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

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* 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
This commit is contained in:
Kyrylo Tkachov 2015-05-13 15:26:14 +00:00 • committed by Kyrylo Tkachov
parent da80c6b81f
commit b7dce216c7
9 changed files with 492 additions and 86 deletions
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14
gcc/ChangeLog
View file

@ -1,3 +1,17 @@
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.

8
gcc/params.def
View file

@ -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.

8
gcc/testsuite/ChangeLog
View file

@ -1,3 +1,11 @@
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

6
gcc/testsuite/gcc.dg/pow-sqrt-1.c Normal file
View file

@ -0,0 +1,6 @@
/* { 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"

5
gcc/testsuite/gcc.dg/pow-sqrt-2.c Normal file
View file

@ -0,0 +1,5 @@
/* { dg-do run } */
/* { dg-options "-O2 -ffast-math --param max-pow-sqrt-depth=5" } */
#define EXPN (-5.875)
#include "pow-sqrt.x"

5
gcc/testsuite/gcc.dg/pow-sqrt-3.c Normal file
View file

@ -0,0 +1,5 @@
/* { dg-do run } */
/* { dg-options "-O2 -ffast-math --param max-pow-sqrt-depth=3" } */
#define EXPN (1.25)
#include "pow-sqrt.x"

30
gcc/testsuite/gcc.dg/pow-sqrt.x Normal file
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@ -0,0 +1,30 @@
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;
}

38
gcc/testsuite/gcc.target/aarch64/pow-sqrt-synth-1.c Normal file
View file

@ -0,0 +1,38 @@
/* { 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" } } */

464
gcc/tree-ssa-math-opts.c
View file

@ -143,6 +143,7 @@ along with GCC; see the file COPYING3. If not see
#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. */
@ -1148,6 +1149,357 @@ build_and_insert_cast (gimple_stmt_iterator *gsi, location_t loc,
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
@ -1157,13 +1509,17 @@ static tree
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)
@ -1179,7 +1535,7 @@ gimple_expand_builtin_pow (gimple_stmt_iterator *gsi, location_t loc,
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);
@ -1196,49 +1552,8 @@ gimple_expand_builtin_pow (gimple_stmt_iterator *gsi, location_t loc,
&& !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
@ -1263,7 +1578,7 @@ gimple_expand_builtin_pow (gimple_stmt_iterator *gsi, location_t loc,
&& 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))
{
@ -1274,54 +1589,31 @@ gimple_expand_builtin_pow (gimple_stmt_iterator *gsi, location_t loc,
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.
/* 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
&& hw_sqrt_exists
&& (speed_p || REAL_VALUES_EQUAL (c, dconst1_4))
&& !HONOR_SIGNED_ZEROS (mode))
{
unsigned int max_depth = speed_p
? PARAM_VALUE (PARAM_MAX_POW_SQRT_DEPTH)
: 2;
tree expand_with_sqrts
= expand_pow_as_sqrts (gsi, loc, arg0, arg1, max_depth);
if (expand_with_sqrts)
return expand_with_sqrts;
}
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);
if (flag_unsafe_math_optimizations
&& sqrtfn
&& c2_is_int
&& !c_is_int
&& optimize_function_for_speed_p (cfun))
{
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;
}
/* 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);
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;
}
/* Optimize pow(x,c), where 3c = n for some nonzero integer n, into
powi(x, n/3) * powi(cbrt(x), n%3), n > 0;