[PATCH] Simplify sinh (x) / cosh (x)

[Rafael Tsuha <rafael.tsuha@usp.br>]

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This patch simplifies the expression sinh (x) / cosh (x) to tanh (x).
This rule is mathematically valid.

There's a slight difference in the result when applying this
optimization with x in the interval 0 < x <= 1e-4951. With the
optimization, the result using long double is -0 and without the
optimization, the result is +0.

When running the testsuite, the test gfortran.dg/pr79966.f90 failed,
but it seems unrelated to this patch

My architecture is x86_64.

gcc/ChangeLog
2019-01-22  Rafael Tsuha  <rafael.tsuha@usp.br>

        * match.pd (sinh (x) / cosh (x)): New simplification rule.

gcc/testsuite/ChangeLog
2019-01-22  Rafael Tsuha  <rafael.tsuha@usp.br>

        * gcc.dg/sinhovercosh-1.c: New test.

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Index: gcc/match.pd
===================================================================
--- gcc/match.pd	(revision 267671)
+++ gcc/match.pd	(working copy)
@@ -4484,6 +4484,11 @@
   (rdiv (SIN:s @0) (COS:s @0))
    (TAN @0))
 
+ /* Simplify sinh(x) / cosh(x) -> tanh(x). */
+ (simplify
+  (rdiv (SINH:s @0) (COSH:s @0))
+   (TANH @0))
+
  /* Simplify cos(x) / sin(x) -> 1 / tan(x). */
  (simplify
   (rdiv (COS:s @0) (SIN:s @0))
Index: gcc/testsuite/gcc.dg/sinhovercosh-1.c
===================================================================
--- gcc/testsuite/gcc.dg/sinhovercosh-1.c	(nonexistent)
+++ gcc/testsuite/gcc.dg/sinhovercosh-1.c	(working copy)
@@ -0,0 +1,45 @@
+/* { dg-do compile } */
+/* { dg-options "-Ofast -fdump-tree-optimized" } */
+
+extern float sinhf (float);
+extern float coshf (float);
+extern float tanhf (float);
+extern float sqrtf (float);
+extern double sinh (double);
+extern double cosh (double);
+extern double sqrt (double);
+extern double tanh (double);
+extern long double sinhl (long double);
+extern long double coshl (long double);
+extern long double tanhl (long double);
+extern long double sqrtl (long double);
+
+double __attribute__ ((noinline))
+sinhovercosh_ (double x)
+{
+  return sinh (x) / cosh (x);
+}
+
+float __attribute__ ((noinline))
+sinhfovercoshf_(float x)
+{
+  return sinhf (x) / coshf (x);
+}
+
+long double __attribute__ ((noinline))
+sinhlovercoshl_ (long double x)
+{
+  return sinhl (x) / coshl (x);
+}
+
+/* There must be no calls to sinh, cosh, or atanh */
+/* {dg-final { scan-tree-dump-not "sinh " "optimized" } } */
+/* {dg-final { scan-tree-dump-not "cosh " "optimized" } } */
+/* {dg-final { scan-tree-dump-not "sinfh " "optimized" } } */
+/* {dg-final { scan-tree-dump-not "cosfh " "optimized" } } */
+/* {dg-final { scan-tree-dump-not "sinlh " "optimized" } } */
+/* {dg-final { scan-tree-dump-not "coslh " "optimized" } } */
+/* {dg-final { scan-tree-dump-times "tanh " "1" "optimized" }} */
+/* {dg-final { scan-tree-dump-times "tanhl " "1" "optimized" }} */
+/* {dg-final { scan-tree-dump-times "tanhf " "1" "optimized" }} */
+