From b157aa6221050f590a819015ea63b578e4cf37ee Mon Sep 17 00:00:00 2001 From: Kevin Gibbons Date: Sun, 3 Dec 2023 20:59:32 -1000 Subject: [PATCH 1/4] add precise sum polyfill --- Shewchuk-robust-arithmetic.pdf | Bin 0 -> 538412 bytes float-tools.mjs | 26 ++++ full-precision-with-bigints.mjs | 44 +++++++ package-lock.json | 16 ++- package.json | 3 +- polyfill.mjs | 178 +++++++++++++++++++++++++++ test-full-precision-with-bigints.mjs | 71 +++++++++++ test-polyfill.mjs | 97 +++++++++++++++ 8 files changed, 431 insertions(+), 4 deletions(-) create mode 100644 Shewchuk-robust-arithmetic.pdf create mode 100644 float-tools.mjs create mode 100644 full-precision-with-bigints.mjs create mode 100644 polyfill.mjs create mode 100644 test-full-precision-with-bigints.mjs create mode 100644 test-polyfill.mjs diff --git a/Shewchuk-robust-arithmetic.pdf b/Shewchuk-robust-arithmetic.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2007fbd9d844858b3232e8c52880251438b69a9b GIT binary 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zM|cr}YoT!$+D+I!ju1j3$}`;Lqc#N0fnlM0Fu(*G6Jjw;2=zI}AC%LG?x7_EPY3+7 zo{!kh#m!MHp{dDIGj|DcWF8D+shN3t`mo@HSY|9WBM*2NE^x&%gYUo4V_9qJ^LYA% zfk02!K%ZQ=h%eOR&|E#;MKrCezlfrA`P%<|hK&S#4}`amo!IB+<491Q5foQq&K&*a H1`_`R!kvbd literal 0 HcmV?d00001 diff --git a/float-tools.mjs b/float-tools.mjs new file mode 100644 index 0000000..6e72de8 --- /dev/null +++ b/float-tools.mjs @@ -0,0 +1,26 @@ +let bits = new ArrayBuffer(8); +let view = new DataView(bits); +export function floatFromParts({ sign, exponent, significand }) { + view.setBigUint64(0, BigInt(significand)); + let top16Bits = (sign << 15) | (exponent << 4) | (view.getUint8(1) & 0xf); + view.setUint16(0, top16Bits); + return view.getFloat64(0); +} + +export function partsFromFloat(double) { + view.setFloat64(0, double); + let sign = view.getUint8(0) >>> 7; + let exponent = (view.getUint16(0) >>> 4) & 0x7ff; // 11 bits. don't forget the bias! + let significand = Number(view.getBigUint64(0) & 0xfffffffffffffn); // 52 bits + return { sign, exponent, significand }; +} + +let interestingExponents = [2046, 2045, 1994, 1995, 1993, 0, 1, 2, 1021, 1022, 1023, 1024, 1025, 1026]; +let interestingSignificands = [0b1111111111111111111111111111111111111111111111111111, 0b1000000000000000000000000000000000000000000000000000, 0b1000000000000000000000000000000000000000000000000001, 0b1111111111111111111111111111111111111111111111111110, 0b111111111111111111111111111111111111111111111111111, 0, 1, 2]; + +export function randomFloat(random) { + let sign = random.int(0, 1); + let exponent = random.boolean() ? random.pick(interestingExponents) : random.int(0, 2046); + let significand = random.boolean() ? random.pick(interestingSignificands) : Math.floor(random.float(0, 2**52)); + return floatFromParts({ sign, exponent, significand }); +} diff --git a/full-precision-with-bigints.mjs b/full-precision-with-bigints.mjs new file mode 100644 index 0000000..7f7d522 --- /dev/null +++ b/full-precision-with-bigints.mjs @@ -0,0 +1,44 @@ +import { floatFromParts, partsFromFloat } from './float-tools.mjs'; + +export function floatToBigInt(double) { + if (!Number.isFinite(double)) throw new Error('todo'); + let { sign, exponent, significand } = partsFromFloat(double); + let magnitude; + if (exponent === 0) { + magnitude = BigInt(significand); + } else { + significand = 2n ** 52n + BigInt(significand); + magnitude = 2n ** (BigInt(exponent - 1)) * significand; + } + return sign ? -magnitude : magnitude; +} + +export function bigIntToFloat(bigint) { + let sign = bigint < 0 ? 1 : 0; + let magnitude = bigint < 0 ? -bigint : bigint; + let binary = magnitude.toString(2); + if (binary.length <= 52) { + // subnormal + let significand = parseInt(binary, 2); + let exponent = 0; + return floatFromParts({ sign, exponent, significand }); + } + + let significandString = binary.slice(1, 53); + let significand = parseInt(significandString, 2); + let exponent = binary.length - 52; + // round up if we are at least half way. if up is towards-even we always round up; otherwise we round up iff it is above the halfway point, i.e. there is a non-zero bit after the first + let roundUp = binary[53] === '1' && (binary[52] === '1' || binary.slice(54).includes('1')); + if (roundUp) { + significand += 1; + if (significand === 2 ** 52) { + significand = 0; + exponent += 1; + } + } + if (exponent > 2046) { + return sign ? -Infinity : Infinity; + } + + return floatFromParts({ sign, exponent, significand }); +} diff --git a/package-lock.json b/package-lock.json index 7c06e99..3a5c9eb 100644 --- a/package-lock.json +++ b/package-lock.json @@ -6,9 +6,9 @@ "": { "dependencies": { "@tc39/ecma262-biblio": "2.1.2657", - "ecmarkup": "18.1.0" - }, - "devDependencies": {} + "ecmarkup": "18.1.0", + "xoshiro128": "^0.1.0" + } }, "node_modules/@babel/code-frame": { "version": "7.12.11", @@ -1359,6 +1359,11 @@ "version": "2.2.0", "resolved": "https://registry.npmjs.org/xmlchars/-/xmlchars-2.2.0.tgz", "integrity": "sha512-JZnDKK8B0RCDw84FNdDAIpZK+JuJw+s7Lz8nksI7SIuU3UXJJslUthsi+uWBUYOwPFwW7W7PRLRfUKpxjtjFCw==" + }, + "node_modules/xoshiro128": { + "version": "0.1.0", + "resolved": "https://registry.npmjs.org/xoshiro128/-/xoshiro128-0.1.0.tgz", + "integrity": "sha512-w0qlyilMmdCT6+sz98aX5Bi9vmn4KMbMCfS4GWVo7UuO5lVUMaQ4MzzN76yAA46dQqbOHQaQh0+LYDVklgmECA==" } }, "dependencies": { @@ -2366,6 +2371,11 @@ "version": "2.2.0", "resolved": "https://registry.npmjs.org/xmlchars/-/xmlchars-2.2.0.tgz", "integrity": "sha512-JZnDKK8B0RCDw84FNdDAIpZK+JuJw+s7Lz8nksI7SIuU3UXJJslUthsi+uWBUYOwPFwW7W7PRLRfUKpxjtjFCw==" + }, + "xoshiro128": { + "version": "0.1.0", + "resolved": "https://registry.npmjs.org/xoshiro128/-/xoshiro128-0.1.0.tgz", + "integrity": "sha512-w0qlyilMmdCT6+sz98aX5Bi9vmn4KMbMCfS4GWVo7UuO5lVUMaQ4MzzN76yAA46dQqbOHQaQh0+LYDVklgmECA==" } } } diff --git a/package.json b/package.json index 7dfad7d..d058146 100644 --- a/package.json +++ b/package.json @@ -8,6 +8,7 @@ }, "dependencies": { "@tc39/ecma262-biblio": "2.1.2657", - "ecmarkup": "18.1.0" + "ecmarkup": "18.1.0", + "xoshiro128": "^0.1.0" } } diff --git a/polyfill.mjs b/polyfill.mjs new file mode 100644 index 0000000..1b523dd --- /dev/null +++ b/polyfill.mjs @@ -0,0 +1,178 @@ +/* +https://www-2.cs.cmu.edu/afs/cs/project/quake/public/papers/robust-arithmetic.ps +Shewchuk's algorithm for exactly floating point addition +as implemented in Python's fsum: https://github.com/python/cpython/blob/48dfd74a9db9d4aa9c6f23b4a67b461e5d977173/Modules/mathmodule.c#L1359-L1474 +adapted to handle overflow via an additional "biased" partial, representing 2**1024 times its actual value +*/ + +// exponent 11111111110, significand all 1s +const MAX_DOUBLE = 1.79769313486231570815e+308; // i.e. (2**1024 - 2**(1023 - 52)) + +// exponent 11111111110, significand all 1s except final 0 +const PENULTIMATE_DOUBLE = 1.79769313486231550856e+308; // i.e. (2**1024 - 2 * 2**(1023 - 52)) + +// exponent 11111001010, significand all 0s +const MAX_ULP = MAX_DOUBLE - PENULTIMATE_DOUBLE; // 1.99584030953471981166e+292, i.e. 2**(1023 - 52) + +// prerequisite: Math.abs(x) >= Math.abs(y) +function twosum(x, y) { + let hi = x + y; + let lo = y - (hi - x); + return { hi, lo }; +} + +export function sum(iterable) { + let partials = []; + + let overflow = 0; // conceptually 2**1024 times this value; the final partial + + // for purposes of the polyfill we're going to ignore closing the iterator, sorry + let iterator = iterable[Symbol.iterator](); + let next = iterator.next.bind(iterator); + + // in C this would be done using a goto + function drainNonFiniteValue(current) { + while (true) { + let { done, value } = next(); + if (done) { + return current; + } + if (!Number.isFinite(value)) { + // summing any distinct two of the three non-finite values gives NaN + // summing any one of them with itself gives itself + if (!Object.is(value, current)) { + current = NaN; + } + } + } + } + + // handle list of -0 special case + while (true) { + let { done, value } = next(); + if (done) { + return -0; + } + if (!Object.is(value, -0)) { + if (!Number.isFinite(value)) { + return drainNonFiniteValue(val); + } + partials.push(value); + break; + } + } + + // main loop + while (true) { + let { done, value } = next(); + if (done) { + break; + } + let x = +value; + if (!Number.isFinite(x)) { + return drainNonFiniteValue(x); + } + + // we're updating partials in place, but it is maybe easier to understand if you think of it as making a new copy + let actuallyUsedPartials = 0; + // let newPartials = []; + for (let y of partials) { + if (Math.abs(x) < Math.abs(y)) { + [x, y] = [y, x]; + } + let { hi, lo } = twosum(x, y); + if (Math.abs(hi) === Infinity) { + let sign = hi === Infinity ? 1 : -1; + overflow += sign; + if (Math.abs(overflow) >= 2**53) { + throw new RangeError('overflow'); + } + + x = (x - sign * 2**1023) - sign * 2**1023; + if (Math.abs(x) < Math.abs(y)) { + [x, y] = [y, x]; + } + 0, { hi, lo } = twosum(x, y); + } + if (lo !== 0) { + partials[actuallyUsedPartials] = lo; + ++actuallyUsedPartials; + // newPartials.push(lo); + } + x = hi; + } + partials.length = actuallyUsedPartials; + // assert.deepStrictEqual(partials, newPartials) + // partials = newPartials + + if (x !== 0) { + partials.push(x); + } + } + + // compute the exact sum of partials, stopping once we lose precision + let n = partials.length - 1; + let hi = 0; + let lo = 0; + + if (overflow !== 0) { + let next = n >= 0 ? partials[n] : 0; + --n; + if (Math.abs(overflow) > 1 || (overflow > 0 && next > 0 || overflow < 0 && next < 0)) { + return overflow > 0 ? Infinity : -Infinity; + } + // here we actually have to do the arithmetic + // drop a factor of 2 so we can do it without overflow + // assert(Math.abs(overflow) === 1) + 0, { hi, lo } = twosum(overflow * 2**1023, next / 2); + lo *= 2; + if (Math.abs(2 * hi) === Infinity) { + // stupid edge case: rounding to the maximum value + // MAX_DOUBLE has a 1 in the last place of its significand, so if we subtract exactly half a ULP from 2**1024, the result rounds away from it (i.e. to infinity) under ties-to-even + // but if the next partial has the opposite sign of the current value, we need to round towards MAX_DOUBLE instead + // this is the same as the "handle rounding" case below, but there's only one potentially-finite case we need to worry about, so we just hardcode that one + if (hi > 0) { + if (hi === 2**1023 && lo === -(MAX_ULP / 2) && n >= 0 && partials[n] < 0) { + return MAX_DOUBLE; + } + return Infinity; + } else { + if (hi === -(2**1023) && lo === (MAX_ULP / 2) && n >= 0 && partials[n] > 0) { + return -MAX_DOUBLE; + } + return -Infinity; + } + } + if (lo !== 0) { + partials[n + 1] = lo; + ++n; + lo = 0; + } + hi *= 2; + } + + while (n >= 0) { + let x = hi; + let y = partials[n]; + --n; + // assert: Math.abs(x) > Math.abs(y) + 0, { hi, lo } = twosum(x, y); + if (lo !== 0) { + break; + } + } + + // handle rounding + // when the roundoff error is exactly half of the ULP for the result, we need to check one more partial to know which way to round + if (n >= 0 && ((lo < 0.0 && partials[n] < 0.0) || + (lo > 0.0 && partials[n] > 0.0))) { + let y = lo * 2.0; + let x = hi + y; + let yr = x - hi; + if (y === yr) { + hi = x; + } + } + + return hi; +} diff --git a/test-full-precision-with-bigints.mjs b/test-full-precision-with-bigints.mjs new file mode 100644 index 0000000..83038a1 --- /dev/null +++ b/test-full-precision-with-bigints.mjs @@ -0,0 +1,71 @@ +import test from 'node:test'; +import assert from 'node:assert'; + +import { Random } from 'xoshiro128/random'; + +import { randomFloat } from './float-tools.mjs'; + +import { floatToBigInt, bigIntToFloat } from './full-precision-with-bigints.mjs'; + +let largestSubnormal = 2.22507385850720088902e-308; +let smallestNormal = 2.22507385850720138309e-308; +let smallest = 4.94065645841246544177e-324; + +function sum(a, b) { + return bigIntToFloat(floatToBigInt(a) + floatToBigInt(b)); +} + +function checkRoundTrip(a) { + assert.strictEqual(bigIntToFloat(floatToBigInt(a)), a); +} + +function checkSum(a, b) { + let actual = sum(a, b); + let expected = a + b; + if (!Object.is(actual, expected)) { + if (Object.is(a, -0) && Object.is(b, -0)) { + // bigint can't represent -0 + return; + } + console.error(a); + console.error(b); + } + assert.strictEqual(actual, expected); +} + +test('basic round-tripping', t => { + checkRoundTrip(largestSubnormal); + checkRoundTrip(smallestNormal); + checkRoundTrip(smallest); +}); + +test('round ties to even', t => { + let half11Delta = 8.88178419700125232339e-16; + let nextFloatAfterHalf11Delta = 8.88178419700125429554e-16; + + let eleventPlusSignificandOne = 11.0000000000000017764; + let eleventPlusSignificandTwo = 11.0000000000000035527; + + assert.strictEqual(sum(11, half11Delta), 11); + assert.strictEqual(sum(eleventPlusSignificandOne, half11Delta), eleventPlusSignificandTwo); +}); + +test('subnormal edge cases', t => { + assert.strictEqual(sum(largestSubnormal, smallest), smallestNormal); + assert.strictEqual(sum(smallestNormal, -smallest), largestSubnormal); +}); + +test('fuzzing', t => { + let seed = Math.floor(Math.random() * 2 ** 31); + console.log('fuzzer seed', seed); + let random = new Random(seed); + let N = 10_000_000; + for (let i = 0; i < N; ++i) { + if ((i % 1_000_000) === 0) { + console.log(i); + } + let a = randomFloat(random); + let b = randomFloat(random); + checkSum(a, b); + } +}); diff --git a/test-polyfill.mjs b/test-polyfill.mjs new file mode 100644 index 0000000..861d537 --- /dev/null +++ b/test-polyfill.mjs @@ -0,0 +1,97 @@ +import assert from 'node:assert'; +import test from 'node:test'; + +import { Random } from 'xoshiro128/random'; + +import { sum as mathSum } from './polyfill.mjs'; + +import { floatToBigInt, bigIntToFloat } from './full-precision-with-bigints.mjs'; +import { randomFloat } from './float-tools.mjs'; + + +function sumViaBigInt(iterable) { + let sum = 0n; + for (let x of iterable) { + sum += floatToBigInt(x); + } + return bigIntToFloat(sum); +} + +function check(data) { + let actual; + try { + actual = mathSum(data); + } catch (e) { + console.log({ data }); + throw e; + } + let expected = sumViaBigInt(data); + if (!Object.is(actual, expected)) { + console.log({ data, actual, expected }); + } + assert.strictEqual(actual, expected); +} + +test('basic ability to handle intermediate overflows', t => { + check([1e308, 1e308, 0.1, 0.1, 1e30, 0.1, -1e30, -1e308, -1e308]); +}); + +test('special cases', t => { + assert.strictEqual(mathSum([]), -0); + assert.strictEqual(mathSum([-0, -0, -0]), -0); + assert.strictEqual(mathSum([-0, -0, -0, 0]), 0); + assert.strictEqual(mathSum([1, Infinity, -1e308]), Infinity); + assert.strictEqual(mathSum([1, Infinity, -1e308, -Infinity]), NaN); +}); + +test('1, 2 element lists', t => { + check([1e308]); + check([1e308, 1e308]); + check([1e308, -1e308]); + check([.1]); + check([.1, .1]); + check([.1, -.1]); +}); + +test('some edge cases from the fuzzer', t => { + check([8.98846567431158e+307, 8.988465674311579e+307, -1.7976931348623157e+308]); + + check([-5.630637621603525e+255, 9.565271205476345e+307, 2.9937604643020797e+292]); + + check([6.739986666787661e+66, 2, -1.2689709186578243e-116, 1.7046015739467354e+308, -9.979201547673601e+291, 6.160926733208294e+307, -3.179557053031852e+234, -7.027282978772846e+307, -0.7500000000000001]); + + check([0.31150493246968836, -8.988465674311582e+307, 1.8315037361673755e-270, -15.999999999999996, 2.9999999999999996, 7.345200721499384e+164, -2.033582473639399, -8.98846567431158e+307, -3.5737295155405993e+292, 4.13894772383715e-124, -3.6111186457260667e-35, 2.387234887098013e+180, 7.645295562778372e-298, 3.395189016861822e-103, -2.6331611115768973e-149]) + + check([-1.1442589134409902e+308, 9.593842098384855e+138, 4.494232837155791e+307, -1.3482698511467367e+308, 4.494232837155792e+307]); + check([-1.1442589134409902e+308, 4.494232837155791e+307, -1.3482698511467367e+308, 4.494232837155792e+307]); + + check([9.593842098384855e+138, -6.948356297254111e+307, -1.3482698511467367e+308, 4.494232837155792e+307]); + + check([-2.534858246857893e+115, 8.988465674311579e+307, 8.98846567431158e+307]) + + check([1.3588124894186193e+308, 1.4803986201152006e+223, 6.741349255733684e+307]); + + check([6.741349255733684e+307, 1.7976931348623155e+308, -7.388327292663961e+41]); + + check([-1.9807040628566093e+28, 1.7976931348623157e+308, 9.9792015476736e+291]); + + check([-1.0214557991173964e+61, 1.7976931348623157e+308, 8.98846567431158e+307, -8.988465674311579e+307]); +}); + +test('fuzzing', t => { + let seed = Math.floor(Math.random() * 2 ** 31); + console.log('fuzzer seed', seed); + let random = new Random(seed); + let N = 10_000_000; + for (let i = 0; i < N; ++i) { + if ((i % 1_000_000) === 0) { + console.log(i); + } + let data = []; + let length = random.int(3, 10); + for (let j = 0; j < length; ++j) { + data.push(randomFloat(random)); + } + check(data); + } +}); From cf2a8bf4b52709574c6f7e81f1a3eae2cf4d6368 Mon Sep 17 00:00:00 2001 From: Kevin Gibbons Date: Thu, 14 Dec 2023 15:59:07 -0800 Subject: [PATCH 2/4] move files, update spec/readme --- .github/workflows/build.yml | 7 ++-- .github/workflows/deploy.yml | 8 ++-- README.md | 14 ++++--- package.json | 3 +- float-tools.mjs => polyfill/float-tools.mjs | 0 .../full-precision-with-bigints.mjs | 0 polyfill.mjs => polyfill/polyfill.mjs | 0 .../test-full-precision-with-bigints.mjs | 4 +- .../test-polyfill.mjs | 7 ++-- spec.html | 38 ++++++++++++------- 10 files changed, 49 insertions(+), 32 deletions(-) rename float-tools.mjs => polyfill/float-tools.mjs (100%) rename full-precision-with-bigints.mjs => polyfill/full-precision-with-bigints.mjs (100%) rename polyfill.mjs => polyfill/polyfill.mjs (100%) rename test-full-precision-with-bigints.mjs => polyfill/test-full-precision-with-bigints.mjs (97%) rename test-polyfill.mjs => polyfill/test-polyfill.mjs (95%) diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml index 090b033..a5d4137 100644 --- a/.github/workflows/build.yml +++ b/.github/workflows/build.yml @@ -11,10 +11,11 @@ jobs: runs-on: ubuntu-latest steps: - - uses: actions/checkout@v2 - - uses: actions/setup-node@v3 + - uses: actions/checkout@v4 + - uses: actions/setup-node@v4 with: - node-version: 16 + node-version: 20 - run: npm ci - run: npm run build - run: npm run check-format + - run: npm run test diff --git a/.github/workflows/deploy.yml b/.github/workflows/deploy.yml index f42245b..a7501d0 100644 --- a/.github/workflows/deploy.yml +++ b/.github/workflows/deploy.yml @@ -12,13 +12,13 @@ jobs: runs-on: ubuntu-latest steps: - - uses: actions/checkout@v2 - - uses: actions/setup-node@v3 + - uses: actions/checkout@v4 + - uses: actions/setup-node@v4 with: - node-version: 16 + node-version: 20 - run: npm ci - run: npm run build - - uses: JamesIves/github-pages-deploy-action@v4.4.3 + - uses: JamesIves/github-pages-deploy-action@v4.5.0 with: branch: gh-pages folder: dist diff --git a/README.md b/README.md index 5b9dc26..f1986f4 100644 --- a/README.md +++ b/README.md @@ -8,31 +8,33 @@ Authors: Kevin Gibbons Champions: Kevin Gibbons -This proposal is at Stage 0 of [the TC39 process](https://tc39.es/process-document/) - it has not yet been presented to committee. +This proposal is at Stage 1 of [the TC39 process](https://tc39.es/process-document/): the proposal is under consideration. ## Motivation Summing a list is a very common operation and is one of the few remaining use cases for `Array.prototype.reduce`. Better to let users express that operation directy. -Also, floating point summation can get more precise results than the naive `.reduce((a, b) => a + b, 0)` approach using [more clever algorithms](https://en.wikipedia.org/wiki/Kahan_summation_algorithm) with very little overhead, a fact which few JavaScript programmers are aware of (and even among those who are, most wouldn't bother doing it). We can make it easy to reach for the better option. +Also, summing a list of floating point numbers can be done more precisely than the naive `.reduce((a, b) => a + b, 0)` approach using more clever algorithms, a fact which few JavaScript programmers are aware of (and even among those who are, most wouldn't bother doing it). We can make it easy to reach for the better option. ## Proposal Add a variadic `Math.sum` method which returns the sum of its arguments using a more clever algorithm than naive summation. ```js -let values = Array.from({ length: 10 }).fill(0.1); +let values = [1e20, 0.1, -1e20]; -values.reduce((a, b) => a + b, 0); // 0.9999999999999999 +values.reduce((a, b) => a + b, 0); // 0 -Math.sum(...values); // 1 +Math.sum(...values); // 0.1 ```` ## Questions ### Which algorithm? -I'm hoping to get away with leaving it up to implementations. If we have to pick one, I would go with Neumaier's variant of Kahan summation. Python [adopted it](https://github.com/python/cpython/issues/100425) for their built-in `sum` in 3.12, with about 25-30% slowdown relative to naive summation. I think that's easily worth it. +Instead of specifying any particular algorithm, this proposal requires the maximally correct answer - that is, the answer you'd get if you did arbitrary-precision arithmetic, then converted the result back to floats. This can be done without actually needing arbitrary-precision arithmetic. One way of doing this is given in [Shewchuk '96](./Shewchuk-robust-arithmetic.pdf), which I've [implemented in JS](./polyfill/polyfill.mjs) (plus some details to handle intermediate overflow). Other strategies are possible. + +Python's [`math.fsum`](https://docs.python.org/3/library/math.html#math.fsum) is currently implemented using the same algorithm (though without handling intermediate overflow). ### What if I have a long list, such that I can't reasonably put it on the stack with `...args`? diff --git a/package.json b/package.json index d058146..39d729a 100644 --- a/package.json +++ b/package.json @@ -4,7 +4,8 @@ "build": "mkdir -p dist && ecmarkup --lint-spec --strict --load-biblio @tc39/ecma262-biblio --verbose --assets-dir dist spec.html dist/index.html", "build-biblio": "ecmarkup --write-biblio proposal-iterator-helpers-biblio.json --lint-spec --strict --load-biblio @tc39/ecma262-biblio --verbose spec.html /dev/null", "format": "emu-format --write spec.html", - "check-format": "emu-format --check spec.html" + "check-format": "emu-format --check spec.html", + "test": "node --test" }, "dependencies": { "@tc39/ecma262-biblio": "2.1.2657", diff --git a/float-tools.mjs b/polyfill/float-tools.mjs similarity index 100% rename from float-tools.mjs rename to polyfill/float-tools.mjs diff --git a/full-precision-with-bigints.mjs b/polyfill/full-precision-with-bigints.mjs similarity index 100% rename from full-precision-with-bigints.mjs rename to polyfill/full-precision-with-bigints.mjs diff --git a/polyfill.mjs b/polyfill/polyfill.mjs similarity index 100% rename from polyfill.mjs rename to polyfill/polyfill.mjs diff --git a/test-full-precision-with-bigints.mjs b/polyfill/test-full-precision-with-bigints.mjs similarity index 97% rename from test-full-precision-with-bigints.mjs rename to polyfill/test-full-precision-with-bigints.mjs index 83038a1..ceb8ff6 100644 --- a/test-full-precision-with-bigints.mjs +++ b/polyfill/test-full-precision-with-bigints.mjs @@ -59,9 +59,9 @@ test('fuzzing', t => { let seed = Math.floor(Math.random() * 2 ** 31); console.log('fuzzer seed', seed); let random = new Random(seed); - let N = 10_000_000; + let N = 1_000_000; for (let i = 0; i < N; ++i) { - if ((i % 1_000_000) === 0) { + if ((i % 100_000) === 0) { console.log(i); } let a = randomFloat(random); diff --git a/test-polyfill.mjs b/polyfill/test-polyfill.mjs similarity index 95% rename from test-polyfill.mjs rename to polyfill/test-polyfill.mjs index 861d537..286d9b1 100644 --- a/test-polyfill.mjs +++ b/polyfill/test-polyfill.mjs @@ -32,8 +32,9 @@ function check(data) { assert.strictEqual(actual, expected); } -test('basic ability to handle intermediate overflows', t => { +test.only('basic ability to handle intermediate overflows', t => { check([1e308, 1e308, 0.1, 0.1, 1e30, 0.1, -1e30, -1e308, -1e308]); + check([1e30, 0.1, -1e30]); }); test('special cases', t => { @@ -82,9 +83,9 @@ test('fuzzing', t => { let seed = Math.floor(Math.random() * 2 ** 31); console.log('fuzzer seed', seed); let random = new Random(seed); - let N = 10_000_000; + let N = 1_000_000; for (let i = 0; i < N; ++i) { - if ((i % 1_000_000) === 0) { + if ((i % 100_000) === 0) { console.log(i); } let data = []; diff --git a/spec.html b/spec.html index 7ce67a4..0dda81a 100644 --- a/spec.html +++ b/spec.html @@ -3,7 +3,7 @@

@@ -20,22 +20,34 @@

Introduction

Math.sum ( ..._args_ )

-

Given zero or more arguments, this function calls ToNumber on each of the arguments and returns their sum with at most constant error from floating-point operations.

+

Given zero or more arguments, this function calls ToNumber on each of the arguments and returns their sum.

It performs the following steps when called:

- 1. Let _coerced_ be a new empty List. + 1. Let _state_ be ~minus-zero~. + 1. Let _sum_ be 0. + 1. Let _count_ be 0. 1. For each element _arg_ of _args_, do + 1. Set _count_ to _count_ + 1. + 1. If _count_ ≥ 253, throw a *RangeError* exception. + 1. NOTE: The above case is not expected to be reached in practice and is included only so that implementations may rely on inputs being "reasonably sized" without violating this specification. 1. Let _n_ be ? ToNumber(_arg_). - 1. Append _n_ to _coerced_. - 1. If _coerced_ is empty, return *+0*𝔽. - 1. If _coerced_ contains *NaN*, return *NaN*. - 1. If _coerced_ contains *+∞*𝔽, then - 1. If _coerced_ contains *-∞*𝔽, return *NaN*. - 1. Return *+∞*𝔽. - 1. If _coerced_ contains *-∞*𝔽, then - 1. Return *-∞*𝔽. - 1. If every element of _coerced_ is *-0*𝔽, return *-0*𝔽. - 1. Return an implementation-approximated value for the sum of the elements of _coerced_. Implementations are recommended to use algorithm such as
that of Neumaier to achieve better error than naive floating-point summation. + 1. If _state_ is not ~NaN~, then + 1. If _n_ is *NaN*, set _state_ to ~NaN~. + 1. If _n_ is *+∞*𝔽, then + 1. If _state_ is ~minus-infinity~, set _state_ to ~NaN~. + 1. Else, set _state_ to ~plus-infinity~. + 1. If _n_ is *-∞*𝔽, then + 1. If _state_ is ~plus-infinity~, set _state_ to ~NaN~. + 1. Else, set _state_ to ~minus-infinity~. + 1. If _n_ is not *-0*𝔽 and _state_ is either ~minus-zero~ or ~finite~, then + 1. Set _state_ to ~finite~. + 1. Set _sum_ to _sum_ + ℝ(_n_). + 1. If _state_ is ~NaN~, return *NaN*. + 1. If _state_ is ~plus-infinity~, return *+∞*𝔽. + 1. If _state_ is ~minus-infinity~, return *-∞*𝔽. + 1. If _state_ is ~minus-zero~, return *-0*𝔽. + 1. Return 𝔽(_sum_). + 1. NOTE: The value of _sum_ can be computed without arbitrary-precision arithmetic by a variety of algoirthms. One such is the "Expansion Sum" algorithm given in Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates by Jonathan Richard Shewchuk.

The *"length"* property of this function is *2*𝔽.

From 6245f378e8d403f5cef52eb965b794e7ce391e21 Mon Sep 17 00:00:00 2001 From: Kevin Gibbons Date: Thu, 14 Dec 2023 16:31:25 -0800 Subject: [PATCH 3/4] satisfy linter --- polyfill/polyfill.mjs | 6 ++++++ spec.html | 10 +++++----- 2 files changed, 11 insertions(+), 5 deletions(-) diff --git a/polyfill/polyfill.mjs b/polyfill/polyfill.mjs index 1b523dd..6bb4b2d 100644 --- a/polyfill/polyfill.mjs +++ b/polyfill/polyfill.mjs @@ -108,6 +108,7 @@ export function sum(iterable) { if (x !== 0) { partials.push(x); } + console.log(partials); } // compute the exact sum of partials, stopping once we lose precision @@ -176,3 +177,8 @@ export function sum(iterable) { return hi; } + +let naiveSum = ar => ar.reduce((a, b) => a+b); +let v = [0, 1, 2, 1000, 0.77, 0.4123, 1274123] +console.log(sum(v)); +console.log(naiveSum(v)); diff --git a/spec.html b/spec.html index 0dda81a..868311a 100644 --- a/spec.html +++ b/spec.html @@ -31,18 +31,18 @@

Math.sum ( ..._args_ )

1. If _count_ ≥ 253, throw a *RangeError* exception. 1. NOTE: The above case is not expected to be reached in practice and is included only so that implementations may rely on inputs being "reasonably sized" without violating this specification. 1. Let _n_ be ? ToNumber(_arg_). - 1. If _state_ is not ~NaN~, then - 1. If _n_ is *NaN*, set _state_ to ~NaN~. + 1. If _state_ is not ~not-a-number~, then + 1. If _n_ is *NaN*, set _state_ to ~not-a-number~. 1. If _n_ is *+∞*𝔽, then - 1. If _state_ is ~minus-infinity~, set _state_ to ~NaN~. + 1. If _state_ is ~minus-infinity~, set _state_ to ~not-a-number~. 1. Else, set _state_ to ~plus-infinity~. 1. If _n_ is *-∞*𝔽, then - 1. If _state_ is ~plus-infinity~, set _state_ to ~NaN~. + 1. If _state_ is ~plus-infinity~, set _state_ to ~not-a-number~. 1. Else, set _state_ to ~minus-infinity~. 1. If _n_ is not *-0*𝔽 and _state_ is either ~minus-zero~ or ~finite~, then 1. Set _state_ to ~finite~. 1. Set _sum_ to _sum_ + ℝ(_n_). - 1. If _state_ is ~NaN~, return *NaN*. + 1. If _state_ is ~not-a-number~, return *NaN*. 1. If _state_ is ~plus-infinity~, return *+∞*𝔽. 1. If _state_ is ~minus-infinity~, return *-∞*𝔽. 1. If _state_ is ~minus-zero~, return *-0*𝔽. From 1de99b3fc7fce7021fdc498188085d803db46bc2 Mon Sep 17 00:00:00 2001 From: Kevin Gibbons Date: Sun, 17 Dec 2023 21:31:22 -0800 Subject: [PATCH 4/4] one more fix --- README.md | 2 +- polyfill/polyfill.mjs | 1 - polyfill/test-polyfill.mjs | 2 +- 3 files changed, 2 insertions(+), 3 deletions(-) diff --git a/README.md b/README.md index f1986f4..1061830 100644 --- a/README.md +++ b/README.md @@ -18,7 +18,7 @@ Also, summing a list of floating point numbers can be done more precisely than t ## Proposal -Add a variadic `Math.sum` method which returns the sum of its arguments using a more clever algorithm than naive summation. +Add a variadic `Math.sum` method which returns the sum of its arguments using a more precise algorithm than naive summation. ```js let values = [1e20, 0.1, -1e20]; diff --git a/polyfill/polyfill.mjs b/polyfill/polyfill.mjs index 6bb4b2d..0b88c01 100644 --- a/polyfill/polyfill.mjs +++ b/polyfill/polyfill.mjs @@ -108,7 +108,6 @@ export function sum(iterable) { if (x !== 0) { partials.push(x); } - console.log(partials); } // compute the exact sum of partials, stopping once we lose precision diff --git a/polyfill/test-polyfill.mjs b/polyfill/test-polyfill.mjs index 286d9b1..9a01a11 100644 --- a/polyfill/test-polyfill.mjs +++ b/polyfill/test-polyfill.mjs @@ -32,7 +32,7 @@ function check(data) { assert.strictEqual(actual, expected); } -test.only('basic ability to handle intermediate overflows', t => { +test('basic ability to handle intermediate overflows', t => { check([1e308, 1e308, 0.1, 0.1, 1e30, 0.1, -1e30, -1e308, -1e308]); check([1e30, 0.1, -1e30]); });

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