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