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/* e_rem_pio2f.c -- float version of e_rem_pio2.c
Copyright (C) 2011-2017 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;
}
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