#include "target.h"
#include "gimple-pretty-print.h"
#include "builtins.h"
+#include "params.h"
/* FIXME: RTL headers have to be included here for optabs. */
#include "rtl.h" /* Because optabs.h wants enum rtx_code. */
return result;
}
+struct pow_synth_sqrt_info
+{
+ bool *factors;
+ unsigned int deepest;
+ unsigned int num_mults;
+};
+
+/* Return true iff the real value C can be represented as a
+ sum of powers of 0.5 up to N. That is:
+ C == SUM<i from 1..N> (a[i]*(0.5**i)) where a[i] is either 0 or 1.
+ Record in INFO the various parameters of the synthesis algorithm such
+ as the factors a[i], the maximum 0.5 power and the number of
+ multiplications that will be required. */
+
+bool
+representable_as_half_series_p (REAL_VALUE_TYPE c, unsigned n,
+ struct pow_synth_sqrt_info *info)
+{
+ REAL_VALUE_TYPE factor = dconsthalf;
+ REAL_VALUE_TYPE remainder = c;
+
+ info->deepest = 0;
+ info->num_mults = 0;
+ memset (info->factors, 0, n * sizeof (bool));
+
+ for (unsigned i = 0; i < n; i++)
+ {
+ REAL_VALUE_TYPE res;
+
+ /* If something inexact happened bail out now. */
+ if (REAL_ARITHMETIC (res, MINUS_EXPR, remainder, factor))
+ return false;
+
+ /* We have hit zero. The number is representable as a sum
+ of powers of 0.5. */
+ if (REAL_VALUES_EQUAL (res, dconst0))
+ {
+ info->factors[i] = true;
+ info->deepest = i + 1;
+ return true;
+ }
+ else if (!REAL_VALUE_NEGATIVE (res))
+ {
+ remainder = res;
+ info->factors[i] = true;
+ info->num_mults++;
+ }
+ else
+ info->factors[i] = false;
+
+ REAL_ARITHMETIC (factor, MULT_EXPR, factor, dconsthalf);
+ }
+ return false;
+}
+
+/* Return the tree corresponding to FN being applied
+ to ARG N times at GSI and LOC.
+ Look up previous results from CACHE if need be.
+ cache[0] should contain just plain ARG i.e. FN applied to ARG 0 times. */
+
+static tree
+get_fn_chain (tree arg, unsigned int n, gimple_stmt_iterator *gsi,
+ tree fn, location_t loc, tree *cache)
+{
+ tree res = cache[n];
+ if (!res)
+ {
+ tree prev = get_fn_chain (arg, n - 1, gsi, fn, loc, cache);
+ res = build_and_insert_call (gsi, loc, fn, prev);
+ cache[n] = res;
+ }
+
+ return res;
+}
+
+/* Print to STREAM the repeated application of function FNAME to ARG
+ N times. So, for FNAME = "foo", ARG = "x", N = 2 it would print:
+ "foo (foo (x))". */
+
+static void
+print_nested_fn (FILE* stream, const char *fname, const char* arg,
+ unsigned int n)
+{
+ if (n == 0)
+ fprintf (stream, "%s", arg);
+ else
+ {
+ fprintf (stream, "%s (", fname);
+ print_nested_fn (stream, fname, arg, n - 1);
+ fprintf (stream, ")");
+ }
+}
+
+/* Print to STREAM the fractional sequence of sqrt chains
+ applied to ARG, described by INFO. Used for the dump file. */
+
+static void
+dump_fractional_sqrt_sequence (FILE *stream, const char *arg,
+ struct pow_synth_sqrt_info *info)
+{
+ for (unsigned int i = 0; i < info->deepest; i++)
+ {
+ bool is_set = info->factors[i];
+ if (is_set)
+ {
+ print_nested_fn (stream, "sqrt", arg, i + 1);
+ if (i != info->deepest - 1)
+ fprintf (stream, " * ");
+ }
+ }
+}
+
+/* Print to STREAM a representation of raising ARG to an integer
+ power N. Used for the dump file. */
+
+static void
+dump_integer_part (FILE *stream, const char* arg, HOST_WIDE_INT n)
+{
+ if (n > 1)
+ fprintf (stream, "powi (%s, " HOST_WIDE_INT_PRINT_DEC ")", arg, n);
+ else if (n == 1)
+ fprintf (stream, "%s", arg);
+}
+
+/* Attempt to synthesize a POW[F] (ARG0, ARG1) call using chains of
+ square roots. Place at GSI and LOC. Limit the maximum depth
+ of the sqrt chains to MAX_DEPTH. Return the tree holding the
+ result of the expanded sequence or NULL_TREE if the expansion failed.
+
+ This routine assumes that ARG1 is a real number with a fractional part
+ (the integer exponent case will have been handled earlier in
+ gimple_expand_builtin_pow).
+
+ For ARG1 > 0.0:
+ * For ARG1 composed of a whole part WHOLE_PART and a fractional part
+ FRAC_PART i.e. WHOLE_PART == floor (ARG1) and
+ FRAC_PART == ARG1 - WHOLE_PART:
+ Produce POWI (ARG0, WHOLE_PART) * POW (ARG0, FRAC_PART) where
+ POW (ARG0, FRAC_PART) is expanded as a product of square root chains
+ if it can be expressed as such, that is if FRAC_PART satisfies:
+ FRAC_PART == <SUM from i = 1 until MAX_DEPTH> (a[i] * (0.5**i))
+ where integer a[i] is either 0 or 1.
+
+ Example:
+ POW (x, 3.625) == POWI (x, 3) * POW (x, 0.625)
+ --> POWI (x, 3) * SQRT (x) * SQRT (SQRT (SQRT (x)))
+
+ For ARG1 < 0.0 there are two approaches:
+ * (A) Expand to 1.0 / POW (ARG0, -ARG1) where POW (ARG0, -ARG1)
+ is calculated as above.
+
+ Example:
+ POW (x, -5.625) == 1.0 / POW (x, 5.625)
+ --> 1.0 / (POWI (x, 5) * SQRT (x) * SQRT (SQRT (SQRT (x))))
+
+ * (B) : WHOLE_PART := - ceil (abs (ARG1))
+ FRAC_PART := ARG1 - WHOLE_PART
+ and expand to POW (x, FRAC_PART) / POWI (x, WHOLE_PART).
+ Example:
+ POW (x, -5.875) == POW (x, 0.125) / POWI (X, 6)
+ --> SQRT (SQRT (SQRT (x))) / (POWI (x, 6))
+
+ For ARG1 < 0.0 we choose between (A) and (B) depending on
+ how many multiplications we'd have to do.
+ So, for the example in (B): POW (x, -5.875), if we were to
+ follow algorithm (A) we would produce:
+ 1.0 / POWI (X, 5) * SQRT (X) * SQRT (SQRT (X)) * SQRT (SQRT (SQRT (X)))
+ which contains more multiplications than approach (B).
+
+ Hopefully, this approach will eliminate potentially expensive POW library
+ calls when unsafe floating point math is enabled and allow the compiler to
+ further optimise the multiplies, square roots and divides produced by this
+ function. */
+
+static tree
+expand_pow_as_sqrts (gimple_stmt_iterator *gsi, location_t loc,
+ tree arg0, tree arg1, HOST_WIDE_INT max_depth)
+{
+ tree type = TREE_TYPE (arg0);
+ machine_mode mode = TYPE_MODE (type);
+ tree sqrtfn = mathfn_built_in (type, BUILT_IN_SQRT);
+ bool one_over = true;
+
+ if (!sqrtfn)
+ return NULL_TREE;
+
+ if (TREE_CODE (arg1) != REAL_CST)
+ return NULL_TREE;
+
+ REAL_VALUE_TYPE exp_init = TREE_REAL_CST (arg1);
+
+ gcc_assert (max_depth > 0);
+ tree *cache = XALLOCAVEC (tree, max_depth + 1);
+
+ struct pow_synth_sqrt_info synth_info;
+ synth_info.factors = XALLOCAVEC (bool, max_depth + 1);
+ synth_info.deepest = 0;
+ synth_info.num_mults = 0;
+
+ bool neg_exp = REAL_VALUE_NEGATIVE (exp_init);
+ REAL_VALUE_TYPE exp = real_value_abs (&exp_init);
+
+ /* The whole and fractional parts of exp. */
+ REAL_VALUE_TYPE whole_part;
+ REAL_VALUE_TYPE frac_part;
+
+ real_floor (&whole_part, mode, &exp);
+ REAL_ARITHMETIC (frac_part, MINUS_EXPR, exp, whole_part);
+
+
+ REAL_VALUE_TYPE ceil_whole = dconst0;
+ REAL_VALUE_TYPE ceil_fract = dconst0;
+
+ if (neg_exp)
+ {
+ real_ceil (&ceil_whole, mode, &exp);
+ REAL_ARITHMETIC (ceil_fract, MINUS_EXPR, ceil_whole, exp);
+ }
+
+ if (!representable_as_half_series_p (frac_part, max_depth, &synth_info))
+ return NULL_TREE;
+
+ /* Check whether it's more profitable to not use 1.0 / ... */
+ if (neg_exp)
+ {
+ struct pow_synth_sqrt_info alt_synth_info;
+ alt_synth_info.factors = XALLOCAVEC (bool, max_depth + 1);
+ alt_synth_info.deepest = 0;
+ alt_synth_info.num_mults = 0;
+
+ if (representable_as_half_series_p (ceil_fract, max_depth,
+ &alt_synth_info)
+ && alt_synth_info.deepest <= synth_info.deepest
+ && alt_synth_info.num_mults < synth_info.num_mults)
+ {
+ whole_part = ceil_whole;
+ frac_part = ceil_fract;
+ synth_info.deepest = alt_synth_info.deepest;
+ synth_info.num_mults = alt_synth_info.num_mults;
+ memcpy (synth_info.factors, alt_synth_info.factors,
+ (max_depth + 1) * sizeof (bool));
+ one_over = false;
+ }
+ }
+
+ HOST_WIDE_INT n = real_to_integer (&whole_part);
+ REAL_VALUE_TYPE cint;
+ real_from_integer (&cint, VOIDmode, n, SIGNED);
+
+ if (!real_identical (&whole_part, &cint))
+ return NULL_TREE;
+
+ if (powi_cost (n) + synth_info.num_mults > POWI_MAX_MULTS)
+ return NULL_TREE;
+
+ memset (cache, 0, (max_depth + 1) * sizeof (tree));
+
+ tree integer_res = n == 0 ? build_real (type, dconst1) : arg0;
+
+ /* Calculate the integer part of the exponent. */
+ if (n > 1)
+ {
+ integer_res = gimple_expand_builtin_powi (gsi, loc, arg0, n);
+ if (!integer_res)
+ return NULL_TREE;
+ }
+
+ if (dump_file)
+ {
+ char string[64];
+
+ real_to_decimal (string, &exp_init, sizeof (string), 0, 1);
+ fprintf (dump_file, "synthesizing pow (x, %s) as:\n", string);
+
+ if (neg_exp)
+ {
+ if (one_over)
+ {
+ fprintf (dump_file, "1.0 / (");
+ dump_integer_part (dump_file, "x", n);
+ if (n > 0)
+ fprintf (dump_file, " * ");
+ dump_fractional_sqrt_sequence (dump_file, "x", &synth_info);
+ fprintf (dump_file, ")");
+ }
+ else
+ {
+ dump_fractional_sqrt_sequence (dump_file, "x", &synth_info);
+ fprintf (dump_file, " / (");
+ dump_integer_part (dump_file, "x", n);
+ fprintf (dump_file, ")");
+ }
+ }
+ else
+ {
+ dump_fractional_sqrt_sequence (dump_file, "x", &synth_info);
+ if (n > 0)
+ fprintf (dump_file, " * ");
+ dump_integer_part (dump_file, "x", n);
+ }
+
+ fprintf (dump_file, "\ndeepest sqrt chain: %d\n", synth_info.deepest);
+ }
+
+
+ tree fract_res = NULL_TREE;
+ cache[0] = arg0;
+
+ /* Calculate the fractional part of the exponent. */
+ for (unsigned i = 0; i < synth_info.deepest; i++)
+ {
+ if (synth_info.factors[i])
+ {
+ tree sqrt_chain = get_fn_chain (arg0, i + 1, gsi, sqrtfn, loc, cache);
+
+ if (!fract_res)
+ fract_res = sqrt_chain;
+
+ else
+ fract_res = build_and_insert_binop (gsi, loc, "powroot", MULT_EXPR,
+ fract_res, sqrt_chain);
+ }
+ }
+
+ tree res = NULL_TREE;
+
+ if (neg_exp)
+ {
+ if (one_over)
+ {
+ if (n > 0)
+ res = build_and_insert_binop (gsi, loc, "powroot", MULT_EXPR,
+ fract_res, integer_res);
+ else
+ res = fract_res;
+
+ res = build_and_insert_binop (gsi, loc, "powrootrecip", RDIV_EXPR,
+ build_real (type, dconst1), res);
+ }
+ else
+ {
+ res = build_and_insert_binop (gsi, loc, "powroot", RDIV_EXPR,
+ fract_res, integer_res);
+ }
+ }
+ else
+ res = build_and_insert_binop (gsi, loc, "powroot", MULT_EXPR,
+ fract_res, integer_res);
+ return res;
+}
+
/* ARG0 and ARG1 are the two arguments to a pow builtin call in GSI
with location info LOC. If possible, create an equivalent and
less expensive sequence of statements prior to GSI, and return an
gimple_expand_builtin_pow (gimple_stmt_iterator *gsi, location_t loc,
tree arg0, tree arg1)
{
- REAL_VALUE_TYPE c, cint, dconst1_4, dconst3_4, dconst1_3, dconst1_6;
+ REAL_VALUE_TYPE c, cint, dconst1_3, dconst1_4, dconst1_6;
REAL_VALUE_TYPE c2, dconst3;
HOST_WIDE_INT n;
- tree type, sqrtfn, cbrtfn, sqrt_arg0, sqrt_sqrt, result, cbrt_x, powi_cbrt_x;
+ tree type, sqrtfn, cbrtfn, sqrt_arg0, result, cbrt_x, powi_cbrt_x;
machine_mode mode;
+ bool speed_p = optimize_bb_for_speed_p (gsi_bb (*gsi));
bool hw_sqrt_exists, c_is_int, c2_is_int;
+ dconst1_4 = dconst1;
+ SET_REAL_EXP (&dconst1_4, REAL_EXP (&dconst1_4) - 2);
+
/* If the exponent isn't a constant, there's nothing of interest
to be done. */
if (TREE_CODE (arg1) != REAL_CST)
if (c_is_int
&& ((n >= -1 && n <= 2)
|| (flag_unsafe_math_optimizations
- && optimize_bb_for_speed_p (gsi_bb (*gsi))
+ && speed_p
&& powi_cost (n) <= POWI_MAX_MULTS)))
return gimple_expand_builtin_powi (gsi, loc, arg0, n);
&& !HONOR_SIGNED_ZEROS (mode))
return build_and_insert_call (gsi, loc, sqrtfn, arg0);
- /* Optimize pow(x,0.25) = sqrt(sqrt(x)). Assume on most machines that
- a builtin sqrt instruction is smaller than a call to pow with 0.25,
- so do this optimization even if -Os. Don't do this optimization
- if we don't have a hardware sqrt insn. */
- dconst1_4 = dconst1;
- SET_REAL_EXP (&dconst1_4, REAL_EXP (&dconst1_4) - 2);
hw_sqrt_exists = optab_handler (sqrt_optab, mode) != CODE_FOR_nothing;
- if (flag_unsafe_math_optimizations
- && sqrtfn
- && REAL_VALUES_EQUAL (c, dconst1_4)
- && hw_sqrt_exists)
- {
- /* sqrt(x) */
- sqrt_arg0 = build_and_insert_call (gsi, loc, sqrtfn, arg0);
-
- /* sqrt(sqrt(x)) */
- return build_and_insert_call (gsi, loc, sqrtfn, sqrt_arg0);
- }
-
- /* Optimize pow(x,0.75) = sqrt(x) * sqrt(sqrt(x)) unless we are
- optimizing for space. Don't do this optimization if we don't have
- a hardware sqrt insn. */
- real_from_integer (&dconst3_4, VOIDmode, 3, SIGNED);
- SET_REAL_EXP (&dconst3_4, REAL_EXP (&dconst3_4) - 2);
-
- if (flag_unsafe_math_optimizations
- && sqrtfn
- && optimize_function_for_speed_p (cfun)
- && REAL_VALUES_EQUAL (c, dconst3_4)
- && hw_sqrt_exists)
- {
- /* sqrt(x) */
- sqrt_arg0 = build_and_insert_call (gsi, loc, sqrtfn, arg0);
-
- /* sqrt(sqrt(x)) */
- sqrt_sqrt = build_and_insert_call (gsi, loc, sqrtfn, sqrt_arg0);
-
- /* sqrt(x) * sqrt(sqrt(x)) */
- return build_and_insert_binop (gsi, loc, "powroot", MULT_EXPR,
- sqrt_arg0, sqrt_sqrt);
- }
-
/* Optimize pow(x,1./3.) = cbrt(x). This requires unsafe math
optimizations since 1./3. is not exactly representable. If x
is negative and finite, the correct value of pow(x,1./3.) is
&& sqrtfn
&& cbrtfn
&& (gimple_val_nonnegative_real_p (arg0) || !HONOR_NANS (mode))
- && optimize_function_for_speed_p (cfun)
+ && speed_p
&& hw_sqrt_exists
&& REAL_VALUES_EQUAL (c, dconst1_6))
{
return build_and_insert_call (gsi, loc, cbrtfn, sqrt_arg0);
}
- /* Optimize pow(x,c), where n = 2c for some nonzero integer n
- and c not an integer, into
-
- sqrt(x) * powi(x, n/2), n > 0;
- 1.0 / (sqrt(x) * powi(x, abs(n/2))), n < 0.
-
- Do not calculate the powi factor when n/2 = 0. */
- real_arithmetic (&c2, MULT_EXPR, &c, &dconst2);
- n = real_to_integer (&c2);
- real_from_integer (&cint, VOIDmode, n, SIGNED);
- c2_is_int = real_identical (&c2, &cint);
+ /* Attempt to expand the POW as a product of square root chains.
+ Expand the 0.25 case even when otpimising for size. */
if (flag_unsafe_math_optimizations
&& sqrtfn
- && c2_is_int
- && !c_is_int
- && optimize_function_for_speed_p (cfun))
+ && hw_sqrt_exists
+ && (speed_p || REAL_VALUES_EQUAL (c, dconst1_4))
+ && !HONOR_SIGNED_ZEROS (mode))
{
- tree powi_x_ndiv2 = NULL_TREE;
-
- /* Attempt to fold powi(arg0, abs(n/2)) into multiplies. If not
- possible or profitable, give up. Skip the degenerate case when
- n is 1 or -1, where the result is always 1. */
- if (absu_hwi (n) != 1)
- {
- powi_x_ndiv2 = gimple_expand_builtin_powi (gsi, loc, arg0,
- abs_hwi (n / 2));
- if (!powi_x_ndiv2)
- return NULL_TREE;
- }
+ unsigned int max_depth = speed_p
+ ? PARAM_VALUE (PARAM_MAX_POW_SQRT_DEPTH)
+ : 2;
- /* Calculate sqrt(x). When n is not 1 or -1, multiply it by the
- result of the optimal multiply sequence just calculated. */
- sqrt_arg0 = build_and_insert_call (gsi, loc, sqrtfn, arg0);
+ tree expand_with_sqrts
+ = expand_pow_as_sqrts (gsi, loc, arg0, arg1, max_depth);
- if (absu_hwi (n) == 1)
- result = sqrt_arg0;
- else
- result = build_and_insert_binop (gsi, loc, "powroot", MULT_EXPR,
- sqrt_arg0, powi_x_ndiv2);
-
- /* If n is negative, reciprocate the result. */
- if (n < 0)
- result = build_and_insert_binop (gsi, loc, "powroot", RDIV_EXPR,
- build_real (type, dconst1), result);
- return result;
+ if (expand_with_sqrts)
+ return expand_with_sqrts;
}
+ real_arithmetic (&c2, MULT_EXPR, &c, &dconst2);
+ n = real_to_integer (&c2);
+ real_from_integer (&cint, VOIDmode, n, SIGNED);
+ c2_is_int = real_identical (&c2, &cint);
+
/* Optimize pow(x,c), where 3c = n for some nonzero integer n, into
powi(x, n/3) * powi(cbrt(x), n%3), n > 0;
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