/*
* Return the IEEE remainder and set *quo to the last n bits of the
* quotient, rounded to the nearest integer. We choose n=31 because
* we wind up computing all the integer bits of the quotient anyway as
* a side-effect of computing the remainder by the shift and subtract
* method. In practice, this is far more bits than are needed to use
* remquo in reduction algorithms.
*
* Assumptions:
* - The low part of the mantissa fits in a manl_t exactly.
* - The high part of the mantissa fits in an int64_t with enough room
* for an explicit integer bit in front of the fractional bits.
*/
long double remquol(long double x, long double y, int *quo)
{
union IEEEl2bits ux, uy;
int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
manh_t hy;
manl_t lx,ly,lz;
int ix,iy,n,q,sx,sxy;
ux.e = x;
uy.e = y;
sx = ux.bits.sign;
sxy = sx ^ uy.bits.sign;
ux.bits.sign = 0; /* |x| */
uy.bits.sign = 0; /* |y| */
x = ux.e;
/* purge off exception values */
if ((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
(ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */
(uy.bits.exp == BIAS + LDBL_MAX_EXP &&
((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
return (x*y)/(x*y);
if (ux.bits.exp <= uy.bits.exp) {
if ((ux.bits.exp < uy.bits.exp) ||
(ux.bits.manh <= uy.bits.manh &&
(ux.bits.manh < uy.bits.manh ||
ux.bits.manl < uy.bits.manl))) {
q = 0;
goto fixup; /* |x|<|y| return x or x-y */
}
if (ux.bits.manh == uy.bits.manh && ux.bits.manl == uy.bits.manl) {
*quo = sxy ? -1 : 1;
return Zero[sx]; /* |x|=|y| return x*0*/
}
}
/* determine ix = ilogb(x) */
if (ux.bits.exp == 0) { /* subnormal x */
ux.e *= 0x1.0p512;
ix = ux.bits.exp - (BIAS + 512);
} else {
ix = ux.bits.exp - BIAS;
}
/* determine iy = ilogb(y) */
if (uy.bits.exp == 0) { /* subnormal y */
uy.e *= 0x1.0p512;
iy = uy.bits.exp - (BIAS + 512);
} else {
iy = uy.bits.exp - BIAS;
}
/* set up {hx,lx}, {hy,ly} and align y to x */
hx = SET_NBIT(ux.bits.manh);
hy = SET_NBIT(uy.bits.manh);
lx = ux.bits.manl;
ly = uy.bits.manl;
/* fix point fmod */
n = ix - iy;
q = 0;
while (n--) {
hz = hx - hy;
lz = lx - ly;
if (lx < ly)
hz -= 1;
if (hz < 0) {
hx = hx + hx + (lx>>MANL_SHIFT);
lx = lx + lx;
} else {
/*
* fmodl(x,y)
* Return x mod y in exact arithmetic
* Method: shift and subtract
*
* Assumptions:
* - The low part of the mantissa fits in a manl_t exactly.
* - The high part of the mantissa fits in an int64_t with enough room
* for an explicit integer bit in front of the fractional bits.
*/
long double
fmodl(long double x, long double y)
{
union {
long double e;
struct ieee_ext bits;
} ux, uy;
int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
uint32_t hy;
uint32_t lx,ly,lz;
int ix,iy,n,sx;
ux.e = x;
uy.e = y;
sx = ux.bits.ext_sign;
/* purge off exception values */
if((uy.bits.ext_exp|uy.bits.ext_frach|uy.bits.ext_fracl)==0 || /* y=0 */
(ux.bits.ext_exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */
(uy.bits.ext_exp == BIAS + LDBL_MAX_EXP &&
((uy.bits.ext_frach&~LDBL_NBIT)|uy.bits.ext_fracl)!=0)) /* or y is NaN */
return (x*y)/(x*y);
if(ux.bits.ext_exp<=uy.bits.ext_exp) {
if((ux.bits.ext_exp<uy.bits.ext_exp) ||
(ux.bits.ext_frach<=uy.bits.ext_frach &&
(ux.bits.ext_frach<uy.bits.ext_frach ||
ux.bits.ext_fracl<uy.bits.ext_fracl))) {
return x; /* |x|<|y| return x or x-y */
}
if(ux.bits.ext_frach==uy.bits.ext_frach &&
ux.bits.ext_fracl==uy.bits.ext_fracl) {
return Zero[sx]; /* |x|=|y| return x*0*/
}
}
/* determine ix = ilogb(x) */
if(ux.bits.ext_exp == 0) { /* subnormal x */
ux.e *= 0x1.0p512;
ix = ux.bits.ext_exp - (BIAS + 512);
} else {
ix = ux.bits.ext_exp - BIAS;
}
/* determine iy = ilogb(y) */
if(uy.bits.ext_exp == 0) { /* subnormal y */
uy.e *= 0x1.0p512;
iy = uy.bits.ext_exp - (BIAS + 512);
} else {
iy = uy.bits.ext_exp - BIAS;
}
/* set up {hx,lx}, {hy,ly} and align y to x */
hx = SET_NBIT(ux.bits.ext_frach);
hy = SET_NBIT(uy.bits.ext_frach);
lx = ux.bits.ext_fracl;
ly = uy.bits.ext_fracl;
/* fix point fmod */
n = ix - iy;
while(n--) {
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
else {
if ((hz|lz)==0) /* return sign(x)*0 */
