long double
_IEEE_REMAINDER_D_H(long double argx, float argy)
{
union _ieee_ldouble {
long double ldword;
long lword[2];
};
long double __remainder_d(long double x, long double y);
long double y_val;
int xfpclas = _fpclassifyl(argx);
int yfpclas = _fpclassifyf(argy);
if ((xfpclas == FP_INFINITE) || yfpclas == FP_ZERO) {
union _ieee_ldouble xval;
int j;
xval.ldword = _DBL_NaN;
/* need to emit invalid exception */
j = FE_INVALID;
feraiseexcept(j);
return(xval.ldword);
}
y_val = (long double) argy;
return(__remainder_d(argx, y_val));
}
double
_IEEE_REMAINDER_H_R(float argx, double argy)
{
union _ieee_double {
double dword;
long lword;
};
double __remainder_r(double x, double y);
double x_val;
int xfpclas = _fpclassifyf(argx);
int yfpclas = _fpclassify(argy);
if ((xfpclas == FP_INFINITE) || yfpclas == FP_ZERO) {
union _ieee_double x_val;
int j;
x_val.dword = _SGL_NaN;
/* need to emit invalid exception */
j = FE_INVALID;
feraiseexcept(j);
return(x_val.dword);
}
x_val = (double) argx;
return(__remainder_r(x_val, argy));
}
float
_IEEE_BINARY_SCALE_H_I4(float x, short n)
{
/* Union defined to work with IEEE 64-bit floating point. */
union _ieee_double {
float dword;
short lword;
unsigned short ulword;
struct {
unsigned int sign : 1;
unsigned int exponent : IEEE_32_EXPO_BITS;
unsigned int mantissa : IEEE_32_MANT_BITS;
} parts;
};
int fp_class = _fpclassifyf(x);
if (fp_class==FP_NORMAL) {
union _ieee_double x_val;
long exponent;
x_val.dword = x;
exponent = x_val.parts.exponent + (int) n;
if (exponent <= 0) {
int j;
long full_mantissa = x_val.parts.mantissa;
/* need to emit underflow exception */
j = FE_UNDERFLOW;
feraiseexcept(j);
/* add implicit bit to mantissa */
full_mantissa |= IEEE_32_IMPLICIT_BIT;
/* shift mantissa over by exponent remaining */
full_mantissa >>= -exponent + 1;
/* return denormal number */
x_val.parts.exponent = 0;
x_val.parts.mantissa = full_mantissa;
} else if ((exponent>>IEEE_32_EXPO_BITS) != 0) {
float
_IEEE_EXPONENT_H_H(float x)
{
union _ieee_float {
float dword;
int lword;
struct {
#if defined(_LITTLE_ENDIAN)
unsigned int mantissa : IEEE_32_MANT_BITS;
unsigned int exponent : IEEE_32_EXPO_BITS;
unsigned int sign : 1;
#else
unsigned int sign : 1;
unsigned int exponent : IEEE_32_EXPO_BITS;
unsigned int mantissa : IEEE_32_MANT_BITS;
#endif
} parts;
};
switch (_fpclassifyf(x)) {
case FP_NAN:
return(x);
case FP_INFINITE:
{
union _ieee_float x_val;
x_val.lword = IEEE_32_INFINITY;
return(x_val.dword);
}
case FP_NORMAL:
{
union _ieee_float x_val;
x_val.dword = x;
return(x_val.parts.exponent - IEEE_32_EXPO_BIAS);
}
case FP_SUBNORMAL:
{
union _ieee_float x_val;
x_val.dword = x;
/* _leadz returns number of zeros before first 1
* in mantissa. Add 8 to exclude exponent bits,
* but count sign bit since implicit bit needs to
* be counted.
*/
return(-IEEE_32_EXPO_BIAS -
(_leadz(x_val.parts.mantissa) - 32) +
IEEE_32_EXPO_BITS);
}
case FP_ZERO:
{
union _ieee_float x_val;
int j;
/* raise divide-by-zero exception */
j = FE_DIVBYZERO;
feraiseexcept(j);
/* return negative infinity */
x_val.dword = IEEE_32_INFINITY;
x_val.parts.sign = 1;
return(x_val.dword);
}
}
}
double
_IEEE_NEXT_AFTER_R_H(double x, float y)
{
/* Union defined to work with IEEE 64-bit floating point. */
union _ieee_double {
double dword;
long long lword;
struct {
#if __BYTE_ORDER == __LITTLE_ENDIAN
unsigned int mantissa : IEEE_64_MANT_BITS;
unsigned int exponent : IEEE_64_EXPO_BITS;
unsigned int sign : 1;
#else
unsigned int sign : 1;
unsigned int exponent : IEEE_64_EXPO_BITS;
unsigned int mantissa : IEEE_64_MANT_BITS;
#endif
} parts;
};
int xfpclas = _fpclassify(x);
int yfpclas = _fpclassifyf(y);
if (xfpclas == FP_NAN) {
return x;
} else if (yfpclas == FP_NAN) {
union _ieee_double x_val;
x_val.dword = _SGL_NaN;
return(x_val.dword);
} else if (xfpclas == FP_ZERO && yfpclas == FP_ZERO) {
return x;
} else if (xfpclas == FP_INFINITE) {
return x;
} else if (x == (double) y) {
return x;
} else if (xfpclas == FP_ZERO) {
union _ieee_double x_val;
x_val.dword = DBL_MIN;
x_val.parts.sign = x > (double) y;
/* return smallest normal number */
return(x_val.dword);
} else { /* first argument is normal or denormal */
union _ieee_double x_val;
int j;
int resfpclas;
x_val.dword = x;
/* move one bit in the correct direction.
** Because of the way the implicit bit works,
** the exponent field is handled correctly.
*/
if (x > 0) {
x_val.lword += (x > (double) y) ? -1 : 1;
} else {
x_val.lword += (x > (double) y) ? 1 : -1;
}
/* test for underflow or overflow */
if (_isnormal(x_val.dword))
return(x_val.dword);
/*
* Raise overflow exception for infinite result and
* underflow exception for too small result. Raise
* inexact exception for both cases. Allow subnormal
* values to return without exception.
*/
resfpclas = _fpclassify(x_val.dword);
if (resfpclas == FP_INFINITE) {
j = FE_OVERFLOW;
feraiseexcept(j);
} else if (resfpclas == FP_ZERO) {
j = FE_UNDERFLOW;
feraiseexcept(j);
} else {
return(x_val.dword);
}
j = FE_INEXACT;
feraiseexcept(j);
return(x_val.dword);
}
}
float
_IEEE_REMAINDER_H_H(float argx, float argy)
{
union _ieee_flot {
float fpword;
unsigned int usword;
int int32;
struct {
unsigned int sign : 1;
unsigned int exponent : IEEE_32_EXPO_BITS;
unsigned int mantissa : IEEE_32_MANT_BITS;
} parts;
};
union _ieee_flot x_val, y_val, nearint, tdiv, evenchk, tmp, res;
unsigned int even_x = 0X00000001;
int xfpclas = _fpclassifyf(argx);
int yfpclas = _fpclassifyf(argy);
x_val.fpword = argx;
y_val.fpword = argy;
if ((xfpclas == FP_INFINITE) || yfpclas == FP_ZERO) {
union _ieee_flot x_val;
int j;
x_val.fpword = _HALF_NaN;
/* need to emit invalid exception */
j = FE_INVALID;
feraiseexcept(j);
return(x_val.fpword);
}
tdiv.fpword = argx / argy;
tmp.usword = tdiv.usword & (~IEEE_32_SIGN_BIT);
/* check for 2**23 or greater = already integer */
if (tmp.fpword < 8388608) {
/* calculate fraction */
evenchk.fpword =
tdiv.fpword - (float)((int)tdiv.fpword);
if (tdiv.fpword < 0.0) {
nearint.int32 = (int) (tdiv.fpword - 0.5);
if ((evenchk.fpword == -0.5) &&
((nearint.usword & even_x) != 0))
nearint.int32 += 1;
} else {
nearint.int32 = (int) (tdiv.fpword + 0.5);
if ((evenchk.fpword == 0.5) &&
((nearint.usword & even_x) != 0))
nearint.int32 -= 1;
}
tdiv.fpword = (float) nearint.int32;
}
/* algorithm for ieee in 64-bits for x - (x/y)*y. */
res.fpword = (float) ((double) x_val.fpword -
((double) tdiv.fpword * (double) y_val.fpword));
if (res.fpword == 0.0)
res.usword= res.usword | (x_val.usword & IEEE_32_SIGN_BIT);
return(res.fpword);
}
long double
_IEEE_EXPONENT_D_H(float x)
{
/* Union defined to work with IEEE 128 bit floating point. */
union _ieee_ldouble {
long double dword;
long lword[2];
struct {
unsigned int sign : 1;
unsigned int exponent : IEEE_128_EXPO_BITS;
unsigned int mantissa_up : IEEE_128_MANT_BITS_UP;
unsigned int mantissa_low : IEEE_128_MANT_BITS_LOW;
} lparts;
};
union _ieee_fdouble {
float dwrd;
int lwrd;
struct {
#if __BYTE_ORDER == __LITTLE_ENDIAN
unsigned int mantissa : IEEE_32_MANT_BITS;
unsigned int expon : IEEE_32_EXPO_BITS;
unsigned int sgn : 1;
#else
unsigned int sgn : 1;
unsigned int expon : IEEE_32_EXPO_BITS;
unsigned int mantissa : IEEE_32_MANT_BITS;
#endif
} parts;
};
switch (_fpclassifyf(x)) {
case FP_NAN:
{
union _ieee_ldouble x_val;
x_val.dword = _DBL_NaN;
return(x_val.dword);
}
case FP_INFINITE:
{
union _ieee_ldouble x_val;
x_val.lword[0] = INFINITY_128_UP;
x_val.lword[1] = INFINITY_128_LOW;
x_val.lparts.sign = 0;
return(x_val.dword);
}
case FP_NORMAL:
{
union _ieee_fdouble x_val;
x_val.dwrd = x;
return(x_val.parts.expon - IEEE_32_EXPO_BIAS);
}
case FP_SUBNORMAL:
{
union _ieee_fdouble x_val;
int y;
x_val.dwrd = x;
/* _leadz returns number of zeros before first 1
* in mantissa. Add IEEE_32_EXPO_BITS to exclude
* exponent bits, but count sign bit since
* implicit bit needs to be counted.
*/
return(-IEEE_32_EXPO_BIAS -
(_leadz(x_val.parts.mantissa) - 32) +
IEEE_32_EXPO_BITS);
}
case FP_ZERO:
{
int j;
union _ieee_ldouble x_val;
/* raise divide-by-zero exception */
j = FE_DIVBYZERO;
feraiseexcept(j);
/* return negative infinity */
x_val.lword[0] = INFINITY_128_UP;
x_val.lword[1] = INFINITY_128_LOW;
x_val.lparts.sign = 1;
return(x_val.dword);
}
}
}
float
_IEEE_NEXT_AFTER_H_R(float x, double y)
{
/* Union defined to work with IEEE 32-bit floating point. */
union _ieee_double {
float dword;
short lword;
struct {
unsigned int sign : 1;
unsigned int exponent : IEEE_32_EXPO_BITS;
unsigned int mantissa : IEEE_32_MANT_BITS;
} parts;
};
int xfpclas = _fpclassifyf(x);
int yfpclas = _fpclassify(y);
if (xfpclas == FP_NAN) {
return x;
} else if (yfpclas == FP_NAN) {
union _ieee_double x_val;
x_val.dword = _HALF_NaN;
return(x_val.dword);
} else if (xfpclas == FP_ZERO && yfpclas == FP_ZERO) {
return x;
} else if (xfpclas == FP_INFINITE) {
return x;
} else if ((double) x == y) {
return x;
} else if (xfpclas == FP_ZERO) {
union _ieee_double x_val;
x_val.dword = FLT_MIN;
x_val.parts.sign = (double) x > y;
/* return smallest normal number */
return(x_val.dword);
} else { /* first argument is normal or denormal */
union _ieee_double x_val;
int j;
int resfpclas;
x_val.dword = x;
/* move one bit in the correct direction.
** Because of the way the implicit bit works,
** the exponent field is handled correctly.
*/
if (x > 0) {
x_val.lword += ((double) x > y) ? -1 : 1;
} else {
x_val.lword += ((double) x > y) ? 1 : -1;
}
/* test for underflow or overflow */
if (_isnormalf(x_val.dword))
return(x_val.dword);
/*
* Raise overflow exception for infinite result and
* underflow exception for too small result. Raise
* inexact exception for both cases. Allow subnormal
* values to return without exception.
*/
resfpclas = _fpclassifyf(x_val.dword);
if (resfpclas == FP_INFINITE) {
j = FE_OVERFLOW;
feraiseexcept(j);
} else if (resfpclas == FP_ZERO) {
j = FE_UNDERFLOW;
feraiseexcept(j);
} else {
return(x_val.dword);
}
j = FE_INEXACT;
feraiseexcept(j);
return(x_val.dword);
}
}