1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Double-precision vector cospi 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 float64x2_t range_val; 18*f3087befSAndrew Turner } data = { 19*f3087befSAndrew Turner /* Polynomial coefficients generated using Remez algorithm, 20*f3087befSAndrew Turner see sinpi.sollya for details. */ 21*f3087befSAndrew Turner .poly = { V2 (0x1.921fb54442d184p1), V2 (-0x1.4abbce625be53p2), 22*f3087befSAndrew Turner V2 (0x1.466bc6775ab16p1), V2 (-0x1.32d2cce62dc33p-1), 23*f3087befSAndrew Turner V2 (0x1.507834891188ep-4), V2 (-0x1.e30750a28c88ep-8), 24*f3087befSAndrew Turner V2 (0x1.e8f48308acda4p-12), V2 (-0x1.6fc0032b3c29fp-16), 25*f3087befSAndrew Turner V2 (0x1.af86ae521260bp-21), V2 (-0x1.012a9870eeb7dp-25) }, 26*f3087befSAndrew Turner .range_val = V2 (0x1p63), 27*f3087befSAndrew Turner }; 28*f3087befSAndrew Turner 29*f3087befSAndrew Turner static float64x2_t VPCS_ATTR NOINLINE 30*f3087befSAndrew Turner special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp) 31*f3087befSAndrew Turner { 32*f3087befSAndrew Turner /* Fall back to scalar code. */ 33*f3087befSAndrew Turner y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd)); 34*f3087befSAndrew Turner return v_call_f64 (arm_math_cospi, x, y, cmp); 35*f3087befSAndrew Turner } 36*f3087befSAndrew Turner 37*f3087befSAndrew Turner /* Approximation for vector double-precision cospi(x). 38*f3087befSAndrew Turner Maximum Error 3.06 ULP: 39*f3087befSAndrew Turner _ZGVnN2v_cospi(0x1.7dd4c0b03cc66p-5) got 0x1.fa854babfb6bep-1 40*f3087befSAndrew Turner want 0x1.fa854babfb6c1p-1. */ 41*f3087befSAndrew Turner float64x2_t VPCS_ATTR V_NAME_D1 (cospi) (float64x2_t x) 42*f3087befSAndrew Turner { 43*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data); 44*f3087befSAndrew Turner 45*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT 46*f3087befSAndrew Turner float64x2_t r = vabsq_f64 (x); 47*f3087befSAndrew Turner uint64x2_t cmp = vcaleq_f64 (v_f64 (0x1p64), x); 48*f3087befSAndrew Turner 49*f3087befSAndrew Turner /* When WANT_SIMD_EXCEPT = 1, special lanes should be zero'd 50*f3087befSAndrew Turner to avoid them overflowing and throwing exceptions. */ 51*f3087befSAndrew Turner r = v_zerofy_f64 (r, cmp); 52*f3087befSAndrew Turner uint64x2_t odd = vshlq_n_u64 (vcvtnq_u64_f64 (r), 63); 53*f3087befSAndrew Turner 54*f3087befSAndrew Turner #else 55*f3087befSAndrew Turner float64x2_t r = x; 56*f3087befSAndrew Turner uint64x2_t cmp = vcageq_f64 (r, d->range_val); 57*f3087befSAndrew Turner uint64x2_t odd 58*f3087befSAndrew Turner = vshlq_n_u64 (vreinterpretq_u64_s64 (vcvtaq_s64_f64 (r)), 63); 59*f3087befSAndrew Turner 60*f3087befSAndrew Turner #endif 61*f3087befSAndrew Turner 62*f3087befSAndrew Turner r = vsubq_f64 (r, vrndaq_f64 (r)); 63*f3087befSAndrew Turner 64*f3087befSAndrew Turner /* cospi(x) = sinpi(0.5 - abs(x)) for values -1/2 .. 1/2. */ 65*f3087befSAndrew Turner r = vsubq_f64 (v_f64 (0.5), vabsq_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 /* Fallback to scalar. */ 73*f3087befSAndrew Turner if (unlikely (v_any_u64 (cmp))) 74*f3087befSAndrew Turner return special_case (x, y, odd, cmp); 75*f3087befSAndrew Turner 76*f3087befSAndrew Turner /* Reintroduce the sign bit for inputs which round to odd. */ 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 (cospi), 2.56) 82*f3087befSAndrew Turner TEST_DISABLE_FENV_IF_NOT (V_NAME_D1 (cospi), WANT_SIMD_EXCEPT) 83*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0, 0x1p-63, 5000) 84*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0x1p-63, 0.5, 10000) 85*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0.5, 0x1p51, 10000) 86*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0x1p51, inf, 10000) 87*f3087befSAndrew Turner #endif 88