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 <wschm...@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 =
