1 /* 2 * Helper for single-precision SVE sincospi 3 * 4 * Copyright (c) 2024, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "sv_poly_f32.h" 10 11 const static struct sv_sincospif_data 12 { 13 float c0, c2, c4; 14 float c1, c3, c5; 15 float range_val; 16 } sv_sincospif_data = { 17 /* Taylor series coefficents for sin(pi * x). */ 18 .c0 = 0x1.921fb6p1f, 19 .c1 = -0x1.4abbcep2f, 20 .c2 = 0x1.466bc6p1f, 21 .c3 = -0x1.32d2ccp-1f, 22 .c4 = 0x1.50783p-4f, 23 .c5 = -0x1.e30750p-8f, 24 /* Exclusive upper bound for a signed integer. */ 25 .range_val = 0x1p31f, 26 }; 27 28 /* Single-precision vector function allowing calculation of both sinpi and 29 cospi in one function call, using shared argument reduction and polynomials. 30 Worst-case error for sin is 3.04 ULP: 31 _ZGVsMxvl4l4_sincospif_sin(0x1.b51b8p-2) got 0x1.f28b5ep-1 want 32 0x1.f28b58p-1. 33 Worst-case error for cos is 3.18 ULP: 34 _ZGVsMxvl4l4_sincospif_cos(0x1.d341a8p-5) got 0x1.f7cd56p-1 want 35 0x1.f7cd5p-1. */ 36 static inline svfloat32x2_t 37 sv_sincospif_inline (svbool_t pg, svfloat32_t x, 38 const struct sv_sincospif_data *d) 39 { 40 const svbool_t pt = svptrue_b32 (); 41 42 /* r = x - rint(x). */ 43 svfloat32_t rx = svrinta_x (pg, x); 44 svfloat32_t sr = svsub_x (pt, x, rx); 45 46 /* cospi(x) = sinpi(0.5 - abs(r)) for values -1/2 .. 1/2. */ 47 svfloat32_t cr = svsubr_x (pt, svabs_x (pg, sr), 0.5f); 48 49 /* Pairwise Horner approximation for y = sin(r * pi). */ 50 svfloat32_t sr2 = svmul_x (pt, sr, sr); 51 svfloat32_t sr4 = svmul_x (pt, sr2, sr2); 52 svfloat32_t cr2 = svmul_x (pt, cr, cr); 53 svfloat32_t cr4 = svmul_x (pt, cr2, cr2); 54 55 /* If rint(x) is odd, the sign of the result should be inverted for sinpi and 56 re-introduced for cospi. cmp filters rxs that saturate to max sint. */ 57 svbool_t cmp = svaclt (pg, x, d->range_val); 58 svuint32_t odd = svlsl_x (pt, svreinterpret_u32 (svcvt_s32_z (pg, rx)), 31); 59 sr = svreinterpret_f32 (sveor_x (pt, svreinterpret_u32 (sr), odd)); 60 cr = svreinterpret_f32 (sveor_m (cmp, svreinterpret_u32 (cr), odd)); 61 62 svfloat32_t c135 = svld1rq_f32 (svptrue_b32 (), &d->c1); 63 64 svfloat32_t sp01 = svmla_lane (sv_f32 (d->c0), sr2, c135, 0); 65 svfloat32_t sp23 = svmla_lane (sv_f32 (d->c2), sr2, c135, 1); 66 svfloat32_t sp45 = svmla_lane (sv_f32 (d->c4), sr2, c135, 2); 67 68 svfloat32_t cp01 = svmla_lane (sv_f32 (d->c0), cr2, c135, 0); 69 svfloat32_t cp23 = svmla_lane (sv_f32 (d->c2), cr2, c135, 1); 70 svfloat32_t cp45 = svmla_lane (sv_f32 (d->c4), cr2, c135, 2); 71 72 svfloat32_t sp = svmla_x (pg, sp23, sr4, sp45); 73 svfloat32_t cp = svmla_x (pg, cp23, cr4, cp45); 74 75 sp = svmla_x (pg, sp01, sr4, sp); 76 cp = svmla_x (pg, cp01, cr4, cp); 77 78 svfloat32_t sinpix = svmul_x (pt, sp, sr); 79 svfloat32_t cospix = svmul_x (pt, cp, cr); 80 81 return svcreate2 (sinpix, cospix); 82 } 83