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
|
// Special Cases:
//
// - sinh(+-0) = +-0
// - sinh(+-inf) = +-inf
// - sinh(nan) = nan
const builtin = @import("builtin");
const std = @import("../index.zig");
const math = std.math;
const assert = std.debug.assert;
const expo2 = @import("expo2.zig").expo2;
pub fn sinh(x: var) -> @typeOf(x) {
const T = @typeOf(x);
return switch (T) {
f32 => sinh32(x),
f64 => sinh64(x),
else => @compileError("sinh not implemented for " ++ @typeName(T)),
};
}
// sinh(x) = (exp(x) - 1 / exp(x)) / 2
// = (exp(x) - 1 + (exp(x) - 1) / exp(x)) / 2
// = x + x^3 / 6 + o(x^5)
fn sinh32(x: f32) -> f32 {
const u = @bitCast(u32, x);
const ux = u & 0x7FFFFFFF;
const ax = @bitCast(f32, ux);
if (x == 0.0 or math.isNan(x)) {
return x;
}
var h: f32 = 0.5;
if (u >> 31 != 0) {
h = -h;
}
// |x| < log(FLT_MAX)
if (ux < 0x42B17217) {
const t = math.expm1(ax);
if (ux < 0x3F800000) {
if (ux < 0x3F800000 - (12 << 23)) {
return x;
} else {
return h * (2 * t - t * t / (t + 1));
}
}
return h * (t + t / (t + 1));
}
// |x| > log(FLT_MAX) or nan
return 2 * h * expo2(ax);
}
fn sinh64(x: f64) -> f64 {
@setFloatMode(this, @import("builtin").FloatMode.Strict);
const u = @bitCast(u64, x);
const w = u32(u >> 32);
const ax = @bitCast(f64, u & (@maxValue(u64) >> 1));
if (x == 0.0 or math.isNan(x)) {
return x;
}
var h: f32 = 0.5;
if (u >> 63 != 0) {
h = -h;
}
// |x| < log(FLT_MAX)
if (w < 0x40862E42) {
const t = math.expm1(ax);
if (w < 0x3FF00000) {
if (w < 0x3FF00000 - (26 << 20)) {
return x;
} else {
return h * (2 * t - t * t / (t + 1));
}
}
// NOTE: |x| > log(0x1p26) + eps could be h * exp(x)
return h * (t + t / (t + 1));
}
// |x| > log(DBL_MAX) or nan
return 2 * h * expo2(ax);
}
test "math.sinh" {
if (builtin.os == builtin.Os.windows and builtin.arch == builtin.Arch.i386) {
// TODO get this test passing
// https://github.com/zig-lang/zig/issues/537
return;
}
assert(sinh(f32(1.5)) == sinh32(1.5));
assert(sinh(f64(1.5)) == sinh64(1.5));
}
test "math.sinh32" {
const epsilon = 0.000001;
assert(math.approxEq(f32, sinh32(0.0), 0.0, epsilon));
assert(math.approxEq(f32, sinh32(0.2), 0.201336, epsilon));
assert(math.approxEq(f32, sinh32(0.8923), 1.015512, epsilon));
assert(math.approxEq(f32, sinh32(1.5), 2.129279, epsilon));
}
test "math.sinh64" {
const epsilon = 0.000001;
assert(math.approxEq(f64, sinh64(0.0), 0.0, epsilon));
assert(math.approxEq(f64, sinh64(0.2), 0.201336, epsilon));
assert(math.approxEq(f64, sinh64(0.8923), 1.015512, epsilon));
assert(math.approxEq(f64, sinh64(1.5), 2.129279, epsilon));
}
test "math.sinh32.special" {
assert(sinh32(0.0) == 0.0);
assert(sinh32(-0.0) == -0.0);
assert(math.isPositiveInf(sinh32(math.inf(f32))));
assert(math.isNegativeInf(sinh32(-math.inf(f32))));
assert(math.isNan(sinh32(math.nan(f32))));
}
test "math.sinh64.special" {
assert(sinh64(0.0) == 0.0);
assert(sinh64(-0.0) == -0.0);
assert(math.isPositiveInf(sinh64(math.inf(f64))));
assert(math.isNegativeInf(sinh64(-math.inf(f64))));
assert(math.isNan(sinh64(math.nan(f64))));
}
|
