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
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
|
//! 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/sinf.c
//! https://git.musl-libc.org/cgit/musl/tree/src/math/sin.c
const std = @import("std");
const builtin = @import("builtin");
const arch = builtin.cpu.arch;
const math = std.math;
const mem = std.mem;
const expect = std.testing.expect;
const common = @import("common.zig");
const trig = @import("trig.zig");
const rem_pio2 = @import("rem_pio2.zig").rem_pio2;
const rem_pio2f = @import("rem_pio2f.zig").rem_pio2f;
pub const panic = common.panic;
comptime {
@export(&__sinh, .{ .name = "__sinh", .linkage = common.linkage, .visibility = common.visibility });
@export(&sinf, .{ .name = "sinf", .linkage = common.linkage, .visibility = common.visibility });
@export(&sin, .{ .name = "sin", .linkage = common.linkage, .visibility = common.visibility });
@export(&__sinx, .{ .name = "__sinx", .linkage = common.linkage, .visibility = common.visibility });
if (common.want_ppc_abi) {
@export(&sinq, .{ .name = "sinf128", .linkage = common.linkage, .visibility = common.visibility });
}
@export(&sinq, .{ .name = "sinq", .linkage = common.linkage, .visibility = common.visibility });
@export(&sinl, .{ .name = "sinl", .linkage = common.linkage, .visibility = common.visibility });
}
pub fn __sinh(x: f16) callconv(.c) f16 {
// TODO: more efficient implementation
return @floatCast(sinf(x));
}
pub fn sinf(x: f32) callconv(.c) f32 {
// Small multiples of pi/2 rounded to double precision.
const s1pio2: f64 = 1.0 * math.pi / 2.0; // 0x3FF921FB, 0x54442D18
const s2pio2: f64 = 2.0 * math.pi / 2.0; // 0x400921FB, 0x54442D18
const s3pio2: f64 = 3.0 * math.pi / 2.0; // 0x4012D97C, 0x7F3321D2
const s4pio2: f64 = 4.0 * math.pi / 2.0; // 0x401921FB, 0x54442D18
var ix: u32 = @bitCast(x);
const sign = ix >> 31 != 0;
ix &= 0x7fffffff;
if (ix <= 0x3f490fda) { // |x| ~<= pi/4
if (ix < 0x39800000) { // |x| < 2**-12
// raise inexact if x!=0 and underflow if subnormal
if (common.want_float_exceptions) {
if (ix < 0x00800000) {
mem.doNotOptimizeAway(x / 0x1p120);
} else {
mem.doNotOptimizeAway(x + 0x1p120);
}
}
return x;
}
return trig.__sindf(x);
}
if (ix <= 0x407b53d1) { // |x| ~<= 5*pi/4
if (ix <= 0x4016cbe3) { // |x| ~<= 3pi/4
if (sign) {
return -trig.__cosdf(x + s1pio2);
} else {
return trig.__cosdf(x - s1pio2);
}
}
return trig.__sindf(if (sign) -(x + s2pio2) else -(x - s2pio2));
}
if (ix <= 0x40e231d5) { // |x| ~<= 9*pi/4
if (ix <= 0x40afeddf) { // |x| ~<= 7*pi/4
if (sign) {
return trig.__cosdf(x + s3pio2);
} else {
return -trig.__cosdf(x - s3pio2);
}
}
return trig.__sindf(if (sign) x + s4pio2 else x - s4pio2);
}
// sin(Inf or NaN) is NaN
if (ix >= 0x7f800000) {
return x - x;
}
var y: f64 = undefined;
const n = rem_pio2f(x, &y);
return switch (n & 3) {
0 => trig.__sindf(y),
1 => trig.__cosdf(y),
2 => trig.__sindf(-y),
else => -trig.__cosdf(y),
};
}
pub fn sin(x: f64) callconv(.c) f64 {
var ix = @as(u64, @bitCast(x)) >> 32;
ix &= 0x7fffffff;
// |x| ~< pi/4
if (ix <= 0x3fe921fb) {
if (ix < 0x3e500000) { // |x| < 2**-26
// raise inexact if x != 0 and underflow if subnormal
if (common.want_float_exceptions) {
if (ix < 0x00100000) {
mem.doNotOptimizeAway(x / 0x1p120);
} else {
mem.doNotOptimizeAway(x + 0x1p120);
}
}
return x;
}
return trig.__sin(x, 0.0, 0);
}
// sin(Inf or NaN) is NaN
if (ix >= 0x7ff00000) {
return x - x;
}
var y: [2]f64 = undefined;
const n = rem_pio2(x, &y);
return switch (n & 3) {
0 => trig.__sin(y[0], y[1], 1),
1 => trig.__cos(y[0], y[1]),
2 => -trig.__sin(y[0], y[1], 1),
else => -trig.__cos(y[0], y[1]),
};
}
pub fn __sinx(x: f80) callconv(.c) f80 {
// TODO: more efficient implementation
return @floatCast(sinq(x));
}
pub fn sinq(x: f128) callconv(.c) f128 {
// TODO: more correct implementation
return sin(@floatCast(x));
}
pub fn sinl(x: c_longdouble) callconv(.c) c_longdouble {
switch (@typeInfo(c_longdouble).float.bits) {
16 => return __sinh(x),
32 => return sinf(x),
64 => return sin(x),
80 => return __sinx(x),
128 => return sinq(x),
else => @compileError("unreachable"),
}
}
test "sin32" {
const epsilon = 0.00001;
try expect(math.approxEqAbs(f32, sinf(0.0), 0.0, epsilon));
try expect(math.approxEqAbs(f32, sinf(0.2), 0.198669, epsilon));
try expect(math.approxEqAbs(f32, sinf(0.8923), 0.778517, epsilon));
try expect(math.approxEqAbs(f32, sinf(1.5), 0.997495, epsilon));
try expect(math.approxEqAbs(f32, sinf(-1.5), -0.997495, epsilon));
try expect(math.approxEqAbs(f32, sinf(37.45), -0.246544, epsilon));
try expect(math.approxEqAbs(f32, sinf(89.123), 0.916166, epsilon));
}
test "sin64" {
const epsilon = 0.000001;
try expect(math.approxEqAbs(f64, sin(0.0), 0.0, epsilon));
try expect(math.approxEqAbs(f64, sin(0.2), 0.198669, epsilon));
try expect(math.approxEqAbs(f64, sin(0.8923), 0.778517, epsilon));
try expect(math.approxEqAbs(f64, sin(1.5), 0.997495, epsilon));
try expect(math.approxEqAbs(f64, sin(-1.5), -0.997495, epsilon));
try expect(math.approxEqAbs(f64, sin(37.45), -0.246543, epsilon));
try expect(math.approxEqAbs(f64, sin(89.123), 0.916166, epsilon));
}
test "sin32.special" {
try expect(sinf(0.0) == 0.0);
try expect(sinf(-0.0) == -0.0);
try expect(math.isNan(sinf(math.inf(f32))));
try expect(math.isNan(sinf(-math.inf(f32))));
try expect(math.isNan(sinf(math.nan(f32))));
}
test "sin64.special" {
try expect(sin(0.0) == 0.0);
try expect(sin(-0.0) == -0.0);
try expect(math.isNan(sin(math.inf(f64))));
try expect(math.isNan(sin(-math.inf(f64))));
try expect(math.isNan(sin(math.nan(f64))));
}
test "sin32 #9901" {
const float: f32 = @bitCast(@as(u32, 0b11100011111111110000000000000000));
_ = sinf(float);
}
test "sin64 #9901" {
const float: f64 = @bitCast(@as(u64, 0b1111111101000001000000001111110111111111100000000000000000000001));
_ = sin(float);
}
|
