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