Use fabs(x) instead of branching on signedness of input to sin and cos

The sin and cos code is inconsistent about its use of fabs to get the
absolute value of X where in some places it conditionalizes the code
while in others it uses fabs.  fabs seems to be a better candidate in
most cases because it avoids a branch.  Similarly there is an attempt
to make it easier for the compiler to emit conditional assignment
instructions (like fcsel on aarch64) where it can, by isolating
conditional assignment constructs from the rest of the expression.

A further benefit of this change is to identify common constructs
across functions and consolidate them in future patches.

	* sysdeps/ieee754/dbl-64/s_sin.c (do_cos_slow): Use ternary
	instead of if/else.
	(do_sin_slow): Likewise.
	(do_sincos_1): Use fabs instead of if/else.
	(do_sincos_2): Likewise.
	(__sin): Likewise.
	(__cos): Likewise.
	(slow2): Likewise.
	(sloww): Likewise.
	(sloww1): Likewise.  Drop argument M.
	(sloww2): Use fabs instead of if/else.
	(bsloww): Likewise.
	(bsloww1): Likewise.
	(bsloww2): Likewise.

2 files changed, 100 insertions, 148 deletions

diff --git a/ChangeLog b/ChangeLog
index ae56776..418bdae 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,5 +1,20 @@
 2016-08-30  Siddhesh Poyarekar  <siddhesh@sourceware.org>
 
+	* sysdeps/ieee754/dbl-64/s_sin.c (do_cos_slow): Use ternary
+	instead of if/else.
+	(do_sin_slow): Likewise.
+	(do_sincos_1): Use fabs instead of if/else.
+	(do_sincos_2): Likewise.
+	(__sin): Likewise.
+	(__cos): Likewise.
+	(slow2): Likewise.
+	(sloww): Likewise.
+	(sloww1): Likewise.  Drop argument M.
+	(sloww2): Use fabs instead of if/else.
+	(bsloww): Likewise.
+	(bsloww1): Likewise.
+	(bsloww2): Likewise.
+
 	* sysdeps/ieee754/dbl-64/s_sin.c (reduce_and_compute): Add
 	fall through comment.
 	(do_sincos_1): Likewise.
diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c
index a7f612a..9ecba05 100644
--- a/sysdeps/ieee754/dbl-64/s_sin.c
+++ b/sysdeps/ieee754/dbl-64/s_sin.c
@@ -133,7 +133,7 @@ static double slow (double x);
 static double slow1 (double x);
 static double slow2 (double x);
 static double sloww (double x, double dx, double orig, int n);
-static double sloww1 (double x, double dx, double orig, int m, int n);
+static double sloww1 (double x, double dx, double orig, int n);
 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);
@@ -181,10 +181,7 @@ do_cos_slow (mynumber u, double x, double dx, double eps, double *corp)
   cor = cor + ((cs - y) - e1 * x1);
   res = y + cor;
   cor = (y - res) + cor;
-  if (cor > 0)
-    cor = 1.0005 * cor + eps;
-  else
-    cor = 1.0005 * cor - eps;
+  cor = 1.0005 * cor + ((cor > 0) ? eps : -eps);
   *corp = cor;
   return res;
 }
@@ -229,10 +226,7 @@ do_sin_slow (mynumber u, double x, double dx, double eps, double *corp)
   cor = cor + ((sn - y) + c1 * x1);
   res = y + cor;
   cor = (y - res) + cor;
-  if (cor > 0)
-    cor = 1.0005 * cor + eps;
-  else
-    cor = 1.0005 * cor - eps;
+  cor = 1.0005 * cor + ((cor > 0) ? eps : -eps);
   *corp = cor;
   return res;
 }
@@ -297,7 +291,6 @@ do_sincos_1 (double a, double da, double x, int4 n, int4 k)
 {
   double xx, retval, res, cor, y;
   mynumber u;
-  int m;
   double eps = fabs (x) * 1.2e-30;
 
   int k1 = (n + k) & 3;
@@ -318,37 +311,28 @@ do_sincos_1 (double a, double da, double x, int4 n, int4 k)
 	}
       else
 	{
-	  if (a > 0)
-	    m = 1;
-	  else
-	    {
-	      m = 0;
-	      a = -a;
-	      da = -da;
-	    }
-	  u.x = big + a;
-	  y = a - (u.x - big);
-	  res = do_sin (u, y, da, &cor);
+	  double db = (a > 0 ? da : -da);
+	  u.x = big + fabs (a);
+	  y = fabs (a) - (u.x - big);
+	  res = do_sin (u, y, db, &cor);
 	  cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
-	  retval = ((res == res + cor) ? ((m) ? res : -res)
-		    : sloww1 (a, da, x, m, k));
+	  retval = ((res == res + cor) ? ((a > 0) ? res : -res)
+		    : sloww1 (a, da, x, k));
 	}
       break;
 
     case 1:
     case 3:
-      if (a < 0)
 	{
-	  a = -a;
-	  da = -da;
+	  double db = (a > 0 ? da : -da);
+	  u.x = big + fabs (a);
+	  y = fabs (a) - (u.x - big) + db;
+	  res = do_cos (u, y, &cor);
+	  cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
+	  retval = ((res == res + cor) ? ((k1 & 2) ? -res : res)
+		    : sloww2 (a, da, x, n));
+	  break;
 	}
-      u.x = big + a;
-      y = a - (u.x - big) + da;
-      res = do_cos (u, y, &cor);
-      cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
-      retval = ((res == res + cor) ? ((k1 & 2) ? -res : res)
-		: sloww2 (a, da, x, n));
-      break;
     }
 
   return retval;
@@ -410,43 +394,28 @@ do_sincos_2 (double a, double da, double x, int4 n, int4 k)
 	}
       else
 	{
-	  double t, db, y;
-	  int m;
-	  if (a > 0)
-	    {
-	      m = 1;
-	      t = a;
-	      db = da;
-	    }
-	  else
-	    {
-	      m = 0;
-	      t = -a;
-	      db = -da;
-	    }
-	  u.x = big + t;
-	  y = t - (u.x - big);
+	  double db = (a > 0 ? da : -da);
+	  u.x = big + fabs (a);
+	  double y = fabs (a) - (u.x - big);
 	  res = do_sin (u, y, db, &cor);
 	  cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
-	  retval = ((res == res + cor) ? ((m) ? res : -res)
+	  retval = ((res == res + cor) ? ((a > 0) ? res : -res)
 		    : bsloww1 (a, da, x, n));
 	}
       break;
 
     case 1:
     case 3:
-      if (a < 0)
 	{
-	  a = -a;
-	  da = -da;
+	  double db = (a > 0 ? da : -da);
+	  u.x = big + fabs (a);
+	  double y = fabs (a) - (u.x - big) + db;
+	  res = do_cos (u, y, &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));
+	  break;
 	}
-      u.x = big + a;
-      double y = a - (u.x - big) + da;
-      res = do_cos (u, y, &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));
-      break;
     }
 
   return retval;
@@ -494,8 +463,10 @@ __sin (double x)
 /*---------------------------- 0.25<|x|< 0.855469---------------------- */
   else if (k < 0x3feb6000)
     {
-      u.x = (m > 0) ? big + x : big - x;
-      y = (m > 0) ? x - (u.x - big) : x + (u.x - big);
+      u.x = big + fabs (x);
+      y = fabs (x) - (u.x - big);
+      y = (x > 0 ? y : -y);
+
       xx = y * y;
       s = y + y * xx * (sn3 + xx * sn5);
       c = xx * (cs2 + xx * (cs4 + xx * cs6));
@@ -515,17 +486,11 @@ __sin (double x)
   else if (k < 0x400368fd)
     {
 
-      y = (m > 0) ? hp0 - x : hp0 + x;
-      if (y >= 0)
-	{
-	  u.x = big + y;
-	  y = (y - (u.x - big)) + hp1;
-	}
-      else
-	{
-	  u.x = big - y;
-	  y = (-hp1) - (y + (u.x - big));
-	}
+      t = hp0 - fabs (x);
+      u.x = big + fabs (t);
+      y = fabs (t) - (u.x - big);
+      y = ((t >= 0) ? hp1 : -hp1) + y;
+
       res = do_cos (u, y, &cor);
       retval = (res == res + 1.020 * cor) ? ((m > 0) ? res : -res) : slow2 (x);
     }				/*   else  if (k < 0x400368fd)    */
@@ -619,22 +584,13 @@ __cos (double x)
 	}
       else
 	{
-	  if (a > 0)
-	    {
-	      m = 1;
-	    }
-	  else
-	    {
-	      m = 0;
-	      a = -a;
-	      da = -da;
-	    }
-	  u.x = big + a;
-	  y = a - (u.x - big);
-	  res = do_sin (u, y, da, &cor);
+	  double db = (a > 0 ? da : -da);
+	  u.x = big + fabs (a);
+	  y = fabs (a) - (u.x - big);
+	  res = do_sin (u, y, db, &cor);
 	  cor = (cor > 0) ? 1.035 * cor + 1.0e-31 : 1.035 * cor - 1.0e-31;
-	  retval = ((res == res + cor) ? ((m) ? res : -res)
-		    : sloww1 (a, da, x, m, 1));
+	  retval = ((res == res + cor) ? ((a > 0) ? res : -res)
+		    : sloww1 (a, da, x, 1));
 	}
 
     }				/*   else  if (k < 0x400368fd)    */
@@ -728,20 +684,11 @@ slow2 (double x)
   mynumber u;
   double w[2], y, y1, y2, cor, res, del;
 
-  y = fabs (x);
-  y = hp0 - y;
-  if (y >= 0)
-    {
-      u.x = big + y;
-      y = y - (u.x - big);
-      del = hp1;
-    }
-  else
-    {
-      u.x = big - y;
-      y = -(y + (u.x - big));
-      del = -hp1;
-    }
+  double t = hp0 - fabs (x);
+  u.x = big + fabs (t);
+  y = fabs (t) - (u.x - big);
+  del = (t >= 0) ? hp1 : -hp1;
+
   res = do_cos_slow (u, y, del, 0, &cor);
   if (res == res + cor)
     return (x > 0) ? res : -res;
@@ -773,19 +720,18 @@ sloww (double x, double dx, double orig, int k)
   int4 n;
   res = TAYLOR_SLOW (x, dx, cor);
 
-  if (cor > 0)
-    cor = 1.0005 * cor + fabs (orig) * 3.1e-30;
-  else
-    cor = 1.0005 * cor - fabs (orig) * 3.1e-30;
+  double eps = fabs (orig) * 3.1e-30;
+
+  cor = 1.0005 * cor + ((cor > 0) ? eps : -eps);
 
   if (res == res + cor)
     return res;
 
-  (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
-  if (w[1] > 0)
-    cor = 1.000000001 * w[1] + fabs (orig) * 1.1e-30;
-  else
-    cor = 1.000000001 * w[1] - fabs (orig) * 1.1e-30;
+  a = fabs (x);
+  da = (x > 0) ? dx : -dx;
+  __dubsin (a, da, w);
+  eps = fabs (orig) * 1.1e-30;
+  cor = 1.000000001 * w[1] + ((w[1] > 0) ? eps : -eps);
 
   if (w[0] == w[0] + cor)
     return (x > 0) ? w[0] : -w[0];
@@ -807,11 +753,11 @@ sloww (double x, double dx, double orig, int k)
       a = -a;
       da = -da;
     }
-  (a > 0) ? __dubsin (a, da, w) : __dubsin (-a, -da, w);
-  if (w[1] > 0)
-    cor = 1.000000001 * w[1] + fabs (orig) * 1.1e-40;
-  else
-    cor = 1.000000001 * w[1] - fabs (orig) * 1.1e-40;
+  x = fabs (a);
+  dx = (a > 0) ? da : -da;
+  __dubsin (x, dx, w);
+  eps = fabs (orig) * 1.1e-40;
+  cor = 1.000000001 * w[1] + ((w[1] > 0) ? eps : -eps);
 
   if (w[0] == w[0] + cor)
     return (a > 0) ? w[0] : -w[0];
@@ -828,27 +774,26 @@ sloww (double x, double dx, double orig, int k)
 
 static double
 SECTION
-sloww1 (double x, double dx, double orig, int m, int k)
+sloww1 (double x, double dx, double orig, int k)
 {
   mynumber u;
   double w[2], y, cor, res;
 
-  u.x = big + x;
-  y = x - (u.x - big);
+  u.x = big + fabs (x);
+  y = fabs (x) - (u.x - big);
+  dx = (x > 0 ? dx : -dx);
   res = do_sin_slow (u, y, dx, 3.1e-30 * fabs (orig), &cor);
 
   if (res == res + cor)
-    return (m > 0) ? res : -res;
+    return (x > 0) ? res : -res;
 
-  __dubsin (x, dx, w);
+  __dubsin (fabs (x), dx, w);
 
-  if (w[1] > 0)
-    cor = 1.000000005 * w[1] + 1.1e-30 * fabs (orig);
-  else
-    cor = 1.000000005 * w[1] - 1.1e-30 * fabs (orig);
+  double eps = 1.1e-30 * fabs (orig);
+  cor = 1.000000005 * w[1] + ((w[1] > 0) ? eps : -eps);
 
   if (w[0] == w[0] + cor)
-    return (m > 0) ? w[0] : -w[0];
+    return (x > 0) ? w[0] : -w[0];
 
   return (k == 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
 }
@@ -867,19 +812,18 @@ sloww2 (double x, double dx, double orig, int n)
   mynumber u;
   double w[2], y, cor, res;
 
-  u.x = big + x;
-  y = x - (u.x - big);
+  u.x = big + fabs (x);
+  y = fabs (x) - (u.x - big);
+  dx = (x > 0 ? dx : -dx);
   res = do_cos_slow (u, y, dx, 3.1e-30 * fabs (orig), &cor);
 
   if (res == res + cor)
     return (n & 2) ? -res : res;
 
-  __docos (x, dx, w);
+  __docos (fabs (x), dx, w);
 
-  if (w[1] > 0)
-    cor = 1.000000005 * w[1] + 1.1e-30 * fabs (orig);
-  else
-    cor = 1.000000005 * w[1] - 1.1e-30 * fabs (orig);
+  double eps = 1.1e-30 * fabs (orig);
+  cor = 1.000000005 * w[1] + ((w[1] > 0) ? eps : -eps);
 
   if (w[0] == w[0] + cor)
     return (n & 2) ? -w[0] : w[0];
@@ -899,18 +843,17 @@ static double
 SECTION
 bsloww (double x, double dx, double orig, int n)
 {
-  double res, cor, w[2];
+  double res, cor, w[2], a, da;
 
   res = TAYLOR_SLOW (x, dx, cor);
-  cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
+  cor = 1.0005 * cor + ((cor > 0) ? 1.1e-24 : -1.1e-24);
   if (res == res + cor)
     return res;
 
-  (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;
+  a = fabs (x);
+  da = (x > 0) ? dx : -dx;
+  __dubsin (a, da, w);
+  cor = 1.000000001 * w[1] + ((w[1] > 0) ? 1.1e-24 : -1.1e-24);
 
   if (w[0] == w[0] + cor)
     return (x > 0) ? w[0] : -w[0];
@@ -942,10 +885,7 @@ bsloww1 (double x, double dx, double orig, int n)
 
   __dubsin (fabs (x), dx, w);
 
-  if (w[1] > 0)
-    cor = 1.000000005 * w[1] + 1.1e-24;
-  else
-    cor = 1.000000005 * w[1] - 1.1e-24;
+  cor = 1.000000005 * w[1] + ((w[1] > 0) ? 1.1e-24 : -1.1e-24);
 
   if (w[0] == w[0] + cor)
     return (x > 0) ? w[0] : -w[0];
@@ -977,10 +917,7 @@ bsloww2 (double x, double dx, double orig, int n)
 
   __docos (fabs (x), dx, w);
 
-  if (w[1] > 0)
-    cor = 1.000000005 * w[1] + 1.1e-24;
-  else
-    cor = 1.000000005 * w[1] - 1.1e-24;
+  cor = 1.000000005 * w[1] + ((w[1] > 0) ? 1.1e-24 : -1.1e-24);
 
   if (w[0] == w[0] + cor)
     return (n & 2) ? -w[0] : w[0];