1 /* 2 * Single-precision vector atan2f(x) function. 3 * 4 * Copyright (c) 2021-2024, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "test_sig.h" 10 #include "test_defs.h" 11 #include "sv_poly_f32.h" 12 13 static const struct data 14 { 15 float32_t poly[8]; 16 float32_t pi_over_2; 17 } data = { 18 /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on 19 [2**-128, 1.0]. */ 20 .poly = { -0x1.55555p-2f, 0x1.99935ep-3f, -0x1.24051ep-3f, 0x1.bd7368p-4f, 21 -0x1.491f0ep-4f, 0x1.93a2c0p-5f, -0x1.4c3c60p-6f, 0x1.01fd88p-8f }, 22 .pi_over_2 = 0x1.921fb6p+0f, 23 }; 24 25 /* Special cases i.e. 0, infinity, nan (fall back to scalar calls). */ 26 static svfloat32_t NOINLINE 27 special_case (svfloat32_t y, svfloat32_t x, svfloat32_t ret, 28 const svbool_t cmp) 29 { 30 return sv_call2_f32 (atan2f, y, x, ret, cmp); 31 } 32 33 /* Returns a predicate indicating true if the input is the bit representation 34 of 0, infinity or nan. */ 35 static inline svbool_t 36 zeroinfnan (svuint32_t i, const svbool_t pg) 37 { 38 return svcmpge (pg, svsub_x (pg, svlsl_x (pg, i, 1), 1), 39 sv_u32 (2 * 0x7f800000lu - 1)); 40 } 41 42 /* Fast implementation of SVE atan2f based on atan(x) ~ shift + z + z^3 * 43 P(z^2) with reduction to [0,1] using z=1/x and shift = pi/2. Maximum 44 observed error is 2.95 ULP: 45 _ZGVsMxvv_atan2f (0x1.93836cp+6, 0x1.8cae1p+6) got 0x1.967f06p-1 46 want 0x1.967f00p-1. */ 47 svfloat32_t SV_NAME_F2 (atan2) (svfloat32_t y, svfloat32_t x, 48 const svbool_t pg) 49 { 50 const struct data *data_ptr = ptr_barrier (&data); 51 52 svuint32_t ix = svreinterpret_u32 (x); 53 svuint32_t iy = svreinterpret_u32 (y); 54 55 svbool_t cmp_x = zeroinfnan (ix, pg); 56 svbool_t cmp_y = zeroinfnan (iy, pg); 57 svbool_t cmp_xy = svorr_z (pg, cmp_x, cmp_y); 58 59 svfloat32_t ax = svabs_x (pg, x); 60 svfloat32_t ay = svabs_x (pg, y); 61 svuint32_t iax = svreinterpret_u32 (ax); 62 svuint32_t iay = svreinterpret_u32 (ay); 63 64 svuint32_t sign_x = sveor_x (pg, ix, iax); 65 svuint32_t sign_y = sveor_x (pg, iy, iay); 66 svuint32_t sign_xy = sveor_x (pg, sign_x, sign_y); 67 68 svbool_t pred_aygtax = svcmpgt (pg, ay, ax); 69 70 /* Set up z for call to atan. */ 71 svfloat32_t n = svsel (pred_aygtax, svneg_x (pg, ax), ay); 72 svfloat32_t d = svsel (pred_aygtax, ay, ax); 73 svfloat32_t z = svdiv_x (pg, n, d); 74 75 /* Work out the correct shift. */ 76 svfloat32_t shift = svreinterpret_f32 (svlsr_x (pg, sign_x, 1)); 77 shift = svsel (pred_aygtax, sv_f32 (1.0), shift); 78 shift = svreinterpret_f32 (svorr_x (pg, sign_x, svreinterpret_u32 (shift))); 79 shift = svmul_x (pg, shift, sv_f32 (data_ptr->pi_over_2)); 80 81 /* Use pure Estrin scheme for P(z^2) with deg(P)=7. */ 82 svfloat32_t z2 = svmul_x (pg, z, z); 83 svfloat32_t z4 = svmul_x (pg, z2, z2); 84 svfloat32_t z8 = svmul_x (pg, z4, z4); 85 86 svfloat32_t ret = sv_estrin_7_f32_x (pg, z2, z4, z8, data_ptr->poly); 87 88 /* ret = shift + z + z^3 * P(z^2). */ 89 svfloat32_t z3 = svmul_x (pg, z2, z); 90 ret = svmla_x (pg, z, z3, ret); 91 92 ret = svadd_m (pg, ret, shift); 93 94 /* Account for the sign of x and y. */ 95 96 if (unlikely (svptest_any (pg, cmp_xy))) 97 return special_case ( 98 y, x, 99 svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (ret), sign_xy)), 100 cmp_xy); 101 102 return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (ret), sign_xy)); 103 } 104 105 /* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h. */ 106 TEST_SIG (SV, F, 2, atan2) 107 TEST_ULP (SV_NAME_F2 (atan2), 2.45) 108 TEST_DISABLE_FENV (SV_NAME_F2 (atan2)) 109 TEST_INTERVAL (SV_NAME_F2 (atan2), 0.0, 1.0, 40000) 110 TEST_INTERVAL (SV_NAME_F2 (atan2), 1.0, 100.0, 40000) 111 TEST_INTERVAL (SV_NAME_F2 (atan2), 100, inf, 40000) 112 TEST_INTERVAL (SV_NAME_F2 (atan2), -0, -inf, 40000) 113 CLOSE_SVE_ATTR 114