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e_rem_pio2.c
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e_rem_pio2.c
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/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_rem_pio2(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
* use __kernel_rem_pio2()
*/
#ifndef __FDLIBM_H__
#include "fdlibm.h"
#endif
int32_t __ieee754_rem_pio2(double x, double *y)
{
double z, w, t, r, fn;
double tx[3];
int32_t e0, i, j, nx, n, ix, hx;
uint32_t low;
static const int32_t npio2_hw[] = {
IC(0x3FF921FB), IC(0x400921FB), IC(0x4012D97C), IC(0x401921FB), IC(0x401F6A7A), IC(0x4022D97C),
IC(0x4025FDBB), IC(0x402921FB), IC(0x402C463A), IC(0x402F6A7A), IC(0x4031475C), IC(0x4032D97C),
IC(0x40346B9C), IC(0x4035FDBB), IC(0x40378FDB), IC(0x403921FB), IC(0x403AB41B), IC(0x403C463A),
IC(0x403DD85A), IC(0x403F6A7A), IC(0x40407E4C), IC(0x4041475C), IC(0x4042106C), IC(0x4042D97C),
IC(0x4043A28C), IC(0x40446B9C), IC(0x404534AC), IC(0x4045FDBB), IC(0x4046C6CB), IC(0x40478FDB),
IC(0x404858EB), IC(0x404921FB)
};
/*
* invpio2: 53 bits of 2/pi
* pio2_1: first 33 bit of pi/2
* pio2_1t: pi/2 - pio2_1
* pio2_2: second 33 bit of pi/2
* pio2_2t: pi/2 - (pio2_1+pio2_2)
* pio2_3: third 33 bit of pi/2
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
*/
static const double zero = 0.00000000000000000000e+00; /* 0x00000000, 0x00000000 */
static const double half = 5.00000000000000000000e-01; /* 0x3FE00000, 0x00000000 */
static const double two24 = 1.67772160000000000000e+07; /* 0x41700000, 0x00000000 */
static const double invpio2 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */
static const double pio2_1 = 1.57079632673412561417e+00; /* 0x3FF921FB, 0x54400000 */
static const double pio2_1t = 6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */
static const double pio2_2 = 6.07710050630396597660e-11; /* 0x3DD0B461, 0x1A600000 */
static const double pio2_2t = 2.02226624879595063154e-21; /* 0x3BA3198A, 0x2E037073 */
static const double pio2_3 = 2.02226624871116645580e-21; /* 0x3BA3198A, 0x2E000000 */
static const double pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
GET_HIGH_WORD(hx, x); /* high word of x */
ix = hx & IC(0x7fffffff);
if (ix <= IC(0x3fe921fb)) /* |x| ~<= pi/4 , no need for reduction */
{
y[0] = x;
y[1] = 0;
return 0;
}
if (ix < IC(0x4002d97c))
{ /* |x| < 3pi/4, special case with n=+-1 */
if (hx > 0)
{
z = x - pio2_1;
if (ix != IC(0x3ff921fb))
{ /* 33+53 bit pi is good enough */
y[0] = z - pio2_1t;
y[1] = (z - y[0]) - pio2_1t;
} else
{ /* near pi/2, use 33+33+53 bit pi */
z -= pio2_2;
y[0] = z - pio2_2t;
y[1] = (z - y[0]) - pio2_2t;
}
return 1;
} else
{ /* negative x */
z = x + pio2_1;
if (ix != IC(0x3ff921fb))
{ /* 33+53 bit pi is good enough */
y[0] = z + pio2_1t;
y[1] = (z - y[0]) + pio2_1t;
} else
{ /* near pi/2, use 33+33+53 bit pi */
z += pio2_2;
y[0] = z + pio2_2t;
y[1] = (z - y[0]) + pio2_2t;
}
return -1;
}
}
if (ix <= IC(0x413921fb))
{ /* |x| ~<= 2^19*(pi/2), medium size */
t = __ieee754_fabs(x);
n = (int32_t) (t * invpio2 + half);
fn = (double) n;
r = t - fn * pio2_1;
w = fn * pio2_1t; /* 1st round good to 85 bit */
if (n < 32 && ix != npio2_hw[n - 1])
{
y[0] = r - w; /* quick check no cancellation */
} else
{
uint32_t high;
j = ix >> IEEE754_DOUBLE_SHIFT;
y[0] = r - w;
GET_HIGH_WORD(high, y[0]);
i = j - ((high >> IEEE754_DOUBLE_SHIFT) & IEEE754_DOUBLE_MAXEXP);
if (i > 16)
{ /* 2nd iteration needed, good to 118 */
t = r;
w = fn * pio2_2;
r = t - w;
w = fn * pio2_2t - ((t - r) - w);
y[0] = r - w;
GET_HIGH_WORD(high, y[0]);
i = j - ((high >> IEEE754_DOUBLE_SHIFT) & IEEE754_DOUBLE_MAXEXP);
if (i > 49)
{ /* 3rd iteration need, 151 bits acc */
t = r; /* will cover all possible cases */
w = fn * pio2_3;
r = t - w;
w = fn * pio2_3t - ((t - r) - w);
y[0] = r - w;
}
}
}
y[1] = (r - y[0]) - w;
if (hx < 0)
{
y[0] = -y[0];
y[1] = -y[1];
return -n;
} else
return n;
}
/*
* all other (large) arguments
*/
if (ix >= IC(0x7ff00000))
{ /* x is inf or NaN */
y[0] = y[1] = x - x;
return 0;
}
/* set z = scalbn(|x|,ilogb(x)-23) */
GET_LOW_WORD(low, x);
e0 = (ix >> IEEE754_DOUBLE_SHIFT) - (IEEE754_DOUBLE_BIAS + 23); /* e0 = ilogb(z)-23; */
INSERT_WORDS(z, ix - (e0 << IEEE754_DOUBLE_SHIFT), low);
for (i = 0; i < 2; i++)
{
tx[i] = (double) ((int32_t) (z));
z = (z - tx[i]) * two24;
}
tx[2] = z;
nx = 3;
while (tx[nx - 1] == zero)
nx--; /* skip zero term */
n = __kernel_rem_pio2(tx, y, e0, nx, 2);
if (hx < 0)
{
y[0] = -y[0];
y[1] = -y[1];
return -n;
}
return n;
}