1 /* 2 * Helper for Single-precision vector sincospi function. 3 * 4 * Copyright (c) 2024, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 #include "mathlib.h" 8 #include "v_math.h" 9 #include "v_poly_f32.h" 10 11 const static struct v_sincospif_data 12 { 13 float32x4_t poly[6], range_val; 14 } v_sincospif_data = { 15 /* Taylor series coefficents for sin(pi * x). */ 16 .poly = { V4 (0x1.921fb6p1f), V4 (-0x1.4abbcep2f), V4 (0x1.466bc6p1f), 17 V4 (-0x1.32d2ccp-1f), V4 (0x1.50783p-4f), V4 (-0x1.e30750p-8f) }, 18 .range_val = V4 (0x1p31f), 19 }; 20 21 /* Single-precision vector function allowing calculation of both sinpi and 22 cospi in one function call, using shared argument reduction and polynomials. 23 Worst-case error for sin is 3.04 ULP: 24 _ZGVnN4v_sincospif_sin(0x1.1d341ap-1) got 0x1.f7cd56p-1 want 0x1.f7cd5p-1. 25 Worst-case error for cos is 3.18 ULP: 26 _ZGVnN4v_sincospif_cos(0x1.d341a8p-5) got 0x1.f7cd56p-1 want 0x1.f7cd5p-1. 27 */ 28 static inline float32x4x2_t 29 v_sincospif_inline (float32x4_t x, const struct v_sincospif_data *d) 30 { 31 /* If r is odd, the sign of the result should be inverted for sinpi and 32 reintroduced for cospi. */ 33 uint32x4_t cmp = vcgeq_f32 (x, d->range_val); 34 uint32x4_t odd = vshlq_n_u32 ( 35 vbicq_u32 (vreinterpretq_u32_s32 (vcvtaq_s32_f32 (x)), cmp), 31); 36 37 /* r = x - rint(x). */ 38 float32x4_t sr = vsubq_f32 (x, vrndaq_f32 (x)); 39 /* cospi(x) = sinpi(0.5 - abs(x)) for values -1/2 .. 1/2. */ 40 float32x4_t cr = vsubq_f32 (v_f32 (0.5f), vabsq_f32 (sr)); 41 42 /* Pairwise Horner approximation for y = sin(r * pi). */ 43 float32x4_t sr2 = vmulq_f32 (sr, sr); 44 float32x4_t sr4 = vmulq_f32 (sr2, sr2); 45 float32x4_t cr2 = vmulq_f32 (cr, cr); 46 float32x4_t cr4 = vmulq_f32 (cr2, cr2); 47 48 float32x4_t ss = vmulq_f32 (v_pw_horner_5_f32 (sr2, sr4, d->poly), sr); 49 float32x4_t cc = vmulq_f32 (v_pw_horner_5_f32 (cr2, cr4, d->poly), cr); 50 51 float32x4_t sinpix 52 = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (ss), odd)); 53 float32x4_t cospix 54 = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (cc), odd)); 55 56 return (float32x4x2_t){ sinpix, cospix }; 57 } 58