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Format e_pow.c

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Siddhesh Poyarekar 2013-10-08 16:23:16 +05:30
parent e7b2d1dd62
commit 885766357d
2 changed files with 315 additions and 260 deletions
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@ -1,5 +1,7 @@
2013-10-08 Siddhesh Poyarekar <siddhesh@redhat.com> 2013-10-08 Siddhesh Poyarekar <siddhesh@redhat.com>
* sysdeps/ieee754/dbl-64/e_pow.c: Fix code formatting.
* sysdeps/ieee754/dbl-64/e_exp.c: Fix code formatting. * sysdeps/ieee754/dbl-64/e_exp.c: Fix code formatting.
* sysdeps/generic/math_private.h (__mpsin1): Remove * sysdeps/generic/math_private.h (__mpsin1): Remove

573
sysdeps/ieee754/dbl-64/e_pow.c
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@ -49,354 +49,407 @@
static const double huge = 1.0e300, tiny = 1.0e-300; static const double huge = 1.0e300, tiny = 1.0e-300;
double __exp1(double x, double xx, double error); double __exp1 (double x, double xx, double error);
static double log1(double x, double *delta, double *error); static double log1 (double x, double *delta, double *error);
static double my_log2(double x, double *delta, double *error); static double my_log2 (double x, double *delta, double *error);
double __slowpow(double x, double y,double z); double __slowpow (double x, double y, double z);
static double power1(double x, double y); static double power1 (double x, double y);
static int checkint(double x); static int checkint (double x);
/***************************************************************************/ /* An ultimate power routine. Given two IEEE double machine numbers y, x it
/* An ultimate power routine. Given two IEEE double machine numbers y,x */ computes the correctly rounded (to nearest) value of X^y. */
/* it computes the correctly rounded (to nearest) value of X^y. */
/***************************************************************************/
double double
SECTION SECTION
__ieee754_pow(double x, double y) { __ieee754_pow (double x, double y)
double z,a,aa,error, t,a1,a2,y1,y2; {
mynumber u,v; double z, a, aa, error, t, a1, a2, y1, y2;
mynumber u, v;
int k; int k;
int4 qx,qy; int4 qx, qy;
v.x=y; v.x = y;
u.x=x; u.x = x;
if (v.i[LOW_HALF] == 0) { /* of y */ if (v.i[LOW_HALF] == 0)
qx = u.i[HIGH_HALF]&0x7fffffff; { /* of y */
/* Is x a NaN? */ qx = u.i[HIGH_HALF] & 0x7fffffff;
if (((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000)) /* Is x a NaN? */
return x; if (((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000))
if (y == 1.0) return x; return x;
if (y == 2.0) return x*x; if (y == 1.0)
if (y == -1.0) return 1.0/x; return x;
if (y == 0) return 1.0; if (y == 2.0)
} return x * x;
if (y == -1.0)
return 1.0 / x;
if (y == 0)
return 1.0;
}
/* else */ /* else */
if(((u.i[HIGH_HALF]>0 && u.i[HIGH_HALF]<0x7ff00000)|| /* x>0 and not x->0 */ 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)) && (u.i[HIGH_HALF] == 0 && u.i[LOW_HALF] != 0)) &&
/* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */ /* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */
(v.i[HIGH_HALF]&0x7fffffff) < 0x4ff00000) { /* if y<-1 or y>1 */ (v.i[HIGH_HALF] & 0x7fffffff) < 0x4ff00000)
double retval; { /* if y<-1 or y>1 */
double retval;
SET_RESTORE_ROUND (FE_TONEAREST); SET_RESTORE_ROUND (FE_TONEAREST);
/* Avoid internal underflow for tiny y. The exact value of y does /* Avoid internal underflow for tiny y. The exact value of y does
not matter if |y| <= 2**-64. */ not matter if |y| <= 2**-64. */
if (ABS (y) < 0x1p-64) if (ABS (y) < 0x1p-64)
y = y < 0 ? -0x1p-64 : 0x1p-64; y = y < 0 ? -0x1p-64 : 0x1p-64;
z = log1(x,&aa,&error); /* x^y =e^(y log (X)) */ z = log1 (x, &aa, &error); /* x^y =e^(y log (X)) */
t = y*CN; t = y * CN;
y1 = t - (t-y); y1 = t - (t - y);
y2 = y - y1; y2 = y - y1;
t = z*CN; t = z * CN;
a1 = t - (t-z); a1 = t - (t - z);
a2 = (z - a1)+aa; a2 = (z - a1) + aa;
a = y1*a1; a = y1 * a1;
aa = y2*a1 + y*a2; aa = y2 * a1 + y * a2;
a1 = a+aa; a1 = a + aa;
a2 = (a-a1)+aa; a2 = (a - a1) + aa;
error = error*ABS(y); error = error * ABS (y);
t = __exp1(a1,a2,1.9e16*error); /* return -10 or 0 if wasn't computed exactly */ t = __exp1 (a1, a2, 1.9e16 * error); /* return -10 or 0 if wasn't computed exactly */
retval = (t>0)?t:power1(x,y); retval = (t > 0) ? t : power1 (x, y);
return retval; return retval;
} }
if (x == 0) { if (x == 0)
if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0) {
|| (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */ if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0)
return y; || (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */
if (ABS(y) > 1.0e20) return (y>0)?0:1.0/0.0; return y;
k = checkint(y); if (ABS (y) > 1.0e20)
if (k == -1) return (y > 0) ? 0 : 1.0 / 0.0;
return y < 0 ? 1.0/x : x; k = checkint (y);
else if (k == -1)
return y < 0 ? 1.0/0.0 : 0.0; /* return 0 */ 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 */ qx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */
qy = v.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 */ if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) /* NaN */
return x; return x;
if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0)) /* NaN */ if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0)) /* NaN */
return x == 1.0 ? 1.0 : y; return x == 1.0 ? 1.0 : y;
/* if x<0 */ /* if x<0 */
if (u.i[HIGH_HALF] < 0) { if (u.i[HIGH_HALF] < 0)
k = checkint(y); {
if (k==0) { k = checkint (y);
if (qy == 0x7ff00000) { if (k == 0)
if (x == -1.0) return 1.0; {
else if (x > -1.0) return v.i[HIGH_HALF] < 0 ? INF.x : 0.0; if (qy == 0x7ff00000)
else return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x; {
} 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) else if (qx == 0x7ff00000)
return y < 0 ? 0.0 : INF.x; {
return (x - x) / (x - x); /* y not integer and x<0 */ if (k < 0)
return y < 0 ? nZERO.x : nINF.x;
else
return y < 0 ? 0.0 : INF.x;
}
/* if y even or odd */
return (k == 1) ? __ieee754_pow (-x, y) : -__ieee754_pow (-x, y);
} }
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 */ /* x>0 */
if (qx == 0x7ff00000) /* x= 2^-0x3ff */ if (qx == 0x7ff00000) /* x= 2^-0x3ff */
return y > 0 ? x : 0; return y > 0 ? x : 0;
if (qy > 0x45f00000 && qy < 0x7ff00000) { if (qy > 0x45f00000 && qy < 0x7ff00000)
if (x == 1.0) return 1.0; {
if (y>0) return (x>1.0)?huge*huge:tiny*tiny; if (x == 1.0)
if (y<0) return (x<1.0)?huge*huge:tiny*tiny; 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 (x == 1.0)
if (y>0) return (x>1.0)?INF.x:0; return 1.0;
if (y<0) return (x<1.0)?INF.x:0; if (y > 0)
return 0; /* unreachable, to make the compiler happy */ 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 */
} }
#ifndef __ieee754_pow #ifndef __ieee754_pow
strong_alias (__ieee754_pow, __pow_finite) strong_alias (__ieee754_pow, __pow_finite)
#endif #endif
/**************************************************************************/ /* Compute x^y using more accurate but more slow log routine. */
/* Computing x^y using more accurate but more slow log routine */
/**************************************************************************/
static double static double
SECTION SECTION
power1(double x, double y) { power1 (double x, double y)
double z,a,aa,error, t,a1,a2,y1,y2; {
z = my_log2(x,&aa,&error); double z, a, aa, error, t, a1, a2, y1, y2;
t = y*CN; z = my_log2 (x, &aa, &error);
y1 = t - (t-y); t = y * CN;
y1 = t - (t - y);
y2 = y - y1; y2 = y - y1;
t = z*CN; t = z * CN;
a1 = t - (t-z); a1 = t - (t - z);
a2 = z - a1; a2 = z - a1;
a = y*z; a = y * z;
aa = ((y1*a1-a)+y1*a2+y2*a1)+y2*a2+aa*y; aa = ((y1 * a1 - a) + y1 * a2 + y2 * a1) + y2 * a2 + aa * y;
a1 = a+aa; a1 = a + aa;
a2 = (a-a1)+aa; a2 = (a - a1) + aa;
error = error*ABS(y); error = error * ABS (y);
t = __exp1(a1,a2,1.9e16*error); t = __exp1 (a1, a2, 1.9e16 * error);
return (t >= 0)?t:__slowpow(x,y,z); return (t >= 0) ? t : __slowpow (x, y, z);
} }
/****************************************************************************/ /* Compute log(x) (x is left argument). The result is the returned double + the
/* Computing log(x) (x is left argument). The result is the returned double */ parameter DELTA. The result is bounded by ERROR. */
/* + the parameter delta. */
/* The result is bounded by error (rightmost argument) */
/****************************************************************************/
static double static double
SECTION SECTION
log1(double x, double *delta, double *error) { log1 (double x, double *delta, double *error)
int i,j,m; {
double uu,vv,eps,nx,e,e1,e2,t,t1,t2,res,add=0; int i, j, m;
mynumber u,v; double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0;
mynumber u, v;
#ifdef BIG_ENDI #ifdef BIG_ENDI
mynumber mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */
/**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */
#else #else
#ifdef LITTLE_ENDI # ifdef LITTLE_ENDI
mynumber mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */
/**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */ # endif
#endif
#endif #endif
u.x = x; u.x = x;
m = u.i[HIGH_HALF]; m = u.i[HIGH_HALF];
*error = 0; *error = 0;
*delta = 0; *delta = 0;
if (m < 0x00100000) /* 1<x<2^-1007 */ if (m < 0x00100000) /* 1<x<2^-1007 */
{ x = x*t52.x; add = -52.0; u.x = x; m = u.i[HIGH_HALF];} {
x = x * t52.x;
add = -52.0;
u.x = x;
m = u.i[HIGH_HALF];
}
if ((m&0x000fffff) < 0x0006a09e) if ((m & 0x000fffff) < 0x0006a09e)
{u.i[HIGH_HALF] = (m&0x000fffff)|0x3ff00000; two52.i[LOW_HALF]=(m>>20); } {
u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000;
two52.i[LOW_HALF] = (m >> 20);
}
else else
{u.i[HIGH_HALF] = (m&0x000fffff)|0x3fe00000; two52.i[LOW_HALF]=(m>>20)+1; } {
u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000;
two52.i[LOW_HALF] = (m >> 20) + 1;
}
v.x = u.x + bigu.x; v.x = u.x + bigu.x;
uu = v.x - bigu.x; uu = v.x - bigu.x;
i = (v.i[LOW_HALF]&0x000003ff)<<2; i = (v.i[LOW_HALF] & 0x000003ff) << 2;
if (two52.i[LOW_HALF] == 1023) /* nx = 0 */ if (two52.i[LOW_HALF] == 1023) /* nx = 0 */
{ {
if (i > 1192 && i < 1208) /* |x-1| < 1.5*2**-10 */ if (i > 1192 && i < 1208) /* |x-1| < 1.5*2**-10 */
{ {
t = x - 1.0; t = x - 1.0;
t1 = (t+5.0e6)-5.0e6; t1 = (t + 5.0e6) - 5.0e6;
t2 = t-t1; t2 = t - t1;
e1 = t - 0.5*t1*t1; e1 = t - 0.5 * t1 * t1;
e2 = t*t*t*(r3+t*(r4+t*(r5+t*(r6+t*(r7+t*r8)))))-0.5*t2*(t+t1); e2 = (t * t * t * (r3 + t * (r4 + t * (r5 + t * (r6 + t
res = e1+e2; * (r7 + t * r8)))))
*error = 1.0e-21*ABS(t); - 0.5 * t2 * (t + t1));
*delta = (e1-res)+e2; res = e1 + e2;
*error = 1.0e-21 * ABS (t);
*delta = (e1 - res) + e2;
return res; return res;
} /* |x-1| < 1.5*2**-10 */ } /* |x-1| < 1.5*2**-10 */
else else
{ {
v.x = u.x*(ui.x[i]+ui.x[i+1])+bigv.x; v.x = u.x * (ui.x[i] + ui.x[i + 1]) + bigv.x;
vv = v.x-bigv.x; vv = v.x - bigv.x;
j = v.i[LOW_HALF]&0x0007ffff; j = v.i[LOW_HALF] & 0x0007ffff;
j = j+j+j; j = j + j + j;
eps = u.x - uu*vv; eps = u.x - uu * vv;
e1 = eps*ui.x[i]; e1 = eps * ui.x[i];
e2 = eps*(ui.x[i+1]+vj.x[j]*(ui.x[i]+ui.x[i+1])); e2 = eps * (ui.x[i + 1] + vj.x[j] * (ui.x[i] + ui.x[i + 1]));
e = e1+e2; e = e1 + e2;
e2 = ((e1-e)+e2); e2 = ((e1 - e) + e2);
t=ui.x[i+2]+vj.x[j+1]; t = ui.x[i + 2] + vj.x[j + 1];
t1 = t+e; t1 = t + e;
t2 = (((t-t1)+e)+(ui.x[i+3]+vj.x[j+2]))+e2+e*e*(p2+e*(p3+e*p4)); t2 = ((((t - t1) + e) + (ui.x[i + 3] + vj.x[j + 2])) + e2 + e * e
res=t1+t2; * (p2 + e * (p3 + e * p4)));
res = t1 + t2;
*error = 1.0e-24; *error = 1.0e-24;
*delta = (t1-res)+t2; *delta = (t1 - res) + t2;
return res; return res;
} }
} /* nx = 0 */ } /* nx = 0 */
else /* nx != 0 */ else /* nx != 0 */
{ {
eps = u.x - uu; eps = u.x - uu;
nx = (two52.x - two52e.x)+add; nx = (two52.x - two52e.x) + add;
e1 = eps*ui.x[i]; e1 = eps * ui.x[i];
e2 = eps*ui.x[i+1]; e2 = eps * ui.x[i + 1];
e=e1+e2; e = e1 + e2;
e2 = (e1-e)+e2; e2 = (e1 - e) + e2;
t=nx*ln2a.x+ui.x[i+2]; t = nx * ln2a.x + ui.x[i + 2];
t1=t+e; t1 = t + e;
t2=(((t-t1)+e)+nx*ln2b.x+ui.x[i+3]+e2)+e*e*(q2+e*(q3+e*(q4+e*(q5+e*q6)))); t2 = ((((t - t1) + e) + nx * ln2b.x + ui.x[i + 3] + e2) + e * e
res = t1+t2; * (q2 + e * (q3 + e * (q4 + e * (q5 + e * q6)))));
res = t1 + t2;
*error = 1.0e-21; *error = 1.0e-21;
*delta = (t1-res)+t2; *delta = (t1 - res) + t2;
return res; return res;
} /* nx != 0 */ } /* nx != 0 */
} }
/****************************************************************************/ /* Slower but more accurate routine of log. The returned result is double +
/* More slow but more accurate routine of log */ DELTA. The result is bounded by ERROR. */
/* Computing log(x)(x is left argument).The result is return double + delta.*/
/* The result is bounded by error (right argument) */
/****************************************************************************/
static double static double
SECTION SECTION
my_log2(double x, double *delta, double *error) { my_log2 (double x, double *delta, double *error)
int i,j,m; {
double uu,vv,eps,nx,e,e1,e2,t,t1,t2,res,add=0; int i, j, m;
double ou1,ou2,lu1,lu2,ov,lv1,lv2,a,a1,a2; double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0;
double y,yy,z,zz,j1,j2,j7,j8; double ou1, ou2, lu1, lu2, ov, lv1, lv2, a, a1, a2;
double y, yy, z, zz, j1, j2, j7, j8;
#ifndef DLA_FMS #ifndef DLA_FMS
double j3,j4,j5,j6; double j3, j4, j5, j6;
#endif #endif
mynumber u,v; mynumber u, v;
#ifdef BIG_ENDI #ifdef BIG_ENDI
mynumber mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */
/**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */
#else #else
#ifdef LITTLE_ENDI # ifdef LITTLE_ENDI
mynumber mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */
/**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */ # endif
#endif
#endif #endif
u.x = x; u.x = x;
m = u.i[HIGH_HALF]; m = u.i[HIGH_HALF];
*error = 0; *error = 0;
*delta = 0; *delta = 0;
add=0; add = 0;
if (m<0x00100000) { /* x < 2^-1022 */ if (m < 0x00100000)
x = x*t52.x; add = -52.0; u.x = x; m = u.i[HIGH_HALF]; } { /* x < 2^-1022 */
x = x * t52.x;
add = -52.0;
u.x = x;
m = u.i[HIGH_HALF];
}
if ((m&0x000fffff) < 0x0006a09e) if ((m & 0x000fffff) < 0x0006a09e)
{u.i[HIGH_HALF] = (m&0x000fffff)|0x3ff00000; two52.i[LOW_HALF]=(m>>20); } {
u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000;
two52.i[LOW_HALF] = (m >> 20);
}
else else
{u.i[HIGH_HALF] = (m&0x000fffff)|0x3fe00000; two52.i[LOW_HALF]=(m>>20)+1; } {
u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000;
two52.i[LOW_HALF] = (m >> 20) + 1;
}
v.x = u.x + bigu.x; v.x = u.x + bigu.x;
uu = v.x - bigu.x; uu = v.x - bigu.x;
i = (v.i[LOW_HALF]&0x000003ff)<<2; i = (v.i[LOW_HALF] & 0x000003ff) << 2;
/*------------------------------------- |x-1| < 2**-11------------------------------- */ /*------------------------------------- |x-1| < 2**-11------------------------------- */
if ((two52.i[LOW_HALF] == 1023) && (i == 1200)) if ((two52.i[LOW_HALF] == 1023) && (i == 1200))
{ {
t = x - 1.0; t = x - 1.0;
EMULV(t,s3,y,yy,j1,j2,j3,j4,j5); EMULV (t, s3, y, yy, j1, j2, j3, j4, j5);
ADD2(-0.5,0,y,yy,z,zz,j1,j2); ADD2 (-0.5, 0, y, yy, z, zz, j1, j2);
MUL2(t,0,z,zz,y,yy,j1,j2,j3,j4,j5,j6,j7,j8); MUL2 (t, 0, z, zz, y, yy, j1, j2, j3, j4, j5, j6, j7, j8);
MUL2(t,0,y,yy,z,zz,j1,j2,j3,j4,j5,j6,j7,j8); MUL2 (t, 0, y, yy, z, zz, j1, j2, j3, j4, j5, j6, j7, j8);
e1 = t+z; e1 = t + z;
e2 = (((t-e1)+z)+zz)+t*t*t*(ss3+t*(s4+t*(s5+t*(s6+t*(s7+t*s8))))); e2 = ((((t - e1) + z) + zz) + t * t * t
res = e1+e2; * (ss3 + t * (s4 + t * (s5 + t * (s6 + t * (s7 + t * s8))))));
*error = 1.0e-25*ABS(t); res = e1 + e2;
*delta = (e1-res)+e2; *error = 1.0e-25 * ABS (t);
*delta = (e1 - res) + e2;
return res; return res;
} }
/*----------------------------- |x-1| > 2**-11 -------------------------- */ /*----------------------------- |x-1| > 2**-11 -------------------------- */
else else
{ /*Computing log(x) according to log table */ { /*Computing log(x) according to log table */
nx = (two52.x - two52e.x)+add; nx = (two52.x - two52e.x) + add;
ou1 = ui.x[i]; ou1 = ui.x[i];
ou2 = ui.x[i+1]; ou2 = ui.x[i + 1];
lu1 = ui.x[i+2]; lu1 = ui.x[i + 2];
lu2 = ui.x[i+3]; lu2 = ui.x[i + 3];
v.x = u.x*(ou1+ou2)+bigv.x; v.x = u.x * (ou1 + ou2) + bigv.x;
vv = v.x-bigv.x; vv = v.x - bigv.x;
j = v.i[LOW_HALF]&0x0007ffff; j = v.i[LOW_HALF] & 0x0007ffff;
j = j+j+j; j = j + j + j;
eps = u.x - uu*vv; eps = u.x - uu * vv;
ov = vj.x[j]; ov = vj.x[j];
lv1 = vj.x[j+1]; lv1 = vj.x[j + 1];
lv2 = vj.x[j+2]; lv2 = vj.x[j + 2];
a = (ou1+ou2)*(1.0+ov); a = (ou1 + ou2) * (1.0 + ov);
a1 = (a+1.0e10)-1.0e10; a1 = (a + 1.0e10) - 1.0e10;
a2 = a*(1.0-a1*uu*vv); a2 = a * (1.0 - a1 * uu * vv);
e1 = eps*a1; e1 = eps * a1;
e2 = eps*a2; e2 = eps * a2;
e = e1+e2; e = e1 + e2;
e2 = (e1-e)+e2; e2 = (e1 - e) + e2;
t=nx*ln2a.x+lu1+lv1; t = nx * ln2a.x + lu1 + lv1;
t1 = t+e; t1 = t + e;
t2 = (((t-t1)+e)+(lu2+lv2+nx*ln2b.x+e2))+e*e*(p2+e*(p3+e*p4)); t2 = ((((t - t1) + e) + (lu2 + lv2 + nx * ln2b.x + e2)) + e * e
res=t1+t2; * (p2 + e * (p3 + e * p4)));
res = t1 + t2;
*error = 1.0e-27; *error = 1.0e-27;
*delta = (t1-res)+t2; *delta = (t1 - res) + t2;
return res; return res;
} }
} }
/**********************************************************************/ /* This function receives a double x and checks if it is an integer. If not,
/* Routine receives a double x and checks if it is an integer. If not */ it returns 0, else it returns 1 if even or -1 if odd. */
/* it returns 0, else it returns 1 if even or -1 if odd. */
/**********************************************************************/
static int static int
SECTION SECTION
checkint(double x) { checkint (double x)
union {int4 i[2]; double x;} u; {
int k,m,n; union
{
int4 i[2];
double x;
} u;
int k, m, n;
u.x = x; u.x = x;
m = u.i[HIGH_HALF]&0x7fffffff; /* no sign */ m = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */
if (m >= 0x7ff00000) return 0; /* x is +/-inf or NaN */ if (m >= 0x7ff00000)
if (m >= 0x43400000) return 1; /* |x| >= 2**53 */ return 0; /* x is +/-inf or NaN */
if (m < 0x40000000) return 0; /* |x| < 2, can not be 0 or 1 */ if (m >= 0x43400000)
return 1; /* |x| >= 2**53 */
if (m < 0x40000000)
return 0; /* |x| < 2, can not be 0 or 1 */
n = u.i[LOW_HALF]; n = u.i[LOW_HALF];
k = (m>>20)-1023; /* 1 <= k <= 52 */ k = (m >> 20) - 1023; /* 1 <= k <= 52 */
if (k == 52) return (n&1)? -1:1; /* odd or even*/ if (k == 52)
if (k>20) { return (n & 1) ? -1 : 1; /* odd or even */
if (n<<(k-20)) return 0; /* if not integer */ if (k > 20)
return (n<<(k-21))?-1:1; {
} if (n << (k - 20))
if (n) return 0; /*if not integer*/ return 0; /* if not integer */
if (k == 20) return (m&1)? -1:1; return (n << (k - 21)) ? -1 : 1;
if (m<<(k+12)) return 0; }
return (m<<(k+11))?-1:1; if (n)
return 0; /*if not integer */
if (k == 20)
return (m & 1) ? -1 : 1;
if (m << (k + 12))
return 0;
return (m << (k + 11)) ? -1 : 1;
} }