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* [PATCH] Add powi-to-multiply expansion to cse_sincos pass
@ 2011-05-19 17:33 William J. Schmidt
  2011-05-23 14:05 ` Richard Guenther
  0 siblings, 1 reply; 5+ messages in thread
From: William J. Schmidt @ 2011-05-19 17:33 UTC (permalink / raw)
  To: gcc-patches

As Richard Guenther suggested, I'm submitting a separate patch to add
powi expansion to multiplies during the cse_sincos pass.  This was
originally submitted as part of a larger patch to fix PR46728.

Richard noted that tree_expand_builtin_powi, powi_as_mults, and
powi_as_mults_1 more properly belong in tree-ssa-math-opts.c.  I've
moved those here.  These were originally in builtins.c because they
require some #defines, a static table of values, and a couple of static
functions in builtins.c.  Those items will also belong in
tree-ssa-math-opts.c once the similar RTL logic is removed.

I chose to duplicate the required items into tree-ssa-math-opts.c for
now.  They will be removed from builtins.c in a future patch.  This
seemed more reasonable than exposing everything in a .h temporarily, and
then removing the .h code later.  But I can change to go that route if
you prefer. 

Bootstrap/regtest complete on powerpc target.

Seeking approval for mainline -- thanks!

Bill


2011-05-19  Bill Schmidt  <wschmidt@linux.vnet.ibm.com>

	* tree-ssa-math-opts.c (POWI_MAX_MULTS): Copied from builtins.c;
	will be deleted from builtins.c in a later patch.
	(POWI_TABLE_SIZE): Likewise.
	(POWI_WINDOW_SIZE): Likewise.
	(powi_table): Likewise.
	(powi_lookup_cost): Likewise.
	(powi_cost): Likewise.
	(powi_as_mults_1): New.
	(powi_as_mults): New.
	(tree_expand_builtin_powi): New.
	(execute_cse_sincos): Add switch case for BUILT_IN_POWI.
	(gate_cse_sincos): Remove sincos/cexp restriction.


Index: gcc/tree-ssa-math-opts.c
===================================================================
--- gcc/tree-ssa-math-opts.c	(revision 173908)
+++ gcc/tree-ssa-math-opts.c	(working copy)
@@ -795,8 +795,239 @@ execute_cse_sincos_1 (tree name)
   return cfg_changed;
 }
 
+/* To evaluate powi(x,n), the floating point value x raised to the
+   constant integer exponent n, we use a hybrid algorithm that
+   combines the "window method" with look-up tables.  For an
+   introduction to exponentiation algorithms and "addition chains",
+   see section 4.6.3, "Evaluation of Powers" of Donald E. Knuth,
+   "Seminumerical Algorithms", Vol. 2, "The Art of Computer Programming",
+   3rd Edition, 1998, and Daniel M. Gordon, "A Survey of Fast Exponentiation
+   Methods", Journal of Algorithms, Vol. 27, pp. 129-146, 1998.  */
+
+/* Provide a default value for POWI_MAX_MULTS, the maximum number of
+   multiplications to inline before calling the system library's pow
+   function.  powi(x,n) requires at worst 2*bits(n)-2 multiplications,
+   so this default never requires calling pow, powf or powl.  */
+
+#ifndef POWI_MAX_MULTS
+#define POWI_MAX_MULTS  (2*HOST_BITS_PER_WIDE_INT-2)
+#endif
+
+/* The size of the "optimal power tree" lookup table.  All
+   exponents less than this value are simply looked up in the
+   powi_table below.  This threshold is also used to size the
+   cache of pseudo registers that hold intermediate results.  */
+#define POWI_TABLE_SIZE 256
+
+/* The size, in bits of the window, used in the "window method"
+   exponentiation algorithm.  This is equivalent to a radix of
+   (1<<POWI_WINDOW_SIZE) in the corresponding "m-ary method".  */
+#define POWI_WINDOW_SIZE 3
+
+/* The following table is an efficient representation of an
+   "optimal power tree".  For each value, i, the corresponding
+   value, j, in the table states than an optimal evaluation
+   sequence for calculating pow(x,i) can be found by evaluating
+   pow(x,j)*pow(x,i-j).  An optimal power tree for the first
+   100 integers is given in Knuth's "Seminumerical algorithms".  */
+
+static const unsigned char powi_table[POWI_TABLE_SIZE] =
+  {
+      0,   1,   1,   2,   2,   3,   3,   4,  /*   0 -   7 */
+      4,   6,   5,   6,   6,  10,   7,   9,  /*   8 -  15 */
+      8,  16,   9,  16,  10,  12,  11,  13,  /*  16 -  23 */
+     12,  17,  13,  18,  14,  24,  15,  26,  /*  24 -  31 */
+     16,  17,  17,  19,  18,  33,  19,  26,  /*  32 -  39 */
+     20,  25,  21,  40,  22,  27,  23,  44,  /*  40 -  47 */
+     24,  32,  25,  34,  26,  29,  27,  44,  /*  48 -  55 */
+     28,  31,  29,  34,  30,  60,  31,  36,  /*  56 -  63 */
+     32,  64,  33,  34,  34,  46,  35,  37,  /*  64 -  71 */
+     36,  65,  37,  50,  38,  48,  39,  69,  /*  72 -  79 */
+     40,  49,  41,  43,  42,  51,  43,  58,  /*  80 -  87 */
+     44,  64,  45,  47,  46,  59,  47,  76,  /*  88 -  95 */
+     48,  65,  49,  66,  50,  67,  51,  66,  /*  96 - 103 */
+     52,  70,  53,  74,  54, 104,  55,  74,  /* 104 - 111 */
+     56,  64,  57,  69,  58,  78,  59,  68,  /* 112 - 119 */
+     60,  61,  61,  80,  62,  75,  63,  68,  /* 120 - 127 */
+     64,  65,  65, 128,  66, 129,  67,  90,  /* 128 - 135 */
+     68,  73,  69, 131,  70,  94,  71,  88,  /* 136 - 143 */
+     72, 128,  73,  98,  74, 132,  75, 121,  /* 144 - 151 */
+     76, 102,  77, 124,  78, 132,  79, 106,  /* 152 - 159 */
+     80,  97,  81, 160,  82,  99,  83, 134,  /* 160 - 167 */
+     84,  86,  85,  95,  86, 160,  87, 100,  /* 168 - 175 */
+     88, 113,  89,  98,  90, 107,  91, 122,  /* 176 - 183 */
+     92, 111,  93, 102,  94, 126,  95, 150,  /* 184 - 191 */
+     96, 128,  97, 130,  98, 133,  99, 195,  /* 192 - 199 */
+    100, 128, 101, 123, 102, 164, 103, 138,  /* 200 - 207 */
+    104, 145, 105, 146, 106, 109, 107, 149,  /* 208 - 215 */
+    108, 200, 109, 146, 110, 170, 111, 157,  /* 216 - 223 */
+    112, 128, 113, 130, 114, 182, 115, 132,  /* 224 - 231 */
+    116, 200, 117, 132, 118, 158, 119, 206,  /* 232 - 239 */
+    120, 240, 121, 162, 122, 147, 123, 152,  /* 240 - 247 */
+    124, 166, 125, 214, 126, 138, 127, 153,  /* 248 - 255 */
+  };
+
+
+/* Return the number of multiplications required to calculate
+   powi(x,n) where n is less than POWI_TABLE_SIZE.  This is a
+   subroutine of powi_cost.  CACHE is an array indicating
+   which exponents have already been calculated.  */
+
+static int
+powi_lookup_cost (unsigned HOST_WIDE_INT n, bool *cache)
+{
+  /* If we've already calculated this exponent, then this evaluation
+     doesn't require any additional multiplications.  */
+  if (cache[n])
+    return 0;
+
+  cache[n] = true;
+  return powi_lookup_cost (n - powi_table[n], cache)
+	 + powi_lookup_cost (powi_table[n], cache) + 1;
+}
+
+/* Return the number of multiplications required to calculate
+   powi(x,n) for an arbitrary x, given the exponent N.  This
+   function needs to be kept in sync with expand_powi below.  */
+
+static int
+powi_cost (HOST_WIDE_INT n)
+{
+  bool cache[POWI_TABLE_SIZE];
+  unsigned HOST_WIDE_INT digit;
+  unsigned HOST_WIDE_INT val;
+  int result;
+
+  if (n == 0)
+    return 0;
+
+  /* Ignore the reciprocal when calculating the cost.  */
+  val = (n < 0) ? -n : n;
+
+  /* Initialize the exponent cache.  */
+  memset (cache, 0, POWI_TABLE_SIZE * sizeof (bool));
+  cache[1] = true;
+
+  result = 0;
+
+  while (val >= POWI_TABLE_SIZE)
+    {
+      if (val & 1)
+	{
+	  digit = val & ((1 << POWI_WINDOW_SIZE) - 1);
+	  result += powi_lookup_cost (digit, cache)
+		    + POWI_WINDOW_SIZE + 1;
+	  val >>= POWI_WINDOW_SIZE;
+	}
+      else
+	{
+	  val >>= 1;
+	  result++;
+	}
+    }
+
+  return result + powi_lookup_cost (val, cache);
+}
+
+/* Recursive subroutine of powi_as_mults.  This function takes the
+   array, CACHE, of already calculated exponents and an exponent N and
+   returns a tree that corresponds to CACHE[1]**N, with type TYPE.  */
+
+static tree
+powi_as_mults_1 (gimple_stmt_iterator *gsi, location_t loc, tree type,
+		 HOST_WIDE_INT n, tree *cache)
+{
+  tree op0, op1, target;
+  unsigned HOST_WIDE_INT digit;
+  gimple mult_stmt;
+
+  if (n < POWI_TABLE_SIZE)
+    {
+      if (cache[n])
+	return cache[n];
+
+      target = create_tmp_var (type, "powmult");
+      add_referenced_var (target);
+      target = make_ssa_name (target, NULL);
+      cache[n] = target;
+
+      op0 = powi_as_mults_1 (gsi, loc, type, n - powi_table[n], cache);
+      op1 = powi_as_mults_1 (gsi, loc, type, powi_table[n], cache);
+    }
+  else if (n & 1)
+    {
+      target = create_tmp_var (type, "powmult");
+      add_referenced_var (target);
+      target = make_ssa_name (target, NULL);
+      digit = n & ((1 << POWI_WINDOW_SIZE) - 1);
+      op0 = powi_as_mults_1 (gsi, loc, type, n - digit, cache);
+      op1 = powi_as_mults_1 (gsi, loc, type, digit, cache);
+    }
+  else
+    {
+      target = create_tmp_var (type, "powmult");
+      add_referenced_var (target);
+      target = make_ssa_name (target, NULL);
+      op0 = powi_as_mults_1 (gsi, loc, type, n >> 1, cache);
+      op1 = op0;
+    }
+
+  mult_stmt = gimple_build_assign_with_ops (MULT_EXPR, target, op0, op1);
+  SSA_NAME_DEF_STMT (target) = mult_stmt;
+  gsi_insert_before (gsi, mult_stmt, GSI_SAME_STMT);
+
+  return target;
+}
+
+/* Convert ARG0**N to a tree of multiplications of ARG0 with itself.
+   This function needs to be kept in sync with powi_cost in builtins.c.  */
+
+static tree
+powi_as_mults (gimple_stmt_iterator *gsi, location_t loc,
+	       tree arg0, HOST_WIDE_INT n)
+{
+  tree cache[POWI_TABLE_SIZE], result, type = TREE_TYPE (arg0);
+
+  if (n == 0)
+    return omit_one_operand_loc (loc, type, build_real (type, dconst1), arg0);
+
+  memset (cache, 0,  sizeof (cache));
+  cache[1] = arg0;
+
+  result = powi_as_mults_1 (gsi, loc, type, (n < 0) ? -n : n, cache);
+
+  /* If the original exponent was negative, reciprocate the result.  */
+  if (n < 0)
+    result = build2_loc (loc, RDIV_EXPR, type,
+			 build_real (type, dconst1), result);
+  return result;
+}
+
+/* ARGS are the two arguments to a powi builtin in GSI with location info
+   LOC.  If the arguments are appropriate, create an equivalent set of
+   statements prior to GSI using an optimal number of multiplications,
+   and return an expession holding the result.  */
+
+static tree
+tree_expand_builtin_powi (gimple_stmt_iterator *gsi, location_t loc, tree *args)
+{
+  HOST_WIDE_INT n = TREE_INT_CST_LOW (args[1]);
+  HOST_WIDE_INT n_hi = TREE_INT_CST_HIGH (args[1]);
+
+  if ((n_hi == 0 || n_hi == -1)
+      /* Avoid largest negative number.  */
+      && (n != -n)
+      && ((n >= -1 && n <= 2)
+	  || (optimize_function_for_speed_p (cfun)
+	      && powi_cost (n) <= POWI_MAX_MULTS)))
+    return powi_as_mults (gsi, loc, args[0], n);
+
+  return NULL_TREE;
+}
+
 /* Go through all calls to sin, cos and cexpi and call execute_cse_sincos_1
-   on the SSA_NAME argument of each of them.  */
+   on the SSA_NAME argument of each of them.  Also expand powi(x,n) into
+   an optimal number of multiplies, when n is a constant.  */
 
 static unsigned int
 execute_cse_sincos (void)
@@ -821,7 +1052,7 @@ execute_cse_sincos (void)
 	      && (fndecl = gimple_call_fndecl (stmt))
 	      && DECL_BUILT_IN_CLASS (fndecl) == BUILT_IN_NORMAL)
 	    {
-	      tree arg;
+	      tree arg, *args;
 
 	      switch (DECL_FUNCTION_CODE (fndecl))
 		{
@@ -833,6 +1064,23 @@ execute_cse_sincos (void)
 		    cfg_changed |= execute_cse_sincos_1 (arg);
 		  break;
 
+		CASE_FLT_FN (BUILT_IN_POWI):
+		  args = gimple_call_arg_ptr (stmt, 0);
+		  if (host_integerp (args[1], 0) && !TREE_OVERFLOW (args[1]))
+		    {
+		      tree result = NULL_TREE;
+		      location_t loc = gimple_location (stmt);
+		      result = tree_expand_builtin_powi (&gsi, loc, args);
+		      if (result)
+			{
+			  tree lhs = gimple_get_lhs (stmt);
+			  gimple new_stmt = gimple_build_assign (lhs, result);
+			  gimple_set_location (new_stmt, loc);
+			  gsi_replace (&gsi, new_stmt, true);
+			}
+		    }
+		  break;
+
 		default:;
 		}
 	    }
@@ -849,10 +1097,9 @@ execute_cse_sincos (void)
 static bool
 gate_cse_sincos (void)
 {
-  /* Make sure we have either sincos or cexp.  */
-  return (TARGET_HAS_SINCOS
-	  || TARGET_C99_FUNCTIONS)
-	 && optimize;
+  /* We no longer require either sincos or cexp, since powi expansion
+     piggybacks on this pass.  */
+  return optimize;
 }
 
 struct gimple_opt_pass pass_cse_sincos =


^ permalink raw reply	[flat|nested] 5+ messages in thread
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2011-05-19 17:33 [PATCH] Add powi-to-multiply expansion to cse_sincos pass William J. Schmidt
2011-05-23 14:05 ` Richard Guenther
2011-05-23 20:23   ` William J. Schmidt
2011-05-24 15:14     ` Richard Guenther
2011-05-24 15:28       ` William J. Schmidt

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