 0] }, { input: kValue.f32.negative.subnormal.max, expected: [kValue.f16.negative.subnormal.max, 0] }, { input: 0, expected: 0 }, { input: kValue.f32.positive.subnormal.min, expected: [0, kValue.f16.positive.subnormal.min] }, { input: kValue.f16.positive.subnormal.min, expected: [0, kValue.f16.positive.subnormal.min] }, { input: kValue.f16.positive.subnormal.max, expected: [0, kValue.f16.positive.subnormal.max] }, { input: kValue.f16.positive.min, expected: kValue.f16.positive.min }, { input: 0.1, expected: kConstantCorrectlyRoundedExpectation['f16']['0.1'] }, // ~0.1 { input: 1, expected: 1 }, { input: 1.9, expected: kConstantCorrectlyRoundedExpectation['f16']['1.9'] }, // ~1.9 { input: kValue.f16.positive.max, expected: kValue.f16.positive.max }, { input: kValue.f32.positive.max, expected: kUnboundedEndpoints }, { input: kValue.f32.positive.infinity, expected: kUnboundedEndpoints }, ] ) .fn(t => { const expected = FP.f32.toInterval(t.params.expected); const got = FP.f32.quantizeToF16Interval(t.params.input); t.expect( objectEquals(expected, got), `f32.quantizeToF16Interval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kRadiansIntervalCases = { f32: [ { input: -180, expected: [kMinusOneULPFunctions['f32'](kValue.f32.negative.pi.whole), kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.whole)] }, { input: -135, expected: [kMinusOneULPFunctions['f32'](kValue.f32.negative.pi.three_quarters), kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.three_quarters)] }, { input: -90, expected: [kMinusOneULPFunctions['f32'](kValue.f32.negative.pi.half), kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.half)] }, { input: -60, expected: [kMinusOneULPFunctions['f32'](kValue.f32.negative.pi.third), kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.third)] }, { input: -45, expected: [kMinusOneULPFunctions['f32'](kValue.f32.negative.pi.quarter), kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.quarter)] }, { input: -30, expected: [kMinusOneULPFunctions['f32'](kValue.f32.negative.pi.sixth), kPlusOneULPFunctions['f32'](kValue.f32.negative.pi.sixth)] }, { input: 30, expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.sixth), kPlusOneULPFunctions['f32'](kValue.f32.positive.pi.sixth)] }, { input: 45, expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.quarter), kPlusOneULPFunctions['f32'](kValue.f32.positive.pi.quarter)] }, { input: 60, expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.third), kPlusOneULPFunctions['f32'](kValue.f32.positive.pi.third)] }, { input: 90, expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.half), kPlusOneULPFunctions['f32'](kValue.f32.positive.pi.half)] }, { input: 135, expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.three_quarters), kPlusOneULPFunctions['f32'](kValue.f32.positive.pi.three_quarters)] }, { input: 180, expected: [kMinusOneULPFunctions['f32'](kValue.f32.positive.pi.whole), kPlusOneULPFunctions['f32'](kValue.f32.positive.pi.whole)] }, ] as ScalarToIntervalCase[], f16: [ { input: -180, expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.whole), kPlusOneULPFunctions['f16'](kValue.f16.negative.pi.whole)] }, { input: -135, expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.three_quarters), kPlusOneULPFunctions['f16'](kValue.f16.negative.pi.three_quarters)] }, { input: -90, expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.half), kPlusOneULPFunctions['f16'](kValue.f16.negative.pi.half)] }, { input: -60, expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.third), kPlusOneULPFunctions['f16'](kValue.f16.negative.pi.third)] }, { input: -45, expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.quarter), kPlusOneULPFunctions['f16'](kValue.f16.negative.pi.quarter)] }, { input: -30, expected: [kMinusOneULPFunctions['f16'](kValue.f16.negative.pi.sixth), kPlusOneULPFunctions['f16'](kValue.f16.negative.pi.sixth)] }, { input: 30, expected: [kMinusOneULPFunctions['f16'](kValue.f16.positive.pi.sixth), kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.sixth)] }, { input: 45, expected: [kMinusOneULPFunctions['f16'](kValue.f16.positive.pi.quarter), kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.quarter)] }, { input: 60, expected: [kMinusOneULPFunctions['f16'](kValue.f16.positive.pi.third), kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.third)] }, { input: 90, expected: [kMinusOneULPFunctions['f16'](kValue.f16.positive.pi.half), kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.half)] }, { input: 135, expected: [kMinusOneULPFunctions['f16'](kValue.f16.positive.pi.three_quarters), kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.three_quarters)] }, { input: 180, expected: [kMinusOneULPFunctions['f16'](kValue.f16.positive.pi.whole), kPlusOneULPFunctions['f16'](kValue.f16.positive.pi.whole)] }, ] as ScalarToIntervalCase[], } as const; g.test('radiansInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = p.trait; const constants = FP[trait].constants(); // prettier-ignore return [ { input: constants.positive.infinity, expected: kUnboundedEndpoints }, { input: 0, expected: 0 }, { input: constants.negative.infinity, expected: kUnboundedEndpoints }, ...kRadiansIntervalCases[trait] ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.radiansInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.radiansInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // Large but still representable integer const kRoundIntervalCases = { f32: [ { input: 2 ** 30, expected: 2 ** 30 }, { input: -(2 ** 30), expected: -(2 ** 30) }, { input: 0x8000_0000, expected: 0x8000_0000 }, // https://github.com/gpuweb/cts/issues/2766 ], f16: [ { input: 2 ** 14, expected: 2 ** 14 }, { input: -(2 ** 14), expected: -(2 ** 14) }, { input: 0x8000, expected: 0x8000 }, // https://github.com/gpuweb/cts/issues/2766 ], abstract: [ { input: 2 ** 62, expected: 2 ** 62 }, { input: -(2 ** 62), expected: -(2 ** 62) }, { input: 0x8000_0000_0000_0000, expected: 0x8000_0000_0000_0000, }, // https://github.com/gpuweb/cts/issues/2766 ], } as const; g.test('roundInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore return [ { input: 0, expected: 0 }, { input: 0.1, expected: 0 }, { input: 0.5, expected: 0 }, // Testing tie breaking { input: 0.9, expected: 1 }, { input: 1.0, expected: 1 }, { input: 1.1, expected: 1 }, { input: 1.5, expected: 2 }, // Testing tie breaking { input: 1.9, expected: 2 }, { input: -0.1, expected: 0 }, { input: -0.5, expected: 0 }, // Testing tie breaking { input: -0.9, expected: -1 }, { input: -1.0, expected: -1 }, { input: -1.1, expected: -1 }, { input: -1.5, expected: -2 }, // Testing tie breaking { input: -1.9, expected: -2 }, // Edge cases { input: constants.positive.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: constants.positive.max }, { input: constants.positive.min, expected: 0 }, { input: constants.negative.min, expected: constants.negative.min }, { input: constants.negative.max, expected: 0 }, ...kRoundIntervalCases[p.trait], // Subnormals { input: constants.positive.subnormal.max, expected: 0 }, { input: constants.positive.subnormal.min, expected: 0 }, { input: constants.negative.subnormal.min, expected: 0 }, { input: constants.negative.subnormal.max, expected: 0 }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.roundInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.roundInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); g.test('saturateInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore return [ // Normals { input: 0, expected: 0 }, { input: 0.1, expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, { input: 1, expected: 1.0 }, { input: -0.1, expected: 0 }, { input: -1, expected: 0 }, { input: -10, expected: 0 }, { input: 10, expected: 1.0 }, { input: 11.1, expected: 1.0 }, { input: constants.positive.max, expected: 1.0 }, { input: constants.positive.min, expected: constants.positive.min }, { input: constants.negative.max, expected: 0.0 }, { input: constants.negative.min, expected: 0.0 }, // Subnormals { input: constants.positive.subnormal.max, expected: [0.0, constants.positive.subnormal.max] }, { input: constants.positive.subnormal.min, expected: [0.0, constants.positive.subnormal.min] }, { input: constants.negative.subnormal.min, expected: [constants.negative.subnormal.min, 0.0] }, { input: constants.negative.subnormal.max, expected: [constants.negative.subnormal.max, 0.0] }, // Infinities { input: constants.positive.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.infinity, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.saturateInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.saturationInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); g.test('signInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore return [ { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: -1 }, { input: -10, expected: -1 }, { input: -1, expected: -1 }, { input: -0.1, expected: -1 }, { input: constants.negative.max, expected: -1 }, { input: constants.negative.subnormal.min, expected: [-1, 0] }, { input: constants.negative.subnormal.max, expected: [-1, 0] }, { input: 0, expected: 0 }, { input: constants.positive.subnormal.max, expected: [0, 1] }, { input: constants.positive.subnormal.min, expected: [0, 1] }, { input: constants.positive.min, expected: 1 }, { input: 0.1, expected: 1 }, { input: 1, expected: 1 }, { input: 10, expected: 1 }, { input: constants.positive.max, expected: 1 }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.signInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.signInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); g.test('sinInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore return [ // This test does not include some common cases, i.e. f(x = -π|π) = 0, // because the difference between true x and x as a f32 is sufficiently // large, such that the high slope of f @ x causes the results to be // substantially different, so instead of getting 0 you get a value on the // order of 10^-8 away from it, thus difficult to express in a // human-readable manner. { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: kUnboundedEndpoints }, { input: constants.negative.pi.half, expected: [-1, kPlusOneULPFunctions[p.trait](-1)] }, { input: 0, expected: 0 }, { input: constants.positive.pi.half, expected: [kMinusOneULPFunctions[p.trait](1), 1] }, { input: constants.positive.max, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const error = (_: number): number => { return t.params.trait === 'f32' ? 2 ** -11 : 2 ** -7; }; const expected = trait.toInterval(applyError(t.params.expected, error)); const got = trait.sinInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.sinInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // Some of these are hard coded, since the error intervals are difficult to express in a closed // human-readable form due to the inherited nature of the errors. // prettier-ignore const kSinhIntervalCases = { f32: [ { input: -1, expected: [reinterpretU32AsF32(0xbf966d05), reinterpretU32AsF32(0xbf966cf8)] }, // ~-1.175... { input: 0, expected: [reinterpretU32AsF32(0xb4600000), reinterpretU32AsF32(0x34600000)] }, // ~0 { input: 1, expected: [reinterpretU32AsF32(0x3f966cf8), reinterpretU32AsF32(0x3f966d05)] }, // ~1.175... ] as ScalarToIntervalCase[], f16: [ { input: -1, expected: [reinterpretU16AsF16(0xbcb8), reinterpretU16AsF16(0xbcaf)] }, // ~-1.175... { input: 0, expected: [reinterpretU16AsF16(0x9200), reinterpretU16AsF16(0x1200)] }, // ~0 { input: 1, expected: [reinterpretU16AsF16(0x3caf), reinterpretU16AsF16(0x3cb8)] }, // ~1.175... ] as ScalarToIntervalCase[], } as const; g.test('sinhInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ ...kSinhIntervalCases[p.trait], { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.sinhInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.sinhInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // For sqrt interval inherited from 1.0 / inverseSqrt(x), errors come from: // 1. Rounding of input x, if any; // 2. 2 ULP from inverseSqrt; // 3. And 2.5 ULP from division. // The last 2.5ULP is handled in test and not included in the expected values here. // prettier-ignore const kSqrtIntervalCases = { f32: [ // 0.01 rounded to f32 0x3C23D70A or 0x3C23D70B. // For inverseSqrt interval, floor_f32(1.0/sqrt(0x3C23D70B))-2ULP=0x411FFFFD, // ceil_f32(1.0/sqrt(0x3C23D70A))+2ULP=0x41200003. // For division, 1.0/0x41200003=0.09999997138977868544997855067803 rounded to f32 0x3DCCCCC8 or 0x3DCCCCC9, // 1.0/0x411FFFFD=0.100000028610237685454662304067 rounded to f32 0x3DCCCCD0 or 0x3DCCCCD1. { input: 0.01, expected: [reinterpretU32AsF32(0x3DCCCCC8), reinterpretU32AsF32(0x3DCCCCD1)] }, // ~0.1 // For inverseSqrt interval, 1.0/sqrt(1.0)-2ULP=0x3F7FFFFE, 1.0/sqrt(1.0)+2ULP=0x3F800001. // For division, 1.0/0x3F800001=0.9999998807907246108530328709735 rounded to f32 0x3F7FFFFE or 0x3F7FFFFF, // 1.0/0x3F7FFFFE=1.0000001192093038108564210027667 rounded to f32 0x3F800001 or 0x3F800002. { input: 1, expected: [reinterpretU32AsF32(0x3F7FFFFE), reinterpretU32AsF32(0x3F800002)] }, // ~1 // For inverseSqrt interval, 1.0/sqrt(4.0)-2ULP=0x3EFFFFFE, 1.0/sqrt(4.0)+2ULP=0x3F000001. // For division, 1.0/0x3F000001=1.999999761581449221706065741947 rounded to f32 0x3FFFFFFE or 0x3FFFFFFF, // 1.0/0x3EFFFFFE=2.0000002384186076217128420055334 rounded to f32 0x40000001 or 0x40000002. { input: 4, expected: [reinterpretU32AsF32(0x3FFFFFFE), reinterpretU32AsF32(0x40000002)] }, // ~2 // For inverseSqrt interval, floor_f32(1.0/sqrt(100.0))-2ULP=0x3DCCCCCA, // ceil_f32(1.0/sqrt(100.0))+2ULP=0x3DCCCCCF. // For division, 1.0/0x3DCCCCCF=9.9999983608725376739278142322684 rounded to f32 0x411FFFFE or 0x411FFFFF, // 1.0/0x3DCCCCCA=10.000002086163002207516386565905 rounded to f32 0x41200002 or 0x41200003. { input: 100, expected: [reinterpretU32AsF32(0x411FFFFE), reinterpretU32AsF32(0x41200003)] }, // ~10 ] as ScalarToIntervalCase[], f16: [ // 0.01 rounded to f16 0x211E or 0x211F. // For inverseSqrt interval, floor_f16(1.0/sqrt(0x211F))-2ULP=0x48FD, // ceil_f16(1.0/sqrt(0x211E))+2ULP=0x4903. // For division, 1.0/0x4903=0.09976617303195635229929851909587 rounded to f16 0x2E62 or 0x2E63, // 1.0/0x48FD=0.10023492560689115113547376664056 rounded to f16 0x2E6A or 0x2E6B. { input: 0.01, expected: [reinterpretU16AsF16(0x2E62), reinterpretU16AsF16(0x2E6B)] }, // ~0.1 // For inverseSqrt interval, 1.0/sqrt(1.0)-2ULP=0x3BFE, 1.0/sqrt(1.0)+2ULP=0x3C01. // For division, 1.0/0x3C01=0.99902439024390243902439024390244 rounded to f16 0x3BFE or 0x3BFF, // 1.0/0x3BFE=1.000977517106549364613880742913 rounded to f16 0x3C01 or 0x3C02. { input: 1, expected: [reinterpretU16AsF16(0x3BFE), reinterpretU16AsF16(0x3C02)] }, // ~1 // For inverseSqrt interval, 1.0/sqrt(4.0)-2ULP=0x37FE, 1.0/sqrt(4.0)+2ULP=0x3801. // For division, 1.0/0x3801=1.9980487804878048780487804878049 rounded to f16 0x3FFE or 0x3FFF, // 1.0/0x37FE=2.001955034213098729227761485826 rounded to f16 0x4001 or 0x4002. { input: 4, expected: [reinterpretU16AsF16(0x3FFE), reinterpretU16AsF16(0x4002)] }, // ~2 // For inverseSqrt interval, floor_f16(1.0/sqrt(100.0))-2ULP=0x2E64, // ceil_f16(1.0/sqrt(100.0))+2ULP=0x2E69. // For division, 1.0/0x2E69=9.9841560024374942258493264279108 rounded to f16 0x48FD or 0x48FE, // 1.0/0x2E64=10.014669926650366748166259168704 rounded to f16 0x4901 or 0x4902. { input: 100, expected: [reinterpretU16AsF16(0x48FD), reinterpretU16AsF16(0x4902)] }, // ~10 ] as ScalarToIntervalCase[], } as const; g.test('sqrtInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // Cases that input and/or result not exactly representable ...kSqrtIntervalCases[p.trait], // Cases out of definition domain { input: -1, expected: kUnboundedEndpoints }, { input: 0, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; // The expected error interval is inherited from 1.0 / inverseSqrt(x), the 2.5ULP for division // is handled here. const error = (n: number): number => { return 2.5 * trait.oneULP(n); }; const expected = trait.toInterval(applyError(t.params.expected, error)); const got = trait.sqrtInterval(t.params.input); t.expect( objectEquals(expected, got), `FP.${t.params.trait}.sqrtInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // All of these are hard coded, since the error intervals are difficult to express in a closed // human-readable form. // Some easy looking cases like f(x = -π|π) = 0 are actually quite difficult. This is because the // interval is calculated from the results of sin(x)/cos(x), which becomes very messy at x = -π|π, // since π is irrational, thus does not have an exact representation as a float. // // Even at 0, which has a precise f32/f16 value, there is still the problem that result of sin(0) // and cos(0) will be intervals due to the inherited nature of errors, so the proper interval will // be an interval calculated from dividing an interval by another interval and applying an error // function to that. // // This complexity is why the entire interval framework was developed. // // The examples here have been manually traced to confirm the expectation values are correct. // prettier-ignore const kTanIntervalCases = { f32: [ { input: kValue.f32.negative.pi.whole, expected: [reinterpretU64AsF64(0xbf40_02bc_9000_0000n), reinterpretU64AsF64(0x3f40_0144_f000_0000n)] }, // ~0.0 { input: kValue.f32.negative.pi.three_quarters, expected: [reinterpretU64AsF64(0x3fef_f4b1_3000_0000n), reinterpretU64AsF64(0x3ff0_05a9_9000_0000n)] }, // ~1.0 { input: kValue.f32.negative.pi.third, expected: [reinterpretU64AsF64(0xbffb_c16b_d000_0000n), reinterpretU64AsF64(0xbffb_ab8f_9000_0000n)] }, // ~-√3 { input: kValue.f32.negative.pi.quarter, expected: [reinterpretU64AsF64(0xbff0_05a9_b000_0000n), reinterpretU64AsF64(0xbfef_f4b1_5000_0000n)] }, // ~-1.0 { input: kValue.f32.negative.pi.sixth, expected: [reinterpretU64AsF64(0xbfe2_80f1_f000_0000n), reinterpretU64AsF64(0xbfe2_725e_d000_0000n)] }, // ~-1/√3 { input: 0, expected: [reinterpretU64AsF64(0xbf40_0200_b000_0000n), reinterpretU64AsF64(0x3f40_0200_b000_0000n)] }, // ~0.0 { input: kValue.f32.positive.pi.sixth, expected: [reinterpretU64AsF64(0x3fe2_725e_d000_0000n), reinterpretU64AsF64(0x3fe2_80f1_f000_0000n)] }, // ~1/√3 { input: kValue.f32.positive.pi.quarter, expected: [reinterpretU64AsF64(0x3fef_f4b1_5000_0000n), reinterpretU64AsF64(0x3ff0_05a9_b000_0000n)] }, // ~1.0 { input: kValue.f32.positive.pi.third, expected: [reinterpretU64AsF64(0x3ffb_ab8f_9000_0000n), reinterpretU64AsF64(0x3ffb_c16b_d000_0000n)] }, // ~√3 { input: kValue.f32.positive.pi.three_quarters, expected: [reinterpretU64AsF64(0xbff0_05a9_9000_0000n), reinterpretU64AsF64(0xbfef_f4b1_3000_0000n)] }, // ~-1.0 { input: kValue.f32.positive.pi.whole, expected: [reinterpretU64AsF64(0xbf40_0144_f000_0000n), reinterpretU64AsF64(0x3f40_02bc_9000_0000n)] }, // ~0.0 ] as ScalarToIntervalCase[], f16: [ { input: kValue.f16.negative.pi.whole, expected: [reinterpretU64AsF64(0xbf7c_5600_0000_0000n), reinterpretU64AsF64(0x3f82_2e00_0000_0000n)] }, // ~0.0 { input: kValue.f16.negative.pi.three_quarters, expected: [reinterpretU64AsF64(0x3fef_4600_0000_0000n), reinterpretU64AsF64(0x3ff0_7200_0000_0000n)] }, // ~1.0 { input: kValue.f16.negative.pi.third, expected: [reinterpretU64AsF64(0xbffc_7600_0000_0000n), reinterpretU64AsF64(0xbffa_f600_0000_0000n)] }, // ~-√3 { input: kValue.f16.negative.pi.quarter, expected: [reinterpretU64AsF64(0xbff0_6600_0000_0000n), reinterpretU64AsF64(0xbfef_3600_0000_0000n)] }, // ~-1.0 { input: kValue.f16.negative.pi.sixth, expected: [reinterpretU64AsF64(0xbfe2_fe00_0000_0000n), reinterpretU64AsF64(0xbfe1_f600_0000_0000n)] }, // ~-1/√3 { input: 0, expected: [reinterpretU64AsF64(0xbf80_2e00_0000_0000n), reinterpretU64AsF64(0x3f80_2e00_0000_0000n)] }, // ~0.0 { input: kValue.f16.positive.pi.sixth, expected: [reinterpretU64AsF64(0x3fe1_f600_0000_0000n), reinterpretU64AsF64(0x3fe2_fe00_0000_0000n)] }, // ~1/√3 { input: kValue.f16.positive.pi.quarter, expected: [reinterpretU64AsF64(0x3fef_3600_0000_0000n), reinterpretU64AsF64(0x3ff0_6600_0000_0000n)] }, // ~1.0 { input: kValue.f16.positive.pi.third, expected: [reinterpretU64AsF64(0x3ffa_f600_0000_0000n), reinterpretU64AsF64(0x3ffc_7600_0000_0000n)] }, // ~√3 { input: kValue.f16.positive.pi.three_quarters, expected: [reinterpretU64AsF64(0xbff0_7200_0000_0000n), reinterpretU64AsF64(0xbfef_4600_0000_0000n)] }, // ~-1.0 { input: kValue.f16.positive.pi.whole, expected: [reinterpretU64AsF64(0xbf82_2e00_0000_0000n), reinterpretU64AsF64(0x3f7c_5600_0000_0000n)] }, // ~0.0 ] as ScalarToIntervalCase[], } as const; g.test('tanInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ ...kTanIntervalCases[p.trait], // Cases that result in unbounded interval. { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: kUnboundedEndpoints }, { input: constants.negative.pi.half, expected: kUnboundedEndpoints }, { input: constants.positive.pi.half, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.tanInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.tanInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); // Some of these are hard coded, since the error intervals are difficult to express in a closed // human-readable form due to the inherited nature of the errors. // prettier-ignore const kTanhIntervalCases = { f32: [ { input: -1, expected: [reinterpretU64AsF64(0xbfe8_5f0f_b8b_588e3n), reinterpretU64AsF64(0xbfe8_5ee5_a74a_771dn)] }, // ~-0.7615... { input: 0, expected: [reinterpretU64AsF64(0xbee4_f8b5_88e3_68f1n), reinterpretU64AsF64(0x3ee4_f8b5_88e3_68f1n)] }, // ~0 { input: 1, expected: [reinterpretU64AsF64(0x3fe8_5ee5_a74a_771dn), reinterpretU64AsF64(0x3fe8_5f0f_b8b5_88e3n)] }, // ~0.7615... ] as ScalarToIntervalCase[], f16: [ { input: -1, expected: [reinterpretU64AsF64(0xbfe8_9600_0000_0000n), reinterpretU64AsF64(0xbfe8_2e00_0000_0000n)] }, // ~-0.7615... { input: 0, expected: [reinterpretU64AsF64(0xbf48_0e00_0000_0000n), reinterpretU64AsF64(0x3f48_0e00_0000_0000n)] }, // ~0 { input: 1, expected: [reinterpretU64AsF64(0x3fe8_2e00_0000_0000n), reinterpretU64AsF64(0x3fe8_9600_0000_0000n)] }, // ~0.7615... ] as ScalarToIntervalCase[], } as const; g.test('tanhInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ ...kTanhIntervalCases[p.trait], { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.min, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: kUnboundedEndpoints }, { input: constants.positive.infinity, expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.tanhInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.tanhInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); g.test('truncInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // Normals { input: 0, expected: 0 }, { input: 0.1, expected: 0 }, { input: 0.9, expected: 0 }, { input: 1.0, expected: 1 }, { input: 1.1, expected: 1 }, { input: 1.9, expected: 1 }, { input: -0.1, expected: 0 }, { input: -0.9, expected: 0 }, { input: -1.0, expected: -1 }, { input: -1.1, expected: -1 }, { input: -1.9, expected: -1 }, // Subnormals { input: constants.positive.subnormal.max, expected: 0 }, { input: constants.positive.subnormal.min, expected: 0 }, { input: constants.negative.subnormal.min, expected: 0 }, { input: constants.negative.subnormal.max, expected: 0 }, // Edge cases { input: constants.positive.infinity, expected: kUnboundedEndpoints }, { input: constants.negative.infinity, expected: kUnboundedEndpoints }, { input: constants.positive.max, expected: constants.positive.max }, { input: constants.positive.min, expected: 0 }, { input: constants.negative.min, expected: constants.negative.min }, { input: constants.negative.max, expected: 0 }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.truncInterval(t.params.input); t.expect( objectEquals(expected, got), `FP.${t.params.trait}.truncInterval(${t.params.input}) returned ${got}. Expected ${expected}` ); }); interface ScalarPairToIntervalCase { // input is a pair of independent values, not a range, so should not be // converted to a FPInterval. input: [number, number]; expected: number | IntervalEndpoints; } // prettier-ignore const kAdditionInterval64BitsNormalCases = { f32: [ // 0.1 falls between f32 0x3DCCCCCC and 0x3DCCCCCD, -0.1 falls between f32 0xBDCCCCCD and 0xBDCCCCCC // f32 0x3DCCCCCC+0x3DCCCCCC=0x3E4CCCCC, 0x3DCCCCCD+0x3DCCCCCD=0x3E4CCCCD { input: [0.1, 0.1], expected: [reinterpretU32AsF32(0x3e4ccccc), reinterpretU32AsF32(0x3e4ccccd)] }, // ~0.2 // f32 0xBDCCCCCD+0xBDCCCCCD=0xBE4CCCCD, 0xBDCCCCCC+0xBDCCCCCC=0xBE4CCCCD { input: [-0.1, -0.1], expected: [reinterpretU32AsF32(0xbe4ccccd), reinterpretU32AsF32(0xbe4ccccc)] }, // ~-0.2 // 0.1+(-0.1) expect f32 interval [0x3DCCCCCC+0xBDCCCCCD, 0x3DCCCCCD+0xBDCCCCCC] { input: [0.1, -0.1], expected: [reinterpretU32AsF32(0x3dcccccc) + reinterpretU32AsF32(0xbdcccccd), reinterpretU32AsF32(0x3dcccccd) + reinterpretU32AsF32(0xbdcccccc)] }, // ~0.0 // -0.1+0.1 expect f32 interval [0xBDCCCCCD+0x3DCCCCCC, 0xBDCCCCCC+0x3DCCCCCD] { input: [-0.1, 0.1], expected: [reinterpretU32AsF32(0xbdcccccd) + reinterpretU32AsF32(0x3dcccccc), reinterpretU32AsF32(0xbdcccccc) + reinterpretU32AsF32(0x3dcccccd)] }, // ~0.0 { input: [1, kValue.f32.positive.min], expected: [1.0, reinterpretU32AsF32(0x3f800001)] }, { input: [1, kValue.f32.negative.max], expected: [reinterpretU32AsF32(0x3f7fffff), 1.0] }, { input: [-1, kValue.f32.positive.min], expected: [-1.0, reinterpretU32AsF32(0xbf7fffff)] }, { input: [-1, kValue.f32.negative.max], expected: [reinterpretU32AsF32(0xbf800001), -1.0] }, { input: [1, kValue.f32.positive.max], expected: kUnboundedEndpoints }, { input: [1, kValue.f32.negative.min], expected: [reinterpretU32AsF32(0xff7fffff), reinterpretU32AsF32(0xff7ffffe)] }, { input: [-1, kValue.f32.positive.max], expected: [reinterpretU32AsF32(0x7f7ffffe), reinterpretU32AsF32(0x7f7fffff)] }, { input: [-1, kValue.f32.negative.min], expected: kUnboundedEndpoints }, // Symmetry with the above test cases. { input: [kValue.f32.positive.min, 1], expected: [1.0, reinterpretU32AsF32(0x3f800001)] }, { input: [kValue.f32.negative.max, 1], expected: [reinterpretU32AsF32(0x3f7fffff), 1.0] }, { input: [kValue.f32.positive.min, -1], expected: [-1.0, reinterpretU32AsF32(0xbf7fffff)] }, { input: [kValue.f32.negative.max, -1], expected: [reinterpretU32AsF32(0xbf800001), -1.0] }, { input: [kValue.f32.positive.max, 1], expected: kUnboundedEndpoints }, { input: [kValue.f32.negative.min, 1], expected: [reinterpretU32AsF32(0xff7fffff), reinterpretU32AsF32(0xff7ffffe)] }, { input: [kValue.f32.positive.max, -1], expected: [reinterpretU32AsF32(0x7f7ffffe), reinterpretU32AsF32(0x7f7fffff)] }, { input: [kValue.f32.negative.min, -1], expected: kUnboundedEndpoints }, ] as ScalarPairToIntervalCase[], f16: [ // 0.1 falls between f16 0x2E66 and 0x2E67, -0.1 falls between f16 0xAE67 and 0xAE66 // f16 0x2E66+0x2E66=0x3266, 0x2E67+0x2E67=0x3267 { input: [0.1, 0.1], expected: [reinterpretU16AsF16(0x3266), reinterpretU16AsF16(0x3267)] }, // ~0.2 // f16 0xAE67+0xAE67=0xB267, 0xAE66+0xAE66=0xB266 { input: [-0.1, -0.1], expected: [reinterpretU16AsF16(0xb267), reinterpretU16AsF16(0xb266)] }, // ~-0.2 // 0.1+(-0.1) expect f16 interval [0x2E66+0xAE67, 0x2E67+0xAE66] { input: [0.1, -0.1], expected: [reinterpretU16AsF16(0x2e66) + reinterpretU16AsF16(0xae67), reinterpretU16AsF16(0x2e67) + reinterpretU16AsF16(0xae66)] }, // ~0.0 // -0.1+0.1 expect f16 interval [0xAE67+0x2E66, 0xAE66+0x2E67] { input: [-0.1, 0.1], expected: [reinterpretU16AsF16(0xae67)+reinterpretU16AsF16(0x2e66), reinterpretU16AsF16(0xae66)+reinterpretU16AsF16(0x2e67)] }, // ~0.0 ] as ScalarPairToIntervalCase[], } as const; g.test('additionInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // Representable normals { input: [0, 0], expected: 0 }, { input: [1, 0], expected: 1 }, { input: [0, 1], expected: 1 }, { input: [-1, 0], expected: -1 }, { input: [0, -1], expected: -1 }, { input: [1, 1], expected: 2 }, { input: [1, -1], expected: 0 }, { input: [-1, 1], expected: 0 }, { input: [-1, -1], expected: -2 }, // 0.1 should be correctly rounded { input: [0.1, 0], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, { input: [0, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // -0.1 should be correctly rounded { input: [-0.1, 0], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, { input: [0, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // 64-bit normals that can not be exactly represented ...kAdditionInterval64BitsNormalCases[p.trait], // Subnormals { input: [constants.positive.subnormal.max, 0], expected: [0, constants.positive.subnormal.max] }, { input: [0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, { input: [constants.positive.subnormal.min, 0], expected: [0, constants.positive.subnormal.min] }, { input: [0, constants.positive.subnormal.min], expected: [0, constants.positive.subnormal.min] }, { input: [constants.negative.subnormal.max, 0], expected: [constants.negative.subnormal.max, 0] }, { input: [0, constants.negative.subnormal.max], expected: [constants.negative.subnormal.max, 0] }, { input: [constants.negative.subnormal.min, 0], expected: [constants.negative.subnormal.min, 0] }, { input: [0, constants.negative.subnormal.min], expected: [constants.negative.subnormal.min, 0] }, // Infinities { input: [0, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, 0], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [0, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, 0], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const [x, y] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.additionInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.additionInterval(${x}, ${y}) returned ${got}. Expected ${expected}` ); }); // Cases for Atan2Interval. The positive x & y quadrant is tested in more detail, and the other // quadrants are spot checked that values are pointing in the right direction. // Note: atan2's parameters are labelled (y, x) instead of (x, y) // prettier-ignore const kAtan2IntervalCases = { // atan has 4096ULP error boundary for f32. f32: [ // positive y, positive x // √3 rounded to f32 0x3FDDB3D7, atan2(1, 0x3FDDB3D7)=0.52359877749051820266056630237827 ~ pi/6 rounded to f32 0x3F060A91 or 0x3F060A92, // kValue.f32.positive.pi.sixth is 0x3F060A92. { input: [1, reinterpretU32AsF32(0x3fddb3d7)], expected: [kMinusNULPFunctions['f32'](kValue.f32.positive.pi.sixth, 4097), kPlusNULPFunctions['f32'](kValue.f32.positive.pi.sixth, 4096)] }, // atan2(1, 1)=0.78539816339744830961566084581988 ~ pi/4 rounded to f32 0x3F490FDA or 0x3F490FDB, // kValue.f32.positive.pi.quarter is 0x3F490FDB. { input: [1, 1], expected: [kMinusNULPFunctions['f32'](kValue.f32.positive.pi.quarter, 4097), kPlusNULPFunctions['f32'](kValue.f32.positive.pi.quarter, 4096)] }, // √3 rounded to f32 0x3FDDB3D7, atan2(0x3FDDB3D7, 1) = 1.0471975493043784165707553892615 ~ pi/3 rounded to f32 0x3F860A91 or 0x3F860A92, // kValue.f32.positive.pi.third is 0x3F860A92. { input: [reinterpretU32AsF32(0x3fddb3d7), 1], expected: [kMinusNULPFunctions['f32'](kValue.f32.positive.pi.third, 4097), kPlusNULPFunctions['f32'](kValue.f32.positive.pi.third, 4096)] }, // positive y, negative x // atan2(1, -1)=pi*3/4=2.3561944901923449288469825374591 rounded to f32 0x4016CBE3 or 0x4016CBE4, // kValue.f32.positive.pi.three_quarters is 0x4016CBE4. { input: [1, -1], expected: [kMinusNULPFunctions['f32'](kValue.f32.positive.pi.three_quarters, 4097), kPlusNULPFunctions['f32'](kValue.f32.positive.pi.three_quarters, 4096)] }, // negative y, negative x // atan2(-1, -1)=-pi*3/4=-2.3561944901923449288469825374591 rounded to f32 0xC016CBE4 or 0xC016CBE3, // kValue.f32.negative.pi.three_quarters is 0xC016CBE4. { input: [-1, -1], expected: [kMinusNULPFunctions['f32'](kValue.f32.negative.pi.three_quarters, 4096), kPlusNULPFunctions['f32'](kValue.f32.negative.pi.three_quarters, 4097)] }, // negative y, positive x // atan2(-1, 1)=-pi/4=-0.78539816339744830961566084581988 rounded to f32 0xBF490FDB or 0xBF490FDA, // kValue.f32.negative.pi.quarter is 0xBF490FDB. { input: [-1, 1], expected: [kMinusNULPFunctions['f32'](kValue.f32.negative.pi.quarter, 4096), kPlusNULPFunctions['f32'](kValue.f32.negative.pi.quarter, 4097)] }, // When y/x ~ 0, test that ULP applied to result of atan2, not the intermediate y/x value. // y/x ~ 0, y<0, x<0, atan2(y,x) ~ -pi rounded to f32 0xC0490FDB or 0xC0490FDA, // kValue.f32.negative.pi.whole is 0xC0490FDB. {input: [kValue.f32.negative.max, -1], expected: [kMinusNULPFunctions['f32'](kValue.f32.negative.pi.whole, 4096), kPlusNULPFunctions['f32'](kValue.f32.negative.pi.whole, 4097)] }, // y/x ~ 0, y>0, x<0, atan2(y,x) ~ pi rounded to f32 0x40490FDA or 0x40490FDB, // kValue.f32.positive.pi.whole is 0x40490FDB. {input: [kValue.f32.positive.min, -1], expected: [kMinusNULPFunctions['f32'](kValue.f32.positive.pi.whole, 4097), kPlusNULPFunctions['f32'](kValue.f32.positive.pi.whole, 4096)] }, ] as ScalarPairToIntervalCase[], // atan has 5ULP error boundary for f16. f16: [ // positive y, positive x // √3 rounded to f16 0x3EED, atan2(1, 0x3EED)=0.52375018906301191131992842392268 ~ pi/6 rounded to f16 0x3830 or 0x3831, // kValue.f16.positive.pi.sixth is 0x3830. { input: [1, reinterpretU16AsF16(0x3eed)], expected: [kMinusNULPFunctions['f16'](kValue.f16.positive.pi.sixth, 5), kPlusNULPFunctions['f16'](kValue.f16.positive.pi.sixth, 6)] }, // atan2(1, 1)=0.78539816339744830961566084581988 ~ pi/4 rounded to f16 0x3A48 or 0x3A49, // kValue.f16.positive.pi.quarter is 0x3A48. { input: [1, 1], expected: [kMinusNULPFunctions['f16'](kValue.f16.positive.pi.quarter, 5), kPlusNULPFunctions['f16'](kValue.f16.positive.pi.quarter, 6)] }, // √3 rounded to f16 0x3EED, atan2(0x3EED, 1) = 1.0470461377318847079113932677171 ~ pi/3 rounded to f16 0x3C30 or 0x3C31, // kValue.f16.positive.pi.third is 0x3C30. { input: [reinterpretU16AsF16(0x3eed), 1], expected: [kMinusNULPFunctions['f16'](kValue.f16.positive.pi.third, 5), kPlusNULPFunctions['f16'](kValue.f16.positive.pi.third, 6)] }, // positive y, negative x // atan2(1, -1)=pi*3/4=2.3561944901923449288469825374591 rounded to f16 0x40B6 or 0x40B7, // kValue.f16.positive.pi.three_quarters is 0x40B6. { input: [1, -1], expected: [kMinusNULPFunctions['f16'](kValue.f16.positive.pi.three_quarters, 5), kPlusNULPFunctions['f16'](kValue.f16.positive.pi.three_quarters, 6)] }, // negative y, negative x // atan2(-1, -1)=-pi*3/4=-2.3561944901923449288469825374591 rounded to f16 0xC0B7 or 0xC0B6, // kValue.f16.negative.pi.three_quarters is 0xC0B6. { input: [-1, -1], expected: [kMinusNULPFunctions['f16'](kValue.f16.negative.pi.three_quarters, 6), kPlusNULPFunctions['f16'](kValue.f16.negative.pi.three_quarters, 5)] }, // negative y, positive x // atan2(-1, 1)=-pi/4=-0.78539816339744830961566084581988 rounded to f16 0xBA49 or 0xBA48, // kValue.f16.negative.pi.quarter is 0xBA48. { input: [-1, 1], expected: [kMinusNULPFunctions['f16'](kValue.f16.negative.pi.quarter, 6), kPlusNULPFunctions['f16'](kValue.f16.negative.pi.quarter, 5)] }, // When y/x ~ 0, test that ULP applied to result of atan2, not the intermediate y/x value. // y/x ~ 0, y<0, x<0, atan2(y,x) ~ -pi rounded to f16 0xC249 or 0xC248, // kValue.f16.negative.pi.whole is 0xC248. {input: [kValue.f16.negative.max, -1], expected: [kMinusNULPFunctions['f16'](kValue.f16.negative.pi.whole, 6), kPlusNULPFunctions['f16'](kValue.f16.negative.pi.whole, 5)] }, // y/x ~ 0, y>0, x<0, atan2(y,x) ~ pi rounded to f16 0x4248 or 0x4249, // kValue.f16.positive.pi.whole is 0x4248. {input: [kValue.f16.positive.min, -1], expected: [kMinusNULPFunctions['f16'](kValue.f16.positive.pi.whole, 5), kPlusNULPFunctions['f16'](kValue.f16.positive.pi.whole, 6)] }, ] as ScalarPairToIntervalCase[], } as const; g.test('atan2Interval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore return [ ...kAtan2IntervalCases[p.trait], // Cases that y out of bound. // positive y, positive x { input: [Number.POSITIVE_INFINITY, 1], expected: kUnboundedEndpoints }, // positive y, negative x { input: [Number.POSITIVE_INFINITY, -1], expected: kUnboundedEndpoints }, // negative y, negative x { input: [Number.NEGATIVE_INFINITY, -1], expected: kUnboundedEndpoints }, // negative y, positive x { input: [Number.NEGATIVE_INFINITY, 1], expected: kUnboundedEndpoints }, // Discontinuity @ origin (0,0) { input: [0, 0], expected: kUnboundedEndpoints }, { input: [0, constants.positive.subnormal.max], expected: kUnboundedEndpoints }, { input: [0, constants.negative.subnormal.min], expected: kUnboundedEndpoints }, { input: [0, constants.positive.min], expected: kUnboundedEndpoints }, { input: [0, constants.negative.max], expected: kUnboundedEndpoints }, { input: [0, constants.positive.max], expected: kUnboundedEndpoints }, { input: [0, constants.negative.min], expected: kUnboundedEndpoints }, { input: [0, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [0, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [0, 1], expected: kUnboundedEndpoints }, { input: [constants.positive.subnormal.max, 1], expected: kUnboundedEndpoints }, { input: [constants.negative.subnormal.min, 1], expected: kUnboundedEndpoints }, // Very large |x| values should cause kUnboundedEndpoints to be returned, due to the restrictions on division { input: [1, constants.positive.max], expected: kUnboundedEndpoints }, { input: [1, constants.positive.nearest_max], expected: kUnboundedEndpoints }, { input: [1, constants.negative.min], expected: kUnboundedEndpoints }, { input: [1, constants.negative.nearest_min], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const [y, x] = t.params.input; const expected = trait.toInterval(t.params.expected); const got = trait.atan2Interval(y, x); t.expect( objectEquals(expected, got), `${t.params.trait}.atan2Interval(${y}, ${x}) returned ${got}]. Expected ${expected}` ); }); g.test('distanceIntervalScalar') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ { input: [1.0, 0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [0.0, 1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [-0.0, -1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [0.0, -1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [0.1, 0], expected: kRootSumSquareExpectationInterval[p.trait]['[0.1]'] }, // ~0.1 { input: [0, 0.1], expected: kRootSumSquareExpectationInterval[p.trait]['[0.1]'] }, // ~0.1 { input: [-0.1, 0], expected: kRootSumSquareExpectationInterval[p.trait]['[0.1]'] }, // ~0.1 { input: [0, -0.1], expected: kRootSumSquareExpectationInterval[p.trait]['[0.1]'] }, // ~0.1 { input: [10.0, 0], expected: kRootSumSquareExpectationInterval[p.trait]['[10]'] }, // ~10 { input: [0, 10.0], expected: kRootSumSquareExpectationInterval[p.trait]['[10]'] }, // ~10 { input: [-10.0, 0], expected: kRootSumSquareExpectationInterval[p.trait]['[10]'] }, // ~10 { input: [0, -10.0], expected: kRootSumSquareExpectationInterval[p.trait]['[10]'] }, // ~10 // distance(x, y), where x - y = 0 has an acceptance interval of kUnboundedEndpoints, // because distance(x, y) = length(x - y), and length(0) = kUnboundedEndpoints { input: [0, 0], expected: kUnboundedEndpoints }, { input: [1.0, 1.0], expected: kUnboundedEndpoints }, { input: [-1.0, -1.0], expected: kUnboundedEndpoints }, // Subnormal Cases { input: [constants.negative.subnormal.min, 0], expected: kUnboundedEndpoints }, { input: [constants.negative.subnormal.max, 0], expected: kUnboundedEndpoints }, { input: [constants.positive.subnormal.min, 0], expected: kUnboundedEndpoints }, { input: [constants.positive.subnormal.max, 0], expected: kUnboundedEndpoints }, // Edge cases { input: [constants.positive.infinity, 0], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, 0], expected: kUnboundedEndpoints }, { input: [constants.negative.min, 0], expected: kUnboundedEndpoints }, { input: [constants.negative.max, 0], expected: kUnboundedEndpoints }, { input: [constants.positive.min, 0], expected: kUnboundedEndpoints }, { input: [constants.positive.max, 0], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.distanceInterval(...t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.distanceInterval(${t.params.input[0]}, ${t.params.input[1]}) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kDivisionInterval64BitsNormalCases = { f32: [ // Zero divided by any non-zero finite value results in zero. { input: [0, 0.1], expected: 0 }, { input: [0, -0.1], expected: 0 }, // 0.1 rounded to f32 0x3DCCCCCC or 0x3DCCCCCD, // 1.0/0x3DCCCCCD = 9.9999998509883902204460179966303 rounded to f32 0x411FFFFF or 0x41200000, // 1.0/0x3DCCCCCC = 10.000000596046483527138934924167 rounded to f32 0x41200000 or 0x41200001. { input: [1, 0.1], expected: [reinterpretU32AsF32(0x411fffff), reinterpretU32AsF32(0x41200001)] }, // ~10.0 // The same for -1/-0.1 { input: [-1, -0.1], expected: [reinterpretU32AsF32(0x411fffff), reinterpretU32AsF32(0x41200001)] }, // ~10.0 // -10.000000596046483527138934924167 rounded to f32 0xC1200001 or 0xC1200000, // -9.9999998509883902204460179966303 rounded to f32 0xC1200000 or 0xC11FFFFF. { input: [-1, 0.1], expected: [reinterpretU32AsF32(0xc1200001), reinterpretU32AsF32(0xc11fffff)] }, // ~-10.0 { input: [1, -0.1], expected: [reinterpretU32AsF32(0xc1200001), reinterpretU32AsF32(0xc11fffff)] }, // ~-10.0 // Cases that expected interval larger than +-1ULP. // 0.000001 rounded to f32 0x358637BD or 0x358637BE, // 1.0/0x358637BE = 999999.88883793195700674522548684 rounded to f32 0x497423FE or 0x497423FF, // 1.0/0x358637BD = 1000000.0025247573063743994399971 rounded to f32 0x49742400 or 0x49742401. { input: [1, 0.000001], expected: [reinterpretU32AsF32(0x497423fe), reinterpretU32AsF32(0x49742401)] }, // ~1000000.0 { input: [1, -0.000001], expected: [reinterpretU32AsF32(0xc9742401), reinterpretU32AsF32(0xc97423fe)] }, // ~-1000000.0 ] as ScalarPairToIntervalCase[], f16: [ // Zero divided by any non-zero finite value results in zero. { input: [0, 0.1], expected: 0 }, { input: [0, -0.1], expected: 0 }, // 0.1 rounded to f16 0x2E66 or 0x2E67, // 1.0/0x2E67 = 9.9963392312385600976205003050641 rounded to f16 0x48FF or 0x4900, // 1.0/0x2E66 = 10.002442002442002442002442002442 rounded to f16 0x4900 or 0x4901. { input: [1, 0.1], expected: [reinterpretU16AsF16(0x48ff), reinterpretU16AsF16(0x4901)] }, // ~10.0 // The same for -1/-0.1 { input: [-1, -0.1], expected: [reinterpretU16AsF16(0x48ff), reinterpretU16AsF16(0x4901)] }, // ~10.0 // -10.002442002442002442002442002442 rounded to f16 0xC901 or 0xC900, // -9.9963392312385600976205003050641 rounded to f16 0xC900 or 0xC8FF. { input: [-1, 0.1], expected: [reinterpretU16AsF16(0xc901), reinterpretU16AsF16(0xc8ff)] }, // ~-10.0 { input: [1, -0.1], expected: [reinterpretU16AsF16(0xc901), reinterpretU16AsF16(0xc8ff)] }, // ~-10.0 // Cases that expected interval larger than +-1ULP. // 0.001 rounded to f16 0x1418 or 0x1419, // 1.0/0x1419 = 999.59580552907535977846384072716 rounded to f16 0x63CF or 0x63D0, // 1.0/0x1418 = 1000.5496183206106870229007633588 rounded to f16 0x63D1 or 0x63D2. { input: [1, 0.001], expected: [reinterpretU16AsF16(0x63cf), reinterpretU16AsF16(0x63d2)] }, // ~1000.0 { input: [1, -0.001], expected: [reinterpretU16AsF16(0xe3d2), reinterpretU16AsF16(0xe3cf)] }, // ~-1000.0 ] as ScalarPairToIntervalCase[], } as const; g.test('divisionInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const fp = FP[p.trait]; const constants = fp.constants(); // prettier-ignore return [ // Representable normals { input: [0, 1], expected: 0 }, { input: [0, -1], expected: 0 }, { input: [1, 1], expected: 1 }, { input: [1, -1], expected: -1 }, { input: [-1, 1], expected: -1 }, { input: [-1, -1], expected: 1 }, { input: [4, 2], expected: 2 }, { input: [-4, 2], expected: -2 }, { input: [4, -2], expected: -2 }, { input: [-4, -2], expected: 2 }, // 64-bit normals that can not be exactly represented ...kDivisionInterval64BitsNormalCases[p.trait], // Denominator out of range { input: [1, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [1, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [1, constants.positive.max], expected: kUnboundedEndpoints }, { input: [1, constants.negative.min], expected: kUnboundedEndpoints }, { input: [1, 0], expected: kUnboundedEndpoints }, { input: [1, constants.positive.subnormal.max], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const fp = FP[t.params.trait]; const error = (n: number): number => { return 2.5 * fp.oneULP(n); }; const [x, y] = t.params.input; const expected = FP[t.params.trait].toInterval(applyError(t.params.expected, error)); const got = FP[t.params.trait].divisionInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.divisionInterval(${x}, ${y}) returned ${got}. Expected ${expected}` ); }); const kLdexpIntervalCases = { f32: [ // 64-bit normals { input: [1.0000000001, 1], expected: [2, kPlusNULPFunctions['f32'](2, 2)] }, // ~2, additional ULP error due to first param not being f32 precise { input: [-1.0000000001, 1], expected: [kMinusNULPFunctions['f32'](-2, 2), -2] }, // ~-2, additional ULP error due to first param not being f32 precise // Edge Cases // f32 0b0_01111111_11111111111111111111111 = 1.9999998807907104, // 1.9999998807907104 * 2 ** 127 = f32.positive.max { input: [1.9999998807907104, 127], expected: kValue.f32.positive.max }, // f32.positive.min = 1 * 2 ** -126 { input: [1, -126], expected: kValue.f32.positive.min }, // f32.positive.subnormal.max = 0.9999998807907104 * 2 ** -126 { input: [0.9999998807907104, -126], expected: [0, kValue.f32.positive.subnormal.max] }, // f32.positive.subnormal.min = 1.1920928955078125e-07 * 2 ** -126 { input: [1.1920928955078125e-7, -126], expected: [0, kValue.f32.positive.subnormal.min] }, { input: [-1.1920928955078125e-7, -126], expected: [kValue.f32.negative.subnormal.max, 0] }, { input: [-0.9999998807907104, -126], expected: [kValue.f32.negative.subnormal.min, 0] }, { input: [-1, -126], expected: kValue.f32.negative.max }, { input: [-1.9999998807907104, 127], expected: kValue.f32.negative.min }, // e2 + bias <= 0, expect correctly rounded intervals. { input: [2 ** 120, -130], expected: 2 ** -10 }, // Out of Bounds { input: [1, 128], expected: kUnboundedEndpoints }, { input: [-1, 128], expected: kUnboundedEndpoints }, { input: [100, 126], expected: kUnboundedEndpoints }, { input: [-100, 126], expected: kUnboundedEndpoints }, { input: [2 ** 100, 100], expected: kUnboundedEndpoints }, ] as ScalarPairToIntervalCase[], f16: [ // 64-bit normals { input: [1.0000000001, 1], expected: [2, kPlusNULPFunctions['f16'](2, 2)] }, // ~2, additional ULP error due to first param not being f16 precise { input: [-1.0000000001, 1], expected: [kMinusNULPFunctions['f16'](-2, 2), -2] }, // ~-2, additional ULP error due to first param not being f16 precise // Edge Cases // f16 0b0_01111_1111111111 = 1.9990234375, 1.9990234375 * 2 ** 15 = f16.positive.max { input: [1.9990234375, 15], expected: kValue.f16.positive.max }, // f16.positive.min = 1 * 2 ** -14 { input: [1, -14], expected: kValue.f16.positive.min }, // f16.positive.subnormal.max = 0.9990234375 * 2 ** -14 { input: [0.9990234375, -14], expected: [0, kValue.f16.positive.subnormal.max] }, // f16.positive.subnormal.min = 1 * 2 ** -10 * 2 ** -14 = 0.0009765625 * 2 ** -14 { input: [0.0009765625, -14], expected: [0, kValue.f16.positive.subnormal.min] }, { input: [-0.0009765625, -14], expected: [kValue.f16.negative.subnormal.max, 0] }, { input: [-0.9990234375, -14], expected: [kValue.f16.negative.subnormal.min, 0] }, { input: [-1, -14], expected: kValue.f16.negative.max }, { input: [-1.9990234375, 15], expected: kValue.f16.negative.min }, // e2 + bias <= 0, expect correctly rounded intervals. { input: [2 ** 12, -18], expected: 2 ** -6 }, // Out of Bounds { input: [1, 16], expected: kUnboundedEndpoints }, { input: [-1, 16], expected: kUnboundedEndpoints }, { input: [100, 14], expected: kUnboundedEndpoints }, { input: [-100, 14], expected: kUnboundedEndpoints }, { input: [2 ** 10, 10], expected: kUnboundedEndpoints }, ] as ScalarPairToIntervalCase[], abstract: [ // Edge Cases // 1.9999999999999997779553950749686919152736663818359375 * 2 ** 1023 = f64.positive.max { input: [1.9999999999999997779553950749686919152736663818359375, 1023], expected: kValue.f64.positive.max, }, // f64.positive.min = 1 * 2 ** -1022 { input: [1, -1022], expected: kValue.f64.positive.min }, // f64.positive.subnormal.max = 1.9999999999999997779553950749686919152736663818359375 * 2 ** -1022 { input: [0.9999999999999997779553950749686919152736663818359375, -1022], expected: [0, kValue.f64.positive.subnormal.max], }, // f64.positive.subnormal.min = 0.0000000000000002220446049250313080847263336181640625 * 2 ** -1022 { input: [0.0000000000000002220446049250313080847263336181640625, -1022], expected: [0, kValue.f64.positive.subnormal.min], }, { input: [-0.0000000000000002220446049250313080847263336181640625, -1022], expected: [kValue.f64.negative.subnormal.max, 0], }, { input: [-0.9999999999999997779553950749686919152736663818359375, -1022], expected: [kValue.f64.negative.subnormal.min, 0], }, { input: [-1, -1022], expected: kValue.f64.negative.max }, { input: [-1.9999999999999997779553950749686919152736663818359375, 1023], expected: kValue.f64.negative.min, }, // e2 + bias <= 0, expect correctly rounded intervals. { input: [2 ** 120, -130], expected: 2 ** -10 }, // Out of Bounds { input: [1, 1024], expected: kUnboundedEndpoints }, { input: [-1, 1024], expected: kUnboundedEndpoints }, { input: [100, 1024], expected: kUnboundedEndpoints }, { input: [-100, 1024], expected: kUnboundedEndpoints }, { input: [2 ** 100, 1000], expected: kUnboundedEndpoints }, ] as ScalarPairToIntervalCase[], } as const; g.test('ldexpInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // always exactly representable cases { input: [0, 0], expected: 0 }, { input: [0, 1], expected: 0 }, { input: [0, -1], expected: 0 }, { input: [1, 1], expected: 2 }, { input: [1, -1], expected: 0.5 }, { input: [-1, 1], expected: -2 }, { input: [-1, -1], expected: -0.5 }, ...kLdexpIntervalCases[p.trait], // Extremely negative e2, any float value should be scale to 0.0 as the ground truth // f64 e1 * 2 ** e2 would be 0.0 for e2 = -2147483648. { input: [constants.positive.max, kValue.i32.negative.min], expected: 0 }, { input: [constants.negative.min, kValue.i32.negative.min], expected: 0 }, // Out of Bounds { input: [constants.positive.max, kValue.i32.positive.max], expected: kUnboundedEndpoints }, { input: [constants.negative.min, kValue.i32.positive.max], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const [x, y] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.ldexpInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.ldexpInterval(${x}, ${y}) returned ${got}. Expected ${expected}` ); }); g.test('maxInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // Representable normals { input: [0, 0], expected: 0 }, { input: [1, 0], expected: 1 }, { input: [0, 1], expected: 1 }, { input: [-1, 0], expected: 0 }, { input: [0, -1], expected: 0 }, { input: [1, 1], expected: 1 }, { input: [1, -1], expected: 1 }, { input: [-1, 1], expected: 1 }, { input: [-1, -1], expected: -1 }, // 0.1 and -0.1 should be correctly rounded { input: [-0.1, 0], expected: 0 }, { input: [0, -0.1], expected: 0 }, { input: [0.1, 0], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 { input: [0, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 { input: [0.1, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 { input: [0.1, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 { input: [-0.1, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 { input: [-0.1, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // ~-0.1 // Representable subnormals { input: [constants.positive.subnormal.max, 0], expected: [0, constants.positive.subnormal.max] }, { input: [0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, { input: [constants.positive.subnormal.min, 0], expected: [0, constants.positive.subnormal.min] }, { input: [0, constants.positive.subnormal.min], expected: [0, constants.positive.subnormal.min] }, { input: [constants.negative.subnormal.max, 0], expected: [constants.negative.subnormal.max, 0] }, { input: [0, constants.negative.subnormal.max], expected: [constants.negative.subnormal.max, 0] }, { input: [constants.negative.subnormal.min, 0], expected: [constants.negative.subnormal.min, 0] }, { input: [0, constants.negative.subnormal.min], expected: [constants.negative.subnormal.min, 0] }, { input: [1, constants.positive.subnormal.max], expected: 1 }, { input: [constants.negative.subnormal.min, constants.positive.subnormal.max], expected: [constants.negative.subnormal.min, constants.positive.subnormal.max] }, // Infinities { input: [0, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, 0], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [0, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, 0], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const [x, y] = t.params.input; const expected = trait.toInterval(t.params.expected); const got = trait.maxInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.maxInterval(${x}, ${y}) returned ${got}. Expected ${expected}` ); }); g.test('minInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // Representable normals { input: [0, 0], expected: 0 }, { input: [1, 0], expected: 0 }, { input: [0, 1], expected: 0 }, { input: [-1, 0], expected: -1 }, { input: [0, -1], expected: -1 }, { input: [1, 1], expected: 1 }, { input: [1, -1], expected: -1 }, { input: [-1, 1], expected: -1 }, { input: [-1, -1], expected: -1 }, // 64-bit normals that not exactly representable { input: [0.1, 0], expected: 0 }, { input: [0, 0.1], expected: 0 }, { input: [-0.1, 0], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // ~-0.1 { input: [0, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // ~-0.1 { input: [0.1, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, // ~0.1 { input: [0.1, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // ~-0.1 { input: [-0.1, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // ~-0.1 { input: [-0.1, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // ~-0.1 // Representable subnormals { input: [constants.positive.subnormal.max, 0], expected: [0, constants.positive.subnormal.max] }, { input: [0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, { input: [constants.positive.subnormal.min, 0], expected: [0, constants.positive.subnormal.min] }, { input: [0, constants.positive.subnormal.min], expected: [0, constants.positive.subnormal.min] }, { input: [constants.negative.subnormal.max, 0], expected: [constants.negative.subnormal.max, 0] }, { input: [0, constants.negative.subnormal.max], expected: [constants.negative.subnormal.max, 0] }, { input: [constants.negative.subnormal.min, 0], expected: [constants.negative.subnormal.min, 0] }, { input: [0, constants.negative.subnormal.min], expected: [constants.negative.subnormal.min, 0] }, { input: [-1, constants.positive.subnormal.max], expected: -1 }, { input: [constants.negative.subnormal.min, constants.positive.subnormal.max], expected: [constants.negative.subnormal.min, constants.positive.subnormal.max] }, // Infinities { input: [0, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, 0], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [0, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, 0], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const [x, y] = t.params.input; const expected = trait.toInterval(t.params.expected); const got = trait.minInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.minInterval(${x}, ${y}) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kMultiplicationInterval64BitsNormalCases = { f32: [ // 0.1*0.1, 0.1 falls between f32 0x3DCCCCCC and 0x3DCCCCCD, // min result 0x3DCCCCCC*0x3DCCCCCC=0.00999999880790713952713681734167 rounded to f32 0x3C23D708 or 0x3C23D709, // max result 0x3DCCCCCD*0x3DCCCCCD=0.01000000029802322622044605108385 rounded to f32 0x3C23D70A or 0x3C23D70B. { input: [0.1, 0.1], expected: [reinterpretU32AsF32(0x3c23d708), reinterpretU32AsF32(0x3c23d70b)] }, // ~0.01 { input: [-0.1, -0.1], expected: [reinterpretU32AsF32(0x3c23d708), reinterpretU32AsF32(0x3c23d70b)] }, // ~0.01 // -0.01000000029802322622044605108385 rounded to f32 0xBC23D70B or 0xBC23D70A, // -0.00999999880790713952713681734167 rounded to f32 0xBC23D709 or 0xBC23D708. { input: [0.1, -0.1], expected: [reinterpretU32AsF32(0xbc23d70b), reinterpretU32AsF32(0xbc23d708)] }, // ~-0.01 { input: [-0.1, 0.1], expected: [reinterpretU32AsF32(0xbc23d70b), reinterpretU32AsF32(0xbc23d708)] }, // ~-0.01 ] as ScalarPairToIntervalCase[], f16: [ // 0.1*0.1, 0.1 falls between f16 0x2E66 and 0x2E67, // min result 0x2E66*0x2E66=0.00999511778354644775390625 rounded to f16 0x211E or 0x211F, // max result 0x2E67*0x2E67=0.0100073255598545074462890625 rounded to f16 0x211F or 0x2120. { input: [0.1, 0.1], expected: [reinterpretU16AsF16(0x211e), reinterpretU16AsF16(0x2120)] }, // ~0.01 { input: [-0.1, -0.1], expected: [reinterpretU16AsF16(0x211e), reinterpretU16AsF16(0x2120)] }, // ~0.01 // -0.0100073255598545074462890625 rounded to f16 0xA120 or 0xA11F, // -0.00999511778354644775390625 rounded to f16 0xA11F or 0xA11E. { input: [0.1, -0.1], expected: [reinterpretU16AsF16(0xa120), reinterpretU16AsF16(0xa11e)] }, // ~-0.01 { input: [-0.1, 0.1], expected: [reinterpretU16AsF16(0xa120), reinterpretU16AsF16(0xa11e)] }, // ~-0.01 ] as ScalarPairToIntervalCase[], } as const; g.test('multiplicationInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // Representable normals { input: [0, 0], expected: 0 }, { input: [1, 0], expected: 0 }, { input: [0, 1], expected: 0 }, { input: [-1, 0], expected: 0 }, { input: [0, -1], expected: 0 }, { input: [1, 1], expected: 1 }, { input: [1, -1], expected: -1 }, { input: [-1, 1], expected: -1 }, { input: [-1, -1], expected: 1 }, { input: [2, 1], expected: 2 }, { input: [1, -2], expected: -2 }, { input: [-2, 1], expected: -2 }, { input: [-2, -1], expected: 2 }, { input: [2, 2], expected: 4 }, { input: [2, -2], expected: -4 }, { input: [-2, 2], expected: -4 }, { input: [-2, -2], expected: 4 }, // 64-bit normals that can not be exactly represented // Finite values multiply zero result in zero { input: [0.1, 0], expected: 0 }, { input: [0, 0.1], expected: 0 }, { input: [-0.1, 0], expected: 0 }, { input: [0, -0.1], expected: 0 }, // Finite value multiply +/-1.0 { input: [0.1, 1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, { input: [-1, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, { input: [-0.1, 1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, { input: [-1, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, // Other cases ...kMultiplicationInterval64BitsNormalCases[p.trait], // Infinities { input: [0, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [1, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [-1, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [0, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [1, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [-1, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, // Edges { input: [constants.positive.max, constants.positive.max], expected: kUnboundedEndpoints }, { input: [constants.negative.min, constants.negative.min], expected: kUnboundedEndpoints }, { input: [constants.positive.max, constants.negative.min], expected: kUnboundedEndpoints }, { input: [constants.negative.min, constants.positive.max], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const [x, y] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.multiplicationInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.multiplicationInterval(${x}, ${y}) returned ${got}. Expected ${expected}` ); }); // Some of these are hard coded, since the error intervals are difficult to express in a closed // human-readable form due to the inherited nature of the errors. // prettier-ignore const kPowIntervalCases = { f32 : [ { input: [1, 0], expected: [kMinusNULPFunctions['f32'](1, 3), reinterpretU64AsF64(0x3ff0_0000_3000_0000n)] }, // ~1 { input: [2, 0], expected: [kMinusNULPFunctions['f32'](1, 3), reinterpretU64AsF64(0x3ff0_0000_3000_0000n)] }, // ~1 { input: [kValue.f32.positive.max, 0], expected: [kMinusNULPFunctions['f32'](1, 3), reinterpretU64AsF64(0x3ff0_0000_3000_0000n)] }, // ~1 { input: [1, 1], expected: [reinterpretU64AsF64(0x3fef_fffe_dfff_fe00n), reinterpretU64AsF64(0x3ff0_0000_c000_0200n)] }, // ~1 { input: [1, 100], expected: [reinterpretU64AsF64(0x3fef_ffba_3fff_3800n), reinterpretU64AsF64(0x3ff0_0023_2000_c800n)] }, // ~1 { input: [2, 1], expected: [reinterpretU64AsF64(0x3fff_fffe_a000_0200n), reinterpretU64AsF64(0x4000_0001_0000_0200n)] }, // ~2 { input: [2, 2], expected: [reinterpretU64AsF64(0x400f_fffd_a000_0400n), reinterpretU64AsF64(0x4010_0001_a000_0400n)] }, // ~4 { input: [10, 10], expected: [reinterpretU64AsF64(0x4202_a04f_51f7_7000n), reinterpretU64AsF64(0x4202_a070_ee08_e000n)] }, // ~10000000000 { input: [10, 1], expected: [reinterpretU64AsF64(0x4023_fffe_0b65_8b00n), reinterpretU64AsF64(0x4024_0002_149a_7c00n)] }, // ~10 ] as ScalarPairToIntervalCase[], f16 : [ { input: [1, 0], expected: [reinterpretU64AsF64(0x3fef_fc00_0000_0000n), reinterpretU64AsF64(0x3ff0_0200_0000_0000n)] }, // ~1 { input: [2, 0], expected: [reinterpretU64AsF64(0x3fef_fc00_0000_0000n), reinterpretU64AsF64(0x3ff0_0200_0000_0000n)] }, // ~1 { input: [kValue.f16.positive.max, 0], expected: [reinterpretU64AsF64(0x3fef_fc00_0000_0000n), reinterpretU64AsF64(0x3ff0_0200_0000_0000n)] }, // ~1 { input: [1, 1], expected: [reinterpretU64AsF64(0x3fef_cbf0_0000_0000n), reinterpretU64AsF64(0x3ff0_1c10_0000_0000n)] }, // ~1 { input: [1, 100], expected: [reinterpretU64AsF64(0x3fe2_91c0_0000_0000n), reinterpretU64AsF64(0x3ffb_8a40_0000_0000n)] }, // ~1 { input: [2, 1], expected: [reinterpretU64AsF64(0x3fff_c410_0000_0000n), reinterpretU64AsF64(0x4000_2410_0000_0000n)] }, // ~2 { input: [2, 2], expected: [reinterpretU64AsF64(0x400f_9020_0000_0000n), reinterpretU64AsF64(0x4010_4420_0000_0000n)] }, // ~4 { input: [5, 5], expected: [reinterpretU64AsF64(0x40a7_5f70_0000_0000n), reinterpretU64AsF64(0x40a9_5520_0000_0000n)] }, // ~3125 { input: [10, 1], expected: [reinterpretU64AsF64(0x4023_c57c_0000_0000n), reinterpretU64AsF64(0x4024_36a0_0000_0000n)] }, // ~10 ] as ScalarPairToIntervalCase[], } as const; g.test('powInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ { input: [-1, 0], expected: kUnboundedEndpoints }, { input: [0, 0], expected: kUnboundedEndpoints }, { input: [0, 1], expected: kUnboundedEndpoints }, { input: [1, constants.positive.max], expected: kUnboundedEndpoints }, { input: [constants.positive.max, 1], expected: kUnboundedEndpoints }, ...kPowIntervalCases[p.trait], ]; }) ) .fn(t => { const [x, y] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.powInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.powInterval(${x}, ${y}) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kRemainderCases = { f32: [ { input: [1, 0.1], expected: [reinterpretU32AsF32(0xb4000000), reinterpretU32AsF32(0x3dccccd8)] }, // ~[0, 0.1] { input: [-1, 0.1], expected: [reinterpretU32AsF32(0xbdccccd8), reinterpretU32AsF32(0x34000000)] }, // ~[-0.1, 0] { input: [1, -0.1], expected: [reinterpretU32AsF32(0xb4000000), reinterpretU32AsF32(0x3dccccd8)] }, // ~[0, 0.1] { input: [-1, -0.1], expected: [reinterpretU32AsF32(0xbdccccd8), reinterpretU32AsF32(0x34000000)] }, // ~[-0.1, 0] ] as ScalarPairToIntervalCase[], f16: [ { input: [1, 0.1], expected: [reinterpretU16AsF16(0x9400), reinterpretU16AsF16(0x2e70)] }, // ~[0, 0.1] { input: [-1, 0.1], expected: [reinterpretU16AsF16(0xae70), reinterpretU16AsF16(0x1400)] }, // ~[-0.1, 0] { input: [1, -0.1], expected: [reinterpretU16AsF16(0x9400), reinterpretU16AsF16(0x2e70)] }, // ~[0, 0.1] { input: [-1, -0.1], expected: [reinterpretU16AsF16(0xae70), reinterpretU16AsF16(0x1400)] }, // ~[-0.1, 0] ] as ScalarPairToIntervalCase[], } as const; g.test('remainderInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = kFPTraitForULP[p.trait]; const constants = FP[trait].constants(); // prettier-ignore return [ ...kRemainderCases[trait], // Normals { input: [0, 1], expected: 0 }, { input: [0, -1], expected: 0 }, { input: [1, 1], expected: [0, 1] }, { input: [1, -1], expected: [0, 1] }, { input: [-1, 1], expected: [-1, 0] }, { input: [-1, -1], expected: [-1, 0] }, { input: [4, 2], expected: [0, 2] }, { input: [-4, 2], expected: [-2, 0] }, { input: [4, -2], expected: [0, 2] }, { input: [-4, -2], expected: [-2, 0] }, { input: [2, 4], expected: [2, 2] }, { input: [-2, 4], expected: -2 }, { input: [2, -4], expected: 2 }, { input: [-2, -4], expected: [-2, -2] }, { input: [0, 0.1], expected: 0 }, { input: [0, -0.1], expected: 0 }, { input: [8.5, 2], expected: 0.5 }, { input: [1.125, 1], expected: 0.125 }, // Denominator out of range { input: [1, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [1, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [1, constants.positive.max], expected: kUnboundedEndpoints }, { input: [1, constants.negative.min], expected: kUnboundedEndpoints }, { input: [1, 0], expected: kUnboundedEndpoints }, { input: [1, constants.positive.subnormal.max], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const [x, y] = t.params.input; const expected = trait.toInterval(t.params.expected); const got = trait.remainderInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.remainderInterval(${x}, ${y}) returned ${got}. Expected ${expected}` ); }); g.test('stepInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore return [ // 32-bit normals { input: [0, 0], expected: 1 }, { input: [1, 1], expected: 1 }, { input: [0, 1], expected: 1 }, { input: [1, 0], expected: 0 }, { input: [-1, -1], expected: 1 }, { input: [0, -1], expected: 0 }, { input: [-1, 0], expected: 1 }, { input: [-1, 1], expected: 1 }, { input: [1, -1], expected: 0 }, // 64-bit normals // number is f64 internally, so the value representing the literal // 0.1/-0.1 will always be exactly representable in AbstractFloat, // since AF is also f64 internally. // It is impossible with normals to cause the rounding ambiguity that // causes the 0 or 1 result. { input: [0.1, 0.1], expected: p.trait === 'abstract' ? 1 : [0, 1] }, { input: [0, 0.1], expected: 1 }, { input: [0.1, 0], expected: 0 }, { input: [0.1, 1], expected: 1 }, { input: [1, 0.1], expected: 0 }, { input: [-0.1, -0.1], expected: p.trait === 'abstract' ? 1 : [0, 1] }, { input: [0, -0.1], expected: 0 }, { input: [-0.1, 0], expected: 1 }, { input: [-0.1, -1], expected: 0 }, { input: [-1, -0.1], expected: 1 }, // Subnormals { input: [0, constants.positive.subnormal.max], expected: 1 }, { input: [0, constants.positive.subnormal.min], expected: 1 }, { input: [0, constants.negative.subnormal.max], expected: [0, 1] }, { input: [0, constants.negative.subnormal.min], expected: [0, 1] }, { input: [1, constants.positive.subnormal.max], expected: 0 }, { input: [1, constants.positive.subnormal.min], expected: 0 }, { input: [1, constants.negative.subnormal.max], expected: 0 }, { input: [1, constants.negative.subnormal.min], expected: 0 }, { input: [-1, constants.positive.subnormal.max], expected: 1 }, { input: [-1, constants.positive.subnormal.min], expected: 1 }, { input: [-1, constants.negative.subnormal.max], expected: 1 }, { input: [-1, constants.negative.subnormal.min], expected: 1 }, { input: [constants.positive.subnormal.max, 0], expected: [0, 1] }, { input: [constants.positive.subnormal.min, 0], expected: [0, 1] }, { input: [constants.negative.subnormal.max, 0], expected: 1 }, { input: [constants.negative.subnormal.min, 0], expected: 1 }, { input: [constants.positive.subnormal.max, 1], expected: 1 }, { input: [constants.positive.subnormal.min, 1], expected: 1 }, { input: [constants.negative.subnormal.max, 1], expected: 1 }, { input: [constants.negative.subnormal.min, 1], expected: 1 }, { input: [constants.positive.subnormal.max, -1], expected: 0 }, { input: [constants.positive.subnormal.min, -1], expected: 0 }, { input: [constants.negative.subnormal.max, -1], expected: 0 }, { input: [constants.negative.subnormal.min, -1], expected: 0 }, { input: [constants.negative.subnormal.min, constants.positive.subnormal.max], expected: 1 }, { input: [constants.positive.subnormal.max, constants.negative.subnormal.min], expected: [0, 1] }, // Infinities { input: [0, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, 0], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [0, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, 0], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const [edge, x] = t.params.input; const expected = trait.toInterval(t.params.expected); const got = trait.stepInterval(edge, x); t.expect( objectEquals(expected, got), `${t.params.trait}.stepInterval(${edge}, ${x}) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kSubtractionInterval64BitsNormalCases = { f32: [ // 0.1 falls between f32 0x3DCCCCCC and 0x3DCCCCCD, -0.1 falls between f32 0xBDCCCCCD and 0xBDCCCCCC // Expect f32 interval [0x3DCCCCCC-0x3DCCCCCD, 0x3DCCCCCD-0x3DCCCCCC] { input: [0.1, 0.1], expected: [reinterpretU32AsF32(0x3dcccccc)-reinterpretU32AsF32(0x3dcccccd), reinterpretU32AsF32(0x3dcccccd)-reinterpretU32AsF32(0x3dcccccc)] }, // Expect f32 interval [0xBDCCCCCD-0xBDCCCCCC, 0xBDCCCCCC-0xBDCCCCCD] { input: [-0.1, -0.1], expected: [reinterpretU32AsF32(0xbdcccccd)-reinterpretU32AsF32(0xbdcccccc), reinterpretU32AsF32(0xbdcccccc)-reinterpretU32AsF32(0xbdcccccd)] }, // Expect f32 interval [0x3DCCCCCC-0xBDCCCCCC, 0x3DCCCCCD-0xBDCCCCCD] { input: [0.1, -0.1], expected: [reinterpretU32AsF32(0x3dcccccc)-reinterpretU32AsF32(0xbdcccccc), reinterpretU32AsF32(0x3dcccccd)-reinterpretU32AsF32(0xbdcccccd)] }, // Expect f32 interval [0xBDCCCCCD-0x3DCCCCCD, 0xBDCCCCCC-0x3DCCCCCC] { input: [-0.1, 0.1], expected: [reinterpretU32AsF32(0xbdcccccd)-reinterpretU32AsF32(0x3dcccccd), reinterpretU32AsF32(0xbdcccccc)-reinterpretU32AsF32(0x3dcccccc)] }, { input: [1, kValue.f32.positive.min], expected: [reinterpretU32AsF32(0x3f7fffff), 1.0] }, { input: [1, kValue.f32.negative.max], expected: [ 1.0, reinterpretU32AsF32(0x3f800001)] }, { input: [-1, kValue.f32.positive.min], expected: [reinterpretU32AsF32(0xbf800001), -1.0] }, { input: [-1, kValue.f32.negative.max], expected: [-1.0, reinterpretU32AsF32(0xbf7fffff)] }, { input: [1, kValue.f32.positive.max], expected: [reinterpretU32AsF32(0xff7fffff), reinterpretU32AsF32(0xff7ffffe)]}, { input: [1, kValue.f32.negative.min], expected: kUnboundedEndpoints}, { input: [-1, kValue.f32.positive.max], expected:kUnboundedEndpoints}, { input: [-1, kValue.f32.negative.min], expected: [reinterpretU32AsF32(0x7f7ffffe) , reinterpretU32AsF32(0x7f7fffff)] }, // Symmetric with above (expected will be anti-symmetric) { input: [kValue.f32.positive.min, 1], expected: [-1.0 , reinterpretU32AsF32(0xbf7fffff)] }, { input: [kValue.f32.negative.max, 1], expected: [reinterpretU32AsF32(0xbf800001), -1.0] }, { input: [kValue.f32.positive.min, -1], expected: [1.0, reinterpretU32AsF32(0x3f800001)] }, { input: [kValue.f32.negative.max, -1], expected: [reinterpretU32AsF32(0x3f7fffff), 1.0] }, { input: [kValue.f32.positive.max, 1], expected: [reinterpretU32AsF32(0x7f7ffffe), reinterpretU32AsF32(0x7f7fffff)]}, { input: [kValue.f32.negative.min, 1], expected: kUnboundedEndpoints}, { input: [kValue.f32.positive.max, -1], expected:kUnboundedEndpoints}, { input: [kValue.f32.negative.min, -1], expected: [reinterpretU32AsF32(0xff7fffff) , reinterpretU32AsF32(0xff7ffffe)] }, ] as ScalarPairToIntervalCase[], f16: [ // 0.1 falls between f16 0x2E66 and 0x2E67, -0.1 falls between f16 0xAE67 and 0xAE66 // Expect f16 interval [0x2E66-0x2E67, 0x2E67-0x2E66] { input: [0.1, 0.1], expected: [reinterpretU16AsF16(0x2e66)-reinterpretU16AsF16(0x2e67), reinterpretU16AsF16(0x2e67)-reinterpretU16AsF16(0x2e66)] }, // Expect f16 interval [0xAE67-0xAE66, 0xAE66-0xAE67] { input: [-0.1, -0.1], expected: [reinterpretU16AsF16(0xae67)-reinterpretU16AsF16(0xae66), reinterpretU16AsF16(0xae66)-reinterpretU16AsF16(0xae67)] }, // Expect f16 interval [0x2E66-0xAE66, 0x2E67-0xAE67] { input: [0.1, -0.1], expected: [reinterpretU16AsF16(0x2e66)-reinterpretU16AsF16(0xae66), reinterpretU16AsF16(0x2e67)-reinterpretU16AsF16(0xae67)] }, // Expect f16 interval [0xAE67-0x2E67, 0xAE66-0x2E66] { input: [-0.1, 0.1], expected: [reinterpretU16AsF16(0xae67)-reinterpretU16AsF16(0x2e67), reinterpretU16AsF16(0xae66)-reinterpretU16AsF16(0x2e66)] }, ] as ScalarPairToIntervalCase[], } as const; g.test('subtractionInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // Representable normals { input: [0, 0], expected: 0 }, { input: [1, 0], expected: 1 }, { input: [0, 1], expected: -1 }, { input: [-1, 0], expected: -1 }, { input: [0, -1], expected: 1 }, { input: [1, 1], expected: 0 }, { input: [1, -1], expected: 2 }, { input: [-1, 1], expected: -2 }, { input: [-1, -1], expected: 0 }, // 64-bit normals that can not be exactly represented in f32/f16 { input: [0.1, 0], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, { input: [0, -0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1'] }, { input: [-0.1, 0], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, { input: [0, 0.1], expected: kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'] }, ...kSubtractionInterval64BitsNormalCases[p.trait], // Subnormals { input: [constants.positive.subnormal.max, 0], expected: [0, constants.positive.subnormal.max] }, { input: [0, constants.positive.subnormal.max], expected: [constants.negative.subnormal.min, 0] }, { input: [constants.positive.subnormal.min, 0], expected: [0, constants.positive.subnormal.min] }, { input: [0, constants.positive.subnormal.min], expected: [constants.negative.subnormal.max, 0] }, { input: [constants.negative.subnormal.max, 0], expected: [constants.negative.subnormal.max, 0] }, { input: [0, constants.negative.subnormal.max], expected: [0, constants.positive.subnormal.min] }, { input: [constants.negative.subnormal.min, 0], expected: [constants.negative.subnormal.min, 0] }, { input: [0, constants.negative.subnormal.min], expected: [0, constants.positive.subnormal.max] }, // Infinities { input: [0, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, 0], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [0, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, 0], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const [x, y] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.subtractionInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.subtractionInterval(${x}, ${y}) returned ${got}. Expected ${expected}` ); }); interface ScalarTripleToIntervalCase { input: [number, number, number]; expected: number | IntervalEndpoints; } g.test('clampMedianInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // Normals { input: [0, 0, 0], expected: 0 }, { input: [1, 0, 0], expected: 0 }, { input: [0, 1, 0], expected: 0 }, { input: [0, 0, 1], expected: 0 }, { input: [1, 0, 1], expected: 1 }, { input: [1, 1, 0], expected: 1 }, { input: [0, 1, 1], expected: 1 }, { input: [1, 1, 1], expected: 1 }, { input: [1, 10, 100], expected: 10 }, { input: [10, 1, 100], expected: 10 }, { input: [100, 1, 10], expected: 10 }, { input: [-10, 1, 100], expected: 1 }, { input: [10, 1, -100], expected: 1 }, { input: [-10, 1, -100], expected: -10 }, { input: [-10, -10, -10], expected: -10 }, // Subnormals { input: [constants.positive.subnormal.max, 0, 0], expected: 0 }, { input: [0, constants.positive.subnormal.max, 0], expected: 0 }, { input: [0, 0, constants.positive.subnormal.max], expected: 0 }, { input: [constants.positive.subnormal.max, 0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, { input: [constants.positive.subnormal.max, constants.positive.subnormal.max, 0], expected: [0, constants.positive.subnormal.max] }, { input: [0, constants.positive.subnormal.max, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, { input: [constants.positive.subnormal.max, constants.positive.subnormal.max, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, { input: [constants.positive.subnormal.max, constants.positive.subnormal.min, constants.negative.subnormal.max], expected: [0, constants.positive.subnormal.min] }, { input: [constants.positive.subnormal.max, constants.negative.subnormal.min, constants.negative.subnormal.max], expected: [constants.negative.subnormal.max, 0] }, { input: [constants.positive.max, constants.positive.max, constants.positive.subnormal.min], expected: constants.positive.max }, // Infinities { input: [0, 1, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [0, constants.positive.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const [x, y, z] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.clampMedianInterval(x, y, z); t.expect( objectEquals(expected, got), `${t.params.trait}.clampMedianInterval(${x}, ${y}, ${z}) returned ${got}. Expected ${expected}` ); }); g.test('clampMinMaxInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // Normals { input: [0, 0, 0], expected: 0 }, { input: [1, 0, 0], expected: 0 }, { input: [0, 1, 0], expected: 0 }, { input: [0, 0, 1], expected: 0 }, { input: [1, 0, 1], expected: 1 }, { input: [1, 1, 0], expected: 0 }, { input: [0, 1, 1], expected: 1 }, { input: [1, 1, 1], expected: 1 }, { input: [1, 10, 100], expected: 10 }, { input: [10, 1, 100], expected: 10 }, { input: [100, 1, 10], expected: 10 }, { input: [-10, 1, 100], expected: 1 }, { input: [10, 1, -100], expected: -100 }, { input: [-10, 1, -100], expected: -100 }, { input: [-10, -10, -10], expected: -10 }, // Subnormals { input: [constants.positive.subnormal.max, 0, 0], expected: [0, constants.positive.subnormal.max] }, { input: [0, constants.positive.subnormal.max, 0], expected: [0, constants.positive.subnormal.max] }, { input: [0, 0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, { input: [constants.positive.subnormal.max, 0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, { input: [constants.positive.subnormal.max, constants.positive.subnormal.max, 0], expected: [0, constants.positive.subnormal.max] }, { input: [0, constants.positive.subnormal.max, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, { input: [constants.positive.subnormal.max, constants.positive.subnormal.max, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, { input: [constants.positive.subnormal.max, constants.positive.subnormal.min, constants.negative.subnormal.max], expected: [constants.negative.subnormal.max, constants.positive.subnormal.max] }, { input: [constants.positive.subnormal.max, constants.negative.subnormal.min, constants.negative.subnormal.max], expected: [constants.negative.subnormal.min, constants.positive.subnormal.max] }, { input: [constants.positive.max, constants.positive.max, constants.positive.subnormal.min], expected: [0, constants.positive.subnormal.min] }, // Infinities { input: [0, 1, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [0, constants.positive.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const [x, y, z] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.clampMinMaxInterval(x, y, z); t.expect( objectEquals(expected, got), `${t.params.trait}.clampMinMaxInterval(${x}, ${y}, ${z}) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kFmaIntervalCases = { f32: [ // positive.subnormal.max * positive.subnormal.max is much smaller than positive.subnormal.min but larger than 0, rounded to [0, positive.subnormal.min] { input: [kValue.f32.positive.subnormal.max, kValue.f32.positive.subnormal.max, 0], expected: [0, kValue.f32.positive.subnormal.min] }, // positive.subnormal.max * positive.subnormal.max rounded to 0 or positive.subnormal.min, // 0 + constants.positive.subnormal.max rounded to [0, constants.positive.subnormal.max], // positive.subnormal.min + constants.positive.subnormal.max = constants.positive.min. { input: [kValue.f32.positive.subnormal.max, kValue.f32.positive.subnormal.max, kValue.f32.positive.subnormal.max], expected: [0, kValue.f32.positive.min] }, // positive.subnormal.max * positive.subnormal.max rounded to 0 or positive.subnormal.min, // negative.subnormal.max may flushed to 0, // minimum case: 0 + negative.subnormal.max rounded to [negative.subnormal.max, 0], // maximum case: positive.subnormal.min + 0 rounded to [0, positive.subnormal.min]. { input: [kValue.f32.positive.subnormal.max, kValue.f32.positive.subnormal.min, kValue.f32.negative.subnormal.max], expected: [kValue.f32.negative.subnormal.max, kValue.f32.positive.subnormal.min] }, // positive.subnormal.max * negative.subnormal.min rounded to -0.0 or negative.subnormal.max = -1 * [subnormal ulp], // negative.subnormal.max = -1 * [subnormal ulp] may flushed to -0.0, // minimum case: -1 * [subnormal ulp] + -1 * [subnormal ulp] rounded to [-2 * [subnormal ulp], 0], // maximum case: -0.0 + -0.0 = 0. { input: [kValue.f32.positive.subnormal.max, kValue.f32.negative.subnormal.min, kValue.f32.negative.subnormal.max], expected: [-2 * FP['f32'].oneULP(0, 'no-flush'), 0] }, ] as ScalarTripleToIntervalCase[], f16: [ // positive.subnormal.max * positive.subnormal.max is much smaller than positive.subnormal.min but larger than 0, rounded to [0, positive.subnormal.min] { input: [kValue.f16.positive.subnormal.max, kValue.f16.positive.subnormal.max, 0], expected: [0, kValue.f16.positive.subnormal.min] }, // positive.subnormal.max * positive.subnormal.max rounded to 0 or positive.subnormal.min, // 0 + constants.positive.subnormal.max rounded to [0, constants.positive.subnormal.max], // positive.subnormal.min + constants.positive.subnormal.max = constants.positive.min. { input: [kValue.f16.positive.subnormal.max, kValue.f16.positive.subnormal.max, kValue.f16.positive.subnormal.max], expected: [0, kValue.f16.positive.min] }, // positive.subnormal.max * positive.subnormal.max rounded to 0 or positive.subnormal.min, // negative.subnormal.max may flushed to 0, // minimum case: 0 + negative.subnormal.max rounded to [negative.subnormal.max, 0], // maximum case: positive.subnormal.min + 0 rounded to [0, positive.subnormal.min]. { input: [kValue.f16.positive.subnormal.max, kValue.f16.positive.subnormal.min, kValue.f16.negative.subnormal.max], expected: [kValue.f16.negative.subnormal.max, kValue.f16.positive.subnormal.min] }, // positive.subnormal.max * negative.subnormal.min rounded to -0.0 or negative.subnormal.max = -1 * [subnormal ulp], // negative.subnormal.max = -1 * [subnormal ulp] may flushed to -0.0, // minimum case: -1 * [subnormal ulp] + -1 * [subnormal ulp] rounded to [-2 * [subnormal ulp], 0], // maximum case: -0.0 + -0.0 = 0. { input: [kValue.f16.positive.subnormal.max, kValue.f16.negative.subnormal.min, kValue.f16.negative.subnormal.max], expected: [-2 * FP['f16'].oneULP(0, 'no-flush'), 0] }, ] as ScalarTripleToIntervalCase[], } as const; g.test('fmaInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // Normals { input: [0, 0, 0], expected: 0 }, { input: [1, 0, 0], expected: 0 }, { input: [0, 1, 0], expected: 0 }, { input: [0, 0, 1], expected: 1 }, { input: [1, 0, 1], expected: 1 }, { input: [1, 1, 0], expected: 1 }, { input: [0, 1, 1], expected: 1 }, { input: [1, 1, 1], expected: 2 }, { input: [1, 10, 100], expected: 110 }, { input: [10, 1, 100], expected: 110 }, { input: [100, 1, 10], expected: 110 }, { input: [-10, 1, 100], expected: 90 }, { input: [10, 1, -100], expected: -90 }, { input: [-10, 1, -100], expected: -110 }, { input: [-10, -10, -10], expected: 90 }, // Subnormals { input: [constants.positive.subnormal.max, 0, 0], expected: 0 }, { input: [0, constants.positive.subnormal.max, 0], expected: 0 }, { input: [0, 0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, { input: [constants.positive.subnormal.max, 0, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, { input: [0, constants.positive.subnormal.max, constants.positive.subnormal.max], expected: [0, constants.positive.subnormal.max] }, // Infinities { input: [0, 1, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [0, constants.positive.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.max, constants.positive.max, constants.positive.subnormal.min], expected: kUnboundedEndpoints }, ...kFmaIntervalCases[p.trait], ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.fmaInterval(...t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.fmaInterval(${t.params.input.join( ',' )}) returned ${got}. Expected ${expected}` ); }); // Some of these are hard coded, since the error intervals are difficult to express in a closed // human-readable form due to the inherited nature of the errors. // prettier-ignore const kMixImpreciseIntervalCases = { f32: [ // [0.0, 1.0] cases { input: [0.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0x3fb9_9999_8000_0000n), reinterpretU64AsF64(0x3fb9_9999_a000_0000n)] }, // ~0.1 { input: [0.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fec_cccc_c000_0000n), reinterpretU64AsF64(0x3fec_cccc_e000_0000n)] }, // ~0.9 // [1.0, 0.0] cases { input: [1.0, 0.0, 0.1], expected: [reinterpretU64AsF64(0x3fec_cccc_c000_0000n), reinterpretU64AsF64(0x3fec_cccc_e000_0000n)] }, // ~0.9 { input: [1.0, 0.0, 0.9], expected: [reinterpretU64AsF64(0x3fb9_9999_0000_0000n), reinterpretU64AsF64(0x3fb9_999a_0000_0000n)] }, // ~0.1 // [0.0, 10.0] cases { input: [0.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x3fef_ffff_e000_0000n), reinterpretU64AsF64(0x3ff0_0000_2000_0000n)] }, // ~1 { input: [0.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4021_ffff_e000_0000n), reinterpretU64AsF64(0x4022_0000_2000_0000n)] }, // ~9 // [2.0, 10.0] cases { input: [2.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x4006_6666_6000_0000n), reinterpretU64AsF64(0x4006_6666_8000_0000n)] }, // ~2.8 { input: [2.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4022_6666_6000_0000n), reinterpretU64AsF64(0x4022_6666_8000_0000n)] }, // ~9.2 // [-1.0, 1.0] cases { input: [-1.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0xbfe9_9999_a000_0000n), reinterpretU64AsF64(0xbfe9_9999_8000_0000n)] }, // ~-0.8 { input: [-1.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fe9_9999_8000_0000n), reinterpretU64AsF64(0x3fe9_9999_c000_0000n)] }, // ~0.8 // Showing how precise and imprecise versions diff // Note that this expectation is unbounded [-inf,inf] in f32 as |10.0| is much smaller than // |f32.negative.min|. The implementation of imprecise is is := x + (y - x) * z // So that 10 - f32.negative.min == [f32.positive.max, inf] due to correctly rounding of unbounded precision. { input: [kValue.f32.negative.min, 10.0, 1.0], expected: kUnboundedEndpoints}, // -10.0 is the same, however due to smaller than f32.negative.min we end up with [ULP_neg(f32.positive.max), f32.positive.max] { input: [kValue.f32.negative.min, -10.0, 1.0], expected: [reinterpretU32AsF32(0xf3800000), 0.0] }, { input: [kValue.f32.negative.min, 10.0, 5.0], expected: kUnboundedEndpoints }, { input: [kValue.f32.negative.min, -10.0, 5.0], expected: kUnboundedEndpoints }, { input: [kValue.f32.negative.min, 10.0, 0.5], expected: kUnboundedEndpoints }, { input: [kValue.f32.negative.min, -10.0, 0.5], expected: [reinterpretU32AsF32(0xff000000), reinterpretU32AsF32(0xfeffffff) ]}, // Test the case of unbounded precision of mix when implementing the subtraction intermediate value. { input: [kValue.f32.positive.min, 1.0, kValue.f32.positive.min], expected: [reinterpretU32AsF32(0x00800000),reinterpretU32AsF32(0x01000000)]}, ] as ScalarTripleToIntervalCase[], f16: [ // [0.0, 1.0] cases { input: [0.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0x3fb9_9800_0000_0000n), reinterpretU64AsF64(0x3fb9_9c00_0000_0000n)] }, // ~0.1 { input: [0.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fec_cc00_0000_0000n), reinterpretU64AsF64(0x3fec_d000_0000_0000n)] }, // ~0.9 // [1.0, 0.0] cases { input: [1.0, 0.0, 0.1], expected: [reinterpretU64AsF64(0x3fec_cc00_0000_0000n), reinterpretU64AsF64(0x3fec_d000_0000_0000n)] }, // ~0.9 { input: [1.0, 0.0, 0.9], expected: [reinterpretU64AsF64(0x3fb9_8000_0000_0000n), reinterpretU64AsF64(0x3fb9_a000_0000_0000n)] }, // ~0.1 // [0.0, 10.0] cases { input: [0.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x3fef_fc00_0000_0000n), reinterpretU64AsF64(0x3ff0_0400_0000_0000n)] }, // ~1 { input: [0.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4021_fc00_0000_0000n), reinterpretU64AsF64(0x4022_0400_0000_0000n)] }, // ~9 // [2.0, 10.0] cases { input: [2.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x4006_6400_0000_0000n), reinterpretU64AsF64(0x4006_6800_0000_0000n)] }, // ~2.8 { input: [2.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4022_6400_0000_0000n), reinterpretU64AsF64(0x4022_6800_0000_0000n)] }, // ~9.2 // [-1.0, 1.0] cases { input: [-1.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0xbfe9_9c00_0000_0000n), reinterpretU64AsF64(0xbfe9_9800_0000_0000n)] }, // ~-0.8 { input: [-1.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fe9_9800_0000_0000n), reinterpretU64AsF64(0x3fe9_a000_0000_0000n)] }, // ~0.8 // Showing how precise and imprecise versions diff // In imprecise version, we compute (y - x), where y = 10 and x = -65504, the result is 65514 // and cause an overflow in f16. { input: [kValue.f16.negative.min, 10.0, 1.0], expected: kUnboundedEndpoints }, // (y - x) * 1.0, where y = -10 and x = -65504, the result is 65494 rounded to 65472 or 65504. // The result is -65504 + 65472 = -32 or -65504 + 65504 = 0. { input: [kValue.f16.negative.min, -10.0, 1.0], expected: [-32, 0] }, { input: [kValue.f16.negative.min, 10.0, 5.0], expected: kUnboundedEndpoints }, { input: [kValue.f16.negative.min, -10.0, 5.0], expected: kUnboundedEndpoints }, { input: [kValue.f16.negative.min, 10.0, 0.5], expected: kUnboundedEndpoints }, { input: [kValue.f16.negative.min, -10.0, 0.5], expected: [-32768.0, -32752.0] }, ] as ScalarTripleToIntervalCase[], } as const; g.test('mixImpreciseInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ ...kMixImpreciseIntervalCases[p.trait], // [0.0, 1.0] cases { input: [0.0, 1.0, -1.0], expected: -1.0 }, { input: [0.0, 1.0, 0.0], expected: 0.0 }, { input: [0.0, 1.0, 0.5], expected: 0.5 }, { input: [0.0, 1.0, 1.0], expected: 1.0 }, { input: [0.0, 1.0, 2.0], expected: 2.0 }, // [1.0, 0.0] cases { input: [1.0, 0.0, -1.0], expected: 2.0 }, { input: [1.0, 0.0, 0.0], expected: 1.0 }, { input: [1.0, 0.0, 0.5], expected: 0.5 }, { input: [1.0, 0.0, 1.0], expected: 0.0 }, { input: [1.0, 0.0, 2.0], expected: -1.0 }, // [0.0, 10.0] cases { input: [0.0, 10.0, -1.0], expected: -10.0 }, { input: [0.0, 10.0, 0.0], expected: 0.0 }, { input: [0.0, 10.0, 0.5], expected: 5.0 }, { input: [0.0, 10.0, 1.0], expected: 10.0 }, { input: [0.0, 10.0, 2.0], expected: 20.0 }, // [2.0, 10.0] cases { input: [2.0, 10.0, -1.0], expected: -6.0 }, { input: [2.0, 10.0, 0.0], expected: 2.0 }, { input: [2.0, 10.0, 0.5], expected: 6.0 }, { input: [2.0, 10.0, 1.0], expected: 10.0 }, { input: [2.0, 10.0, 2.0], expected: 18.0 }, // [-1.0, 1.0] cases { input: [-1.0, 1.0, -2.0], expected: -5.0 }, { input: [-1.0, 1.0, 0.0], expected: -1.0 }, { input: [-1.0, 1.0, 0.5], expected: 0.0 }, { input: [-1.0, 1.0, 1.0], expected: 1.0 }, { input: [-1.0, 1.0, 2.0], expected: 3.0 }, // Infinities { input: [0.0, constants.positive.infinity, 0.5], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, 0.0, 0.5], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, 1.0, 0.5], expected: kUnboundedEndpoints }, { input: [1.0, constants.negative.infinity, 0.5], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity, 0.5], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.negative.infinity, 0.5], expected: kUnboundedEndpoints }, { input: [0.0, 1.0, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [1.0, 0.0, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [0.0, 1.0, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [1.0, 0.0, constants.positive.infinity], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const [x, y, z] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.mixImpreciseInterval(x, y, z); t.expect( objectEquals(expected, got), `${t.params.trait}.mixImpreciseInterval(${x}, ${y}, ${z}) returned ${got}. Expected ${expected}` ); }); // Some of these are hard coded, since the error intervals are difficult to express in a closed // human-readable form due to the inherited nature of the errors. // prettier-ignore const kMixPreciseIntervalCases = { f32: [ // [0.0, 1.0] cases { input: [0.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0x3fb9_9999_8000_0000n), reinterpretU64AsF64(0x3fb9_9999_a000_0000n)] }, // ~0.1 { input: [0.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fec_cccc_c000_0000n), reinterpretU64AsF64(0x3fec_cccc_e000_0000n)] }, // ~0.9 // [1.0, 0.0] cases { input: [1.0, 0.0, 0.1], expected: [reinterpretU64AsF64(0x3fec_cccc_c000_0000n), reinterpretU64AsF64(0x3fec_cccc_e000_0000n)] }, // ~0.9 { input: [1.0, 0.0, 0.9], expected: [reinterpretU64AsF64(0x3fb9_9999_0000_0000n), reinterpretU64AsF64(0x3fb9_999a_0000_0000n)] }, // ~0.1 // [0.0, 10.0] cases { input: [0.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x3fef_ffff_e000_0000n), reinterpretU64AsF64(0x3ff0_0000_2000_0000n)] }, // ~1 { input: [0.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4021_ffff_e000_0000n), reinterpretU64AsF64(0x4022_0000_2000_0000n)] }, // ~9 // [2.0, 10.0] cases { input: [2.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x4006_6666_4000_0000n), reinterpretU64AsF64(0x4006_6666_8000_0000n)] }, // ~2.8 { input: [2.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4022_6666_4000_0000n), reinterpretU64AsF64(0x4022_6666_a000_0000n)] }, // ~9.2 // [-1.0, 1.0] cases { input: [-1.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0xbfe9_9999_c000_0000n), reinterpretU64AsF64(0xbfe9_9999_8000_0000n)] }, // ~-0.8 { input: [-1.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fe9_9999_8000_0000n), reinterpretU64AsF64(0x3fe9_9999_c000_0000n)] }, // ~0.8 // Showing how precise and imprecise versions diff { input: [kValue.f32.negative.min, 10.0, 1.0], expected: 10 }, { input: [kValue.f32.negative.min, -10.0, 1.0], expected: -10 }, { input: [kValue.f32.negative.min, 10.0, 5.0], expected: kUnboundedEndpoints }, { input: [kValue.f32.negative.min, -10.0, 5.0], expected: kUnboundedEndpoints }, { input: [kValue.f32.negative.min, 10.0, 0.5], expected: [reinterpretU32AsF32(0xfeffffff), reinterpretU32AsF32(0xfefffffe) ] }, { input: [kValue.f32.negative.min, -10.0, 0.5], expected: [reinterpretU32AsF32(0xff000000),reinterpretU32AsF32(0xfeffffff) ] }, // Intermediate OOB { input: [1.0, 2.0, kPlusOneULPFunctions['f32'](kValue.f32.positive.max / 2)], expected: kUnboundedEndpoints }, ] as ScalarTripleToIntervalCase[], f16: [ // [0.0, 1.0] cases { input: [0.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0x3fb9_9800_0000_0000n), reinterpretU64AsF64(0x3fb9_9c00_0000_0000n)] }, // ~0.1 { input: [0.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fec_cc00_0000_0000n), reinterpretU64AsF64(0x3fec_d000_0000_0000n)] }, // ~0.9 // [1.0, 0.0] cases { input: [1.0, 0.0, 0.1], expected: [reinterpretU64AsF64(0x3fec_cc00_0000_0000n), reinterpretU64AsF64(0x3fec_d000_0000_0000n)] }, // ~0.9 { input: [1.0, 0.0, 0.9], expected: [reinterpretU64AsF64(0x3fb9_8000_0000_0000n), reinterpretU64AsF64(0x3fb9_a000_0000_0000n)] }, // ~0.1 // [0.0, 10.0] cases { input: [0.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x3fef_fc00_0000_0000n), reinterpretU64AsF64(0x3ff0_0400_0000_0000n)] }, // ~1 { input: [0.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4021_fc00_0000_0000n), reinterpretU64AsF64(0x4022_0400_0000_0000n)] }, // ~9 // [2.0, 10.0] cases { input: [2.0, 10.0, 0.1], expected: [reinterpretU64AsF64(0x4006_6400_0000_0000n), reinterpretU64AsF64(0x4006_6c00_0000_0000n)] }, // ~2.8 { input: [2.0, 10.0, 0.9], expected: [reinterpretU64AsF64(0x4022_6000_0000_0000n), reinterpretU64AsF64(0x4022_6c00_0000_0000n)] }, // ~9.2 // [-1.0, 1.0] cases { input: [-1.0, 1.0, 0.1], expected: [reinterpretU64AsF64(0xbfe9_a000_0000_0000n), reinterpretU64AsF64(0xbfe9_9800_0000_0000n)] }, // ~-0.8 { input: [-1.0, 1.0, 0.9], expected: [reinterpretU64AsF64(0x3fe9_9800_0000_0000n), reinterpretU64AsF64(0x3fe9_a000_0000_0000n)] }, // ~0.8 // Showing how precise and imprecise versions diff { input: [kValue.f64.negative.min, 10.0, 1.0], expected: kUnboundedEndpoints }, { input: [kValue.f64.negative.min, -10.0, 1.0], expected: kUnboundedEndpoints }, { input: [kValue.f64.negative.min, 10.0, 5.0], expected: kUnboundedEndpoints }, { input: [kValue.f64.negative.min, -10.0, 5.0], expected: kUnboundedEndpoints }, { input: [kValue.f64.negative.min, 10.0, 0.5], expected: kUnboundedEndpoints }, { input: [kValue.f64.negative.min, -10.0, 0.5], expected: kUnboundedEndpoints }, // Intermediate OOB { input: [1.0, 2.0, kPlusOneULPFunctions['f16'](kValue.f16.positive.max / 2)], expected: kUnboundedEndpoints }, ] as ScalarTripleToIntervalCase[], } as const; g.test('mixPreciseInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ ...kMixPreciseIntervalCases[p.trait], // [0.0, 1.0] cases { input: [0.0, 1.0, -1.0], expected: -1.0 }, { input: [0.0, 1.0, 0.0], expected: 0.0 }, { input: [0.0, 1.0, 0.5], expected: 0.5 }, { input: [0.0, 1.0, 1.0], expected: 1.0 }, { input: [0.0, 1.0, 2.0], expected: 2.0 }, // [1.0, 0.0] cases { input: [1.0, 0.0, -1.0], expected: 2.0 }, { input: [1.0, 0.0, 0.0], expected: 1.0 }, { input: [1.0, 0.0, 0.5], expected: 0.5 }, { input: [1.0, 0.0, 1.0], expected: 0.0 }, { input: [1.0, 0.0, 2.0], expected: -1.0 }, // [0.0, 10.0] cases { input: [0.0, 10.0, -1.0], expected: -10.0 }, { input: [0.0, 10.0, 0.0], expected: 0.0 }, { input: [0.0, 10.0, 0.5], expected: 5.0 }, { input: [0.0, 10.0, 1.0], expected: 10.0 }, { input: [0.0, 10.0, 2.0], expected: 20.0 }, // [2.0, 10.0] cases { input: [2.0, 10.0, -1.0], expected: -6.0 }, { input: [2.0, 10.0, 0.0], expected: 2.0 }, { input: [2.0, 10.0, 0.5], expected: 6.0 }, { input: [2.0, 10.0, 1.0], expected: 10.0 }, { input: [2.0, 10.0, 2.0], expected: 18.0 }, // [-1.0, 1.0] cases { input: [-1.0, 1.0, -2.0], expected: -5.0 }, { input: [-1.0, 1.0, 0.0], expected: -1.0 }, { input: [-1.0, 1.0, 0.5], expected: 0.0 }, { input: [-1.0, 1.0, 1.0], expected: 1.0 }, { input: [-1.0, 1.0, 2.0], expected: 3.0 }, // Infinities { input: [0.0, constants.positive.infinity, 0.5], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, 0.0, 0.5], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, 1.0, 0.5], expected: kUnboundedEndpoints }, { input: [1.0, constants.negative.infinity, 0.5], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, constants.positive.infinity, 0.5], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, constants.negative.infinity, 0.5], expected: kUnboundedEndpoints }, { input: [0.0, 1.0, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [1.0, 0.0, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [0.0, 1.0, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [1.0, 0.0, constants.positive.infinity], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const [x, y, z] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.mixPreciseInterval(x, y, z); t.expect( objectEquals(expected, got), `${t.params.trait}.mixPreciseInterval(${x}, ${y}, ${z}) returned ${got}. Expected ${expected}` ); }); // Some of these are hard coded, since the error intervals are difficult to express in a closed // human-readable form due to the inherited nature of the errors. // prettier-ignore const kSmoothStepIntervalCases = { f32: [ // Normals { input: [0, 1, 0], expected: [0, kValue.f32.positive.subnormal.min] }, { input: [0, 1, 1], expected: [reinterpretU32AsF32(0x3f7ffffa), reinterpretU32AsF32(0x3f800003)] }, // ~1 { input: [0, 2, 1], expected: [reinterpretU32AsF32(0x3efffff8), reinterpretU32AsF32(0x3f000007)] }, // ~0.5 { input: [0, 2, 0.5], expected: [reinterpretU32AsF32(0x3e1ffffb), reinterpretU32AsF32(0x3e200007)] }, // ~0.15625... { input: [2, 0, 1], expected: [reinterpretU32AsF32(0x3efffff8), reinterpretU32AsF32(0x3f000007)] }, // ~0.5 { input: [2, 0, 1.5], expected: [reinterpretU32AsF32(0x3e1ffffb), reinterpretU32AsF32(0x3e200007)] }, // ~0.15625... { input: [0, 100, 50], expected: [reinterpretU32AsF32(0x3efffff8), reinterpretU32AsF32(0x3f000007)] }, // ~0.5 { input: [0, 100, 25], expected: [reinterpretU32AsF32(0x3e1ffffb), reinterpretU32AsF32(0x3e200007)] }, // ~0.15625... { input: [0, -2, -1], expected: [reinterpretU32AsF32(0x3efffff8), reinterpretU32AsF32(0x3f000007)] }, // ~0.5 { input: [0, -2, -0.5], expected: [reinterpretU32AsF32(0x3e1ffffb), reinterpretU32AsF32(0x3e200007)] }, // ~0.15625... // Subnormals { input: [kValue.f32.positive.subnormal.max, 2, 1], expected: [reinterpretU32AsF32(0x3efffff4), reinterpretU32AsF32(0x3f00000b)] }, // ~0.5 { input: [kValue.f32.positive.subnormal.min, 2, 1], expected: [reinterpretU32AsF32(0x3efffff4), reinterpretU32AsF32(0x3f00000b)] }, // ~0.5 { input: [kValue.f32.negative.subnormal.max, 2, 1], expected: [reinterpretU32AsF32(0x3efffff2), reinterpretU32AsF32(0x3f00000c)] }, // ~0.5 { input: [kValue.f32.negative.subnormal.min, 2, 1], expected: [reinterpretU32AsF32(0x3efffff2), reinterpretU32AsF32(0x3f00000c)] }, // ~0.5 { input: [0, 2, kValue.f32.positive.subnormal.max], expected: [0, kValue.f32.positive.subnormal.min] }, { input: [0, 2, kValue.f32.positive.subnormal.min], expected: [0, kValue.f32.positive.subnormal.min] }, { input: [0, 2, kValue.f32.negative.subnormal.max], expected: [0, kValue.f32.positive.subnormal.min] }, { input: [0, 2, kValue.f32.negative.subnormal.min], expected: [0, kValue.f32.positive.subnormal.min] }, // Extra cases for low > high // Normals { input: [1, 0, 1], expected: [0, kValue.f32.positive.subnormal.min] }, { input: [1, 0, 0], expected: [reinterpretU32AsF32(0x3f7ffffa), reinterpretU32AsF32(0x3f800003)] }, // ~1 // Subnormals { input: [2, kValue.f32.positive.subnormal.max, 1], expected: [reinterpretU32AsF32(0x3efffff6), reinterpretU32AsF32(0x3f00000b)] }, // ~0.5 { input: [2, kValue.f32.positive.subnormal.min, 1], expected: [reinterpretU32AsF32(0x3efffff6), reinterpretU32AsF32(0x3f00000b)] }, // ~0.5 { input: [2, kValue.f32.negative.subnormal.max, 1], expected: [reinterpretU32AsF32(0x3efffff4), reinterpretU32AsF32(0x3f000008)] }, // ~0.5 { input: [2, kValue.f32.negative.subnormal.min, 1], expected: [reinterpretU32AsF32(0x3efffff4), reinterpretU32AsF32(0x3f000008)] }, // ~0.5 ] as ScalarTripleToIntervalCase[], f16: [ // Normals { input: [0, 1, 0], expected: [0, reinterpretU16AsF16(0x0002)] }, { input: [0, 1, 1], expected: [reinterpretU16AsF16(0x3bfa), reinterpretU16AsF16(0x3c03)] }, // ~1 { input: [0, 2, 1], expected: [reinterpretU16AsF16(0x37f8), reinterpretU16AsF16(0x3807)] }, // ~0.5 { input: [0, 2, 0.5], expected: [reinterpretU16AsF16(0x30fb), reinterpretU16AsF16(0x3107)] }, // ~0.15625... { input: [2, 0, 1], expected: [reinterpretU16AsF16(0x37f8), reinterpretU16AsF16(0x3807)] }, // ~0.5 { input: [2, 0, 1.5], expected: [reinterpretU16AsF16(0x30fb), reinterpretU16AsF16(0x3107)] }, // ~0.15625... { input: [0, 100, 50], expected: [reinterpretU16AsF16(0x37f8), reinterpretU16AsF16(0x3807)] }, // ~0.5 { input: [0, 100, 25], expected: [reinterpretU16AsF16(0x30fb), reinterpretU16AsF16(0x3107)] }, // ~0.15625... { input: [0, -2, -1], expected: [reinterpretU16AsF16(0x37f8), reinterpretU16AsF16(0x3807)] }, // ~0.5 { input: [0, -2, -0.5], expected: [reinterpretU16AsF16(0x30fb), reinterpretU16AsF16(0x3107)] }, // ~0.15625... // Subnormals { input: [kValue.f16.positive.subnormal.max, 2, 1], expected: [reinterpretU16AsF16(0x37f4), reinterpretU16AsF16(0x380b)] }, // ~0.5 { input: [kValue.f16.positive.subnormal.min, 2, 1], expected: [reinterpretU16AsF16(0x37f4), reinterpretU16AsF16(0x380b)] }, // ~0.5 { input: [kValue.f16.negative.subnormal.max, 2, 1], expected: [reinterpretU16AsF16(0x37f2), reinterpretU16AsF16(0x380c)] }, // ~0.5 { input: [kValue.f16.negative.subnormal.min, 2, 1], expected: [reinterpretU16AsF16(0x37f2), reinterpretU16AsF16(0x380c)] }, // ~0.5 { input: [0, 2, kValue.f16.positive.subnormal.max], expected: [0, reinterpretU16AsF16(0x0002)] }, { input: [0, 2, kValue.f16.positive.subnormal.min], expected: [0, reinterpretU16AsF16(0x0002)] }, { input: [0, 2, kValue.f32.negative.subnormal.max], expected: [0, reinterpretU16AsF16(0x0002)] }, { input: [0, 2, kValue.f32.negative.subnormal.min], expected: [0, reinterpretU16AsF16(0x0002)] }, // Extra cases for low > high // Normals { input: [1, 0, 1], expected: [0, reinterpretU16AsF16(0x0002)] }, { input: [1, 0, 0], expected: [reinterpretU16AsF16(0x3bfa), reinterpretU16AsF16(0x3c03)] }, // ~1 // Subnormals { input: [2, kValue.f16.positive.subnormal.max, 1], expected: [reinterpretU16AsF16(0x37f6), reinterpretU16AsF16(0x380b)] }, // ~0.5 { input: [2, kValue.f16.positive.subnormal.min, 1], expected: [reinterpretU16AsF16(0x37f6), reinterpretU16AsF16(0x380b)] }, // ~0.5 { input: [2, kValue.f16.negative.subnormal.max, 1], expected: [reinterpretU16AsF16(0x37f4), reinterpretU16AsF16(0x3808)] }, // ~0.5 { input: [2, kValue.f16.negative.subnormal.min, 1], expected: [reinterpretU16AsF16(0x37f4), reinterpretU16AsF16(0x3808)] }, // ~0.5 ] as ScalarTripleToIntervalCase[], } as const; g.test('smoothStepInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ ...kSmoothStepIntervalCases[p.trait], // Normals { input: [0, 1, 10], expected: 1 }, { input: [0, 1, -10], expected: 0 }, // Subnormals { input: [0, constants.positive.subnormal.max, 1], expected: kUnboundedEndpoints }, { input: [0, constants.positive.subnormal.min, 1], expected: kUnboundedEndpoints }, { input: [0, constants.negative.subnormal.max, 1], expected: kUnboundedEndpoints }, { input: [0, constants.negative.subnormal.min, 1], expected: kUnboundedEndpoints }, // Infinities { input: [0, 2, constants.positive.infinity], expected: kUnboundedEndpoints }, { input: [0, 2, constants.negative.infinity], expected: kUnboundedEndpoints }, { input: [constants.positive.infinity, 2, 1], expected: kUnboundedEndpoints }, { input: [constants.negative.infinity, 2, 1], expected: kUnboundedEndpoints }, { input: [0, constants.positive.infinity, 1], expected: kUnboundedEndpoints }, { input: [0, constants.negative.infinity, 1], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const [low, high, x] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.smoothStepInterval(low, high, x); t.expect( objectEquals(expected, got), `${t.params.trait}.smoothStepInterval(${low}, ${high}, ${x}) returned ${got}. Expected ${expected}` ); }); interface ScalarToVectorCase { input: number; expected: (number | IntervalEndpoints)[]; } g.test('unpack2x16floatInterval') .paramsSubcasesOnly( // prettier-ignore [ // f16 normals { input: 0x00000000, expected: [0, 0] }, { input: 0x80000000, expected: [0, 0] }, { input: 0x00008000, expected: [0, 0] }, { input: 0x80008000, expected: [0, 0] }, { input: 0x00003c00, expected: [1, 0] }, { input: 0x3c000000, expected: [0, 1] }, { input: 0x3c003c00, expected: [1, 1] }, { input: 0xbc00bc00, expected: [-1, -1] }, { input: 0x49004900, expected: [10, 10] }, { input: 0xc900c900, expected: [-10, -10] }, // f16 subnormals { input: 0x000003ff, expected: [[0, kValue.f16.positive.subnormal.max], 0] }, { input: 0x000083ff, expected: [[kValue.f16.negative.subnormal.min, 0], 0] }, // f16 out of bounds { input: 0x7c000000, expected: [kUnboundedEndpoints, kUnboundedEndpoints] }, { input: 0xffff0000, expected: [kUnboundedEndpoints, kUnboundedEndpoints] }, ] ) .fn(t => { const expected = FP.f32.toVector(t.params.expected); const got = FP.f32.unpack2x16floatInterval(t.params.input); t.expect( objectEquals(expected, got), `unpack2x16floatInterval(${t.params.input}) returned [${got}]. Expected [${expected}]` ); }); // Scope for unpack2x16snormInterval tests so that they can have constants for // magic numbers that don't pollute the global namespace or have unwieldy long // names. { const kZeroEndpoints: IntervalEndpoints = [ reinterpretU32AsF32(0x81400000), reinterpretU32AsF32(0x01400000), ]; const kOneEndpointsSnorm: IntervalEndpoints = [ reinterpretU64AsF64(0x3fef_ffff_a000_0000n), reinterpretU64AsF64(0x3ff0_0000_3000_0000n), ]; const kNegOneEndpointsSnorm: IntervalEndpoints = [ reinterpretU64AsF64(0xbff0_0000_3000_0000n), reinterpretU64AsF64(0xbfef_ffff_a000_0000n), ]; const kHalfEndpoints2x16snorm: IntervalEndpoints = [ reinterpretU64AsF64(0x3fe0_001f_a000_0000n), reinterpretU64AsF64(0x3fe0_0020_8000_0000n), ]; // ~0.5..., due to lack of precision in i16 const kNegHalfEndpoints2x16snorm: IntervalEndpoints = [ reinterpretU64AsF64(0xbfdf_ffc0_6000_0000n), reinterpretU64AsF64(0xbfdf_ffbf_8000_0000n), ]; // ~-0.5..., due to lack of precision in i16 g.test('unpack2x16snormInterval') .paramsSubcasesOnly( // prettier-ignore [ { input: 0x00000000, expected: [kZeroEndpoints, kZeroEndpoints] }, { input: 0x00007fff, expected: [kOneEndpointsSnorm, kZeroEndpoints] }, { input: 0x7fff0000, expected: [kZeroEndpoints, kOneEndpointsSnorm] }, { input: 0x7fff7fff, expected: [kOneEndpointsSnorm, kOneEndpointsSnorm] }, { input: 0x80018001, expected: [kNegOneEndpointsSnorm, kNegOneEndpointsSnorm] }, { input: 0x40004000, expected: [kHalfEndpoints2x16snorm, kHalfEndpoints2x16snorm] }, { input: 0xc001c001, expected: [kNegHalfEndpoints2x16snorm, kNegHalfEndpoints2x16snorm] }, ] ) .fn(t => { const expected = FP.f32.toVector(t.params.expected); const got = FP.f32.unpack2x16snormInterval(t.params.input); t.expect( objectEquals(expected, got), `unpack2x16snormInterval(${t.params.input}) returned [${got}]. Expected [${expected}]` ); }); } // Scope for unpack2x16unormInterval tests so that they can have constants for // magic numbers that don't pollute the global namespace or have unwieldy long // names. { const kZeroEndpoints: IntervalEndpoints = [ reinterpretU32AsF32(0x8140_0000), reinterpretU32AsF32(0x0140_0000), ]; // ~0 const kOneEndpoints: IntervalEndpoints = [ reinterpretU64AsF64(0x3fef_ffff_a000_0000n), reinterpretU64AsF64(0x3ff0_0000_3000_0000n), ]; // ~1 const kHalfEndpoints: IntervalEndpoints = [ reinterpretU64AsF64(0x3fe0_000f_a000_0000n), reinterpretU64AsF64(0x3fe0_0010_8000_0000n), ]; // ~0.5..., due to the lack of accuracy in u16 g.test('unpack2x16unormInterval') .paramsSubcasesOnly( // prettier-ignore [ { input: 0x00000000, expected: [kZeroEndpoints, kZeroEndpoints] }, { input: 0x0000ffff, expected: [kOneEndpoints, kZeroEndpoints] }, { input: 0xffff0000, expected: [kZeroEndpoints, kOneEndpoints] }, { input: 0xffffffff, expected: [kOneEndpoints, kOneEndpoints] }, { input: 0x80008000, expected: [kHalfEndpoints, kHalfEndpoints] }, ] ) .fn(t => { const expected = FP.f32.toVector(t.params.expected); const got = FP.f32.unpack2x16unormInterval(t.params.input); t.expect( objectEquals(expected, got), `unpack2x16unormInterval(${t.params.input})\n\tReturned [${got}]\n\tExpected [${expected}]` ); }); } // Scope for unpack4x8snormInterval tests so that they can have constants for // magic numbers that don't pollute the global namespace or have unwieldy long // names. { const kZeroEndpoints: IntervalEndpoints = [ reinterpretU32AsF32(0x8140_0000), reinterpretU32AsF32(0x0140_0000), ]; // ~0 const kOneEndpoints: IntervalEndpoints = [ reinterpretU64AsF64(0x3fef_ffff_a000_0000n), reinterpretU64AsF64(0x3ff0_0000_3000_0000n), ]; // ~1 const kNegOneEndpoints: IntervalEndpoints = [ reinterpretU64AsF64(0xbff0_0000_3000_0000n), reinterpretU64AsF64(0xbfef_ffff_a0000_000n), ]; // ~-1 const kHalfEndpoints: IntervalEndpoints = [ reinterpretU64AsF64(0x3fe0_2040_2000_0000n), reinterpretU64AsF64(0x3fe0_2041_0000_0000n), ]; // ~0.50196..., due to lack of precision in i8 const kNegHalfEndpoints: IntervalEndpoints = [ reinterpretU64AsF64(0xbfdf_bf7f_6000_0000n), reinterpretU64AsF64(0xbfdf_bf7e_8000_0000n), ]; // ~-0.49606..., due to lack of precision in i8 g.test('unpack4x8snormInterval') .paramsSubcasesOnly( // prettier-ignore [ { input: 0x00000000, expected: [kZeroEndpoints, kZeroEndpoints, kZeroEndpoints, kZeroEndpoints] }, { input: 0x0000007f, expected: [kOneEndpoints, kZeroEndpoints, kZeroEndpoints, kZeroEndpoints] }, { input: 0x00007f00, expected: [kZeroEndpoints, kOneEndpoints, kZeroEndpoints, kZeroEndpoints] }, { input: 0x007f0000, expected: [kZeroEndpoints, kZeroEndpoints, kOneEndpoints, kZeroEndpoints] }, { input: 0x7f000000, expected: [kZeroEndpoints, kZeroEndpoints, kZeroEndpoints, kOneEndpoints] }, { input: 0x00007f7f, expected: [kOneEndpoints, kOneEndpoints, kZeroEndpoints, kZeroEndpoints] }, { input: 0x7f7f0000, expected: [kZeroEndpoints, kZeroEndpoints, kOneEndpoints, kOneEndpoints] }, { input: 0x7f007f00, expected: [kZeroEndpoints, kOneEndpoints, kZeroEndpoints, kOneEndpoints] }, { input: 0x007f007f, expected: [kOneEndpoints, kZeroEndpoints, kOneEndpoints, kZeroEndpoints] }, { input: 0x7f7f7f7f, expected: [kOneEndpoints, kOneEndpoints, kOneEndpoints, kOneEndpoints] }, { input: 0x81818181, expected: [kNegOneEndpoints, kNegOneEndpoints, kNegOneEndpoints, kNegOneEndpoints] }, { input: 0x40404040, expected: [kHalfEndpoints, kHalfEndpoints, kHalfEndpoints, kHalfEndpoints] }, { input: 0xc1c1c1c1, expected: [kNegHalfEndpoints, kNegHalfEndpoints, kNegHalfEndpoints, kNegHalfEndpoints] }, ] ) .fn(t => { const expected = FP.f32.toVector(t.params.expected); const got = FP.f32.unpack4x8snormInterval(t.params.input); t.expect( objectEquals(expected, got), `unpack4x8snormInterval(${t.params.input})\n\tReturned [${got}]\n\tExpected [${expected}]` ); }); } // Scope for unpack4x8unormInterval tests so that they can have constants for // magic numbers that don't pollute the global namespace or have unwieldy long // names. { const kZeroEndpoints: IntervalEndpoints = [ reinterpretU32AsF32(0x8140_0000), reinterpretU32AsF32(0x0140_0000), ]; // ~0 const kOneEndpoints: IntervalEndpoints = [ reinterpretU64AsF64(0x3fef_ffff_a000_0000n), reinterpretU64AsF64(0x3ff0_0000_3000_0000n), ]; // ~1 const kHalfEndpoints: IntervalEndpoints = [ reinterpretU64AsF64(0x3fe0_100f_a000_0000n), reinterpretU64AsF64(0x3fe0_1010_8000_0000n), ]; // ~0.50196..., due to lack of precision in u8 g.test('unpack4x8unormInterval') .paramsSubcasesOnly( // prettier-ignore [ { input: 0x00000000, expected: [kZeroEndpoints, kZeroEndpoints, kZeroEndpoints, kZeroEndpoints] }, { input: 0x000000ff, expected: [kOneEndpoints, kZeroEndpoints, kZeroEndpoints, kZeroEndpoints] }, { input: 0x0000ff00, expected: [kZeroEndpoints, kOneEndpoints, kZeroEndpoints, kZeroEndpoints] }, { input: 0x00ff0000, expected: [kZeroEndpoints, kZeroEndpoints, kOneEndpoints, kZeroEndpoints] }, { input: 0xff000000, expected: [kZeroEndpoints, kZeroEndpoints, kZeroEndpoints, kOneEndpoints] }, { input: 0x0000ffff, expected: [kOneEndpoints, kOneEndpoints, kZeroEndpoints, kZeroEndpoints] }, { input: 0xffff0000, expected: [kZeroEndpoints, kZeroEndpoints, kOneEndpoints, kOneEndpoints] }, { input: 0xff00ff00, expected: [kZeroEndpoints, kOneEndpoints, kZeroEndpoints, kOneEndpoints] }, { input: 0x00ff00ff, expected: [kOneEndpoints, kZeroEndpoints, kOneEndpoints, kZeroEndpoints] }, { input: 0xffffffff, expected: [kOneEndpoints, kOneEndpoints, kOneEndpoints, kOneEndpoints] }, { input: 0x80808080, expected: [kHalfEndpoints, kHalfEndpoints, kHalfEndpoints, kHalfEndpoints] }, ] ) .fn(t => { const expected = FP.f32.toVector(t.params.expected); const got = FP.f32.unpack4x8unormInterval(t.params.input); t.expect( objectEquals(expected, got), `unpack4x8unormInterval(${t.params.input})\n\tReturned [${got}]\n\tExpected [${expected}]` ); }); } interface VectorToIntervalCase { input: number[]; expected: number | IntervalEndpoints; } g.test('lengthIntervalVector') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // vec2 {input: [1.0, 0.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 {input: [0.0, 1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 {input: [1.0, 1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0]'] }, // ~√2 {input: [-1.0, -1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0]'] }, // ~√2 {input: [-1.0, 1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0]'] }, // ~√2 {input: [0.1, 0.0], expected: kRootSumSquareExpectationInterval[p.trait]['[0.1]'] }, // ~0.1 // vec3 {input: [1.0, 0.0, 0.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 {input: [0.0, 1.0, 0.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 {input: [0.0, 0.0, 1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 {input: [1.0, 1.0, 1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0, 1.0]'] }, // ~√3 {input: [-1.0, -1.0, -1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0, 1.0]'] }, // ~√3 {input: [1.0, -1.0, -1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0, 1.0]'] }, // ~√3 {input: [0.1, 0.0, 0.0], expected: kRootSumSquareExpectationInterval[p.trait]['[0.1]'] }, // ~0.1 // vec4 {input: [1.0, 0.0, 0.0, 0.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 {input: [0.0, 1.0, 0.0, 0.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 {input: [0.0, 0.0, 1.0, 0.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 {input: [0.0, 0.0, 0.0, 1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 {input: [1.0, 1.0, 1.0, 1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0, 1.0, 1.0]'] }, // ~2 {input: [-1.0, -1.0, -1.0, -1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0, 1.0, 1.0]'] }, // ~2 {input: [-1.0, 1.0, -1.0, 1.0], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0, 1.0, 1.0]'] }, // ~2 {input: [0.1, 0.0, 0.0, 0.0], expected: kRootSumSquareExpectationInterval[p.trait]['[0.1]'] }, // ~0.1 // Test that dot going OOB in the intermediate calculations propagates { input: [constants.positive.nearest_max, constants.positive.max, constants.negative.min], expected: kUnboundedEndpoints }, { input: [constants.positive.max, constants.positive.nearest_max, constants.negative.min], expected: kUnboundedEndpoints }, { input: [constants.negative.min, constants.positive.max, constants.positive.nearest_max], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.lengthInterval(t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.lengthInterval([${t.params.input}]) returned ${got}. Expected ${expected}` ); }); interface VectorPairToIntervalCase { input: [number[], number[]]; expected: number | IntervalEndpoints; } g.test('distanceIntervalVector') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { // prettier-ignore return [ // distance(x, y), where x - y = 0 has an acceptance interval of kUnboundedEndpoints, // because distance(x, y) = length(x - y), and length(0) = kUnboundedEndpoints. // vec2 { input: [[1.0, 0.0], [1.0, 0.0]], expected: kUnboundedEndpoints }, { input: [[1.0, 0.0], [0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 0.0], [1.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[-1.0, 0.0], [0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 0.0], [-1.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 1.0], [-1.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0]'] }, // ~√2 { input: [[0.1, 0.0], [0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[0.1]'] }, // ~0.1 // vec3 { input: [[1.0, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: kUnboundedEndpoints }, { input: [[1.0, 0.0, 0.0], [0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 1.0, 0.0], [0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 0.0, 1.0], [0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 0.0, 0.0], [0.0, 1.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 0.0, 0.0], [0.0, 0.0, 1.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[1.0, 1.0, 1.0], [0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0, 1.0]'] }, // ~√3 { input: [[0.0, 0.0, 0.0], [1.0, 1.0, 1.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0, 1.0]'] }, // ~√3 { input: [[-1.0, -1.0, -1.0], [0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0, 1.0]'] }, // ~√3 { input: [[0.0, 0.0, 0.0], [-1.0, -1.0, -1.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0, 1.0]'] }, // ~√3 { input: [[0.1, 0.0, 0.0], [0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[0.1]'] }, // ~0.1 { input: [[0.0, 0.0, 0.0], [0.1, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[0.1]'] }, // ~0.1 // vec4 { input: [[1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: kUnboundedEndpoints }, { input: [[1.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 0.0, 0.0, 1.0], [0.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0]'] }, // ~1 { input: [[1.0, 1.0, 1.0, 1.0], [0.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0, 1.0, 1.0]'] }, // ~2 { input: [[0.0, 0.0, 0.0, 0.0], [1.0, 1.0, 1.0, 1.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0, 1.0, 1.0]'] }, // ~2 { input: [[-1.0, 1.0, -1.0, 1.0], [0.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0, 1.0, 1.0]'] }, // ~2 { input: [[0.0, 0.0, 0.0, 0.0], [1.0, -1.0, 1.0, -1.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[1.0, 1.0, 1.0, 1.0]'] }, // ~2 { input: [[0.1, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[0.1]'] }, // ~0.1 { input: [[0.0, 0.0, 0.0, 0.0], [0.1, 0.0, 0.0, 0.0]], expected: kRootSumSquareExpectationInterval[p.trait]['[0.1]'] }, // ~0.1 ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.distanceInterval(...t.params.input); t.expect( objectEquals(expected, got), `${t.params.trait}.lengthInterval([${t.params.input[0]}, ${t.params.input[1]}]) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kDotIntervalCases = { f32: [ // Due to unbounded precision, intermediate correctly rounded computations could result in intervals that include infinity. // This is because the computation kValue.f32.negative.min - 4.0 = [-inf, kValue.f32.negative.min] // due to the ULP_neg(kValue.f32.negative.min) => -inf // See: https://www.w3.org/TR/WGSL/#floating-point-accuracy { input: [[kValue.f32.positive.max, 1.0, 2.0, 3.0], [-1.0, kValue.f32.positive.max, -2.0, -3.0]], expected: kUnboundedEndpoints}, { input: [[kValue.f32.positive.max, 1.0, 2.0, 3.0], [1.0, kValue.f32.negative.min, 2.0, 3.0]], expected: kUnboundedEndpoints }, // Exactly as above but simply 2 ulp magnitude smaller (away from kValue.f32.positive.max). // This avoids intermediate intervals that overflow into infinity and we end up with large but finite intervals. { input: [[reinterpretU32AsF32(0x7f7ffffd), 1.0, 2.0, 3.0], [-1.0, kValue.f32.positive.max, -2.0, -3.0]], expected: [0.0, reinterpretU32AsF32(0x74000000)]}, { input: [[reinterpretU32AsF32(0x7f7ffffd), 1.0, 2.0, 3.0], [1.0, kValue.f32.negative.min, 2.0, 3.0]], expected: [reinterpretU32AsF32(0xf4000000), 0.0] }, ] as VectorPairToIntervalCase[], f16: [ // Inputs with large values but cancel out to finite result. In these cases, 2.0*2.0 = 4.0 and // 3.0*3.0 = 9.0 is not small enough comparing to kValue.f16.positive.max = 65504, as a result // kValue.f16.positive.max + 9.0 = 65513 is exactly representable in f32 and f64. So, if the // positive and negative large number don't cancel each other first, the computation will // overflow f16 and result in unbounded endpoints. // https://github.com/gpuweb/cts/issues/2155 { input: [[kValue.f16.positive.max, 1.0, 2.0, 3.0], [-1.0, kValue.f16.positive.max, -2.0, -3.0]], expected: kUnboundedEndpoints }, { input: [[kValue.f16.positive.max, 1.0, 2.0, 3.0], [1.0, kValue.f16.negative.min, 2.0, 3.0]], expected: kUnboundedEndpoints }, ] as VectorPairToIntervalCase[], } as const; g.test('dotInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // vec2 { input: [[1.0, 0.0], [1.0, 0.0]], expected: 1.0 }, { input: [[0.0, 1.0], [0.0, 1.0]], expected: 1.0 }, { input: [[1.0, 1.0], [1.0, 1.0]], expected: 2.0 }, { input: [[-1.0, -1.0], [-1.0, -1.0]], expected: 2.0 }, { input: [[-1.0, 1.0], [1.0, -1.0]], expected: -2.0 }, { input: [[0.1, 0.0], [1.0, 0.0]], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1']}, // correctly rounded of 0.1 // vec3 { input: [[1.0, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: 1.0 }, { input: [[0.0, 1.0, 0.0], [0.0, 1.0, 0.0]], expected: 1.0 }, { input: [[0.0, 0.0, 1.0], [0.0, 0.0, 1.0]], expected: 1.0 }, { input: [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], expected: 3.0 }, { input: [[-1.0, -1.0, -1.0], [-1.0, -1.0, -1.0]], expected: 3.0 }, { input: [[1.0, -1.0, -1.0], [-1.0, 1.0, -1.0]], expected: -1.0 }, { input: [[0.1, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1']}, // correctly rounded of 0.1 // vec4 { input: [[1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: 1.0 }, { input: [[0.0, 1.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0]], expected: 1.0 }, { input: [[0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 1.0, 0.0]], expected: 1.0 }, { input: [[0.0, 0.0, 0.0, 1.0], [0.0, 0.0, 0.0, 1.0]], expected: 1.0 }, { input: [[1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0]], expected: 4.0 }, { input: [[-1.0, -1.0, -1.0, -1.0], [-1.0, -1.0, -1.0, -1.0]], expected: 4.0 }, { input: [[-1.0, 1.0, -1.0, 1.0], [1.0, -1.0, 1.0, -1.0]], expected: -4.0 }, { input: [[0.1, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: kConstantCorrectlyRoundedExpectation[p.trait]['0.1']}, // correclt rounded of 0.1 ...kDotIntervalCases[p.trait], // Test that going out of bounds in the intermediate calculations is caught correctly. { input: [[constants.positive.nearest_max, constants.positive.max, constants.negative.min], [1.0, 1.0, 1.0]], expected: kUnboundedEndpoints }, { input: [[constants.positive.nearest_max, constants.negative.min, constants.positive.max], [1.0, 1.0, 1.0]], expected: kUnboundedEndpoints }, { input: [[constants.positive.max, constants.positive.nearest_max, constants.negative.min], [1.0, 1.0, 1.0]], expected: kUnboundedEndpoints }, { input: [[constants.negative.min, constants.positive.nearest_max, constants.positive.max], [1.0, 1.0, 1.0]], expected: kUnboundedEndpoints }, { input: [[constants.positive.max, constants.negative.min, constants.positive.nearest_max], [1.0, 1.0, 1.0]], expected: kUnboundedEndpoints }, { input: [[constants.negative.min, constants.positive.max, constants.positive.nearest_max], [1.0, 1.0, 1.0]], expected: kUnboundedEndpoints }, ]; }) ) .fn(t => { const [x, y] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.dotInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.dotInterval([${x}], [${y}]) returned ${got}. Expected ${expected}` ); }); interface VectorToVectorCase { input: number[]; expected: (number | IntervalEndpoints)[]; } // prettier-ignore const kNormalizeIntervalCases = { f32: [ // vec2 { input: [1.0, 0.0], expected: [[reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~1.0, ~0.0] { input: [0.0, 1.0], expected: [[reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)]] }, // [ ~0.0, ~1.0] { input: [-1.0, 0.0], expected: [[reinterpretU64AsF64(0xbff0_0000_b000_0000n), reinterpretU64AsF64(0xbfef_fffe_7000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~1.0, ~0.0] { input: [1.0, 1.0], expected: [[reinterpretU64AsF64(0x3fe6_a09d_5000_0000n), reinterpretU64AsF64(0x3fe6_a09f_9000_0000n)], [reinterpretU64AsF64(0x3fe6_a09d_5000_0000n), reinterpretU64AsF64(0x3fe6_a09f_9000_0000n)]] }, // [ ~1/√2, ~1/√2] // vec3 { input: [1.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~1.0, ~0.0, ~0.0] { input: [0.0, 1.0, 0.0], expected: [[reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~0.0, ~1.0, ~0.0] { input: [0.0, 0.0, 1.0], expected: [[reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)]] }, // [ ~0.0, ~0.0, ~1.0] { input: [-1.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0xbff0_0000_b000_0000n), reinterpretU64AsF64(0xbfef_fffe_7000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~1.0, ~0.0, ~0.0] { input: [1.0, 1.0, 1.0], expected: [[reinterpretU64AsF64(0x3fe2_79a6_5000_0000n), reinterpretU64AsF64(0x3fe2_79a8_5000_0000n)], [reinterpretU64AsF64(0x3fe2_79a6_5000_0000n), reinterpretU64AsF64(0x3fe2_79a8_5000_0000n)], [reinterpretU64AsF64(0x3fe2_79a6_5000_0000n), reinterpretU64AsF64(0x3fe2_79a8_5000_0000n)]] }, // [ ~1/√3, ~1/√3, ~1/√3] // vec4 { input: [1.0, 0.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~1.0, ~0.0, ~0.0, ~0.0] { input: [0.0, 1.0, 0.0, 0.0], expected: [[reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~0.0, ~1.0, ~0.0, ~0.0] { input: [0.0, 0.0, 1.0, 0.0], expected: [[reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~0.0, ~0.0, ~1.0, ~0.0] { input: [0.0, 0.0, 0.0, 1.0], expected: [[reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU64AsF64(0x3fef_fffe_7000_0000n), reinterpretU64AsF64(0x3ff0_0000_b000_0000n)]] }, // [ ~0.0, ~0.0, ~0.0, ~1.0] { input: [-1.0, 0.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0xbff0_0000_b000_0000n), reinterpretU64AsF64(0xbfef_fffe_7000_0000n)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)], [reinterpretU32AsF32(0x81200000), reinterpretU32AsF32(0x01200000)]] }, // [ ~1.0, ~0.0, ~0.0, ~0.0] { input: [1.0, 1.0, 1.0, 1.0], expected: [[reinterpretU64AsF64(0x3fdf_fffe_7000_0000n), reinterpretU64AsF64(0x3fe0_0000_b000_0000n)], [reinterpretU64AsF64(0x3fdf_fffe_7000_0000n), reinterpretU64AsF64(0x3fe0_0000_b000_0000n)], [reinterpretU64AsF64(0x3fdf_fffe_7000_0000n), reinterpretU64AsF64(0x3fe0_0000_b000_0000n)], [reinterpretU64AsF64(0x3fdf_fffe_7000_0000n), reinterpretU64AsF64(0x3fe0_0000_b000_0000n)]] }, // [ ~1/√4, ~1/√4, ~1/√4] ] as VectorToVectorCase[], f16: [ // vec2 { input: [1.0, 0.0], expected: [[reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~1.0, ~0.0] { input: [0.0, 1.0], expected: [[reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)]] }, // [ ~0.0, ~1.0] { input: [-1.0, 0.0], expected: [[reinterpretU64AsF64(0xbff0_1600_0000_0000n), reinterpretU64AsF64(0xbfef_ce00_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~1.0, ~0.0] { input: [1.0, 1.0], expected: [[reinterpretU64AsF64(0x3fe6_7e00_0000_0000n), reinterpretU64AsF64(0x3fe6_c600_0000_0000n)], [reinterpretU64AsF64(0x3fe6_7e00_0000_0000n), reinterpretU64AsF64(0x3fe6_c600_0000_0000n)]] }, // [ ~1/√2, ~1/√2] // vec3 { input: [1.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~1.0, ~0.0, ~0.0] { input: [0.0, 1.0, 0.0], expected: [[reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~0.0, ~1.0, ~0.0] { input: [0.0, 0.0, 1.0], expected: [[reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)]] }, // [ ~0.0, ~0.0, ~1.0] { input: [-1.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0xbff0_1600_0000_0000n), reinterpretU64AsF64(0xbfef_ce00_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~1.0, ~0.0, ~0.0] { input: [1.0, 1.0, 1.0], expected: [[reinterpretU64AsF64(0x3fe2_5a00_0000_0000n), reinterpretU64AsF64(0x3fe2_9a00_0000_0000n)], [reinterpretU64AsF64(0x3fe2_5a00_0000_0000n), reinterpretU64AsF64(0x3fe2_9a00_0000_0000n)], [reinterpretU64AsF64(0x3fe2_5a00_0000_0000n), reinterpretU64AsF64(0x3fe2_9a00_0000_0000n)]] }, // [ ~1/√3, ~1/√3, ~1/√3] // vec4 { input: [1.0, 0.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~1.0, ~0.0, ~0.0, ~0.0] { input: [0.0, 1.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~0.0, ~1.0, ~0.0, ~0.0] { input: [0.0, 0.0, 1.0, 0.0], expected: [[reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~0.0, ~0.0, ~1.0, ~0.0] { input: [0.0, 0.0, 0.0, 1.0], expected: [[reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0x3fef_ce00_0000_0000n), reinterpretU64AsF64(0x3ff0_1600_0000_0000n)]] }, // [ ~0.0, ~0.0, ~0.0, ~1.0] { input: [-1.0, 0.0, 0.0, 0.0], expected: [[reinterpretU64AsF64(0xbff0_1600_0000_0000n), reinterpretU64AsF64(0xbfef_ce00_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)], [reinterpretU64AsF64(0xbf24_0000_0000_0000n), reinterpretU64AsF64(0x3f24_0000_0000_0000n)]] }, // [ ~1.0, ~0.0, ~0.0, ~0.0] { input: [1.0, 1.0, 1.0, 1.0], expected: [[reinterpretU64AsF64(0x3fdf_ce00_0000_0000n), reinterpretU64AsF64(0x3fe0_1600_0000_0000n)], [reinterpretU64AsF64(0x3fdf_ce00_0000_0000n), reinterpretU64AsF64(0x3fe0_1600_0000_0000n)], [reinterpretU64AsF64(0x3fdf_ce00_0000_0000n), reinterpretU64AsF64(0x3fe0_1600_0000_0000n)], [reinterpretU64AsF64(0x3fdf_ce00_0000_0000n), reinterpretU64AsF64(0x3fe0_1600_0000_0000n)]] }, // [ ~1/√4, ~1/√4, ~1/√4] ] as VectorToVectorCase[], } as const; g.test('normalizeInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ ...kNormalizeIntervalCases[p.trait], // Very small vectors go OOB due to division { input: [constants.positive.subnormal.max, constants.positive.subnormal.max], expected: [kUnboundedEndpoints, kUnboundedEndpoints], }, // Very large vectors go OOB due to overflow { input: [constants.positive.max, constants.positive.max], expected: [kUnboundedEndpoints, kUnboundedEndpoints], }, ]; }) ) .fn(t => { const x = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toVector(t.params.expected); const got = trait.normalizeInterval(x); t.expect( objectEquals(expected, got), `${t.params.trait}.normalizeInterval([${x}]) returned ${got}. Expected ${expected}` ); }); interface VectorPairToVectorCase { input: [number[], number[]]; expected: (number | IntervalEndpoints)[]; } // prettier-ignore const kCrossIntervalCases = { f32: [ { input: [ [kValue.f32.positive.subnormal.max, kValue.f32.negative.subnormal.max, kValue.f32.negative.subnormal.min], [kValue.f32.negative.subnormal.min, kValue.f32.positive.subnormal.min, kValue.f32.negative.subnormal.max] ], expected: [ [0.0, reinterpretU32AsF32(0x00000002)], // ~0 [0.0, reinterpretU32AsF32(0x00000002)], // ~0 [kValue.f32.negative.subnormal.max, kValue.f32.positive.subnormal.min] // ~0 ] }, { input: [ [0.1, -0.1, -0.1], [-0.1, 0.1, -0.1] ], expected: [ [reinterpretU32AsF32(0x3ca3d708), reinterpretU32AsF32(0x3ca3d70b)], // ~0.02 [reinterpretU32AsF32(0x3ca3d708), reinterpretU32AsF32(0x3ca3d70b)], // ~0.02 [reinterpretU32AsF32(0xb1400000), reinterpretU32AsF32(0x31400000)], // ~0 ] }, ] as VectorPairToVectorCase[], f16: [ { input: [ [kValue.f16.positive.subnormal.max, kValue.f16.negative.subnormal.max, kValue.f16.negative.subnormal.min], [kValue.f16.negative.subnormal.min, kValue.f16.positive.subnormal.min, kValue.f16.negative.subnormal.max] ], expected: [ [0.0, reinterpretU16AsF16(0x0002)], // ~0 [0.0, reinterpretU16AsF16(0x0002)], // ~0 [kValue.f16.negative.subnormal.max, kValue.f16.positive.subnormal.min] // ~0 ] }, { input: [ [0.1, -0.1, -0.1], [-0.1, 0.1, -0.1] ], expected: [ [reinterpretU16AsF16(0x251e), reinterpretU16AsF16(0x2520)], // ~0.02 [reinterpretU16AsF16(0x251e), reinterpretU16AsF16(0x2520)], // ~0.02 [reinterpretU16AsF16(0x8100), reinterpretU16AsF16(0x0100)] // ~0 ] }, ] as VectorPairToVectorCase[], } as const; g.test('crossInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // parallel vectors, AXB == 0 { input: [[1.0, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: [0.0, 0.0, 0.0] }, { input: [[0.0, 1.0, 0.0], [0.0, 1.0, 0.0]], expected: [0.0, 0.0, 0.0] }, { input: [[0.0, 0.0, 1.0], [0.0, 0.0, 1.0]], expected: [0.0, 0.0, 0.0] }, { input: [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], expected: [0.0, 0.0, 0.0] }, { input: [[-1.0, -1.0, -1.0], [-1.0, -1.0, -1.0]], expected: [0.0, 0.0, 0.0] }, { input: [[0.1, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: [0.0, 0.0, 0.0] }, { input: [[constants.positive.subnormal.max, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: [0.0, 0.0, 0.0] }, // non-parallel vectors, AXB != 0 { input: [[1.0, -1.0, -1.0], [-1.0, 1.0, -1.0]], expected: [2.0, 2.0, 0.0] }, { input: [[1.0, 2, 3], [1.0, 5.0, 7.0]], expected: [-1, -4, 3] }, ...kCrossIntervalCases[p.trait], // OOB { input: [[constants.positive.max, 1.0, 1.0], [1.0, constants.positive.max, -1.0]], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, ]; }) ) .fn(t => { const [x, y] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toVector(t.params.expected); const got = trait.crossInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.crossInterval([${x}], [${y}]) returned ${got}. Expected ${expected}` ); }); // prettier-ignore const kReflectIntervalCases = { f32: [ // vec2s { input: [[0.1, 0.1], [1.0, 1.0]], expected: [[reinterpretU32AsF32(0xbe99999a), reinterpretU32AsF32(0xbe999998)], [reinterpretU32AsF32(0xbe99999a), reinterpretU32AsF32(0xbe999998)]] }, // [~-0.3, ~-0.3] { input: [[kValue.f32.positive.subnormal.max, kValue.f32.negative.subnormal.max], [1.0, 1.0]], expected: [[reinterpretU32AsF32(0x80fffffe), reinterpretU32AsF32(0x00800001)], [reinterpretU32AsF32(0x80ffffff), reinterpretU32AsF32(0x00000002)]] }, // [~0.0, ~0.0] // vec3s { input: [[0.1, 0.1, 0.1], [1.0, 1.0, 1.0]], expected: [[reinterpretU32AsF32(0xbf000001), reinterpretU32AsF32(0xbefffffe)], [reinterpretU32AsF32(0xbf000001), reinterpretU32AsF32(0xbefffffe)], [reinterpretU32AsF32(0xbf000001), reinterpretU32AsF32(0xbefffffe)]] }, // [~-0.5, ~-0.5, ~-0.5] { input: [[kValue.f32.positive.subnormal.max, kValue.f32.negative.subnormal.max, 0.0], [1.0, 1.0, 1.0]], expected: [[reinterpretU32AsF32(0x80fffffe), reinterpretU32AsF32(0x00800001)], [reinterpretU32AsF32(0x80ffffff), reinterpretU32AsF32(0x00000002)], [reinterpretU32AsF32(0x80fffffe), reinterpretU32AsF32(0x00000002)]] }, // [~0.0, ~0.0, ~0.0] // vec4s { input: [[0.1, 0.1, 0.1, 0.1], [1.0, 1.0, 1.0, 1.0]], expected: [[reinterpretU32AsF32(0xbf333335), reinterpretU32AsF32(0xbf333332)], [reinterpretU32AsF32(0xbf333335), reinterpretU32AsF32(0xbf333332)], [reinterpretU32AsF32(0xbf333335), reinterpretU32AsF32(0xbf333332)], [reinterpretU32AsF32(0xbf333335), reinterpretU32AsF32(0xbf333332)]] }, // [~-0.7, ~-0.7, ~-0.7, ~-0.7] { input: [[kValue.f32.positive.subnormal.max, kValue.f32.negative.subnormal.max, 0.0, 0.0], [1.0, 1.0, 1.0, 1.0]], expected: [[reinterpretU32AsF32(0x80fffffe), reinterpretU32AsF32(0x00800001)], [reinterpretU32AsF32(0x80ffffff), reinterpretU32AsF32(0x00000002)], [reinterpretU32AsF32(0x80fffffe), reinterpretU32AsF32(0x00000002)], [reinterpretU32AsF32(0x80fffffe), reinterpretU32AsF32(0x00000002)]] }, // [~0.0, ~0.0, ~0.0, ~0.0] ] as VectorPairToVectorCase[], f16: [ // vec2s { input: [[0.1, 0.1], [1.0, 1.0]], expected: [[reinterpretU16AsF16(0xb4ce), reinterpretU16AsF16(0xb4cc)], [reinterpretU16AsF16(0xb4ce), reinterpretU16AsF16(0xb4cc)]] }, // [~-0.3, ~-0.3] { input: [[kValue.f16.positive.subnormal.max, kValue.f16.negative.subnormal.max], [1.0, 1.0]], expected: [[reinterpretU16AsF16(0x87fe), reinterpretU16AsF16(0x0401)], [reinterpretU16AsF16(0x87ff), reinterpretU16AsF16(0x0002)]] }, // [~0.0, ~0.0] // vec3s { input: [[0.1, 0.1, 0.1], [1.0, 1.0, 1.0]], expected: [[reinterpretU16AsF16(0xb802), reinterpretU16AsF16(0xb7fe)], [reinterpretU16AsF16(0xb802), reinterpretU16AsF16(0xb7fe)], [reinterpretU16AsF16(0xb802), reinterpretU16AsF16(0xb7fe)]] }, // [~-0.5, ~-0.5, ~-0.5] { input: [[kValue.f16.positive.subnormal.max, kValue.f16.negative.subnormal.max, 0.0], [1.0, 1.0, 1.0]], expected: [[reinterpretU16AsF16(0x87fe), reinterpretU16AsF16(0x0401)], [reinterpretU16AsF16(0x87ff), reinterpretU16AsF16(0x0002)], [reinterpretU16AsF16(0x87fe), reinterpretU16AsF16(0x0002)]] }, // [~0.0, ~0.0, ~0.0] // vec4s { input: [[0.1, 0.1, 0.1, 0.1], [1.0, 1.0, 1.0, 1.0]], expected: [[reinterpretU16AsF16(0xb99c), reinterpretU16AsF16(0xb998)], [reinterpretU16AsF16(0xb99c), reinterpretU16AsF16(0xb998)], [reinterpretU16AsF16(0xb99c), reinterpretU16AsF16(0xb998)], [reinterpretU16AsF16(0xb99c), reinterpretU16AsF16(0xb998)]] }, // [~-0.7, ~-0.7, ~-0.7, ~-0.7] { input: [[kValue.f16.positive.subnormal.max, kValue.f16.negative.subnormal.max, 0.0, 0.0], [1.0, 1.0, 1.0, 1.0]], expected: [[reinterpretU16AsF16(0x87fe), reinterpretU16AsF16(0x0401)], [reinterpretU16AsF16(0x87ff), reinterpretU16AsF16(0x0002)], [reinterpretU16AsF16(0x87fe), reinterpretU16AsF16(0x0002)], [reinterpretU16AsF16(0x87fe), reinterpretU16AsF16(0x0002)]] }, // [~0.0, ~0.0, ~0.0, ~0.0] ] as VectorPairToVectorCase[], } as const; g.test('reflectInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ ...kReflectIntervalCases[p.trait], // vec2s { input: [[1.0, 0.0], [1.0, 0.0]], expected: [-1.0, 0.0] }, { input: [[1.0, 0.0], [0.0, 1.0]], expected: [1.0, 0.0] }, { input: [[0.0, 1.0], [0.0, 1.0]], expected: [0.0, -1.0] }, { input: [[0.0, 1.0], [1.0, 0.0]], expected: [0.0, 1.0] }, { input: [[1.0, 1.0], [1.0, 1.0]], expected: [-3.0, -3.0] }, { input: [[-1.0, -1.0], [1.0, 1.0]], expected: [3.0, 3.0] }, // vec3s { input: [[1.0, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: [-1.0, 0.0, 0.0] }, { input: [[0.0, 1.0, 0.0], [1.0, 0.0, 0.0]], expected: [0.0, 1.0, 0.0] }, { input: [[0.0, 0.0, 1.0], [1.0, 0.0, 0.0]], expected: [0.0, 0.0, 1.0] }, { input: [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0]], expected: [1.0, 0.0, 0.0] }, { input: [[1.0, 0.0, 0.0], [0.0, 0.0, 1.0]], expected: [1.0, 0.0, 0.0] }, { input: [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], expected: [-5.0, -5.0, -5.0] }, { input: [[-1.0, -1.0, -1.0], [1.0, 1.0, 1.0]], expected: [5.0, 5.0, 5.0] }, // vec4s { input: [[1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: [-1.0, 0.0, 0.0, 0.0] }, { input: [[0.0, 1.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: [0.0, 1.0, 0.0, 0.0] }, { input: [[0.0, 0.0, 1.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: [0.0, 0.0, 1.0, 0.0] }, { input: [[0.0, 0.0, 0.0, 1.0], [1.0, 0.0, 0.0, 0.0]], expected: [0.0, 0.0, 0.0, 1.0] }, { input: [[1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0]], expected: [1.0, 0.0, 0.0, 0.0] }, { input: [[1.0, 0.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0]], expected: [1.0, 0.0, 0.0, 0.0] }, { input: [[1.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0]], expected: [1.0, 0.0, 0.0, 0.0] }, { input: [[-1.0, -1.0, -1.0, -1.0], [1.0, 1.0, 1.0, 1.0]], expected: [7.0, 7.0, 7.0, 7.0] }, // Test that dot going OOB in the intermediate calculations propagates { input: [[constants.positive.nearest_max, constants.positive.max, constants.negative.min], [1.0, 1.0, 1.0]], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, { input: [[constants.positive.nearest_max, constants.negative.min, constants.positive.max], [1.0, 1.0, 1.0]], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, { input: [[constants.positive.max, constants.positive.nearest_max, constants.negative.min], [1.0, 1.0, 1.0]], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, { input: [[constants.negative.min, constants.positive.nearest_max, constants.positive.max], [1.0, 1.0, 1.0]], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, { input: [[constants.positive.max, constants.negative.min, constants.positive.nearest_max], [1.0, 1.0, 1.0]], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, { input: [[constants.negative.min, constants.positive.max, constants.positive.nearest_max], [1.0, 1.0, 1.0]], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, // Test that post-dot going OOB propagates { input: [[constants.positive.max, 1.0, 2.0, 3.0], [-1.0, constants.positive.max, -2.0, -3.0]], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, ]; }) ) .fn(t => { const [x, y] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toVector(t.params.expected); const got = trait.reflectInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.reflectInterval([${x}], [${y}]) returned ${JSON.stringify( got )}. Expected ${JSON.stringify(expected)}` ); }); interface MatrixToScalarCase { input: number[][]; expected: number | IntervalEndpoints; } g.test('determinantInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .combineWithParams([ // Extreme values, i.e. subnormals, very large magnitudes, and those lead to // non-precise products, are intentionally not tested, since the accuracy of // determinant is restricted to well behaving inputs. Handling all cases // requires ~23! options to be calculated in the 4x4 case, so is not // feasible. { input: [ [1, 2], [3, 4], ], expected: -2, }, { input: [ [-1, 2], [-3, 4], ], expected: 2, }, { input: [ [11, 22], [33, 44], ], expected: -242, }, { input: [ [5, 6], [8, 9], ], expected: -3, }, { input: [ [4, 6], [7, 9], ], expected: -6, }, { input: [ [4, 5], [7, 8], ], expected: -3, }, { input: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], ], expected: 0, }, { input: [ [-1, 2, 3], [-4, 5, 6], [-7, 8, 9], ], expected: 0, }, { input: [ [4, 1, -1], [-3, 0, 5], [5, 3, 2], ], expected: -20, }, { input: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], ], expected: 0, }, { input: [ [4, 0, 0, 0], [3, 1, -1, 3], [2, -3, 3, 1], [2, 3, 3, 1], ], expected: -240, }, ]) ) .fn(t => { const input = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toInterval(t.params.expected); const got = trait.determinantInterval(input); t.expect( objectEquals(expected, got), `${t.params.trait}.determinantInterval([${JSON.stringify( input )}]) returned '${got}. Expected '${expected}'` ); }); interface MatrixToMatrixCase { input: number[][]; expected: (number | IntervalEndpoints)[][]; } g.test('transposeInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); return [ { input: [ [1, 2], [3, 4], ], expected: [ [1, 3], [2, 4], ], }, { input: [ [1, 2], [3, 4], [5, 6], ], expected: [ [1, 3, 5], [2, 4, 6], ], }, { input: [ [1, 2], [3, 4], [5, 6], [7, 8], ], expected: [ [1, 3, 5, 7], [2, 4, 6, 8], ], }, { input: [ [1, 2, 3], [4, 5, 6], ], expected: [ [1, 4], [2, 5], [3, 6], ], }, { input: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], ], expected: [ [1, 4, 7], [2, 5, 8], [3, 6, 9], ], }, { input: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], ], expected: [ [1, 4, 7, 10], [2, 5, 8, 11], [3, 6, 9, 12], ], }, { input: [ [1, 2, 3, 4], [5, 6, 7, 8], ], expected: [ [1, 5], [2, 6], [3, 7], [4, 8], ], }, { input: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], ], expected: [ [1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12], ], }, { input: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], ], expected: [ [1, 5, 9, 13], [2, 6, 10, 14], [3, 7, 11, 15], [4, 8, 12, 16], ], }, { input: [ [constants.positive.subnormal.max, constants.positive.subnormal.min], [constants.negative.subnormal.min, constants.negative.subnormal.max], ], expected: [ [ [0, constants.positive.subnormal.max], [constants.negative.subnormal.min, 0], ], [ [0, constants.positive.subnormal.min], [constants.negative.subnormal.max, 0], ], ], }, ]; }) ) .fn(t => { const input = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toMatrix(t.params.expected); const got = trait.transposeInterval(input); t.expect( objectEquals(expected, got), `FP.${t.params.trait}.transposeInterval([${JSON.stringify( input )}]) returned '[${JSON.stringify(got)}]'. Expected '[${JSON.stringify(expected)}]'` ); }); interface MatrixPairToMatrixCase { input: [number[][], number[][]]; expected: (number | IntervalEndpoints)[][]; } g.test('additionMatrixMatrixInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); return [ // Only testing that different shapes of matrices are handled correctly // here, to reduce test duplication. // additionMatrixMatrixInterval uses AdditionIntervalOp for calculating intervals, // so the testing for additionInterval covers the actual interval // calculations. { input: [ [ [1, 2], [3, 4], ], [ [10, 20], [30, 40], ], ], expected: [ [11, 22], [33, 44], ], }, { input: [ [ [1, 2], [3, 4], [5, 6], ], [ [10, 20], [30, 40], [50, 60], ], ], expected: [ [11, 22], [33, 44], [55, 66], ], }, { input: [ [ [1, 2], [3, 4], [5, 6], [7, 8], ], [ [10, 20], [30, 40], [50, 60], [70, 80], ], ], expected: [ [11, 22], [33, 44], [55, 66], [77, 88], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], ], [ [10, 20, 30], [40, 50, 60], ], ], expected: [ [11, 22, 33], [44, 55, 66], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], [7, 8, 9], ], [ [10, 20, 30], [40, 50, 60], [70, 80, 90], ], ], expected: [ [11, 22, 33], [44, 55, 66], [77, 88, 99], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], ], [ [10, 20, 30], [40, 50, 60], [70, 80, 90], [1000, 1100, 1200], ], ], expected: [ [11, 22, 33], [44, 55, 66], [77, 88, 99], [1010, 1111, 1212], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], ], [ [10, 20, 30, 40], [50, 60, 70, 80], ], ], expected: [ [11, 22, 33, 44], [55, 66, 77, 88], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], ], [ [10, 20, 30, 40], [50, 60, 70, 80], [90, 1000, 1100, 1200], ], ], expected: [ [11, 22, 33, 44], [55, 66, 77, 88], [99, 1010, 1111, 1212], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], ], [ [10, 20, 30, 40], [50, 60, 70, 80], [90, 1000, 1100, 1200], [1300, 1400, 1500, 1600], ], ], expected: [ [11, 22, 33, 44], [55, 66, 77, 88], [99, 1010, 1111, 1212], [1313, 1414, 1515, 1616], ], }, // Test the OOB is handled component-wise { input: [ [ [constants.positive.max, 2], [3, 4], ], [ [constants.positive.max, 20], [30, 40], ], ], expected: [ [kUnboundedEndpoints, 22], [33, 44], ], }, ]; }) ) .fn(t => { const [x, y] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toMatrix(t.params.expected); const got = trait.additionMatrixMatrixInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.additionMatrixMatrixInterval([${JSON.stringify(x)}], [${JSON.stringify( y )}]) returned '[${JSON.stringify(got)}]'. Expected '[${JSON.stringify(expected)}]'` ); }); g.test('subtractionMatrixMatrixInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); return [ // Only testing that different shapes of matrices are handled correctly // here, to reduce test duplication. // subtractionMatrixMatrixInterval uses SubtractionIntervalOp for calculating intervals, // so the testing for subtractionInterval covers the actual interval // calculations. { input: [ [ [1, 2], [3, 4], ], [ [-10, -20], [-30, -40], ], ], expected: [ [11, 22], [33, 44], ], }, { input: [ [ [1, 2], [3, 4], [5, 6], ], [ [-10, -20], [-30, -40], [-50, -60], ], ], expected: [ [11, 22], [33, 44], [55, 66], ], }, { input: [ [ [1, 2], [3, 4], [5, 6], [7, 8], ], [ [-10, -20], [-30, -40], [-50, -60], [-70, -80], ], ], expected: [ [11, 22], [33, 44], [55, 66], [77, 88], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], ], [ [-10, -20, -30], [-40, -50, -60], ], ], expected: [ [11, 22, 33], [44, 55, 66], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], [7, 8, 9], ], [ [-10, -20, -30], [-40, -50, -60], [-70, -80, -90], ], ], expected: [ [11, 22, 33], [44, 55, 66], [77, 88, 99], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], ], [ [-10, -20, -30], [-40, -50, -60], [-70, -80, -90], [-1000, -1100, -1200], ], ], expected: [ [11, 22, 33], [44, 55, 66], [77, 88, 99], [1010, 1111, 1212], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], ], [ [-10, -20, -30, -40], [-50, -60, -70, -80], ], ], expected: [ [11, 22, 33, 44], [55, 66, 77, 88], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], ], [ [-10, -20, -30, -40], [-50, -60, -70, -80], [-90, -1000, -1100, -1200], ], ], expected: [ [11, 22, 33, 44], [55, 66, 77, 88], [99, 1010, 1111, 1212], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], ], [ [-10, -20, -30, -40], [-50, -60, -70, -80], [-90, -1000, -1100, -1200], [-1300, -1400, -1500, -1600], ], ], expected: [ [11, 22, 33, 44], [55, 66, 77, 88], [99, 1010, 1111, 1212], [1313, 1414, 1515, 1616], ], }, // Test the OOB is handled component-wise { input: [ [ [constants.positive.max, 2], [3, 4], ], [ [constants.negative.min, -20], [-30, -40], ], ], expected: [ [kUnboundedEndpoints, 22], [33, 44], ], }, ]; }) ) .fn(t => { const [x, y] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toMatrix(t.params.expected); const got = trait.subtractionMatrixMatrixInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.subtractionMatrixMatrixInterval([${JSON.stringify(x)}], [${JSON.stringify( y )}]) returned '[${JSON.stringify(got)}]'. Expected '[${JSON.stringify(expected)}]'` ); }); g.test('multiplicationMatrixMatrixInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .combineWithParams([ // Only testing that different shapes of matrices are handled correctly // here, to reduce test duplication. // multiplicationMatrixMatrixInterval uses and transposeInterval & // dotInterval for calculating intervals, so the testing for those functions // will cover the actual interval calculations. // Keep all expected result integer no larger than 2047 to ensure that all result is exactly // represeantable in both f32 and f16. { input: [ [ [1, 2], [3, 4], ], [ [11, 22], [33, 44], ], ], expected: [ [77, 110], [165, 242], ], }, { input: [ [ [1, 2], [3, 4], ], [ [11, 22], [33, 44], [55, 66], ], ], expected: [ [77, 110], [165, 242], [253, 374], ], }, { input: [ [ [1, 2], [3, 4], ], [ [11, 22], [33, 44], [55, 66], [77, 88], ], ], expected: [ [77, 110], [165, 242], [253, 374], [341, 506], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], ], [ [11, 22], [33, 44], ], ], expected: [ [99, 132, 165], [209, 286, 363], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], ], [ [11, 22], [33, 44], [55, 66], ], ], expected: [ [99, 132, 165], [209, 286, 363], [319, 440, 561], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], ], [ [11, 22], [33, 44], [55, 66], [77, 88], ], ], expected: [ [99, 132, 165], [209, 286, 363], [319, 440, 561], [429, 594, 759], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], ], [ [11, 22], [33, 44], ], ], expected: [ [121, 154, 187, 220], [253, 330, 407, 484], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], ], [ [11, 22], [33, 44], [55, 66], ], ], expected: [ [121, 154, 187, 220], [253, 330, 407, 484], [385, 506, 627, 748], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], ], [ [11, 22], [33, 44], [55, 66], [77, 88], ], ], expected: [ [121, 154, 187, 220], [253, 330, 407, 484], [385, 506, 627, 748], [517, 682, 847, 1012], ], }, { input: [ [ [1, 2], [3, 4], [5, 6], ], [ [11, 22, 33], [44, 55, 66], ], ], expected: [ [242, 308], [539, 704], ], }, { input: [ [ [1, 2], [3, 4], [5, 6], ], [ [11, 22, 33], [44, 55, 66], [77, 88, 99], ], ], expected: [ [242, 308], [539, 704], [836, 1100], ], }, { input: [ [ [1, 2], [3, 4], [5, 6], ], [ [11, 22, 33], [44, 55, 66], [77, 88, 99], [10, 11, 12], ], ], expected: [ [242, 308], [539, 704], [836, 1100], [103, 136], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], [7, 8, 9], ], [ [11, 22, 33], [44, 55, 66], ], ], expected: [ [330, 396, 462], [726, 891, 1056], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], [7, 8, 9], ], [ [11, 22, 33], [44, 55, 66], [77, 88, 99], ], ], expected: [ [330, 396, 462], [726, 891, 1056], [1122, 1386, 1650], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], [7, 8, 9], ], [ [11, 22, 33], [44, 55, 66], [77, 88, 99], [10, 11, 12], ], ], expected: [ [330, 396, 462], [726, 891, 1056], [1122, 1386, 1650], [138, 171, 204], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], ], [ [11, 12, 13], [21, 22, 23], ], ], expected: [ [188, 224, 260, 296], [338, 404, 470, 536], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], ], [ [11, 12, 13], [21, 22, 23], [31, 32, 33], ], ], expected: [ [188, 224, 260, 296], [338, 404, 470, 536], [488, 584, 680, 776], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], ], [ [11, 12, 13], [21, 22, 23], [31, 32, 33], [41, 42, 43], ], ], expected: [ [188, 224, 260, 296], [338, 404, 470, 536], [488, 584, 680, 776], [638, 764, 890, 1016], ], }, { input: [ [ [1, 2], [3, 4], [5, 6], [7, 8], ], [ [11, 22, 33, 44], [55, 66, 77, 88], ], ], expected: [ [550, 660], [1254, 1540], ], }, { input: [ [ [1, 2], [3, 4], [5, 6], [7, 8], ], [ [11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], ], ], expected: [ [210, 260], [370, 460], [530, 660], ], }, { input: [ [ [1, 2], [3, 4], [5, 6], [7, 8], ], [ [11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44], ], ], expected: [ [210, 260], [370, 460], [530, 660], [690, 860], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], ], [ [11, 12, 13, 14], [21, 22, 23, 24], ], ], expected: [ [290, 340, 390], [510, 600, 690], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], ], [ [11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], ], ], expected: [ [290, 340, 390], [510, 600, 690], [730, 860, 990], ], }, { input: [ [ [1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], ], [ [11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44], ], ], expected: [ [290, 340, 390], [510, 600, 690], [730, 860, 990], [950, 1120, 1290], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], ], [ [11, 12, 13, 14], [21, 22, 23, 24], ], ], expected: [ [370, 420, 470, 520], [650, 740, 830, 920], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], ], [ [11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], ], ], expected: [ [370, 420, 470, 520], [650, 740, 830, 920], [930, 1060, 1190, 1320], ], }, { input: [ [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], ], [ [11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44], ], ], expected: [ [370, 420, 470, 520], [650, 740, 830, 920], [930, 1060, 1190, 1320], [1210, 1380, 1550, 1720], ], }, ]) ) .fn(t => { const [x, y] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toMatrix(t.params.expected); const got = trait.multiplicationMatrixMatrixInterval(x, y); t.expect( objectEquals(expected, got), `${t.params.trait}.multiplicationMatrixMatrixInterval([${JSON.stringify( x )}], [${JSON.stringify(y)}]) returned '[${JSON.stringify(got)}]'. Expected '[${JSON.stringify( expected )}]'` ); }); interface MatrixScalarToMatrixCase { matrix: number[][]; scalar: number; expected: (number | IntervalEndpoints)[][]; } const kMultiplicationMatrixScalarIntervalCases = { f32: [ // From https://github.com/gpuweb/cts/issues/3044 { matrix: [ [kValue.f32.negative.min, 0], [0, 0], ], scalar: kValue.f32.negative.subnormal.min, expected: [ [[0, reinterpretU32AsF32(0x407ffffe)], 0], // [[0, 3.9999995...], 0], [0, 0], ], }, ] as MatrixScalarToMatrixCase[], f16: [ // From https://github.com/gpuweb/cts/issues/3044 { matrix: [ [kValue.f16.negative.min, 0], [0, 0], ], scalar: kValue.f16.negative.subnormal.min, expected: [ [[0, reinterpretU16AsF16(0x43fe)], 0], // [[0, 3.99609375], 0] [0, 0], ], }, ] as MatrixScalarToMatrixCase[], } as const; g.test('multiplicationMatrixScalarInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // Primarily testing that different shapes of matrices are handled correctly // here, to reduce test duplication. Additional testing for edge case // discovered in https://github.com/gpuweb/cts/issues/3044. // // multiplicationMatrixScalarInterval uses for calculating intervals, // so the testing for multiplicationInterval covers the actual interval // calculations. return [ { matrix: [ [1, 2], [3, 4], ], scalar: 10, expected: [ [10, 20], [30, 40], ], }, { matrix: [ [1, 2], [3, 4], [5, 6], ], scalar: 10, expected: [ [10, 20], [30, 40], [50, 60], ], }, { matrix: [ [1, 2], [3, 4], [5, 6], [7, 8], ], scalar: 10, expected: [ [10, 20], [30, 40], [50, 60], [70, 80], ], }, { matrix: [ [1, 2, 3], [4, 5, 6], ], scalar: 10, expected: [ [10, 20, 30], [40, 50, 60], ], }, { matrix: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], ], scalar: 10, expected: [ [10, 20, 30], [40, 50, 60], [70, 80, 90], ], }, { matrix: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], ], scalar: 10, expected: [ [10, 20, 30], [40, 50, 60], [70, 80, 90], [100, 110, 120], ], }, { matrix: [ [1, 2, 3, 4], [5, 6, 7, 8], ], scalar: 10, expected: [ [10, 20, 30, 40], [50, 60, 70, 80], ], }, { matrix: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], ], scalar: 10, expected: [ [10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120], ], }, { matrix: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], ], scalar: 10, expected: [ [10, 20, 30, 40], [50, 60, 70, 80], [90, 100, 110, 120], [130, 140, 150, 160], ], }, ...kMultiplicationMatrixScalarIntervalCases[p.trait], // Test that OOB is component-wise { matrix: [ [1, 2], [constants.positive.max, 4], ], scalar: 10, expected: [ [10, 20], [kUnboundedEndpoints, 40], ], }, ]; }) ) .fn(t => { const matrix = t.params.matrix; const scalar = t.params.scalar; const trait = FP[t.params.trait]; const expected = trait.toMatrix(t.params.expected); const got = trait.multiplicationMatrixScalarInterval(matrix, scalar); t.expect( objectEquals(expected, got), `${t.params.trait}.multiplicationMatrixScalarInterval([${JSON.stringify( matrix )}], ${scalar}) returned '[${JSON.stringify(got)}]'. Expected '[${JSON.stringify(expected)}]'` ); }); // There are no explicit tests for multiplicationScalarMatrixInterval, since it // is just a pass-through to multiplicationMatrixScalarInterval interface MatrixVectorToVectorCase { matrix: number[][]; vector: number[]; expected: (number | IntervalEndpoints)[]; } g.test('multiplicationMatrixVectorInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .combineWithParams([ // Only testing that different shapes of matrices are handled correctly // here, to reduce test duplication. // multiplicationMatrixVectorInterval uses DotIntervalOp & // TransposeIntervalOp for calculating intervals, so the testing for // dotInterval & transposeInterval covers the actual interval // calculations. { matrix: [ [1, 2], [3, 4], ], vector: [11, 22], expected: [77, 110], }, { matrix: [ [1, 2, 3], [4, 5, 6], ], vector: [11, 22], expected: [99, 132, 165], }, { matrix: [ [1, 2, 3, 4], [5, 6, 7, 8], ], vector: [11, 22], expected: [121, 154, 187, 220], }, { matrix: [ [1, 2], [3, 4], [5, 6], ], vector: [11, 22, 33], expected: [242, 308], }, { matrix: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], ], vector: [11, 22, 33], expected: [330, 396, 462], }, { matrix: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], ], vector: [11, 22, 33], expected: [418, 484, 550, 616], }, { matrix: [ [1, 2], [3, 4], [5, 6], [7, 8], ], vector: [11, 22, 33, 44], expected: [550, 660], }, { matrix: [ [1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], ], vector: [11, 22, 33, 44], expected: [770, 880, 990], }, { matrix: [ [1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], ], vector: [11, 22, 33, 44], expected: [990, 1100, 1210, 1320], }, ]) ) .fn(t => { const matrix = t.params.matrix; const vector = t.params.vector; const trait = FP[t.params.trait]; const expected = trait.toVector(t.params.expected); const got = trait.multiplicationMatrixVectorInterval(matrix, vector); t.expect( objectEquals(expected, got), `${t.params.trait}.multiplicationMatrixVectorInterval([${JSON.stringify( matrix )}], [${JSON.stringify(vector)}]) returned '[${JSON.stringify( got )}]'. Expected '[${JSON.stringify(expected)}]'` ); }); interface VectorMatrixToVectorCase { vector: number[]; matrix: number[][]; expected: (number | IntervalEndpoints)[]; } g.test('multiplicationVectorMatrixInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .combineWithParams([ // Only testing that different shapes of matrices are handled correctly // here, to reduce test duplication. // multiplicationVectorMatrixInterval uses DotIntervalOp for calculating // intervals, so the testing for dotInterval covers the actual interval // calculations. // Keep all expected result integer no larger than 2047 to ensure that // all result is exactly representable in both f32 and f16. { vector: [1, 2], matrix: [ [11, 22], [33, 44], ], expected: [55, 121], }, { vector: [1, 2], matrix: [ [11, 22], [33, 44], [55, 66], ], expected: [55, 121, 187], }, { vector: [1, 2], matrix: [ [11, 22], [33, 44], [55, 66], [77, 88], ], expected: [55, 121, 187, 253], }, { vector: [1, 2, 3], matrix: [ [11, 12, 13], [21, 22, 23], ], expected: [74, 134], }, { vector: [1, 2, 3], matrix: [ [11, 12, 13], [21, 22, 23], [31, 32, 33], ], expected: [74, 134, 194], }, { vector: [1, 2, 3], matrix: [ [11, 12, 13], [21, 22, 23], [31, 32, 33], [41, 42, 43], ], expected: [74, 134, 194, 254], }, { vector: [1, 2, 3, 4], matrix: [ [11, 12, 13, 14], [21, 22, 23, 24], ], expected: [130, 230], }, { vector: [1, 2, 3, 4], matrix: [ [11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], ], expected: [130, 230, 330], }, { vector: [1, 2, 3, 4], matrix: [ [11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44], ], expected: [130, 230, 330, 430], }, ]) ) .fn(t => { const vector = t.params.vector; const matrix = t.params.matrix; const trait = FP[t.params.trait]; const expected = trait.toVector(t.params.expected); const got = trait.multiplicationVectorMatrixInterval(vector, matrix); t.expect( objectEquals(expected, got), `${t.params.trait}.multiplicationVectorMatrixInterval([${JSON.stringify( vector )}], [${JSON.stringify(matrix)}]) returned '[${JSON.stringify( got )}]'. Expected '[${JSON.stringify(expected)}]'` ); }); // API - Acceptance Intervals w/ bespoke implementations interface FaceForwardCase { input: [number[], number[], number[]]; expected: ((number | IntervalEndpoints)[] | undefined)[]; } g.test('faceForwardIntervals') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ // vec2 { input: [[1.0, 0.0], [1.0, 0.0], [1.0, 0.0]], expected: [[-1.0, 0.0]] }, { input: [[-1.0, 0.0], [1.0, 0.0], [1.0, 0.0]], expected: [[1.0, 0.0]] }, { input: [[1.0, 0.0], [-1.0, 1.0], [1.0, -1.0]], expected: [[1.0, 0.0]] }, { input: [[-1.0, 0.0], [-1.0, 1.0], [1.0, -1.0]], expected: [[-1.0, 0.0]] }, { input: [[10.0, 0.0], [10.0, 0.0], [10.0, 0.0]], expected: [[-10.0, 0.0]] }, { input: [[-10.0, 0.0], [10.0, 0.0], [10.0, 0.0]], expected: [[10.0, 0.0]] }, { input: [[10.0, 0.0], [-10.0, 10.0], [10.0, -10.0]], expected: [[10.0, 0.0]] }, { input: [[-10.0, 0.0], [-10.0, 10.0], [10.0, -10.0]], expected: [[-10.0, 0.0]] }, { input: [[0.1, 0.0], [0.1, 0.0], [0.1, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'], 0.0]] }, { input: [[-0.1, 0.0], [0.1, 0.0], [0.1, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['0.1'], 0.0]] }, { input: [[0.1, 0.0], [-0.1, 0.1], [0.1, -0.1]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['0.1'], 0.0]] }, { input: [[-0.1, 0.0], [-0.1, 0.1], [0.1, -0.1]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'], 0.0]] }, // vec3 { input: [[1.0, 0.0, 0.0], [1.0, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: [[-1.0, 0.0, 0.0]] }, { input: [[-1.0, 0.0, 0.0], [1.0, 0.0, 0.0], [1.0, 0.0, 0.0]], expected: [[1.0, 0.0, 0.0]] }, { input: [[1.0, 0.0, 0.0], [-1.0, 1.0, 0.0], [1.0, -1.0, 0.0]], expected: [[1.0, 0.0, 0.0]] }, { input: [[-1.0, 0.0, 0.0], [-1.0, 1.0, 0.0], [1.0, -1.0, 0.0]], expected: [[-1.0, 0.0, 0.0]] }, { input: [[10.0, 0.0, 0.0], [10.0, 0.0, 0.0], [10.0, 0.0, 0.0]], expected: [[-10.0, 0.0, 0.0]] }, { input: [[-10.0, 0.0, 0.0], [10.0, 0.0, 0.0], [10.0, 0.0, 0.0]], expected: [[10.0, 0.0, 0.0]] }, { input: [[10.0, 0.0, 0.0], [-10.0, 10.0, 0.0], [10.0, -10.0, 0.0]], expected: [[10.0, 0.0, 0.0]] }, { input: [[-10.0, 0.0, 0.0], [-10.0, 10.0, 0.0], [10.0, -10.0, 0.0]], expected: [[-10.0, 0.0, 0.0]] }, { input: [[0.1, 0.0, 0.0], [0.1, 0.0, 0.0], [0.1, 0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'], 0.0, 0.0]] }, { input: [[-0.1, 0.0, 0.0], [0.1, 0.0, 0.0], [0.1, 0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['0.1'], 0.0, 0.0]] }, { input: [[0.1, 0.0, 0.0], [-0.1, 0.0, 0.0], [0.1, -0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['0.1'], 0.0, 0.0]] }, { input: [[-0.1, 0.0, 0.0], [-0.1, 0.0, 0.0], [0.1, -0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'], 0.0, 0.0]] }, // vec4 { input: [[1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: [[-1.0, 0.0, 0.0, 0.0]] }, { input: [[-1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]], expected: [[1.0, 0.0, 0.0, 0.0]] }, { input: [[1.0, 0.0, 0.0, 0.0], [-1.0, 1.0, 0.0, 0.0], [1.0, -1.0, 0.0, 0.0]], expected: [[1.0, 0.0, 0.0, 0.0]] }, { input: [[-1.0, 0.0, 0.0, 0.0], [-1.0, 1.0, 0.0, 0.0], [1.0, -1.0, 0.0, 0.0]], expected: [[-1.0, 0.0, 0.0, 0.0]] }, { input: [[10.0, 0.0, 0.0, 0.0], [10.0, 0.0, 0.0, 0.0], [10.0, 0.0, 0.0, 0.0]], expected: [[-10.0, 0.0, 0.0, 0.0]] }, { input: [[-10.0, 0.0, 0.0, 0.0], [10.0, 0.0, 0.0, 0.0], [10.0, 0.0, 0.0, 0.0]], expected: [[10.0, 0.0, 0.0, 0.0]] }, { input: [[10.0, 0.0, 0.0, 0.0], [-10.0, 10.0, 0.0, 0.0], [10.0, -10.0, 0.0, 0.0]], expected: [[10.0, 0.0, 0.0, 0.0]] }, { input: [[-10.0, 0.0, 0.0, 0.0], [-10.0, 10.0, 0.0, 0.0], [10.0, -10.0, 0.0, 0.0]], expected: [[-10.0, 0.0, 0.0, 0.0]] }, { input: [[0.1, 0.0, 0.0, 0.0], [0.1, 0.0, 0.0, 0.0], [0.1, 0.0, 0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'], 0.0, 0.0, 0.0]] }, { input: [[-0.1, 0.0, 0.0, 0.0], [0.1, 0.0, 0.0, 0.0], [0.1, 0.0, 0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['0.1'], 0.0, 0.0, 0.0]] }, { input: [[0.1, 0.0, 0.0, 0.0], [-0.1, 0.0, 0.0, 0.0], [0.1, -0.0, 0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['0.1'], 0.0, 0.0, 0.0]] }, { input: [[-0.1, 0.0, 0.0, 0.0], [-0.1, 0.0, 0.0, 0.0], [0.1, -0.0, 0.0, 0.0]], expected: [[kConstantCorrectlyRoundedExpectation[p.trait]['-0.1'], 0.0, 0.0, 0.0]] }, // dot(y, z) === 0 { input: [[1.0, 1.0], [1.0, 0.0], [0.0, 1.0]], expected: [[-1.0, -1.0]] }, // subnormals, also dot(y, z) spans 0 { input: [[constants.positive.subnormal.max, 0.0], [constants.positive.subnormal.min, 0.0], [constants.negative.subnormal.min, 0.0]], expected: [[[0.0, constants.positive.subnormal.max], 0.0], [[constants.negative.subnormal.min, 0], 0.0]] }, // dot going OOB returns [undefined, x, -x] { input: [[1.0, 1.0], [constants.positive.max, constants.positive.max], [constants.positive.max, constants.positive.max]], expected: [undefined, [1, 1], [-1, -1]] }, ]; }) ) .fn(t => { const [x, y, z] = t.params.input; const trait = FP[t.params.trait]; const expected = t.params.expected.map(e => (e !== undefined ? trait.toVector(e) : undefined)); const got = trait.faceForwardIntervals(x, y, z); t.expect( objectEquals(expected, got), `${t.params.trait}.faceForwardInterval([${x}], [${y}], [${z}]) returned [${got}]. Expected [${expected}]` ); }); interface ModfCase { input: number; fract: number | IntervalEndpoints; whole: number | IntervalEndpoints; } g.test('modfInterval') .params(u => u .combine('trait', ['f32', 'f16', 'abstract'] as const) .beginSubcases() .expandWithParams(p => { const constants = FP[p.trait].constants(); // prettier-ignore return [ // Normals { input: 0, fract: 0, whole: 0 }, { input: 1, fract: 0, whole: 1 }, { input: -1, fract: 0, whole: -1 }, { input: 0.5, fract: 0.5, whole: 0 }, { input: -0.5, fract: -0.5, whole: 0 }, { input: 2.5, fract: 0.5, whole: 2 }, { input: -2.5, fract: -0.5, whole: -2 }, { input: 10.0, fract: 0, whole: 10 }, { input: -10.0, fract: 0, whole: -10 }, // Subnormals { input: constants.positive.subnormal.min, fract: [0, constants.positive.subnormal.min], whole: 0 }, { input: constants.positive.subnormal.max, fract: [0, constants.positive.subnormal.max], whole: 0 }, { input: constants.negative.subnormal.min, fract: [constants.negative.subnormal.min, 0], whole: 0 }, { input: constants.negative.subnormal.max, fract: [constants.negative.subnormal.max, 0], whole: 0 }, // Boundaries { input: constants.negative.min, fract: 0, whole: constants.negative.min }, { input: constants.negative.max, fract: constants.negative.max, whole: 0 }, { input: constants.positive.min, fract: constants.positive.min, whole: 0 }, { input: constants.positive.max, fract: 0, whole: constants.positive.max }, ]; }) ) .fn(t => { const trait = FP[t.params.trait]; const expected = { fract: trait.toInterval(t.params.fract), whole: trait.toInterval(t.params.whole), }; const got = trait.modfInterval(t.params.input); t.expect( objectEquals(expected, got), `${trait}.modfInterval([${t.params.input}) returned { fract: [${got.fract}], whole: [${got.whole}] }. Expected { fract: [${expected.fract}], whole: [${expected.whole}] }` ); }); interface RefractCase { input: [number[], number[], number]; expected: (number | IntervalEndpoints)[]; } // Scope for refractInterval tests so that they can have constants for magic // numbers that don't pollute the global namespace or have unwieldy long names. { const kNegativeOneEndpoints = { f32: [ reinterpretU64AsF64(0xbff0_0000_c000_0000n), reinterpretU64AsF64(0xbfef_ffff_4000_0000n), ] as IntervalEndpoints, f16: [reinterpretU16AsF16(0xbc06), reinterpretU16AsF16(0xbbfa)] as IntervalEndpoints, } as const; // prettier-ignore const kRefractIntervalCases = { f32: [ // k > 0 // vec2 { input: [[1, -2], [3, 4], 5], expected: [[reinterpretU32AsF32(0x40ce87a4), reinterpretU32AsF32(0x40ce8840)], // ~6.454... [reinterpretU32AsF32(0xc100fae8), reinterpretU32AsF32(0xc100fa80)]] }, // ~-8.061... // vec3 { input: [[1, -2, 3], [-4, 5, -6], 7], expected: [[reinterpretU32AsF32(0x40d24480), reinterpretU32AsF32(0x40d24c00)], // ~6.571... [reinterpretU32AsF32(0xc1576f80), reinterpretU32AsF32(0xc1576ad0)], // ~-13.464... [reinterpretU32AsF32(0x41a2d9b0), reinterpretU32AsF32(0x41a2dc80)]] }, // ~20.356... // vec4 { input: [[1, -2, 3, -4], [-5, 6, -7, 8], 9], expected: [[reinterpretU32AsF32(0x410ae480), reinterpretU32AsF32(0x410af240)], // ~8.680... [reinterpretU32AsF32(0xc18cf7c0), reinterpretU32AsF32(0xc18cef80)], // ~-17.620... [reinterpretU32AsF32(0x41d46cc0), reinterpretU32AsF32(0x41d47660)], // ~26.553... [reinterpretU32AsF32(0xc20dfa80), reinterpretU32AsF32(0xc20df500)]] }, // ~-35.494... ] as RefractCase[], f16: [ // k > 0 // vec2 { input: [[1, -2], [3, 4], 5], expected: [[reinterpretU16AsF16(0x4620), reinterpretU16AsF16(0x46bc)], // ~6.454... [reinterpretU16AsF16(0xc840), reinterpretU16AsF16(0xc7b0)]] }, // ~-8.061... // vec3 { input: [[1, -2, 3], [-4, 5, -6], 7], expected: [[reinterpretU16AsF16(0x4100), reinterpretU16AsF16(0x4940)], // ~6.571... [reinterpretU16AsF16(0xcc98), reinterpretU16AsF16(0xc830)], // ~-13.464... [reinterpretU16AsF16(0x4b20), reinterpretU16AsF16(0x4e90)]] }, // ~20.356... // vec4 // x = [1, -2, 3, -4], y = [-5, 6, -7, 8], z = 9, // dot(y, x) = -71, k = 1.0 - 9 * 9 * (1.0 - 71 * 71) = 408241 overflow f16. { input: [[1, -2, 3, -4], [-5, 6, -7, 8], 9], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, // x = [1, -2, 3, -4], y = [-5, 4, -3, 2], z = 2.5, // dot(y, x) = -30, k = 1.0 - 2.5 * 2.5 * (1.0 - 30 * 30) = 5619.75. // a = z * dot(y, x) + sqrt(k) = ~-0.035, result is about z * x - a * y = [~2.325, ~-4.86, ~7.4025, ~-9.93] { input: [[1, -2, 3, -4], [-5, 4, -3, 2], 2.5], expected: [[reinterpretU16AsF16(0x3900), reinterpretU16AsF16(0x4410)], // ~2.325 [reinterpretU16AsF16(0xc640), reinterpretU16AsF16(0xc300)], // ~-4.86 [reinterpretU16AsF16(0x4660), reinterpretU16AsF16(0x4838)], // ~7.4025 [reinterpretU16AsF16(0xc950), reinterpretU16AsF16(0xc8a0)]] }, // ~-9.93 ] as RefractCase[], } as const; g.test('refractInterval') .params(u => u .combine('trait', ['f32', 'f16'] as const) .beginSubcases() .expandWithParams(p => { const trait = FP[p.trait]; const constants = trait.constants(); // prettier-ignore return [ ...kRefractIntervalCases[p.trait], // k < 0 { input: [[1, 1], [0.1, 0], 10], expected: [0, 0] }, // k contains 0 { input: [[1, 1], [0.1, 0], 1.005038], expected: [kUnboundedEndpoints, kUnboundedEndpoints] }, // k > 0 // vec2 { input: [[1, 1], [1, 0], 1], expected: [kNegativeOneEndpoints[p.trait], 1] }, // vec3 { input: [[1, 1, 1], [1, 0, 0], 1], expected: [kNegativeOneEndpoints[p.trait], 1, 1] }, // vec4 { input: [[1, 1, 1, 1], [1, 0, 0, 0], 1], expected: [kNegativeOneEndpoints[p.trait], 1, 1, 1] }, // Test that dot going OOB in the intermediate calculations propagates { input: [[constants.positive.nearest_max, constants.positive.max, constants.negative.min], [1.0, 1.0, 1.0], 1], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, { input: [[constants.positive.nearest_max, constants.negative.min, constants.positive.max], [1.0, 1.0, 1.0], 1], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, { input: [[constants.positive.max, constants.positive.nearest_max, constants.negative.min], [1.0, 1.0, 1.0], 1], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, { input: [[constants.negative.min, constants.positive.nearest_max, constants.positive.max], [1.0, 1.0, 1.0], 1], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, { input: [[constants.positive.max, constants.negative.min, constants.positive.nearest_max], [1.0, 1.0, 1.0], 1], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, { input: [[constants.negative.min, constants.positive.max, constants.positive.nearest_max], [1.0, 1.0, 1.0], 1], expected: [kUnboundedEndpoints, kUnboundedEndpoints, kUnboundedEndpoints] }, ]; }) ) .fn(t => { const [i, s, r] = t.params.input; const trait = FP[t.params.trait]; const expected = trait.toVector(t.params.expected); const got = trait.refractInterval(i, s, r); t.expect( objectEquals(expected, got), `${t.params.trait}.refractIntervals([${i}], [${s}], ${r}) returned [${got}]. Expected [${expected}]` ); }); }