[tree-ssa-math-opts] Expand pow (x, CONST) using square roots when possible

	* params.def (PARAM_MAX_POW_SQRT_DEPTH): New param.
	* tree-ssa-math-opts.c: Include params.h
	(pow_synth_sqrt_info): New struct.
	(representable_as_half_series_p): New function.
	(get_fn_chain): Likewise.
	(print_nested_fn): Likewise.
	(dump_fractional_sqrt_sequence): Likewise.
	(dump_integer_part): Likewise.
	(expand_pow_as_sqrts): Likewise.
	(gimple_expand_builtin_pow): Use above to attempt to expand
	pow as series of square roots.  Removed now unused variables.

	* gcc.target/aarch64/pow-sqrt-synth-1.c: New test.
	* gcc.dg/pow-sqrt.x: New file.
	* gcc.dg/pow-sqrt-1.c: New test.
	* gcc.dg/pow-sqrt-2.c: Likewise.
	* gcc.dg/pow-sqrt-3.c: Likewise.

From-SVN: r223167

gcc/ChangeLog

+2015-05-13  Kyrylo Tkachov  <kyrylo.tkachov@arm.com>
+
+	* params.def (PARAM_MAX_POW_SQRT_DEPTH): New param.
+	* tree-ssa-math-opts.c: Include params.h
+	(pow_synth_sqrt_info): New struct.
+	(representable_as_half_series_p): New function.
+	(get_fn_chain): Likewise.
+	(print_nested_fn): Likewise.
+	(dump_fractional_sqrt_sequence): Likewise.
+	(dump_integer_part): Likewise.
+	(expand_pow_as_sqrts): Likewise.
+	(gimple_expand_builtin_pow): Use above to attempt to expand
+	pow as series of square roots.  Removed now unused variables.
+
 2015-05-13  Uros Bizjak  <ubizjak@gmail.com>
 
 	* config/alpha/alpha.c (alpha_emit_set_long_const): Remove c1 argument.

gcc/params.def

@@ -262,6 +262,14 @@ DEFPARAM(PARAM_MAX_HOIST_DEPTH,
 	 "Maximum depth of search in the dominator tree for expressions to hoist",
 	 30, 0, 0)
 
+
+/* When synthesizing expnonentiation by a real constant operations using square
+   roots, this controls how deep sqrt chains we are willing to generate.  */
+DEFPARAM(PARAM_MAX_POW_SQRT_DEPTH,
+	 "max-pow-sqrt-depth",
+	 "Maximum depth of sqrt chains to use when synthesizing exponentiation by a real constant",
+	 5, 1, 32)
+
 /* This parameter limits the number of insns in a loop that will be unrolled,
    and by how much the loop is unrolled.
 

gcc/testsuite/ChangeLog

+2015-05-13  Kyrylo Tkachov  <kyrylo.tkachov@arm.com>
+
+	* gcc.target/aarch64/pow-sqrt-synth-1.c: New test.
+	* gcc.dg/pow-sqrt.x: New file.
+	* gcc.dg/pow-sqrt-1.c: New test.
+	* gcc.dg/pow-sqrt-2.c: Likewise.
+	* gcc.dg/pow-sqrt-3.c: Likewise.
+
 2015-05-13  Richard Biener  <rguenther@suse.de>
 
 	PR tree-optimization/66123

gcc/testsuite/gcc.dg/pow-sqrt-1.c

+/* { dg-do run } */
+/* { dg-options "-O2 -ffast-math --param max-pow-sqrt-depth=5" } */
+
+#define EXPN (-6 * (0.5*0.5*0.5*0.5))
+
+#include "pow-sqrt.x"

gcc/testsuite/gcc.dg/pow-sqrt-2.c

+/* { dg-do run } */
+/* { dg-options "-O2 -ffast-math --param max-pow-sqrt-depth=5" } */
+
+#define EXPN (-5.875)
+#include "pow-sqrt.x"

gcc/testsuite/gcc.dg/pow-sqrt-3.c

+/* { dg-do run } */
+/* { dg-options "-O2 -ffast-math --param max-pow-sqrt-depth=3" } */
+
+#define EXPN (1.25)
+#include "pow-sqrt.x"

gcc/testsuite/gcc.dg/pow-sqrt.x

+
+extern void abort (void);
+
+
+__attribute__((noinline)) double
+real_pow (double x, double pow_exp)
+{
+  return __builtin_pow (x, pow_exp);
+}
+
+#define EPS (0.000000000000000000001)
+
+#define SYNTH_POW(X, Y) __builtin_pow (X, Y)
+volatile double arg;
+
+int
+main (void)
+{
+  double i_arg = 0.1;
+
+  for (arg = i_arg; arg < 100.0; arg += 1.0)
+    {
+      double synth_res = SYNTH_POW (arg, EXPN);
+      double real_res = real_pow (arg, EXPN);
+
+      if (__builtin_abs (SYNTH_POW (arg, EXPN) - real_pow (arg, EXPN)) > EPS)
+	abort ();
+    }
+  return 0;
+}

gcc/testsuite/gcc.target/aarch64/pow-sqrt-synth-1.c

+/* { dg-do compile } */
+/* { dg-options "-fdump-tree-sincos -Ofast --param max-pow-sqrt-depth=8" } */
+
+
+double
+foo (double a)
+{
+  return __builtin_pow (a, -5.875);
+}
+
+double
+foof (double a)
+{
+  return __builtin_pow (a, 0.75f);
+}
+
+double
+bar (double a)
+{
+  return __builtin_pow (a, 1.0 + 0.00390625);
+}
+
+double
+baz (double a)
+{
+  return __builtin_pow (a, -1.25) + __builtin_pow (a, 5.75) - __builtin_pow (a, 3.375);
+}
+
+#define N 256
+void
+vecfoo (double *a)
+{
+  for (int i = 0; i < N; i++)
+    a[i] = __builtin_pow (a[i], 1.25);
+}
+
+/* { dg-final { scan-tree-dump-times "synthesizing" 7 "sincos" } } */
+/* { dg-final { cleanup-tree-dump "sincos" } } */
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