Consolidate sin and cos code for 105414350 <|x|< 281474976710656

The sin and cos computation for this range of input is identical
except for a difference in quadrants by 1.  Exploit that fact and the
common argument reduction to reduce computations for sincos.

diff --git a/ChangeLog b/ChangeLog
index c8281dd0592d06be949790f73634337caf176d8d..2228769d6a30902a2564d58f121d4f0700e14d2a 100644 (file)
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,5 +1,10 @@
 2015-12-21  Siddhesh Poyarekar  <siddhesh.poyarekar@linaro.org>
 
+       * sysdeps/ieee754/dbl-64/s_sin.c (__sin, __cos): Move common
+       code to new functions.
+       (reduce_sincos_2, do_sincos_2): New functions.
+       * sysdeps/ieee754/dbl-64/s_sincos.c (__sincos): Use them.
+
        * sysdeps/ieee754/dbl-64/s_sin.c (__sin) [!IN_SINCOS]: Skip
        common code for sincos.
        (__cos) [!IN_SINCOS]: Likewise.

diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c
index b619905dcb2565198b98a5c7d6ed7178fe09235e..3b26a61c8e8db74774587b243de79092835ab1cb 100644 (file)
--- a/sysdeps/ieee754/dbl-64/s_sin.c
+++ b/sysdeps/ieee754/dbl-64/s_sin.c
@@ -276,6 +276,104 @@ reduce_and_compute (double x, unsigned int k)
   return retval;
 }
 
+static inline int4
+__always_inline
+reduce_sincos_2 (double x, double *a, double *da)
+{
+  mynumber v;
+
+  double t = (x * hpinv + toint);
+  double xn = t - toint;
+  v.x = t;
+  double xn1 = (xn + 8.0e22) - 8.0e22;
+  double xn2 = xn - xn1;
+  double y = ((((x - xn1 * mp1) - xn1 * mp2) - xn2 * mp1) - xn2 * mp2);
+  int4 n = v.i[LOW_HALF] & 3;
+  double db = xn1 * pp3;
+  t = y - db;
+  db = (y - t) - db;
+  db = (db - xn2 * pp3) - xn * pp4;
+  double b = t + db;
+  db = (t - b) + db;
+
+  *a = b;
+  *da = db;
+
+  return n;
+}
+
+/* Compute sin (A + DA).  cos can be computed by shifting the quadrant N
+   clockwise.  */
+static double
+__always_inline
+do_sincos_2 (double a, double da, double x, int4 n, int4 k)
+{
+  double res, retval, cor, xx;
+  mynumber u;
+
+  double eps = 1.0e-24;
+
+  k = (n + k) & 3;
+
+  switch (k)
+    {
+    case 2:
+      a = -a;
+      da = -da;
+      /* Fall through.  */
+    case 0:
+      xx = a * a;
+      if (xx < 0.01588)
+       {
+         /* Taylor series.  */
+         res = TAYLOR_SIN (xx, a, da, cor);
+         cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
+         retval = (res == res + cor) ? res : bsloww (a, da, x, n);
+       }
+      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);
+         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)
+                   : bsloww1 (a, da, x, n));
+       }
+      break;
+
+    case 1:
+    case 3:
+      if (a < 0)
+       {
+         a = -a;
+         da = -da;
+       }
+      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;
+}
+
 /*******************************************************************/
 /* An ultimate sin routine. Given an IEEE double machine number x   */
 /* it computes the correctly rounded (to nearest) value of sin(x)  */
@@ -288,8 +386,7 @@ SECTION
 #endif
 __sin (double x)
 {
-  double xx, res, t, cor, y, s, c, sn, ssn, cs, ccs, xn, a, da, db, eps, xn1,
-    xn2;
+  double xx, res, t, cor, y, s, c, sn, ssn, cs, ccs, xn, a, da, eps;
   mynumber u, v;
   int4 k, m, n;
   double retval = 0;
@@ -421,83 +518,16 @@ __sin (double x)
        }
     }                          /*   else  if (k <  0x419921FB )    */
 
+#ifndef IN_SINCOS
 /*---------------------105414350 <|x|< 281474976710656 --------------------*/
   else if (k < 0x42F00000)
     {
-      t = (x * hpinv + toint);
-      xn = t - toint;
-      v.x = t;
-      xn1 = (xn + 8.0e22) - 8.0e22;
-      xn2 = xn - xn1;
-      y = ((((x - xn1 * mp1) - xn1 * mp2) - xn2 * mp1) - xn2 * mp2);
-      n = v.i[LOW_HALF] & 3;
-      da = xn1 * pp3;
-      t = y - da;
-      da = (y - t) - da;
-      da = (da - xn2 * pp3) - xn * pp4;
-      a = t + da;
-      da = (t - a) + da;
-      eps = 1.0e-24;
+      double a, da;
 
-      switch (n)
-       {
-       case 0:
-       case 2:
-         xx = a * a;
-         if (n)
-           {
-             a = -a;
-             da = -da;
-           }
-         if (xx < 0.01588)
-           {
-             /* Taylor series.  */
-             res = TAYLOR_SIN (xx, a, da, cor);
-             cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
-             retval = (res == res + cor) ? res : bsloww (a, da, x, n);
-           }
-         else
-           {
-             double t;
-             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);
-             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)
-                       : bsloww1 (a, da, x, n));
-           }
-         break;
-
-       case 1:
-       case 3:
-         if (a < 0)
-           {
-             a = -a;
-             da = -da;
-           }
-         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) ? ((n & 2) ? -res : res)
-                   : bsloww2 (a, da, x, n));
-         break;
-       }
+      int4 n = reduce_sincos_2 (x, &a, &da);
+      retval = do_sincos_2 (a, da, x, n, 0);
     }                          /*   else  if (k <  0x42F00000 )   */
 
-#ifndef IN_SINCOS
 /* -----------------281474976710656 <|x| <2^1024----------------------------*/
   else if (k < 0x7ff00000)
     retval = reduce_and_compute (x, 0);
@@ -528,8 +558,7 @@ SECTION
 #endif
 __cos (double x)
 {
-  double y, xx, res, t, cor, xn, a, da, db, eps, xn1,
-    xn2;
+  double y, xx, res, t, cor, xn, a, da, eps;
   mynumber u, v;
   int4 k, m, n;
 
@@ -657,81 +686,15 @@ __cos (double x)
        }
     }                          /*   else  if (k <  0x419921FB )    */
 
+#ifndef IN_SINCOS
   else if (k < 0x42F00000)
     {
-      t = (x * hpinv + toint);
-      xn = t - toint;
-      v.x = t;
-      xn1 = (xn + 8.0e22) - 8.0e22;
-      xn2 = xn - xn1;
-      y = ((((x - xn1 * mp1) - xn1 * mp2) - xn2 * mp1) - xn2 * mp2);
-      n = v.i[LOW_HALF] & 3;
-      da = xn1 * pp3;
-      t = y - da;
-      da = (y - t) - da;
-      da = (da - xn2 * pp3) - xn * pp4;
-      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)
-           {
-             res = TAYLOR_SIN (xx, a, da, cor);
-             cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
-             retval = (res == res + cor) ? res : bsloww (a, da, x, n);
-           }
-         else
-           {
-             double t;
-             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);
-             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)
-                       : bsloww1 (a, da, x, n));
-           }
-         break;
+      double a, da;
 
-       case 0:
-       case 2:
-         if (a < 0)
-           {
-             a = -a;
-             da = -da;
-           }
-         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) ? ((n) ? -res : res)
-                   : bsloww2 (a, da, x, n));
-         break;
-       }
+      int4 n = reduce_sincos_2 (x, &a, &da);
+      retval = do_sincos_2 (a, da, x, n, 1);
     }                          /*   else  if (k <  0x42F00000 )    */
 
-#ifndef IN_SINCOS
   /* 281474976710656 <|x| <2^1024 */
   else if (k < 0x7ff00000)
     retval = reduce_and_compute (x, 1);

diff --git a/sysdeps/ieee754/dbl-64/s_sincos.c b/sysdeps/ieee754/dbl-64/s_sincos.c
index f50ffa625ffb03965758c9bcc771628f35873602..7f78b4106f9419224492a4e454c1dbd9ffd1c82f 100644 (file)
--- a/sysdeps/ieee754/dbl-64/s_sincos.c
+++ b/sysdeps/ieee754/dbl-64/s_sincos.c
@@ -69,10 +69,20 @@ __sincos (double x, double *sinx, double *cosx)
   u.x = x;
   k = 0x7fffffff & u.i[HIGH_HALF];
 
-  if (k < 0x42F00000)
+  if (k < 0x419921FB)
     {
       *sinx = __sin_local (x);
       *cosx = __cos_local (x);
+      return;
+    }
+  if (k < 0x42F00000)
+    {
+      double a, da;
+      int4 n = reduce_sincos_2 (x, &a, &da);
+
+      *sinx = do_sincos_2 (a, da, x, n, 0);
+      *cosx = do_sincos_2 (a, da, x, n, 1);
+
       return;
     }
   if (k < 0x7ff00000)