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| 1 | +'use strict'; |
| 2 | +// based on Shewchuk's algorithm for exactly floating point addition |
| 3 | +// adapted from https://github.com/tc39/proposal-math-sum/blob/3513d58323a1ae25560e8700aa5294500c6c9287/polyfill/polyfill.mjs |
| 4 | +var $ = require('../internals/export'); |
| 5 | +var uncurryThis = require('../internals/function-uncurry-this'); |
| 6 | +var iterate = require('../internals/iterate'); |
| 7 | + |
| 8 | +var $RangeError = RangeError; |
| 9 | +var $TypeError = TypeError; |
| 10 | +var $Infinity = Infinity; |
| 11 | +var $NaN = NaN; |
| 12 | +var abs = Math.abs; |
| 13 | +var pow = Math.pow; |
| 14 | +var push = uncurryThis([].push); |
| 15 | + |
| 16 | +var POW_2_1023 = pow(2, 1023); |
| 17 | +var MAX_SAFE_INTEGER = pow(2, 53) - 1; |
| 18 | +// exponent 11111111110, significand all 1s |
| 19 | +var MAX_DOUBLE = 1.79769313486231570815e+308; // 2 ** 1024 - 2 ** (1023 - 52) |
| 20 | +// exponent 11111111110, significand all 1s except final 0 |
| 21 | +var PENULTIMATE_DOUBLE = 1.79769313486231550856e+308; // 2 ** 1024 - 2 * 2 ** (1023 - 52) |
| 22 | +// exponent 11111001010, significand all 0s |
| 23 | +var MAX_ULP = MAX_DOUBLE - PENULTIMATE_DOUBLE; // 1.99584030953471981166e+292, <- 2 ** (1023 - 52) |
| 24 | + |
| 25 | +var NOT_A_NUMBER = {}; |
| 26 | +var MINUS_INFINITY = {}; |
| 27 | +var PLUS_INFINITY = {}; |
| 28 | +var MINUS_ZERO = {}; |
| 29 | +var FINITE = {}; |
| 30 | + |
| 31 | +// prerequisite: abs(x) >= abs(y) |
| 32 | +var twosum = function (x, y) { |
| 33 | + var hi = x + y; |
| 34 | + var lo = y - (hi - x); |
| 35 | + return { hi: hi, lo: lo }; |
| 36 | +}; |
| 37 | + |
| 38 | +// `Math.sumPrecise` method |
| 39 | +// https://github.com/tc39/proposal-math-sum |
| 40 | +$({ target: 'Math', stat: true, forced: true }, { |
| 41 | + // eslint-disable-next-line max-statements -- ok |
| 42 | + sumPrecise: function sumPrecise(items) { |
| 43 | + var numbers = []; |
| 44 | + var count = 0; |
| 45 | + var state = MINUS_ZERO; |
| 46 | + |
| 47 | + iterate(items, function (n) { |
| 48 | + if (++count >= MAX_SAFE_INTEGER) throw new $RangeError('Maximum allowed index exceeded'); |
| 49 | + if (typeof n != 'number') throw new $TypeError('Value is not a number'); |
| 50 | + if (state !== NOT_A_NUMBER) { |
| 51 | + // eslint-disable-next-line no-self-compare -- NaN check |
| 52 | + if (n !== n) state = NOT_A_NUMBER; |
| 53 | + else if (n === $Infinity) state = state === MINUS_INFINITY ? NOT_A_NUMBER : PLUS_INFINITY; |
| 54 | + else if (n === -$Infinity) state = state === PLUS_INFINITY ? NOT_A_NUMBER : MINUS_INFINITY; |
| 55 | + else if ((n !== 0 || (1 / n) === $Infinity) && (state === MINUS_ZERO || state === FINITE)) { |
| 56 | + state = FINITE; |
| 57 | + push(numbers, n); |
| 58 | + } |
| 59 | + } |
| 60 | + }); |
| 61 | + |
| 62 | + switch (state) { |
| 63 | + case NOT_A_NUMBER: return $NaN; |
| 64 | + case MINUS_INFINITY: return -$Infinity; |
| 65 | + case PLUS_INFINITY: return $Infinity; |
| 66 | + case MINUS_ZERO: return -0; |
| 67 | + } |
| 68 | + |
| 69 | + var partials = []; |
| 70 | + var overflow = 0; // conceptually 2**1024 times this value; the final partial is biased by this amount |
| 71 | + var x, y, sum, hi, lo, tmp; |
| 72 | + |
| 73 | + for (var i = 0; i < numbers.length; i++) { |
| 74 | + x = numbers[i]; |
| 75 | + var actuallyUsedPartials = 0; |
| 76 | + for (var j = 0; j < partials.length; j++) { |
| 77 | + y = partials[j]; |
| 78 | + if (abs(x) < abs(y)) { |
| 79 | + tmp = x; |
| 80 | + x = y; |
| 81 | + y = tmp; |
| 82 | + } |
| 83 | + sum = twosum(x, y); |
| 84 | + hi = sum.hi; |
| 85 | + lo = sum.lo; |
| 86 | + if (abs(hi) === $Infinity) { |
| 87 | + var sign = hi === $Infinity ? 1 : -1; |
| 88 | + overflow += sign; |
| 89 | + |
| 90 | + x = (x - (sign * POW_2_1023)) - (sign * POW_2_1023); |
| 91 | + if (abs(x) < abs(y)) { |
| 92 | + tmp = x; |
| 93 | + x = y; |
| 94 | + y = tmp; |
| 95 | + } |
| 96 | + sum = twosum(x, y); |
| 97 | + hi = sum.hi; |
| 98 | + lo = sum.lo; |
| 99 | + } |
| 100 | + if (lo !== 0) { |
| 101 | + partials[actuallyUsedPartials] = lo; |
| 102 | + actuallyUsedPartials += 1; |
| 103 | + } |
| 104 | + x = hi; |
| 105 | + } |
| 106 | + partials.length = actuallyUsedPartials; |
| 107 | + if (x !== 0) partials[partials.length] = x; |
| 108 | + } |
| 109 | + |
| 110 | + // compute the exact sum of partials, stopping once we lose precision |
| 111 | + var n = partials.length - 1; |
| 112 | + hi = 0; |
| 113 | + lo = 0; |
| 114 | + |
| 115 | + if (overflow !== 0) { |
| 116 | + var next = n >= 0 ? partials[n] : 0; |
| 117 | + n -= 1; |
| 118 | + if (abs(overflow) > 1 || (overflow > 0 && next > 0) || (overflow < 0 && next < 0)) { |
| 119 | + return overflow > 0 ? $Infinity : -$Infinity; |
| 120 | + } |
| 121 | + // here we actually have to do the arithmetic |
| 122 | + // drop a factor of 2 so we can do it without overflow |
| 123 | + // assert(abs(overflow) === 1) |
| 124 | + sum = twosum(overflow * POW_2_1023, next / 2); |
| 125 | + hi = sum.hi; |
| 126 | + lo = sum.lo; |
| 127 | + lo *= 2; |
| 128 | + if (abs(2 * hi) === $Infinity) { |
| 129 | + // rounding to the maximum value |
| 130 | + if (hi > 0) { |
| 131 | + return (hi === POW_2_1023 && lo === -(MAX_ULP / 2) && n >= 0 && partials[n] < 0) ? MAX_DOUBLE : $Infinity; |
| 132 | + } return (hi === -POW_2_1023 && lo === (MAX_ULP / 2) && n >= 0 && partials[n] > 0) ? -MAX_DOUBLE : -$Infinity; |
| 133 | + } |
| 134 | + |
| 135 | + if (lo !== 0) { |
| 136 | + partials[n + 1] = lo; |
| 137 | + n += 1; |
| 138 | + lo = 0; |
| 139 | + } |
| 140 | + |
| 141 | + hi *= 2; |
| 142 | + } |
| 143 | + |
| 144 | + while (n >= 0) { |
| 145 | + x = hi; |
| 146 | + y = partials[n]; |
| 147 | + n -= 1; |
| 148 | + sum = twosum(x, y); |
| 149 | + hi = sum.hi; |
| 150 | + lo = sum.lo; |
| 151 | + if (lo !== 0) break; |
| 152 | + } |
| 153 | + |
| 154 | + if (n >= 0 && ((lo < 0.0 && partials[n] < 0.0) || (lo > 0.0 && partials[n] > 0.0))) { |
| 155 | + y = lo * 2.0; |
| 156 | + x = hi + y; |
| 157 | + if (y === x - hi) hi = x; |
| 158 | + } |
| 159 | + |
| 160 | + return hi; |
| 161 | + } |
| 162 | +}); |
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