1 /* 2 * Double-precision vector atan2(x) function. 3 * 4 * Copyright (c) 2021-2023, 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 #include "poly_sve_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 /* Useful constants. */ 31 #define SignMask sv_u64 (0x8000000000000000) 32 33 /* Special cases i.e. 0, infinity, nan (fall back to scalar calls). */ 34 static svfloat64_t NOINLINE 35 special_case (svfloat64_t y, svfloat64_t x, svfloat64_t ret, 36 const svbool_t cmp) 37 { 38 return sv_call2_f64 (atan2, y, x, ret, cmp); 39 } 40 41 /* Returns a predicate indicating true if the input is the bit representation 42 of 0, infinity or nan. */ 43 static inline svbool_t 44 zeroinfnan (svuint64_t i, const svbool_t pg) 45 { 46 return svcmpge (pg, svsub_x (pg, svlsl_x (pg, i, 1), 1), 47 sv_u64 (2 * asuint64 (INFINITY) - 1)); 48 } 49 50 /* Fast implementation of SVE atan2. Errors are greatest when y and 51 x are reasonably close together. The greatest observed error is 2.28 ULP: 52 _ZGVsMxvv_atan2 (-0x1.5915b1498e82fp+732, 0x1.54d11ef838826p+732) 53 got -0x1.954f42f1fa841p-1 want -0x1.954f42f1fa843p-1. */ 54 svfloat64_t SV_NAME_D2 (atan2) (svfloat64_t y, svfloat64_t x, const svbool_t pg) 55 { 56 const struct data *data_ptr = ptr_barrier (&data); 57 58 svuint64_t ix = svreinterpret_u64 (x); 59 svuint64_t iy = svreinterpret_u64 (y); 60 61 svbool_t cmp_x = zeroinfnan (ix, pg); 62 svbool_t cmp_y = zeroinfnan (iy, pg); 63 svbool_t cmp_xy = svorr_z (pg, cmp_x, cmp_y); 64 65 svuint64_t sign_x = svand_x (pg, ix, SignMask); 66 svuint64_t sign_y = svand_x (pg, iy, SignMask); 67 svuint64_t sign_xy = sveor_x (pg, sign_x, sign_y); 68 69 svfloat64_t ax = svabs_x (pg, x); 70 svfloat64_t ay = svabs_x (pg, y); 71 72 svbool_t pred_xlt0 = svcmplt (pg, x, 0.0); 73 svbool_t pred_aygtax = svcmpgt (pg, ay, ax); 74 75 /* Set up z for call to atan. */ 76 svfloat64_t n = svsel (pred_aygtax, svneg_x (pg, ax), ay); 77 svfloat64_t d = svsel (pred_aygtax, ay, ax); 78 svfloat64_t z = svdiv_x (pg, n, d); 79 80 /* Work out the correct shift. */ 81 svfloat64_t shift = svsel (pred_xlt0, sv_f64 (-2.0), sv_f64 (0.0)); 82 shift = svsel (pred_aygtax, svadd_x (pg, shift, 1.0), 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 ret = svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (ret), sign_xy)); 103 104 if (unlikely (svptest_any (pg, cmp_xy))) 105 return special_case (y, x, ret, cmp_xy); 106 107 return ret; 108 } 109 110 /* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h. */ 111 PL_SIG (SV, D, 2, atan2) 112 PL_TEST_ULP (SV_NAME_D2 (atan2), 1.78) 113 PL_TEST_INTERVAL (SV_NAME_D2 (atan2), 0.0, 1.0, 40000) 114 PL_TEST_INTERVAL (SV_NAME_D2 (atan2), 1.0, 100.0, 40000) 115 PL_TEST_INTERVAL (SV_NAME_D2 (atan2), 100, inf, 40000) 116 PL_TEST_INTERVAL (SV_NAME_D2 (atan2), -0, -inf, 40000) 117