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fdlibm-pieces.c
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fdlibm-pieces.c
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#include <string.h>
// Code based on Sun's fdlibm
static const double
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
static double zero = 0.0;
double log(double);
double log1p(double);
double log1pmd(double);
static inline __attribute__((always_inline))
double log1p_k(double, int, int);
static inline __attribute__((always_inline))
double log1pmd_k(double, double, int, int);
/* ASSUME LITTLE ENDIAN */
#define __HI(x) *(1+(int*)&x)
#define __LO(x) *(int*)&x
double log(double x)
{
double f;
int k,hx,i;
unsigned lx;
hx = __HI(x); /* high word of x */
lx = __LO(x); /* low word of x */
k=0;
if (hx < 0x00100000) { /* x < 2**-1022 */
if (((hx&0x7fffffff)|lx)==0)
return -two54/zero; /* log(+-0)=-inf */
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
k -= 54; x *= two54; /* subnormal number, scale up x */
hx = __HI(x); /* high word of x */
}
if (hx >= 0x7ff00000) return x+x;
k += (hx>>20)-1023;
hx &= 0x000fffff;
i = (hx+0x95f64)&0x100000;
__HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */
k += (i>>20);
f = x-1.0;
return log1p_k(f, k, hx);
}
static inline __attribute__((always_inline))
double log1p_k(double f, int k, int hx)
{
double s,R,dk;
if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
if(f==zero) {
if(k==0) return zero; else {dk=(double)k;
return dk*ln2_hi+dk*ln2_lo;}}
R = f*f*(0.5-0.33333333333333333*f);
if(k==0) return f-R; else {dk=(double)k;
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
}
s = f/(2.0+f);
return log1pmd_k(s, f, k, hx);
}
double log1p(double f)
{
int x = f + 1.0;
int hx = __HI(x); /* high word of x */
return log1p_k(f, 0, hx);
}
static inline __attribute__((always_inline))
double log1pmd_k(double s, double f, int k, int hx)
{
double hfsq,z,R,w,t1,t2,dk;
int i,j;
dk = (double)k;
z = s*s;
i = hx-0x6147a;
w = z*z;
j = 0x6b851-hx;
t1= w*(Lg2+w*(Lg4+w*Lg6));
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
i |= j;
R = t2+t1;
if(i>0) {
hfsq=0.5*f*f;
if(k==0) return f-(hfsq-s*(hfsq+R)); else
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
} else {
if(k==0) return f-s*(f-R); else
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
}
}
double log1pmd(double s)
{
double f = 2.0*s / (1 - s);
int x = f + 1.0;
int hx = __HI(x); /* high word of x */
return log1pmd_k(s, f, 0, hx);
}