1 /* 2 * Double-precision vector cospi 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 "v_math.h" 10 #include "poly_advsimd_f64.h" 11 #include "pl_sig.h" 12 #include "pl_test.h" 13 14 static const struct data 15 { 16 float64x2_t poly[10]; 17 float64x2_t range_val; 18 } data = { 19 /* Polynomial coefficients generated using Remez algorithm, 20 see sinpi.sollya for details. */ 21 .poly = { V2 (0x1.921fb54442d184p1), V2 (-0x1.4abbce625be53p2), 22 V2 (0x1.466bc6775ab16p1), V2 (-0x1.32d2cce62dc33p-1), 23 V2 (0x1.507834891188ep-4), V2 (-0x1.e30750a28c88ep-8), 24 V2 (0x1.e8f48308acda4p-12), V2 (-0x1.6fc0032b3c29fp-16), 25 V2 (0x1.af86ae521260bp-21), V2 (-0x1.012a9870eeb7dp-25) }, 26 .range_val = V2 (0x1p63), 27 }; 28 29 static float64x2_t VPCS_ATTR NOINLINE 30 special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp) 31 { 32 /* Fall back to scalar code. */ 33 y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd)); 34 return v_call_f64 (cospi, x, y, cmp); 35 } 36 37 /* Approximation for vector double-precision cospi(x). 38 Maximum Error 3.06 ULP: 39 _ZGVnN2v_cospi(0x1.7dd4c0b03cc66p-5) got 0x1.fa854babfb6bep-1 40 want 0x1.fa854babfb6c1p-1. */ 41 float64x2_t VPCS_ATTR V_NAME_D1 (cospi) (float64x2_t x) 42 { 43 const struct data *d = ptr_barrier (&data); 44 45 #if WANT_SIMD_EXCEPT 46 float64x2_t r = vabsq_f64 (x); 47 uint64x2_t cmp = vcaleq_f64 (v_f64 (0x1p64), x); 48 49 /* When WANT_SIMD_EXCEPT = 1, special lanes should be zero'd 50 to avoid them overflowing and throwing exceptions. */ 51 r = v_zerofy_f64 (r, cmp); 52 uint64x2_t odd = vshlq_n_u64 (vcvtnq_u64_f64 (r), 63); 53 54 #else 55 float64x2_t r = x; 56 uint64x2_t cmp = vcageq_f64 (r, d->range_val); 57 uint64x2_t odd 58 = vshlq_n_u64 (vreinterpretq_u64_s64 (vcvtaq_s64_f64 (r)), 63); 59 60 #endif 61 62 r = vsubq_f64 (r, vrndaq_f64 (r)); 63 64 /* cospi(x) = sinpi(0.5 - abs(x)) for values -1/2 .. 1/2. */ 65 r = vsubq_f64 (v_f64 (0.5), vabsq_f64 (r)); 66 67 /* y = sin(r). */ 68 float64x2_t r2 = vmulq_f64 (r, r); 69 float64x2_t r4 = vmulq_f64 (r2, r2); 70 float64x2_t y = vmulq_f64 (v_pw_horner_9_f64 (r2, r4, d->poly), r); 71 72 /* Fallback to scalar. */ 73 if (unlikely (v_any_u64 (cmp))) 74 return special_case (x, y, odd, cmp); 75 76 /* Reintroduce the sign bit for inputs which round to odd. */ 77 return vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), odd)); 78 } 79 80 PL_SIG (V, D, 1, cospi, -0.9, 0.9) 81 PL_TEST_ULP (V_NAME_D1 (cospi), 2.56) 82 PL_TEST_EXPECT_FENV (V_NAME_D1 (cospi), WANT_SIMD_EXCEPT) 83 PL_TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0, 0x1p-63, 5000) 84 PL_TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0x1p-63, 0.5, 10000) 85 PL_TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0.5, 0x1p51, 10000) 86 PL_TEST_SYM_INTERVAL (V_NAME_D1 (cospi), 0x1p51, inf, 10000) 87