/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c */
/*
* ====================================================
* 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.
* ====================================================
*
* Optimized by Bruce D. Evans.
*/
/* __rem_pio2(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
* use __rem_pio2_large() for large x
*/
#include "libm.h"
/*
* 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
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 */
/* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
int __rem_pio2(double x, double *y)
{
double z,w,t,r,fn;
double tx[3],ty[2];
int32_t e0,i,j,nx,n,ix,hx;
uint32_t low;
GET_HIGH_WORD(hx,x);
ix = hx & 0x7fffffff;
if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */
if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */
goto medium; /* cancellation -- use medium case */
if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */
if (hx > 0) {
z = x - pio2_1; /* one round good to 85 bits */
y[0] = z - pio2_1t;
y[1] = (z-y[0]) - pio2_1t;
return 1;
} else {
z = x + pio2_1;
y[0] = z + pio2_1t;
y[1] = (z-y[0]) + pio2_1t;
return -1;
}
} else {
if (hx > 0) {
z = x - 2*pio2_1;
y[0] = z - 2*pio2_1t;
y[1] = (z-y[0]) - 2*pio2_1t;
return 2;
} else {
z = x + 2*pio2_1;
y[0] = z + 2*pio2_1t;
y[1] = (z-y[0]) + 2*pio2_1t;
return -2;
}
}
}
if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */
if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */
if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */
goto medium;
if (hx > 0) {
z = x - 3*pio2_1;
y[0] = z - 3*pio2_1t;
y[1] = (z-y[0]) - 3*pio2_1t;
return 3;
} else {
z = x + 3*pio2_1;
y[0] = z + 3*pio2_1t;
y[1] = (z-y[0]) + 3*pio2_1t;
return -3;
}
} else {
if (ix == 0x401921fb) /* |x| ~= 4pi/2 */
goto medium;
if (hx > 0) {
z = x - 4*pio2_1;
y[0] = z - 4*pio2_1t;
y[1] = (z-y[0]) - 4*pio2_1t;
return 4;
} else {
z = x + 4*pio2_1;
y[0] = z + 4*pio2_1t;
y[1] = (z-y[0]) + 4*pio2_1t;
return -4;
}
}
}
if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */
uint32_t high;
medium:
/* Use a specialized rint() to get fn. Assume round-to-nearest. */
fn = x*invpio2 + 0x1.8p52;
fn = fn - 0x1.8p52;
// FIXME
#ifdef HAVE_EFFICIENT_IRINT
n = irint(fn);
#else
n = (int32_t)fn;
#endif
r = x - fn*pio2_1;
w = fn*pio2_1t; /* 1st round, good to 85 bits */
j = ix>>20;
y[0] = r - w;
GET_HIGH_WORD(high,y[0]);
i = j - ((high>>20)&0x7ff);
if (i > 16) { /* 2nd round, good to 118 bits */
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 round, good to 151 bits, covers all cases */
t = r;
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 (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);
e0 = (ix>>20) - 1046; /* e0 = ilogb(z)-23; */
INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), 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] == 0.0) nx--; /* skip zero term */
n = __rem_pio2_large(tx,ty,e0,nx,1);
if (hx < 0) {
y[0] = -ty[0];
y[1] = -ty[1];
return -n;
}
y[0] = ty[0];
y[1] = ty[1];
return n;
}
