2011-09-08 04:10:26 +02:00
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/* e_rem_pio2f.c -- float version of e_rem_pio2.c
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2016-01-04 17:05:18 +01:00
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Copyright (C) 2011-2016 Free Software Foundation, Inc.
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2011-09-08 04:10:26 +02:00
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This file is part of the GNU C Library.
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Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Library General Public License as
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published by the Free Software Foundation; either version 2 of the
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License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Library General Public License for more details.
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You should have received a copy of the GNU Library General Public
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2012-02-10 00:18:22 +01:00
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License along with the GNU C Library; see the file COPYING.LIB. If
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not, see <http://www.gnu.org/licenses/>. */
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2011-09-08 04:10:26 +02:00
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#include <math.h>
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2012-03-09 20:29:16 +01:00
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#include <math_private.h>
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2011-09-08 04:10:26 +02:00
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#include "s_float_bitwise.h"
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/* defined in sysdeps/powerpc/fpu/k_rem_pio2f.c */
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int __fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx);
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/* __ieee754_rem_pio2f(x,y)
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*
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* return the remainder of x rem pi/2 in y[0]+y[1]
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*/
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static const float npio2_hw[] = {
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1.57077026e+00, 3.14154053e+00, 4.71228027e+00, 6.28308105e+00,
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7.85388184e+00, 9.42456055e+00, 1.09953613e+01, 1.25661621e+01,
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1.41369629e+01, 1.57077637e+01, 1.72783203e+01, 1.88491211e+01,
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2.04199219e+01, 2.19907227e+01, 2.35615234e+01, 2.51323242e+01,
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2.67031250e+01, 2.82739258e+01, 2.98447266e+01, 3.14155273e+01,
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3.29863281e+01, 3.45566406e+01, 3.61279297e+01, 3.76982422e+01,
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3.92695312e+01, 4.08398438e+01, 4.24111328e+01, 4.39814453e+01,
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4.55527344e+01, 4.71230469e+01, 4.86943359e+01, 5.02646484e+01
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};
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static const float zero = 0.0000000000e+00;
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static const float two8 = 2.5600000000e+02;
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static const float half = 5.0000000000e-01;
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static const float invpio2 = 6.3661980629e-01;
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static const float pio2_1 = 1.5707855225e+00;
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static const float pio2_1t = 1.0804334124e-05;
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static const float pio2_2 = 1.0804273188e-05;
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static const float pio2_2t = 6.0770999344e-11;
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static const float pio2_3 = 6.0770943833e-11;
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static const float pio2_3t = 6.1232342629e-17;
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static const float pio4 = 7.8539801e-01;
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static const float pio3_4 = 2.3561945e+00;
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static const float pio2_24b = 1.5707951e+00;
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static const float pio2_2e7 = 2.0106054e+02;
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int32_t
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__ieee754_rem_pio2f (float x, float *y)
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{
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float ax, z, n, r, w, t, e0;
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float tx[3];
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int32_t i, nx;
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ax = __builtin_fabsf (x);
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if (ax <= pio4)
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{
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y[0] = x;
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y[1] = 0;
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return 0;
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}
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if (ax < pio3_4)
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{
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if (x > 0)
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{
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z = x - pio2_1;
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if (!__float_and_test28 (ax, pio2_24b))
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{
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y[0] = z - pio2_1t;
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y[1] = (z - y[0]) - pio2_1t;
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}
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else
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{
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z -= pio2_2;
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y[0] = z - pio2_2t;
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y[1] = (z - y[0]) - pio2_2t;
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}
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return 1;
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}
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else
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{
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z = x + pio2_1;
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if (!__float_and_test28 (ax, pio2_24b))
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{
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y[0] = z + pio2_1t;
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y[1] = (z - y[0]) + pio2_1t;
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}
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else
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{
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z += pio2_2;
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y[0] = z + pio2_2t;
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y[1] = (z - y[0]) + pio2_2t;
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}
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return -1;
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}
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}
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if (ax <= pio2_2e7)
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{
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2011-09-15 11:16:03 +02:00
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n = __floorf (ax * invpio2 + half);
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2011-09-08 04:10:26 +02:00
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i = (int32_t) n;
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r = ax - n * pio2_1;
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w = n * pio2_1t; /* 1st round good to 40 bit */
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if (i < 32 && !__float_and_test24 (ax, npio2_hw[i - 1]))
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{
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y[0] = r - w;
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}
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else
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{
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float i, j;
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j = __float_and8 (ax);
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y[0] = r - w;
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i = __float_and8 (y[0]);
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if (j / i > 256.0 || j / i < 3.9062500e-3)
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{ /* 2nd iterations needed, good to 57 */
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t = r;
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w = n * pio2_2;
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r = t - w;
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w = n * pio2_2t - ((t - r) - w);
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y[0] = r - w;
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i = __float_and8 (y[0]);
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if (j / i > 33554432 || j / i < 2.9802322e-8)
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{ /* 3rd iteration needed, 74 bits acc */
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t = r;
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w = n * pio2_3;
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r = t - w;
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w = n * pio2_3t - ((t - r) - w);
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y[0] = r - w;
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}
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}
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}
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y[1] = (r - y[0]) - w;
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if (x < 0)
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{
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y[0] = -y[0];
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y[1] = -y[1];
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return -i;
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}
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else
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{
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return i;
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}
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}
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/* all other (large) arguments */
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if (isnanf (x) || isinff (x))
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{
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y[0] = y[1] = x - x;
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return 0;
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}
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/* set z = scalbn(|x|,ilogb(x)-7) */
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e0 = __float_and8 (ax / 128.0);
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z = ax / e0;
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2011-09-15 11:16:03 +02:00
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tx[0] = __floorf (z);
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2011-09-08 04:10:26 +02:00
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z = (z - tx[0]) * two8;
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2011-09-15 11:16:03 +02:00
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tx[1] = __floorf (z);
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2011-09-08 04:10:26 +02:00
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z = (z - tx[1]) * two8;
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2011-09-15 11:16:03 +02:00
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tx[2] = __floorf (z);
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2011-09-08 04:10:26 +02:00
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nx = 3;
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while (tx[nx - 1] == zero)
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nx--;
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i = __fp_kernel_rem_pio2f (tx, y, e0, nx);
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if (x < 0)
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{
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y[0] = -y[0];
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y[1] = -y[1];
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return -i;
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}
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return i;
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}
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