/* k_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"
static const float two_over_pi[] = {
1.62000000e+02, 2.49000000e+02, 1.31000000e+02, 1.10000000e+02,
7.80000000e+01, 6.80000000e+01, 2.10000000e+01, 4.10000000e+01,
2.52000000e+02, 3.90000000e+01, 8.70000000e+01, 2.09000000e+02,
2.45000000e+02, 5.20000000e+01, 2.21000000e+02, 1.92000000e+02,
2.19000000e+02, 9.80000000e+01, 1.49000000e+02, 1.53000000e+02,
6.00000000e+01, 6.70000000e+01, 1.44000000e+02, 6.50000000e+01,
2.54000000e+02, 8.10000000e+01, 9.90000000e+01, 1.71000000e+02,
2.22000000e+02, 1.87000000e+02, 1.97000000e+02, 9.70000000e+01,
1.83000000e+02, 3.60000000e+01, 1.10000000e+02, 5.80000000e+01,
6.60000000e+01, 7.70000000e+01, 2.10000000e+02, 2.24000000e+02,
6.00000000e+00, 7.30000000e+01, 4.60000000e+01, 2.34000000e+02,
9.00000000e+00, 2.09000000e+02, 1.46000000e+02, 2.80000000e+01,
2.54000000e+02, 2.90000000e+01, 2.35000000e+02, 2.80000000e+01,
1.77000000e+02, 4.10000000e+01, 1.67000000e+02, 6.20000000e+01,
2.32000000e+02, 1.30000000e+02, 5.30000000e+01, 2.45000000e+02,
4.60000000e+01, 1.87000000e+02, 6.80000000e+01, 1.32000000e+02,
2.33000000e+02, 1.56000000e+02, 1.12000000e+02, 3.80000000e+01,
1.80000000e+02, 9.50000000e+01, 1.26000000e+02, 6.50000000e+01,
5.70000000e+01, 1.45000000e+02, 2.14000000e+02, 5.70000000e+01,
1.31000000e+02, 8.30000000e+01, 5.70000000e+01, 2.44000000e+02,
1.56000000e+02, 1.32000000e+02, 9.50000000e+01, 1.39000000e+02,
1.89000000e+02, 2.49000000e+02, 4.00000000e+01, 5.90000000e+01,
3.10000000e+01, 2.48000000e+02, 1.51000000e+02, 2.55000000e+02,
2.22000000e+02, 5.00000000e+00, 1.52000000e+02, 1.50000000e+01,
2.39000000e+02, 4.70000000e+01, 1.70000000e+01, 1.39000000e+02,
9.00000000e+01, 1.00000000e+01, 1.09000000e+02, 3.10000000e+01,
1.09000000e+02, 5.40000000e+01, 1.26000000e+02, 2.07000000e+02,
3.90000000e+01, 2.03000000e+02, 9.00000000e+00, 1.83000000e+02,
7.90000000e+01, 7.00000000e+01, 6.30000000e+01, 1.02000000e+02,
1.58000000e+02, 9.50000000e+01, 2.34000000e+02, 4.50000000e+01,
1.17000000e+02, 3.90000000e+01, 1.86000000e+02, 1.99000000e+02,
2.35000000e+02, 2.29000000e+02, 2.41000000e+02, 1.23000000e+02,
6.10000000e+01, 7.00000000e+00, 5.70000000e+01, 2.47000000e+02,
1.38000000e+02, 8.20000000e+01, 1.46000000e+02, 2.34000000e+02,
1.07000000e+02, 2.51000000e+02, 9.50000000e+01, 1.77000000e+02,
3.10000000e+01, 1.41000000e+02, 9.30000000e+01, 8.00000000e+00,
8.60000000e+01, 3.00000000e+00, 4.80000000e+01, 7.00000000e+01,
2.52000000e+02, 1.23000000e+02, 1.07000000e+02, 1.71000000e+02,
2.40000000e+02, 2.07000000e+02, 1.88000000e+02, 3.20000000e+01,
1.54000000e+02, 2.44000000e+02, 5.40000000e+01, 2.90000000e+01,
1.69000000e+02, 2.27000000e+02, 1.45000000e+02, 9.70000000e+01,
9.40000000e+01, 2.30000000e+02, 2.70000000e+01, 8.00000000e+00,
1.01000000e+02, 1.53000000e+02, 1.33000000e+02, 9.50000000e+01,
2.00000000e+01, 1.60000000e+02, 1.04000000e+02, 6.40000000e+01,
1.41000000e+02, 2.55000000e+02, 2.16000000e+02, 1.28000000e+02,
7.70000000e+01, 1.15000000e+02, 3.90000000e+01, 4.90000000e+01,
6.00000000e+00, 6.00000000e+00, 2.10000000e+01, 8.60000000e+01,
2.02000000e+02, 1.15000000e+02, 1.68000000e+02, 2.01000000e+02,
9.60000000e+01, 2.26000000e+02, 1.23000000e+02, 1.92000000e+02,
1.40000000e+02, 1.07000000e+02
};
static const float PIo2[] = {
1.5703125000e+00, /* 0x3fc90000 */
4.5776367188e-04, /* 0x39f00000 */
2.5987625122e-05, /* 0x37da0000 */
7.5437128544e-08, /* 0x33a20000 */
6.0026650317e-11, /* 0x2e840000 */
7.3896444519e-13, /* 0x2b500000 */
5.3845816694e-15, /* 0x27c20000 */
5.6378512969e-18, /* 0x22d00000 */
8.3009228831e-20, /* 0x1fc40000 */
3.2756352257e-22, /* 0x1bc60000 */
6.3331015649e-25, /* 0x17440000 */
};
static const float zero = 0.0000000000e+00;
static const float one = 1.0000000000;
static const float twon8 = 3.9062500000e-03;
static const float two8 = 2.5600000000e+02;
int32_t
__fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx)
{
int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih, exp;
float z, fw, f[20], fq[20], q[20];
/* initialize jk */
jp = jk = 9;
/* determine jx,jv,q0, note that 3>q0 */
jx = nx - 1;
exp = __float_get_exp (e0) - 127;
jv = (exp - 3) / 8;
if (jv < 0)
jv = 0;
q0 = exp - 8 * (jv + 1);
/* set up f[0] to f[jx+jk] where f[jx+jk] = two_over_pi[jv+jk] */
j = jv - jx;
m = jx + jk;
for (i = 0; i <= m; i++, j++)
f[i] = (j < 0) ? zero : two_over_pi[j];
/* compute q[0],q[1],...q[jk] */
for (i = 0; i <= jk; i++)
{
for (j = 0, fw = 0.0; j <= jx; j++)
fw += x[j] * f[jx + i - j];
q[i] = fw;
}
jz = jk;
recompute:
/* distill q[] into iq[] reversingly */
for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--)
{
fw = __truncf (twon8 * z);
iq[i] = (int32_t) (z - two8 * fw);
z = q[j - 1] + fw;
}
/* compute n */
z = __scalbnf (z, q0); /* actual value of z */
z -= 8.0 * __floorf (z * 0.125); /* trim off integer >= 8 */
n = (int32_t) z;
z -= __truncf (z);
ih = 0;
if (q0 > 0)
{ /* need iq[jz-1] to determine n */
i = (iq[jz - 1] >> (8 - q0));
n += i;
iq[jz - 1] -= i << (8 - q0);
ih = iq[jz - 1] >> (7 - q0);
}
else if (q0 == 0)
ih = iq[jz - 1] >> 7;
else if (z >= 0.5)
ih = 2;
if (ih > 0)
{ /* q > 0.5 */
n += 1;
carry = 0;
for (i = 0; i < jz; i++)
{ /* compute 1-q */
j = iq[i];
if (carry == 0)
{
if (j != 0)
{
carry = 1;
iq[i] = 0x100 - j;
}
}
else
iq[i] = 0xff - j;
}
if (q0 > 0)
{ /* rare case: chance is 1 in 12 */
switch (q0)
{
case 1:
iq[jz - 1] &= 0x7f;
break;
case 2:
iq[jz - 1] &= 0x3f;
break;
}
}
if (ih == 2)
{
z = one - z;
if (carry != 0)
z -= __scalbnf (one, q0);
}
}
/* check if recomputation is needed */
if (z == zero)
{
j = 0;
for (i = jz - 1; i >= jk; i--)
j |= iq[i];
if (j == 0)
{ /* need recomputation */
for (k = 1; iq[jk - k] == 0; k++); /* k = no. of terms needed */
for (i = jz + 1; i <= jz + k; i++)
{ /* add q[jz+1] to q[jz+k] */
f[jx + i] = two_over_pi[jv + i];
for (j = 0, fw = 0.0; j <= jx; j++)
fw += x[j] * f[jx + i - j];
q[i] = fw;
}
jz += k;
goto recompute;
}
}
/* chop off zero terms */
if (z == 0.0)
{
jz -= 1;
q0 -= 8;
while (iq[jz] == 0)
{
jz--;
q0 -= 8;
}
}
else
{ /* break z into 8-bit if necessary */
z = __scalbnf (z, -q0);
if (z >= two8)
{
fw = __truncf (twon8 * z);
iq[jz] = (int32_t) (z - two8 * fw);
jz += 1;
q0 += 8;
iq[jz] = (int32_t) fw;
}
else
iq[jz] = (int32_t) z;
}
/* convert integer "bit" chunk to floating-point value */
fw = __scalbnf (one, q0);
for (i = jz; i >= 0; i--)
{
q[i] = fw * (float) iq[i];
fw *= twon8;
}
/* compute PIo2[0,...,jp]*q[jz,...,0] */
for (i = jz; i >= 0; i--)
{
for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++)
fw += PIo2[k] * q[i + k];
fq[jz - i] = fw;
}
/* compress fq[] into y[] */
fw = 0.0;
for (i = jz; i >= 0; i--)
fw += fq[i];
y[0] = (ih == 0) ? fw : -fw;
fw = fq[0] - fw;
for (i = 1; i <= jz; i++)
fw += fq[i];
y[1] = (ih == 0) ? fw : -fw;
return n & 7;
}