1 /* 2 * Double-precision SVE sin(x) function. 3 * 4 * Copyright (c) 2019-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "pl_sig.h" 10 #include "pl_test.h" 11 12 static const struct data 13 { 14 double inv_pi, pi_1, pi_2, pi_3, shift, range_val; 15 double poly[7]; 16 } data = { 17 .poly = { -0x1.555555555547bp-3, 0x1.1111111108a4dp-7, -0x1.a01a019936f27p-13, 18 0x1.71de37a97d93ep-19, -0x1.ae633919987c6p-26, 19 0x1.60e277ae07cecp-33, -0x1.9e9540300a1p-41, }, 20 21 .inv_pi = 0x1.45f306dc9c883p-2, 22 .pi_1 = 0x1.921fb54442d18p+1, 23 .pi_2 = 0x1.1a62633145c06p-53, 24 .pi_3 = 0x1.c1cd129024e09p-106, 25 .shift = 0x1.8p52, 26 .range_val = 0x1p23, 27 }; 28 29 #define C(i) sv_f64 (d->poly[i]) 30 31 static svfloat64_t NOINLINE 32 special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp) 33 { 34 return sv_call_f64 (sin, x, y, cmp); 35 } 36 37 /* A fast SVE implementation of sin. 38 Maximum observed error in [-pi/2, pi/2], where argument is not reduced, 39 is 2.87 ULP: 40 _ZGVsMxv_sin (0x1.921d5c6a07142p+0) got 0x1.fffffffa7dc02p-1 41 want 0x1.fffffffa7dc05p-1 42 Maximum observed error in the entire non-special domain ([-2^23, 2^23]) 43 is 3.22 ULP: 44 _ZGVsMxv_sin (0x1.5702447b6f17bp+22) got 0x1.ffdcd125c84fbp-3 45 want 0x1.ffdcd125c84f8p-3. */ 46 svfloat64_t SV_NAME_D1 (sin) (svfloat64_t x, const svbool_t pg) 47 { 48 const struct data *d = ptr_barrier (&data); 49 50 /* Load some values in quad-word chunks to minimise memory access. */ 51 const svbool_t ptrue = svptrue_b64 (); 52 svfloat64_t shift = sv_f64 (d->shift); 53 svfloat64_t inv_pi_and_pi1 = svld1rq (ptrue, &d->inv_pi); 54 svfloat64_t pi2_and_pi3 = svld1rq (ptrue, &d->pi_2); 55 56 /* n = rint(|x|/pi). */ 57 svfloat64_t n = svmla_lane (shift, x, inv_pi_and_pi1, 0); 58 svuint64_t odd = svlsl_x (pg, svreinterpret_u64 (n), 63); 59 n = svsub_x (pg, n, shift); 60 61 /* r = |x| - n*(pi/2) (range reduction into -pi/2 .. pi/2). */ 62 svfloat64_t r = x; 63 r = svmls_lane (r, n, inv_pi_and_pi1, 1); 64 r = svmls_lane (r, n, pi2_and_pi3, 0); 65 r = svmls_lane (r, n, pi2_and_pi3, 1); 66 67 /* sin(r) poly approx. */ 68 svfloat64_t r2 = svmul_x (pg, r, r); 69 svfloat64_t r3 = svmul_x (pg, r2, r); 70 svfloat64_t r4 = svmul_x (pg, r2, r2); 71 72 svfloat64_t t1 = svmla_x (pg, C (4), C (5), r2); 73 svfloat64_t t2 = svmla_x (pg, C (2), C (3), r2); 74 svfloat64_t t3 = svmla_x (pg, C (0), C (1), r2); 75 76 svfloat64_t y = svmla_x (pg, t1, C (6), r4); 77 y = svmla_x (pg, t2, y, r4); 78 y = svmla_x (pg, t3, y, r4); 79 y = svmla_x (pg, r, y, r3); 80 81 svbool_t cmp = svacle (pg, x, d->range_val); 82 cmp = svnot_z (pg, cmp); 83 if (unlikely (svptest_any (pg, cmp))) 84 return special_case (x, 85 svreinterpret_f64 (sveor_z ( 86 svnot_z (pg, cmp), svreinterpret_u64 (y), odd)), 87 cmp); 88 89 /* Copy sign. */ 90 return svreinterpret_f64 (sveor_z (pg, svreinterpret_u64 (y), odd)); 91 } 92 93 PL_SIG (SV, D, 1, sin, -3.1, 3.1) 94 PL_TEST_ULP (SV_NAME_D1 (sin), 2.73) 95 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (sin), 0, 0x1p23, 1000000) 96 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (sin), 0x1p23, inf, 10000) 97