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/* e_rem_pio2f.c -- float version of e_rem_pio2.c
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
* Debugged and optimized by Bruce D. Evans.
*/
/*
* ====================================================
* 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.
* ====================================================
*/
#ifndef lint
static char rcsid[] = "$FreeBSD$";
#endif
/* __ieee754_rem_pio2f(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
* use double precision internally
* use __kernel_rem_pio2() for large x
*/
#include "math.h"
#include "math_private.h"
/*
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
*/
static const int32_t two_over_pi[] = {
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,
};
/*
* invpio2: 53 bits of 2/pi
* e1pio2: 1*pi/2 rounded to 53 bits
* e2pio2: 2*pi/2 rounded to 53 bits
* e3pio2: 3*pi/2 rounded to 53 bits
* e4pio2: 4*pi/2 rounded to 53 bits
* pio2_1: first 33 bit of pi/2
* pio2_1t: pi/2 - pio2_1
*/
static const double
zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
e1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */
e2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */
e3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */
e4pio2 = 4*M_PI_2, /* 0x401921FB, 0x54442D18 */
pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
pio2_1t = 6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */
int32_t __ieee754_rem_pio2f(float x, float *y)
{
double z,w,t,r,fn;
double tx[3];
int32_t e0,i,nx,n,ix,hx;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix<=0x3f490fda) /* |x| ~<= pi/4, reduction is null */
{y[0] = x; y[1] = 0; return 0;}
/* 53 bit pi is good enough for special cases */
if(ix<=0x407b53d1) { /* |x| ~<= 5*pi/4 */
if(ix<=0x4016cbe3) { /* |x| ~<= 3*pi/4 */
if(hx>0) {
z = x - e1pio2;
n = 1;
} else {
z = x + e1pio2;
n = 3;
}
y[0] = z;
y[1] = z - y[0];
return n;
} else {
if(hx>0)
z = x - e2pio2;
else
z = x + e2pio2;
y[0] = z;
y[1] = z - y[0];
return 2;
}
}
if(ix<=0x40e231d5) { /* |x| ~<= 9*pi/4*/
if(ix<=0x40afeddf) { /* |x| ~<= 7*pi/4 */
if(hx>0) {
z = x - e3pio2;
n = 3;
} else {
z = x + e3pio2;
n = 1;
}
y[0] = z;
y[1] = z - y[0];
return n;
} else {
if(hx>0)
z = x - e4pio2;
else
z = x + e4pio2;
y[0] = z;
y[1] = z - y[0];
return 0;
}
}
/* 33+53 bit pi is good enough for medium size */
if(ix<=0x49490f80) { /* |x| ~<= 2^19*(pi/2), medium size */
t = fabsf(x);
n = (int32_t) (t*invpio2+half);
fn = (double)n;
r = t-fn*pio2_1;
w = fn*pio2_1t;
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>=0x7f800000) { /* x is inf or NaN */
y[0]=y[1]=x-x; return 0;
}
/* set z = scalbn(|x|,ilogb(x)-23) */
z = x;
GET_HIGH_WORD(hx,z);
ix = hx&0x7fffffff;
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,&z,e0,nx,1,two_over_pi);
y[0] = z;
y[1] = z - y[0];
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
return n;
}
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