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
|
// SPDX-License-Identifier: MIT
// Copyright (c) 2015-2021 Zig Contributors
// This file is part of [zig](https://ziglang.org/), which is MIT licensed.
// The MIT license requires this copyright notice to be included in all copies
// and substantial portions of the software.
// Ported from musl, which is licensed under the MIT license:
// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
//
// https://git.musl-libc.org/cgit/musl/tree/src/math/scalbnf.c
// https://git.musl-libc.org/cgit/musl/tree/src/math/scalbn.c
const std = @import("std");
const math = std.math;
const assert = std.debug.assert;
const expect = std.testing.expect;
/// Returns x * 2^n.
pub fn scalbn(x: anytype, n: i32) @TypeOf(x) {
var base = x;
var shift = n;
const T = @TypeOf(base);
const IntT = std.meta.Int(.unsigned, @bitSizeOf(T));
if (@typeInfo(T) != .Float) {
@compileError("scalbn not implemented for " ++ @typeName(T));
}
const mantissa_bits = math.floatMantissaBits(T);
const exponent_bits = math.floatExponentBits(T);
const exponent_bias = (1 << (exponent_bits - 1)) - 1;
const exponent_min = 1 - exponent_bias;
const exponent_max = exponent_bias;
// fix double rounding errors in subnormal ranges
// https://git.musl-libc.org/cgit/musl/commit/src/math/scalbn.c?id=8c44a060243f04283ca68dad199aab90336141db
const scale_min_expo = exponent_min + mantissa_bits + 1;
const scale_min = @bitCast(T, @as(IntT, scale_min_expo + exponent_bias) << mantissa_bits);
const scale_max = @bitCast(T, @intCast(IntT, exponent_max + exponent_bias) << mantissa_bits);
// scale `shift` within floating point limits, if possible
// second pass is possible due to subnormal range
// third pass always results in +/-0.0 or +/-inf
if (shift > exponent_max) {
base *= scale_max;
shift -= exponent_max;
if (shift > exponent_max) {
base *= scale_max;
shift -= exponent_max;
if (shift > exponent_max) shift = exponent_max;
}
} else if (shift < exponent_min) {
base *= scale_min;
shift -= scale_min_expo;
if (shift < exponent_min) {
base *= scale_min;
shift -= scale_min_expo;
if (shift < exponent_min) shift = exponent_min;
}
}
return base * @bitCast(T, @intCast(IntT, shift + exponent_bias) << mantissa_bits);
}
test "math.scalbn" {
// basic usage
try expect(scalbn(@as(f16, 1.5), 4) == 24.0);
try expect(scalbn(@as(f32, 1.5), 4) == 24.0);
try expect(scalbn(@as(f64, 1.5), 4) == 24.0);
try expect(scalbn(@as(f128, 1.5), 4) == 24.0);
// subnormals
try expect(math.isNormal(scalbn(@as(f16, 1.0), -14)));
try expect(!math.isNormal(scalbn(@as(f16, 1.0), -15)));
try expect(math.isNormal(scalbn(@as(f32, 1.0), -126)));
try expect(!math.isNormal(scalbn(@as(f32, 1.0), -127)));
try expect(math.isNormal(scalbn(@as(f64, 1.0), -1022)));
try expect(!math.isNormal(scalbn(@as(f64, 1.0), -1023)));
try expect(math.isNormal(scalbn(@as(f128, 1.0), -16382)));
try expect(!math.isNormal(scalbn(@as(f128, 1.0), -16383)));
// unreliable due to lack of native f16 support, see talk on PR #8733
// try expect(scalbn(@as(f16, 0x1.1FFp-1), -14 - 9) == math.f16_true_min);
try expect(scalbn(@as(f32, 0x1.3FFFFFp-1), -126 - 22) == math.f32_true_min);
try expect(scalbn(@as(f64, 0x1.7FFFFFFFFFFFFp-1), -1022 - 51) == math.f64_true_min);
try expect(scalbn(@as(f128, 0x1.7FFFFFFFFFFFFFFFFFFFFFFFFFFFp-1), -16382 - 111) == math.f128_true_min);
// float limits
try expect(scalbn(@as(f32, math.f32_max), -128 - 149) > 0.0);
try expect(scalbn(@as(f32, math.f32_max), -128 - 149 - 1) == 0.0);
try expect(!math.isPositiveInf(scalbn(@as(f16, math.f16_true_min), 15 + 24)));
try expect(math.isPositiveInf(scalbn(@as(f16, math.f16_true_min), 15 + 24 + 1)));
try expect(!math.isPositiveInf(scalbn(@as(f32, math.f32_true_min), 127 + 149)));
try expect(math.isPositiveInf(scalbn(@as(f32, math.f32_true_min), 127 + 149 + 1)));
try expect(!math.isPositiveInf(scalbn(@as(f64, math.f64_true_min), 1023 + 1074)));
try expect(math.isPositiveInf(scalbn(@as(f64, math.f64_true_min), 1023 + 1074 + 1)));
try expect(!math.isPositiveInf(scalbn(@as(f128, math.f128_true_min), 16383 + 16494)));
try expect(math.isPositiveInf(scalbn(@as(f128, math.f128_true_min), 16383 + 16494 + 1)));
}
|
