1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
|
// |reftest| shell-option(--enable-float16array) skip-if(!Math.f16round)
// Some tests regarding conversion to Float16
assertEq(Math.f16round(), NaN);
// Special values
assertEq(Math.f16round(NaN), NaN);
assertEq(Math.f16round(-Infinity), -Infinity);
assertEq(Math.f16round(Infinity), Infinity);
assertEq(Math.f16round(-0), -0);
assertEq(Math.f16round(+0), +0);
// Polyfill function for Float16 conversion, adapted from
// https://github.com/petamoriken/float16/.
// The original license is preseved below.
function toFloat16(num) {
// MIT License
// Copyright (c) 2017-2024 Kenta Moriuchi
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
const INVERSE_OF_EPSILON = 1 / Number.EPSILON;
/**
* rounds to the nearest value;
* if the number falls midway, it is rounded to the nearest value with an even least significant digit
* @param {number} num
* @returns {number}
*/
function roundTiesToEven(num) {
return (num + INVERSE_OF_EPSILON) - INVERSE_OF_EPSILON;
}
const FLOAT16_MIN_VALUE = 6.103515625e-05;
const FLOAT16_MAX_VALUE = 65504;
const FLOAT16_EPSILON = 0.0009765625;
const FLOAT16_EPSILON_MULTIPLIED_BY_FLOAT16_MIN_VALUE = FLOAT16_EPSILON * FLOAT16_MIN_VALUE;
const FLOAT16_EPSILON_DEVIDED_BY_EPSILON = FLOAT16_EPSILON * INVERSE_OF_EPSILON;
function roundToFloat16(num) {
const number = +num;
// NaN, Infinity, -Infinity, 0, -0
if (!isFinite(number) || number === 0) {
return number;
}
// finite except 0, -0
const sign = number > 0 ? 1 : -1;
const absolute = Math.abs(number);
// small number
if (absolute < FLOAT16_MIN_VALUE) {
return sign * roundTiesToEven(absolute / FLOAT16_EPSILON_MULTIPLIED_BY_FLOAT16_MIN_VALUE) * FLOAT16_EPSILON_MULTIPLIED_BY_FLOAT16_MIN_VALUE;
}
const temp = (1 + FLOAT16_EPSILON_DEVIDED_BY_EPSILON) * absolute;
const result = temp - (temp - absolute);
// large number
if (result > FLOAT16_MAX_VALUE || isNaN(result)) {
return sign * Infinity;
}
return sign * result;
}
return roundToFloat16(num);
};
// A test on a certain range of numbers, including big numbers, so that
// we get a loss in precision for some of them.
for (var i = 0; i < 64; ++i) {
var p = Math.pow(2, i) + 1;
assertEq(Math.f16round(p), toFloat16(p));
assertEq(Math.f16round(-p), toFloat16(-p));
}
/********************************************
/* Tests on maximal Float16 / Double values *
/*******************************************/
function maxValue(exponentWidth, significandWidth) {
var n = 0;
var maxExp = Math.pow(2, exponentWidth - 1) - 1;
for (var i = significandWidth; i >= 0; i--)
n += Math.pow(2, maxExp - i);
return n;
}
var DBL_MAX = maxValue(11, 52);
assertEq(DBL_MAX, Number.MAX_VALUE); // sanity check
// Finite as a double, too big for a float16
assertEq(Math.f16round(DBL_MAX), Infinity);
var FLT16_MAX = maxValue(5, 10);
assertEq(Math.f16round(FLT16_MAX), FLT16_MAX);
assertEq(Math.f16round(65519), FLT16_MAX); // round-nearest rounds down to FLT16_MAX
assertEq(Math.f16round(65520), Infinity); // no longer rounds down to FLT16_MAX
/*********************************************************
/******* Tests on denormalizations and roundings *********
/********************************************************/
function minValue(exponentWidth, significandWidth) {
return Math.pow(2, -(Math.pow(2, exponentWidth - 1) - 2) - significandWidth);
}
var DBL_MIN = Math.pow(2, -1074);
assertEq(DBL_MIN, Number.MIN_VALUE); // sanity check
// Too small for a float16
assertEq(Math.f16round(DBL_MIN), 0);
var FLT16_MIN = minValue(5, 10);
assertEq(Math.f16round(FLT16_MIN), FLT16_MIN);
assertEq(Math.f16round(FLT16_MIN / 2), 0); // halfway, round-nearest rounds down to 0 (even)
// FLT16_MIN + a small amount rounds up to FLT16_MIN
// Constant taken from https://github.com/petamoriken/float16/
assertEq(Math.f16round(2.980232238769531911744490042422139897126953655970282852649688720703125e-8), FLT16_MIN);
assertEq(Math.f16round(-FLT16_MIN), -FLT16_MIN);
assertEq(Math.f16round(-FLT16_MIN / 2), -0); // halfway, round-nearest rounds up to -0 (even)
// -FLT16_MIN - a small amount rounds down to -FLT16_MIN
// Constant taken from https://github.com/petamoriken/float16/
assertEq(Math.f16round(2.980232238769531911744490042422139897126953655970282852649688720703125e-8), FLT16_MIN);
// Test some constants from https://github.com/petamoriken/float16/
assertEq(Math.f16round(0.499994), 0.5);
assertEq(Math.f16round(1.337), 1.3369140625);
// This will round incorrectly if the implementation first rounds to Float32,
// then to Float16
assertEq(Math.f16round(1.00048828125000022204), 1.0009765625);
reportCompare(0, 0, "ok");
|
