[PATCH] Fix up sqrt(x) < c and sqrt(x) >= c match.pd folding (PR tree-optimization/91734)

[PATCH] Fix up sqrt(x) < c and sqrt(x) >= c match.pd folding (PR tree-optimization/91734)

[Jakub Jelinek]

Hi!

As mentioned in the PR, the sqrt (x) < c optimization into x < c*c
sometimes breaks the boundary case, if c2=c*c is inexact then in some cases
we need to optimize it into x <= c*c rather than x < c*c.  The original
bugreport is when c is small and c2 is 0.0, then obviously we need <= 0.0
rather than < 0.0, but the testcase includes another example where it makes
a difference, plus has a >= testcase too.

Bootstrapped/regtested on powerpc64le-linux, ok for trunk?

2019-09-13  Jakub Jelinek  <jakub@redhat.com>

	PR tree-optimization/91734
	* generic-match-head.c: Include fold-const-call.h.
	* match.pd (sqrt(x) < c, sqrt(x) >= c): Check the boundary value and
	in case inexact computation of c*c affects comparison of the boundary,
	turn LT_EXPR into LE_EXPR or GE_EXPR into GT_EXPR.

	* gcc.dg/pr91734.c: New test.

--- gcc/generic-match-head.c.jj	2019-07-20 21:02:09.296821929 +0200
+++ gcc/generic-match-head.c	2019-09-12 10:52:33.091366624 +0200
@@ -29,6 +29,7 @@ along with GCC; see the file COPYING3.
 #include "cgraph.h"
 #include "vec-perm-indices.h"
 #include "fold-const.h"
+#include "fold-const-call.h"
 #include "stor-layout.h"
 #include "tree-dfa.h"
 #include "builtins.h"
--- gcc/match.pd.jj	2019-09-11 21:50:54.933504293 +0200
+++ gcc/match.pd	2019-09-12 11:12:11.150987786 +0200
@@ -3541,56 +3541,71 @@ (define_operator_list COND_TERNARY
 	  if x is negative or NaN.  Due to -funsafe-math-optimizations,
 	  the results for other x follow from natural arithmetic.  */
        (cmp @0 @1)))
-     (if (cmp == GT_EXPR || cmp == GE_EXPR)
+     (if (cmp == LT_EXPR || cmp == LE_EXPR || cmp == GT_EXPR || cmp == GE_EXPR)
       (with
        {
-         REAL_VALUE_TYPE c2;
+	 REAL_VALUE_TYPE c2;
+	 enum tree_code ncmp = cmp;
 	 real_arithmetic (&c2, MULT_EXPR,
 			  &TREE_REAL_CST (@1), &TREE_REAL_CST (@1));
 	 real_convert (&c2, TYPE_MODE (TREE_TYPE (@0)), &c2);
+	 /* See PR91734: if c2 is inexact and sqrt(c2) < c (or sqrt(c2) >= c),
+	    then change LT_EXPR into LE_EXPR or GE_EXPR into GT_EXPR.  */
+	 if ((cmp == LT_EXPR || cmp == GE_EXPR) && !REAL_VALUE_ISINF (c2))
+	   {
+	     tree c3 = fold_const_call (CFN_SQRT, TREE_TYPE (@0),
+					build_real (TREE_TYPE (@0), c2));
+	     if (c3 == NULL_TREE || TREE_CODE (c3) != REAL_CST)
+	       ncmp = ERROR_MARK;
+	     else if (real_less (&TREE_REAL_CST (c3), &TREE_REAL_CST (@1)))
+	       ncmp = cmp == LT_EXPR ? LE_EXPR : GT_EXPR;
+	   }
        }
-       (if (REAL_VALUE_ISINF (c2))
-	/* sqrt(x) > y is x == +Inf, when y is very large.  */
-	(if (HONOR_INFINITIES (@0))
-	 (eq @0 { build_real (TREE_TYPE (@0), c2); })
-	 { constant_boolean_node (false, type); })
-	/* sqrt(x) > c is the same as x > c*c.  */
-	(cmp @0 { build_real (TREE_TYPE (@0), c2); }))))
-     (if (cmp == LT_EXPR || cmp == LE_EXPR)
-      (with
-       {
-       	 REAL_VALUE_TYPE c2;
-	 real_arithmetic (&c2, MULT_EXPR,
-			  &TREE_REAL_CST (@1), &TREE_REAL_CST (@1));
-	 real_convert (&c2, TYPE_MODE (TREE_TYPE (@0)), &c2);
-       }
-       (if (REAL_VALUE_ISINF (c2))
-        (switch
-	 /* sqrt(x) < y is always true, when y is a very large
-	    value and we don't care about NaNs or Infinities.  */
-	 (if (! HONOR_NANS (@0) && ! HONOR_INFINITIES (@0))
-	  { constant_boolean_node (true, type); })
-	 /* sqrt(x) < y is x != +Inf when y is very large and we
-	    don't care about NaNs.  */
-	 (if (! HONOR_NANS (@0))
-	  (ne @0 { build_real (TREE_TYPE (@0), c2); }))
-	 /* sqrt(x) < y is x >= 0 when y is very large and we
-	    don't care about Infinities.  */
-	 (if (! HONOR_INFINITIES (@0))
-	  (ge @0 { build_real (TREE_TYPE (@0), dconst0); }))
-	 /* sqrt(x) < y is x >= 0 && x != +Inf, when y is large.  */
-	 (if (GENERIC)
-	  (truth_andif
-	   (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
-	   (ne @0 { build_real (TREE_TYPE (@0), c2); }))))
-	/* sqrt(x) < c is the same as x < c*c, if we ignore NaNs.  */
-	(if (! HONOR_NANS (@0))
-	 (cmp @0 { build_real (TREE_TYPE (@0), c2); })
-	 /* sqrt(x) < c is the same as x >= 0 && x < c*c.  */
-	 (if (GENERIC)
-	  (truth_andif
-	   (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
-	   (cmp @0 { build_real (TREE_TYPE (@0), c2); })))))))))
+       (if (cmp == GT_EXPR || cmp == GE_EXPR)
+	(if (REAL_VALUE_ISINF (c2))
+	 /* sqrt(x) > y is x == +Inf, when y is very large.  */
+	 (if (HONOR_INFINITIES (@0))
+	  (eq @0 { build_real (TREE_TYPE (@0), c2); })
+	  { constant_boolean_node (false, type); })
+	 /* sqrt(x) > c is the same as x > c*c.  */
+	 (if (ncmp != ERROR_MARK)
+	  (if (ncmp == GE_EXPR)
+	   (ge @0 { build_real (TREE_TYPE (@0), c2); })
+	   (gt @0 { build_real (TREE_TYPE (@0), c2); }))))
+	/* else if (cmp == LT_EXPR || cmp == LE_EXPR)  */
+	(if (REAL_VALUE_ISINF (c2))
+	 (switch
+	  /* sqrt(x) < y is always true, when y is a very large
+	     value and we don't care about NaNs or Infinities.  */
+	  (if (! HONOR_NANS (@0) && ! HONOR_INFINITIES (@0))
+	   { constant_boolean_node (true, type); })
+	  /* sqrt(x) < y is x != +Inf when y is very large and we
+	     don't care about NaNs.  */
+	  (if (! HONOR_NANS (@0))
+	   (ne @0 { build_real (TREE_TYPE (@0), c2); }))
+	  /* sqrt(x) < y is x >= 0 when y is very large and we
+	     don't care about Infinities.  */
+	  (if (! HONOR_INFINITIES (@0))
+	   (ge @0 { build_real (TREE_TYPE (@0), dconst0); }))
+	  /* sqrt(x) < y is x >= 0 && x != +Inf, when y is large.  */
+	  (if (GENERIC)
+	   (truth_andif
+	    (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
+	    (ne @0 { build_real (TREE_TYPE (@0), c2); }))))
+	 /* sqrt(x) < c is the same as x < c*c, if we ignore NaNs.  */
+	 (if (ncmp != ERROR_MARK && ! HONOR_NANS (@0))
+	  (if (ncmp == LT_EXPR)
+	   (lt @0 { build_real (TREE_TYPE (@0), c2); })
+	   (le @0 { build_real (TREE_TYPE (@0), c2); }))
+	  /* sqrt(x) < c is the same as x >= 0 && x < c*c.  */
+	  (if (ncmp != ERROR_MARK && GENERIC)
+	   (if (ncmp == LT_EXPR)
+	    (truth_andif
+	     (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
+	     (lt @0 { build_real (TREE_TYPE (@0), c2); }))
+	    (truth_andif
+	     (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
+	     (le @0 { build_real (TREE_TYPE (@0), c2); })))))))))))
    /* Transform sqrt(x) cmp sqrt(y) -> x cmp y.  */
    (simplify
     (cmp (sq @0) (sq @1))
--- gcc/testsuite/gcc.dg/pr91734.c.jj	2019-09-12 10:52:33.094366596 +0200
+++ gcc/testsuite/gcc.dg/pr91734.c	2019-09-12 10:49:10.000000000 +0200
@@ -0,0 +1,34 @@
+/* PR tree-optimization/91734 */
+/* { dg-do run } */
+/* { dg-add-options ieee } */
+/* { dg-additional-options "-ffast-math -O2 -std=gnu99" } */
+
+__attribute__((noipa)) int
+foo (float x)
+{
+  return __builtin_sqrtf (x) < __FLT_MIN__;
+}
+
+__attribute__((noipa)) int
+bar (float x)
+{
+  return __builtin_sqrtf (x) < 0x1.2dd3d0p-65f;
+}
+
+__attribute__((noipa)) int
+baz (float x)
+{
+  return __builtin_sqrtf (x) >= 0x1.2dd3d0p-65f;
+}
+
+int
+main ()
+{
+  if (!foo (0.0f))
+    __builtin_abort ();
+  if (!bar (0x1.63dbc0p-130f))
+    __builtin_abort ();
+  if (baz (0x1.63dbc0p-130f))
+    __builtin_abort ();
+  return 0;
+}

	Jakub

Re: [PATCH] Fix up sqrt(x) < c and sqrt(x) >= c match.pd folding (PR tree-optimization/91734)

[Richard Biener]

[-- Attachment #1: Type: text/plain, Size: 8232 bytes --]

On Sat, 14 Sep 2019, Jakub Jelinek wrote:

> Hi!
> 
> As mentioned in the PR, the sqrt (x) < c optimization into x < c*c
> sometimes breaks the boundary case, if c2=c*c is inexact then in some cases
> we need to optimize it into x <= c*c rather than x < c*c.  The original
> bugreport is when c is small and c2 is 0.0, then obviously we need <= 0.0
> rather than < 0.0, but the testcase includes another example where it makes
> a difference, plus has a >= testcase too.
> 
> Bootstrapped/regtested on powerpc64le-linux, ok for trunk?

I was hoping Joseph might chime in here...  anyway, does this assume
round-to-nearest or does it work with round to +-Inf as well?  I
realize this all is under flag_unsafe_math_optimizations, but
this flag is notoriously underspecified...  So the question is
whether we should disable the transform if c*c isn't exact and
flag_rounding_math?  The transform also doesn't seem to guard
against isnan (c) (-funsafe-math-optimizations sets
-fno-trapping-math and -fno-signed-zeros but not -ffinite-math-only
or disables itself on -frounding-math)

Otherwise the patch looks OK to me.

Thanks,
Richard.


> 2019-09-13  Jakub Jelinek  <jakub@redhat.com>
> 
> 	PR tree-optimization/91734
> 	* generic-match-head.c: Include fold-const-call.h.
> 	* match.pd (sqrt(x) < c, sqrt(x) >= c): Check the boundary value and
> 	in case inexact computation of c*c affects comparison of the boundary,
> 	turn LT_EXPR into LE_EXPR or GE_EXPR into GT_EXPR.
> 
> 	* gcc.dg/pr91734.c: New test.
> 
> --- gcc/generic-match-head.c.jj	2019-07-20 21:02:09.296821929 +0200
> +++ gcc/generic-match-head.c	2019-09-12 10:52:33.091366624 +0200
> @@ -29,6 +29,7 @@ along with GCC; see the file COPYING3.
>  #include "cgraph.h"
>  #include "vec-perm-indices.h"
>  #include "fold-const.h"
> +#include "fold-const-call.h"
>  #include "stor-layout.h"
>  #include "tree-dfa.h"
>  #include "builtins.h"
> --- gcc/match.pd.jj	2019-09-11 21:50:54.933504293 +0200
> +++ gcc/match.pd	2019-09-12 11:12:11.150987786 +0200
> @@ -3541,56 +3541,71 @@ (define_operator_list COND_TERNARY
>  	  if x is negative or NaN.  Due to -funsafe-math-optimizations,
>  	  the results for other x follow from natural arithmetic.  */
>         (cmp @0 @1)))
> -     (if (cmp == GT_EXPR || cmp == GE_EXPR)
> +     (if (cmp == LT_EXPR || cmp == LE_EXPR || cmp == GT_EXPR || cmp == GE_EXPR)
>        (with
>         {
> -         REAL_VALUE_TYPE c2;
> +	 REAL_VALUE_TYPE c2;
> +	 enum tree_code ncmp = cmp;
>  	 real_arithmetic (&c2, MULT_EXPR,
>  			  &TREE_REAL_CST (@1), &TREE_REAL_CST (@1));
>  	 real_convert (&c2, TYPE_MODE (TREE_TYPE (@0)), &c2);
> +	 /* See PR91734: if c2 is inexact and sqrt(c2) < c (or sqrt(c2) >= c),
> +	    then change LT_EXPR into LE_EXPR or GE_EXPR into GT_EXPR.  */
> +	 if ((cmp == LT_EXPR || cmp == GE_EXPR) && !REAL_VALUE_ISINF (c2))
> +	   {
> +	     tree c3 = fold_const_call (CFN_SQRT, TREE_TYPE (@0),
> +					build_real (TREE_TYPE (@0), c2));
> +	     if (c3 == NULL_TREE || TREE_CODE (c3) != REAL_CST)
> +	       ncmp = ERROR_MARK;
> +	     else if (real_less (&TREE_REAL_CST (c3), &TREE_REAL_CST (@1)))
> +	       ncmp = cmp == LT_EXPR ? LE_EXPR : GT_EXPR;
> +	   }
>         }
> -       (if (REAL_VALUE_ISINF (c2))
> -	/* sqrt(x) > y is x == +Inf, when y is very large.  */
> -	(if (HONOR_INFINITIES (@0))
> -	 (eq @0 { build_real (TREE_TYPE (@0), c2); })
> -	 { constant_boolean_node (false, type); })
> -	/* sqrt(x) > c is the same as x > c*c.  */
> -	(cmp @0 { build_real (TREE_TYPE (@0), c2); }))))
> -     (if (cmp == LT_EXPR || cmp == LE_EXPR)
> -      (with
> -       {
> -       	 REAL_VALUE_TYPE c2;
> -	 real_arithmetic (&c2, MULT_EXPR,
> -			  &TREE_REAL_CST (@1), &TREE_REAL_CST (@1));
> -	 real_convert (&c2, TYPE_MODE (TREE_TYPE (@0)), &c2);
> -       }
> -       (if (REAL_VALUE_ISINF (c2))
> -        (switch
> -	 /* sqrt(x) < y is always true, when y is a very large
> -	    value and we don't care about NaNs or Infinities.  */
> -	 (if (! HONOR_NANS (@0) && ! HONOR_INFINITIES (@0))
> -	  { constant_boolean_node (true, type); })
> -	 /* sqrt(x) < y is x != +Inf when y is very large and we
> -	    don't care about NaNs.  */
> -	 (if (! HONOR_NANS (@0))
> -	  (ne @0 { build_real (TREE_TYPE (@0), c2); }))
> -	 /* sqrt(x) < y is x >= 0 when y is very large and we
> -	    don't care about Infinities.  */
> -	 (if (! HONOR_INFINITIES (@0))
> -	  (ge @0 { build_real (TREE_TYPE (@0), dconst0); }))
> -	 /* sqrt(x) < y is x >= 0 && x != +Inf, when y is large.  */
> -	 (if (GENERIC)
> -	  (truth_andif
> -	   (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
> -	   (ne @0 { build_real (TREE_TYPE (@0), c2); }))))
> -	/* sqrt(x) < c is the same as x < c*c, if we ignore NaNs.  */
> -	(if (! HONOR_NANS (@0))
> -	 (cmp @0 { build_real (TREE_TYPE (@0), c2); })
> -	 /* sqrt(x) < c is the same as x >= 0 && x < c*c.  */
> -	 (if (GENERIC)
> -	  (truth_andif
> -	   (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
> -	   (cmp @0 { build_real (TREE_TYPE (@0), c2); })))))))))
> +       (if (cmp == GT_EXPR || cmp == GE_EXPR)
> +	(if (REAL_VALUE_ISINF (c2))
> +	 /* sqrt(x) > y is x == +Inf, when y is very large.  */
> +	 (if (HONOR_INFINITIES (@0))
> +	  (eq @0 { build_real (TREE_TYPE (@0), c2); })
> +	  { constant_boolean_node (false, type); })
> +	 /* sqrt(x) > c is the same as x > c*c.  */
> +	 (if (ncmp != ERROR_MARK)
> +	  (if (ncmp == GE_EXPR)
> +	   (ge @0 { build_real (TREE_TYPE (@0), c2); })
> +	   (gt @0 { build_real (TREE_TYPE (@0), c2); }))))
> +	/* else if (cmp == LT_EXPR || cmp == LE_EXPR)  */
> +	(if (REAL_VALUE_ISINF (c2))
> +	 (switch
> +	  /* sqrt(x) < y is always true, when y is a very large
> +	     value and we don't care about NaNs or Infinities.  */
> +	  (if (! HONOR_NANS (@0) && ! HONOR_INFINITIES (@0))
> +	   { constant_boolean_node (true, type); })
> +	  /* sqrt(x) < y is x != +Inf when y is very large and we
> +	     don't care about NaNs.  */
> +	  (if (! HONOR_NANS (@0))
> +	   (ne @0 { build_real (TREE_TYPE (@0), c2); }))
> +	  /* sqrt(x) < y is x >= 0 when y is very large and we
> +	     don't care about Infinities.  */
> +	  (if (! HONOR_INFINITIES (@0))
> +	   (ge @0 { build_real (TREE_TYPE (@0), dconst0); }))
> +	  /* sqrt(x) < y is x >= 0 && x != +Inf, when y is large.  */
> +	  (if (GENERIC)
> +	   (truth_andif
> +	    (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
> +	    (ne @0 { build_real (TREE_TYPE (@0), c2); }))))
> +	 /* sqrt(x) < c is the same as x < c*c, if we ignore NaNs.  */
> +	 (if (ncmp != ERROR_MARK && ! HONOR_NANS (@0))
> +	  (if (ncmp == LT_EXPR)
> +	   (lt @0 { build_real (TREE_TYPE (@0), c2); })
> +	   (le @0 { build_real (TREE_TYPE (@0), c2); }))
> +	  /* sqrt(x) < c is the same as x >= 0 && x < c*c.  */
> +	  (if (ncmp != ERROR_MARK && GENERIC)
> +	   (if (ncmp == LT_EXPR)
> +	    (truth_andif
> +	     (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
> +	     (lt @0 { build_real (TREE_TYPE (@0), c2); }))
> +	    (truth_andif
> +	     (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
> +	     (le @0 { build_real (TREE_TYPE (@0), c2); })))))))))))
>     /* Transform sqrt(x) cmp sqrt(y) -> x cmp y.  */
>     (simplify
>      (cmp (sq @0) (sq @1))
> --- gcc/testsuite/gcc.dg/pr91734.c.jj	2019-09-12 10:52:33.094366596 +0200
> +++ gcc/testsuite/gcc.dg/pr91734.c	2019-09-12 10:49:10.000000000 +0200
> @@ -0,0 +1,34 @@
> +/* PR tree-optimization/91734 */
> +/* { dg-do run } */
> +/* { dg-add-options ieee } */
> +/* { dg-additional-options "-ffast-math -O2 -std=gnu99" } */
> +
> +__attribute__((noipa)) int
> +foo (float x)
> +{
> +  return __builtin_sqrtf (x) < __FLT_MIN__;
> +}
> +
> +__attribute__((noipa)) int
> +bar (float x)
> +{
> +  return __builtin_sqrtf (x) < 0x1.2dd3d0p-65f;
> +}
> +
> +__attribute__((noipa)) int
> +baz (float x)
> +{
> +  return __builtin_sqrtf (x) >= 0x1.2dd3d0p-65f;
> +}
> +
> +int
> +main ()
> +{
> +  if (!foo (0.0f))
> +    __builtin_abort ();
> +  if (!bar (0x1.63dbc0p-130f))
> +    __builtin_abort ();
> +  if (baz (0x1.63dbc0p-130f))
> +    __builtin_abort ();
> +  return 0;
> +}
> 
> 	Jakub
> 

-- 
Richard Biener <rguenther@suse.de>
SUSE Software Solutions Germany GmbH, Maxfeldstrasse 5, 90409 Nuernberg,
Germany; GF: Felix Imendörffer; HRB 247165 (AG MÌnchen)

[PATCH] Fix up sqrt(x) < c and sqrt(x) >= c match.pd folding (PR tree-optimization/91734, take 2)

[Jakub Jelinek]

[-- Attachment #1: Type: text/plain, Size: 12529 bytes --]

On Mon, Sep 16, 2019 at 08:56:58AM +0200, Richard Biener wrote:
> > As mentioned in the PR, the sqrt (x) < c optimization into x < c*c
> > sometimes breaks the boundary case, if c2=c*c is inexact then in some cases
> > we need to optimize it into x <= c*c rather than x < c*c.  The original
> > bugreport is when c is small and c2 is 0.0, then obviously we need <= 0.0
> > rather than < 0.0, but the testcase includes another example where it makes
> > a difference, plus has a >= testcase too.
> > 
> > Bootstrapped/regtested on powerpc64le-linux, ok for trunk?
> 
> I was hoping Joseph might chime in here...  anyway, does this assume
> round-to-nearest or does it work with round to +-Inf as well?  I
> realize this all is under flag_unsafe_math_optimizations, but
> this flag is notoriously underspecified...  So the question is
> whether we should disable the transform if c*c isn't exact and
> flag_rounding_math?  The transform also doesn't seem to guard
> against isnan (c) (-funsafe-math-optimizations sets
> -fno-trapping-math and -fno-signed-zeros but not -ffinite-math-only
> or disables itself on -frounding-math)

Here is an updated patch, which on top of the previous patch:
1) punts for -frounding-math
2) punts for sqrt comparisons against NaN constant
3) for the c*c inexact also handles the other two comparisons that
apparently need to be handled too
4) for all 4 comparisons also checks nexttoward (c2, 0.0) or nexttoward (c2,
inf) depending on the comparison kind, because as Joseph correctly noted,
with rounding to nearest up to 3 different floating point values can have
the same sqrt result, and if c2 is the middle one from them, we need to use
the 1 ulp smaller or larger one in the comparison
5) had to adjust the testcase, because while it worked fine on powerpc64le,
on x86_64 if the test is linked with -ffast-math/-Ofast etc., crtfastmath.o
is linked in and subnormals are flushed to zero, which is not what we want
for the testcase (at least for a subset of the tests).

Bootstrapped/regtested on x86_64-linux and i686-linux, ok for trunk?

BTW, I've used attached programs to look for the problematic cases on random
float/doubles and the cases the patch handles seem to be the only
problematic ones, there is never need to go further than one nexttoward to 0
or inf.

2019-09-21  Jakub Jelinek  <jakub@redhat.com>

	PR tree-optimization/91734
	* generic-match-head.c: Include fold-const-call.h.
	* match.pd (sqrt(x) cmp c): Check the boundary value and
	in case inexact computation of c*c affects comparison of the boundary,
	turn LT_EXPR into LE_EXPR, GE_EXPR into GT_EXPR, LE_EXPR into LT_EXPR
	or GT_EXPR into GE_EXPR.  Punt for sqrt comparisons against NaN and
	for -frounding-math.  For c2, try the next smaller or larger floating
	point constant depending on comparison code and if it has the same
	sqrt as c2, use it instead of c2.

	* gcc.dg/pr91734.c: New test.

--- gcc/generic-match-head.c.jj	2019-09-20 12:24:56.376189996 +0200
+++ gcc/generic-match-head.c	2019-09-20 12:43:08.017273166 +0200
@@ -29,6 +29,7 @@ along with GCC; see the file COPYING3.
 #include "cgraph.h"
 #include "vec-perm-indices.h"
 #include "fold-const.h"
+#include "fold-const-call.h"
 #include "stor-layout.h"
 #include "tree-dfa.h"
 #include "builtins.h"
--- gcc/match.pd.jj	2019-09-20 12:25:27.323710388 +0200
+++ gcc/match.pd	2019-09-20 17:20:22.974316837 +0200
@@ -3711,8 +3711,7 @@ (define_operator_list COND_TERNARY
      (cmp { tem; } @1)))))
 
  /* Fold comparisons against built-in math functions.  */
- (if (flag_unsafe_math_optimizations
-      && ! flag_errno_math)
+ (if (flag_unsafe_math_optimizations && ! flag_errno_math)
   (for sq (SQRT)
    (simplify
     (cmp (sq @0) REAL_CST@1)
@@ -3747,56 +3746,108 @@ (define_operator_list COND_TERNARY
 	  if x is negative or NaN.  Due to -funsafe-math-optimizations,
 	  the results for other x follow from natural arithmetic.  */
        (cmp @0 @1)))
-     (if (cmp == GT_EXPR || cmp == GE_EXPR)
+     (if ((cmp == LT_EXPR
+	   || cmp == LE_EXPR
+	   || cmp == GT_EXPR
+	   || cmp == GE_EXPR)
+	  && !REAL_VALUE_ISNAN (TREE_REAL_CST (@1))
+	  /* Give up for -frounding-math.  */
+	  && !HONOR_SIGN_DEPENDENT_ROUNDING (TREE_TYPE (@0)))
       (with
        {
-         REAL_VALUE_TYPE c2;
+	 REAL_VALUE_TYPE c2;
+	 enum tree_code ncmp = cmp;
+	 const real_format *fmt
+	   = REAL_MODE_FORMAT (TYPE_MODE (TREE_TYPE (@0)));
 	 real_arithmetic (&c2, MULT_EXPR,
 			  &TREE_REAL_CST (@1), &TREE_REAL_CST (@1));
-	 real_convert (&c2, TYPE_MODE (TREE_TYPE (@0)), &c2);
+	 real_convert (&c2, fmt, &c2);
+	 /* See PR91734: if c2 is inexact and sqrt(c2) < c (or sqrt(c2) >= c),
+	    then change LT_EXPR into LE_EXPR or GE_EXPR into GT_EXPR.  */
+	 if (!REAL_VALUE_ISINF (c2))
+	   {
+	     tree c3 = fold_const_call (CFN_SQRT, TREE_TYPE (@0),
+					build_real (TREE_TYPE (@0), c2));
+	     if (c3 == NULL_TREE || TREE_CODE (c3) != REAL_CST)
+	       ncmp = ERROR_MARK;
+	     else if ((cmp == LT_EXPR || cmp == GE_EXPR)
+		      && real_less (&TREE_REAL_CST (c3), &TREE_REAL_CST (@1)))
+	       ncmp = cmp == LT_EXPR ? LE_EXPR : GT_EXPR;
+	     else if ((cmp == LE_EXPR || cmp == GT_EXPR)
+		      && real_less (&TREE_REAL_CST (@1), &TREE_REAL_CST (c3)))
+	       ncmp = cmp == LE_EXPR ? LT_EXPR : GE_EXPR;
+	     else
+	       {
+		 /* With rounding to even, sqrt of up to 3 different values
+		    gives the same normal result, so in some cases c2 needs
+		    to be adjusted.  */
+		 REAL_VALUE_TYPE c2alt, tow;
+		 if (cmp == LT_EXPR || cmp == GE_EXPR)
+		   tow = dconst0;
+		 else
+		   real_inf (&tow);
+		 real_nextafter (&c2alt, fmt, &c2, &tow);
+		 real_convert (&c2alt, fmt, &c2alt);
+		 if (REAL_VALUE_ISINF (c2alt))
+		   ncmp = ERROR_MARK;
+		 else
+		   {
+		     c3 = fold_const_call (CFN_SQRT, TREE_TYPE (@0),
+					   build_real (TREE_TYPE (@0), c2alt));
+		     if (c3 == NULL_TREE || TREE_CODE (c3) != REAL_CST)
+		       ncmp = ERROR_MARK;
+		     else if (real_equal (&TREE_REAL_CST (c3),
+					  &TREE_REAL_CST (@1)))
+		       c2 = c2alt;
+		   }
+	       }
+	   }
        }
-       (if (REAL_VALUE_ISINF (c2))
-	/* sqrt(x) > y is x == +Inf, when y is very large.  */
-	(if (HONOR_INFINITIES (@0))
-	 (eq @0 { build_real (TREE_TYPE (@0), c2); })
-	 { constant_boolean_node (false, type); })
-	/* sqrt(x) > c is the same as x > c*c.  */
-	(cmp @0 { build_real (TREE_TYPE (@0), c2); }))))
-     (if (cmp == LT_EXPR || cmp == LE_EXPR)
-      (with
-       {
-       	 REAL_VALUE_TYPE c2;
-	 real_arithmetic (&c2, MULT_EXPR,
-			  &TREE_REAL_CST (@1), &TREE_REAL_CST (@1));
-	 real_convert (&c2, TYPE_MODE (TREE_TYPE (@0)), &c2);
-       }
-       (if (REAL_VALUE_ISINF (c2))
-        (switch
-	 /* sqrt(x) < y is always true, when y is a very large
-	    value and we don't care about NaNs or Infinities.  */
-	 (if (! HONOR_NANS (@0) && ! HONOR_INFINITIES (@0))
-	  { constant_boolean_node (true, type); })
-	 /* sqrt(x) < y is x != +Inf when y is very large and we
-	    don't care about NaNs.  */
-	 (if (! HONOR_NANS (@0))
-	  (ne @0 { build_real (TREE_TYPE (@0), c2); }))
-	 /* sqrt(x) < y is x >= 0 when y is very large and we
-	    don't care about Infinities.  */
-	 (if (! HONOR_INFINITIES (@0))
-	  (ge @0 { build_real (TREE_TYPE (@0), dconst0); }))
-	 /* sqrt(x) < y is x >= 0 && x != +Inf, when y is large.  */
-	 (if (GENERIC)
-	  (truth_andif
-	   (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
-	   (ne @0 { build_real (TREE_TYPE (@0), c2); }))))
-	/* sqrt(x) < c is the same as x < c*c, if we ignore NaNs.  */
-	(if (! HONOR_NANS (@0))
-	 (cmp @0 { build_real (TREE_TYPE (@0), c2); })
-	 /* sqrt(x) < c is the same as x >= 0 && x < c*c.  */
-	 (if (GENERIC)
-	  (truth_andif
-	   (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
-	   (cmp @0 { build_real (TREE_TYPE (@0), c2); })))))))))
+       (if (cmp == GT_EXPR || cmp == GE_EXPR)
+	(if (REAL_VALUE_ISINF (c2))
+	 /* sqrt(x) > y is x == +Inf, when y is very large.  */
+	 (if (HONOR_INFINITIES (@0))
+	  (eq @0 { build_real (TREE_TYPE (@0), c2); })
+	  { constant_boolean_node (false, type); })
+	 /* sqrt(x) > c is the same as x > c*c.  */
+	 (if (ncmp != ERROR_MARK)
+	  (if (ncmp == GE_EXPR)
+	   (ge @0 { build_real (TREE_TYPE (@0), c2); })
+	   (gt @0 { build_real (TREE_TYPE (@0), c2); }))))
+	/* else if (cmp == LT_EXPR || cmp == LE_EXPR)  */
+	(if (REAL_VALUE_ISINF (c2))
+	 (switch
+	  /* sqrt(x) < y is always true, when y is a very large
+	     value and we don't care about NaNs or Infinities.  */
+	  (if (! HONOR_NANS (@0) && ! HONOR_INFINITIES (@0))
+	   { constant_boolean_node (true, type); })
+	  /* sqrt(x) < y is x != +Inf when y is very large and we
+	     don't care about NaNs.  */
+	  (if (! HONOR_NANS (@0))
+	   (ne @0 { build_real (TREE_TYPE (@0), c2); }))
+	  /* sqrt(x) < y is x >= 0 when y is very large and we
+	     don't care about Infinities.  */
+	  (if (! HONOR_INFINITIES (@0))
+	   (ge @0 { build_real (TREE_TYPE (@0), dconst0); }))
+	  /* sqrt(x) < y is x >= 0 && x != +Inf, when y is large.  */
+	  (if (GENERIC)
+	   (truth_andif
+	    (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
+	    (ne @0 { build_real (TREE_TYPE (@0), c2); }))))
+	 /* sqrt(x) < c is the same as x < c*c, if we ignore NaNs.  */
+	 (if (ncmp != ERROR_MARK && ! HONOR_NANS (@0))
+	  (if (ncmp == LT_EXPR)
+	   (lt @0 { build_real (TREE_TYPE (@0), c2); })
+	   (le @0 { build_real (TREE_TYPE (@0), c2); }))
+	  /* sqrt(x) < c is the same as x >= 0 && x < c*c.  */
+	  (if (ncmp != ERROR_MARK && GENERIC)
+	   (if (ncmp == LT_EXPR)
+	    (truth_andif
+	     (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
+	     (lt @0 { build_real (TREE_TYPE (@0), c2); }))
+	    (truth_andif
+	     (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
+	     (le @0 { build_real (TREE_TYPE (@0), c2); })))))))))))
    /* Transform sqrt(x) cmp sqrt(y) -> x cmp y.  */
    (simplify
     (cmp (sq @0) (sq @1))
--- gcc/testsuite/gcc.dg/pr91734.c.jj	2019-09-20 12:43:08.019273135 +0200
+++ gcc/testsuite/gcc.dg/pr91734.c	2019-09-21 07:57:26.102273700 +0200
@@ -0,0 +1,97 @@
+/* PR tree-optimization/91734 */
+/* { dg-do run } */
+/* { dg-add-options ieee } */
+/* { dg-additional-options "-O2 -std=gnu99" } */
+
+__attribute__((noipa, optimize ("Ofast"))) int
+f1 (float x)
+{
+  return __builtin_sqrtf (x) < __FLT_MIN__;
+}
+
+__attribute__((noipa, optimize ("Ofast"))) int
+f2 (float x)
+{
+  return __builtin_sqrtf (x) < 0x1.2dd3d0p-65f;
+}
+
+__attribute__((noipa, optimize ("Ofast"))) int
+f3 (float x)
+{
+  return __builtin_sqrtf (x) >= 0x1.2dd3d0p-65f;
+}
+
+__attribute__((noipa, optimize ("Ofast"))) int
+f4 (float x)
+{
+  return __builtin_sqrtf (x) >= 0x1.5642e6p+54f;
+}
+
+__attribute__((noipa, optimize ("Ofast"))) int
+f5 (float x)
+{
+  return __builtin_sqrtf (x) > 0x1.5642e6p+54f;
+}
+
+__attribute__((noipa, optimize ("Ofast"))) int
+f6 (float x)
+{
+  return __builtin_sqrtf (x) < 0x1.4da1cp-19f;
+}
+
+__attribute__((noipa, optimize ("Ofast"))) int
+f7 (float x)
+{
+  return __builtin_sqrtf (x) <= 0x1.4da1cp-19f;
+}
+
+__attribute__((noipa, optimize ("Ofast"))) int
+f8 (float x)
+{
+  return __builtin_sqrtf (x) < 0x1.50cb62p-65f;
+}
+
+__attribute__((noipa, optimize ("Ofast"))) int
+f9 (float x)
+{
+  return __builtin_sqrtf (x) <= 0x1.4fc00cp-73f;
+}
+
+__attribute__((noipa, optimize ("Ofast"))) int
+f10 (float x)
+{
+  return __builtin_sqrtf (x) < 0x1.001002p+0f;
+}
+
+int
+main ()
+{
+  if (__FLT_RADIX__ != 2
+      || __FLT_MANT_DIG__ != 24
+      || __FLT_MIN_EXP__ != -125
+      || __FLT_MAX_EXP__ != 128
+      || __FLT_HAS_DENORM__ != 1
+      || __FLT_HAS_INFINITY__ != 1)
+    return 0;
+  if (!f1 (0.0f) || f1 (0x1.0p-149f))
+    __builtin_abort ();
+  if (!f2 (0x1.63dbc0p-130f))
+    __builtin_abort ();
+  if (f3 (0x1.63dbc0p-130f))
+    __builtin_abort ();
+  if (!f4 (0x1.c996d0p+108f) || !f4 (0x1.c996cep+108f) || f4 (0x1.c996ccp+108f))
+    __builtin_abort ();
+  if (f5 (0x1.c996d0p+108f) || f5 (0x1.c996d2p+108f) || !f5 (0x1.c996d4p+108f))
+    __builtin_abort ();
+  if (!f6 (0x1.b2ce3p-38f) || f6 (0x1.b2ce32p-38f) || f6 (0x1.b2ce34p-38f))
+    __builtin_abort ();
+  if (!f7 (0x1.b2ce3p-38f) || !f7 (0x1.b2ce34p-38f) || !f7 (0x1.b2ce36p-38f) || f7 (0x1.b2ce38p-38f))
+    __builtin_abort ();
+  if (!f8 (0x1.bb166p-130f) || !f8 (0x1.bb168p-130f) || f8 (0x1.bb16ap-130f) || f8 (0x1.bb16cp-130f))
+    __builtin_abort ();
+  if (!f9 (0x1.8p-146f) || !f9 (0x1.ap-146f) || f9 (0x1.cp-146f) || f9 (0x1.ep-146f))
+    __builtin_abort ();
+  if (f10 (0x1.002004p+0f))
+    __builtin_abort ();
+  return 0;
+}


	Jakub

[-- Attachment #2: pr91734-3.c --]
[-- Type: text/plain, Size: 2048 bytes --]

#include <stdlib.h>
#include <math.h>

int
main ()
{
  union U { float f; unsigned int i; } u;
  for (int i = 0; i < 10000000; i++)
    {
      u.i = ((unsigned) random () << 8) ^ random ();
      float c = u.f;
      if (!isnormal (c) || c < 0)
	continue;
      float c2 = c * c;
      for (int j = -15; j <= 15; j++)
	{
	  float x = c2;
	  if (j < 0)
	    {
	      for (int k = j; k != 0; k++)
		x = nexttowardf (x, -1.0f);
	    }
	  else if (j > 0)
	    {
	      for (int k = j; k != 0; k--)
		x = nexttowardf (x, __builtin_inff ());
	    }
	  if (x < 0)
	    continue;
	  if (isinf (c2))
	    continue;
	  float c3 = __builtin_sqrtf (c2);
	  float c4 = c2, c5 = c2;
#ifdef FIXME
	  c4 = nexttowardf (c2, 0.0);
	  float c4s = __builtin_sqrtf (c4);
	  if (c3 >= c && c4s == c)
	    ;
	  else
	    c4 = c2;
	  c5 = nexttowardf (c2, __builtin_inff ());
	  float c5s = __builtin_sqrtf (c5);
	  if (c3 <= c && !isinf (c5) && c5s == c)
	    ;
	  else
	    c5 = c2;
	  if (c3 < c
	      && (__builtin_sqrtf (x) < c) == (x <= c2)
	      && (__builtin_sqrtf (x) >= c) == (x > c2))
	    ;
	  else
#endif
	  if ((__builtin_sqrtf (x) < c) != (x < c4))
	    {
	      if ((__builtin_sqrtf (x) >= c) != (x >= c4))
		__builtin_printf ("</>= c %.12a c4 %.12a x %.12a %d\n", c, c4, x, j);
	      else
		__builtin_printf ("< c %.12a c4 %.12a x %.12a %d\n", c, c4, x, j);
	    }
	  else if ((__builtin_sqrtf (x) >= c) != (x >= c4))
	    __builtin_printf (">= c %.12a c4 %.12a x %.12a %d\n", c, c4, x, j);
#ifdef FIXME
	  if (c3 > c
	      && (__builtin_sqrtf (x) <= c) == (x < c2)
	      && (__builtin_sqrtf (x) > c) == (x >= c2))
	    ;
	  else
#endif
	  if ((__builtin_sqrtf (x) <= c) != (x <= c5))
	    {
	      if ((__builtin_sqrtf (x) > c) != (x > c5))
		__builtin_printf ("<=/> c %.12a c5 %.12a x %.12a %d\n", c, c5, x, j);
	      else
		__builtin_printf ("<= c %.12a c5 %.12a x %.12a %d\n", c, c5, x, j);
	    }
	  else if ((__builtin_sqrtf (x) > c) != (x > c5))
	    __builtin_printf ("> c %.12a c5 %.12a x %.12a %d\n", c, c5, x, j);
	}
    }
  return 0;
}

[-- Attachment #3: pr91734-4.c --]
[-- Type: text/plain, Size: 2113 bytes --]

#include <stdlib.h>
#include <math.h>

int
main ()
{
  union U { double f; unsigned long long int i; } u;
  for (int i = 0; i < 10000000; i++)
    {
      u.i = ((unsigned long long) random () << 40) ^ ((unsigned long long) random () << 20) ^ random ();
      double c = u.f;
      if (!isnormal (c) || c < 0)
	continue;
      double c2 = c * c;
      for (int j = -15; j <= 15; j++)
	{
	  double x = c2;
	  if (j < 0)
	    {
	      for (int k = j; k != 0; k++)
		x = nexttoward (x, -1.0f);
	    }
	  else if (j > 0)
	    {
	      for (int k = j; k != 0; k--)
		x = nexttoward (x, __builtin_inf ());
	    }
	  if (x < 0)
	    continue;
	  if (isinf (c2))
	    continue;
	  double c3 = __builtin_sqrt (c2);
	  double c4 = c2, c5 = c2;
#ifdef FIXME
	  double c4 = nexttoward (c2, 0.0);
	  double c4s = __builtin_sqrt (c4);
	  if (c3 >= c && c4s == c)
	    ;
	  else
	    c4 = c2;
	  double c5 = nexttoward (c2, __builtin_inf ());
	  double c5s = __builtin_sqrt (c5);
	  if (c3 <= c && !isinf (c5) && c5s == c)
	    ;
	  else
	    c5 = c2;
	  if (c3 < c
	      && (__builtin_sqrt (x) < c) == (x <= c2)
	      && (__builtin_sqrt (x) >= c) == (x > c2))
	    ;
	  else
#endif
	  if ((__builtin_sqrt (x) < c) != (x < c4))
	    {
	      if ((__builtin_sqrt (x) >= c) != (x >= c4))
		__builtin_printf ("</>= c %.12a c4 %.12a x %.12a %d\n", c, c4, x, j);
	      else
		__builtin_printf ("< c %.12a c4 %.12a x %.12a %d\n", c, c4, x, j);
	    }
	  else if ((__builtin_sqrt (x) >= c) != (x >= c4))
	    __builtin_printf (">= c %.12a c4 %.12a x %.12a %d\n", c, c4, x, j);
#ifdef FIXME
	  if (c3 > c
	      && (__builtin_sqrt (x) <= c) == (x < c2)
	      && (__builtin_sqrt (x) > c) == (x >= c2))
	    ;
	  else
#endif
	  if ((__builtin_sqrt (x) <= c) != (x <= c5))
	    {
	      if ((__builtin_sqrt (x) > c) != (x > c5))
		__builtin_printf ("<=/> c %.12a c5 %.12a x %.12a %d\n", c, c5, x, j);
	      else
		__builtin_printf ("<= c %.12a c5 %.12a x %.12a %d\n", c, c5, x, j);
	    }
	  else if ((__builtin_sqrt (x) > c) != (x > c5))
	    __builtin_printf ("> c %.12a c5 %.12a x %.12a %d\n", c, c5, x, j);
	}
    }
  return 0;
}

Patch ping

[Jakub Jelinek]

Hi!

On Sat, Sep 21, 2019 at 08:14:13AM +0200, Jakub Jelinek wrote:
> 2019-09-21  Jakub Jelinek  <jakub@redhat.com>
> 
> 	PR tree-optimization/91734
> 	* generic-match-head.c: Include fold-const-call.h.
> 	* match.pd (sqrt(x) cmp c): Check the boundary value and
> 	in case inexact computation of c*c affects comparison of the boundary,
> 	turn LT_EXPR into LE_EXPR, GE_EXPR into GT_EXPR, LE_EXPR into LT_EXPR
> 	or GT_EXPR into GE_EXPR.  Punt for sqrt comparisons against NaN and
> 	for -frounding-math.  For c2, try the next smaller or larger floating
> 	point constant depending on comparison code and if it has the same
> 	sqrt as c2, use it instead of c2.
> 
> 	* gcc.dg/pr91734.c: New test.

I'd like to ping this patch (
https://gcc.gnu.org/ml/gcc-patches/2019-09/msg01281.html
).  Thanks.

	Jakub

Re: [PATCH] Fix up sqrt(x) < c and sqrt(x) >= c match.pd folding (PR tree-optimization/91734, take 2)

[Jeff Law]

On 9/21/19 12:14 AM, Jakub Jelinek wrote:
> On Mon, Sep 16, 2019 at 08:56:58AM +0200, Richard Biener wrote:
>>> As mentioned in the PR, the sqrt (x) < c optimization into x < c*c
>>> sometimes breaks the boundary case, if c2=c*c is inexact then in some cases
>>> we need to optimize it into x <= c*c rather than x < c*c.  The original
>>> bugreport is when c is small and c2 is 0.0, then obviously we need <= 0.0
>>> rather than < 0.0, but the testcase includes another example where it makes
>>> a difference, plus has a >= testcase too.
>>>
>>> Bootstrapped/regtested on powerpc64le-linux, ok for trunk?
>>
>> I was hoping Joseph might chime in here...  anyway, does this assume
>> round-to-nearest or does it work with round to +-Inf as well?  I
>> realize this all is under flag_unsafe_math_optimizations, but
>> this flag is notoriously underspecified...  So the question is
>> whether we should disable the transform if c*c isn't exact and
>> flag_rounding_math?  The transform also doesn't seem to guard
>> against isnan (c) (-funsafe-math-optimizations sets
>> -fno-trapping-math and -fno-signed-zeros but not -ffinite-math-only
>> or disables itself on -frounding-math)
> 
> Here is an updated patch, which on top of the previous patch:
> 1) punts for -frounding-math
> 2) punts for sqrt comparisons against NaN constant
> 3) for the c*c inexact also handles the other two comparisons that
> apparently need to be handled too
> 4) for all 4 comparisons also checks nexttoward (c2, 0.0) or nexttoward (c2,
> inf) depending on the comparison kind, because as Joseph correctly noted,
> with rounding to nearest up to 3 different floating point values can have
> the same sqrt result, and if c2 is the middle one from them, we need to use
> the 1 ulp smaller or larger one in the comparison
> 5) had to adjust the testcase, because while it worked fine on powerpc64le,
> on x86_64 if the test is linked with -ffast-math/-Ofast etc., crtfastmath.o
> is linked in and subnormals are flushed to zero, which is not what we want
> for the testcase (at least for a subset of the tests).
> 
> Bootstrapped/regtested on x86_64-linux and i686-linux, ok for trunk?
> 
> BTW, I've used attached programs to look for the problematic cases on random
> float/doubles and the cases the patch handles seem to be the only
> problematic ones, there is never need to go further than one nexttoward to 0
> or inf.
> 
> 2019-09-21  Jakub Jelinek  <jakub@redhat.com>
> 
> 	PR tree-optimization/91734
> 	* generic-match-head.c: Include fold-const-call.h.
> 	* match.pd (sqrt(x) cmp c): Check the boundary value and
> 	in case inexact computation of c*c affects comparison of the boundary,
> 	turn LT_EXPR into LE_EXPR, GE_EXPR into GT_EXPR, LE_EXPR into LT_EXPR
> 	or GT_EXPR into GE_EXPR.  Punt for sqrt comparisons against NaN and
> 	for -frounding-math.  For c2, try the next smaller or larger floating
> 	point constant depending on comparison code and if it has the same
> 	sqrt as c2, use it instead of c2.
> 
> 	* gcc.dg/pr91734.c: New test.
OK.  One might argue that some of this code needs to be refactored into
functions to make visual parsing simpler.  But I'm not going to insist
on it right now.

jeff

Re: [PATCH] Fix up sqrt(x) < c and sqrt(x) >= c match.pd folding (PR tree-optimization/91734)

[Joseph Myers]

On Sat, 14 Sep 2019, Jakub Jelinek wrote:

> Hi!
> 
> As mentioned in the PR, the sqrt (x) < c optimization into x < c*c
> sometimes breaks the boundary case, if c2=c*c is inexact then in some cases
> we need to optimize it into x <= c*c rather than x < c*c.  The original

And in some cases the boundary case is wrong in the other direction and we 
need to optimize it into x < nextdown (c*c).  For example, say c == 
0x1.001002p+0f; (double) c * c == 0x1.002005004004p+0, and rounding to 
nearest float gives c * c == 0x1.002006p+0f, so nextdownf (c * c) == 
0x1.002004p+0f; in double precision, sqrt (0x1.002004p+0f) == 
0x1.0010017fe8006p+0, and rounding to nearest float gives c again.  So x < 
c*c does not in fact imply sqrt (x) < c in that case.

-- 
Joseph S. Myers
joseph@codesourcery.com