double pow(double x, double y) /* wrapper pow */
{
#ifdef _IEEE_LIBM
return __ieee754_pow(x,y);
#else
double z;
z=__ieee754_pow(x,y);
if(_LIB_VERSION == _IEEE_|| isnan(y)) return z;
if(isnan(x)) {
if(y==0.0)
return __kernel_standard(x,y,42); /* pow(NaN,0.0) */
else
return z;
}
if(x==0.0){
if(y==0.0)
return __kernel_standard(x,y,20); /* pow(0.0,0.0) */
if(finite(y)&&y<0.0)
return __kernel_standard(x,y,23); /* pow(0.0,negative) */
return z;
}
if(!finite(z)) {
if(finite(x)&&finite(y)) {
if(isnan(z))
return __kernel_standard(x,y,24); /* pow neg**non-int */
else
return __kernel_standard(x,y,21); /* pow overflow */
}
}
if(z==0.0&&finite(x)&&finite(y))
return __kernel_standard(x,y,22); /* pow underflow */
return z;
#endif
}
/* wrapper powf */
float
powf (float x, float y)
{
#if defined(__UCLIBC_HAS_FENV__)
float z = (float) __ieee754_pow ((double) x, (double) y);
if (__builtin_expect (!isfinite (z), 0))
{
if (_LIB_VERSION != _IEEE_)
{
if (isnan (x))
{
if (y == 0.0f)
/* pow(NaN,0.0) */
return __kernel_standard_f (x, y, 142);
}
else if (isfinite (x) && isfinite (y))
{
if (isnan (z))
/* pow neg**non-int */
return __kernel_standard_f (x, y, 124);
else if (x == 0.0f && y < 0.0f)
{
if (signbit (x) && signbit (z))
/* pow(-0.0,negative) */
return __kernel_standard_f (x, y, 123);
else
/* pow(+0.0,negative) */
return __kernel_standard_f (x, y, 143);
}
else
/* pow overflow */
return __kernel_standard_f (x, y, 121);
}
}
}
else if (__builtin_expect (z == 0.0f, 0) && isfinite (x) && isfinite (y)
&& _LIB_VERSION != _IEEE_)
{
if (x == 0.0f)
{
if (y == 0.0f)
/* pow(0.0,0.0) */
return __kernel_standard_f (x, y, 120);
}
else
/* pow underflow */
return __kernel_standard_f (x, y, 122);
}
return z;
#else
return (float) __ieee754_pow ((double) x, (double) y);
#endif /* __UCLIBC_HAS_FENV__ */
}
void
Math_pow(void *fp)
{
F_Math_pow *f;
f = fp;
*f->ret = __ieee754_pow(f->x, f->y);
}
/* wrapper pow */
double
__pow (double x, double y)
{
double z = __ieee754_pow (x, y);
if (__builtin_expect (!__finite (z), 0))
{
if (_LIB_VERSION != _IEEE_)
{
if (__isnan (x))
{
if (y == 0.0)
/* pow(NaN,0.0) */
return __kernel_standard (x, y, 42);
}
else if (__finite (x) && __finite (y))
{
if (__isnan (z))
/* pow neg**non-int */
return __kernel_standard (x, y, 24);
else if (x == 0.0 && y < 0.0)
{
if (signbit (x) && signbit (z))
/* pow(-0.0,negative) */
return __kernel_standard (x, y, 23);
else
/* pow(+0.0,negative) */
return __kernel_standard (x, y, 43);
}
else
/* pow overflow */
return __kernel_standard (x, y, 21);
}
}
}
else if (__builtin_expect (z == 0.0, 0) && __finite (x) && __finite (y)
&& _LIB_VERSION != _IEEE_)
{
if (x == 0.0)
{
if (y == 0.0)
/* pow(0.0,0.0) */
return __kernel_standard (x, y, 20);
}
else
/* pow underflow */
return __kernel_standard (x, y, 22);
}
return z;
}
double pow(double x, double y) /* wrapper pow */
{
#ifdef CYGSEM_LIBM_COMPAT_IEEE_ONLY
return __ieee754_pow(x,y);
#else
double z;
z=__ieee754_pow(x,y);
if(cyg_libm_get_compat_mode() == CYGNUM_LIBM_COMPAT_IEEE||
isnan(y))
return z;
if(isnan(x)) {
if(y==0.0)
return __kernel_standard(x,y,42); /* pow(NaN,0.0) */
else
return z;
}
if(x==0.0){
if(y==0.0)
return __kernel_standard(x,y,20); /* pow(0.0,0.0) */
if(finite(y)&&y<0.0)
return __kernel_standard(x,y,23); /* pow(0.0,negative) */
return z;
}
if(!finite(z)) {
if(finite(x)&&finite(y)) {
if(isnan(z))
return __kernel_standard(x,y,24);/* pow neg**non-int */
else
return __kernel_standard(x,y,21); /* pow overflow */
}
}
if(z==0.0&&finite(x)&&finite(y))
return __kernel_standard(x,y,22); /* pow underflow */
return z;
#endif
}
EXPORT(sqInt) primitiveRaisedToPower(void) {
double rcvr;
double result;
double arg;
arg = interpreterProxy->stackFloatValue(0);
rcvr = interpreterProxy->stackFloatValue(1);
if (interpreterProxy->failed()) {
return null;
}
result = __ieee754_pow(rcvr, arg);
if (isnan(result)) {
return interpreterProxy->primitiveFail();
}
interpreterProxy->pop((interpreterProxy->methodArgumentCount()) + 1);
interpreterProxy->pushFloat(result);
}
primitiveRaisedToPower(void)
{
// FloatMathPlugin>>#primitiveRaisedToPower
double arg;
double rcvr;
double result;
arg = stackFloatValue(0);
rcvr = stackFloatValue(1);
if (failed()) {
return null;
}
result = __ieee754_pow(rcvr, arg);
if (isnan(result)) {
return primitiveFail();
}
pop((methodArgumentCount()) + 1);
pushFloat(result);
}
double
SECTION
__ieee754_pow(double x, double y) {
double z,a,aa,error, t,a1,a2,y1,y2;
#if 0
double gor=1.0;
#endif
mynumber u,v;
int k;
int4 qx,qy;
v.x=y;
u.x=x;
if (v.i[LOW_HALF] == 0) { /* of y */
qx = u.i[HIGH_HALF]&0x7fffffff;
/* Checking if x is not too small to compute */
if (((qx==0x7ff00000)&&(u.i[LOW_HALF]!=0))||(qx>0x7ff00000)) return NaNQ.x;
if (y == 1.0) return x;
if (y == 2.0) return x*x;
if (y == -1.0) return 1.0/x;
if (y == 0) return 1.0;
}
/* else */
if(((u.i[HIGH_HALF]>0 && u.i[HIGH_HALF]<0x7ff00000)|| /* x>0 and not x->0 */
(u.i[HIGH_HALF]==0 && u.i[LOW_HALF]!=0)) &&
/* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */
(v.i[HIGH_HALF]&0x7fffffff) < 0x4ff00000) { /* if y<-1 or y>1 */
double retval;
SET_RESTORE_ROUND (FE_TONEAREST);
/* Avoid internal underflow for tiny y. The exact value of y does
not matter if |y| <= 2**-64. */
if (ABS (y) < 0x1p-64)
y = y < 0 ? -0x1p-64 : 0x1p-64;
z = log1(x,&aa,&error); /* x^y =e^(y log (X)) */
t = y*134217729.0;
y1 = t - (t-y);
y2 = y - y1;
t = z*134217729.0;
a1 = t - (t-z);
a2 = (z - a1)+aa;
a = y1*a1;
aa = y2*a1 + y*a2;
a1 = a+aa;
a2 = (a-a1)+aa;
error = error*ABS(y);
t = __exp1(a1,a2,1.9e16*error); /* return -10 or 0 if wasn't computed exactly */
retval = (t>0)?t:power1(x,y);
return retval;
}
if (x == 0) {
if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0)
|| (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000)
return y;
if (ABS(y) > 1.0e20) return (y>0)?0:1.0/0.0;
k = checkint(y);
if (k == -1)
return y < 0 ? 1.0/x : x;
else
return y < 0 ? 1.0/0.0 : 0.0; /* return 0 */
}
qx = u.i[HIGH_HALF]&0x7fffffff; /* no sign */
qy = v.i[HIGH_HALF]&0x7fffffff; /* no sign */
if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) return NaNQ.x;
if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0))
return x == 1.0 ? 1.0 : NaNQ.x;
/* if x<0 */
if (u.i[HIGH_HALF] < 0) {
k = checkint(y);
if (k==0) {
if (qy == 0x7ff00000) {
if (x == -1.0) return 1.0;
else if (x > -1.0) return v.i[HIGH_HALF] < 0 ? INF.x : 0.0;
else return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x;
}
else if (qx == 0x7ff00000)
return y < 0 ? 0.0 : INF.x;
return NaNQ.x; /* y not integer and x<0 */
}
else if (qx == 0x7ff00000)
{
if (k < 0)
return y < 0 ? nZERO.x : nINF.x;
else
return y < 0 ? 0.0 : INF.x;
}
return (k==1)?__ieee754_pow(-x,y):-__ieee754_pow(-x,y); /* if y even or odd */
}
/* x>0 */
if (qx == 0x7ff00000) /* x= 2^-0x3ff */
{if (y == 0) return NaNQ.x;
return (y>0)?x:0; }
if (qy > 0x45f00000 && qy < 0x7ff00000) {
if (x == 1.0) return 1.0;
if (y>0) return (x>1.0)?huge*huge:tiny*tiny;
if (y<0) return (x<1.0)?huge*huge:tiny*tiny;
}
if (x == 1.0) return 1.0;
if (y>0) return (x>1.0)?INF.x:0;
if (y<0) return (x<1.0)?INF.x:0;
return 0; /* unreachable, to make the compiler happy */
}
/* An ultimate power routine. Given two IEEE double machine numbers y, x it
computes the correctly rounded (to nearest) value of X^y. */
double
SECTION
__ieee754_pow (double x, double y)
{
double z, a, aa, error, t, a1, a2, y1, y2;
mynumber u, v;
int k;
int4 qx, qy;
v.x = y;
u.x = x;
if (v.i[LOW_HALF] == 0)
{ /* of y */
qx = u.i[HIGH_HALF] & 0x7fffffff;
/* Is x a NaN? */
if ((((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000))
&& (y != 0 || issignaling (x)))
return x + x;
if (y == 1.0)
return x;
if (y == 2.0)
return x * x;
if (y == -1.0)
return 1.0 / x;
if (y == 0)
return 1.0;
}
/* else */
if (((u.i[HIGH_HALF] > 0 && u.i[HIGH_HALF] < 0x7ff00000) || /* x>0 and not x->0 */
(u.i[HIGH_HALF] == 0 && u.i[LOW_HALF] != 0)) &&
/* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */
(v.i[HIGH_HALF] & 0x7fffffff) < 0x4ff00000)
{ /* if y<-1 or y>1 */
double retval;
{
SET_RESTORE_ROUND (FE_TONEAREST);
/* Avoid internal underflow for tiny y. The exact value of y does
not matter if |y| <= 2**-64. */
if (fabs (y) < 0x1p-64)
y = y < 0 ? -0x1p-64 : 0x1p-64;
z = log1 (x, &aa, &error); /* x^y =e^(y log (X)) */
t = y * CN;
y1 = t - (t - y);
y2 = y - y1;
t = z * CN;
a1 = t - (t - z);
a2 = (z - a1) + aa;
a = y1 * a1;
aa = y2 * a1 + y * a2;
a1 = a + aa;
a2 = (a - a1) + aa;
error = error * fabs (y);
t = __exp1 (a1, a2, 1.9e16 * error); /* return -10 or 0 if wasn't computed exactly */
retval = (t > 0) ? t : power1 (x, y);
}
if (isinf (retval))
retval = huge * huge;
else if (retval == 0)
retval = tiny * tiny;
else
math_check_force_underflow_nonneg (retval);
return retval;
}
if (x == 0)
{
if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0)
|| (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */
return y + y;
if (fabs (y) > 1.0e20)
return (y > 0) ? 0 : 1.0 / 0.0;
k = checkint (y);
if (k == -1)
return y < 0 ? 1.0 / x : x;
else
return y < 0 ? 1.0 / 0.0 : 0.0; /* return 0 */
}
qx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */
qy = v.i[HIGH_HALF] & 0x7fffffff; /* no sign */
if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) /* NaN */
return x + y;
if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0)) /* NaN */
return x == 1.0 && !issignaling (y) ? 1.0 : y + y;
/* if x<0 */
if (u.i[HIGH_HALF] < 0)
{
k = checkint (y);
if (k == 0)
{
if (qy == 0x7ff00000)
{
if (x == -1.0)
return 1.0;
else if (x > -1.0)
return v.i[HIGH_HALF] < 0 ? INF.x : 0.0;
else
return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x;
}
else if (qx == 0x7ff00000)
return y < 0 ? 0.0 : INF.x;
return (x - x) / (x - x); /* y not integer and x<0 */
}
else if (qx == 0x7ff00000)
{
if (k < 0)
return y < 0 ? nZERO.x : nINF.x;
else
return y < 0 ? 0.0 : INF.x;
}
/* if y even or odd */
if (k == 1)
return __ieee754_pow (-x, y);
else
{
double retval;
{
SET_RESTORE_ROUND (FE_TONEAREST);
retval = -__ieee754_pow (-x, y);
}
if (isinf (retval))
retval = -huge * huge;
else if (retval == 0)
retval = -tiny * tiny;
return retval;
}
}
/* x>0 */
if (qx == 0x7ff00000) /* x= 2^-0x3ff */
return y > 0 ? x : 0;
if (qy > 0x45f00000 && qy < 0x7ff00000)
{
if (x == 1.0)
return 1.0;
if (y > 0)
return (x > 1.0) ? huge * huge : tiny * tiny;
if (y < 0)
return (x < 1.0) ? huge * huge : tiny * tiny;
}
if (x == 1.0)
return 1.0;
if (y > 0)
return (x > 1.0) ? INF.x : 0;
if (y < 0)
return (x < 1.0) ? INF.x : 0;
return 0; /* unreachable, to make the compiler happy */
}
Err mathlib_pow(UInt16 refnum, double x, double y, double *result) {
#pragma unused(refnum)
*result = __ieee754_pow(x, y);
return mlErrNone;
}
static double
gamma_positive (double x, int *exp2_adj)
{
int local_signgam;
if (x < 0.5)
{
*exp2_adj = 0;
return __ieee754_exp (__ieee754_lgamma_r (x + 1, &local_signgam)) / x;
}
else if (x <= 1.5)
{
*exp2_adj = 0;
return __ieee754_exp (__ieee754_lgamma_r (x, &local_signgam));
}
else if (x < 6.5)
{
/* Adjust into the range for using exp (lgamma). */
*exp2_adj = 0;
double n = __ceil (x - 1.5);
double x_adj = x - n;
double eps;
double prod = __gamma_product (x_adj, 0, n, &eps);
return (__ieee754_exp (__ieee754_lgamma_r (x_adj, &local_signgam))
* prod * (1.0 + eps));
}
else
{
double eps = 0;
double x_eps = 0;
double x_adj = x;
double prod = 1;
if (x < 12.0)
{
/* Adjust into the range for applying Stirling's
approximation. */
double n = __ceil (12.0 - x);
#if FLT_EVAL_METHOD != 0
volatile
#endif
double x_tmp = x + n;
x_adj = x_tmp;
x_eps = (x - (x_adj - n));
prod = __gamma_product (x_adj - n, x_eps, n, &eps);
}
/* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)).
Compute gamma (X_ADJ + X_EPS) using Stirling's approximation,
starting by computing pow (X_ADJ, X_ADJ) with a power of 2
factored out. */
double exp_adj = -eps;
double x_adj_int = __round (x_adj);
double x_adj_frac = x_adj - x_adj_int;
int x_adj_log2;
double x_adj_mant = __frexp (x_adj, &x_adj_log2);
if (x_adj_mant < M_SQRT1_2)
{
x_adj_log2--;
x_adj_mant *= 2.0;
}
*exp2_adj = x_adj_log2 * (int) x_adj_int;
double ret = (__ieee754_pow (x_adj_mant, x_adj)
* __ieee754_exp2 (x_adj_log2 * x_adj_frac)
* __ieee754_exp (-x_adj)
* __ieee754_sqrt (2 * M_PI / x_adj)
/ prod);
exp_adj += x_eps * __ieee754_log (x);
double bsum = gamma_coeff[NCOEFF - 1];
double x_adj2 = x_adj * x_adj;
for (size_t i = 1; i <= NCOEFF - 1; i++)
bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i];
exp_adj += bsum / x_adj;
return ret + ret * __expm1 (exp_adj);
}
}
