1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Single-precision vector cospi function. 3*f3087befSAndrew Turner * 4*f3087befSAndrew Turner * Copyright (c) 2023-2024, Arm Limited. 5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6*f3087befSAndrew Turner */ 7*f3087befSAndrew Turner 8*f3087befSAndrew Turner #include "mathlib.h" 9*f3087befSAndrew Turner #include "v_math.h" 10*f3087befSAndrew Turner #include "v_poly_f32.h" 11*f3087befSAndrew Turner #include "test_sig.h" 12*f3087befSAndrew Turner #include "test_defs.h" 13*f3087befSAndrew Turner 14*f3087befSAndrew Turner static const struct data 15*f3087befSAndrew Turner { 16*f3087befSAndrew Turner float32x4_t poly[6]; 17*f3087befSAndrew Turner float32x4_t range_val; 18*f3087befSAndrew Turner } data = { 19*f3087befSAndrew Turner /* Taylor series coefficents for sin(pi * x). */ 20*f3087befSAndrew Turner .poly = { V4 (0x1.921fb6p1f), V4 (-0x1.4abbcep2f), V4 (0x1.466bc6p1f), 21*f3087befSAndrew Turner V4 (-0x1.32d2ccp-1f), V4 (0x1.50783p-4f), V4 (-0x1.e30750p-8f) }, 22*f3087befSAndrew Turner .range_val = V4 (0x1p31f), 23*f3087befSAndrew Turner }; 24*f3087befSAndrew Turner 25*f3087befSAndrew Turner static float32x4_t VPCS_ATTR NOINLINE 26*f3087befSAndrew Turner special_case (float32x4_t x, float32x4_t y, uint32x4_t odd, uint32x4_t cmp) 27*f3087befSAndrew Turner { 28*f3087befSAndrew Turner y = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd)); 29*f3087befSAndrew Turner return v_call_f32 (arm_math_cospif, x, y, cmp); 30*f3087befSAndrew Turner } 31*f3087befSAndrew Turner 32*f3087befSAndrew Turner /* Approximation for vector single-precision cospi(x) 33*f3087befSAndrew Turner Maximum Error: 3.17 ULP: 34*f3087befSAndrew Turner _ZGVnN4v_cospif(0x1.d341a8p-5) got 0x1.f7cd56p-1 35*f3087befSAndrew Turner want 0x1.f7cd5p-1. */ 36*f3087befSAndrew Turner float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (cospi) (float32x4_t x) 37*f3087befSAndrew Turner { 38*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data); 39*f3087befSAndrew Turner 40*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT 41*f3087befSAndrew Turner float32x4_t r = vabsq_f32 (x); 42*f3087befSAndrew Turner uint32x4_t cmp = vcaleq_f32 (v_f32 (0x1p32f), x); 43*f3087befSAndrew Turner 44*f3087befSAndrew Turner /* When WANT_SIMD_EXCEPT = 1, special lanes should be zero'd 45*f3087befSAndrew Turner to avoid them overflowing and throwing exceptions. */ 46*f3087befSAndrew Turner r = v_zerofy_f32 (r, cmp); 47*f3087befSAndrew Turner uint32x4_t odd = vshlq_n_u32 (vcvtnq_u32_f32 (r), 31); 48*f3087befSAndrew Turner 49*f3087befSAndrew Turner #else 50*f3087befSAndrew Turner float32x4_t r = x; 51*f3087befSAndrew Turner uint32x4_t cmp = vcageq_f32 (r, d->range_val); 52*f3087befSAndrew Turner 53*f3087befSAndrew Turner uint32x4_t odd 54*f3087befSAndrew Turner = vshlq_n_u32 (vreinterpretq_u32_s32 (vcvtaq_s32_f32 (r)), 31); 55*f3087befSAndrew Turner 56*f3087befSAndrew Turner #endif 57*f3087befSAndrew Turner 58*f3087befSAndrew Turner /* r = x - rint(x). */ 59*f3087befSAndrew Turner r = vsubq_f32 (r, vrndaq_f32 (r)); 60*f3087befSAndrew Turner 61*f3087befSAndrew Turner /* cospi(x) = sinpi(0.5 - abs(x)) for values -1/2 .. 1/2. */ 62*f3087befSAndrew Turner r = vsubq_f32 (v_f32 (0.5f), vabsq_f32 (r)); 63*f3087befSAndrew Turner 64*f3087befSAndrew Turner /* Pairwise Horner approximation for y = sin(r * pi). */ 65*f3087befSAndrew Turner float32x4_t r2 = vmulq_f32 (r, r); 66*f3087befSAndrew Turner float32x4_t r4 = vmulq_f32 (r2, r2); 67*f3087befSAndrew Turner float32x4_t y = vmulq_f32 (v_pw_horner_5_f32 (r2, r4, d->poly), r); 68*f3087befSAndrew Turner 69*f3087befSAndrew Turner /* Fallback to scalar. */ 70*f3087befSAndrew Turner if (unlikely (v_any_u32 (cmp))) 71*f3087befSAndrew Turner return special_case (x, y, odd, cmp); 72*f3087befSAndrew Turner 73*f3087befSAndrew Turner /* Reintroduce the sign bit for inputs which round to odd. */ 74*f3087befSAndrew Turner return vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd)); 75*f3087befSAndrew Turner } 76*f3087befSAndrew Turner 77*f3087befSAndrew Turner HALF_WIDTH_ALIAS_F1 (cospi) 78*f3087befSAndrew Turner 79*f3087befSAndrew Turner #if WANT_TRIGPI_TESTS 80*f3087befSAndrew Turner TEST_ULP (V_NAME_F1 (cospi), 2.67) 81*f3087befSAndrew Turner TEST_DISABLE_FENV_IF_NOT (V_NAME_F1 (cospi), WANT_SIMD_EXCEPT) 82*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_F1 (cospi), 0, 0x1p-31, 5000) 83*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_F1 (cospi), 0x1p-31, 0.5, 10000) 84*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_F1 (cospi), 0.5, 0x1p32f, 10000) 85*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_F1 (cospi), 0x1p32f, inf, 10000) 86*f3087befSAndrew Turner #endif 87