1 /* 2 * Single-precision SVE asin(x) function. 3 * 4 * Copyright (c) 2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "poly_sve_f32.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 13 static const struct data 14 { 15 float32_t poly[5]; 16 float32_t pi_over_2f; 17 } data = { 18 /* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) on 19 [ 0x1p-24 0x1p-2 ] order = 4 rel error: 0x1.00a23bbp-29 . */ 20 .poly = { 0x1.55555ep-3, 0x1.33261ap-4, 0x1.70d7dcp-5, 0x1.b059dp-6, 21 0x1.3af7d8p-5, }, 22 .pi_over_2f = 0x1.921fb6p+0f, 23 }; 24 25 /* Single-precision SVE implementation of vector asin(x). 26 27 For |x| in [0, 0.5], use order 4 polynomial P such that the final 28 approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2). 29 30 The largest observed error in this region is 0.83 ulps, 31 _ZGVsMxv_asinf (0x1.ea00f4p-2) got 0x1.fef15ep-2 32 want 0x1.fef15cp-2. 33 34 For |x| in [0.5, 1.0], use same approximation with a change of variable 35 36 asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z). 37 38 The largest observed error in this region is 2.41 ulps, 39 _ZGVsMxv_asinf (-0x1.00203ep-1) got -0x1.0c3a64p-1 40 want -0x1.0c3a6p-1. */ 41 svfloat32_t SV_NAME_F1 (asin) (svfloat32_t x, const svbool_t pg) 42 { 43 const struct data *d = ptr_barrier (&data); 44 45 svuint32_t sign = svand_x (pg, svreinterpret_u32 (x), 0x80000000); 46 47 svfloat32_t ax = svabs_x (pg, x); 48 svbool_t a_ge_half = svacge (pg, x, 0.5); 49 50 /* Evaluate polynomial Q(x) = y + y * z * P(z) with 51 z = x ^ 2 and y = |x| , if |x| < 0.5 52 z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */ 53 svfloat32_t z2 = svsel (a_ge_half, svmls_x (pg, sv_f32 (0.5), ax, 0.5), 54 svmul_x (pg, x, x)); 55 svfloat32_t z = svsqrt_m (ax, a_ge_half, z2); 56 57 /* Use a single polynomial approximation P for both intervals. */ 58 svfloat32_t p = sv_horner_4_f32_x (pg, z2, d->poly); 59 /* Finalize polynomial: z + z * z2 * P(z2). */ 60 p = svmla_x (pg, z, svmul_x (pg, z, z2), p); 61 62 /* asin(|x|) = Q(|x|) , for |x| < 0.5 63 = pi/2 - 2 Q(|x|), for |x| >= 0.5. */ 64 svfloat32_t y = svmad_m (a_ge_half, p, sv_f32 (-2.0), d->pi_over_2f); 65 66 /* Copy sign. */ 67 return svreinterpret_f32 (svorr_x (pg, svreinterpret_u32 (y), sign)); 68 } 69 70 PL_SIG (SV, F, 1, asin, -1.0, 1.0) 71 PL_TEST_ULP (SV_NAME_F1 (asin), 1.91) 72 PL_TEST_INTERVAL (SV_NAME_F1 (asin), 0, 0.5, 50000) 73 PL_TEST_INTERVAL (SV_NAME_F1 (asin), 0.5, 1.0, 50000) 74 PL_TEST_INTERVAL (SV_NAME_F1 (asin), 1.0, 0x1p11, 50000) 75 PL_TEST_INTERVAL (SV_NAME_F1 (asin), 0x1p11, inf, 20000) 76 PL_TEST_INTERVAL (SV_NAME_F1 (asin), -0, -inf, 20000)