/* @(#)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. | |
* ==================================================== | |
*/ | |
#include <LibConfig.h> | |
#include <sys/EfiCdefs.h> | |
#if defined(LIBM_SCCS) && !defined(lint) | |
__RCSID("$NetBSD: e_rem_pio2.c,v 1.11 2002/05/26 22:01:52 wiz 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.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, | |
}; | |
static const int32_t npio2_hw[] = { | |
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) | |
*/ | |
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 */ | |
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 */ | |
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; | |
u_int32_t low; | |
z = 0; | |
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; | |
} |