/* origin: FreeBSD /usr/src/lib/msun/ld80/e_rem_pio2.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
* Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
*
* 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.
* ====================================================
*
* Optimized by Bruce D. Evans.
*/
#include "libm.h"
#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
/* ld80 version of __rem_pio2(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
* use __rem_pio2_large() for large x
*/
#define BIAS (LDBL_MAX_EXP - 1)
/*
* invpio2: 64 bits of 2/pi
* pio2_1: first 39 bits of pi/2
* pio2_1t: pi/2 - pio2_1
* pio2_2: second 39 bits of pi/2
* pio2_2t: pi/2 - (pio2_1+pio2_2)
* pio2_3: third 39 bits of pi/2
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
*/
static const double
zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
pio2_1 = 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */
pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */
pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */
// FIXME: this should be verified (maybe old gcc specific hack)
//#if defined(__amd64__) || defined(__i386__)
/* Long double constants are slow on these arches, and broken on i386. */
static const volatile double
invpio2hi = 6.3661977236758138e-01, /* 0x145f306dc9c883.0p-53 */
invpio2lo = -3.9356538861223811e-17, /* -0x16b00000000000.0p-107 */
pio2_1thi = -1.0746346554971943e-12, /* -0x12e7b9676733af.0p-92 */
pio2_1tlo = 8.8451028997905949e-29, /* 0x1c080000000000.0p-146 */
pio2_2thi = 6.3683171635109499e-25, /* 0x18a2e03707344a.0p-133 */
pio2_2tlo = 2.3183081793789774e-41, /* 0x10280000000000.0p-187 */
pio2_3thi = -2.7529965190440717e-37, /* -0x176b7ed8fbbacc.0p-174 */
pio2_3tlo = -4.2006647512740502e-54; /* -0x19c00000000000.0p-230 */
#define invpio2 ((long double)invpio2hi + invpio2lo)
#define pio2_1t ((long double)pio2_1thi + pio2_1tlo)
#define pio2_2t ((long double)pio2_2thi + pio2_2tlo)
#define pio2_3t ((long double)pio2_3thi + pio2_3tlo)
//#else
#if 0
static const long double
invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */
pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */
pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
#endif
static inline int __rem_pio2l(long double x, long double *y)
{
union IEEEl2bits u,u1;
long double z,w,t,r,fn;
double tx[3],ty[2];
int e0,ex,i,j,nx,n;
int16_t expsign;
u.e = x;
expsign = u.xbits.expsign;
ex = expsign & 0x7fff;
if (ex < BIAS + 25 || (ex == BIAS + 25 && u.bits.manh < 0xc90fdaa2)) {
union IEEEl2bits u2;
int ex1;
/* |x| ~< 2^25*(pi/2), medium size */
/* Use a specialized rint() to get fn. Assume round-to-nearest. */
fn = x*invpio2 + 0x1.8p63;
fn = fn - 0x1.8p63;
// FIXME
//#ifdef HAVE_EFFICIENT_IRINT
// n = irint(fn);
//#else
n = fn;
//#endif
r = x-fn*pio2_1;
w = fn*pio2_1t; /* 1st round good to 102 bit */
j = ex;
y[0] = r-w;
u2.e = y[0];
ex1 = u2.xbits.expsign & 0x7fff;
i = j-ex1;
if (i > 22) { /* 2nd iteration needed, good to 141 */
t = r;
w = fn*pio2_2;
r = t-w;
w = fn*pio2_2t-((t-r)-w);
y[0] = r-w;
u2.e = y[0];
ex1 = u2.xbits.expsign & 0x7fff;
i = j-ex1;
if (i > 61) { /* 3rd iteration need, 180 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;
return n;
}
/*
* all other (large) arguments
*/
if (ex == 0x7fff) { /* x is inf or NaN */
y[0] = y[1] = x - x;
return 0;
}
/* set z = scalbn(|x|,ilogb(x)-23) */
u1.e = x;
e0 = ex - BIAS - 23; /* e0 = ilogb(|x|)-23; */
u1.xbits.expsign = ex - e0;
z = u1.e;
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 = __rem_pio2_large(tx,ty,e0,nx,2);
r = (long double)ty[0] + ty[1];
w = ty[1] - (r - ty[0]);
if (expsign < 0) {
y[0] = -r;
y[1] = -w;
return -n;
}
y[0] = r;
y[1] = w;
return n;
}
#endif
