Factor out division by squares

This patch implements the some of the division optimizations discussed in
https://gcc.gnu.org/bugzilla/show_bug.cgi?id=71026.

The division reciprocal optimization now handles divisions by squares:

     x / (y * y) -> x  * (1 / y) * (1 / y)

This requires at least one more division by y before it triggers - the
3 divisions of (1/ y) are then CSEd into a single division.  Overall
this changes 1 division into 1 multiply, which is generally much faster.


2017-11-24  Jackson Woodruff  <jackson.woodruff@arm.com>

    gcc/
	PR tree-optimization/71026
	* tree-ssa-math-opts (is_division_by_square, is_square_of): New.
	(insert_reciprocals): Change to insert reciprocals before a division
	by a square and to insert the square of a reciprocal.
	(execute_cse_reciprocals_1): Change to consider division by a square.
	(register_division_in): Add importance parameter.

    testsuite/
	PR tree-optimization/71026
	* gfortran.dg/extract_recip_1.f: New test.
	* gcc.dg/extract_recip_3.c: New test.
	* gcc.dg/extract_recip_4.c: New test.

From-SVN: r255141

gcc/ChangeLog

+2017-11-24  Jackson Woodruff  <jackson.woodruff@arm.com>
+
+	PR tree-optimization/71026
+	* tree-ssa-math-opts (is_division_by_square, is_square_of): New.
+	(insert_reciprocals): Change to insert reciprocals before a division
+	by a square and to insert the square of a reciprocal.
+	(execute_cse_reciprocals_1): Change to consider division by a square.
+	(register_division_in): Add importance parameter.
+
 2017-11-24  Richard Biener  <rguenther@suse.de>
 
 	PR tree-optimization/82402

gcc/testsuite/ChangeLog

+2017-11-24  Jackson Woodruff  <jackson.woodruff@arm.com>
+
+	PR tree-optimization/71026
+	* gfortran.dg/extract_recip_1.f: New test.
+	* gcc.dg/extract_recip_3.c: New test.
+	* gcc.dg/extract_recip_4.c: New test.
+
 2017-11-24  Richard Biener  <rguenther@suse.de>
 
 	PR tree-optimization/82402

gcc/testsuite/gcc.dg/extract_recip_3.c

+/* { dg-do compile } */
+/* { dg-options "-Ofast -fdump-tree-optimized-raw" } */
+
+float
+extract_square (float *a, float *b, float x, float y)
+{
+  *a = 3 / (y * y);
+  *b = 5 / (y * y);
+
+  return x / (y * y);
+}
+
+/* Don't expect the 'powmult' (calculation of y * y)
+   to be deleted until a later pass, so look for one
+   more multiplication than strictly necessary.  */
+float
+extract_recip (float *a, float *b, float x, float y, float z)
+{
+  *a = 7 / y;
+  *b = x / (y * y);
+
+  return z / y;
+}
+
+/* 4 multiplications in 'extract_square', and 4 in 'extract_recip'.  */
+/* { dg-final { scan-tree-dump-times "mult_expr" 8 "optimized" } } */
+
+/* 1 division in 'extract_square', 1 division in 'extract_recip'. */
+/* { dg-final { scan-tree-dump-times "rdiv_expr" 2 "optimized" } } */

gcc/testsuite/gcc.dg/extract_recip_4.c

+/* { dg-do compile } */
+/* { dg-options "-Ofast -fdump-tree-optimized-raw" } */
+
+/* Don't expect any of these divisions to be extracted.  */
+double f (double x, int p)
+{
+  if (p > 0)
+    {
+      return 1.0/(x * x);
+    }
+
+  if (p > -1)
+    {
+      return x * x * x;
+    }
+  return  1.0 /(x);
+}
+
+/* Expect a reciprocal to be extracted here.  */
+double g (double *a, double x, double y)
+{
+  *a = 3 / y;
+  double k = x / (y * y);
+
+  if (y * y == 2.0)
+    return k + 1 / y;
+  else
+    return k - 1 / y;
+}
+
+/* Expect 2 divisions in 'f' and 1 in 'g'.  */
+/* { dg-final { scan-tree-dump-times "rdiv_expr" 3 "optimized" } } */
+/* Expect 3 multiplications in 'f' and 4 in 'g'.  */
+/* { dg-final { scan-tree-dump-times "mult_expr" 7 "optimized" } } */

gcc/testsuite/gfortran.dg/extract_recip_1.f

+! { dg-do compile }
+! { dg-options "-Ofast -fdump-tree-optimized-raw" }
+
+      SUBROUTINE F(N,X,Y,Z,A,B)
+          DIMENSION X(4,4), Y(4), Z(4)
+          REAL, INTENT(INOUT) :: A, B
+
+          A = 1 / (Y(N)*Y(N))
+
+          DO I = 1, NV
+          X(I, I) = 1 + X(I, I)
+          ENDDO
+
+          Z(1) =  B / Y(N)
+          Z(2) =  N / Y(N)
+          RETURN
+      END
+
+! { dg-final { scan-tree-dump-times "rdiv_expr" 1 "optimized" } }