1 /* 2 * Single-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 #if SV_SUPPORTED 13 14 #define A3 (sv_f32 (__sv_sinf_data.coeffs[3])) 15 #define A5 (sv_f32 (__sv_sinf_data.coeffs[2])) 16 #define A7 (sv_f32 (__sv_sinf_data.coeffs[1])) 17 #define A9 (sv_f32 (__sv_sinf_data.coeffs[0])) 18 19 #define NegPi1 (sv_f32 (-0x1.921fb6p+1f)) 20 #define NegPi2 (sv_f32 (0x1.777a5cp-24f)) 21 #define NegPi3 (sv_f32 (0x1.ee59dap-49f)) 22 #define RangeVal (sv_f32 (0x1p20f)) 23 #define InvPi (sv_f32 (0x1.45f306p-2f)) 24 #define Shift (sv_f32 (0x1.8p+23f)) 25 #define AbsMask (0x7fffffff) 26 27 static NOINLINE sv_f32_t 28 __sv_sinf_specialcase (sv_f32_t x, sv_f32_t y, svbool_t cmp) 29 { 30 return sv_call_f32 (sinf, x, y, cmp); 31 } 32 33 /* A fast SVE implementation of sinf. 34 Maximum error: 1.89 ULPs. 35 This maximum error is achieved at multiple values in [-2^18, 2^18] 36 but one example is: 37 __sv_sinf(0x1.9247a4p+0) got 0x1.fffff6p-1 want 0x1.fffffap-1. */ 38 sv_f32_t 39 __sv_sinf_x (sv_f32_t x, const svbool_t pg) 40 { 41 sv_f32_t n, r, r2, y; 42 sv_u32_t sign, odd; 43 svbool_t cmp; 44 45 r = sv_as_f32_u32 (svand_n_u32_x (pg, sv_as_u32_f32 (x), AbsMask)); 46 sign = svand_n_u32_x (pg, sv_as_u32_f32 (x), ~AbsMask); 47 cmp = svcmpge_u32 (pg, sv_as_u32_f32 (r), sv_as_u32_f32 (RangeVal)); 48 49 /* n = rint(|x|/pi). */ 50 n = sv_fma_f32_x (pg, InvPi, r, Shift); 51 odd = svlsl_n_u32_x (pg, sv_as_u32_f32 (n), 31); 52 n = svsub_f32_x (pg, n, Shift); 53 54 /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */ 55 r = sv_fma_f32_x (pg, NegPi1, n, r); 56 r = sv_fma_f32_x (pg, NegPi2, n, r); 57 r = sv_fma_f32_x (pg, NegPi3, n, r); 58 59 /* sin(r) approx using a degree 9 polynomial from the Taylor series 60 expansion. Note that only the odd terms of this are non-zero. */ 61 r2 = svmul_f32_x (pg, r, r); 62 y = sv_fma_f32_x (pg, A9, r2, A7); 63 y = sv_fma_f32_x (pg, y, r2, A5); 64 y = sv_fma_f32_x (pg, y, r2, A3); 65 y = sv_fma_f32_x (pg, svmul_f32_x (pg, y, r2), r, r); 66 67 /* sign = y^sign^odd. */ 68 y = sv_as_f32_u32 ( 69 sveor_u32_x (pg, sv_as_u32_f32 (y), sveor_u32_x (pg, sign, odd))); 70 71 /* No need to pass pg to specialcase here since cmp is a strict subset, 72 guaranteed by the cmpge above. */ 73 if (unlikely (svptest_any (pg, cmp))) 74 return __sv_sinf_specialcase (x, y, cmp); 75 return y; 76 } 77 78 PL_ALIAS (__sv_sinf_x, _ZGVsMxv_sinf) 79 80 PL_SIG (SV, F, 1, sin, -3.1, 3.1) 81 PL_TEST_ULP (__sv_sinf, 1.40) 82 PL_TEST_INTERVAL (__sv_sinf, 0, 0xffff0000, 10000) 83 PL_TEST_INTERVAL (__sv_sinf, 0x1p-4, 0x1p4, 500000) 84 #endif 85