ciabatta/code/math/division.c

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C
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2022-06-11 22:34:36 +00:00
#include <math.h>
#include <stdint.h>
double remquo(double x, double y, int *quo) {
union {double f; uint64_t i;} ux = {x}, uy = {y};
int ex = ux.i>>52 & 0x7ff;
int ey = uy.i>>52 & 0x7ff;
int sx = ux.i>>63;
int sy = uy.i>>63;
uint32_t q;
uint64_t i;
uint64_t uxi = ux.i;
*quo = 0;
if (uy.i<<1 == 0 || isnan(y) || ex == 0x7ff)
return (x*y)/(x*y);
if (ux.i<<1 == 0)
return x;
/* normalize x and y */
if (!ex) {
for (i = uxi<<12; i>>63 == 0; ex--, i <<= 1);
uxi <<= -ex + 1;
} else {
uxi &= -1ULL >> 12;
uxi |= 1ULL << 52;
}
if (!ey) {
for (i = uy.i<<12; i>>63 == 0; ey--, i <<= 1);
uy.i <<= -ey + 1;
} else {
uy.i &= -1ULL >> 12;
uy.i |= 1ULL << 52;
}
q = 0;
if (ex < ey) {
if (ex+1 == ey)
goto end;
return x;
}
/* x mod y */
for (; ex > ey; ex--) {
i = uxi - uy.i;
if (i >> 63 == 0) {
uxi = i;
q++;
}
uxi <<= 1;
q <<= 1;
}
i = uxi - uy.i;
if (i >> 63 == 0) {
uxi = i;
q++;
}
if (uxi == 0)
ex = -60;
else
for (; uxi>>52 == 0; uxi <<= 1, ex--);
end:
/* scale result and decide between |x| and |x|-|y| */
if (ex > 0) {
uxi -= 1ULL << 52;
uxi |= (uint64_t)ex << 52;
} else {
uxi >>= -ex + 1;
}
ux.i = uxi;
x = ux.f;
if (sy)
y = -y;
if (ex == ey || (ex+1 == ey && (2*x > y || (2*x == y && q%2)))) {
x -= y;
q++;
}
q &= 0x7fffffff;
*quo = sx^sy ? -(int)q : (int)q;
return sx ? -x : x;
}
float remquof(float x, float y, int *quo) {
union {float f; uint32_t i;} ux = {x}, uy = {y};
int ex = ux.i>>23 & 0xff;
int ey = uy.i>>23 & 0xff;
int sx = ux.i>>31;
int sy = uy.i>>31;
uint32_t q;
uint32_t i;
uint32_t uxi = ux.i;
*quo = 0;
if (uy.i<<1 == 0 || isnan(y) || ex == 0xff)
return (x*y)/(x*y);
if (ux.i<<1 == 0)
return x;
/* normalize x and y */
if (!ex) {
for (i = uxi<<9; i>>31 == 0; ex--, i <<= 1);
uxi <<= -ex + 1;
} else {
uxi &= -1U >> 9;
uxi |= 1U << 23;
}
if (!ey) {
for (i = uy.i<<9; i>>31 == 0; ey--, i <<= 1);
uy.i <<= -ey + 1;
} else {
uy.i &= -1U >> 9;
uy.i |= 1U << 23;
}
q = 0;
if (ex < ey) {
if (ex+1 == ey)
goto end;
return x;
}
/* x mod y */
for (; ex > ey; ex--) {
i = uxi - uy.i;
if (i >> 31 == 0) {
uxi = i;
q++;
}
uxi <<= 1;
q <<= 1;
}
i = uxi - uy.i;
if (i >> 31 == 0) {
uxi = i;
q++;
}
if (uxi == 0)
ex = -30;
else
for (; uxi>>23 == 0; uxi <<= 1, ex--);
end:
/* scale result and decide between |x| and |x|-|y| */
if (ex > 0) {
uxi -= 1U << 23;
uxi |= (uint32_t)ex << 23;
} else {
uxi >>= -ex + 1;
}
ux.i = uxi;
x = ux.f;
if (sy)
y = -y;
if (ex == ey || (ex+1 == ey && (2*x > y || (2*x == y && q%2)))) {
x -= y;
q++;
}
q &= 0x7fffffff;
*quo = sx^sy ? -(int)q : (int)q;
return sx ? -x : x;
}
long double remquol(long double x, long double y, int *quo) {
return remquo(x, y, quo);
}
double remainder(double x, double y) {
int q;
return remquo(x, y, &q);
}
float remainderf(float x, float y) {
int q;
return remquof(x, y, &q);
}
long double remainderl(long double x, long double y) {
return remainder(x, y);
}
double modf(double x, double *iptr) {
union {double f; uint64_t i;} u = {x};
uint64_t mask;
int e = (int)(u.i>>52 & 0x7ff) - 0x3ff;
/* no fractional part */
if (e >= 52) {
*iptr = x;
if (e == 0x400 && u.i<<12 != 0) /* nan */
return x;
u.i &= 1ULL<<63;
return u.f;
}
/* no integral part*/
if (e < 0) {
u.i &= 1ULL<<63;
*iptr = u.f;
return x;
}
mask = -1ULL>>12>>e;
if ((u.i & mask) == 0) {
*iptr = x;
u.i &= 1ULL<<63;
return u.f;
}
u.i &= ~mask;
*iptr = u.f;
return x - u.f;
}
float modff(float x, float *iptr) {
union {float f; uint32_t i;} u = {x};
uint32_t mask;
int e = (int)(u.i>>23 & 0xff) - 0x7f;
/* no fractional part */
if (e >= 23) {
*iptr = x;
if (e == 0x80 && u.i<<9 != 0) { /* nan */
return x;
}
u.i &= 0x80000000;
return u.f;
}
/* no integral part */
if (e < 0) {
u.i &= 0x80000000;
*iptr = u.f;
return x;
}
mask = 0x007fffff>>e;
if ((u.i & mask) == 0) {
*iptr = x;
u.i &= 0x80000000;
return u.f;
}
u.i &= ~mask;
*iptr = u.f;
return x - u.f;
}
long double modfl(long double x, long double *iptr) {
double d;
long double r = modf(x, &d);
*iptr = d;
return r;
}