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 =
162 ctx.make((PrimU::cvt_from(1) << (PrimF::MANTISSA_FIELD_WIDTH + 1.to())).to());
163 // if `x` is finite and bigger than `max_contiguous_integer`, then x is an even integer
164 let in_range = x.abs().lt(max_contiguous_integer); // use `lt` so nans are counted as out-of-range
165 let is_finite = x.is_finite();
166 let nan: VecF = ctx.make(f32::NAN.to());
167 let zero_f: VecF = ctx.make(0.to());
168 let one_f: VecF = ctx.make(1.to());
169 let zero_i: VecF::SignedBitsType = ctx.make(0.to());
170 let one_i: VecF::SignedBitsType = ctx.make(1.to());
171 let two_i: VecF::SignedBitsType = ctx.make(2.to());
172 let out_of_range_sin = is_finite.select(zero_f, nan);
173 let out_of_range_cos = is_finite.select(one_f, nan);
174 let xi = (x * two_f).round();
175 let xk = x - xi * one_half;
176 let sk = sin_pi_kernel(ctx, xk);
177 let ck = cos_pi_kernel(ctx, xk);
178 let xi = VecF::SignedBitsType::cvt_from(xi);
179 let bit_0_clear = (xi & one_i).eq(zero_i);
180 let st = bit_0_clear.select(sk, ck);
181 let ct = bit_0_clear.select(ck, sk);
182 let s = (xi & two_i).eq(zero_i).select(st, -st);
183 let c = ((xi + one_i) & two_i).eq(zero_i).select(ct, -ct);
185 in_range.select(s, out_of_range_sin),
186 in_range.select(c, out_of_range_cos),
190 /// computes `(sin(pi * x), cos(pi * x))`
191 /// not guaranteed to give correct sign for zero results
192 /// has an error of up to 2ULP
193 pub fn sin_cos_pi_f16<Ctx: Context>(ctx: Ctx, x: Ctx::VecF16) -> (Ctx::VecF16, Ctx::VecF16) {
194 sin_cos_pi_impl(ctx, x, sin_pi_kernel_f16, cos_pi_kernel_f16)
197 /// computes `sin(pi * x)`
198 /// not guaranteed to give correct sign for zero results
199 /// has an error of up to 2ULP
200 pub fn sin_pi_f16<Ctx: Context>(ctx: Ctx, x: Ctx::VecF16) -> Ctx::VecF16 {
201 sin_cos_pi_f16(ctx, x).0
204 /// computes `cos(pi * x)`
205 /// not guaranteed to give correct sign for zero results
206 /// has an error of up to 2ULP
207 pub fn cos_pi_f16<Ctx: Context>(ctx: Ctx, x: Ctx::VecF16) -> Ctx::VecF16 {
208 sin_cos_pi_f16(ctx, x).1
211 /// computes `(sin(pi * x), cos(pi * x))`
212 /// not guaranteed to give correct sign for zero results
213 /// has an error of up to 2ULP
214 pub fn sin_cos_pi_f32<Ctx: Context>(ctx: Ctx, x: Ctx::VecF32) -> (Ctx::VecF32, Ctx::VecF32) {
215 sin_cos_pi_impl(ctx, x, sin_pi_kernel_f32, cos_pi_kernel_f32)
218 /// computes `sin(pi * x)`
219 /// not guaranteed to give correct sign for zero results
220 /// has an error of up to 2ULP
221 pub fn sin_pi_f32<Ctx: Context>(ctx: Ctx, x: Ctx::VecF32) -> Ctx::VecF32 {
222 sin_cos_pi_f32(ctx, x).0
225 /// computes `cos(pi * x)`
226 /// not guaranteed to give correct sign for zero results
227 /// has an error of up to 2ULP
228 pub fn cos_pi_f32<Ctx: Context>(ctx: Ctx, x: Ctx::VecF32) -> Ctx::VecF32 {
229 sin_cos_pi_f32(ctx, x).1
232 /// computes `(sin(pi * x), cos(pi * x))`
233 /// not guaranteed to give correct sign for zero results
234 /// has an error of up to 2ULP
235 pub fn sin_cos_pi_f64<Ctx: Context>(ctx: Ctx, x: Ctx::VecF64) -> (Ctx::VecF64, Ctx::VecF64) {
236 sin_cos_pi_impl(ctx, x, sin_pi_kernel_f64, cos_pi_kernel_f64)
239 /// computes `sin(pi * x)`
240 /// not guaranteed to give correct sign for zero results
241 /// has an error of up to 2ULP
242 pub fn sin_pi_f64<Ctx: Context>(ctx: Ctx, x: Ctx::VecF64) -> Ctx::VecF64 {
243 sin_cos_pi_f64(ctx, x).0
246 /// computes `cos(pi * x)`
247 /// not guaranteed to give correct sign for zero results
248 /// has an error of up to 2ULP
249 pub fn cos_pi_f64<Ctx: Context>(ctx: Ctx, x: Ctx::VecF64) -> Ctx::VecF64 {
250 sin_cos_pi_f64(ctx, x).1
258 scalar::{Scalar, Value},
262 struct CheckUlpCallbackArg<F, I> {
270 fn check_ulp<T: PrimFloat>(
272 is_ok: impl Fn(CheckUlpCallbackArg<T, u64>) -> bool,
273 fn_f16: impl Fn(T) -> T,
274 fn_reference: impl Fn(f64) -> f64,
276 let x_f64: f64 = x.to();
277 let expected_f64 = fn_reference(x_f64);
278 let expected: T = expected_f64.to();
279 let result = fn_f16(x);
280 if result == expected {
283 if result.is_nan() && expected.is_nan() {
286 let expected_bits: i64 = expected.to_bits().to();
287 let result_bits: i64 = result.to_bits().to();
288 let distance_in_ulp = (expected_bits - result_bits).unsigned_abs();
290 && !expected.is_nan()
291 && is_ok(CheckUlpCallbackArg {
302 x = {x:?} {x_bits:#X}, \
303 result = {result:?} {result_bits:#X}, \
304 expected = {expected:?} {expected_bits:#X}, \
305 distance_in_ulp = {distance_in_ulp}",
307 x_bits = x.to_bits(),
309 result_bits = result.to_bits(),
311 expected_bits = expected.to_bits(),
312 distance_in_ulp = distance_in_ulp,
318 not(feature = "f16"),
319 should_panic(expected = "f16 feature is not enabled")
321 fn test_sin_pi_kernel_f16() {
325 |arg| arg.distance_in_ulp <= if arg.expected == 0.to() { 0 } else { 2 },
326 |x| sin_pi_kernel_f16(Scalar, Value(x)).0,
327 |x| (f64::consts::PI * x).sin(),
330 let quarter = F16::to_bits(0.25f32.to());
331 for bits in (0..=quarter).rev() {
332 check(F16::from_bits(bits));
333 check(-F16::from_bits(bits));
339 not(feature = "f16"),
340 should_panic(expected = "f16 feature is not enabled")
342 fn test_cos_pi_kernel_f16() {
346 |arg| arg.distance_in_ulp <= 2 && arg.result <= 1.to(),
347 |x| cos_pi_kernel_f16(Scalar, Value(x)).0,
348 |x| (f64::consts::PI * x).cos(),
351 let quarter = F16::to_bits(0.25f32.to());
352 for bits in (0..=quarter).rev() {
353 check(F16::from_bits(bits));
354 check(-F16::from_bits(bits));
359 #[cfg(feature = "full_tests")]
360 fn test_sin_pi_kernel_f32() {
364 |arg| arg.distance_in_ulp <= if arg.expected == 0. { 0 } else { 2 },
365 |x| sin_pi_kernel_f32(Scalar, Value(x)).0,
366 |x| (f64::consts::PI * x).sin(),
369 let quarter = 0.25f32.to_bits();
370 for bits in (0..=quarter).rev() {
371 check(f32::from_bits(bits));
372 check(-f32::from_bits(bits));
377 #[cfg(feature = "full_tests")]
378 fn test_cos_pi_kernel_f32() {
382 |arg| arg.distance_in_ulp <= 2 && arg.result <= 1.,
383 |x| cos_pi_kernel_f32(Scalar, Value(x)).0,
384 |x| (f64::consts::PI * x).cos(),
387 let quarter = 0.25f32.to_bits();
388 for bits in (0..=quarter).rev() {
389 check(f32::from_bits(bits));
390 check(-f32::from_bits(bits));
395 #[cfg(feature = "full_tests")]
396 fn test_sin_pi_kernel_f64() {
400 sin_cos_pi_check_ulp_callback,
401 |x| sin_pi_kernel_f64(Scalar, Value(x)).0,
402 |x| reference_sin_cos_pi_f64(x).0,
405 let quarter = 0.25f32.to_bits();
406 for bits in (0..=quarter).rev().step_by(1 << 5) {
407 check(f32::from_bits(bits) as f64);
408 check(-f32::from_bits(bits) as f64);
413 #[cfg(feature = "full_tests")]
414 fn test_cos_pi_kernel_f64() {
418 sin_cos_pi_check_ulp_callback,
419 |x| cos_pi_kernel_f64(Scalar, Value(x)).0,
420 |x| reference_sin_cos_pi_f64(x).1,
423 let quarter = 0.25f32.to_bits();
424 for bits in (0..=quarter).rev().step_by(1 << 5) {
425 check(f32::from_bits(bits) as f64);
426 check(-f32::from_bits(bits) as f64);
430 fn sin_cos_pi_check_ulp_callback<F: PrimFloat>(arg: CheckUlpCallbackArg<F, u64>) -> bool {
431 if arg.x % 0.5.to() == 0.0.to() {
432 arg.distance_in_ulp == 0
434 arg.distance_in_ulp <= 2 && arg.result.abs() <= 1.to()
440 not(feature = "f16"),
441 should_panic(expected = "f16 feature is not enabled")
443 fn test_sin_pi_f16() {
444 for bits in 0..=u16::MAX {
446 F16::from_bits(bits),
447 sin_cos_pi_check_ulp_callback,
448 |x| sin_pi_f16(Scalar, Value(x)).0,
449 |x| (f64::consts::PI * x).sin(),
456 not(feature = "f16"),
457 should_panic(expected = "f16 feature is not enabled")
459 fn test_cos_pi_f16() {
460 for bits in 0..=u16::MAX {
462 F16::from_bits(bits),
463 sin_cos_pi_check_ulp_callback,
464 |x| cos_pi_f16(Scalar, Value(x)).0,
465 |x| (f64::consts::PI * x).cos(),
470 fn reference_sin_cos_pi_f32(mut v: f64) -> (f64, f64) {
472 return (f64::NAN, f64::NAN);
477 } else if v <= -1.0 {
481 let part = v.round() as i32;
483 v *= f64::consts::PI / 2.0;
484 let (sin, cos) = v.sin_cos();
491 _ => panic!("not implemented: part={}", part),
495 fn reference_sin_cos_pi_f64(mut v: f64) -> (f64, f64) {
497 use rug::{float::Constant, Float};
499 return (f64::NAN, f64::NAN);
504 } else if v <= -1.0 {
508 let part = v.round() as i32;
511 let mut v = Float::with_val(precision, v);
512 let pi = Float::with_val(precision, Constant::Pi);
515 let cos = pi_2; // just a temp var, value is ignored
516 let (sin, cos) = v.sin_cos(cos);
517 let sin: f64 = sin.cast();
518 let cos: f64 = cos.cast();
525 _ => panic!("not implemented: part={}", part),
529 macro_rules! test_reference_sin_cos_pi_test_cases {
530 ($case:expr, $ty:ident) => {
531 $case($ty::NAN, $ty::NAN, $ty::NAN);
532 $case($ty::INFINITY, $ty::NAN, $ty::NAN);
533 $case(-$ty::INFINITY, $ty::NAN, $ty::NAN);
537 0.38268343236508977172845998403039886676134456248563,
538 0.92387953251128675612818318939678828682241662586364,
542 0.70710678118654752440084436210484903928483593768847,
543 0.70710678118654752440084436210484903928483593768847,
547 0.92387953251128675612818318939678828682241662586364,
548 0.38268343236508977172845998403039886676134456248563,
550 $case(-3.5, 1., -0.);
553 0.92387953251128675612818318939678828682241662586364,
554 -0.38268343236508977172845998403039886676134456248563,
558 0.70710678118654752440084436210484903928483593768847,
559 -0.70710678118654752440084436210484903928483593768847,
563 0.38268343236508977172845998403039886676134456248563,
564 -0.92387953251128675612818318939678828682241662586364,
566 $case(-3., -0., -1.);
569 -0.38268343236508977172845998403039886676134456248563,
570 -0.92387953251128675612818318939678828682241662586364,
574 -0.70710678118654752440084436210484903928483593768847,
575 -0.70710678118654752440084436210484903928483593768847,
579 -0.92387953251128675612818318939678828682241662586364,
580 -0.38268343236508977172845998403039886676134456248563,
582 $case(-2.5, -1., 0.);
585 -0.92387953251128675612818318939678828682241662586364,
586 0.38268343236508977172845998403039886676134456248563,
590 -0.70710678118654752440084436210484903928483593768847,
591 0.70710678118654752440084436210484903928483593768847,
595 -0.38268343236508977172845998403039886676134456248563,
596 0.92387953251128675612818318939678828682241662586364,
601 0.38268343236508977172845998403039886676134456248563,
602 0.92387953251128675612818318939678828682241662586364,
606 0.70710678118654752440084436210484903928483593768847,
607 0.70710678118654752440084436210484903928483593768847,
611 0.92387953251128675612818318939678828682241662586364,
612 0.38268343236508977172845998403039886676134456248563,
614 $case(-1.5, 1., -0.);
617 0.92387953251128675612818318939678828682241662586364,
618 -0.38268343236508977172845998403039886676134456248563,
622 0.70710678118654752440084436210484903928483593768847,
623 -0.70710678118654752440084436210484903928483593768847,
627 0.38268343236508977172845998403039886676134456248563,
628 -0.92387953251128675612818318939678828682241662586364,
630 $case(-1., -0., -1.);
633 -0.38268343236508977172845998403039886676134456248563,
634 -0.92387953251128675612818318939678828682241662586364,
638 -0.70710678118654752440084436210484903928483593768847,
639 -0.70710678118654752440084436210484903928483593768847,
643 -0.92387953251128675612818318939678828682241662586364,
644 -0.38268343236508977172845998403039886676134456248563,
646 $case(-0.5, -1., 0.);
649 -0.92387953251128675612818318939678828682241662586364,
650 0.38268343236508977172845998403039886676134456248563,
654 -0.70710678118654752440084436210484903928483593768847,
655 0.70710678118654752440084436210484903928483593768847,
659 -0.38268343236508977172845998403039886676134456248563,
660 0.92387953251128675612818318939678828682241662586364,
665 0.38268343236508977172845998403039886676134456248563,
666 0.92387953251128675612818318939678828682241662586364,
670 0.70710678118654752440084436210484903928483593768847,
671 0.70710678118654752440084436210484903928483593768847,
675 0.92387953251128675612818318939678828682241662586364,
676 0.38268343236508977172845998403039886676134456248563,
681 0.92387953251128675612818318939678828682241662586364,
682 -0.38268343236508977172845998403039886676134456248563,
686 0.70710678118654752440084436210484903928483593768847,
687 -0.70710678118654752440084436210484903928483593768847,
691 0.38268343236508977172845998403039886676134456248563,
692 -0.92387953251128675612818318939678828682241662586364,
697 -0.38268343236508977172845998403039886676134456248563,
698 -0.92387953251128675612818318939678828682241662586364,
702 -0.70710678118654752440084436210484903928483593768847,
703 -0.70710678118654752440084436210484903928483593768847,
707 -0.92387953251128675612818318939678828682241662586364,
708 -0.38268343236508977172845998403039886676134456248563,
710 $case(1.5, -1., -0.);
713 -0.92387953251128675612818318939678828682241662586364,
714 0.38268343236508977172845998403039886676134456248563,
718 -0.70710678118654752440084436210484903928483593768847,
719 0.70710678118654752440084436210484903928483593768847,
723 -0.38268343236508977172845998403039886676134456248563,
724 0.92387953251128675612818318939678828682241662586364,
729 0.38268343236508977172845998403039886676134456248563,
730 0.92387953251128675612818318939678828682241662586364,
734 0.70710678118654752440084436210484903928483593768847,
735 0.70710678118654752440084436210484903928483593768847,
739 0.92387953251128675612818318939678828682241662586364,
740 0.38268343236508977172845998403039886676134456248563,
745 0.92387953251128675612818318939678828682241662586364,
746 -0.38268343236508977172845998403039886676134456248563,
750 0.70710678118654752440084436210484903928483593768847,
751 -0.70710678118654752440084436210484903928483593768847,
755 0.38268343236508977172845998403039886676134456248563,
756 -0.92387953251128675612818318939678828682241662586364,
761 -0.38268343236508977172845998403039886676134456248563,
762 -0.92387953251128675612818318939678828682241662586364,
766 -0.70710678118654752440084436210484903928483593768847,
767 -0.70710678118654752440084436210484903928483593768847,
771 -0.92387953251128675612818318939678828682241662586364,
772 -0.38268343236508977172845998403039886676134456248563,
774 $case(3.5, -1., -0.);
777 -0.92387953251128675612818318939678828682241662586364,
778 0.38268343236508977172845998403039886676134456248563,
782 -0.70710678118654752440084436210484903928483593768847,
783 0.70710678118654752440084436210484903928483593768847,
787 -0.38268343236508977172845998403039886676134456248563,
788 0.92387953251128675612818318939678828682241662586364,
795 fn test_reference_sin_cos_pi_f32() {
796 fn approx_same(a: f32, b: f32) -> bool {
797 if a.is_finite() && b.is_finite() {
800 a == b || (a.is_nan() && b.is_nan())
804 fn case(x: f32, expected_sin: f32, expected_cos: f32) {
805 let (ref_sin, ref_cos) = reference_sin_cos_pi_f32(x as f64);
807 approx_same(ref_sin as f32, expected_sin)
808 && approx_same(ref_cos as f32, expected_cos),
809 "case failed: x={x}, expected_sin={expected_sin}, expected_cos={expected_cos}, ref_sin={ref_sin}, ref_cos={ref_cos}",
811 expected_sin=expected_sin,
812 expected_cos=expected_cos,
817 test_reference_sin_cos_pi_test_cases!(case, f32);
821 fn test_reference_sin_cos_pi_f64() {
822 fn same(a: f64, b: f64) -> bool {
823 if a.is_finite() && b.is_finite() {
826 a == b || (a.is_nan() && b.is_nan())
830 fn case(x: f64, expected_sin: f64, expected_cos: f64) {
831 let (ref_sin, ref_cos) = reference_sin_cos_pi_f64(x);
833 same(ref_sin, expected_sin) && same(ref_cos, expected_cos),
834 "case failed: x={x}, expected_sin={expected_sin}, expected_cos={expected_cos}, ref_sin={ref_sin}, ref_cos={ref_cos}",
836 expected_sin=expected_sin,
837 expected_cos=expected_cos,
842 test_reference_sin_cos_pi_test_cases!(case, f64);
846 #[cfg(feature = "full_tests")]
847 fn test_sin_pi_f32() {
848 for bits in 0..=u32::MAX {
850 f32::from_bits(bits),
851 sin_cos_pi_check_ulp_callback,
852 |x| sin_pi_f32(Scalar, Value(x)).0,
853 |x| reference_sin_cos_pi_f32(x).0,
859 #[cfg(feature = "full_tests")]
860 fn test_cos_pi_f32() {
861 for bits in 0..=u32::MAX {
863 f32::from_bits(bits),
864 sin_cos_pi_check_ulp_callback,
865 |x| cos_pi_f32(Scalar, Value(x)).0,
866 |x| reference_sin_cos_pi_f32(x).1,
872 #[cfg(feature = "full_tests")]
873 fn test_sin_pi_f64() {
874 for bits in (0..=u32::MAX).step_by(1 << 7) {
876 f32::from_bits(bits) as f64,
877 sin_cos_pi_check_ulp_callback,
878 |x| sin_pi_f64(Scalar, Value(x)).0,
879 |x| reference_sin_cos_pi_f64(x).0,
885 #[cfg(feature = "full_tests")]
886 fn test_cos_pi_f64() {
887 for bits in (0..=u32::MAX).step_by(1 << 7) {
889 f32::from_bits(bits) as f64,
890 sin_cos_pi_check_ulp_callback,
891 |x| cos_pi_f64(Scalar, Value(x)).0,
892 |x| reference_sin_cos_pi_f64(x).1,