| /* |
| * Copyright (c) 2014 Advanced Micro Devices, Inc. |
| * |
| * Permission is hereby granted, free of charge, to any person obtaining a copy |
| * of this software and associated documentation files (the "Software"), to deal |
| * in the Software without restriction, including without limitation the rights |
| * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
| * copies of the Software, and to permit persons to whom the Software is |
| * furnished to do so, subject to the following conditions: |
| * |
| * The above copyright notice and this permission notice shall be included in |
| * all copies or substantial portions of the Software. |
| * |
| * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
| * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
| * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
| * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
| * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
| * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
| * THE SOFTWARE. |
| */ |
| |
| #include "math32.h" |
| #if !defined(SUBNORMALS_SUPPORTED) |
| #include "floattointconversion.h" |
| #endif //SUBNORMALS_SUPPORTED |
| |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| #define erx 8.4506291151e-01f /* 0x3f58560b */ |
| |
| // Coefficients for approximation to erf on [00.84375] |
| |
| #define efx 1.2837916613e-01f /* 0x3e0375d4 */ |
| #define efx8 1.0270333290e+00f /* 0x3f8375d4 */ |
| |
| #define pp0 1.2837916613e-01f /* 0x3e0375d4 */ |
| #define pp1 -3.2504209876e-01f /* 0xbea66beb */ |
| #define pp2 -2.8481749818e-02f /* 0xbce9528f */ |
| #define pp3 -5.7702702470e-03f /* 0xbbbd1489 */ |
| #define pp4 -2.3763017452e-05f /* 0xb7c756b1 */ |
| #define qq1 3.9791721106e-01f /* 0x3ecbbbce */ |
| #define qq2 6.5022252500e-02f /* 0x3d852a63 */ |
| #define qq3 5.0813062117e-03f /* 0x3ba68116 */ |
| #define qq4 1.3249473704e-04f /* 0x390aee49 */ |
| #define qq5 -3.9602282413e-06f /* 0xb684e21a */ |
| |
| // Coefficients for approximation to erf in [0.843751.25] |
| |
| #define pa0 -2.3621185683e-03f /* 0xbb1acdc6 */ |
| #define pa1 4.1485610604e-01f /* 0x3ed46805 */ |
| #define pa2 -3.7220788002e-01f /* 0xbebe9208 */ |
| #define pa3 3.1834661961e-01f /* 0x3ea2fe54 */ |
| #define pa4 -1.1089469492e-01f /* 0xbde31cc2 */ |
| #define pa5 3.5478305072e-02f /* 0x3d1151b3 */ |
| #define pa6 -2.1663755178e-03f /* 0xbb0df9c0 */ |
| #define qa1 1.0642088205e-01f /* 0x3dd9f331 */ |
| #define qa2 5.4039794207e-01f /* 0x3f0a5785 */ |
| #define qa3 7.1828655899e-02f /* 0x3d931ae7 */ |
| #define qa4 1.2617121637e-01f /* 0x3e013307 */ |
| #define qa5 1.3637083583e-02f /* 0x3c5f6e13 */ |
| #define qa6 1.1984500103e-02f /* 0x3c445aa3 */ |
| |
| // Coefficients for approximation to erfc in [1.251/0.35] |
| |
| #define ra0 -9.8649440333e-03f /* 0xbc21a093 */ |
| #define ra1 -6.9385856390e-01f /* 0xbf31a0b7 */ |
| #define ra2 -1.0558626175e+01f /* 0xc128f022 */ |
| #define ra3 -6.2375331879e+01f /* 0xc2798057 */ |
| #define ra4 -1.6239666748e+02f /* 0xc322658c */ |
| #define ra5 -1.8460508728e+02f /* 0xc3389ae7 */ |
| #define ra6 -8.1287437439e+01f /* 0xc2a2932b */ |
| #define ra7 -9.8143291473e+00f /* 0xc11d077e */ |
| #define sa1 1.9651271820e+01f /* 0x419d35ce */ |
| #define sa2 1.3765776062e+02f /* 0x4309a863 */ |
| #define sa3 4.3456588745e+02f /* 0x43d9486f */ |
| #define sa4 6.4538726807e+02f /* 0x442158c9 */ |
| #define sa5 4.2900814819e+02f /* 0x43d6810b */ |
| #define sa6 1.0863500214e+02f /* 0x42d9451f */ |
| #define sa7 6.5702495575e+00f /* 0x40d23f7c */ |
| #define sa8 -6.0424413532e-02f /* 0xbd777f97 */ |
| |
| // Coefficients for approximation to erfc in [1/.3528] |
| |
| #define rb0 -9.8649431020e-03f /* 0xbc21a092 */ |
| #define rb1 -7.9928326607e-01f /* 0xbf4c9dd4 */ |
| #define rb2 -1.7757955551e+01f /* 0xc18e104b */ |
| #define rb3 -1.6063638306e+02f /* 0xc320a2ea */ |
| #define rb4 -6.3756646729e+02f /* 0xc41f6441 */ |
| #define rb5 -1.0250950928e+03f /* 0xc480230b */ |
| #define rb6 -4.8351919556e+02f /* 0xc3f1c275 */ |
| #define sb1 3.0338060379e+01f /* 0x41f2b459 */ |
| #define sb2 3.2579251099e+02f /* 0x43a2e571 */ |
| #define sb3 1.5367296143e+03f /* 0x44c01759 */ |
| #define sb4 3.1998581543e+03f /* 0x4547fdbb */ |
| #define sb5 2.5530502930e+03f /* 0x451f90ce */ |
| #define sb6 4.7452853394e+02f /* 0x43ed43a7 */ |
| #define sb7 -2.2440952301e+01f /* 0xc1b38712 */ |
| |
| __attribute__((overloadable)) float |
| erf(float x) |
| { |
| |
| int hx = as_uint(x); |
| int ix = hx & 0x7fffffff; |
| float absx = as_float(ix); |
| |
| float x2 = absx * absx; |
| float t = 1.0f / x2; |
| float tt = absx - 1.0f; |
| t = absx < 1.25f ? tt : t; |
| t = absx < 0.84375f ? x2 : t; |
| |
| float u, v, tu, tv; |
| |
| // |x| < 6 |
| u = mad(t, mad(t, mad(t, mad(t, mad(t, mad(t, rb6, rb5), rb4), rb3), rb2), rb1), rb0); |
| v = mad(t, mad(t, mad(t, mad(t, mad(t, mad(t, sb7, sb6), sb5), sb4), sb3), sb2), sb1); |
| |
| tu = mad(t, mad(t, mad(t, mad(t, mad(t, mad(t, mad(t, ra7, ra6), ra5), ra4), ra3), ra2), ra1), ra0); |
| tv = mad(t, mad(t, mad(t, mad(t, mad(t, mad(t, mad(t, sa8, sa7), sa6), sa5), sa4), sa3), sa2), sa1); |
| u = absx < 0x1.6db6dcp+1f ? tu : u; |
| v = absx < 0x1.6db6dcp+1f ? tv : v; |
| |
| tu = mad(t, mad(t, mad(t, mad(t, mad(t, mad(t, pa6, pa5), pa4), pa3), pa2), pa1), pa0); |
| tv = mad(t, mad(t, mad(t, mad(t, mad(t, qa6, qa5), qa4), qa3), qa2), qa1); |
| u = absx < 1.25f ? tu : u; |
| v = absx < 1.25f ? tv : v; |
| |
| tu = mad(t, mad(t, mad(t, mad(t, pp4, pp3), pp2), pp1), pp0); |
| tv = mad(t, mad(t, mad(t, mad(t, qq5, qq4), qq3), qq2), qq1); |
| u = absx < 0.84375f ? tu : u; |
| v = absx < 0.84375f ? tv : v; |
| |
| v = mad(t, v, 1.0f); |
| float q = MATH_DIVIDE(u, v); |
| |
| float ret = 1.0f; |
| |
| // |x| < 6 |
| float z = as_float(ix & 0xfffff000); |
| float r = exp(mad(-z, z, -0.5625f)) * exp(mad(z-absx, z+absx, q)); |
| r = 1.0f - MATH_DIVIDE(r, absx); |
| ret = absx < 6.0f ? r : ret; |
| |
| r = erx + q; |
| ret = absx < 1.25f ? r : ret; |
| |
| ret = as_float((hx & 0x80000000) | as_int(ret)); |
| |
| r = mad(x, q, x); |
| ret = absx < 0.84375f ? r : ret; |
| |
| // Prevent underflow |
| r = 0.125f * mad(8.0f, x, efx8 * x); |
| ret = absx < 0x1.0p-28f ? r : ret; |
| |
| #if !defined(SUBNORMALS_SUPPORTED) |
| |
| double dx = float_uint_to_double(hx); |
| const double sqt4overpi = 1.1283791670955125738961589031215; |
| float ret1 = as_float(double_to_float_uint(sqt4overpi * dx)); |
| int c = as_uint(absx) == 0; |
| float ret2 = hx == 0 ? 0 : -0; |
| ret1 = c ? ret2 : ret1; |
| ret = x == 0. ? ret1 : ret; |
| #endif //SUBNORMALS_SUPPORTED |
| |
| |
| ret = isnan(x) ? x : ret; |
| |
| return ret; |
| } |
| |
