#include "libm.h"
+#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
+#define EPS DBL_EPSILON
+#elif FLT_EVAL_METHOD==2
+#define EPS LDBL_EPSILON
+#endif
+
/*
* invpio2: 53 bits of 2/pi
* pio2_1: first 33 bit of pi/2
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
*/
static const double
-two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
+toint = 1.5/EPS,
+pio4 = 0x1.921fb54442d18p-1,
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
/* 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;
+ union {double f; uint64_t i;} u = {x};
+ double_t z,w,t,r,fn;
double tx[3],ty[2];
- int32_t e0,i,j,nx,n,ix,hx;
- uint32_t low;
+ uint32_t ix;
+ int sign, n, ex, ey, i;
- GET_HIGH_WORD(hx,x);
- ix = hx & 0x7fffffff;
+ sign = u.i>>63;
+ ix = u.i>>32 & 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) {
+ if (!sign) {
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 {
- if (hx > 0) {
+ if (!sign) {
z = x - 2*pio2_1;
y[0] = z - 2*pio2_1t;
y[1] = (z-y[0]) - 2*pio2_1t;
if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */
if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */
goto medium;
- if (hx > 0) {
+ if (!sign) {
z = x - 3*pio2_1;
y[0] = z - 3*pio2_1t;
y[1] = (z-y[0]) - 3*pio2_1t;
} else {
if (ix == 0x401921fb) /* |x| ~= 4pi/2 */
goto medium;
- if (hx > 0) {
+ if (!sign) {
z = x - 4*pio2_1;
y[0] = z - 4*pio2_1t;
y[1] = (z-y[0]) - 4*pio2_1t;
}
}
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
+ /* rint(x/(pi/2)) */
+ fn = (double_t)x*invpio2 + toint - toint;
n = (int32_t)fn;
-#endif
r = x - fn*pio2_1;
w = fn*pio2_1t; /* 1st round, good to 85 bits */
- j = ix>>20;
+ /* Matters with directed rounding. */
+ if (predict_false(r - w < -pio4)) {
+ n--;
+ fn--;
+ r = x - fn*pio2_1;
+ w = fn*pio2_1t;
+ } else if (predict_false(r - w > pio4)) {
+ n++;
+ fn++;
+ r = x - fn*pio2_1;
+ w = fn*pio2_1t;
+ }
y[0] = r - w;
- GET_HIGH_WORD(high,y[0]);
- i = j - ((high>>20)&0x7ff);
- if (i > 16) { /* 2nd round, good to 118 bits */
+ u.f = y[0];
+ ey = u.i>>52 & 0x7ff;
+ ex = ix>>20;
+ if (ex - ey > 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 */
+ u.f = y[0];
+ ey = u.i>>52 & 0x7ff;
+ if (ex - ey > 49) { /* 3rd round, good to 151 bits, covers all cases */
t = r;
w = fn*pio2_3;
r = t - w;
y[0] = r - w;
}
}
- y[1] = (r-y[0]) - w;
+ y[1] = (r - y[0]) - w;
return n;
}
/*
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;
+ /* set z = scalbn(|x|,-ilogb(x)+23) */
+ u.f = x;
+ u.i &= (uint64_t)-1>>12;
+ u.i |= (uint64_t)(0x3ff + 23)<<52;
+ z = u.f;
+ for (i=0; i < 2; i++) {
+ tx[i] = (double)(int32_t)z;
+ z = (z-tx[i])*0x1p24;
}
- 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) {
+ tx[i] = z;
+ /* skip zero terms, first term is non-zero */
+ while (tx[i] == 0.0)
+ i--;
+ n = __rem_pio2_large(tx,ty,(int)(ix>>20)-(0x3ff+23),i+1,1);
+ if (sign) {
y[0] = -ty[0];
y[1] = -ty[1];
return -n;
projects / musl / blobdiff