Format s_sin.c

1 files changed, 1212 insertions, 904 deletions

diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c
index 5038b72..5c388c8 100644
--- a/sysdeps/ieee754/dbl-64/s_sin.c
+++ b/sysdeps/ieee754/dbl-64/s_sin.c
@@ -66,299 +66,359 @@ extern const union
 } __sincostab attribute_hidden;
 
 static const double
-	  sn3 = -1.66666666666664880952546298448555E-01,
-	  sn5 =  8.33333214285722277379541354343671E-03,
-	  cs2 =  4.99999999999999999999950396842453E-01,
-	  cs4 = -4.16666666666664434524222570944589E-02,
-	  cs6 =  1.38888874007937613028114285595617E-03;
-
-void __dubsin(double x, double dx, double w[]);
-void __docos(double x, double dx, double w[]);
-double __mpsin(double x, double dx);
-double __mpcos(double x, double dx);
-double __mpsin1(double x);
-double __mpcos1(double x);
-static double slow(double x);
-static double slow1(double x);
-static double slow2(double x);
-static double sloww(double x, double dx, double orig);
-static double sloww1(double x, double dx, double orig);
-static double sloww2(double x, double dx, double orig, int n);
-static double bsloww(double x, double dx, double orig, int n);
-static double bsloww1(double x, double dx, double orig, int n);
-static double bsloww2(double x, double dx, double orig, int n);
-int __branred(double x, double *a, double *aa);
-static double cslow2(double x);
-static double csloww(double x, double dx, double orig);
-static double csloww1(double x, double dx, double orig);
-static double csloww2(double x, double dx, double orig, int n);
+  sn3 = -1.66666666666664880952546298448555E-01,
+  sn5 = 8.33333214285722277379541354343671E-03,
+  cs2 = 4.99999999999999999999950396842453E-01,
+  cs4 = -4.16666666666664434524222570944589E-02,
+  cs6 = 1.38888874007937613028114285595617E-03;
+
+void __dubsin (double x, double dx, double w[]);
+void __docos (double x, double dx, double w[]);
+double __mpsin (double x, double dx);
+double __mpcos (double x, double dx);
+double __mpsin1 (double x);
+double __mpcos1 (double x);
+static double slow (double x);
+static double slow1 (double x);
+static double slow2 (double x);
+static double sloww (double x, double dx, double orig);
+static double sloww1 (double x, double dx, double orig);
+static double sloww2 (double x, double dx, double orig, int n);
+static double bsloww (double x, double dx, double orig, int n);
+static double bsloww1 (double x, double dx, double orig, int n);
+static double bsloww2 (double x, double dx, double orig, int n);
+int __branred (double x, double *a, double *aa);
+static double cslow2 (double x);
+static double csloww (double x, double dx, double orig);
+static double csloww1 (double x, double dx, double orig);
+static double csloww2 (double x, double dx, double orig, int n);
+
 /*******************************************************************/
 /* An ultimate sin routine. Given an IEEE double machine number x   */
 /* it computes the correctly rounded (to nearest) value of sin(x)  */
 /*******************************************************************/
 double
 SECTION
-__sin(double x){
-	double xx,res,t,cor,y,s,c,sn,ssn,cs,ccs,xn,a,da,db,eps,xn1,xn2;
-	mynumber u,v;
-	int4 k,m,n;
-	double retval = 0;
-
-	SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
-
-	u.x = x;
-	m = u.i[HIGH_HALF];
-	k = 0x7fffffff&m;              /* no sign           */
-	if (k < 0x3e500000)            /* if x->0 =>sin(x)=x */
-	  { retval = x; goto ret; }
+__sin (double x)
+{
+  double xx, res, t, cor, y, s, c, sn, ssn, cs, ccs, xn, a, da, db, eps, xn1,
+    xn2;
+  mynumber u, v;
+  int4 k, m, n;
+  double retval = 0;
+
+  SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
+
+  u.x = x;
+  m = u.i[HIGH_HALF];
+  k = 0x7fffffff & m;		/* no sign           */
+  if (k < 0x3e500000)		/* if x->0 =>sin(x)=x */
+    {
+      retval = x;
+      goto ret;
+    }
  /*---------------------------- 2^-26 < |x|< 0.25 ----------------------*/
-	else  if (k < 0x3fd00000){
-	  xx = x*x;
-	  /*Taylor series */
-	  t = ((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*(xx*x);
-	  res = x+t;
-	  cor = (x-res)+t;
-	  retval = (res == res + 1.07*cor)? res : slow(x);
-	  goto ret;
-	}    /*  else  if (k < 0x3fd00000)    */
+  else if (k < 0x3fd00000)
+    {
+      xx = x * x;
+      /*Taylor series.  */
+      t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + s1.x)
+	   * (xx * x));
+      res = x + t;
+      cor = (x - res) + t;
+      retval = (res == res + 1.07 * cor) ? res : slow (x);
+      goto ret;
+    }				/*  else  if (k < 0x3fd00000)    */
 /*---------------------------- 0.25<|x|< 0.855469---------------------- */
-	else if (k < 0x3feb6000)  {
-	  u.x=(m>0)?big.x+x:big.x-x;
-	  y=(m>0)?x-(u.x-big.x):x+(u.x-big.x);
-	  xx=y*y;
-	  s = y + y*xx*(sn3 +xx*sn5);
-	  c = xx*(cs2 +xx*(cs4 + xx*cs6));
-	  k=u.i[LOW_HALF]<<2;
-	  sn=(m>0)?__sincostab.x[k]:-__sincostab.x[k];
-	  ssn=(m>0)?__sincostab.x[k+1]:-__sincostab.x[k+1];
-	  cs=__sincostab.x[k+2];
-	  ccs=__sincostab.x[k+3];
-	  cor=(ssn+s*ccs-sn*c)+cs*s;
-	  res=sn+cor;
-	  cor=(sn-res)+cor;
-	  retval = (res==res+1.096*cor)? res : slow1(x);
-	  goto ret;
-	}    /*   else  if (k < 0x3feb6000)    */
+  else if (k < 0x3feb6000)
+    {
+      u.x = (m > 0) ? big.x + x : big.x - x;
+      y = (m > 0) ? x - (u.x - big.x) : x + (u.x - big.x);
+      xx = y * y;
+      s = y + y * xx * (sn3 + xx * sn5);
+      c = xx * (cs2 + xx * (cs4 + xx * cs6));
+      k = u.i[LOW_HALF] << 2;
+      sn = (m > 0) ? __sincostab.x[k] : -__sincostab.x[k];
+      ssn = (m > 0) ? __sincostab.x[k + 1] : -__sincostab.x[k + 1];
+      cs = __sincostab.x[k + 2];
+      ccs = __sincostab.x[k + 3];
+      cor = (ssn + s * ccs - sn * c) + cs * s;
+      res = sn + cor;
+      cor = (sn - res) + cor;
+      retval = (res == res + 1.096 * cor) ? res : slow1 (x);
+      goto ret;
+    }				/*   else  if (k < 0x3feb6000)    */
 
 /*----------------------- 0.855469  <|x|<2.426265  ----------------------*/
-	else if (k <  0x400368fd ) {
-
-	  y = (m>0)? hp0.x-x:hp0.x+x;
-	  if (y>=0) {
-	    u.x = big.x+y;
-	    y = (y-(u.x-big.x))+hp1.x;
-	  }
-	  else {
-	    u.x = big.x-y;
-	    y = (-hp1.x) - (y+(u.x-big.x));
-	  }
-	  xx=y*y;
-	  s = y + y*xx*(sn3 +xx*sn5);
-	  c = xx*(cs2 +xx*(cs4 + xx*cs6));
-	  k=u.i[LOW_HALF]<<2;
-	  sn=__sincostab.x[k];
-	  ssn=__sincostab.x[k+1];
-	  cs=__sincostab.x[k+2];
-	  ccs=__sincostab.x[k+3];
-	  cor=(ccs-s*ssn-cs*c)-sn*s;
-	  res=cs+cor;
-	  cor=(cs-res)+cor;
-	  retval = (res==res+1.020*cor)? ((m>0)?res:-res) : slow2(x);
-	  goto ret;
-	} /*   else  if (k < 0x400368fd)    */
+  else if (k < 0x400368fd)
+    {
+
+      y = (m > 0) ? hp0.x - x : hp0.x + x;
+      if (y >= 0)
+	{
+	  u.x = big.x + y;
+	  y = (y - (u.x - big.x)) + hp1.x;
+	}
+      else
+	{
+	  u.x = big.x - y;
+	  y = (-hp1.x) - (y + (u.x - big.x));
+	}
+      xx = y * y;
+      s = y + y * xx * (sn3 + xx * sn5);
+      c = xx * (cs2 + xx * (cs4 + xx * cs6));
+      k = u.i[LOW_HALF] << 2;
+      sn = __sincostab.x[k];
+      ssn = __sincostab.x[k + 1];
+      cs = __sincostab.x[k + 2];
+      ccs = __sincostab.x[k + 3];
+      cor = (ccs - s * ssn - cs * c) - sn * s;
+      res = cs + cor;
+      cor = (cs - res) + cor;
+      retval = (res == res + 1.020 * cor) ? ((m > 0) ? res : -res) : slow2 (x);
+      goto ret;
+    }				/*   else  if (k < 0x400368fd)    */
 
 /*-------------------------- 2.426265<|x|< 105414350 ----------------------*/
-	else if (k < 0x419921FB ) {
-	  t = (x*hpinv.x + toint.x);
-	  xn = t - toint.x;
-	  v.x = t;
-	  y = (x - xn*mp1.x) - xn*mp2.x;
-	  n =v.i[LOW_HALF]&3;
-	  da = xn*mp3.x;
-	  a=y-da;
-	  da = (y-a)-da;
-	  eps = ABS(x)*1.2e-30;
-
-	  switch (n) { /* quarter of unit circle */
-	  case 0:
-	  case 2:
-	    xx = a*a;
-	    if (n) {a=-a;da=-da;}
-	    if (xx < 0.01588) {
-		      /*Taylor series */
-	      t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
-	      res = a+t;
-	      cor = (a-res)+t;
-	      cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
-	      retval = (res == res + cor)? res : sloww(a,da,x);
+  else if (k < 0x419921FB)
+    {
+      t = (x * hpinv.x + toint.x);
+      xn = t - toint.x;
+      v.x = t;
+      y = (x - xn * mp1.x) - xn * mp2.x;
+      n = v.i[LOW_HALF] & 3;
+      da = xn * mp3.x;
+      a = y - da;
+      da = (y - a) - da;
+      eps = ABS (x) * 1.2e-30;
+
+      switch (n)
+	{			/* quarter of unit circle */
+	case 0:
+	case 2:
+	  xx = a * a;
+	  if (n)
+	    {
+	      a = -a;
+	      da = -da;
+	    }
+	  if (xx < 0.01588)
+	    {
+	      /*Taylor series */
+	      t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
+		    + s1.x) * a - 0.5 * da) * xx + da;
+	      res = a + t;
+	      cor = (a - res) + t;
+	      cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
+	      retval = (res == res + cor) ? res : sloww (a, da, x);
 	      goto ret;
 	    }
-	    else  {
-	      if (a>0)
-		{m=1;t=a;db=da;}
+	  else
+	    {
+	      if (a > 0)
+		{
+		  m = 1;
+		  t = a;
+		  db = da;
+		}
 	      else
-		{m=0;t=-a;db=-da;}
-	      u.x=big.x+t;
-	      y=t-(u.x-big.x);
-	      xx=y*y;
-	      s = y + (db+y*xx*(sn3 +xx*sn5));
-	      c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
-	      k=u.i[LOW_HALF]<<2;
-	      sn=__sincostab.x[k];
-	      ssn=__sincostab.x[k+1];
-	      cs=__sincostab.x[k+2];
-	      ccs=__sincostab.x[k+3];
-	      cor=(ssn+s*ccs-sn*c)+cs*s;
-	      res=sn+cor;
-	      cor=(sn-res)+cor;
-	      cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
-	      retval = (res==res+cor)? ((m)?res:-res) : sloww1(a,da,x);
+		{
+		  m = 0;
+		  t = -a;
+		  db = -da;
+		}
+	      u.x = big.x + t;
+	      y = t - (u.x - big.x);
+	      xx = y * y;
+	      s = y + (db + y * xx * (sn3 + xx * sn5));
+	      c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+	      k = u.i[LOW_HALF] << 2;
+	      sn = __sincostab.x[k];
+	      ssn = __sincostab.x[k + 1];
+	      cs = __sincostab.x[k + 2];
+	      ccs = __sincostab.x[k + 3];
+	      cor = (ssn + s * ccs - sn * c) + cs * s;
+	      res = sn + cor;
+	      cor = (sn - res) + cor;
+	      cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
+	      retval = ((res == res + cor) ? ((m) ? res : -res)
+			: sloww1 (a, da, x));
 	      goto ret;
 	    }
-	    break;
-
-	  case 1:
-	  case 3:
-	    if (a<0)
-	      {a=-a;da=-da;}
-	    u.x=big.x+a;
-	    y=a-(u.x-big.x)+da;
-	    xx=y*y;
-	    k=u.i[LOW_HALF]<<2;
-	    sn=__sincostab.x[k];
-	    ssn=__sincostab.x[k+1];
-	    cs=__sincostab.x[k+2];
-	    ccs=__sincostab.x[k+3];
-	    s = y + y*xx*(sn3 +xx*sn5);
-	    c = xx*(cs2 +xx*(cs4 + xx*cs6));
-	    cor=(ccs-s*ssn-cs*c)-sn*s;
-	    res=cs+cor;
-	    cor=(cs-res)+cor;
-	    cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
-	    retval = (res==res+cor)? ((n&2)?-res:res) : sloww2(a,da,x,n);
-	    goto ret;
-
-	    break;
-
-	  }
-
-	}    /*   else  if (k <  0x419921FB )    */
+	  break;
+
+	case 1:
+	case 3:
+	  if (a < 0)
+	    {
+	      a = -a;
+	      da = -da;
+	    }
+	  u.x = big.x + a;
+	  y = a - (u.x - big.x) + da;
+	  xx = y * y;
+	  k = u.i[LOW_HALF] << 2;
+	  sn = __sincostab.x[k];
+	  ssn = __sincostab.x[k + 1];
+	  cs = __sincostab.x[k + 2];
+	  ccs = __sincostab.x[k + 3];
+	  s = y + y * xx * (sn3 + xx * sn5);
+	  c = xx * (cs2 + xx * (cs4 + xx * cs6));
+	  cor = (ccs - s * ssn - cs * c) - sn * s;
+	  res = cs + cor;
+	  cor = (cs - res) + cor;
+	  cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
+	  retval = ((res == res + cor) ? ((n & 2) ? -res : res)
+		    : sloww2 (a, da, x, n));
+	  goto ret;
+
+	  break;
+	}
+
+    }				/*   else  if (k <  0x419921FB )    */
 
 /*---------------------105414350 <|x|< 281474976710656 --------------------*/
-	else if (k < 0x42F00000 ) {
-	  t = (x*hpinv.x + toint.x);
-	  xn = t - toint.x;
-	  v.x = t;
-	  xn1 = (xn+8.0e22)-8.0e22;
-	  xn2 = xn - xn1;
-	  y = ((((x - xn1*mp1.x) - xn1*mp2.x)-xn2*mp1.x)-xn2*mp2.x);
-	  n =v.i[LOW_HALF]&3;
-	  da = xn1*pp3.x;
-	  t=y-da;
-	  da = (y-t)-da;
-	  da = (da - xn2*pp3.x) -xn*pp4.x;
-	  a = t+da;
-	  da = (t-a)+da;
-	  eps = 1.0e-24;
-
-	  switch (n) {
-	  case 0:
-	  case 2:
-	    xx = a*a;
-	    if (n) {a=-a;da=-da;}
-	    if (xx < 0.01588) {
+  else if (k < 0x42F00000)
+    {
+      t = (x * hpinv.x + toint.x);
+      xn = t - toint.x;
+      v.x = t;
+      xn1 = (xn + 8.0e22) - 8.0e22;
+      xn2 = xn - xn1;
+      y = ((((x - xn1 * mp1.x) - xn1 * mp2.x) - xn2 * mp1.x) - xn2 * mp2.x);
+      n = v.i[LOW_HALF] & 3;
+      da = xn1 * pp3.x;
+      t = y - da;
+      da = (y - t) - da;
+      da = (da - xn2 * pp3.x) - xn * pp4.x;
+      a = t + da;
+      da = (t - a) + da;
+      eps = 1.0e-24;
+
+      switch (n)
+	{
+	case 0:
+	case 2:
+	  xx = a * a;
+	  if (n)
+	    {
+	      a = -a;
+	      da = -da;
+	    }
+	  if (xx < 0.01588)
+	    {
 	      /* Taylor series */
-	      t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
-	      res = a+t;
-	      cor = (a-res)+t;
-	      cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
-	      retval = (res == res + cor)? res : bsloww(a,da,x,n);
+	      t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
+		    + s1.x) * a - 0.5 * da) * xx + da;
+	      res = a + t;
+	      cor = (a - res) + t;
+	      cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
+	      retval = (res == res + cor) ? res : bsloww (a, da, x, n);
 	      goto ret;
 	    }
-	    else  {
-	      if (a>0) {m=1;t=a;db=da;}
-	      else {m=0;t=-a;db=-da;}
-	      u.x=big.x+t;
-	      y=t-(u.x-big.x);
-	      xx=y*y;
-	      s = y + (db+y*xx*(sn3 +xx*sn5));
-	      c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
-	      k=u.i[LOW_HALF]<<2;
-	      sn=__sincostab.x[k];
-	      ssn=__sincostab.x[k+1];
-	      cs=__sincostab.x[k+2];
-	      ccs=__sincostab.x[k+3];
-	      cor=(ssn+s*ccs-sn*c)+cs*s;
-	      res=sn+cor;
-	      cor=(sn-res)+cor;
-	      cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
-	      retval = (res==res+cor)? ((m)?res:-res) : bsloww1(a,da,x,n);
+	  else
+	    {
+	      if (a > 0)
+		{
+		  m = 1;
+		  t = a;
+		  db = da;
+		}
+	      else
+		{
+		  m = 0;
+		  t = -a;
+		  db = -da;
+		}
+	      u.x = big.x + t;
+	      y = t - (u.x - big.x);
+	      xx = y * y;
+	      s = y + (db + y * xx * (sn3 + xx * sn5));
+	      c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+	      k = u.i[LOW_HALF] << 2;
+	      sn = __sincostab.x[k];
+	      ssn = __sincostab.x[k + 1];
+	      cs = __sincostab.x[k + 2];
+	      ccs = __sincostab.x[k + 3];
+	      cor = (ssn + s * ccs - sn * c) + cs * s;
+	      res = sn + cor;
+	      cor = (sn - res) + cor;
+	      cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
+	      retval = ((res == res + cor) ? ((m) ? res : -res)
+			: bsloww1 (a, da, x, n));
 	      goto ret;
-		   }
-	    break;
-
-	  case 1:
-	  case 3:
-	    if (a<0)
-	      {a=-a;da=-da;}
-	    u.x=big.x+a;
-	    y=a-(u.x-big.x)+da;
-	    xx=y*y;
-	    k=u.i[LOW_HALF]<<2;
-	    sn=__sincostab.x[k];
-	    ssn=__sincostab.x[k+1];
-	    cs=__sincostab.x[k+2];
-	    ccs=__sincostab.x[k+3];
-	    s = y + y*xx*(sn3 +xx*sn5);
-	    c = xx*(cs2 +xx*(cs4 + xx*cs6));
-	    cor=(ccs-s*ssn-cs*c)-sn*s;
-	    res=cs+cor;
-	    cor=(cs-res)+cor;
-	    cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
-	    retval = (res==res+cor)? ((n&2)?-res:res) : bsloww2(a,da,x,n);
-	    goto ret;
-
-	    break;
-
-	  }
-
-	}    /*   else  if (k <  0x42F00000 )   */
+	    }
+	  break;
+
+	case 1:
+	case 3:
+	  if (a < 0)
+	    {
+	      a = -a;
+	      da = -da;
+	    }
+	  u.x = big.x + a;
+	  y = a - (u.x - big.x) + da;
+	  xx = y * y;
+	  k = u.i[LOW_HALF] << 2;
+	  sn = __sincostab.x[k];
+	  ssn = __sincostab.x[k + 1];
+	  cs = __sincostab.x[k + 2];
+	  ccs = __sincostab.x[k + 3];
+	  s = y + y * xx * (sn3 + xx * sn5);
+	  c = xx * (cs2 + xx * (cs4 + xx * cs6));
+	  cor = (ccs - s * ssn - cs * c) - sn * s;
+	  res = cs + cor;
+	  cor = (cs - res) + cor;
+	  cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
+	  retval = ((res == res + cor) ? ((n & 2) ? -res : res)
+		    : bsloww2 (a, da, x, n));
+	  goto ret;
+
+	  break;
+	}
+    }				/*   else  if (k <  0x42F00000 )   */
 
 /* -----------------281474976710656 <|x| <2^1024----------------------------*/
-	else if (k < 0x7ff00000) {
-
-	  n = __branred(x,&a,&da);
-	  switch (n) {
-	  case 0:
-	    if (a*a < 0.01588) retval = bsloww(a,da,x,n);
-	    else retval = bsloww1(a,da,x,n);
-	    goto ret;
-	    break;
-	  case 2:
-	    if (a*a < 0.01588) retval = bsloww(-a,-da,x,n);
-	    else retval = bsloww1(-a,-da,x,n);
-	    goto ret;
-	    break;
-
-	  case 1:
-	  case 3:
-	    retval = bsloww2(a,da,x,n);
-	    goto ret;
-	    break;
-	  }
-
-	}    /*   else  if (k <  0x7ff00000 )    */
+  else if (k < 0x7ff00000)
+    {
+      n = __branred (x, &a, &da);
+      switch (n)
+	{
+	case 0:
+	  if (a * a < 0.01588)
+	    retval = bsloww (a, da, x, n);
+	  else
+	    retval = bsloww1 (a, da, x, n);
+	  goto ret;
+	  break;
+	case 2:
+	  if (a * a < 0.01588)
+	    retval = bsloww (-a, -da, x, n);
+	  else
+	    retval = bsloww1 (-a, -da, x, n);
+	  goto ret;
+	  break;
 
-/*--------------------- |x| > 2^1024 ----------------------------------*/
-	else {
-	  if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
-	    __set_errno (EDOM);
-	  retval = x / x;
+	case 1:
+	case 3:
+	  retval = bsloww2 (a, da, x, n);
 	  goto ret;
+	  break;
 	}
+    }				/*   else  if (k <  0x7ff00000 )    */
+
+/*--------------------- |x| > 2^1024 ----------------------------------*/
+  else
+    {
+      if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
+	__set_errno (EDOM);
+      retval = x / x;
+      goto ret;
+    }
 
- ret:
-	return retval;
+ret:
+  return retval;
 }
 
 
@@ -369,11 +429,12 @@ __sin(double x){
 
 double
 SECTION
-__cos(double x)
+__cos (double x)
 {
-  double y,xx,res,t,cor,s,c,sn,ssn,cs,ccs,xn,a,da,db,eps,xn1,xn2;
-  mynumber u,v;
-  int4 k,m,n;
+  double y, xx, res, t, cor, s, c, sn, ssn, cs, ccs, xn, a, da, db, eps, xn1,
+    xn2;
+  mynumber u, v;
+  int4 k, m, n;
 
   double retval = 0;
 
@@ -381,251 +442,318 @@ __cos(double x)
 
   u.x = x;
   m = u.i[HIGH_HALF];
-  k = 0x7fffffff&m;
-
-  if (k < 0x3e400000 ) { retval = 1.0; goto ret; } /* |x|<2^-27 => cos(x)=1 */
-
-  else if (k < 0x3feb6000 ) {/* 2^-27 < |x| < 0.855469 */
-    y=ABS(x);
-    u.x = big.x+y;
-    y = y-(u.x-big.x);
-    xx=y*y;
-    s = y + y*xx*(sn3 +xx*sn5);
-    c = xx*(cs2 +xx*(cs4 + xx*cs6));
-    k=u.i[LOW_HALF]<<2;
-    sn=__sincostab.x[k];
-    ssn=__sincostab.x[k+1];
-    cs=__sincostab.x[k+2];
-    ccs=__sincostab.x[k+3];
-    cor=(ccs-s*ssn-cs*c)-sn*s;
-    res=cs+cor;
-    cor=(cs-res)+cor;
-    retval = (res==res+1.020*cor)? res : cslow2(x);
-    goto ret;
-
-}    /*   else  if (k < 0x3feb6000)    */
-
-  else if (k <  0x400368fd ) {/* 0.855469  <|x|<2.426265  */;
-    y=hp0.x-ABS(x);
-    a=y+hp1.x;
-    da=(y-a)+hp1.x;
-    xx=a*a;
-    if (xx < 0.01588) {
-      t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
-      res = a+t;
-      cor = (a-res)+t;
-      cor = (cor>0)? 1.02*cor+1.0e-31 : 1.02*cor -1.0e-31;
-      retval = (res == res + cor)? res : csloww(a,da,x);
-      goto ret;
-    }
-    else  {
-      if (a>0) {m=1;t=a;db=da;}
-      else {m=0;t=-a;db=-da;}
-      u.x=big.x+t;
-      y=t-(u.x-big.x);
-      xx=y*y;
-      s = y + (db+y*xx*(sn3 +xx*sn5));
-      c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
-      k=u.i[LOW_HALF]<<2;
-      sn=__sincostab.x[k];
-      ssn=__sincostab.x[k+1];
-      cs=__sincostab.x[k+2];
-      ccs=__sincostab.x[k+3];
-      cor=(ssn+s*ccs-sn*c)+cs*s;
-      res=sn+cor;
-      cor=(sn-res)+cor;
-      cor = (cor>0)? 1.035*cor+1.0e-31 : 1.035*cor-1.0e-31;
-      retval = (res==res+cor)? ((m)?res:-res) : csloww1(a,da,x);
-      goto ret;
-}
+  k = 0x7fffffff & m;
 
-}    /*   else  if (k < 0x400368fd)    */
-
-
-  else if (k < 0x419921FB ) {/* 2.426265<|x|< 105414350 */
-    t = (x*hpinv.x + toint.x);
-    xn = t - toint.x;
-    v.x = t;
-    y = (x - xn*mp1.x) - xn*mp2.x;
-    n =v.i[LOW_HALF]&3;
-    da = xn*mp3.x;
-    a=y-da;
-    da = (y-a)-da;
-    eps = ABS(x)*1.2e-30;
-
-    switch (n) {
-    case 1:
-    case 3:
-      xx = a*a;
-      if (n == 1) {a=-a;da=-da;}
-      if (xx < 0.01588) {
-	t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
-	res = a+t;
-	cor = (a-res)+t;
-	cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
-	retval = (res == res + cor)? res : csloww(a,da,x);
-	goto ret;
-      }
-      else  {
-	if (a>0) {m=1;t=a;db=da;}
-	else {m=0;t=-a;db=-da;}
-	u.x=big.x+t;
-	y=t-(u.x-big.x);
-	xx=y*y;
-	s = y + (db+y*xx*(sn3 +xx*sn5));
-	c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
-	k=u.i[LOW_HALF]<<2;
-	sn=__sincostab.x[k];
-	ssn=__sincostab.x[k+1];
-	cs=__sincostab.x[k+2];
-	ccs=__sincostab.x[k+3];
-	cor=(ssn+s*ccs-sn*c)+cs*s;
-	res=sn+cor;
-	cor=(sn-res)+cor;
-	cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
-	retval = (res==res+cor)? ((m)?res:-res) : csloww1(a,da,x);
-	goto ret;
-      }
-      break;
-
-  case 0:
-    case 2:
-      if (a<0) {a=-a;da=-da;}
-      u.x=big.x+a;
-      y=a-(u.x-big.x)+da;
-      xx=y*y;
-      k=u.i[LOW_HALF]<<2;
-      sn=__sincostab.x[k];
-      ssn=__sincostab.x[k+1];
-      cs=__sincostab.x[k+2];
-      ccs=__sincostab.x[k+3];
-      s = y + y*xx*(sn3 +xx*sn5);
-      c = xx*(cs2 +xx*(cs4 + xx*cs6));
-      cor=(ccs-s*ssn-cs*c)-sn*s;
-      res=cs+cor;
-      cor=(cs-res)+cor;
-      cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
-      retval = (res==res+cor)? ((n)?-res:res) : csloww2(a,da,x,n);
+  if (k < 0x3e400000)
+    {
+      retval = 1.0;
+      goto ret;
+    }				/* |x|<2^-27 => cos(x)=1 */
+
+  else if (k < 0x3feb6000)
+    {				/* 2^-27 < |x| < 0.855469 */
+      y = ABS (x);
+      u.x = big.x + y;
+      y = y - (u.x - big.x);
+      xx = y * y;
+      s = y + y * xx * (sn3 + xx * sn5);
+      c = xx * (cs2 + xx * (cs4 + xx * cs6));
+      k = u.i[LOW_HALF] << 2;
+      sn = __sincostab.x[k];
+      ssn = __sincostab.x[k + 1];
+      cs = __sincostab.x[k + 2];
+      ccs = __sincostab.x[k + 3];
+      cor = (ccs - s * ssn - cs * c) - sn * s;
+      res = cs + cor;
+      cor = (cs - res) + cor;
+      retval = (res == res + 1.020 * cor) ? res : cslow2 (x);
       goto ret;
+    }				/*   else  if (k < 0x3feb6000)    */
+
+  else if (k < 0x400368fd)
+    { /* 0.855469  <|x|<2.426265  */ ;
+      y = hp0.x - ABS (x);
+      a = y + hp1.x;
+      da = (y - a) + hp1.x;
+      xx = a * a;
+      if (xx < 0.01588)
+	{
+	  t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + s1.x)
+	       * a - 0.5 * da) * xx + da;
+	  res = a + t;
+	  cor = (a - res) + t;
+	  cor = (cor > 0) ? 1.02 * cor + 1.0e-31 : 1.02 * cor - 1.0e-31;
+	  retval = (res == res + cor) ? res : csloww (a, da, x);
+	  goto ret;
+	}
+      else
+	{
+	  if (a > 0)
+	    {
+	      m = 1;
+	      t = a;
+	      db = da;
+	    }
+	  else
+	    {
+	      m = 0;
+	      t = -a;
+	      db = -da;
+	    }
+	  u.x = big.x + t;
+	  y = t - (u.x - big.x);
+	  xx = y * y;
+	  s = y + (db + y * xx * (sn3 + xx * sn5));
+	  c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+	  k = u.i[LOW_HALF] << 2;
+	  sn = __sincostab.x[k];
+	  ssn = __sincostab.x[k + 1];
+	  cs = __sincostab.x[k + 2];
+	  ccs = __sincostab.x[k + 3];
+	  cor = (ssn + s * ccs - sn * c) + cs * s;
+	  res = sn + cor;
+	  cor = (sn - res) + cor;
+	  cor = (cor > 0) ? 1.035 * cor + 1.0e-31 : 1.035 * cor - 1.0e-31;
+	  retval = ((res == res + cor) ? ((m) ? res : -res)
+		    : csloww1 (a, da, x));
+	  goto ret;
+	}
 
-	   break;
+    }				/*   else  if (k < 0x400368fd)    */
 
-    }
 
-  }    /*   else  if (k <  0x419921FB )    */
-
-
-  else if (k < 0x42F00000 ) {
-    t = (x*hpinv.x + toint.x);
-    xn = t - toint.x;
-    v.x = t;
-    xn1 = (xn+8.0e22)-8.0e22;
-    xn2 = xn - xn1;
-    y = ((((x - xn1*mp1.x) - xn1*mp2.x)-xn2*mp1.x)-xn2*mp2.x);
-    n =v.i[LOW_HALF]&3;
-    da = xn1*pp3.x;
-    t=y-da;
-    da = (y-t)-da;
-    da = (da - xn2*pp3.x) -xn*pp4.x;
-    a = t+da;
-    da = (t-a)+da;
-    eps = 1.0e-24;
-
-    switch (n) {
-    case 1:
-    case 3:
-      xx = a*a;
-      if (n==1) {a=-a;da=-da;}
-      if (xx < 0.01588) {
-	t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
-	res = a+t;
-	cor = (a-res)+t;
-	cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
-	retval = (res == res + cor)? res : bsloww(a,da,x,n);
-	goto ret;
-      }
-      else  {
-	if (a>0) {m=1;t=a;db=da;}
-	else {m=0;t=-a;db=-da;}
-	u.x=big.x+t;
-	y=t-(u.x-big.x);
-	xx=y*y;
-	s = y + (db+y*xx*(sn3 +xx*sn5));
-	c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
-	k=u.i[LOW_HALF]<<2;
-	sn=__sincostab.x[k];
-	ssn=__sincostab.x[k+1];
-	cs=__sincostab.x[k+2];
-	ccs=__sincostab.x[k+3];
-	cor=(ssn+s*ccs-sn*c)+cs*s;
-	res=sn+cor;
-	cor=(sn-res)+cor;
-	cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
-	retval = (res==res+cor)? ((m)?res:-res) : bsloww1(a,da,x,n);
-	goto ret;
-      }
-      break;
-
-    case 0:
-    case 2:
-      if (a<0) {a=-a;da=-da;}
-      u.x=big.x+a;
-      y=a-(u.x-big.x)+da;
-      xx=y*y;
-      k=u.i[LOW_HALF]<<2;
-      sn=__sincostab.x[k];
-      ssn=__sincostab.x[k+1];
-      cs=__sincostab.x[k+2];
-      ccs=__sincostab.x[k+3];
-      s = y + y*xx*(sn3 +xx*sn5);
-      c = xx*(cs2 +xx*(cs4 + xx*cs6));
-      cor=(ccs-s*ssn-cs*c)-sn*s;
-      res=cs+cor;
-      cor=(cs-res)+cor;
-      cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
-      retval = (res==res+cor)? ((n)?-res:res) : bsloww2(a,da,x,n);
-      goto ret;
-      break;
+  else if (k < 0x419921FB)
+    {				/* 2.426265<|x|< 105414350 */
+      t = (x * hpinv.x + toint.x);
+      xn = t - toint.x;
+      v.x = t;
+      y = (x - xn * mp1.x) - xn * mp2.x;
+      n = v.i[LOW_HALF] & 3;
+      da = xn * mp3.x;
+      a = y - da;
+      da = (y - a) - da;
+      eps = ABS (x) * 1.2e-30;
+
+      switch (n)
+	{
+	case 1:
+	case 3:
+	  xx = a * a;
+	  if (n == 1)
+	    {
+	      a = -a;
+	      da = -da;
+	    }
+	  if (xx < 0.01588)
+	    {
+	      t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
+		    + s1.x) * a - 0.5 * da) * xx + da;
+	      res = a + t;
+	      cor = (a - res) + t;
+	      cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
+	      retval = (res == res + cor) ? res : csloww (a, da, x);
+	      goto ret;
+	    }
+	  else
+	    {
+	      if (a > 0)
+		{
+		  m = 1;
+		  t = a;
+		  db = da;
+		}
+	      else
+		{
+		  m = 0;
+		  t = -a;
+		  db = -da;
+		}
+	      u.x = big.x + t;
+	      y = t - (u.x - big.x);
+	      xx = y * y;
+	      s = y + (db + y * xx * (sn3 + xx * sn5));
+	      c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+	      k = u.i[LOW_HALF] << 2;
+	      sn = __sincostab.x[k];
+	      ssn = __sincostab.x[k + 1];
+	      cs = __sincostab.x[k + 2];
+	      ccs = __sincostab.x[k + 3];
+	      cor = (ssn + s * ccs - sn * c) + cs * s;
+	      res = sn + cor;
+	      cor = (sn - res) + cor;
+	      cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
+	      retval = ((res == res + cor) ? ((m) ? res : -res)
+			: csloww1 (a, da, x));
+	      goto ret;
+	    }
+	  break;
+
+	case 0:
+	case 2:
+	  if (a < 0)
+	    {
+	      a = -a;
+	      da = -da;
+	    }
+	  u.x = big.x + a;
+	  y = a - (u.x - big.x) + da;
+	  xx = y * y;
+	  k = u.i[LOW_HALF] << 2;
+	  sn = __sincostab.x[k];
+	  ssn = __sincostab.x[k + 1];
+	  cs = __sincostab.x[k + 2];
+	  ccs = __sincostab.x[k + 3];
+	  s = y + y * xx * (sn3 + xx * sn5);
+	  c = xx * (cs2 + xx * (cs4 + xx * cs6));
+	  cor = (ccs - s * ssn - cs * c) - sn * s;
+	  res = cs + cor;
+	  cor = (cs - res) + cor;
+	  cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
+	  retval = ((res == res + cor) ? ((n) ? -res : res)
+		    : csloww2 (a, da, x, n));
+	  goto ret;
 
-    }
+	  break;
+	}
+    }				/*   else  if (k <  0x419921FB )    */
 
-  }    /*   else  if (k <  0x42F00000 )    */
+  else if (k < 0x42F00000)
+    {
+      t = (x * hpinv.x + toint.x);
+      xn = t - toint.x;
+      v.x = t;
+      xn1 = (xn + 8.0e22) - 8.0e22;
+      xn2 = xn - xn1;
+      y = ((((x - xn1 * mp1.x) - xn1 * mp2.x) - xn2 * mp1.x) - xn2 * mp2.x);
+      n = v.i[LOW_HALF] & 3;
+      da = xn1 * pp3.x;
+      t = y - da;
+      da = (y - t) - da;
+      da = (da - xn2 * pp3.x) - xn * pp4.x;
+      a = t + da;
+      da = (t - a) + da;
+      eps = 1.0e-24;
+
+      switch (n)
+	{
+	case 1:
+	case 3:
+	  xx = a * a;
+	  if (n == 1)
+	    {
+	      a = -a;
+	      da = -da;
+	    }
+	  if (xx < 0.01588)
+	    {
+	      t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
+		    + s1.x) * a - 0.5 * da) * xx + da;
+	      res = a + t;
+	      cor = (a - res) + t;
+	      cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
+	      retval = (res == res + cor) ? res : bsloww (a, da, x, n);
+	      goto ret;
+	    }
+	  else
+	    {
+	      if (a > 0)
+		{
+		  m = 1;
+		  t = a;
+		  db = da;
+		}
+	      else
+		{
+		  m = 0;
+		  t = -a;
+		  db = -da;
+		}
+	      u.x = big.x + t;
+	      y = t - (u.x - big.x);
+	      xx = y * y;
+	      s = y + (db + y * xx * (sn3 + xx * sn5));
+	      c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+	      k = u.i[LOW_HALF] << 2;
+	      sn = __sincostab.x[k];
+	      ssn = __sincostab.x[k + 1];
+	      cs = __sincostab.x[k + 2];
+	      ccs = __sincostab.x[k + 3];
+	      cor = (ssn + s * ccs - sn * c) + cs * s;
+	      res = sn + cor;
+	      cor = (sn - res) + cor;
+	      cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
+	      retval = ((res == res + cor) ? ((m) ? res : -res)
+			: bsloww1 (a, da, x, n));
+	      goto ret;
+	    }
+	  break;
+
+	case 0:
+	case 2:
+	  if (a < 0)
+	    {
+	      a = -a;
+	      da = -da;
+	    }
+	  u.x = big.x + a;
+	  y = a - (u.x - big.x) + da;
+	  xx = y * y;
+	  k = u.i[LOW_HALF] << 2;
+	  sn = __sincostab.x[k];
+	  ssn = __sincostab.x[k + 1];
+	  cs = __sincostab.x[k + 2];
+	  ccs = __sincostab.x[k + 3];
+	  s = y + y * xx * (sn3 + xx * sn5);
+	  c = xx * (cs2 + xx * (cs4 + xx * cs6));
+	  cor = (ccs - s * ssn - cs * c) - sn * s;
+	  res = cs + cor;
+	  cor = (cs - res) + cor;
+	  cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
+	  retval = ((res == res + cor) ? ((n) ? -res : res)
+		    : bsloww2 (a, da, x, n));
+	  goto ret;
+	  break;
+	}
+    }				/*   else  if (k <  0x42F00000 )    */
+
+  else if (k < 0x7ff00000)
+    {				/* 281474976710656 <|x| <2^1024 */
+
+      n = __branred (x, &a, &da);
+      switch (n)
+	{
+	case 1:
+	  if (a * a < 0.01588)
+	    retval = bsloww (-a, -da, x, n);
+	  else
+	    retval = bsloww1 (-a, -da, x, n);
+	  goto ret;
+	  break;
+	case 3:
+	  if (a * a < 0.01588)
+	    retval = bsloww (a, da, x, n);
+	  else
+	    retval = bsloww1 (a, da, x, n);
+	  goto ret;
+	  break;
 
-  else if (k < 0x7ff00000) {/* 281474976710656 <|x| <2^1024 */
+	case 0:
+	case 2:
+	  retval = bsloww2 (a, da, x, n);
+	  goto ret;
+	  break;
+	}
+    }				/*   else  if (k <  0x7ff00000 )    */
 
-    n = __branred(x,&a,&da);
-    switch (n) {
-    case 1:
-      if (a*a < 0.01588) retval = bsloww(-a,-da,x,n);
-      else retval = bsloww1(-a,-da,x,n);
+  else
+    {
+      if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
+	__set_errno (EDOM);
+      retval = x / x;		/* |x| > 2^1024 */
       goto ret;
-      break;
-		case 3:
-		  if (a*a < 0.01588) retval = bsloww(a,da,x,n);
-		  else retval = bsloww1(a,da,x,n);
-		  goto ret;
-		  break;
-
-    case 0:
-    case 2:
-      retval = bsloww2(a,da,x,n);
-      goto ret;
-      break;
     }
 
-  }    /*   else  if (k <  0x7ff00000 )    */
-
-
-
-
-  else {
-    if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
-      __set_errno (EDOM);
-    retval = x / x; /* |x| > 2^1024 */
-    goto ret;
-  }
-
- ret:
+ret:
   return retval;
 }
 
@@ -636,25 +764,32 @@ __cos(double x)
 
 static double
 SECTION
-slow(double x) {
-static const double th2_36 = 206158430208.0;   /*    1.5*2**37   */
- double y,x1,x2,xx,r,t,res,cor,w[2];
- x1=(x+th2_36)-th2_36;
- y = aa.x*x1*x1*x1;
- r=x+y;
- x2=x-x1;
- xx=x*x;
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2;
- t=((x-r)+y)+t;
- res=r+t;
- cor = (r-res)+t;
- if (res == res + 1.0007*cor) return res;
- else {
-   __dubsin(ABS(x),0,w);
-   if (w[0] == w[0]+1.000000001*w[1]) return (x>0)?w[0]:-w[0];
-   else return (x>0)?__mpsin(x,0):-__mpsin(-x,0);
- }
+slow (double x)
+{
+  static const double th2_36 = 206158430208.0;	/*    1.5*2**37   */
+  double y, x1, x2, xx, r, t, res, cor, w[2];
+  x1 = (x + th2_36) - th2_36;
+  y = aa.x * x1 * x1 * x1;
+  r = x + y;
+  x2 = x - x1;
+  xx = x * x;
+  t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
+       + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2;
+  t = ((x - r) + y) + t;
+  res = r + t;
+  cor = (r - res) + t;
+  if (res == res + 1.0007 * cor)
+    return res;
+  else
+    {
+      __dubsin (ABS (x), 0, w);
+      if (w[0] == w[0] + 1.000000001 * w[1])
+	return (x > 0) ? w[0] : -w[0];
+      else
+	return (x > 0) ? __mpsin (x, 0) : -__mpsin (-x, 0);
+    }
 }
+
 /*******************************************************************************/
 /* Routine compute sin(x) for   0.25<|x|< 0.855469 by  __sincostab.tbl   and Taylor */
 /* and if result still doesn't accurate enough by mpsin   or dubsin            */
@@ -662,88 +797,102 @@ static const double th2_36 = 206158430208.0;   /*    1.5*2**37   */
 
 static double
 SECTION
-slow1(double x) {
+slow1 (double x)
+{
   mynumber u;
-  double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
+  double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
   static const double t22 = 6291456.0;
   int4 k;
-  y=ABS(x);
-  u.x=big.x+y;
-  y=y-(u.x-big.x);
-  xx=y*y;
-  s = y*xx*(sn3 +xx*sn5);
-  c = xx*(cs2 +xx*(cs4 + xx*cs6));
-  k=u.i[LOW_HALF]<<2;
-  sn=__sincostab.x[k];          /* Data          */
-  ssn=__sincostab.x[k+1];       /*  from         */
-  cs=__sincostab.x[k+2];        /*   tables      */
-  ccs=__sincostab.x[k+3];       /*    __sincostab.tbl */
-  y1 = (y+t22)-t22;
+  y = ABS (x);
+  u.x = big.x + y;
+  y = y - (u.x - big.x);
+  xx = y * y;
+  s = y * xx * (sn3 + xx * sn5);
+  c = xx * (cs2 + xx * (cs4 + xx * cs6));
+  k = u.i[LOW_HALF] << 2;
+  sn = __sincostab.x[k];	/* Data          */
+  ssn = __sincostab.x[k + 1];	/*  from         */
+  cs = __sincostab.x[k + 2];	/*   tables      */
+  ccs = __sincostab.x[k + 3];	/*    __sincostab.tbl */
+  y1 = (y + t22) - t22;
   y2 = y - y1;
-  c1 = (cs+t22)-t22;
-  c2=(cs-c1)+ccs;
-  cor=(ssn+s*ccs+cs*s+c2*y+c1*y2)-sn*c;
-  y=sn+c1*y1;
-  cor = cor+((sn-y)+c1*y1);
-  res=y+cor;
-  cor=(y-res)+cor;
-  if (res == res+1.0005*cor) return (x>0)?res:-res;
-  else {
-    __dubsin(ABS(x),0,w);
-    if (w[0] == w[0]+1.000000005*w[1]) return (x>0)?w[0]:-w[0];
-    else return (x>0)?__mpsin(x,0):-__mpsin(-x,0);
-  }
+  c1 = (cs + t22) - t22;
+  c2 = (cs - c1) + ccs;
+  cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2) - sn * c;
+  y = sn + c1 * y1;
+  cor = cor + ((sn - y) + c1 * y1);
+  res = y + cor;
+  cor = (y - res) + cor;
+  if (res == res + 1.0005 * cor)
+    return (x > 0) ? res : -res;
+  else
+    {
+      __dubsin (ABS (x), 0, w);
+      if (w[0] == w[0] + 1.000000005 * w[1])
+	return (x > 0) ? w[0] : -w[0];
+      else
+	return (x > 0) ? __mpsin (x, 0) : -__mpsin (-x, 0);
+    }
 }
+
 /**************************************************************************/
 /*  Routine compute sin(x) for   0.855469  <|x|<2.426265  by  __sincostab.tbl  */
 /* and if result still doesn't accurate enough by mpsin   or dubsin       */
 /**************************************************************************/
 static double
 SECTION
-slow2(double x) {
+slow2 (double x)
+{
   mynumber u;
-  double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res,del;
+  double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res, del;
   static const double t22 = 6291456.0;
   int4 k;
-  y=ABS(x);
-  y = hp0.x-y;
-  if (y>=0) {
-    u.x = big.x+y;
-    y = y-(u.x-big.x);
-    del = hp1.x;
-  }
-  else {
-    u.x = big.x-y;
-    y = -(y+(u.x-big.x));
-    del = -hp1.x;
-  }
-  xx=y*y;
-  s = y*xx*(sn3 +xx*sn5);
-  c = y*del+xx*(cs2 +xx*(cs4 + xx*cs6));
-  k=u.i[LOW_HALF]<<2;
-  sn=__sincostab.x[k];
-  ssn=__sincostab.x[k+1];
-  cs=__sincostab.x[k+2];
-  ccs=__sincostab.x[k+3];
-  y1 = (y+t22)-t22;
-  y2 = (y - y1)+del;
-  e1 = (sn+t22)-t22;
-  e2=(sn-e1)+ssn;
-  cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
-  y=cs-e1*y1;
-  cor = cor+((cs-y)-e1*y1);
-  res=y+cor;
-  cor=(y-res)+cor;
-  if (res == res+1.0005*cor) return (x>0)?res:-res;
-  else {
-    y=ABS(x)-hp0.x;
-    y1=y-hp1.x;
-    y2=(y-y1)-hp1.x;
-    __docos(y1,y2,w);
-    if (w[0] == w[0]+1.000000005*w[1]) return (x>0)?w[0]:-w[0];
-    else return (x>0)?__mpsin(x,0):-__mpsin(-x,0);
-  }
+  y = ABS (x);
+  y = hp0.x - y;
+  if (y >= 0)
+    {
+      u.x = big.x + y;
+      y = y - (u.x - big.x);
+      del = hp1.x;
+    }
+  else
+    {
+      u.x = big.x - y;
+      y = -(y + (u.x - big.x));
+      del = -hp1.x;
+    }
+  xx = y * y;
+  s = y * xx * (sn3 + xx * sn5);
+  c = y * del + xx * (cs2 + xx * (cs4 + xx * cs6));
+  k = u.i[LOW_HALF] << 2;
+  sn = __sincostab.x[k];
+  ssn = __sincostab.x[k + 1];
+  cs = __sincostab.x[k + 2];
+  ccs = __sincostab.x[k + 3];
+  y1 = (y + t22) - t22;
+  y2 = (y - y1) + del;
+  e1 = (sn + t22) - t22;
+  e2 = (sn - e1) + ssn;
+  cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+  y = cs - e1 * y1;
+  cor = cor + ((cs - y) - e1 * y1);
+  res = y + cor;
+  cor = (y - res) + cor;
+  if (res == res + 1.0005 * cor)
+    return (x > 0) ? res : -res;
+  else
+    {
+      y = ABS (x) - hp0.x;
+      y1 = y - hp1.x;
+      y2 = (y - y1) - hp1.x;
+      __docos (y1, y2, w);
+      if (w[0] == w[0] + 1.000000005 * w[1])
+	return (x > 0) ? w[0] : -w[0];
+      else
+	return (x > 0) ? __mpsin (x, 0) : -__mpsin (-x, 0);
+    }
 }
+
 /***************************************************************************/
 /*  Routine compute sin(x+dx) (Double-Length number) where x is small enough*/
 /* to use Taylor series around zero and   (x+dx)                            */
@@ -754,46 +903,74 @@ slow2(double x) {
 
 static double
 SECTION
-sloww(double x,double dx, double orig) {
-  static const double th2_36 = 206158430208.0;   /*    1.5*2**37   */
-  double y,x1,x2,xx,r,t,res,cor,w[2],a,da,xn;
-  union {int4 i[2]; double x;} v;
+sloww (double x, double dx, double orig)
+{
+  static const double th2_36 = 206158430208.0;	/*    1.5*2**37   */
+  double y, x1, x2, xx, r, t, res, cor, w[2], a, da, xn;
+  union
+  {
+    int4 i[2];
+    double x;
+  } v;
   int4 n;
-  x1=(x+th2_36)-th2_36;
-  y = aa.x*x1*x1*x1;
-  r=x+y;
-  x2=(x-x1)+dx;
-  xx=x*x;
-  t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx;
-  t=((x-r)+y)+t;
-  res=r+t;
-  cor = (r-res)+t;
-  cor = (cor>0)? 1.0005*cor+ABS(orig)*3.1e-30 : 1.0005*cor-ABS(orig)*3.1e-30;
-  if (res == res + cor) return res;
-  else {
-    (x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w);
-    cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-30 : 1.000000001*w[1] - ABS(orig)*1.1e-30;
-    if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
-    else {
-      t = (orig*hpinv.x + toint.x);
-      xn = t - toint.x;
-      v.x = t;
-      y = (orig - xn*mp1.x) - xn*mp2.x;
-      n =v.i[LOW_HALF]&3;
-      da = xn*pp3.x;
-      t=y-da;
-      da = (y-t)-da;
-      y = xn*pp4.x;
-      a = t - y;
-      da = ((t-a)-y)+da;
-      if (n&2) {a=-a; da=-da;}
-      (a>0)? __dubsin(a,da,w) : __dubsin(-a,-da,w);
-      cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-40 : 1.000000001*w[1] - ABS(orig)*1.1e-40;
-      if (w[0] == w[0]+cor) return (a>0)?w[0]:-w[0];
-      else return __mpsin1(orig);
+  x1 = (x + th2_36) - th2_36;
+  y = aa.x * x1 * x1 * x1;
+  r = x + y;
+  x2 = (x - x1) + dx;
+  xx = x * x;
+  t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
+       + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
+  t = ((x - r) + y) + t;
+  res = r + t;
+  cor = (r - res) + t;
+  cor =
+    (cor >
+     0) ? 1.0005 * cor + ABS (orig) * 3.1e-30 : 1.0005 * cor -
+    ABS (orig) * 3.1e-30;
+  if (res == res + cor)
+    return res;
+  else
+    {
+      (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
+      if (w[1] > 0)
+	cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-30;
+      else
+	cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-30;
+
+      if (w[0] == w[0] + cor)
+	return (x > 0) ? w[0] : -w[0];
+      else
+	{
+	  t = (orig * hpinv.x + toint.x);
+	  xn = t - toint.x;
+	  v.x = t;
+	  y = (orig - xn * mp1.x) - xn * mp2.x;
+	  n = v.i[LOW_HALF] & 3;
+	  da = xn * pp3.x;
+	  t = y - da;
+	  da = (y - t) - da;
+	  y = xn * pp4.x;
+	  a = t - y;
+	  da = ((t - a) - y) + da;
+	  if (n & 2)
+	    {
+	      a = -a;
+	      da = -da;
+	    }
+	  (a > 0) ? __dubsin (a, da, w) : __dubsin (-a, -da, w);
+	  if (w[1] > 0)
+	    cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-40;
+	  else
+	    cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-40;
+
+	  if (w[0] == w[0] + cor)
+	    return (a > 0) ? w[0] : -w[0];
+	  else
+	    return __mpsin1 (orig);
+	}
     }
-  }
 }
+
 /***************************************************************************/
 /*  Routine compute sin(x+dx)   (Double-Length number) where x in first or  */
 /*  third quarter of unit circle.Routine receive also (right argument) the  */
@@ -803,41 +980,58 @@ sloww(double x,double dx, double orig) {
 
 static double
 SECTION
-sloww1(double x, double dx, double orig) {
+sloww1 (double x, double dx, double orig)
+{
   mynumber u;
-  double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
+  double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
   static const double t22 = 6291456.0;
   int4 k;
-  y=ABS(x);
-  u.x=big.x+y;
-  y=y-(u.x-big.x);
-  dx=(x>0)?dx:-dx;
-  xx=y*y;
-  s = y*xx*(sn3 +xx*sn5);
-  c = xx*(cs2 +xx*(cs4 + xx*cs6));
-  k=u.i[LOW_HALF]<<2;
-  sn=__sincostab.x[k];
-  ssn=__sincostab.x[k+1];
-  cs=__sincostab.x[k+2];
-  ccs=__sincostab.x[k+3];
-  y1 = (y+t22)-t22;
-  y2 = (y - y1)+dx;
-  c1 = (cs+t22)-t22;
-  c2=(cs-c1)+ccs;
-  cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c;
-  y=sn+c1*y1;
-  cor = cor+((sn-y)+c1*y1);
-  res=y+cor;
-  cor=(y-res)+cor;
-  cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
-  if (res == res + cor) return (x>0)?res:-res;
-  else {
-    __dubsin(ABS(x),dx,w);
-    cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
-    if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
-  else  return __mpsin1(orig);
-  }
+
+  y = ABS (x);
+  u.x = big.x + y;
+  y = y - (u.x - big.x);
+  dx = (x > 0) ? dx : -dx;
+  xx = y * y;
+  s = y * xx * (sn3 + xx * sn5);
+  c = xx * (cs2 + xx * (cs4 + xx * cs6));
+  k = u.i[LOW_HALF] << 2;
+  sn = __sincostab.x[k];
+  ssn = __sincostab.x[k + 1];
+  cs = __sincostab.x[k + 2];
+  ccs = __sincostab.x[k + 3];
+  y1 = (y + t22) - t22;
+  y2 = (y - y1) + dx;
+  c1 = (cs + t22) - t22;
+  c2 = (cs - c1) + ccs;
+  cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2 - sn * y * dx) - sn * c;
+  y = sn + c1 * y1;
+  cor = cor + ((sn - y) + c1 * y1);
+  res = y + cor;
+  cor = (y - res) + cor;
+
+  if (cor > 0)
+    cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
+  else
+    cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+
+  if (res == res + cor)
+    return (x > 0) ? res : -res;
+  else
+    {
+      __dubsin (ABS (x), dx, w);
+
+      if (w[1] > 0)
+	cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
+      else
+	cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
+
+      if (w[0] == w[0] + cor)
+	return (x > 0) ? w[0] : -w[0];
+      else
+	return __mpsin1 (orig);
+    }
 }
+
 /***************************************************************************/
 /*  Routine compute sin(x+dx)   (Double-Length number) where x in second or */
 /*  fourth quarter of unit circle.Routine receive also  the  original value */
@@ -847,42 +1041,59 @@ sloww1(double x, double dx, double orig) {
 
 static double
 SECTION
-sloww2(double x, double dx, double orig, int n) {
+sloww2 (double x, double dx, double orig, int n)
+{
   mynumber u;
-  double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
+  double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
   static const double t22 = 6291456.0;
   int4 k;
-  y=ABS(x);
-  u.x=big.x+y;
-  y=y-(u.x-big.x);
-  dx=(x>0)?dx:-dx;
-  xx=y*y;
-  s = y*xx*(sn3 +xx*sn5);
-  c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
-  k=u.i[LOW_HALF]<<2;
-  sn=__sincostab.x[k];
-  ssn=__sincostab.x[k+1];
-  cs=__sincostab.x[k+2];
-  ccs=__sincostab.x[k+3];
-
-  y1 = (y+t22)-t22;
-  y2 = (y - y1)+dx;
-  e1 = (sn+t22)-t22;
-  e2=(sn-e1)+ssn;
-  cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
-  y=cs-e1*y1;
-  cor = cor+((cs-y)-e1*y1);
-  res=y+cor;
-  cor=(y-res)+cor;
-  cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
-  if (res == res + cor) return (n&2)?-res:res;
-  else {
-   __docos(ABS(x),dx,w);
-   cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
-   if (w[0] == w[0]+cor) return (n&2)?-w[0]:w[0];
-   else  return __mpsin1(orig);
-  }
+
+  y = ABS (x);
+  u.x = big.x + y;
+  y = y - (u.x - big.x);
+  dx = (x > 0) ? dx : -dx;
+  xx = y * y;
+  s = y * xx * (sn3 + xx * sn5);
+  c = y * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
+  k = u.i[LOW_HALF] << 2;
+  sn = __sincostab.x[k];
+  ssn = __sincostab.x[k + 1];
+  cs = __sincostab.x[k + 2];
+  ccs = __sincostab.x[k + 3];
+
+  y1 = (y + t22) - t22;
+  y2 = (y - y1) + dx;
+  e1 = (sn + t22) - t22;
+  e2 = (sn - e1) + ssn;
+  cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+  y = cs - e1 * y1;
+  cor = cor + ((cs - y) - e1 * y1);
+  res = y + cor;
+  cor = (y - res) + cor;
+
+  if (cor > 0)
+    cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
+  else
+    cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+
+  if (res == res + cor)
+    return (n & 2) ? -res : res;
+  else
+    {
+      __docos (ABS (x), dx, w);
+
+      if (w[1] > 0)
+	cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
+      else
+	cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
+
+      if (w[0] == w[0] + cor)
+	return (n & 2) ? -w[0] : w[0];
+      else
+	return __mpsin1 (orig);
+    }
 }
+
 /***************************************************************************/
 /*  Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x   */
 /* is small enough to use Taylor series around zero and   (x+dx)            */
@@ -893,26 +1104,36 @@ sloww2(double x, double dx, double orig, int n) {
 
 static double
 SECTION
-bsloww(double x,double dx, double orig,int n) {
-  static const double th2_36 = 206158430208.0;   /*    1.5*2**37   */
-  double y,x1,x2,xx,r,t,res,cor,w[2];
-  x1=(x+th2_36)-th2_36;
-  y = aa.x*x1*x1*x1;
-  r=x+y;
-  x2=(x-x1)+dx;
-  xx=x*x;
-  t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx;
-  t=((x-r)+y)+t;
-  res=r+t;
-  cor = (r-res)+t;
-  cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24;
-  if (res == res + cor) return res;
-  else {
-    (x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w);
-    cor = (w[1]>0)? 1.000000001*w[1] + 1.1e-24 : 1.000000001*w[1] - 1.1e-24;
-    if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
-    else return (n&1)?__mpcos1(orig):__mpsin1(orig);
-  }
+bsloww (double x, double dx, double orig, int n)
+{
+  static const double th2_36 = 206158430208.0;	/*    1.5*2**37   */
+  double y, x1, x2, xx, r, t, res, cor, w[2];
+
+  x1 = (x + th2_36) - th2_36;
+  y = aa.x * x1 * x1 * x1;
+  r = x + y;
+  x2 = (x - x1) + dx;
+  xx = x * x;
+  t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
+       + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
+  t = ((x - r) + y) + t;
+  res = r + t;
+  cor = (r - res) + t;
+  cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
+  if (res == res + cor)
+    return res;
+  else
+    {
+      (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
+      if (w[1] > 0)
+	cor = 1.000000001 * w[1] + 1.1e-24;
+      else
+	cor = 1.000000001 * w[1] - 1.1e-24;
+      if (w[0] == w[0] + cor)
+	return (x > 0) ? w[0] : -w[0];
+      else
+	return (n & 1) ? __mpcos1 (orig) : __mpsin1 (orig);
+    }
 }
 
 /***************************************************************************/
@@ -924,40 +1145,51 @@ bsloww(double x,double dx, double orig,int n) {
 
 static double
 SECTION
-bsloww1(double x, double dx, double orig,int n) {
-mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
- static const double t22 = 6291456.0;
- int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- dx=(x>0)?dx:-dx;
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- y1 = (y+t22)-t22;
- y2 = (y - y1)+dx;
- c1 = (cs+t22)-t22;
- c2=(cs-c1)+ccs;
- cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c;
- y=sn+c1*y1;
- cor = cor+((sn-y)+c1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24;
- if (res == res + cor) return (x>0)?res:-res;
- else {
-   __dubsin(ABS(x),dx,w);
-   cor = (w[1]>0)? 1.000000005*w[1]+1.1e-24: 1.000000005*w[1]-1.1e-24;
-   if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
-   else  return (n&1)?__mpcos1(orig):__mpsin1(orig);
- }
+bsloww1 (double x, double dx, double orig, int n)
+{
+  mynumber u;
+  double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
+  static const double t22 = 6291456.0;
+  int4 k;
+
+  y = ABS (x);
+  u.x = big.x + y;
+  y = y - (u.x - big.x);
+  dx = (x > 0) ? dx : -dx;
+  xx = y * y;
+  s = y * xx * (sn3 + xx * sn5);
+  c = xx * (cs2 + xx * (cs4 + xx * cs6));
+  k = u.i[LOW_HALF] << 2;
+  sn = __sincostab.x[k];
+  ssn = __sincostab.x[k + 1];
+  cs = __sincostab.x[k + 2];
+  ccs = __sincostab.x[k + 3];
+  y1 = (y + t22) - t22;
+  y2 = (y - y1) + dx;
+  c1 = (cs + t22) - t22;
+  c2 = (cs - c1) + ccs;
+  cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2 - sn * y * dx) - sn * c;
+  y = sn + c1 * y1;
+  cor = cor + ((sn - y) + c1 * y1);
+  res = y + cor;
+  cor = (y - res) + cor;
+  cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
+  if (res == res + cor)
+    return (x > 0) ? res : -res;
+  else
+    {
+      __dubsin (ABS (x), dx, w);
+
+      if (w[1] > 0)
+	cor = 1.000000005 * w[1] + 1.1e-24;
+      else
+	cor = 1.000000005 * w[1] - 1.1e-24;
+
+      if (w[0] == w[0] + cor)
+	return (x > 0) ? w[0] : -w[0];
+      else
+	return (n & 1) ? __mpcos1 (orig) : __mpsin1 (orig);
+    }
 }
 
 /***************************************************************************/
@@ -969,41 +1201,52 @@ mynumber u;
 
 static double
 SECTION
-bsloww2(double x, double dx, double orig, int n) {
-mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
- static const double t22 = 6291456.0;
- int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- dx=(x>0)?dx:-dx;
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
-
- y1 = (y+t22)-t22;
- y2 = (y - y1)+dx;
- e1 = (sn+t22)-t22;
- e2=(sn-e1)+ssn;
- cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
- y=cs-e1*y1;
- cor = cor+((cs-y)-e1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24;
- if (res == res + cor) return (n&2)?-res:res;
- else {
-   __docos(ABS(x),dx,w);
-   cor = (w[1]>0)? 1.000000005*w[1]+1.1e-24 : 1.000000005*w[1]-1.1e-24;
-   if (w[0] == w[0]+cor) return (n&2)?-w[0]:w[0];
-   else  return (n&1)?__mpsin1(orig):__mpcos1(orig);
- }
+bsloww2 (double x, double dx, double orig, int n)
+{
+  mynumber u;
+  double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
+  static const double t22 = 6291456.0;
+  int4 k;
+
+  y = ABS (x);
+  u.x = big.x + y;
+  y = y - (u.x - big.x);
+  dx = (x > 0) ? dx : -dx;
+  xx = y * y;
+  s = y * xx * (sn3 + xx * sn5);
+  c = y * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
+  k = u.i[LOW_HALF] << 2;
+  sn = __sincostab.x[k];
+  ssn = __sincostab.x[k + 1];
+  cs = __sincostab.x[k + 2];
+  ccs = __sincostab.x[k + 3];
+
+  y1 = (y + t22) - t22;
+  y2 = (y - y1) + dx;
+  e1 = (sn + t22) - t22;
+  e2 = (sn - e1) + ssn;
+  cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+  y = cs - e1 * y1;
+  cor = cor + ((cs - y) - e1 * y1);
+  res = y + cor;
+  cor = (y - res) + cor;
+  cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
+  if (res == res + cor)
+    return (n & 2) ? -res : res;
+  else
+    {
+      __docos (ABS (x), dx, w);
+
+      if (w[1] > 0)
+	cor = 1.000000005 * w[1] + 1.1e-24;
+      else
+	cor = 1.000000005 * w[1] - 1.1e-24;
+
+      if (w[0] == w[0] + cor)
+	return (n & 2) ? -w[0] : w[0];
+      else
+	return (n & 1) ? __mpsin1 (orig) : __mpcos1 (orig);
+    }
 }
 
 /************************************************************************/
@@ -1013,39 +1256,44 @@ mynumber u;
 
 static double
 SECTION
-cslow2(double x) {
+cslow2 (double x)
+{
   mynumber u;
-  double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
+  double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
   static const double t22 = 6291456.0;
   int4 k;
-  y=ABS(x);
-  u.x = big.x+y;
-  y = y-(u.x-big.x);
-  xx=y*y;
-  s = y*xx*(sn3 +xx*sn5);
-  c = xx*(cs2 +xx*(cs4 + xx*cs6));
-  k=u.i[LOW_HALF]<<2;
-  sn=__sincostab.x[k];
-  ssn=__sincostab.x[k+1];
-  cs=__sincostab.x[k+2];
-  ccs=__sincostab.x[k+3];
-  y1 = (y+t22)-t22;
+
+  y = ABS (x);
+  u.x = big.x + y;
+  y = y - (u.x - big.x);
+  xx = y * y;
+  s = y * xx * (sn3 + xx * sn5);
+  c = xx * (cs2 + xx * (cs4 + xx * cs6));
+  k = u.i[LOW_HALF] << 2;
+  sn = __sincostab.x[k];
+  ssn = __sincostab.x[k + 1];
+  cs = __sincostab.x[k + 2];
+  ccs = __sincostab.x[k + 3];
+  y1 = (y + t22) - t22;
   y2 = y - y1;
-  e1 = (sn+t22)-t22;
-  e2=(sn-e1)+ssn;
-  cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
-  y=cs-e1*y1;
-  cor = cor+((cs-y)-e1*y1);
-  res=y+cor;
-  cor=(y-res)+cor;
-  if (res == res+1.0005*cor)
+  e1 = (sn + t22) - t22;
+  e2 = (sn - e1) + ssn;
+  cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+  y = cs - e1 * y1;
+  cor = cor + ((cs - y) - e1 * y1);
+  res = y + cor;
+  cor = (y - res) + cor;
+  if (res == res + 1.0005 * cor)
     return res;
-  else {
-    y=ABS(x);
-    __docos(y,0,w);
-    if (w[0] == w[0]+1.000000005*w[1]) return w[0];
-    else return __mpcos(x,0);
-  }
+  else
+    {
+      y = ABS (x);
+      __docos (y, 0, w);
+      if (w[0] == w[0] + 1.000000005 * w[1])
+	return w[0];
+      else
+	return __mpcos (x, 0);
+    }
 }
 
 /***************************************************************************/
@@ -1058,46 +1306,78 @@ cslow2(double x) {
 
 static double
 SECTION
-csloww(double x,double dx, double orig) {
-  static const double th2_36 = 206158430208.0;   /*    1.5*2**37   */
-  double y,x1,x2,xx,r,t,res,cor,w[2],a,da,xn;
-  union {int4 i[2]; double x;} v;
+csloww (double x, double dx, double orig)
+{
+  static const double th2_36 = 206158430208.0;	/*    1.5*2**37   */
+  double y, x1, x2, xx, r, t, res, cor, w[2], a, da, xn;
+  union
+  {
+    int4 i[2];
+    double x;
+  } v;
   int4 n;
-  x1=(x+th2_36)-th2_36;
-  y = aa.x*x1*x1*x1;
-  r=x+y;
-  x2=(x-x1)+dx;
-  xx=x*x;
-    /* Taylor series */
-  t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx;
-  t=((x-r)+y)+t;
-  res=r+t;
-  cor = (r-res)+t;
-  cor = (cor>0)? 1.0005*cor+ABS(orig)*3.1e-30 : 1.0005*cor-ABS(orig)*3.1e-30;
-  if (res == res + cor) return res;
-  else {
-    (x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w);
-    cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-30 : 1.000000001*w[1] - ABS(orig)*1.1e-30;
-    if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
-    else {
-      t = (orig*hpinv.x + toint.x);
-      xn = t - toint.x;
-      v.x = t;
-      y = (orig - xn*mp1.x) - xn*mp2.x;
-      n =v.i[LOW_HALF]&3;
-      da = xn*pp3.x;
-      t=y-da;
-      da = (y-t)-da;
-      y = xn*pp4.x;
-      a = t - y;
-      da = ((t-a)-y)+da;
-      if (n==1) {a=-a; da=-da;}
-      (a>0)? __dubsin(a,da,w) : __dubsin(-a,-da,w);
-      cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-40 : 1.000000001*w[1] - ABS(orig)*1.1e-40;
-      if (w[0] == w[0]+cor) return (a>0)?w[0]:-w[0];
-      else return __mpcos1(orig);
+
+  x1 = (x + th2_36) - th2_36;
+  y = aa.x * x1 * x1 * x1;
+  r = x + y;
+  x2 = (x - x1) + dx;
+  xx = x * x;
+  /* Taylor series */
+  t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
+       + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
+  t = ((x - r) + y) + t;
+  res = r + t;
+  cor = (r - res) + t;
+
+  if (cor > 0)
+    cor = 1.0005 * cor + ABS (orig) * 3.1e-30;
+  else
+    cor = 1.0005 * cor - ABS (orig) * 3.1e-30;
+
+  if (res == res + cor)
+    return res;
+  else
+    {
+      (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
+
+      if (w[1] > 0)
+	cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-30;
+      else
+	cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-30;
+
+      if (w[0] == w[0] + cor)
+	return (x > 0) ? w[0] : -w[0];
+      else
+	{
+	  t = (orig * hpinv.x + toint.x);
+	  xn = t - toint.x;
+	  v.x = t;
+	  y = (orig - xn * mp1.x) - xn * mp2.x;
+	  n = v.i[LOW_HALF] & 3;
+	  da = xn * pp3.x;
+	  t = y - da;
+	  da = (y - t) - da;
+	  y = xn * pp4.x;
+	  a = t - y;
+	  da = ((t - a) - y) + da;
+	  if (n == 1)
+	    {
+	      a = -a;
+	      da = -da;
+	    }
+	  (a > 0) ? __dubsin (a, da, w) : __dubsin (-a, -da, w);
+
+	  if (w[1] > 0)
+	    cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-40;
+	  else
+	    cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-40;
+
+	  if (w[0] == w[0] + cor)
+	    return (a > 0) ? w[0] : -w[0];
+	  else
+	    return __mpcos1 (orig);
+	}
     }
-  }
 }
 
 /***************************************************************************/
@@ -1109,40 +1389,54 @@ csloww(double x,double dx, double orig) {
 
 static double
 SECTION
-csloww1(double x, double dx, double orig) {
+csloww1 (double x, double dx, double orig)
+{
   mynumber u;
-  double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
+  double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
   static const double t22 = 6291456.0;
   int4 k;
-  y=ABS(x);
-  u.x=big.x+y;
-  y=y-(u.x-big.x);
-  dx=(x>0)?dx:-dx;
-  xx=y*y;
-  s = y*xx*(sn3 +xx*sn5);
-  c = xx*(cs2 +xx*(cs4 + xx*cs6));
-  k=u.i[LOW_HALF]<<2;
-  sn=__sincostab.x[k];
-  ssn=__sincostab.x[k+1];
-  cs=__sincostab.x[k+2];
-  ccs=__sincostab.x[k+3];
-  y1 = (y+t22)-t22;
-  y2 = (y - y1)+dx;
-  c1 = (cs+t22)-t22;
-  c2=(cs-c1)+ccs;
-  cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c;
-  y=sn+c1*y1;
-  cor = cor+((sn-y)+c1*y1);
-  res=y+cor;
-  cor=(y-res)+cor;
-  cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
-  if (res == res + cor) return (x>0)?res:-res;
-  else {
-    __dubsin(ABS(x),dx,w);
-    cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
-    if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
-    else  return __mpcos1(orig);
-  }
+
+  y = ABS (x);
+  u.x = big.x + y;
+  y = y - (u.x - big.x);
+  dx = (x > 0) ? dx : -dx;
+  xx = y * y;
+  s = y * xx * (sn3 + xx * sn5);
+  c = xx * (cs2 + xx * (cs4 + xx * cs6));
+  k = u.i[LOW_HALF] << 2;
+  sn = __sincostab.x[k];
+  ssn = __sincostab.x[k + 1];
+  cs = __sincostab.x[k + 2];
+  ccs = __sincostab.x[k + 3];
+  y1 = (y + t22) - t22;
+  y2 = (y - y1) + dx;
+  c1 = (cs + t22) - t22;
+  c2 = (cs - c1) + ccs;
+  cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2 - sn * y * dx) - sn * c;
+  y = sn + c1 * y1;
+  cor = cor + ((sn - y) + c1 * y1);
+  res = y + cor;
+  cor = (y - res) + cor;
+
+  if (cor > 0)
+    cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
+  else
+    cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+
+  if (res == res + cor)
+    return (x > 0) ? res : -res;
+  else
+    {
+      __dubsin (ABS (x), dx, w);
+      if (w[1] > 0)
+	cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
+      else
+	cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
+      if (w[0] == w[0] + cor)
+	return (x > 0) ? w[0] : -w[0];
+      else
+	return __mpcos1 (orig);
+    }
 }
 
 
@@ -1155,41 +1449,55 @@ csloww1(double x, double dx, double orig) {
 
 static double
 SECTION
-csloww2(double x, double dx, double orig, int n) {
+csloww2 (double x, double dx, double orig, int n)
+{
   mynumber u;
-  double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
+  double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
   static const double t22 = 6291456.0;
   int4 k;
-  y=ABS(x);
-  u.x=big.x+y;
-  y=y-(u.x-big.x);
-  dx=(x>0)?dx:-dx;
-  xx=y*y;
-  s = y*xx*(sn3 +xx*sn5);
-  c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
-  k=u.i[LOW_HALF]<<2;
-  sn=__sincostab.x[k];
-  ssn=__sincostab.x[k+1];
-  cs=__sincostab.x[k+2];
-  ccs=__sincostab.x[k+3];
-
-  y1 = (y+t22)-t22;
-  y2 = (y - y1)+dx;
-  e1 = (sn+t22)-t22;
-  e2=(sn-e1)+ssn;
-  cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
-  y=cs-e1*y1;
-  cor = cor+((cs-y)-e1*y1);
-  res=y+cor;
-  cor=(y-res)+cor;
-  cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
-  if (res == res + cor) return (n)?-res:res;
-  else {
-    __docos(ABS(x),dx,w);
-    cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
-    if (w[0] == w[0]+cor) return (n)?-w[0]:w[0];
-    else  return __mpcos1(orig);
-  }
+
+  y = ABS (x);
+  u.x = big.x + y;
+  y = y - (u.x - big.x);
+  dx = (x > 0) ? dx : -dx;
+  xx = y * y;
+  s = y * xx * (sn3 + xx * sn5);
+  c = y * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
+  k = u.i[LOW_HALF] << 2;
+  sn = __sincostab.x[k];
+  ssn = __sincostab.x[k + 1];
+  cs = __sincostab.x[k + 2];
+  ccs = __sincostab.x[k + 3];
+
+  y1 = (y + t22) - t22;
+  y2 = (y - y1) + dx;
+  e1 = (sn + t22) - t22;
+  e2 = (sn - e1) + ssn;
+  cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+  y = cs - e1 * y1;
+  cor = cor + ((cs - y) - e1 * y1);
+  res = y + cor;
+  cor = (y - res) + cor;
+
+  if (cor > 0)
+    cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
+  else
+    cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+
+  if (res == res + cor)
+    return (n) ? -res : res;
+  else
+    {
+      __docos (ABS (x), dx, w);
+      if (w[1] > 0)
+	cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
+      else
+	cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
+      if (w[0] == w[0] + cor)
+	return (n) ? -w[0] : w[0];
+      else
+	return __mpcos1 (orig);
+    }
 }
 
 #ifndef __cos