| /* e_rem_pio2f.c -- float version of e_rem_pio2.c |
| Copyright (C) 2011-2018 Free Software Foundation, Inc. |
| This file is part of the GNU C Library. |
| Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011 |
| |
| The GNU C Library is free software; you can redistribute it and/or |
| modify it under the terms of the GNU Library General Public License as |
| published by the Free Software Foundation; either version 2 of the |
| License, or (at your option) any later version. |
| |
| The GNU C Library is distributed in the hope that it will be useful, |
| but WITHOUT ANY WARRANTY; without even the implied warranty of |
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| Library General Public License for more details. |
| |
| You should have received a copy of the GNU Library General Public |
| License along with the GNU C Library; see the file COPYING.LIB. If |
| not, see <http://www.gnu.org/licenses/>. */ |
| |
| #include <math.h> |
| |
| #include <math_private.h> |
| #include "s_float_bitwise.h" |
| |
| /* defined in sysdeps/powerpc/fpu/k_rem_pio2f.c */ |
| int __fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx); |
| |
| /* __ieee754_rem_pio2f(x,y) |
| * |
| * return the remainder of x rem pi/2 in y[0]+y[1] |
| */ |
| |
| static const float npio2_hw[] = { |
| 1.57077026e+00, 3.14154053e+00, 4.71228027e+00, 6.28308105e+00, |
| 7.85388184e+00, 9.42456055e+00, 1.09953613e+01, 1.25661621e+01, |
| 1.41369629e+01, 1.57077637e+01, 1.72783203e+01, 1.88491211e+01, |
| 2.04199219e+01, 2.19907227e+01, 2.35615234e+01, 2.51323242e+01, |
| 2.67031250e+01, 2.82739258e+01, 2.98447266e+01, 3.14155273e+01, |
| 3.29863281e+01, 3.45566406e+01, 3.61279297e+01, 3.76982422e+01, |
| 3.92695312e+01, 4.08398438e+01, 4.24111328e+01, 4.39814453e+01, |
| 4.55527344e+01, 4.71230469e+01, 4.86943359e+01, 5.02646484e+01 |
| }; |
| |
| |
| static const float zero = 0.0000000000e+00; |
| static const float two8 = 2.5600000000e+02; |
| |
| static const float half = 5.0000000000e-01; |
| static const float invpio2 = 6.3661980629e-01; |
| static const float pio2_1 = 1.5707855225e+00; |
| static const float pio2_1t = 1.0804334124e-05; |
| static const float pio2_2 = 1.0804273188e-05; |
| static const float pio2_2t = 6.0770999344e-11; |
| static const float pio2_3 = 6.0770943833e-11; |
| static const float pio2_3t = 6.1232342629e-17; |
| |
| static const float pio4 = 7.8539801e-01; |
| static const float pio3_4 = 2.3561945e+00; |
| static const float pio2_24b = 1.5707951e+00; |
| static const float pio2_2e7 = 2.0106054e+02; |
| |
| |
| int32_t |
| __ieee754_rem_pio2f (float x, float *y) |
| { |
| float ax, z, n, r, w, t, e0; |
| float tx[3]; |
| int32_t i, nx; |
| |
| ax = __builtin_fabsf (x); |
| if (ax <= pio4) |
| { |
| y[0] = x; |
| y[1] = 0; |
| return 0; |
| } |
| if (ax < pio3_4) |
| { |
| if (x > 0) |
| { |
| z = x - pio2_1; |
| if (!__float_and_test28 (ax, pio2_24b)) |
| { |
| y[0] = z - pio2_1t; |
| y[1] = (z - y[0]) - pio2_1t; |
| } |
| else |
| { |
| z -= pio2_2; |
| y[0] = z - pio2_2t; |
| y[1] = (z - y[0]) - pio2_2t; |
| } |
| return 1; |
| } |
| else |
| { |
| z = x + pio2_1; |
| if (!__float_and_test28 (ax, pio2_24b)) |
| { |
| y[0] = z + pio2_1t; |
| y[1] = (z - y[0]) + pio2_1t; |
| } |
| else |
| { |
| z += pio2_2; |
| y[0] = z + pio2_2t; |
| y[1] = (z - y[0]) + pio2_2t; |
| } |
| return -1; |
| } |
| } |
| if (ax <= pio2_2e7) |
| { |
| n = __floorf (ax * invpio2 + half); |
| i = (int32_t) n; |
| r = ax - n * pio2_1; |
| w = n * pio2_1t; /* 1st round good to 40 bit */ |
| if (i < 32 && !__float_and_test24 (ax, npio2_hw[i - 1])) |
| { |
| y[0] = r - w; |
| } |
| else |
| { |
| float i, j; |
| j = __float_and8 (ax); |
| y[0] = r - w; |
| i = __float_and8 (y[0]); |
| if (j / i > 256.0 || j / i < 3.9062500e-3) |
| { /* 2nd iterations needed, good to 57 */ |
| t = r; |
| w = n * pio2_2; |
| r = t - w; |
| w = n * pio2_2t - ((t - r) - w); |
| y[0] = r - w; |
| i = __float_and8 (y[0]); |
| if (j / i > 33554432 || j / i < 2.9802322e-8) |
| { /* 3rd iteration needed, 74 bits acc */ |
| t = r; |
| w = n * pio2_3; |
| r = t - w; |
| w = n * pio2_3t - ((t - r) - w); |
| y[0] = r - w; |
| } |
| } |
| } |
| y[1] = (r - y[0]) - w; |
| if (x < 0) |
| { |
| y[0] = -y[0]; |
| y[1] = -y[1]; |
| return -i; |
| } |
| else |
| { |
| return i; |
| } |
| } |
| |
| /* all other (large) arguments */ |
| if (isnanf (x) || isinff (x)) |
| { |
| y[0] = y[1] = x - x; |
| return 0; |
| } |
| |
| /* set z = scalbn(|x|,ilogb(x)-7) */ |
| e0 = __float_and8 (ax / 128.0); |
| z = ax / e0; |
| |
| tx[0] = __floorf (z); |
| z = (z - tx[0]) * two8; |
| tx[1] = __floorf (z); |
| z = (z - tx[1]) * two8; |
| tx[2] = __floorf (z); |
| |
| nx = 3; |
| while (tx[nx - 1] == zero) |
| nx--; |
| |
| i = __fp_kernel_rem_pio2f (tx, y, e0, nx); |
| if (x < 0) |
| { |
| y[0] = -y[0]; |
| y[1] = -y[1]; |
| return -i; |
| } |
| return i; |
| } |