mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-25 10:43:34 +08:00
Format e_exp.c
This commit is contained in:
Siddhesh Poyarekar
parent
09544cbcd6
commit
e7b2d1dd62
@ -1,5 +1,7 @@
|
||||
2013-10-08 Siddhesh Poyarekar <siddhesh@redhat.com>
|
||||
|
||||
* sysdeps/ieee754/dbl-64/e_exp.c: Fix code formatting.
|
||||
|
||||
* sysdeps/generic/math_private.h (__mpsin1): Remove
|
||||
declaration.
|
||||
(__mpcos1): Likewise.
|
||||
|
||||
@ -44,221 +44,299 @@
|
||||
# define SECTION
|
||||
#endif
|
||||
|
||||
double __slowexp(double);
|
||||
double __slowexp (double);
|
||||
|
||||
/***************************************************************************/
|
||||
/* An ultimate exp routine. Given an IEEE double machine number x */
|
||||
/* it computes the correctly rounded (to nearest) value of e^x */
|
||||
/***************************************************************************/
|
||||
/* An ultimate exp routine. Given an IEEE double machine number x it computes
|
||||
the correctly rounded (to nearest) value of e^x. */
|
||||
double
|
||||
SECTION
|
||||
__ieee754_exp(double x) {
|
||||
__ieee754_exp (double x)
|
||||
{
|
||||
double bexp, t, eps, del, base, y, al, bet, res, rem, cor;
|
||||
mynumber junk1, junk2, binexp = {{0,0}};
|
||||
int4 i,j,m,n,ex;
|
||||
mynumber junk1, junk2, binexp = {{0, 0}};
|
||||
int4 i, j, m, n, ex;
|
||||
double retval;
|
||||
|
||||
SET_RESTORE_ROUND (FE_TONEAREST);
|
||||
|
||||
junk1.x = x;
|
||||
m = junk1.i[HIGH_HALF];
|
||||
n = m&hugeint;
|
||||
n = m & hugeint;
|
||||
|
||||
if (n > smallint && n < bigint) {
|
||||
if (n > smallint && n < bigint)
|
||||
{
|
||||
y = x * log2e.x + three51.x;
|
||||
bexp = y - three51.x; /* multiply the result by 2**bexp */
|
||||
|
||||
y = x*log2e.x + three51.x;
|
||||
bexp = y - three51.x; /* multiply the result by 2**bexp */
|
||||
junk1.x = y;
|
||||
|
||||
junk1.x = y;
|
||||
eps = bexp * ln_two2.x; /* x = bexp*ln(2) + t - eps */
|
||||
t = x - bexp * ln_two1.x;
|
||||
|
||||
eps = bexp*ln_two2.x; /* x = bexp*ln(2) + t - eps */
|
||||
t = x - bexp*ln_two1.x;
|
||||
y = t + three33.x;
|
||||
base = y - three33.x; /* t rounded to a multiple of 2**-18 */
|
||||
junk2.x = y;
|
||||
del = (t - base) - eps; /* x = bexp*ln(2) + base + del */
|
||||
eps = del + del * del * (p3.x * del + p2.x);
|
||||
|
||||
y = t + three33.x;
|
||||
base = y - three33.x; /* t rounded to a multiple of 2**-18 */
|
||||
junk2.x = y;
|
||||
del = (t - base) - eps; /* x = bexp*ln(2) + base + del */
|
||||
eps = del + del*del*(p3.x*del + p2.x);
|
||||
binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 1023) << 20;
|
||||
|
||||
binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+1023)<<20;
|
||||
i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356;
|
||||
j = (junk2.i[LOW_HALF] & 511) << 1;
|
||||
|
||||
i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
|
||||
j = (junk2.i[LOW_HALF]&511)<<1;
|
||||
al = coar.x[i] * fine.x[j];
|
||||
bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j])
|
||||
+ coar.x[i + 1] * fine.x[j + 1]);
|
||||
|
||||
al = coar.x[i]*fine.x[j];
|
||||
bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];
|
||||
rem = (bet + bet * eps) + al * eps;
|
||||
res = al + rem;
|
||||
cor = (al - res) + rem;
|
||||
if (res == (res + cor * err_0))
|
||||
{
|
||||
retval = res * binexp.x;
|
||||
goto ret;
|
||||
}
|
||||
else
|
||||
{
|
||||
retval = __slowexp (x);
|
||||
goto ret;
|
||||
} /*if error is over bound */
|
||||
}
|
||||
|
||||
rem=(bet + bet*eps)+al*eps;
|
||||
res = al + rem;
|
||||
cor = (al - res) + rem;
|
||||
if (res == (res+cor*err_0)) { retval = res*binexp.x; goto ret; }
|
||||
else { retval = __slowexp(x); goto ret; } /*if error is over bound */
|
||||
}
|
||||
if (n <= smallint)
|
||||
{
|
||||
retval = 1.0;
|
||||
goto ret;
|
||||
}
|
||||
|
||||
if (n <= smallint) { retval = 1.0; goto ret; }
|
||||
if (n >= badint)
|
||||
{
|
||||
if (n > infint)
|
||||
{
|
||||
retval = x + x;
|
||||
goto ret;
|
||||
} /* x is NaN */
|
||||
if (n < infint)
|
||||
{
|
||||
retval = (x > 0) ? (hhuge * hhuge) : (tiny * tiny);
|
||||
goto ret;
|
||||
}
|
||||
/* x is finite, cause either overflow or underflow */
|
||||
if (junk1.i[LOW_HALF] != 0)
|
||||
{
|
||||
retval = x + x;
|
||||
goto ret;
|
||||
} /* x is NaN */
|
||||
retval = (x > 0) ? inf.x : zero; /* |x| = inf; return either inf or 0 */
|
||||
goto ret;
|
||||
}
|
||||
|
||||
if (n >= badint) {
|
||||
if (n > infint) { retval = x+x; goto ret; } /* x is NaN */
|
||||
if (n < infint) { retval = (x>0) ? (hhuge*hhuge) : (tiny*tiny); goto ret; }
|
||||
/* x is finite, cause either overflow or underflow */
|
||||
if (junk1.i[LOW_HALF] != 0) { retval = x+x; goto ret; } /* x is NaN */
|
||||
retval = (x>0)?inf.x:zero; /* |x| = inf; return either inf or 0 */
|
||||
goto ret;
|
||||
}
|
||||
|
||||
y = x*log2e.x + three51.x;
|
||||
y = x * log2e.x + three51.x;
|
||||
bexp = y - three51.x;
|
||||
junk1.x = y;
|
||||
eps = bexp*ln_two2.x;
|
||||
t = x - bexp*ln_two1.x;
|
||||
eps = bexp * ln_two2.x;
|
||||
t = x - bexp * ln_two1.x;
|
||||
y = t + three33.x;
|
||||
base = y - three33.x;
|
||||
junk2.x = y;
|
||||
del = (t - base) - eps;
|
||||
eps = del + del*del*(p3.x*del + p2.x);
|
||||
i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
|
||||
j = (junk2.i[LOW_HALF]&511)<<1;
|
||||
al = coar.x[i]*fine.x[j];
|
||||
bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];
|
||||
rem=(bet + bet*eps)+al*eps;
|
||||
eps = del + del * del * (p3.x * del + p2.x);
|
||||
i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356;
|
||||
j = (junk2.i[LOW_HALF] & 511) << 1;
|
||||
al = coar.x[i] * fine.x[j];
|
||||
bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j])
|
||||
+ coar.x[i + 1] * fine.x[j + 1]);
|
||||
rem = (bet + bet * eps) + al * eps;
|
||||
res = al + rem;
|
||||
cor = (al - res) + rem;
|
||||
if (m>>31) {
|
||||
ex=junk1.i[LOW_HALF];
|
||||
if (res < 1.0) {res+=res; cor+=cor; ex-=1;}
|
||||
if (ex >=-1022) {
|
||||
binexp.i[HIGH_HALF] = (1023+ex)<<20;
|
||||
if (res == (res+cor*err_0)) { retval = res*binexp.x; goto ret; }
|
||||
else { retval = __slowexp(x); goto ret; } /*if error is over bound */
|
||||
if (m >> 31)
|
||||
{
|
||||
ex = junk1.i[LOW_HALF];
|
||||
if (res < 1.0)
|
||||
{
|
||||
res += res;
|
||||
cor += cor;
|
||||
ex -= 1;
|
||||
}
|
||||
if (ex >= -1022)
|
||||
{
|
||||
binexp.i[HIGH_HALF] = (1023 + ex) << 20;
|
||||
if (res == (res + cor * err_0))
|
||||
{
|
||||
retval = res * binexp.x;
|
||||
goto ret;
|
||||
}
|
||||
else
|
||||
{
|
||||
retval = __slowexp (x);
|
||||
goto ret;
|
||||
} /*if error is over bound */
|
||||
}
|
||||
ex = -(1022 + ex);
|
||||
binexp.i[HIGH_HALF] = (1023 - ex) << 20;
|
||||
res *= binexp.x;
|
||||
cor *= binexp.x;
|
||||
eps = 1.0000000001 + err_0 * binexp.x;
|
||||
t = 1.0 + res;
|
||||
y = ((1.0 - t) + res) + cor;
|
||||
res = t + y;
|
||||
cor = (t - res) + y;
|
||||
if (res == (res + eps * cor))
|
||||
{
|
||||
binexp.i[HIGH_HALF] = 0x00100000;
|
||||
retval = (res - 1.0) * binexp.x;
|
||||
goto ret;
|
||||
}
|
||||
else
|
||||
{
|
||||
retval = __slowexp (x);
|
||||
goto ret;
|
||||
} /* if error is over bound */
|
||||
}
|
||||
ex = -(1022+ex);
|
||||
binexp.i[HIGH_HALF] = (1023-ex)<<20;
|
||||
res*=binexp.x;
|
||||
cor*=binexp.x;
|
||||
eps=1.0000000001+err_0*binexp.x;
|
||||
t=1.0+res;
|
||||
y = ((1.0-t)+res)+cor;
|
||||
res=t+y;
|
||||
cor = (t-res)+y;
|
||||
if (res == (res + eps*cor))
|
||||
{ binexp.i[HIGH_HALF] = 0x00100000;
|
||||
retval = (res-1.0)*binexp.x;
|
||||
goto ret;
|
||||
else
|
||||
{
|
||||
binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 767) << 20;
|
||||
if (res == (res + cor * err_0))
|
||||
{
|
||||
retval = res * binexp.x * t256.x;
|
||||
goto ret;
|
||||
}
|
||||
else
|
||||
{
|
||||
retval = __slowexp (x);
|
||||
goto ret;
|
||||
}
|
||||
}
|
||||
else { retval = __slowexp(x); goto ret; } /* if error is over bound */
|
||||
}
|
||||
else {
|
||||
binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+767)<<20;
|
||||
if (res == (res+cor*err_0)) { retval = res*binexp.x*t256.x; goto ret; }
|
||||
else { retval = __slowexp(x); goto ret; }
|
||||
}
|
||||
ret:
|
||||
ret:
|
||||
return retval;
|
||||
}
|
||||
#ifndef __ieee754_exp
|
||||
strong_alias (__ieee754_exp, __exp_finite)
|
||||
#endif
|
||||
|
||||
/************************************************************************/
|
||||
/* Compute e^(x+xx)(Double-Length number) .The routine also receive */
|
||||
/* bound of error of previous calculation .If after computing exp */
|
||||
/* error bigger than allows routine return non positive number */
|
||||
/*else return e^(x + xx) (always positive ) */
|
||||
/************************************************************************/
|
||||
|
||||
/* Compute e^(x+xx). The routine also receives bound of error of previous
|
||||
calculation. If after computing exp the error exceeds the allowed bounds,
|
||||
the routine returns a non-positive number. Otherwise it returns the
|
||||
computed result, which is always positive. */
|
||||
double
|
||||
SECTION
|
||||
__exp1(double x, double xx, double error) {
|
||||
__exp1 (double x, double xx, double error)
|
||||
{
|
||||
double bexp, t, eps, del, base, y, al, bet, res, rem, cor;
|
||||
mynumber junk1, junk2, binexp = {{0,0}};
|
||||
int4 i,j,m,n,ex;
|
||||
mynumber junk1, junk2, binexp = {{0, 0}};
|
||||
int4 i, j, m, n, ex;
|
||||
|
||||
junk1.x = x;
|
||||
m = junk1.i[HIGH_HALF];
|
||||
n = m&hugeint; /* no sign */
|
||||
n = m & hugeint; /* no sign */
|
||||
|
||||
if (n > smallint && n < bigint) {
|
||||
y = x*log2e.x + three51.x;
|
||||
bexp = y - three51.x; /* multiply the result by 2**bexp */
|
||||
if (n > smallint && n < bigint)
|
||||
{
|
||||
y = x * log2e.x + three51.x;
|
||||
bexp = y - three51.x; /* multiply the result by 2**bexp */
|
||||
|
||||
junk1.x = y;
|
||||
junk1.x = y;
|
||||
|
||||
eps = bexp*ln_two2.x; /* x = bexp*ln(2) + t - eps */
|
||||
t = x - bexp*ln_two1.x;
|
||||
eps = bexp * ln_two2.x; /* x = bexp*ln(2) + t - eps */
|
||||
t = x - bexp * ln_two1.x;
|
||||
|
||||
y = t + three33.x;
|
||||
base = y - three33.x; /* t rounded to a multiple of 2**-18 */
|
||||
junk2.x = y;
|
||||
del = (t - base) + (xx-eps); /* x = bexp*ln(2) + base + del */
|
||||
eps = del + del*del*(p3.x*del + p2.x);
|
||||
y = t + three33.x;
|
||||
base = y - three33.x; /* t rounded to a multiple of 2**-18 */
|
||||
junk2.x = y;
|
||||
del = (t - base) + (xx - eps); /* x = bexp*ln(2) + base + del */
|
||||
eps = del + del * del * (p3.x * del + p2.x);
|
||||
|
||||
binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+1023)<<20;
|
||||
binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 1023) << 20;
|
||||
|
||||
i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
|
||||
j = (junk2.i[LOW_HALF]&511)<<1;
|
||||
i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356;
|
||||
j = (junk2.i[LOW_HALF] & 511) << 1;
|
||||
|
||||
al = coar.x[i]*fine.x[j];
|
||||
bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];
|
||||
al = coar.x[i] * fine.x[j];
|
||||
bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j])
|
||||
+ coar.x[i + 1] * fine.x[j + 1]);
|
||||
|
||||
rem=(bet + bet*eps)+al*eps;
|
||||
res = al + rem;
|
||||
cor = (al - res) + rem;
|
||||
if (res == (res+cor*(1.0+error+err_1))) return res*binexp.x;
|
||||
else return -10.0;
|
||||
}
|
||||
rem = (bet + bet * eps) + al * eps;
|
||||
res = al + rem;
|
||||
cor = (al - res) + rem;
|
||||
if (res == (res + cor * (1.0 + error + err_1)))
|
||||
return res * binexp.x;
|
||||
else
|
||||
return -10.0;
|
||||
}
|
||||
|
||||
if (n <= smallint) return 1.0; /* if x->0 e^x=1 */
|
||||
if (n <= smallint)
|
||||
return 1.0; /* if x->0 e^x=1 */
|
||||
|
||||
if (n >= badint) {
|
||||
if (n > infint) return(zero/zero); /* x is NaN, return invalid */
|
||||
if (n < infint) return ( (x>0) ? (hhuge*hhuge) : (tiny*tiny) );
|
||||
/* x is finite, cause either overflow or underflow */
|
||||
if (junk1.i[LOW_HALF] != 0) return (zero/zero); /* x is NaN */
|
||||
return ((x>0)?inf.x:zero ); /* |x| = inf; return either inf or 0 */
|
||||
}
|
||||
if (n >= badint)
|
||||
{
|
||||
if (n > infint)
|
||||
return (zero / zero); /* x is NaN, return invalid */
|
||||
if (n < infint)
|
||||
return ((x > 0) ? (hhuge * hhuge) : (tiny * tiny));
|
||||
/* x is finite, cause either overflow or underflow */
|
||||
if (junk1.i[LOW_HALF] != 0)
|
||||
return (zero / zero); /* x is NaN */
|
||||
return ((x > 0) ? inf.x : zero); /* |x| = inf; return either inf or 0 */
|
||||
}
|
||||
|
||||
y = x*log2e.x + three51.x;
|
||||
y = x * log2e.x + three51.x;
|
||||
bexp = y - three51.x;
|
||||
junk1.x = y;
|
||||
eps = bexp*ln_two2.x;
|
||||
t = x - bexp*ln_two1.x;
|
||||
eps = bexp * ln_two2.x;
|
||||
t = x - bexp * ln_two1.x;
|
||||
y = t + three33.x;
|
||||
base = y - three33.x;
|
||||
junk2.x = y;
|
||||
del = (t - base) + (xx-eps);
|
||||
eps = del + del*del*(p3.x*del + p2.x);
|
||||
i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
|
||||
j = (junk2.i[LOW_HALF]&511)<<1;
|
||||
al = coar.x[i]*fine.x[j];
|
||||
bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];
|
||||
rem=(bet + bet*eps)+al*eps;
|
||||
del = (t - base) + (xx - eps);
|
||||
eps = del + del * del * (p3.x * del + p2.x);
|
||||
i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356;
|
||||
j = (junk2.i[LOW_HALF] & 511) << 1;
|
||||
al = coar.x[i] * fine.x[j];
|
||||
bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j])
|
||||
+ coar.x[i + 1] * fine.x[j + 1]);
|
||||
rem = (bet + bet * eps) + al * eps;
|
||||
res = al + rem;
|
||||
cor = (al - res) + rem;
|
||||
if (m>>31) {
|
||||
ex=junk1.i[LOW_HALF];
|
||||
if (res < 1.0) {res+=res; cor+=cor; ex-=1;}
|
||||
if (ex >=-1022) {
|
||||
binexp.i[HIGH_HALF] = (1023+ex)<<20;
|
||||
if (res == (res+cor*(1.0+error+err_1))) return res*binexp.x;
|
||||
else return -10.0;
|
||||
if (m >> 31)
|
||||
{
|
||||
ex = junk1.i[LOW_HALF];
|
||||
if (res < 1.0)
|
||||
{
|
||||
res += res;
|
||||
cor += cor;
|
||||
ex -= 1;
|
||||
}
|
||||
if (ex >= -1022)
|
||||
{
|
||||
binexp.i[HIGH_HALF] = (1023 + ex) << 20;
|
||||
if (res == (res + cor * (1.0 + error + err_1)))
|
||||
return res * binexp.x;
|
||||
else
|
||||
return -10.0;
|
||||
}
|
||||
ex = -(1022 + ex);
|
||||
binexp.i[HIGH_HALF] = (1023 - ex) << 20;
|
||||
res *= binexp.x;
|
||||
cor *= binexp.x;
|
||||
eps = 1.00000000001 + (error + err_1) * binexp.x;
|
||||
t = 1.0 + res;
|
||||
y = ((1.0 - t) + res) + cor;
|
||||
res = t + y;
|
||||
cor = (t - res) + y;
|
||||
if (res == (res + eps * cor))
|
||||
{
|
||||
binexp.i[HIGH_HALF] = 0x00100000;
|
||||
return (res - 1.0) * binexp.x;
|
||||
}
|
||||
else
|
||||
return -10.0;
|
||||
}
|
||||
else
|
||||
{
|
||||
binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 767) << 20;
|
||||
if (res == (res + cor * (1.0 + error + err_1)))
|
||||
return res * binexp.x * t256.x;
|
||||
else
|
||||
return -10.0;
|
||||
}
|
||||
ex = -(1022+ex);
|
||||
binexp.i[HIGH_HALF] = (1023-ex)<<20;
|
||||
res*=binexp.x;
|
||||
cor*=binexp.x;
|
||||
eps=1.00000000001+(error+err_1)*binexp.x;
|
||||
t=1.0+res;
|
||||
y = ((1.0-t)+res)+cor;
|
||||
res=t+y;
|
||||
cor = (t-res)+y;
|
||||
if (res == (res + eps*cor))
|
||||
{binexp.i[HIGH_HALF] = 0x00100000; return (res-1.0)*binexp.x;}
|
||||
else return -10.0;
|
||||
}
|
||||
else {
|
||||
binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+767)<<20;
|
||||
if (res == (res+cor*(1.0+error+err_1)))
|
||||
return res*binexp.x*t256.x;
|
||||
else return -10.0;
|
||||
}
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user