1 /* 2 * Core approximation for double-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_f64.h" 10 11 static const struct sv_sincospi_data 12 { 13 double c0, c2, c4, c6, c8; 14 double c1, c3, c5, c7, c9; 15 double range_val; 16 } sv_sincospi_data = { 17 /* Polynomial coefficients generated using Remez algorithm, 18 see sinpi.sollya for details. */ 19 .c0 = 0x1.921fb54442d184p1, 20 .c1 = -0x1.4abbce625be53p2, 21 .c2 = 0x1.466bc6775ab16p1, 22 .c3 = -0x1.32d2cce62dc33p-1, 23 .c4 = 0x1.507834891188ep-4, 24 .c5 = -0x1.e30750a28c88ep-8, 25 .c6 = 0x1.e8f48308acda4p-12, 26 .c7 = -0x1.6fc0032b3c29fp-16, 27 .c8 = 0x1.af86ae521260bp-21, 28 .c9 = -0x1.012a9870eeb7dp-25, 29 /* Exclusive upper bound for a signed integer. */ 30 .range_val = 0x1p63 31 }; 32 33 /* Double-precision vector function allowing calculation of both sinpi and 34 cospi in one function call, using shared argument reduction and polynomials. 35 Worst-case error for sin is 3.09 ULP: 36 _ZGVsMxvl8l8_sincospi_sin(0x1.7a41deb4b21e1p+14) got 0x1.fd54d0b327cf1p-1 37 want 0x1.fd54d0b327cf4p-1. 38 Worst-case error for cos is 3.16 ULP: 39 _ZGVsMxvl8l8_sincospi_cos(-0x1.11e3c7e284adep-5) got 0x1.fd2da484ff3ffp-1 40 want 0x1.fd2da484ff402p-1. 41 */ 42 static inline svfloat64x2_t 43 sv_sincospi_inline (svbool_t pg, svfloat64_t x, 44 const struct sv_sincospi_data *d) 45 { 46 const svbool_t pt = svptrue_b64 (); 47 48 /* r = x - rint(x). */ 49 /* pt hints unpredicated instruction. */ 50 svfloat64_t rx = svrinta_x (pg, x); 51 svfloat64_t sr = svsub_x (pt, x, rx); 52 53 /* cospi(x) = sinpi(0.5 - abs(x)) for values -1/2 .. 1/2. */ 54 svfloat64_t cr = svsubr_x (pg, svabs_x (pg, sr), 0.5); 55 56 /* Pairwise Horner approximation for y = sin(r * pi). */ 57 /* pt hints unpredicated instruction. */ 58 svfloat64_t sr2 = svmul_x (pt, sr, sr); 59 svfloat64_t cr2 = svmul_x (pt, cr, cr); 60 svfloat64_t sr4 = svmul_x (pt, sr2, sr2); 61 svfloat64_t cr4 = svmul_x (pt, cr2, cr2); 62 63 /* If rint(x) is odd, the sign of the result should be inverted for sinpi and 64 re-introduced for cospi. cmp filters rxs that saturate to max sint. */ 65 svbool_t cmp = svaclt (pg, x, d->range_val); 66 svuint64_t odd = svlsl_x (pt, svreinterpret_u64 (svcvt_s64_z (pg, rx)), 63); 67 sr = svreinterpret_f64 (sveor_x (pt, svreinterpret_u64 (sr), odd)); 68 cr = svreinterpret_f64 (sveor_m (cmp, svreinterpret_u64 (cr), odd)); 69 70 svfloat64_t sinpix = svmul_x ( 71 pt, sv_lw_pw_horner_9_f64_x (pg, sr2, sr4, &(d->c0), &(d->c1)), sr); 72 svfloat64_t cospix = svmul_x ( 73 pt, sv_lw_pw_horner_9_f64_x (pg, cr2, cr4, &(d->c0), &(d->c1)), cr); 74 75 return svcreate2 (sinpix, cospix); 76 } 77