1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Double-precision vector sinpi function. 3*f3087befSAndrew Turner * 4*f3087befSAndrew Turner * Copyright (c) 2023-2024, Arm Limited. 5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6*f3087befSAndrew Turner */ 7*f3087befSAndrew Turner 8*f3087befSAndrew Turner #include "mathlib.h" 9*f3087befSAndrew Turner #include "v_math.h" 10*f3087befSAndrew Turner #include "v_poly_f64.h" 11*f3087befSAndrew Turner #include "test_sig.h" 12*f3087befSAndrew Turner #include "test_defs.h" 13*f3087befSAndrew Turner 14*f3087befSAndrew Turner static const struct data 15*f3087befSAndrew Turner { 16*f3087befSAndrew Turner float64x2_t poly[10]; 17*f3087befSAndrew Turner } data = { 18*f3087befSAndrew Turner /* Polynomial coefficients generated using Remez algorithm, 19*f3087befSAndrew Turner see sinpi.sollya for details. */ 20*f3087befSAndrew Turner .poly = { V2 (0x1.921fb54442d184p1), V2 (-0x1.4abbce625be53p2), 21*f3087befSAndrew Turner V2 (0x1.466bc6775ab16p1), V2 (-0x1.32d2cce62dc33p-1), 22*f3087befSAndrew Turner V2 (0x1.507834891188ep-4), V2 (-0x1.e30750a28c88ep-8), 23*f3087befSAndrew Turner V2 (0x1.e8f48308acda4p-12), V2 (-0x1.6fc0032b3c29fp-16), 24*f3087befSAndrew Turner V2 (0x1.af86ae521260bp-21), V2 (-0x1.012a9870eeb7dp-25) }, 25*f3087befSAndrew Turner }; 26*f3087befSAndrew Turner 27*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT 28*f3087befSAndrew Turner # define TinyBound v_u64 (0x3bf0000000000000) /* asuint64(0x1p-64). */ 29*f3087befSAndrew Turner /* asuint64(0x1p64) - TinyBound. */ 30*f3087befSAndrew Turner # define Thresh v_u64 (0x07f0000000000000) 31*f3087befSAndrew Turner 32*f3087befSAndrew Turner static float64x2_t VPCS_ATTR NOINLINE 33*f3087befSAndrew Turner special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp) 34*f3087befSAndrew Turner { 35*f3087befSAndrew Turner /* Fall back to scalar code. */ 36*f3087befSAndrew Turner y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd)); 37*f3087befSAndrew Turner return v_call_f64 (arm_math_sinpi, x, y, cmp); 38*f3087befSAndrew Turner } 39*f3087befSAndrew Turner #endif 40*f3087befSAndrew Turner 41*f3087befSAndrew Turner /* Approximation for vector double-precision sinpi(x). 42*f3087befSAndrew Turner Maximum Error 3.05 ULP: 43*f3087befSAndrew Turner _ZGVnN2v_sinpi(0x1.d32750db30b4ap-2) got 0x1.fb295878301c7p-1 44*f3087befSAndrew Turner want 0x1.fb295878301cap-1. */ 45*f3087befSAndrew Turner float64x2_t VPCS_ATTR V_NAME_D1 (sinpi) (float64x2_t x) 46*f3087befSAndrew Turner { 47*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data); 48*f3087befSAndrew Turner 49*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT 50*f3087befSAndrew Turner uint64x2_t ir = vreinterpretq_u64_f64 (vabsq_f64 (x)); 51*f3087befSAndrew Turner uint64x2_t cmp = vcgeq_u64 (vsubq_u64 (ir, TinyBound), Thresh); 52*f3087befSAndrew Turner 53*f3087befSAndrew Turner /* When WANT_SIMD_EXCEPT = 1, special lanes should be set to 0 54*f3087befSAndrew Turner to avoid them under/overflowing and throwing exceptions. */ 55*f3087befSAndrew Turner float64x2_t r = v_zerofy_f64 (x, cmp); 56*f3087befSAndrew Turner #else 57*f3087befSAndrew Turner float64x2_t r = x; 58*f3087befSAndrew Turner #endif 59*f3087befSAndrew Turner 60*f3087befSAndrew Turner /* If r is odd, the sign of the result should be inverted. */ 61*f3087befSAndrew Turner uint64x2_t odd 62*f3087befSAndrew Turner = vshlq_n_u64 (vreinterpretq_u64_s64 (vcvtaq_s64_f64 (r)), 63); 63*f3087befSAndrew Turner 64*f3087befSAndrew Turner /* r = x - rint(x). Range reduction to -1/2 .. 1/2. */ 65*f3087befSAndrew Turner r = vsubq_f64 (r, vrndaq_f64 (r)); 66*f3087befSAndrew Turner 67*f3087befSAndrew Turner /* y = sin(r). */ 68*f3087befSAndrew Turner float64x2_t r2 = vmulq_f64 (r, r); 69*f3087befSAndrew Turner float64x2_t r4 = vmulq_f64 (r2, r2); 70*f3087befSAndrew Turner float64x2_t y = vmulq_f64 (v_pw_horner_9_f64 (r2, r4, d->poly), r); 71*f3087befSAndrew Turner 72*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT 73*f3087befSAndrew Turner if (unlikely (v_any_u64 (cmp))) 74*f3087befSAndrew Turner return special_case (x, y, odd, cmp); 75*f3087befSAndrew Turner #endif 76*f3087befSAndrew Turner 77*f3087befSAndrew Turner return vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd)); 78*f3087befSAndrew Turner } 79*f3087befSAndrew Turner 80*f3087befSAndrew Turner #if WANT_TRIGPI_TESTS 81*f3087befSAndrew Turner TEST_ULP (V_NAME_D1 (sinpi), 2.56) 82*f3087befSAndrew Turner TEST_DISABLE_FENV_IF_NOT (V_NAME_D1 (sinpi), WANT_SIMD_EXCEPT) 83*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (sinpi), 0, 0x1p-63, 5000) 84*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (sinpi), 0x1p-63, 0.5, 10000) 85*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (sinpi), 0.5, 0x1p51, 10000) 86*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (sinpi), 0x1p51, inf, 10000) 87*f3087befSAndrew Turner #endif 88