2 prim::{PrimFloat, PrimUInt},
3 traits::{Compare, Context, ConvertFrom, ConvertTo, Float, Make, Select},
7 #![allow(clippy::excessive_precision)]
10 /// coefficients of taylor series for `sin(pi * x)` centered at `0`
14 /// sinpi: bfloat(taylor(sin(%pi*x),x,0,19))$
15 /// for i: 1 step 2 thru 19 do
16 /// printf(true, "pub(crate) const SINPI_KERNEL_TAYLOR_~d: f64 = ~a;~%", i, ssubst("e", "b", string(coeff(sinpi, x, i))))$
18 pub(crate) const SINPI_KERNEL_TAYLOR_1: f64 =
19 3.1415926535897932384626433832795028841971693993751e0;
20 pub(crate) const SINPI_KERNEL_TAYLOR_3: f64 =
21 -5.1677127800499700292460525111835658670375480943142e0;
22 pub(crate) const SINPI_KERNEL_TAYLOR_5: f64 =
23 2.550164039877345443856177583695296720669172555234e0;
24 pub(crate) const SINPI_KERNEL_TAYLOR_7: f64 =
25 -5.9926452932079207688773938354604004601536358636814e-1;
26 pub(crate) const SINPI_KERNEL_TAYLOR_9: f64 =
27 8.2145886611128228798802365523698344807837460797753e-2;
28 pub(crate) const SINPI_KERNEL_TAYLOR_11: f64 =
29 -7.370430945714350777259089957290781501211638236021e-3;
30 pub(crate) const SINPI_KERNEL_TAYLOR_13: f64 =
31 4.6630280576761256442062891447027174382819981361599e-4;
32 pub(crate) const SINPI_KERNEL_TAYLOR_15: f64 =
33 -2.1915353447830215827384652057094188859248708765956e-5;
34 pub(crate) const SINPI_KERNEL_TAYLOR_17: f64 =
35 7.9520540014755127847832068624575890327682459384282e-7;
36 pub(crate) const SINPI_KERNEL_TAYLOR_19: f64 =
37 -2.2948428997269873110203872385571587856074785581088e-8;
39 /// coefficients of taylor series for `cos(pi * x)` centered at `0`
43 /// cospi: bfloat(taylor(cos(%pi*x),x,0,18))$
44 /// for i: 0 step 2 thru 18 do
45 /// printf(true, "pub(crate) const COSPI_KERNEL_TAYLOR_~d: f64 = ~a;~%", i, ssubst("e", "b", string(coeff(cospi, x, i))))$
47 pub(crate) const COSPI_KERNEL_TAYLOR_0: f64 = 1.0e0;
48 pub(crate) const COSPI_KERNEL_TAYLOR_2: f64 =
49 -4.9348022005446793094172454999380755676568497036204e0;
50 pub(crate) const COSPI_KERNEL_TAYLOR_4: f64 =
51 4.0587121264167682181850138620293796354053160696952e0;
52 pub(crate) const COSPI_KERNEL_TAYLOR_6: f64 =
53 -1.3352627688545894958753047828505831928711354556681e0;
54 pub(crate) const COSPI_KERNEL_TAYLOR_8: f64 =
55 2.3533063035889320454187935277546542154506893530856e-1;
56 pub(crate) const COSPI_KERNEL_TAYLOR_10: f64 =
57 -2.5806891390014060012598294252898849657186441048147e-2;
58 pub(crate) const COSPI_KERNEL_TAYLOR_12: f64 =
59 1.9295743094039230479033455636859576401684718150003e-3;
60 pub(crate) const COSPI_KERNEL_TAYLOR_14: f64 =
61 -1.0463810492484570711801672835223932761029733149091e-4;
62 pub(crate) const COSPI_KERNEL_TAYLOR_16: f64 =
63 4.3030695870329470072978237149669233008960901556009e-6;
64 pub(crate) const COSPI_KERNEL_TAYLOR_18: f64 =
65 -1.387895246221377211446808750399309343777037849978e-7;
68 /// computes `sin(pi * x)` for `-0.25 <= x <= 0.25`
69 /// not guaranteed to give correct sign for zero result
70 /// has an error of up to 2ULP
71 pub fn sin_pi_kernel_f16<Ctx: Context>(ctx: Ctx, x: Ctx::VecF16) -> Ctx::VecF16 {
73 let mut v: Ctx::VecF16 = ctx.make(consts::SINPI_KERNEL_TAYLOR_5.to());
74 v = v.mul_add_fast(x_sq, ctx.make(consts::SINPI_KERNEL_TAYLOR_3.to()));
75 v = v.mul_add_fast(x_sq, ctx.make(consts::SINPI_KERNEL_TAYLOR_1.to()));
79 /// computes `cos(pi * x)` for `-0.25 <= x <= 0.25`
80 /// has an error of up to 2ULP
81 pub fn cos_pi_kernel_f16<Ctx: Context>(ctx: Ctx, x: Ctx::VecF16) -> Ctx::VecF16 {
83 let mut v: Ctx::VecF16 = ctx.make(consts::COSPI_KERNEL_TAYLOR_4.to());
84 v = v.mul_add_fast(x_sq, ctx.make(consts::COSPI_KERNEL_TAYLOR_2.to()));
85 v.mul_add_fast(x_sq, ctx.make(consts::COSPI_KERNEL_TAYLOR_0.to()))
88 /// computes `sin(pi * x)` for `-0.25 <= x <= 0.25`
89 /// not guaranteed to give correct sign for zero result
90 /// has an error of up to 2ULP
91 pub fn sin_pi_kernel_f32<Ctx: Context>(ctx: Ctx, x: Ctx::VecF32) -> Ctx::VecF32 {
93 let mut v: Ctx::VecF32 = ctx.make(consts::SINPI_KERNEL_TAYLOR_9.to());
94 v = v.mul_add_fast(x_sq, ctx.make(consts::SINPI_KERNEL_TAYLOR_7.to()));
95 v = v.mul_add_fast(x_sq, ctx.make(consts::SINPI_KERNEL_TAYLOR_5.to()));
96 v = v.mul_add_fast(x_sq, ctx.make(consts::SINPI_KERNEL_TAYLOR_3.to()));
97 v = v.mul_add_fast(x_sq, ctx.make(consts::SINPI_KERNEL_TAYLOR_1.to()));
101 /// computes `cos(pi * x)` for `-0.25 <= x <= 0.25`
102 /// has an error of up to 2ULP
103 pub fn cos_pi_kernel_f32<Ctx: Context>(ctx: Ctx, x: Ctx::VecF32) -> Ctx::VecF32 {
105 let mut v: Ctx::VecF32 = ctx.make(consts::COSPI_KERNEL_TAYLOR_8.to());
106 v = v.mul_add_fast(x_sq, ctx.make(consts::COSPI_KERNEL_TAYLOR_6.to()));
107 v = v.mul_add_fast(x_sq, ctx.make(consts::COSPI_KERNEL_TAYLOR_4.to()));
108 v = v.mul_add_fast(x_sq, ctx.make(consts::COSPI_KERNEL_TAYLOR_2.to()));
109 v.mul_add_fast(x_sq, ctx.make(consts::COSPI_KERNEL_TAYLOR_0.to()))
112 /// computes `sin(pi * x)` for `-0.25 <= x <= 0.25`
113 /// not guaranteed to give correct sign for zero result
114 /// has an error of up to 2ULP
115 pub fn sin_pi_kernel_f64<Ctx: Context>(ctx: Ctx, x: Ctx::VecF64) -> Ctx::VecF64 {
117 let mut v: Ctx::VecF64 = ctx.make(consts::SINPI_KERNEL_TAYLOR_15.to());
118 v = v.mul_add_fast(x_sq, ctx.make(consts::SINPI_KERNEL_TAYLOR_13.to()));
119 v = v.mul_add_fast(x_sq, ctx.make(consts::SINPI_KERNEL_TAYLOR_11.to()));
120 v = v.mul_add_fast(x_sq, ctx.make(consts::SINPI_KERNEL_TAYLOR_9.to()));
121 v = v.mul_add_fast(x_sq, ctx.make(consts::SINPI_KERNEL_TAYLOR_7.to()));
122 v = v.mul_add_fast(x_sq, ctx.make(consts::SINPI_KERNEL_TAYLOR_5.to()));
123 v = v.mul_add_fast(x_sq, ctx.make(consts::SINPI_KERNEL_TAYLOR_3.to()));
124 v = v.mul_add_fast(x_sq, ctx.make(consts::SINPI_KERNEL_TAYLOR_1.to()));
128 /// computes `cos(pi * x)` for `-0.25 <= x <= 0.25`
129 /// has an error of up to 2ULP
130 pub fn cos_pi_kernel_f64<Ctx: Context>(ctx: Ctx, x: Ctx::VecF64) -> Ctx::VecF64 {
132 let mut v: Ctx::VecF64 = ctx.make(consts::COSPI_KERNEL_TAYLOR_16.to());
133 v = v.mul_add_fast(x_sq, ctx.make(consts::COSPI_KERNEL_TAYLOR_14.to()));
134 v = v.mul_add_fast(x_sq, ctx.make(consts::COSPI_KERNEL_TAYLOR_12.to()));
135 v = v.mul_add_fast(x_sq, ctx.make(consts::COSPI_KERNEL_TAYLOR_10.to()));
136 v = v.mul_add_fast(x_sq, ctx.make(consts::COSPI_KERNEL_TAYLOR_8.to()));
137 v = v.mul_add_fast(x_sq, ctx.make(consts::COSPI_KERNEL_TAYLOR_6.to()));
138 v = v.mul_add_fast(x_sq, ctx.make(consts::COSPI_KERNEL_TAYLOR_4.to()));
139 v = v.mul_add_fast(x_sq, ctx.make(consts::COSPI_KERNEL_TAYLOR_2.to()));
140 v.mul_add_fast(x_sq, ctx.make(consts::COSPI_KERNEL_TAYLOR_0.to()))
143 /// computes `(sin(pi * x), cos(pi * x))`
144 /// not guaranteed to give correct sign for zero results
145 /// inherits error from `sin_pi_kernel` and `cos_pi_kernel`
146 pub fn sin_cos_pi_impl<
148 VecF: Float<PrimFloat = PrimF> + Make<Context = Ctx>,
149 PrimF: PrimFloat<BitsType = PrimU>,
151 SinPiKernel: FnOnce(Ctx, VecF) -> VecF,
152 CosPiKernel: FnOnce(Ctx, VecF) -> VecF,
156 sin_pi_kernel: SinPiKernel,
157 cos_pi_kernel: CosPiKernel,
159 let two_f: VecF = ctx.make(2.0.to());
160 let one_half: VecF = ctx.make(0.5.to());
161 let max_contiguous_integer: VecF = ctx.make(PrimF::max_contiguous_integer());
162 // if `x` is finite and bigger than `max_contiguous_integer`, then x is an even integer
163 let in_range = x.abs().lt(max_contiguous_integer); // use `lt` so nans are counted as out-of-range
164 let is_finite = x.is_finite();
165 let nan: VecF = ctx.make(f32::NAN.to());
166 let zero_f: VecF = ctx.make(0.to());
167 let one_f: VecF = ctx.make(1.to());
168 let zero_i: VecF::SignedBitsType = ctx.make(0.to());
169 let one_i: VecF::SignedBitsType = ctx.make(1.to());
170 let two_i: VecF::SignedBitsType = ctx.make(2.to());
171 let out_of_range_sin = is_finite.select(zero_f, nan);
172 let out_of_range_cos = is_finite.select(one_f, nan);
173 let xi = (x * two_f).round();
174 let xk = x - xi * one_half;
175 let sk = sin_pi_kernel(ctx, xk);
176 let ck = cos_pi_kernel(ctx, xk);
177 let xi = VecF::SignedBitsType::cvt_from(xi);
178 let bit_0_clear = (xi & one_i).eq(zero_i);
179 let st = bit_0_clear.select(sk, ck);
180 let ct = bit_0_clear.select(ck, sk);
181 let s = (xi & two_i).eq(zero_i).select(st, -st);
182 let c = ((xi + one_i) & two_i).eq(zero_i).select(ct, -ct);
184 in_range.select(s, out_of_range_sin),
185 in_range.select(c, out_of_range_cos),
189 /// computes `(sin(pi * x), cos(pi * x))`
190 /// not guaranteed to give correct sign for zero results
191 /// has an error of up to 2ULP
192 pub fn sin_cos_pi_f16<Ctx: Context>(ctx: Ctx, x: Ctx::VecF16) -> (Ctx::VecF16, Ctx::VecF16) {
193 sin_cos_pi_impl(ctx, x, sin_pi_kernel_f16, cos_pi_kernel_f16)
196 /// computes `sin(pi * x)`
197 /// not guaranteed to give correct sign for zero results
198 /// has an error of up to 2ULP
199 pub fn sin_pi_f16<Ctx: Context>(ctx: Ctx, x: Ctx::VecF16) -> Ctx::VecF16 {
200 sin_cos_pi_f16(ctx, x).0
203 /// computes `cos(pi * x)`
204 /// not guaranteed to give correct sign for zero results
205 /// has an error of up to 2ULP
206 pub fn cos_pi_f16<Ctx: Context>(ctx: Ctx, x: Ctx::VecF16) -> Ctx::VecF16 {
207 sin_cos_pi_f16(ctx, x).1
210 /// computes `(sin(pi * x), cos(pi * x))`
211 /// not guaranteed to give correct sign for zero results
212 /// has an error of up to 2ULP
213 pub fn sin_cos_pi_f32<Ctx: Context>(ctx: Ctx, x: Ctx::VecF32) -> (Ctx::VecF32, Ctx::VecF32) {
214 sin_cos_pi_impl(ctx, x, sin_pi_kernel_f32, cos_pi_kernel_f32)
217 /// computes `sin(pi * x)`
218 /// not guaranteed to give correct sign for zero results
219 /// has an error of up to 2ULP
220 pub fn sin_pi_f32<Ctx: Context>(ctx: Ctx, x: Ctx::VecF32) -> Ctx::VecF32 {
221 sin_cos_pi_f32(ctx, x).0
224 /// computes `cos(pi * x)`
225 /// not guaranteed to give correct sign for zero results
226 /// has an error of up to 2ULP
227 pub fn cos_pi_f32<Ctx: Context>(ctx: Ctx, x: Ctx::VecF32) -> Ctx::VecF32 {
228 sin_cos_pi_f32(ctx, x).1
231 /// computes `(sin(pi * x), cos(pi * x))`
232 /// not guaranteed to give correct sign for zero results
233 /// has an error of up to 2ULP
234 pub fn sin_cos_pi_f64<Ctx: Context>(ctx: Ctx, x: Ctx::VecF64) -> (Ctx::VecF64, Ctx::VecF64) {
235 sin_cos_pi_impl(ctx, x, sin_pi_kernel_f64, cos_pi_kernel_f64)
238 /// computes `sin(pi * x)`
239 /// not guaranteed to give correct sign for zero results
240 /// has an error of up to 2ULP
241 pub fn sin_pi_f64<Ctx: Context>(ctx: Ctx, x: Ctx::VecF64) -> Ctx::VecF64 {
242 sin_cos_pi_f64(ctx, x).0
245 /// computes `cos(pi * x)`
246 /// not guaranteed to give correct sign for zero results
247 /// has an error of up to 2ULP
248 pub fn cos_pi_f64<Ctx: Context>(ctx: Ctx, x: Ctx::VecF64) -> Ctx::VecF64 {
249 sin_cos_pi_f64(ctx, x).1
257 scalar::{Scalar, Value},
261 struct CheckUlpCallbackArg<F, I> {
269 fn check_ulp<T: PrimFloat>(
271 is_ok: impl Fn(CheckUlpCallbackArg<T, u64>) -> bool,
272 fn_f16: impl Fn(T) -> T,
273 fn_reference: impl Fn(f64) -> f64,
275 let x_f64: f64 = x.to();
276 let expected_f64 = fn_reference(x_f64);
277 let expected: T = expected_f64.to();
278 let result = fn_f16(x);
279 if result == expected {
282 if result.is_nan() && expected.is_nan() {
285 let expected_bits: i64 = expected.to_bits().to();
286 let result_bits: i64 = result.to_bits().to();
287 let distance_in_ulp = (expected_bits - result_bits).unsigned_abs();
289 && !expected.is_nan()
290 && is_ok(CheckUlpCallbackArg {
301 x = {x:?} {x_bits:#X}, \
302 result = {result:?} {result_bits:#X}, \
303 expected = {expected:?} {expected_bits:#X}, \
304 distance_in_ulp = {distance_in_ulp}",
306 x_bits = x.to_bits(),
308 result_bits = result.to_bits(),
310 expected_bits = expected.to_bits(),
311 distance_in_ulp = distance_in_ulp,
317 not(feature = "f16"),
318 should_panic(expected = "f16 feature is not enabled")
320 fn test_sin_pi_kernel_f16() {
324 |arg| arg.distance_in_ulp <= if arg.expected == 0.to() { 0 } else { 2 },
325 |x| sin_pi_kernel_f16(Scalar, Value(x)).0,
326 |x| (f64::consts::PI * x).sin(),
329 let quarter = F16::to_bits(0.25f32.to());
330 for bits in (0..=quarter).rev() {
331 check(F16::from_bits(bits));
332 check(-F16::from_bits(bits));
338 not(feature = "f16"),
339 should_panic(expected = "f16 feature is not enabled")
341 fn test_cos_pi_kernel_f16() {
345 |arg| arg.distance_in_ulp <= 2 && arg.result <= 1.to(),
346 |x| cos_pi_kernel_f16(Scalar, Value(x)).0,
347 |x| (f64::consts::PI * x).cos(),
350 let quarter = F16::to_bits(0.25f32.to());
351 for bits in (0..=quarter).rev() {
352 check(F16::from_bits(bits));
353 check(-F16::from_bits(bits));
358 #[cfg(feature = "full_tests")]
359 fn test_sin_pi_kernel_f32() {
363 |arg| arg.distance_in_ulp <= if arg.expected == 0. { 0 } else { 2 },
364 |x| sin_pi_kernel_f32(Scalar, Value(x)).0,
365 |x| (f64::consts::PI * x).sin(),
368 let quarter = 0.25f32.to_bits();
369 for bits in (0..=quarter).rev() {
370 check(f32::from_bits(bits));
371 check(-f32::from_bits(bits));
376 #[cfg(feature = "full_tests")]
377 fn test_cos_pi_kernel_f32() {
381 |arg| arg.distance_in_ulp <= 2 && arg.result <= 1.,
382 |x| cos_pi_kernel_f32(Scalar, Value(x)).0,
383 |x| (f64::consts::PI * x).cos(),
386 let quarter = 0.25f32.to_bits();
387 for bits in (0..=quarter).rev() {
388 check(f32::from_bits(bits));
389 check(-f32::from_bits(bits));
394 #[cfg(feature = "full_tests")]
395 fn test_sin_pi_kernel_f64() {
399 sin_cos_pi_check_ulp_callback,
400 |x| sin_pi_kernel_f64(Scalar, Value(x)).0,
401 |x| reference_sin_cos_pi_f64(x).0,
404 let quarter = 0.25f32.to_bits();
405 for bits in (0..=quarter).rev().step_by(1 << 5) {
406 check(f32::from_bits(bits) as f64);
407 check(-f32::from_bits(bits) as f64);
412 #[cfg(feature = "full_tests")]
413 fn test_cos_pi_kernel_f64() {
417 sin_cos_pi_check_ulp_callback,
418 |x| cos_pi_kernel_f64(Scalar, Value(x)).0,
419 |x| reference_sin_cos_pi_f64(x).1,
422 let quarter = 0.25f32.to_bits();
423 for bits in (0..=quarter).rev().step_by(1 << 5) {
424 check(f32::from_bits(bits) as f64);
425 check(-f32::from_bits(bits) as f64);
429 fn sin_cos_pi_check_ulp_callback<F: PrimFloat>(arg: CheckUlpCallbackArg<F, u64>) -> bool {
430 if arg.x % 0.5.to() == 0.0.to() {
431 arg.distance_in_ulp == 0
433 arg.distance_in_ulp <= 2 && arg.result.abs() <= 1.to()
439 not(feature = "f16"),
440 should_panic(expected = "f16 feature is not enabled")
442 fn test_sin_pi_f16() {
443 for bits in 0..=u16::MAX {
445 F16::from_bits(bits),
446 sin_cos_pi_check_ulp_callback,
447 |x| sin_pi_f16(Scalar, Value(x)).0,
448 |x| (f64::consts::PI * x).sin(),
455 not(feature = "f16"),
456 should_panic(expected = "f16 feature is not enabled")
458 fn test_cos_pi_f16() {
459 for bits in 0..=u16::MAX {
461 F16::from_bits(bits),
462 sin_cos_pi_check_ulp_callback,
463 |x| cos_pi_f16(Scalar, Value(x)).0,
464 |x| (f64::consts::PI * x).cos(),
469 fn reference_sin_cos_pi_f32(mut v: f64) -> (f64, f64) {
471 return (f64::NAN, f64::NAN);
476 } else if v <= -1.0 {
480 let part = v.round() as i32;
482 v *= f64::consts::PI / 2.0;
483 let (sin, cos) = v.sin_cos();
490 _ => panic!("not implemented: part={}", part),
494 fn reference_sin_cos_pi_f64(mut v: f64) -> (f64, f64) {
496 use rug::{float::Constant, Float};
498 return (f64::NAN, f64::NAN);
503 } else if v <= -1.0 {
507 let part = v.round() as i32;
510 let mut v = Float::with_val(precision, v);
511 let pi = Float::with_val(precision, Constant::Pi);
514 let cos = pi_2; // just a temp var, value is ignored
515 let (sin, cos) = v.sin_cos(cos);
516 let sin: f64 = sin.cast();
517 let cos: f64 = cos.cast();
524 _ => panic!("not implemented: part={}", part),
528 macro_rules! test_reference_sin_cos_pi_test_cases {
529 ($case:expr, $ty:ident) => {
530 $case($ty::NAN, $ty::NAN, $ty::NAN);
531 $case($ty::INFINITY, $ty::NAN, $ty::NAN);
532 $case(-$ty::INFINITY, $ty::NAN, $ty::NAN);
536 0.38268343236508977172845998403039886676134456248563,
537 0.92387953251128675612818318939678828682241662586364,
541 0.70710678118654752440084436210484903928483593768847,
542 0.70710678118654752440084436210484903928483593768847,
546 0.92387953251128675612818318939678828682241662586364,
547 0.38268343236508977172845998403039886676134456248563,
549 $case(-3.5, 1., -0.);
552 0.92387953251128675612818318939678828682241662586364,
553 -0.38268343236508977172845998403039886676134456248563,
557 0.70710678118654752440084436210484903928483593768847,
558 -0.70710678118654752440084436210484903928483593768847,
562 0.38268343236508977172845998403039886676134456248563,
563 -0.92387953251128675612818318939678828682241662586364,
565 $case(-3., -0., -1.);
568 -0.38268343236508977172845998403039886676134456248563,
569 -0.92387953251128675612818318939678828682241662586364,
573 -0.70710678118654752440084436210484903928483593768847,
574 -0.70710678118654752440084436210484903928483593768847,
578 -0.92387953251128675612818318939678828682241662586364,
579 -0.38268343236508977172845998403039886676134456248563,
581 $case(-2.5, -1., 0.);
584 -0.92387953251128675612818318939678828682241662586364,
585 0.38268343236508977172845998403039886676134456248563,
589 -0.70710678118654752440084436210484903928483593768847,
590 0.70710678118654752440084436210484903928483593768847,
594 -0.38268343236508977172845998403039886676134456248563,
595 0.92387953251128675612818318939678828682241662586364,
600 0.38268343236508977172845998403039886676134456248563,
601 0.92387953251128675612818318939678828682241662586364,
605 0.70710678118654752440084436210484903928483593768847,
606 0.70710678118654752440084436210484903928483593768847,
610 0.92387953251128675612818318939678828682241662586364,
611 0.38268343236508977172845998403039886676134456248563,
613 $case(-1.5, 1., -0.);
616 0.92387953251128675612818318939678828682241662586364,
617 -0.38268343236508977172845998403039886676134456248563,
621 0.70710678118654752440084436210484903928483593768847,
622 -0.70710678118654752440084436210484903928483593768847,
626 0.38268343236508977172845998403039886676134456248563,
627 -0.92387953251128675612818318939678828682241662586364,
629 $case(-1., -0., -1.);
632 -0.38268343236508977172845998403039886676134456248563,
633 -0.92387953251128675612818318939678828682241662586364,
637 -0.70710678118654752440084436210484903928483593768847,
638 -0.70710678118654752440084436210484903928483593768847,
642 -0.92387953251128675612818318939678828682241662586364,
643 -0.38268343236508977172845998403039886676134456248563,
645 $case(-0.5, -1., 0.);
648 -0.92387953251128675612818318939678828682241662586364,
649 0.38268343236508977172845998403039886676134456248563,
653 -0.70710678118654752440084436210484903928483593768847,
654 0.70710678118654752440084436210484903928483593768847,
658 -0.38268343236508977172845998403039886676134456248563,
659 0.92387953251128675612818318939678828682241662586364,
664 0.38268343236508977172845998403039886676134456248563,
665 0.92387953251128675612818318939678828682241662586364,
669 0.70710678118654752440084436210484903928483593768847,
670 0.70710678118654752440084436210484903928483593768847,
674 0.92387953251128675612818318939678828682241662586364,
675 0.38268343236508977172845998403039886676134456248563,
680 0.92387953251128675612818318939678828682241662586364,
681 -0.38268343236508977172845998403039886676134456248563,
685 0.70710678118654752440084436210484903928483593768847,
686 -0.70710678118654752440084436210484903928483593768847,
690 0.38268343236508977172845998403039886676134456248563,
691 -0.92387953251128675612818318939678828682241662586364,
696 -0.38268343236508977172845998403039886676134456248563,
697 -0.92387953251128675612818318939678828682241662586364,
701 -0.70710678118654752440084436210484903928483593768847,
702 -0.70710678118654752440084436210484903928483593768847,
706 -0.92387953251128675612818318939678828682241662586364,
707 -0.38268343236508977172845998403039886676134456248563,
709 $case(1.5, -1., -0.);
712 -0.92387953251128675612818318939678828682241662586364,
713 0.38268343236508977172845998403039886676134456248563,
717 -0.70710678118654752440084436210484903928483593768847,
718 0.70710678118654752440084436210484903928483593768847,
722 -0.38268343236508977172845998403039886676134456248563,
723 0.92387953251128675612818318939678828682241662586364,
728 0.38268343236508977172845998403039886676134456248563,
729 0.92387953251128675612818318939678828682241662586364,
733 0.70710678118654752440084436210484903928483593768847,
734 0.70710678118654752440084436210484903928483593768847,
738 0.92387953251128675612818318939678828682241662586364,
739 0.38268343236508977172845998403039886676134456248563,
744 0.92387953251128675612818318939678828682241662586364,
745 -0.38268343236508977172845998403039886676134456248563,
749 0.70710678118654752440084436210484903928483593768847,
750 -0.70710678118654752440084436210484903928483593768847,
754 0.38268343236508977172845998403039886676134456248563,
755 -0.92387953251128675612818318939678828682241662586364,
760 -0.38268343236508977172845998403039886676134456248563,
761 -0.92387953251128675612818318939678828682241662586364,
765 -0.70710678118654752440084436210484903928483593768847,
766 -0.70710678118654752440084436210484903928483593768847,
770 -0.92387953251128675612818318939678828682241662586364,
771 -0.38268343236508977172845998403039886676134456248563,
773 $case(3.5, -1., -0.);
776 -0.92387953251128675612818318939678828682241662586364,
777 0.38268343236508977172845998403039886676134456248563,
781 -0.70710678118654752440084436210484903928483593768847,
782 0.70710678118654752440084436210484903928483593768847,
786 -0.38268343236508977172845998403039886676134456248563,
787 0.92387953251128675612818318939678828682241662586364,
794 fn test_reference_sin_cos_pi_f32() {
795 fn approx_same(a: f32, b: f32) -> bool {
796 if a.is_finite() && b.is_finite() {
799 a == b || (a.is_nan() && b.is_nan())
803 fn case(x: f32, expected_sin: f32, expected_cos: f32) {
804 let (ref_sin, ref_cos) = reference_sin_cos_pi_f32(x as f64);
806 approx_same(ref_sin as f32, expected_sin)
807 && approx_same(ref_cos as f32, expected_cos),
808 "case failed: x={x}, expected_sin={expected_sin}, expected_cos={expected_cos}, ref_sin={ref_sin}, ref_cos={ref_cos}",
810 expected_sin=expected_sin,
811 expected_cos=expected_cos,
816 test_reference_sin_cos_pi_test_cases!(case, f32);
820 fn test_reference_sin_cos_pi_f64() {
821 fn same(a: f64, b: f64) -> bool {
822 if a.is_finite() && b.is_finite() {
825 a == b || (a.is_nan() && b.is_nan())
829 fn case(x: f64, expected_sin: f64, expected_cos: f64) {
830 let (ref_sin, ref_cos) = reference_sin_cos_pi_f64(x);
832 same(ref_sin, expected_sin) && same(ref_cos, expected_cos),
833 "case failed: x={x}, expected_sin={expected_sin}, expected_cos={expected_cos}, ref_sin={ref_sin}, ref_cos={ref_cos}",
835 expected_sin=expected_sin,
836 expected_cos=expected_cos,
841 test_reference_sin_cos_pi_test_cases!(case, f64);
845 #[cfg(feature = "full_tests")]
846 fn test_sin_pi_f32() {
847 for bits in 0..=u32::MAX {
849 f32::from_bits(bits),
850 sin_cos_pi_check_ulp_callback,
851 |x| sin_pi_f32(Scalar, Value(x)).0,
852 |x| reference_sin_cos_pi_f32(x).0,
858 #[cfg(feature = "full_tests")]
859 fn test_cos_pi_f32() {
860 for bits in 0..=u32::MAX {
862 f32::from_bits(bits),
863 sin_cos_pi_check_ulp_callback,
864 |x| cos_pi_f32(Scalar, Value(x)).0,
865 |x| reference_sin_cos_pi_f32(x).1,
871 #[cfg(feature = "full_tests")]
872 fn test_sin_pi_f64() {
873 for bits in (0..=u32::MAX).step_by(1 << 7) {
875 f32::from_bits(bits) as f64,
876 sin_cos_pi_check_ulp_callback,
877 |x| sin_pi_f64(Scalar, Value(x)).0,
878 |x| reference_sin_cos_pi_f64(x).0,
884 #[cfg(feature = "full_tests")]
885 fn test_cos_pi_f64() {
886 for bits in (0..=u32::MAX).step_by(1 << 7) {
888 f32::from_bits(bits) as f64,
889 sin_cos_pi_check_ulp_callback,
890 |x| cos_pi_f64(Scalar, Value(x)).0,
891 |x| reference_sin_cos_pi_f64(x).1,