/*Converting from double precision to Multi-precision and calculating e^x */
double __slowexp(double x) {
#ifdef NO_LONG_DOUBLE
double w,z,res,eps=3.0e-26;
int p;
mp_no mpx, mpy, mpz,mpw,mpeps,mpcor;
p=6;
__dbl_mp(x,&mpx,p); /* Convert a double precision number x */
/* into a multiple precision number mpx with prec. p. */
__mpexp(&mpx, &mpy, p); /* Multi-Precision exponential function */
__dbl_mp(eps,&mpeps,p);
__mul(&mpeps,&mpy,&mpcor,p);
__add(&mpy,&mpcor,&mpw,p);
__sub(&mpy,&mpcor,&mpz,p);
__mp_dbl(&mpw, &w, p);
__mp_dbl(&mpz, &z, p);
if (w == z) return w;
else { /* if calculating is not exactly */
p = 32;
__dbl_mp(x,&mpx,p);
__mpexp(&mpx, &mpy, p);
__mp_dbl(&mpy, &res, p);
return res;
}
#else
return (double) __ieee754_expl((long double)x);
#endif
}
/*Converting from double precision to Multi-precision and calculating e^x */
double
SECTION
__slowexp(double x) {
double w,z,res,eps=3.0e-26;
#if 0
double y;
#endif
int p;
#if 0
int orig,i;
#endif
mp_no mpx, mpy, mpz,mpw,mpeps,mpcor;
p=6;
__dbl_mp(x,&mpx,p); /* Convert a double precision number x */
/* into a multiple precision number mpx with prec. p. */
__mpexp(&mpx, &mpy, p); /* Multi-Precision exponential function */
__dbl_mp(eps,&mpeps,p);
__mul(&mpeps,&mpy,&mpcor,p);
__add(&mpy,&mpcor,&mpw,p);
__sub(&mpy,&mpcor,&mpz,p);
__mp_dbl(&mpw, &w, p);
__mp_dbl(&mpz, &z, p);
if (w == z) return w;
else { /* if calculating is not exactly */
p = 32;
__dbl_mp(x,&mpx,p);
__mpexp(&mpx, &mpy, p);
__mp_dbl(&mpy, &res, p);
return res;
}
}
double __slowpow(double x, double y, double z) {
double res,res1;
mp_no mpx, mpy, mpz,mpw,mpp,mpr,mpr1;
static const mp_no eps = {-3,{1.0,4.0}};
int p;
res = __halfulp(x,y); /* halfulp() returns -10 or x^y */
if (res >= 0) return res; /* if result was really computed by halfulp */
/* else, if result was not really computed by halfulp */
p = 10; /* p=precision */
__dbl_mp(x,&mpx,p);
__dbl_mp(y,&mpy,p);
__dbl_mp(z,&mpz,p);
__mplog(&mpx, &mpz, p); /* log(x) = z */
__mul(&mpy,&mpz,&mpw,p); /* y * z =w */
__mpexp(&mpw, &mpp, p); /* e^w =pp */
__add(&mpp,&eps,&mpr,p); /* pp+eps =r */
__mp_dbl(&mpr, &res, p);
__sub(&mpp,&eps,&mpr1,p); /* pp -eps =r1 */
__mp_dbl(&mpr1, &res1, p); /* converting into double precision */
if (res == res1) return res;
p = 32; /* if we get here result wasn't calculated exactly, continue */
__dbl_mp(x,&mpx,p); /* for more exact calculation */
__dbl_mp(y,&mpy,p);
__dbl_mp(z,&mpz,p);
__mplog(&mpx, &mpz, p); /* log(c)=z */
__mul(&mpy,&mpz,&mpw,p); /* y*z =w */
__mpexp(&mpw, &mpp, p); /* e^w=pp */
__mp_dbl(&mpp, &res, p); /* converting into double precision */
return res;
}
/*Converting from double precision to Multi-precision and calculating e^x */
double
SECTION
__slowexp (double x)
{
#ifndef USE_LONG_DOUBLE_FOR_MP
double w, z, res, eps = 3.0e-26;
int p;
mp_no mpx, mpy, mpz, mpw, mpeps, mpcor;
/* Use the multiple precision __MPEXP function to compute the exponential
First at 144 bits and if it is not accurate enough, at 768 bits. */
p = 6;
__dbl_mp (x, &mpx, p);
__mpexp (&mpx, &mpy, p);
__dbl_mp (eps, &mpeps, p);
__mul (&mpeps, &mpy, &mpcor, p);
__add (&mpy, &mpcor, &mpw, p);
__sub (&mpy, &mpcor, &mpz, p);
__mp_dbl (&mpw, &w, p);
__mp_dbl (&mpz, &z, p);
if (w == z)
return w;
else
{
p = 32;
__dbl_mp (x, &mpx, p);
__mpexp (&mpx, &mpy, p);
__mp_dbl (&mpy, &res, p);
return res;
}
#else
return (double) __ieee754_expl((long double)x);
#endif
}
void __mplog(mp_no *x, mp_no *y, int p) {
#include "mplog.h"
int i,m;
#if 0
int j,k,m1,m2,n;
double a,b;
#endif
static const int mp[33] = {0,0,0,0,0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,
4,4,4,4,4,4,4,4,4,4,4,4,4,4};
mp_no mpone = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
mp_no mpt1,mpt2;
/* Choose m and initiate mpone */
m = mp[p]; mpone.e = 1; mpone.d[0]=mpone.d[1]=ONE;
/* Perform m newton iterations to solve for y: exp(y)-x=0. */
/* The iterations formula is: y(n+1)=y(n)+(x*exp(-y(n))-1). */
__cpy(y,&mpt1,p);
for (i=0; i<m; i++) {
mpt1.d[0]=-mpt1.d[0];
__mpexp(&mpt1,&mpt2,p);
__mul(x,&mpt2,&mpt1,p);
__sub(&mpt1,&mpone,&mpt2,p);
__add(y,&mpt2,&mpt1,p);
__cpy(&mpt1,y,p);
}
return;
}
/*Converting from double precision to Multi-precision and calculating e^x */
double
SECTION
__slowexp (double x)
{
#ifndef USE_LONG_DOUBLE_FOR_MP
double w, z, res, eps = 3.0e-26;
int p;
mp_no mpx, mpy, mpz, mpw, mpeps, mpcor;
/* Use the multiple precision __MPEXP function to compute the exponential
First at 144 bits and if it is not accurate enough, at 768 bits. */
p = 6;
__dbl_mp (x, &mpx, p);
__mpexp (&mpx, &mpy, p);
__dbl_mp (eps, &mpeps, p);
__mul (&mpeps, &mpy, &mpcor, p);
__add (&mpy, &mpcor, &mpw, p);
__sub (&mpy, &mpcor, &mpz, p);
__mp_dbl (&mpw, &w, p);
__mp_dbl (&mpz, &z, p);
if (w == z)
{
/* Track how often we get to the slow exp code plus
its input/output values. */
LIBC_PROBE (slowexp_p6, 2, &x, &w);
return w;
}
else
{
p = 32;
__dbl_mp (x, &mpx, p);
__mpexp (&mpx, &mpy, p);
__mp_dbl (&mpy, &res, p);
/* Track how often we get to the uber-slow exp code plus
its input/output values. */
LIBC_PROBE (slowexp_p32, 2, &x, &res);
return res;
}
#else
return (double) __ieee754_expl((long double)x);
#endif
}
/*Converting from double precision to Multi-precision and calculating e^x */
double __slowexp(double x) {
double w,z,res,eps=3.0e-26;
#if 0
double y;
#endif
int p;
#if 0
int orig,i;
#endif
mp_no mpx, mpy, mpz,mpw,mpeps,mpcor;
p=6;
__dbl_mp(x,&mpx,p); /* Convert a double precision number x */
/* into a multiple precision number mpx with prec. p. */
__mpexp(&mpx, &mpy, p); /* Multi-Precision exponential function */
__dbl_mp(eps,&mpeps,p);
__mul(&mpeps,&mpy,&mpcor,p);
__add(&mpy,&mpcor,&mpw,p);
__sub(&mpy,&mpcor,&mpz,p);
__mp_dbl(&mpw, &w, p);
__mp_dbl(&mpz, &z, p);
if (w == z) {
/* Track how often we get to the slow exp code plus
its input/output values. */
LIBC_PROBE (slowexp_p6, 2, &x, &w);
return w;
}
else { /* if calculating is not exactly */
p = 32;
__dbl_mp(x,&mpx,p);
__mpexp(&mpx, &mpy, p);
__mp_dbl(&mpy, &res, p);
/* Track how often we get to the uber-slow exp code plus
its input/output values. */
LIBC_PROBE (slowexp_p32, 2, &x, &res);
return res;
}
}
