1 /* 2 * Double-precision vector cos function. 3 * 4 * Copyright (c) 2019-2024, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "mathlib.h" 9 #include "v_math.h" 10 #include "test_defs.h" 11 #include "test_sig.h" 12 13 static const struct data 14 { 15 float64x2_t poly[7]; 16 float64x2_t range_val, inv_pi, pi_1, pi_2, pi_3; 17 } data = { 18 /* Worst-case error is 3.3 ulp in [-pi/2, pi/2]. */ 19 .poly = { V2 (-0x1.555555555547bp-3), V2 (0x1.1111111108a4dp-7), 20 V2 (-0x1.a01a019936f27p-13), V2 (0x1.71de37a97d93ep-19), 21 V2 (-0x1.ae633919987c6p-26), V2 (0x1.60e277ae07cecp-33), 22 V2 (-0x1.9e9540300a1p-41) }, 23 .inv_pi = V2 (0x1.45f306dc9c883p-2), 24 .pi_1 = V2 (0x1.921fb54442d18p+1), 25 .pi_2 = V2 (0x1.1a62633145c06p-53), 26 .pi_3 = V2 (0x1.c1cd129024e09p-106), 27 .range_val = V2 (0x1p23) 28 }; 29 30 #define C(i) d->poly[i] 31 32 static float64x2_t VPCS_ATTR NOINLINE 33 special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp) 34 { 35 y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd)); 36 return v_call_f64 (cos, x, y, cmp); 37 } 38 39 float64x2_t VPCS_ATTR V_NAME_D1 (cos) (float64x2_t x) 40 { 41 const struct data *d = ptr_barrier (&data); 42 float64x2_t n, r, r2, r3, r4, t1, t2, t3, y; 43 uint64x2_t odd, cmp; 44 45 #if WANT_SIMD_EXCEPT 46 r = vabsq_f64 (x); 47 cmp = vcgeq_u64 (vreinterpretq_u64_f64 (r), 48 vreinterpretq_u64_f64 (d->range_val)); 49 if (unlikely (v_any_u64 (cmp))) 50 /* If fenv exceptions are to be triggered correctly, set any special lanes 51 to 1 (which is neutral w.r.t. fenv). These lanes will be fixed by 52 special-case handler later. */ 53 r = vbslq_f64 (cmp, v_f64 (1.0), r); 54 #else 55 cmp = vcageq_f64 (x, d->range_val); 56 r = x; 57 #endif 58 59 /* n = rint((|x|+pi/2)/pi) - 0.5. */ 60 n = vrndaq_f64 (vfmaq_f64 (v_f64 (0.5), r, d->inv_pi)); 61 odd = vshlq_n_u64 (vreinterpretq_u64_s64 (vcvtq_s64_f64 (n)), 63); 62 n = vsubq_f64 (n, v_f64 (0.5f)); 63 64 /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */ 65 r = vfmsq_f64 (r, d->pi_1, n); 66 r = vfmsq_f64 (r, d->pi_2, n); 67 r = vfmsq_f64 (r, d->pi_3, n); 68 69 /* sin(r) poly approx. */ 70 r2 = vmulq_f64 (r, r); 71 r3 = vmulq_f64 (r2, r); 72 r4 = vmulq_f64 (r2, r2); 73 74 t1 = vfmaq_f64 (C (4), C (5), r2); 75 t2 = vfmaq_f64 (C (2), C (3), r2); 76 t3 = vfmaq_f64 (C (0), C (1), r2); 77 78 y = vfmaq_f64 (t1, C (6), r4); 79 y = vfmaq_f64 (t2, y, r4); 80 y = vfmaq_f64 (t3, y, r4); 81 y = vfmaq_f64 (r, y, r3); 82 83 if (unlikely (v_any_u64 (cmp))) 84 return special_case (x, y, odd, cmp); 85 return vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd)); 86 } 87 88 TEST_SIG (V, D, 1, cos, -3.1, 3.1) 89 TEST_ULP (V_NAME_D1 (cos), 3.0) 90 TEST_DISABLE_FENV_IF_NOT (V_NAME_D1 (cos), WANT_SIMD_EXCEPT) 91 TEST_SYM_INTERVAL (V_NAME_D1 (cos), 0, 0x1p23, 500000) 92 TEST_SYM_INTERVAL (V_NAME_D1 (cos), 0x1p23, inf, 10000) 93