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@Yaffle
Yaffle committed Jan 23, 2024
1 parent fa1a693 commit 716d428
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52 changes: 29 additions & 23 deletions BigDecimal.js
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Original file line number Diff line number Diff line change
@@ -1,4 +1,4 @@
/*jslint bigint: true, vars: true, indent: 2*/
/*jslint bigint: true, vars: true, indent: 2, esversion:11*/

// https://github.com/tc39/proposal-decimal
// https://en.wikipedia.org/wiki/Floating-point_arithmetic
Expand All @@ -23,20 +23,6 @@
// a.toPrecision(precision[, roundingMode = "half-up"])
// a.toExponential(fractionDigits[, roundingMode = "half-up"])

// Math: (not in the spec)
// BigDecimal.log(a, rounding)
// BigDecimal.exp(a, rounding)
// BigDecimal.sin(a, rounding)
// BigDecimal.cos(a, rounding)
// BigDecimal.atan(a, rounding)
// BigDecimal.sqrt(a, rounding)

// "simple" Math functions:
// BigDecimal.abs(a)
// BigDecimal.sign(a)
// BigDecimal.max(a, b)
// BigDecimal.min(a, b)

// (!) Note: consider to use only "half-even" rounding mode and rounding to a maximum number of significant digits for floating-point arithmetic,
// or only "floor" rounding to a maximum number of fraction digits for fixed-point arithmetic.
// BigFloat may have better performance.
Expand All @@ -51,6 +37,11 @@ const factory = function (BASE, format = null) {

const defaultRounding = format === 'decimal128' ? {maximumFractionDigits: 6176, maximumSignificantDigits: 34, roundingMode: 'half-even'} : null;

function getExponent(number) {
const e = Math.floor(Math.log(Math.abs(number)) / Math.log(2)) - 1;
return Math.abs(number) / 2**e >= 2 ? e + 1 : e;
}

function convert(value) {
if (value instanceof BigDecimal) {
return value;
Expand Down Expand Up @@ -154,6 +145,21 @@ const toBigInt = function (a) {
}
return bigIntScale(a.significand, exponent);
};

const abs = function (a) {
return a.significand < 0n ? BigDecimal.unaryMinus(a) : a;
};

function getCountOfDigits(a) { // floor(log(abs(a))/log(BASE)) + 1
if (a.significand === 0n) {
throw new RangeError();
}
return BigInt(digits(a.significand)) + BigInt(a.exponent);
}
function exponentiateBase(n) {
return create(BASE, n);
}

function create(significand, exponent) {
return /*Object.freeze(*/new BigDecimal(significand, exponent)/*)*/;
}
Expand Down Expand Up @@ -705,13 +711,13 @@ BigDecimal.prototype.toFixed = function (fractionDigits, roundingMode = "half-up
const value = BASE === 10 ? create(this.significand, sum(this.exponent, fractionDigits)) : BigDecimal.multiply(convert(10n**BigInt(fractionDigits)), this);
const sign = value.significand < 0n ? "-" : "";
const rounded = BigDecimal.round(value, {maximumFractionDigits: 0, roundingMode: roundingMode});
const a = BigDecimal.abs(rounded);
const a = abs(rounded);
return sign + toFixed(toBigInt(a).toString(), 0 - fractionDigits, fractionDigits);
};

function getDecimalSignificantAndExponent(value, precision, roundingMode) {
if (BASE === 10) {
const x = BigDecimal.round(BigDecimal.abs(value), {maximumSignificantDigits: precision, roundingMode: roundingMode});
const x = BigDecimal.round(abs(value), {maximumSignificantDigits: precision, roundingMode: roundingMode});
return {significand: x.significand.toString(), exponent: BigInt(x.exponent)};
}
//TODO: fix performance, test
Expand Down Expand Up @@ -759,7 +765,7 @@ function getDecimalSignificantAndExponent(value, precision, roundingMode) {
let result = undefined;
let fd = 0n;
do {
let x = BigDecimal.abs(value);
let x = abs(value);
fd = 0n - logarithm(x, 10, rounding);
x = BigDecimal.multiply(exponentiate(ten, fd, rounding), x, rounding);
if (BigDecimal.cmp(x, ten) >= 0) {
Expand All @@ -774,15 +780,15 @@ function getDecimalSignificantAndExponent(value, precision, roundingMode) {
fd += BigInt(precision - 1);
//TODO: ?
if (rounding.maximumSignificantDigits > (Math.abs(Number(fd)) + precision) * Math.log2(10) + digits(value.significand)) {
x = BigDecimal.abs(value);
x = abs(value);
x = BigDecimal.multiply(x, exponentiate(ten, fd, rounding), rounding)
result = toBigInt(BigDecimal.abs(roundToInteger(x))).toString();
result = toBigInt(abs(roundToInteger(x))).toString();
} else {
x = BigDecimal.multiply(x, exponentiate(ten, BigInt(precision - 1), rounding), rounding);
x = BigDecimal.abs(x);
const error = BigDecimal.multiply(BigDecimal.multiply(convert(bigIntAbs(fd) + BigInt(precision)), exponentiateBase(BASE, 0 - rounding.maximumSignificantDigits)), x);
x = abs(x);
const error = BigDecimal.multiply(BigDecimal.multiply(convert(bigIntAbs(fd) + BigInt(precision)), exponentiateBase(0 - rounding.maximumSignificantDigits)), x);
if (BigDecimal.cmp(roundToInteger(BigDecimal.add(x, error)), roundToInteger(BigDecimal.subtract(x, error))) === 0) {
result = toBigInt(BigDecimal.abs(roundToInteger(x))).toString();
result = toBigInt(abs(roundToInteger(x))).toString();
}
}
}
Expand Down
166 changes: 145 additions & 21 deletions BigDecimalMath.js
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Original file line number Diff line number Diff line change
@@ -1,19 +1,146 @@
/*jshint esversion:11*/

// Math: (not in the spec)
// BigDecimal.log(a, rounding)
// BigDecimal.exp(a, rounding)
// BigDecimal.sin(a, rounding)
// BigDecimal.cos(a, rounding)
// BigDecimal.atan(a, rounding)
// BigDecimal.sqrt(a, rounding)

// "simple" Math functions:
// BigDecimal.abs(a)
// BigDecimal.sign(a)
// BigDecimal.max(a, b)
// BigDecimal.min(a, b)

function addMath(BigDecimal, BASE) {

const BASE_LOG2_INV = 1 / Math.log2(BASE);
const BIGINT_BASE = BigInt(BASE);

function convert(x) {
return BigDecimal(x);
}

//TODO: REMOVE(?)
const exponentiate = function (x, n) {
if (n < 0n) {
return BigDecimal.divide(convert(1), exponentiate(x, -BigInt(n)));
}
let y = undefined;
while (n >= 1n) {
if (n % 2n === 0n) {
x = BigDecimal.multiply(x, x);
n /= 2n;
} else {
y = y == undefined ? x : BigDecimal.multiply(x, y);
n -= 1n;
}
}
return y == undefined ? convert(1) : y;
};

function exponentiateBase(n) {
//TODO: !?
//return create(1n, n);
return exponentiate(convert(BASE), BigInt(n));
}

function bigIntAbs(a) {
return a < 0n ? 0n - a : a;
}

const NumberSafeBits = Math.floor(Math.log2(Number.MAX_SAFE_INTEGER + 1));

function bitLength(a) {
const s = a.toString(16);
const c = +s.charCodeAt(0) - "0".charCodeAt(0);
if (c <= 0) {
throw new RangeError();
}
return (s.length - 1) * 4 + (32 - Math.clz32(Math.min(c, 8)));
}

function exponentiate(a, n) {
if (+a !== BASE) {
throw new RangeError("a should be BASE");//?
function bigIntLog2(n) {
const k = bitLength(n) - NumberSafeBits;
const leadingDigits = Number(n >> BigInt(k));
return Math.log2(leadingDigits) + k;
}

//TODO: REMOVE(?)
function digits(a) { // floor(log(abs(a)) / log(BASE)) + 1
a = bigIntAbs(a);
if (BASE === 2) {
return bitLength(a);
}
const number = Number(BigInt(a));
if (number < (Number.MAX_SAFE_INTEGER + 1) / 16) {
return Math.floor(Math.log2(number + 0.5) * BASE_LOG2_INV) + 1;
}
const e = (number < 1 / 0 ? Math.log2(number) : bigIntLog2(a)) * BASE_LOG2_INV;
if (Math.floor(e * (1 - 32 / (Number.MAX_SAFE_INTEGER + 1))) === Math.floor(e) &&
Math.floor(e * (1 + 32 / (Number.MAX_SAFE_INTEGER + 1))) === Math.floor(e)) {
return Math.floor(e) + 1;
}
const i = Math.floor(e + 0.5);
return a >= BigInt(cachedPower(i)) ? i + 1 : i;
}

function cachedFunction(f) {
let cache = {};
let cacheSize = 0;
return function (k) {
let lastValue = cache[k];
if (lastValue == null) {
if (cacheSize > 100) {
cache = {};
cacheSize = 0;
}
lastValue = f(k);
cache[k] = lastValue;
cacheSize += 1;
}
return lastValue;
};
}
const cachedBigInt = cachedFunction(function (k) {
// k === maximumFractionDigits
return BigInt(k);
});
const cachedPower = cachedFunction(function (k) {
return BIGINT_BASE**BigInt(k);
});

function bigIntScale(a, scaling) {
if (typeof a !== 'bigint') {
throw new TypeError();
}
return create(1n, n);
return (BASE === 2 ? (a << cachedBigInt(scaling)) : cachedPower(scaling) * a);
}
function exponentiateBase(a, n) {
return exponentiate(a, n);
function bigIntUnscale(a, unscaling) {
if (typeof a !== 'bigint') {
throw new TypeError();
}
return (BASE === 2 ? (a >> cachedBigInt(unscaling)) : a / cachedPower(unscaling));
}

//TODO: remove
const toBigInt = function (a) {
const e = a.exponent;
const exponent = typeof e === 'number' ? e : Number(BigInt(e));
if (exponent === 0) {
return a.significand;
}
if (exponent < 0) {
const result = bigIntUnscale(a.significand, 0 - exponent);
if (bigIntScale(result, 0 - exponent) !== BigInt(a.significand)) {
throw new RangeError("The BigDecimal " + a.toString() + " cannot be converted to a BigInt because it is not an integer");
}
return result;
}
return bigIntScale(a.significand, exponent);
};

function getCountOfDigits(a) { // floor(log(abs(a))/log(BASE)) + 1
if (a.significand === 0n) {
Expand Down Expand Up @@ -59,10 +186,6 @@ function significandDigits(a) {
return to;
}

function getExponent(number) {
const e = Math.floor(Math.log(Math.abs(number)) / Math.log(2)) - 1;
return Math.abs(number) / 2**e >= 2 ? e + 1 : e;
}



Expand Down Expand Up @@ -118,7 +241,7 @@ function tryToMakeCorrectlyRounded(specialValue, f, name) {
result = f(x, internalRounding);
}
// round(result - error) === round(result + error)
error = BigDecimal.multiply(exponentiate(BASE, -BigInt(internalRounding.maximumSignificantDigits)), BigDecimal.abs(result));
error = BigDecimal.multiply(exponentiateBase(-BigInt(internalRounding.maximumSignificantDigits)), BigDecimal.abs(result));
//if (i > 0) {
//console.log(i, f.name, x + "", result + "", error + "", BigDecimal.round(BigDecimal.subtract(result, error), rounding) + "", BigDecimal.round(BigDecimal.add(result, error), rounding) + "");
//}
Expand Down Expand Up @@ -153,15 +276,15 @@ BigDecimal.log = tryToMakeCorrectlyRounded(1, function log(x, rounding) {
if (true) {
//! ln(f * BASE**k) = ln(f) + k * ln(BASE), where (1/BASE) <= f <= BASE
let k = getCountOfDigits(x) - 1n;
let f = BigDecimal.multiply(exponentiate(BASE, -k), x);
let f = BigDecimal.multiply(exponentiateBase(-k), x);
let ff = BigDecimal.round(BigDecimal.multiply(f, f), {maximumSignificantDigits: 3, roundingMode: "half-even"});
if (BigDecimal.cmp(ff, exponentiate(BASE, 1n)) > 0) {
if (BigDecimal.cmp(ff, exponentiateBase(1n)) > 0) {
k += 1n;
f = BigDecimal.multiply(exponentiate(BASE, -1n), f);
f = BigDecimal.multiply(exponentiateBase(-1n), f);
}
if (BigDecimal.cmp(ff, exponentiate(BASE, -1n)) < 0) {
if (BigDecimal.cmp(ff, exponentiateBase(-1n)) < 0) {
k -= 1n;
f = BigDecimal.multiply(exponentiate(BASE, 1n), f);
f = BigDecimal.multiply(exponentiateBase(1n), f);
}
if (k !== 0n) {
return BigDecimal.add(BigDecimal.log(f, internalRounding), BigDecimal.multiply(convert(2n * k), BigDecimal.log(sqrt(convert(BASE), internalRounding), internalRounding)));
Expand Down Expand Up @@ -206,7 +329,7 @@ BigDecimal.exp = tryToMakeCorrectlyRounded(0, function exp(x, rounding) {
const k = BigDecimal.round(BigDecimal.divide(x, logBASE, {maximumSignificantDigits: Math.max(Number(getCountOfDigits(x)), 1), roundingMode: "half-even"}), {maximumFractionDigits: 0, roundingMode: "half-even"});
if (BigDecimal.cmp(k, convert(0)) !== 0) {
const r = BigDecimal.subtract(x, BigDecimal.multiply(k, logBASE));
return BigDecimal.multiply(exponentiate(BASE, toBigInt(k)), BigDecimal.exp(r, internalRounding));
return BigDecimal.multiply(exponentiateBase(toBigInt(k)), BigDecimal.exp(r, internalRounding));
}
}
}
Expand Down Expand Up @@ -317,14 +440,14 @@ BigDecimal.sqrt = function (x, rounding) {
}
// https://en.wikipedia.org/wiki/Nth_root#Using_Newton's_method
const e = getCountOfDigits(x) / 2n;
const t = exponentiate(BASE, e);
const y = BigDecimal.multiply(x, exponentiate(BASE, -(2n * e)));
const t = exponentiateBase(e);
const y = BigDecimal.multiply(x, exponentiateBase(-(2n * e)));
const k = Math.floor(Math.log2(Number.MAX_SAFE_INTEGER + 1) * BASE_LOG2_INV) - 1;
const xn = Number(toBigInt(BigDecimal.round(BigDecimal.multiply(y, exponentiate(BASE, k)), {maximumFractionDigits: 0, roundingMode: "half-even"}))) / BASE**k;
const xn = Number(toBigInt(BigDecimal.round(BigDecimal.multiply(y, exponentiateBase(k)), {maximumFractionDigits: 0, roundingMode: "half-even"}))) / BASE**k;
const r = Math.sqrt(xn);
//TODO: fix
const resultSignificantDigits = 2 * (rounding.maximumSignificantDigits || (rounding.maximumFractionDigits + Math.ceil(significandDigits(x) / 2)) || 1);
let result = BigDecimal.multiply(convert(Math.sign(r) * Math.floor(Math.abs(r) * BASE**k + 0.5)), exponentiate(BASE, -k));
let result = BigDecimal.multiply(convert(Math.sign(r) * Math.floor(Math.abs(r) * BASE**k + 0.5)), exponentiateBase(-k));
const iteration = function (result, internalRounding) {
return BigDecimal.divide(BigDecimal.add(y, BigDecimal.multiply(result, result)), BigDecimal.multiply(convert(2), result), internalRounding);
};
Expand All @@ -338,3 +461,4 @@ BigDecimal.sqrt = function (x, rounding) {

}

export default addMath;
3 changes: 3 additions & 0 deletions README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -33,6 +33,9 @@ It can be compiled using https://www.npmjs.com/package/babel-plugin-transform-bi
BigDecimal.cmp(a, b)

## Math: (not in the spec)
To use:
import addMath from './BigDecimalMath.js';
addMath(BigDecimal, 10);

BigDecimal.abs(a)
BigDecimal.sign(a)
Expand Down
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