On Thu, May 19, 2011 at 4:04 PM, William J. Schmidt
<wschm...@linux.vnet.ibm.com> wrote:
> 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.
No need to mention this.
> (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. */
Please double-check the function comments if they still refer
to the correct functions.
> +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);
Avoid creating multiple variables, just re-use a single temporary
(just pass it along here as an additional argument).
> + 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);
Likewise.
> + 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);
Likewise.
> + 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;
I think setting SSA_NAME_DEF_STMT is already done by
gimple_build_assign_with_ops.
> + 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);
No need for omit_one_operand - simply return build_real (type, dconst1).
> + memset (cache, 0, sizeof (cache));
> + cache[1] = arg0;
Allocate the temporary var here
> + 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);
Please build a final division statement and assign it to a new SSA name
which you return.
> + 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)
A better name would be gimple_expand_builtin_powi now.
> +{
> + 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]))
Please access arguments via gimple_call_arg (stmt, N), simply assign
both to tempoaries and pass them down separately to
tree_expand_builtin_pow, the exponent as HOST_WIDE_INT instead
of as tree. We also do not care for TREE_OVERFLOW
(I realize this is pre-existing code).
> + {
> + 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;
> }
Otherwise this patch looks good to me. Please re-post it with the
suggested adjustments.
The next patch to attack would be to make sure integer valued exponent
pows are folded to powi for -funsafe-math-optimizations.
Thanks,
Richard.
> struct gimple_opt_pass pass_cse_sincos =
>
>
>
