2  * Single-precision vector erf(x) function.
4  * Copyright (c) 2023-2024, Arm Limited.
5  * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
14   float min, max, scale, shift, third;  member
16   .min = 0x1.cp-7f,	   /* 1/64 - 1/512.  */
17   .max = 3.9375,	   /* 4 - 8/128.  */
20   .third = 0x1.555556p-2f, /* 1/3.  */
25 /* Single-precision implementation of vector erf(x).
28    Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r,
30    erf(x) ~ erf(r) + scale * d * [1 - r * d - 1/3 * d^2]
33    For |x| < 0x1.cp-7, the algorithm sets r = 0, erf(r) = 0, and scale = 2 /
38    - [0, 0x1.cp-7]: 1.93 ULP
39      _ZGVsMxv_erff(0x1.c373e6p-9) got 0x1.fd686cp-9 want 0x1.fd6868p-9
40    - [0x1.cp-7, 4.0]: 1.26 ULP
41      _ZGVsMxv_erff(0x1.1d002ep+0) got 0x1.c4eb9ap-1 want 0x1.c4eb98p-1.  */
46   /* |x| > 1/64 - 1/512.  */  in SV_NAME_F1()
47   svbool_t a_gt_min = svacgt (pg, x, dat->min);  in SV_NAME_F1()
49   /* |x| >= 4.0 - 8/128.  */  in SV_NAME_F1()
50   svbool_t a_ge_max = svacge (pg, x, dat->max);  in SV_NAME_F1()
53   svfloat32_t shift = sv_f32 (dat->shift);  in SV_NAME_F1()
58   /* r and erf(r) set to 0 for |x| below min.  */  in SV_NAME_F1()
63   /* scale set to 2/sqrt(pi) for |x| below min.  */  in SV_NAME_F1()
66   scale = svsel (a_gt_min, scale, sv_f32 (dat->scale));  in SV_NAME_F1()
68   /* erf(x) ~ erf(r) + scale * d * (1 - r * d + 1/3 * d^2).  */  in SV_NAME_F1()
71   svfloat32_t y = svmla_x (pg, r, d, dat->third);  in SV_NAME_F1()  local
72   y = svmla_x (pg, erfr, scale, svmls_x (pg, d, d2, y));  in SV_NAME_F1()
75   y = svsel (a_ge_max, sv_f32 (1.0f), y);  in SV_NAME_F1()
79   svuint32_t iy = svreinterpret_u32 (y);  in SV_NAME_F1()
84 TEST_SIG (SV, F, 1, erf, -4.0, 4.0)
87 TEST_SYM_INTERVAL (SV_NAME_F1 (erf), 0, 0x1.cp-7, 40000)
88 TEST_SYM_INTERVAL (SV_NAME_F1 (erf), 0x1.cp-7, 3.9375, 40000)