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
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
|
const std = @import("std");
const builtin = @import("builtin");
const arch = builtin.cpu.arch;
const math = std.math;
const mem = std.mem;
const trig = @import("trig.zig");
const rem_pio2 = @import("rem_pio2.zig").rem_pio2;
const rem_pio2f = @import("rem_pio2f.zig").rem_pio2f;
const common = @import("common.zig");
pub const panic = common.panic;
comptime {
@export(&__sincosh, .{ .name = "__sincosh", .linkage = common.linkage, .visibility = common.visibility });
@export(&sincosf, .{ .name = "sincosf", .linkage = common.linkage, .visibility = common.visibility });
@export(&sincos, .{ .name = "sincos", .linkage = common.linkage, .visibility = common.visibility });
@export(&__sincosx, .{ .name = "__sincosx", .linkage = common.linkage, .visibility = common.visibility });
if (common.want_ppc_abi) {
@export(&sincosq, .{ .name = "sincosf128", .linkage = common.linkage, .visibility = common.visibility });
}
@export(&sincosq, .{ .name = "sincosq", .linkage = common.linkage, .visibility = common.visibility });
@export(&sincosl, .{ .name = "sincosl", .linkage = common.linkage, .visibility = common.visibility });
}
pub fn __sincosh(x: f16, r_sin: *f16, r_cos: *f16) callconv(.c) void {
// TODO: more efficient implementation
var big_sin: f32 = undefined;
var big_cos: f32 = undefined;
sincosf(x, &big_sin, &big_cos);
r_sin.* = @as(f16, @floatCast(big_sin));
r_cos.* = @as(f16, @floatCast(big_cos));
}
pub fn sincosf(x: f32, r_sin: *f32, r_cos: *f32) callconv(.c) void {
const sc1pio2: f64 = 1.0 * math.pi / 2.0; // 0x3FF921FB, 0x54442D18
const sc2pio2: f64 = 2.0 * math.pi / 2.0; // 0x400921FB, 0x54442D18
const sc3pio2: f64 = 3.0 * math.pi / 2.0; // 0x4012D97C, 0x7F3321D2
const sc4pio2: f64 = 4.0 * math.pi / 2.0; // 0x401921FB, 0x54442D18
const pre_ix = @as(u32, @bitCast(x));
const sign = pre_ix >> 31 != 0;
const ix = pre_ix & 0x7fffffff;
// |x| ~<= pi/4
if (ix <= 0x3f490fda) {
// |x| < 2**-12
if (ix < 0x39800000) {
// 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);
}
}
r_sin.* = x;
r_cos.* = 1.0;
return;
}
r_sin.* = trig.__sindf(x);
r_cos.* = trig.__cosdf(x);
return;
}
// |x| ~<= 5*pi/4
if (ix <= 0x407b53d1) {
// |x| ~<= 3pi/4
if (ix <= 0x4016cbe3) {
if (sign) {
r_sin.* = -trig.__cosdf(x + sc1pio2);
r_cos.* = trig.__sindf(x + sc1pio2);
} else {
r_sin.* = trig.__cosdf(sc1pio2 - x);
r_cos.* = trig.__sindf(sc1pio2 - x);
}
return;
}
// -sin(x+c) is not correct if x+c could be 0: -0 vs +0
r_sin.* = -trig.__sindf(if (sign) x + sc2pio2 else x - sc2pio2);
r_cos.* = -trig.__cosdf(if (sign) x + sc2pio2 else x - sc2pio2);
return;
}
// |x| ~<= 9*pi/4
if (ix <= 0x40e231d5) {
// |x| ~<= 7*pi/4
if (ix <= 0x40afeddf) {
if (sign) {
r_sin.* = trig.__cosdf(x + sc3pio2);
r_cos.* = -trig.__sindf(x + sc3pio2);
} else {
r_sin.* = -trig.__cosdf(x - sc3pio2);
r_cos.* = trig.__sindf(x - sc3pio2);
}
return;
}
r_sin.* = trig.__sindf(if (sign) x + sc4pio2 else x - sc4pio2);
r_cos.* = trig.__cosdf(if (sign) x + sc4pio2 else x - sc4pio2);
return;
}
// sin(Inf or NaN) is NaN
if (ix >= 0x7f800000) {
const result = x - x;
r_sin.* = result;
r_cos.* = result;
return;
}
// general argument reduction needed
var y: f64 = undefined;
const n = rem_pio2f(x, &y);
const s = trig.__sindf(y);
const c = trig.__cosdf(y);
switch (n & 3) {
0 => {
r_sin.* = s;
r_cos.* = c;
},
1 => {
r_sin.* = c;
r_cos.* = -s;
},
2 => {
r_sin.* = -s;
r_cos.* = -c;
},
else => {
r_sin.* = -c;
r_cos.* = s;
},
}
}
pub fn sincos(x: f64, r_sin: *f64, r_cos: *f64) callconv(.c) void {
const ix = @as(u32, @truncate(@as(u64, @bitCast(x)) >> 32)) & 0x7fffffff;
// |x| ~< pi/4
if (ix <= 0x3fe921fb) {
// if |x| < 2**-27 * sqrt(2)
if (ix < 0x3e46a09e) {
// 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);
}
}
r_sin.* = x;
r_cos.* = 1.0;
return;
}
r_sin.* = trig.__sin(x, 0.0, 0);
r_cos.* = trig.__cos(x, 0.0);
return;
}
// sincos(Inf or NaN) is NaN
if (ix >= 0x7ff00000) {
const result = x - x;
r_sin.* = result;
r_cos.* = result;
return;
}
// argument reduction needed
var y: [2]f64 = undefined;
const n = rem_pio2(x, &y);
const s = trig.__sin(y[0], y[1], 1);
const c = trig.__cos(y[0], y[1]);
switch (n & 3) {
0 => {
r_sin.* = s;
r_cos.* = c;
},
1 => {
r_sin.* = c;
r_cos.* = -s;
},
2 => {
r_sin.* = -s;
r_cos.* = -c;
},
else => {
r_sin.* = -c;
r_cos.* = s;
},
}
}
pub fn __sincosx(x: f80, r_sin: *f80, r_cos: *f80) callconv(.c) void {
// TODO: more efficient implementation
//return sincos_generic(f80, x, r_sin, r_cos);
var big_sin: f128 = undefined;
var big_cos: f128 = undefined;
sincosq(x, &big_sin, &big_cos);
r_sin.* = @as(f80, @floatCast(big_sin));
r_cos.* = @as(f80, @floatCast(big_cos));
}
pub fn sincosq(x: f128, r_sin: *f128, r_cos: *f128) callconv(.c) void {
// TODO: more correct implementation
//return sincos_generic(f128, x, r_sin, r_cos);
var small_sin: f64 = undefined;
var small_cos: f64 = undefined;
sincos(@as(f64, @floatCast(x)), &small_sin, &small_cos);
r_sin.* = small_sin;
r_cos.* = small_cos;
}
pub fn sincosl(x: c_longdouble, r_sin: *c_longdouble, r_cos: *c_longdouble) callconv(.c) void {
switch (@typeInfo(c_longdouble).float.bits) {
16 => return __sincosh(x, r_sin, r_cos),
32 => return sincosf(x, r_sin, r_cos),
64 => return sincos(x, r_sin, r_cos),
80 => return __sincosx(x, r_sin, r_cos),
128 => return sincosq(x, r_sin, r_cos),
else => @compileError("unreachable"),
}
}
pub const rem_pio2_generic = @compileError("TODO");
/// Ported from musl sincosl.c. Needs the following dependencies to be complete:
/// * rem_pio2_generic ported from __rem_pio2l.c
/// * trig.sin_generic ported from __sinl.c
/// * trig.cos_generic ported from __cosl.c
inline fn sincos_generic(comptime F: type, x: F, r_sin: *F, r_cos: *F) void {
const sc1pio4: F = 1.0 * math.pi / 4.0;
const bits = @typeInfo(F).float.bits;
const I = std.meta.Int(.unsigned, bits);
const ix = @as(I, @bitCast(x)) & (math.maxInt(I) >> 1);
const se: u16 = @truncate(ix >> (bits - 16));
if (se == 0x7fff) {
const result = x - x;
r_sin.* = result;
r_cos.* = result;
return;
}
if (@as(F, @bitCast(ix)) < sc1pio4) {
if (se < 0x3fff - math.floatFractionalBits(F) - 1) {
// raise underflow if subnormal
if (se == 0) {
if (common.want_float_exceptions) mem.doNotOptimizeAway(x * 0x1p-120);
}
r_sin.* = x;
// raise inexact if x!=0
r_cos.* = 1.0 + x;
return;
}
r_sin.* = trig.sin_generic(F, x, 0, 0);
r_cos.* = trig.cos_generic(F, x, 0);
return;
}
var y: [2]F = undefined;
const n = rem_pio2_generic(F, x, &y);
const s = trig.sin_generic(F, y[0], y[1], 1);
const c = trig.cos_generic(F, y[0], y[1]);
switch (n & 3) {
0 => {
r_sin.* = s;
r_cos.* = c;
},
1 => {
r_sin.* = c;
r_cos.* = -s;
},
2 => {
r_sin.* = -s;
r_cos.* = -c;
},
else => {
r_sin.* = -c;
r_cos.* = s;
},
}
}
|
