Format e_pow.c

1 files changed, 313 insertions, 260 deletions

diff --git a/sysdeps/ieee754/dbl-64/e_pow.c b/sysdeps/ieee754/dbl-64/e_pow.c
index 9a766e7224..9cf2309174 100644
--- a/sysdeps/ieee754/dbl-64/e_pow.c
+++ b/sysdeps/ieee754/dbl-64/e_pow.c
@@ -49,354 +49,407 @@
 
 static const double huge = 1.0e300, tiny = 1.0e-300;
 
-double __exp1(double x, double xx, double error);
-static double log1(double x, double *delta, double *error);
-static double my_log2(double x, double *delta, double *error);
-double __slowpow(double x, double y,double z);
-static double power1(double x, double y);
-static int checkint(double x);
+double __exp1 (double x, double xx, double error);
+static double log1 (double x, double *delta, double *error);
+static double my_log2 (double x, double *delta, double *error);
+double __slowpow (double x, double y, double z);
+static double power1 (double x, double y);
+static int checkint (double x);
 
-/***************************************************************************/
-/* An ultimate power routine. Given two IEEE double machine numbers y,x    */
-/* it computes the correctly rounded (to nearest) value of X^y.            */
-/***************************************************************************/
+/* An ultimate power routine. Given two IEEE double machine numbers y, x it
+   computes the correctly rounded (to nearest) value of X^y.  */
 double
 SECTION
-__ieee754_pow(double x, double y) {
-  double z,a,aa,error, t,a1,a2,y1,y2;
-  mynumber u,v;
+__ieee754_pow (double x, double y)
+{
+  double z, a, aa, error, t, a1, a2, y1, y2;
+  mynumber u, v;
   int k;
-  int4 qx,qy;
-  v.x=y;
-  u.x=x;
-  if (v.i[LOW_HALF] == 0) { /* of y */
-    qx = u.i[HIGH_HALF]&0x7fffffff;
-    /* Is x a NaN?  */
-    if (((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000))
-      return x;
-    if (y == 1.0) return x;
-    if (y == 2.0) return x*x;
-    if (y == -1.0) return 1.0/x;
-    if (y == 0) return 1.0;
-  }
+  int4 qx, qy;
+  v.x = y;
+  u.x = x;
+  if (v.i[LOW_HALF] == 0)
+    {				/* of y */
+      qx = u.i[HIGH_HALF] & 0x7fffffff;
+      /* Is x a NaN?  */
+      if (((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000))
+	return x;
+      if (y == 1.0)
+	return x;
+      if (y == 2.0)
+	return x * x;
+      if (y == -1.0)
+	return 1.0 / x;
+      if (y == 0)
+	return 1.0;
+    }
   /* else */
-  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))  &&
-				      /*   2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */
-      (v.i[HIGH_HALF]&0x7fffffff) < 0x4ff00000) {              /* if y<-1 or y>1   */
-    double retval;
+  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)) &&
+      /*   2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */
+      (v.i[HIGH_HALF] & 0x7fffffff) < 0x4ff00000)
+    {				/* 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
-       not matter if |y| <= 2**-64.  */
-    if (ABS (y) < 0x1p-64)
-      y = y < 0 ? -0x1p-64 : 0x1p-64;
-    z = log1(x,&aa,&error);                                 /* x^y  =e^(y log (X)) */
-    t = y*CN;
-    y1 = t - (t-y);
-    y2 = y - y1;
-    t = z*CN;
-    a1 = t - (t-z);
-    a2 = (z - a1)+aa;
-    a = y1*a1;
-    aa = y2*a1 + y*a2;
-    a1 = a+aa;
-    a2 = (a-a1)+aa;
-    error = error*ABS(y);
-    t = __exp1(a1,a2,1.9e16*error);     /* return -10 or 0 if wasn't computed exactly */
-    retval = (t>0)?t:power1(x,y);
+      /* Avoid internal underflow for tiny y.  The exact value of y does
+         not matter if |y| <= 2**-64.  */
+      if (ABS (y) < 0x1p-64)
+	y = y < 0 ? -0x1p-64 : 0x1p-64;
+      z = log1 (x, &aa, &error);	/* x^y  =e^(y log (X)) */
+      t = y * CN;
+      y1 = t - (t - y);
+      y2 = y - y1;
+      t = z * CN;
+      a1 = t - (t - z);
+      a2 = (z - a1) + aa;
+      a = y1 * a1;
+      aa = y2 * a1 + y * a2;
+      a1 = a + aa;
+      a2 = (a - a1) + aa;
+      error = error * ABS (y);
+      t = __exp1 (a1, a2, 1.9e16 * error);	/* return -10 or 0 if wasn't computed exactly */
+      retval = (t > 0) ? t : power1 (x, y);
 
-    return retval;
-  }
+      return retval;
+    }
 
-  if (x == 0) {
-    if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0)
-	|| (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */
-      return y;
-    if (ABS(y) > 1.0e20) return (y>0)?0:1.0/0.0;
-    k = checkint(y);
-    if (k == -1)
-      return y < 0 ? 1.0/x : x;
-    else
-      return y < 0 ? 1.0/0.0 : 0.0;                               /* return 0 */
-  }
+  if (x == 0)
+    {
+      if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0)
+	  || (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000)	/* NaN */
+	return y;
+      if (ABS (y) > 1.0e20)
+	return (y > 0) ? 0 : 1.0 / 0.0;
+      k = checkint (y);
+      if (k == -1)
+	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   */
-  qy = v.i[HIGH_HALF]&0x7fffffff;  /*   no sign   */
+  qx = u.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;
-  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;
 
   /* if x<0 */
-  if (u.i[HIGH_HALF] < 0) {
-    k = checkint(y);
-    if (k==0) {
-      if (qy == 0x7ff00000) {
-	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;
-      }
+  if (u.i[HIGH_HALF] < 0)
+    {
+      k = checkint (y);
+      if (k == 0)
+	{
+	  if (qy == 0x7ff00000)
+	    {
+	      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)
-	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 */
 
-  if (qx == 0x7ff00000)                              /* x= 2^-0x3ff */
+  if (qx == 0x7ff00000)		/* x= 2^-0x3ff */
     return y > 0 ? x : 0;
 
-  if (qy > 0x45f00000 && qy < 0x7ff00000) {
-    if (x == 1.0) 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 (qy > 0x45f00000 && qy < 0x7ff00000)
+    {
+      if (x == 1.0)
+	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 (y>0) 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 */
+  if (x == 1.0)
+    return 1.0;
+  if (y > 0)
+    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
 strong_alias (__ieee754_pow, __pow_finite)
 #endif
 
-/**************************************************************************/
-/* Computing x^y using more accurate but more slow log routine            */
-/**************************************************************************/
+/* Compute x^y using more accurate but more slow log routine.  */
 static double
 SECTION
-power1(double x, double y) {
-  double z,a,aa,error, t,a1,a2,y1,y2;
-  z = my_log2(x,&aa,&error);
-  t = y*CN;
-  y1 = t - (t-y);
+power1 (double x, double y)
+{
+  double z, a, aa, error, t, a1, a2, y1, y2;
+  z = my_log2 (x, &aa, &error);
+  t = y * CN;
+  y1 = t - (t - y);
   y2 = y - y1;
-  t = z*CN;
-  a1 = t - (t-z);
+  t = z * CN;
+  a1 = t - (t - z);
   a2 = z - a1;
-  a = y*z;
-  aa = ((y1*a1-a)+y1*a2+y2*a1)+y2*a2+aa*y;
-  a1 = a+aa;
-  a2 = (a-a1)+aa;
-  error = error*ABS(y);
-  t = __exp1(a1,a2,1.9e16*error);
-  return (t >= 0)?t:__slowpow(x,y,z);
+  a = y * z;
+  aa = ((y1 * a1 - a) + y1 * a2 + y2 * a1) + y2 * a2 + aa * y;
+  a1 = a + aa;
+  a2 = (a - a1) + aa;
+  error = error * ABS (y);
+  t = __exp1 (a1, a2, 1.9e16 * error);
+  return (t >= 0) ? t : __slowpow (x, y, z);
 }
 
-/****************************************************************************/
-/* Computing log(x) (x is left argument). The result is the returned double */
-/* + the parameter delta.                                                   */
-/* The result is bounded by error (rightmost argument)                      */
-/****************************************************************************/
+/* Compute log(x) (x is left argument). The result is the returned double + the
+   parameter DELTA.  The result is bounded by ERROR.  */
 static double
 SECTION
-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;
-  mynumber u,v;
+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;
+  mynumber u, v;
 #ifdef BIG_ENDI
-  mynumber
-/**/ two52          = {{0x43300000, 0x00000000}}; /* 2**52         */
+  mynumber /**/ two52 = {{0x43300000, 0x00000000}};	/* 2**52  */
 #else
-#ifdef LITTLE_ENDI
-  mynumber
-/**/ two52          = {{0x00000000, 0x43300000}}; /* 2**52         */
-#endif
+# ifdef LITTLE_ENDI
+  mynumber /**/ two52 = {{0x00000000, 0x43300000}};	/* 2**52  */
+# endif
 #endif
 
   u.x = x;
   m = u.i[HIGH_HALF];
   *error = 0;
   *delta = 0;
-  if (m < 0x00100000)             /*  1<x<2^-1007 */
-    { x = x*t52.x; add = -52.0; u.x = x; m = u.i[HIGH_HALF];}
+  if (m < 0x00100000)		/*  1<x<2^-1007 */
+    {
+      x = x * t52.x;
+      add = -52.0;
+      u.x = x;
+      m = u.i[HIGH_HALF];
+    }
 
-  if ((m&0x000fffff) < 0x0006a09e)
-    {u.i[HIGH_HALF] = (m&0x000fffff)|0x3ff00000; two52.i[LOW_HALF]=(m>>20); }
+  if ((m & 0x000fffff) < 0x0006a09e)
+    {
+      u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000;
+      two52.i[LOW_HALF] = (m >> 20);
+    }
   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;
   uu = v.x - bigu.x;
-  i = (v.i[LOW_HALF]&0x000003ff)<<2;
-  if (two52.i[LOW_HALF] == 1023)         /* nx = 0              */
-  {
-      if (i > 1192 && i < 1208)          /* |x-1| < 1.5*2**-10  */
-      {
+  i = (v.i[LOW_HALF] & 0x000003ff) << 2;
+  if (two52.i[LOW_HALF] == 1023)	/* nx = 0              */
+    {
+      if (i > 1192 && i < 1208)	/* |x-1| < 1.5*2**-10  */
+	{
 	  t = x - 1.0;
-	  t1 = (t+5.0e6)-5.0e6;
-	  t2 = t-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);
-	  res = e1+e2;
-	  *error = 1.0e-21*ABS(t);
-	  *delta = (e1-res)+e2;
+	  t1 = (t + 5.0e6) - 5.0e6;
+	  t2 = t - 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));
+	  res = e1 + e2;
+	  *error = 1.0e-21 * ABS (t);
+	  *delta = (e1 - res) + e2;
 	  return res;
-      }                  /* |x-1| < 1.5*2**-10  */
+	}			/* |x-1| < 1.5*2**-10  */
       else
-      {
-	  v.x = u.x*(ui.x[i]+ui.x[i+1])+bigv.x;
-	  vv = v.x-bigv.x;
-	  j = v.i[LOW_HALF]&0x0007ffff;
-	  j = j+j+j;
-	  eps = u.x - uu*vv;
-	  e1 = eps*ui.x[i];
-	  e2 = eps*(ui.x[i+1]+vj.x[j]*(ui.x[i]+ui.x[i+1]));
-	  e = e1+e2;
-	  e2 =  ((e1-e)+e2);
-	  t=ui.x[i+2]+vj.x[j+1];
-	  t1 = t+e;
-	  t2 = (((t-t1)+e)+(ui.x[i+3]+vj.x[j+2]))+e2+e*e*(p2+e*(p3+e*p4));
-	  res=t1+t2;
+	{
+	  v.x = u.x * (ui.x[i] + ui.x[i + 1]) + bigv.x;
+	  vv = v.x - bigv.x;
+	  j = v.i[LOW_HALF] & 0x0007ffff;
+	  j = j + j + j;
+	  eps = u.x - uu * vv;
+	  e1 = eps * ui.x[i];
+	  e2 = eps * (ui.x[i + 1] + vj.x[j] * (ui.x[i] + ui.x[i + 1]));
+	  e = e1 + e2;
+	  e2 = ((e1 - e) + e2);
+	  t = ui.x[i + 2] + vj.x[j + 1];
+	  t1 = t + e;
+	  t2 = ((((t - t1) + e) + (ui.x[i + 3] + vj.x[j + 2])) + e2 + e * e
+		* (p2 + e * (p3 + e * p4)));
+	  res = t1 + t2;
 	  *error = 1.0e-24;
-	  *delta = (t1-res)+t2;
+	  *delta = (t1 - res) + t2;
 	  return res;
-      }
-  }   /* nx = 0 */
-  else                            /* nx != 0   */
-  {
+	}
+    }				/* nx = 0 */
+  else				/* nx != 0   */
+    {
       eps = u.x - uu;
-      nx = (two52.x - two52e.x)+add;
-      e1 = eps*ui.x[i];
-      e2 = eps*ui.x[i+1];
-      e=e1+e2;
-      e2 = (e1-e)+e2;
-      t=nx*ln2a.x+ui.x[i+2];
-      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))));
-      res = t1+t2;
+      nx = (two52.x - two52e.x) + add;
+      e1 = eps * ui.x[i];
+      e2 = eps * ui.x[i + 1];
+      e = e1 + e2;
+      e2 = (e1 - e) + e2;
+      t = nx * ln2a.x + ui.x[i + 2];
+      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)))));
+      res = t1 + t2;
       *error = 1.0e-21;
-      *delta = (t1-res)+t2;
+      *delta = (t1 - res) + t2;
       return res;
-  }                                /* nx != 0   */
+    }				/* nx != 0   */
 }
 
-/****************************************************************************/
-/* More slow but more accurate routine of log                               */
-/* Computing log(x)(x is left argument).The result is return double + delta.*/
-/* The result is bounded by error (right argument)                           */
-/****************************************************************************/
+/* Slower but more accurate routine of log.  The returned result is double +
+   DELTA.  The result is bounded by ERROR.  */
 static double
 SECTION
-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;
-  double ou1,ou2,lu1,lu2,ov,lv1,lv2,a,a1,a2;
-  double y,yy,z,zz,j1,j2,j7,j8;
+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;
+  double ou1, ou2, lu1, lu2, ov, lv1, lv2, a, a1, a2;
+  double y, yy, z, zz, j1, j2, j7, j8;
 #ifndef DLA_FMS
-  double j3,j4,j5,j6;
+  double j3, j4, j5, j6;
 #endif
-  mynumber u,v;
+  mynumber u, v;
 #ifdef BIG_ENDI
-  mynumber
-/**/ two52          = {{0x43300000, 0x00000000}}; /* 2**52         */
+  mynumber /**/ two52 = {{0x43300000, 0x00000000}};	/* 2**52  */
 #else
-#ifdef LITTLE_ENDI
-  mynumber
-/**/ two52          = {{0x00000000, 0x43300000}}; /* 2**52         */
-#endif
+# ifdef LITTLE_ENDI
+  mynumber /**/ two52 = {{0x00000000, 0x43300000}};	/* 2**52  */
+# endif
 #endif
 
   u.x = x;
   m = u.i[HIGH_HALF];
   *error = 0;
   *delta = 0;
-  add=0;
-  if (m<0x00100000) {  /* x < 2^-1022 */
-    x = x*t52.x;  add = -52.0; u.x = x; m = u.i[HIGH_HALF]; }
+  add = 0;
+  if (m < 0x00100000)
+    {				/* x < 2^-1022 */
+      x = x * t52.x;
+      add = -52.0;
+      u.x = x;
+      m = u.i[HIGH_HALF];
+    }
 
-  if ((m&0x000fffff) < 0x0006a09e)
-    {u.i[HIGH_HALF] = (m&0x000fffff)|0x3ff00000; two52.i[LOW_HALF]=(m>>20); }
+  if ((m & 0x000fffff) < 0x0006a09e)
+    {
+      u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000;
+      two52.i[LOW_HALF] = (m >> 20);
+    }
   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;
   uu = v.x - bigu.x;
-  i = (v.i[LOW_HALF]&0x000003ff)<<2;
+  i = (v.i[LOW_HALF] & 0x000003ff) << 2;
   /*------------------------------------- |x-1| < 2**-11-------------------------------  */
-  if ((two52.i[LOW_HALF] == 1023)  && (i == 1200))
-  {
+  if ((two52.i[LOW_HALF] == 1023) && (i == 1200))
+    {
       t = x - 1.0;
-      EMULV(t,s3,y,yy,j1,j2,j3,j4,j5);
-      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,y,yy,z,zz,j1,j2,j3,j4,j5,j6,j7,j8);
+      EMULV (t, s3, y, yy, j1, j2, j3, j4, j5);
+      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, y, yy, z, zz, j1, j2, j3, j4, j5, j6, j7, j8);
 
-      e1 = t+z;
-      e2 = (((t-e1)+z)+zz)+t*t*t*(ss3+t*(s4+t*(s5+t*(s6+t*(s7+t*s8)))));
-      res = e1+e2;
-      *error = 1.0e-25*ABS(t);
-      *delta = (e1-res)+e2;
+      e1 = t + z;
+      e2 = ((((t - e1) + z) + zz) + t * t * t
+	    * (ss3 + t * (s4 + t * (s5 + t * (s6 + t * (s7 + t * s8))))));
+      res = e1 + e2;
+      *error = 1.0e-25 * ABS (t);
+      *delta = (e1 - res) + e2;
       return res;
-  }
+    }
   /*----------------------------- |x-1| > 2**-11  --------------------------  */
   else
-  {          /*Computing log(x) according to log table                        */
-      nx = (two52.x - two52e.x)+add;
+    {				/*Computing log(x) according to log table                        */
+      nx = (two52.x - two52e.x) + add;
       ou1 = ui.x[i];
-      ou2 = ui.x[i+1];
-      lu1 = ui.x[i+2];
-      lu2 = ui.x[i+3];
-      v.x = u.x*(ou1+ou2)+bigv.x;
-      vv = v.x-bigv.x;
-      j = v.i[LOW_HALF]&0x0007ffff;
-      j = j+j+j;
-      eps = u.x - uu*vv;
-      ov  = vj.x[j];
-      lv1 = vj.x[j+1];
-      lv2 = vj.x[j+2];
-      a = (ou1+ou2)*(1.0+ov);
-      a1 = (a+1.0e10)-1.0e10;
-      a2 = a*(1.0-a1*uu*vv);
-      e1 = eps*a1;
-      e2 = eps*a2;
-      e = e1+e2;
-      e2 = (e1-e)+e2;
-      t=nx*ln2a.x+lu1+lv1;
-      t1 = t+e;
-      t2 = (((t-t1)+e)+(lu2+lv2+nx*ln2b.x+e2))+e*e*(p2+e*(p3+e*p4));
-      res=t1+t2;
+      ou2 = ui.x[i + 1];
+      lu1 = ui.x[i + 2];
+      lu2 = ui.x[i + 3];
+      v.x = u.x * (ou1 + ou2) + bigv.x;
+      vv = v.x - bigv.x;
+      j = v.i[LOW_HALF] & 0x0007ffff;
+      j = j + j + j;
+      eps = u.x - uu * vv;
+      ov = vj.x[j];
+      lv1 = vj.x[j + 1];
+      lv2 = vj.x[j + 2];
+      a = (ou1 + ou2) * (1.0 + ov);
+      a1 = (a + 1.0e10) - 1.0e10;
+      a2 = a * (1.0 - a1 * uu * vv);
+      e1 = eps * a1;
+      e2 = eps * a2;
+      e = e1 + e2;
+      e2 = (e1 - e) + e2;
+      t = nx * ln2a.x + lu1 + lv1;
+      t1 = t + e;
+      t2 = ((((t - t1) + e) + (lu2 + lv2 + nx * ln2b.x + e2)) + e * e
+	    * (p2 + e * (p3 + e * p4)));
+      res = t1 + t2;
       *error = 1.0e-27;
-      *delta = (t1-res)+t2;
+      *delta = (t1 - res) + t2;
       return res;
-  }
+    }
 }
 
-/**********************************************************************/
-/* 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.              */
-/**********************************************************************/
+/* This function 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.  */
 static int
 SECTION
-checkint(double x) {
-  union {int4 i[2]; double x;} u;
-  int k,m,n;
+checkint (double x)
+{
+  union
+  {
+    int4 i[2];
+    double x;
+  } u;
+  int k, m, n;
   u.x = x;
-  m = u.i[HIGH_HALF]&0x7fffffff;    /* no sign */
-  if (m >= 0x7ff00000) return 0;    /*  x is +/-inf or NaN  */
-  if (m >= 0x43400000) return 1;    /*  |x| >= 2**53   */
-  if (m < 0x40000000) return 0;     /* |x| < 2,  can not be 0 or 1  */
+  m = u.i[HIGH_HALF] & 0x7fffffff;	/* no sign */
+  if (m >= 0x7ff00000)
+    return 0;			/*  x is +/-inf or NaN  */
+  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];
-  k = (m>>20)-1023;                 /*  1 <= k <= 52   */
-  if (k == 52) return (n&1)? -1:1;  /* odd or even*/
-  if (k>20) {
-    if (n<<(k-20)) return 0;        /* if not integer */
-    return (n<<(k-21))?-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;
+  k = (m >> 20) - 1023;		/*  1 <= k <= 52   */
+  if (k == 52)
+    return (n & 1) ? -1 : 1;	/* odd or even */
+  if (k > 20)
+    {
+      if (n << (k - 20))
+	return 0;		/* if not integer */
+      return (n << (k - 21)) ? -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;
 }