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
|
const std = @import("std");
const math = std.math;
const mem = std.mem;
const expect = std.testing.expect;
const common = @import("common.zig");
pub const panic = common.panic;
const trig = @import("trig.zig");
const rem_pio2 = @import("rem_pio2.zig").rem_pio2;
const rem_pio2f = @import("rem_pio2f.zig").rem_pio2f;
comptime {
@export(&__cosh, .{ .name = "__cosh", .linkage = common.linkage, .visibility = common.visibility });
@export(&cosf, .{ .name = "cosf", .linkage = common.linkage, .visibility = common.visibility });
@export(&cos, .{ .name = "cos", .linkage = common.linkage, .visibility = common.visibility });
@export(&__cosx, .{ .name = "__cosx", .linkage = common.linkage, .visibility = common.visibility });
if (common.want_ppc_abi) {
@export(&cosq, .{ .name = "cosf128", .linkage = common.linkage, .visibility = common.visibility });
}
@export(&cosq, .{ .name = "cosq", .linkage = common.linkage, .visibility = common.visibility });
@export(&cosl, .{ .name = "cosl", .linkage = common.linkage, .visibility = common.visibility });
}
pub fn __cosh(a: f16) callconv(.c) f16 {
// TODO: more efficient implementation
return @floatCast(cosf(a));
}
pub fn cosf(x: f32) callconv(.c) f32 {
// Small multiples of pi/2 rounded to double precision.
const c1pio2: f64 = 1.0 * math.pi / 2.0; // 0x3FF921FB, 0x54442D18
const c2pio2: f64 = 2.0 * math.pi / 2.0; // 0x400921FB, 0x54442D18
const c3pio2: f64 = 3.0 * math.pi / 2.0; // 0x4012D97C, 0x7F3321D2
const c4pio2: 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
if (common.want_float_exceptions) mem.doNotOptimizeAway(x + 0x1p120);
return 1.0;
}
return trig.__cosdf(x);
}
if (ix <= 0x407b53d1) { // |x| ~<= 5*pi/4
if (ix > 0x4016cbe3) { // |x| ~> 3*pi/4
return -trig.__cosdf(if (sign) x + c2pio2 else x - c2pio2);
} else {
if (sign) {
return trig.__sindf(x + c1pio2);
} else {
return trig.__sindf(c1pio2 - x);
}
}
}
if (ix <= 0x40e231d5) { // |x| ~<= 9*pi/4
if (ix > 0x40afeddf) { // |x| ~> 7*pi/4
return trig.__cosdf(if (sign) x + c4pio2 else x - c4pio2);
} else {
if (sign) {
return trig.__sindf(-x - c3pio2);
} else {
return trig.__sindf(x - c3pio2);
}
}
}
// cos(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.__cosdf(y),
1 => trig.__sindf(-y),
2 => -trig.__cosdf(y),
else => trig.__sindf(y),
};
}
pub fn cos(x: f64) callconv(.c) f64 {
var ix = @as(u64, @bitCast(x)) >> 32;
ix &= 0x7fffffff;
// |x| ~< pi/4
if (ix <= 0x3fe921fb) {
if (ix < 0x3e46a09e) { // |x| < 2**-27 * sqrt(2)
// raise inexact if x!=0
if (common.want_float_exceptions) mem.doNotOptimizeAway(x + 0x1p120);
return 1.0;
}
return trig.__cos(x, 0);
}
// cos(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.__cos(y[0], y[1]),
1 => -trig.__sin(y[0], y[1], 1),
2 => -trig.__cos(y[0], y[1]),
else => trig.__sin(y[0], y[1], 1),
};
}
pub fn __cosx(a: f80) callconv(.c) f80 {
// TODO: more efficient implementation
return @floatCast(cosq(a));
}
pub fn cosq(a: f128) callconv(.c) f128 {
// TODO: more correct implementation
return cos(@floatCast(a));
}
pub fn cosl(x: c_longdouble) callconv(.c) c_longdouble {
switch (@typeInfo(c_longdouble).float.bits) {
16 => return __cosh(x),
32 => return cosf(x),
64 => return cos(x),
80 => return __cosx(x),
128 => return cosq(x),
else => @compileError("unreachable"),
}
}
test "cos32" {
const epsilon = 0.00001;
try expect(math.approxEqAbs(f32, cosf(0.0), 1.0, epsilon));
try expect(math.approxEqAbs(f32, cosf(0.2), 0.980067, epsilon));
try expect(math.approxEqAbs(f32, cosf(0.8923), 0.627623, epsilon));
try expect(math.approxEqAbs(f32, cosf(1.5), 0.070737, epsilon));
try expect(math.approxEqAbs(f32, cosf(-1.5), 0.070737, epsilon));
try expect(math.approxEqAbs(f32, cosf(37.45), 0.969132, epsilon));
try expect(math.approxEqAbs(f32, cosf(89.123), 0.400798, epsilon));
}
test "cos64" {
const epsilon = 0.000001;
try expect(math.approxEqAbs(f64, cos(0.0), 1.0, epsilon));
try expect(math.approxEqAbs(f64, cos(0.2), 0.980067, epsilon));
try expect(math.approxEqAbs(f64, cos(0.8923), 0.627623, epsilon));
try expect(math.approxEqAbs(f64, cos(1.5), 0.070737, epsilon));
try expect(math.approxEqAbs(f64, cos(-1.5), 0.070737, epsilon));
try expect(math.approxEqAbs(f64, cos(37.45), 0.969132, epsilon));
try expect(math.approxEqAbs(f64, cos(89.123), 0.40080, epsilon));
}
test "cos32.special" {
try expect(math.isNan(cosf(math.inf(f32))));
try expect(math.isNan(cosf(-math.inf(f32))));
try expect(math.isNan(cosf(math.nan(f32))));
}
test "cos64.special" {
try expect(math.isNan(cos(math.inf(f64))));
try expect(math.isNan(cos(-math.inf(f64))));
try expect(math.isNan(cos(math.nan(f64))));
}
|
