1 /* 2 * Double-precision vector atan2(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_f64.h" 12 13 static const struct data 14 { 15 float64_t poly[20]; 16 float64_t pi_over_2; 17 } data = { 18 /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on 19 [2**-1022, 1.0]. */ 20 .poly = { -0x1.5555555555555p-2, 0x1.99999999996c1p-3, -0x1.2492492478f88p-3, 21 0x1.c71c71bc3951cp-4, -0x1.745d160a7e368p-4, 0x1.3b139b6a88ba1p-4, 22 -0x1.11100ee084227p-4, 0x1.e1d0f9696f63bp-5, -0x1.aebfe7b418581p-5, 23 0x1.842dbe9b0d916p-5, -0x1.5d30140ae5e99p-5, 0x1.338e31eb2fbbcp-5, 24 -0x1.00e6eece7de8p-5, 0x1.860897b29e5efp-6, -0x1.0051381722a59p-6, 25 0x1.14e9dc19a4a4ep-7, -0x1.d0062b42fe3bfp-9, 0x1.17739e210171ap-10, 26 -0x1.ab24da7be7402p-13, 0x1.358851160a528p-16, }, 27 .pi_over_2 = 0x1.921fb54442d18p+0, 28 }; 29 30 /* Special cases i.e. 0, infinity, nan (fall back to scalar calls). */ 31 static svfloat64_t NOINLINE 32 special_case (svfloat64_t y, svfloat64_t x, svfloat64_t ret, 33 const svbool_t cmp) 34 { 35 return sv_call2_f64 (atan2, y, x, ret, cmp); 36 } 37 38 /* Returns a predicate indicating true if the input is the bit representation 39 of 0, infinity or nan. */ 40 static inline svbool_t 41 zeroinfnan (svuint64_t i, const svbool_t pg) 42 { 43 return svcmpge (pg, svsub_x (pg, svlsl_x (pg, i, 1), 1), 44 sv_u64 (2 * asuint64 (INFINITY) - 1)); 45 } 46 47 /* Fast implementation of SVE atan2. Errors are greatest when y and 48 x are reasonably close together. The greatest observed error is 2.28 ULP: 49 _ZGVsMxvv_atan2 (-0x1.5915b1498e82fp+732, 0x1.54d11ef838826p+732) 50 got -0x1.954f42f1fa841p-1 want -0x1.954f42f1fa843p-1. */ 51 svfloat64_t SV_NAME_D2 (atan2) (svfloat64_t y, svfloat64_t x, 52 const svbool_t pg) 53 { 54 const struct data *data_ptr = ptr_barrier (&data); 55 56 svuint64_t ix = svreinterpret_u64 (x); 57 svuint64_t iy = svreinterpret_u64 (y); 58 59 svbool_t cmp_x = zeroinfnan (ix, pg); 60 svbool_t cmp_y = zeroinfnan (iy, pg); 61 svbool_t cmp_xy = svorr_z (pg, cmp_x, cmp_y); 62 63 svfloat64_t ax = svabs_x (pg, x); 64 svfloat64_t ay = svabs_x (pg, y); 65 svuint64_t iax = svreinterpret_u64 (ax); 66 svuint64_t iay = svreinterpret_u64 (ay); 67 68 svuint64_t sign_x = sveor_x (pg, ix, iax); 69 svuint64_t sign_y = sveor_x (pg, iy, iay); 70 svuint64_t sign_xy = sveor_x (pg, sign_x, sign_y); 71 72 svbool_t pred_aygtax = svcmpgt (pg, ay, ax); 73 74 /* Set up z for call to atan. */ 75 svfloat64_t n = svsel (pred_aygtax, svneg_x (pg, ax), ay); 76 svfloat64_t d = svsel (pred_aygtax, ay, ax); 77 svfloat64_t z = svdiv_x (pg, n, d); 78 79 /* Work out the correct shift. */ 80 svfloat64_t shift = svreinterpret_f64 (svlsr_x (pg, sign_x, 1)); 81 shift = svsel (pred_aygtax, sv_f64 (1.0), shift); 82 shift = svreinterpret_f64 (svorr_x (pg, sign_x, svreinterpret_u64 (shift))); 83 shift = svmul_x (pg, shift, data_ptr->pi_over_2); 84 85 /* Use split Estrin scheme for P(z^2) with deg(P)=19. */ 86 svfloat64_t z2 = svmul_x (pg, z, z); 87 svfloat64_t x2 = svmul_x (pg, z2, z2); 88 svfloat64_t x4 = svmul_x (pg, x2, x2); 89 svfloat64_t x8 = svmul_x (pg, x4, x4); 90 91 svfloat64_t ret = svmla_x ( 92 pg, sv_estrin_7_f64_x (pg, z2, x2, x4, data_ptr->poly), 93 sv_estrin_11_f64_x (pg, z2, x2, x4, x8, data_ptr->poly + 8), x8); 94 95 /* y = shift + z + z^3 * P(z^2). */ 96 svfloat64_t z3 = svmul_x (pg, z2, z); 97 ret = svmla_x (pg, z, z3, ret); 98 99 ret = svadd_m (pg, ret, shift); 100 101 /* Account for the sign of x and y. */ 102 if (unlikely (svptest_any (pg, cmp_xy))) 103 return special_case ( 104 y, x, 105 svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (ret), sign_xy)), 106 cmp_xy); 107 return svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (ret), sign_xy)); 108 } 109 110 /* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h. */ 111 TEST_SIG (SV, D, 2, atan2) 112 TEST_ULP (SV_NAME_D2 (atan2), 1.78) 113 TEST_DISABLE_FENV (SV_NAME_D2 (atan2)) 114 TEST_INTERVAL (SV_NAME_D2 (atan2), 0.0, 1.0, 40000) 115 TEST_INTERVAL (SV_NAME_D2 (atan2), 1.0, 100.0, 40000) 116 TEST_INTERVAL (SV_NAME_D2 (atan2), 100, inf, 40000) 117 TEST_INTERVAL (SV_NAME_D2 (atan2), -0, -inf, 40000) 118 CLOSE_SVE_ATTR 119