1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Double-precision vector sin function. 3*f3087befSAndrew Turner * 4*f3087befSAndrew Turner * Copyright (c) 2019-2024, 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 "test_defs.h" 9*f3087befSAndrew Turner #include "test_sig.h" 10*f3087befSAndrew Turner #include "mathlib.h" 11*f3087befSAndrew Turner #include "v_math.h" 12*f3087befSAndrew Turner 13*f3087befSAndrew Turner static const struct data 14*f3087befSAndrew Turner { 15*f3087befSAndrew Turner float64x2_t poly[7]; 16*f3087befSAndrew Turner float64x2_t range_val, inv_pi, pi_1, pi_2, pi_3; 17*f3087befSAndrew Turner } data = { 18*f3087befSAndrew Turner .poly = { V2 (-0x1.555555555547bp-3), V2 (0x1.1111111108a4dp-7), 19*f3087befSAndrew Turner V2 (-0x1.a01a019936f27p-13), V2 (0x1.71de37a97d93ep-19), 20*f3087befSAndrew Turner V2 (-0x1.ae633919987c6p-26), V2 (0x1.60e277ae07cecp-33), 21*f3087befSAndrew Turner V2 (-0x1.9e9540300a1p-41) }, 22*f3087befSAndrew Turner 23*f3087befSAndrew Turner .range_val = V2 (0x1p23), 24*f3087befSAndrew Turner .inv_pi = V2 (0x1.45f306dc9c883p-2), 25*f3087befSAndrew Turner .pi_1 = V2 (0x1.921fb54442d18p+1), 26*f3087befSAndrew Turner .pi_2 = V2 (0x1.1a62633145c06p-53), 27*f3087befSAndrew Turner .pi_3 = V2 (0x1.c1cd129024e09p-106), 28*f3087befSAndrew Turner }; 29*f3087befSAndrew Turner 30*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT 31*f3087befSAndrew Turner /* asuint64(0x1p-253)), below which multiply by inv_pi underflows. */ 32*f3087befSAndrew Turner # define TinyBound v_u64 (0x3020000000000000) 33*f3087befSAndrew Turner /* RangeVal - TinyBound. */ 34*f3087befSAndrew Turner # define Thresh v_u64 (0x1160000000000000) 35*f3087befSAndrew Turner #endif 36*f3087befSAndrew Turner 37*f3087befSAndrew Turner #define C(i) d->poly[i] 38*f3087befSAndrew Turner 39*f3087befSAndrew Turner static float64x2_t VPCS_ATTR NOINLINE 40*f3087befSAndrew Turner special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp) 41*f3087befSAndrew Turner { 42*f3087befSAndrew Turner y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd)); 43*f3087befSAndrew Turner return v_call_f64 (sin, x, y, cmp); 44*f3087befSAndrew Turner } 45*f3087befSAndrew Turner 46*f3087befSAndrew Turner /* Vector (AdvSIMD) sin approximation. 47*f3087befSAndrew Turner Maximum observed error in [-pi/2, pi/2], where argument is not reduced, 48*f3087befSAndrew Turner is 2.87 ULP: 49*f3087befSAndrew Turner _ZGVnN2v_sin (0x1.921d5c6a07142p+0) got 0x1.fffffffa7dc02p-1 50*f3087befSAndrew Turner want 0x1.fffffffa7dc05p-1 51*f3087befSAndrew Turner Maximum observed error in the entire non-special domain ([-2^23, 2^23]) 52*f3087befSAndrew Turner is 3.22 ULP: 53*f3087befSAndrew Turner _ZGVnN2v_sin (0x1.5702447b6f17bp+22) got 0x1.ffdcd125c84fbp-3 54*f3087befSAndrew Turner want 0x1.ffdcd125c84f8p-3. */ 55*f3087befSAndrew Turner float64x2_t VPCS_ATTR V_NAME_D1 (sin) (float64x2_t x) 56*f3087befSAndrew Turner { 57*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data); 58*f3087befSAndrew Turner float64x2_t n, r, r2, r3, r4, y, t1, t2, t3; 59*f3087befSAndrew Turner uint64x2_t odd, cmp; 60*f3087befSAndrew Turner 61*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT 62*f3087befSAndrew Turner /* Detect |x| <= TinyBound or |x| >= RangeVal. If fenv exceptions are to be 63*f3087befSAndrew Turner triggered correctly, set any special lanes to 1 (which is neutral w.r.t. 64*f3087befSAndrew Turner fenv). These lanes will be fixed by special-case handler later. */ 65*f3087befSAndrew Turner uint64x2_t ir = vreinterpretq_u64_f64 (vabsq_f64 (x)); 66*f3087befSAndrew Turner cmp = vcgeq_u64 (vsubq_u64 (ir, TinyBound), Thresh); 67*f3087befSAndrew Turner r = vreinterpretq_f64_u64 (vbicq_u64 (vreinterpretq_u64_f64 (x), cmp)); 68*f3087befSAndrew Turner #else 69*f3087befSAndrew Turner r = x; 70*f3087befSAndrew Turner cmp = vcageq_f64 (x, d->range_val); 71*f3087befSAndrew Turner #endif 72*f3087befSAndrew Turner 73*f3087befSAndrew Turner /* n = rint(|x|/pi). */ 74*f3087befSAndrew Turner n = vrndaq_f64 (vmulq_f64 (r, d->inv_pi)); 75*f3087befSAndrew Turner odd = vshlq_n_u64 (vreinterpretq_u64_s64 (vcvtq_s64_f64 (n)), 63); 76*f3087befSAndrew Turner 77*f3087befSAndrew Turner /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */ 78*f3087befSAndrew Turner r = vfmsq_f64 (r, d->pi_1, n); 79*f3087befSAndrew Turner r = vfmsq_f64 (r, d->pi_2, n); 80*f3087befSAndrew Turner r = vfmsq_f64 (r, d->pi_3, n); 81*f3087befSAndrew Turner 82*f3087befSAndrew Turner /* sin(r) poly approx. */ 83*f3087befSAndrew Turner r2 = vmulq_f64 (r, r); 84*f3087befSAndrew Turner r3 = vmulq_f64 (r2, r); 85*f3087befSAndrew Turner r4 = vmulq_f64 (r2, r2); 86*f3087befSAndrew Turner 87*f3087befSAndrew Turner t1 = vfmaq_f64 (C (4), C (5), r2); 88*f3087befSAndrew Turner t2 = vfmaq_f64 (C (2), C (3), r2); 89*f3087befSAndrew Turner t3 = vfmaq_f64 (C (0), C (1), r2); 90*f3087befSAndrew Turner 91*f3087befSAndrew Turner y = vfmaq_f64 (t1, C (6), r4); 92*f3087befSAndrew Turner y = vfmaq_f64 (t2, y, r4); 93*f3087befSAndrew Turner y = vfmaq_f64 (t3, y, r4); 94*f3087befSAndrew Turner y = vfmaq_f64 (r, y, r3); 95*f3087befSAndrew Turner 96*f3087befSAndrew Turner if (unlikely (v_any_u64 (cmp))) 97*f3087befSAndrew Turner return special_case (x, y, odd, cmp); 98*f3087befSAndrew Turner return vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd)); 99*f3087befSAndrew Turner } 100*f3087befSAndrew Turner 101*f3087befSAndrew Turner TEST_SIG (V, D, 1, sin, -3.1, 3.1) 102*f3087befSAndrew Turner TEST_ULP (V_NAME_D1 (sin), 3.0) 103*f3087befSAndrew Turner TEST_DISABLE_FENV_IF_NOT (V_NAME_D1 (sin), WANT_SIMD_EXCEPT) 104*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (sin), 0, 0x1p23, 500000) 105*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_D1 (sin), 0x1p23, inf, 10000) 106