e_rem_pio2.c
Go to the documentation of this file.
/* @(#)e_rem_pio2.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static const char rcsid[] =
"$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $";
#endif
/* __ieee754_rem_pio2(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
* use __kernel_rem_pio2()
*/
#include "math_libm.h"
#include "math_private.h"
libm_hidden_proto(fabs)
/*
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
*/
#ifdef __STDC__
static const int32_t two_over_pi[] = {
#else
static int32_t two_over_pi[] = {
#endif
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
};
#ifdef __STDC__
static const int32_t npio2_hw[] = {
#else
static int32_t npio2_hw[] = {
#endif
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
0x404858EB, 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)
*/
#ifdef __STDC__
static const double
#else
static double
#endif
zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
#ifdef __STDC__
int32_t attribute_hidden
__ieee754_rem_pio2(double x, double *y)
#else
int32_t attribute_hidden
__ieee754_rem_pio2(x, y)
double x, y[];
#endif
{
double z = 0.0, w, t, r, fn;
double tx[3];
int32_t e0, i, j, nx, n, ix, hx;
u_int32_t low;
GET_HIGH_WORD(hx, x); /* high word of x */
ix = hx & 0x7fffffff;
if (ix <= 0x3fe921fb) { /* |x| ~<= pi/4 , no need for reduction */
y[0] = x;
y[1] = 0;
return 0;
}
if (ix < 0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
if (hx > 0) {
z = x - pio2_1;
if (ix != 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 != 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 <= 0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
t = 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 {
u_int32_t high;
j = ix >> 20;
y[0] = r - w;
GET_HIGH_WORD(high, y[0]);
i = j - ((high >> 20) & 0x7ff);
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 >> 20) & 0x7ff);
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 >= 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);
SET_LOW_WORD(z, low);
e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */
SET_HIGH_WORD(z, ix - ((int32_t) (e0 << 20)));
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, two_over_pi);
if (hx < 0) {
y[0] = -y[0];
y[1] = -y[1];
return -n;
}
return n;
}
__ieee754_rem_pio2
int32_t attribute_hidden __ieee754_rem_pio2(double x, y)
Definition: e_rem_pio2.c:94
GET_HIGH_WORD
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:103
r
GLdouble GLdouble GLdouble r
Definition: SDL_opengl.h:2072
n
GLdouble n
Definition: SDL_opengl_glext.h:1952
invpio2
static double invpio2
Definition: e_rem_pio2.c:81
int32_t
signed int int32_t
Definition: SDL_config_windows.h:61
x
GLint GLint GLint GLint GLint x
Definition: SDL_opengl.h:1567
__kernel_rem_pio2
int attribute_hidden __kernel_rem_pio2(x, y, int e0, int nx, int prec, ipio2)
Definition: k_rem_pio2.c:176
half
static double half
Definition: e_rem_pio2.c:79
two24
static double two24
Definition: e_rem_pio2.c:80
pio2_1t
static double pio2_1t
Definition: e_rem_pio2.c:83
attribute_hidden
#define attribute_hidden
Definition: math_private.h:24
SET_HIGH_WORD
#define SET_HIGH_WORD(d, v)
Definition: math_private.h:131
pio2_2
static double pio2_2
Definition: e_rem_pio2.c:84
pio2_3t
static double pio2_3t
Definition: e_rem_pio2.c:87
u_int32_t
unsigned int u_int32_t
Definition: math_private.h:29
y
GLint GLint GLint GLint GLint GLint y
Definition: SDL_opengl.h:1567
pio2_1
static double pio2_1
Definition: e_rem_pio2.c:82
SET_LOW_WORD
#define SET_LOW_WORD(d, v)
Definition: math_private.h:141
math_libm.h
nx
GLbyte nx
Definition: SDL_opengl_glext.h:5713
pio2_3
static double pio2_3
Definition: e_rem_pio2.c:86
fabs
#define fabs
Definition: math_private.h:36
i
return Display return Display Bool Bool int int int return Display XEvent Bool(*) XPointer return Display return Display Drawable _Xconst char unsigned int unsigned int return Display Pixmap Pixmap XColor XColor unsigned int unsigned int return Display _Xconst char char int char return Display Visual unsigned int int int char unsigned int unsigned int in i)
Definition: SDL_x11sym.h:42
pio2_2t
static double pio2_2t
Definition: e_rem_pio2.c:85
z
GLdouble GLdouble z
Definition: SDL_opengl_glext.h:404
GET_LOW_WORD
#define GET_LOW_WORD(i, d)
Definition: math_private.h:112
npio2_hw
static int32_t npio2_hw[]
Definition: e_rem_pio2.c:53
libm_hidden_proto
libm_hidden_proto(fabs)
Definition: e_rem_pio2.c:27
w
GLubyte GLubyte GLubyte GLubyte w
Definition: SDL_opengl_glext.h:731
zero
static double zero
Definition: e_rem_pio2.c:78
math_private.h
t
GLdouble GLdouble t
Definition: SDL_opengl.h:2064
j
return Display return Display Bool Bool int int int return Display XEvent Bool(*) XPointer return Display return Display Drawable _Xconst char unsigned int unsigned int return Display Pixmap Pixmap XColor XColor unsigned int unsigned int return Display _Xconst char char int char return Display Visual unsigned int int int char unsigned int unsigned int int in j)
Definition: SDL_x11sym.h:42