You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
152 lines
4.6 KiB
152 lines
4.6 KiB
4 weeks ago
|
'use strict';
|
||
|
// based on Shewchuk's algorithm for exactly floating point addition
|
||
|
// adapted from https://github.com/tc39/proposal-math-sum/blob/3513d58323a1ae25560e8700aa5294500c6c9287/polyfill/polyfill.mjs
|
||
|
var $ = require('../internals/export');
|
||
|
var uncurryThis = require('../internals/function-uncurry-this');
|
||
|
var iterate = require('../internals/iterate');
|
||
|
|
||
|
var $RangeError = RangeError;
|
||
|
var $TypeError = TypeError;
|
||
|
var $Infinity = Infinity;
|
||
|
var $NaN = NaN;
|
||
|
var abs = Math.abs;
|
||
|
var pow = Math.pow;
|
||
|
var push = uncurryThis([].push);
|
||
|
|
||
|
var POW_2_1023 = pow(2, 1023);
|
||
|
var MAX_SAFE_INTEGER = pow(2, 53) - 1; // 2 ** 53 - 1 === 9007199254740992
|
||
|
var MAX_DOUBLE = Number.MAX_VALUE; // 2 ** 1024 - 2 ** (1023 - 52) === 1.79769313486231570815e+308
|
||
|
var MAX_ULP = pow(2, 971); // 2 ** (1023 - 52) === 1.99584030953471981166e+292
|
||
|
|
||
|
var NOT_A_NUMBER = {};
|
||
|
var MINUS_INFINITY = {};
|
||
|
var PLUS_INFINITY = {};
|
||
|
var MINUS_ZERO = {};
|
||
|
var FINITE = {};
|
||
|
|
||
|
// prerequisite: abs(x) >= abs(y)
|
||
|
var twosum = function (x, y) {
|
||
|
var hi = x + y;
|
||
|
var lo = y - (hi - x);
|
||
|
return { hi: hi, lo: lo };
|
||
|
};
|
||
|
|
||
|
// `Math.sumPrecise` method
|
||
|
// https://github.com/tc39/proposal-math-sum
|
||
|
$({ target: 'Math', stat: true, forced: true }, {
|
||
|
// eslint-disable-next-line max-statements -- ok
|
||
|
sumPrecise: function sumPrecise(items) {
|
||
|
var numbers = [];
|
||
|
var count = 0;
|
||
|
var state = MINUS_ZERO;
|
||
|
|
||
|
iterate(items, function (n) {
|
||
|
if (++count >= MAX_SAFE_INTEGER) throw new $RangeError('Maximum allowed index exceeded');
|
||
|
if (typeof n != 'number') throw new $TypeError('Value is not a number');
|
||
|
if (state !== NOT_A_NUMBER) {
|
||
|
// eslint-disable-next-line no-self-compare -- NaN check
|
||
|
if (n !== n) state = NOT_A_NUMBER;
|
||
|
else if (n === $Infinity) state = state === MINUS_INFINITY ? NOT_A_NUMBER : PLUS_INFINITY;
|
||
|
else if (n === -$Infinity) state = state === PLUS_INFINITY ? NOT_A_NUMBER : MINUS_INFINITY;
|
||
|
else if ((n !== 0 || (1 / n) === $Infinity) && (state === MINUS_ZERO || state === FINITE)) {
|
||
|
state = FINITE;
|
||
|
push(numbers, n);
|
||
|
}
|
||
|
}
|
||
|
});
|
||
|
|
||
|
switch (state) {
|
||
|
case NOT_A_NUMBER: return $NaN;
|
||
|
case MINUS_INFINITY: return -$Infinity;
|
||
|
case PLUS_INFINITY: return $Infinity;
|
||
|
case MINUS_ZERO: return -0;
|
||
|
}
|
||
|
|
||
|
var partials = [];
|
||
|
var overflow = 0; // conceptually 2 ** 1024 times this value; the final partial is biased by this amount
|
||
|
var x, y, sum, hi, lo, tmp;
|
||
|
|
||
|
for (var i = 0; i < numbers.length; i++) {
|
||
|
x = numbers[i];
|
||
|
var actuallyUsedPartials = 0;
|
||
|
for (var j = 0; j < partials.length; j++) {
|
||
|
y = partials[j];
|
||
|
if (abs(x) < abs(y)) {
|
||
|
tmp = x;
|
||
|
x = y;
|
||
|
y = tmp;
|
||
|
}
|
||
|
sum = twosum(x, y);
|
||
|
hi = sum.hi;
|
||
|
lo = sum.lo;
|
||
|
if (abs(hi) === $Infinity) {
|
||
|
var sign = hi === $Infinity ? 1 : -1;
|
||
|
overflow += sign;
|
||
|
|
||
|
x = (x - (sign * POW_2_1023)) - (sign * POW_2_1023);
|
||
|
if (abs(x) < abs(y)) {
|
||
|
tmp = x;
|
||
|
x = y;
|
||
|
y = tmp;
|
||
|
}
|
||
|
sum = twosum(x, y);
|
||
|
hi = sum.hi;
|
||
|
lo = sum.lo;
|
||
|
}
|
||
|
if (lo !== 0) partials[actuallyUsedPartials++] = lo;
|
||
|
x = hi;
|
||
|
}
|
||
|
partials.length = actuallyUsedPartials;
|
||
|
if (x !== 0) push(partials, x);
|
||
|
}
|
||
|
|
||
|
// compute the exact sum of partials, stopping once we lose precision
|
||
|
var n = partials.length - 1;
|
||
|
hi = 0;
|
||
|
lo = 0;
|
||
|
|
||
|
if (overflow !== 0) {
|
||
|
var next = n >= 0 ? partials[n] : 0;
|
||
|
n--;
|
||
|
if (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(abs(overflow) === 1)
|
||
|
sum = twosum(overflow * POW_2_1023, next / 2);
|
||
|
hi = sum.hi;
|
||
|
lo = sum.lo;
|
||
|
lo *= 2;
|
||
|
if (abs(2 * hi) === $Infinity) {
|
||
|
// rounding to the maximum value
|
||
|
if (hi > 0) {
|
||
|
return (hi === POW_2_1023 && lo === -(MAX_ULP / 2) && n >= 0 && partials[n] < 0) ? MAX_DOUBLE : $Infinity;
|
||
|
} return (hi === -POW_2_1023 && lo === (MAX_ULP / 2) && n >= 0 && partials[n] > 0) ? -MAX_DOUBLE : -$Infinity;
|
||
|
}
|
||
|
|
||
|
if (lo !== 0) {
|
||
|
partials[++n] = lo;
|
||
|
lo = 0;
|
||
|
}
|
||
|
|
||
|
hi *= 2;
|
||
|
}
|
||
|
|
||
|
while (n >= 0) {
|
||
|
sum = twosum(hi, partials[n--]);
|
||
|
hi = sum.hi;
|
||
|
lo = sum.lo;
|
||
|
if (lo !== 0) break;
|
||
|
}
|
||
|
|
||
|
if (n >= 0 && ((lo < 0 && partials[n] < 0) || (lo > 0 && partials[n] > 0))) {
|
||
|
y = lo * 2;
|
||
|
x = hi + y;
|
||
|
if (y === x - hi) hi = x;
|
||
|
}
|
||
|
|
||
|
return hi;
|
||
|
}
|
||
|
});
|