1 /* 2 * Double-precision SVE cospi(x) function. 3 * 4 * Copyright (c) 2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "mathlib.h" 9 #include "sv_math.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 #include "poly_sve_f64.h" 13 14 static const struct data 15 { 16 double poly[10]; 17 double range_val; 18 } data = { 19 /* Polynomial coefficients generated using Remez algorithm, 20 see sinpi.sollya for details. */ 21 .poly = { 0x1.921fb54442d184p1, -0x1.4abbce625be53p2, 0x1.466bc6775ab16p1, 22 -0x1.32d2cce62dc33p-1, 0x1.507834891188ep-4, -0x1.e30750a28c88ep-8, 23 0x1.e8f48308acda4p-12, -0x1.6fc0032b3c29fp-16, 24 0x1.af86ae521260bp-21, -0x1.012a9870eeb7dp-25 }, 25 .range_val = 0x1p53, 26 }; 27 28 /* A fast SVE implementation of cospi. 29 Maximum error 3.20 ULP: 30 _ZGVsMxv_cospi(0x1.f18ba32c63159p-6) got 0x1.fdabf595f9763p-1 31 want 0x1.fdabf595f9766p-1. */ 32 svfloat64_t SV_NAME_D1 (cospi) (svfloat64_t x, const svbool_t pg) 33 { 34 const struct data *d = ptr_barrier (&data); 35 36 /* Using cospi(x) = sinpi(0.5 - x) 37 range reduction and offset into sinpi range -1/2 .. 1/2 38 r = 0.5 - |x - rint(x)|. */ 39 svfloat64_t n = svrinta_x (pg, x); 40 svfloat64_t r = svsub_x (pg, x, n); 41 r = svsub_x (pg, sv_f64 (0.5), svabs_x (pg, r)); 42 43 /* Result should be negated based on if n is odd or not. 44 If ax >= 2^53, the result will always be positive. */ 45 svbool_t cmp = svaclt (pg, x, d->range_val); 46 svuint64_t intn = svreinterpret_u64 (svcvt_s64_z (pg, n)); 47 svuint64_t sign = svlsl_z (cmp, intn, 63); 48 49 /* y = sin(r). */ 50 svfloat64_t r2 = svmul_x (pg, r, r); 51 svfloat64_t r4 = svmul_x (pg, r2, r2); 52 svfloat64_t y = sv_pw_horner_9_f64_x (pg, r2, r4, d->poly); 53 y = svmul_x (pg, y, r); 54 55 return svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign)); 56 } 57 58 PL_SIG (SV, D, 1, cospi, -0.9, 0.9) 59 PL_TEST_ULP (SV_NAME_D1 (cospi), 2.71) 60 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0, 0x1p-63, 5000) 61 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0x1p-63, 0.5, 10000) 62 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0.5, 0x1p51, 10000) 63 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (cospi), 0x1p51, inf, 100000) 64