diff --git a/Include/pymath.h b/Include/pymath.h
index 7cea9ae..6ad174d 100644
--- a/Include/pymath.h
+++ b/Include/pymath.h
@@ -77,6 +77,21 @@
 #define Py_MATH_E 2.7182818284590452354
 #endif
 
+/* On x86, Py_FORCE_DOUBLE forces a floating-point number out of an x87 FPU
+   register and into a 64-bit memory location, rounding from extended
+   precision to double precision in the process.  On other platforms it does
+   nothing. */
+
+/* we take double rounding as evidence of x87 usage */
+#ifndef Py_FORCE_DOUBLE
+#  ifdef X87_DOUBLE_ROUNDING
+PyAPI_FUNC(double) _Py_force_double(double);
+#    define Py_FORCE_DOUBLE(X) (_Py_force_double(X))
+#  else
+#    define Py_FORCE_DOUBLE(X) (X)
+#  endif
+#endif
+
 /* Py_IS_NAN(X)
  * Return 1 if float or double arg is a NaN, else 0.
  * Caution:
@@ -87,7 +102,7 @@
  * Note: PC/pyconfig.h defines Py_IS_NAN as _isnan
  */
 #ifndef Py_IS_NAN
-#ifdef HAVE_ISNAN
+#if defined HAVE_DECL_ISNAN && HAVE_DECL_ISNAN == 1
 #define Py_IS_NAN(X) isnan(X)
 #else
 #define Py_IS_NAN(X) ((X) != (X))
@@ -101,14 +116,18 @@
  *    This implementation may set the underflow flag if |X| is very small;
  *    it really can't be implemented correctly (& easily) before C99.
  *    Override in pyconfig.h if you have a better spelling on your platform.
+ *  Py_FORCE_DOUBLE is used to avoid getting false negatives from a
+ *    non-infinite value v sitting in an 80-bit x87 register such that
+ *    v becomes infinite when spilled from the register to 64-bit memory.
  * Note: PC/pyconfig.h defines Py_IS_INFINITY as _isinf
  */
 #ifndef Py_IS_INFINITY
-#ifdef HAVE_ISINF
-#define Py_IS_INFINITY(X) isinf(X)
-#else
-#define Py_IS_INFINITY(X) ((X) && (X)*0.5 == (X))
-#endif
+#  if defined HAVE_DECL_ISINF && HAVE_DECL_ISINF == 1
+#    define Py_IS_INFINITY(X) isinf(X)
+#  else
+#    define Py_IS_INFINITY(X) ((X) &&                                   \
+                               (Py_FORCE_DOUBLE(X)*0.5 == Py_FORCE_DOUBLE(X)))
+#  endif
 #endif
 
 /* Py_IS_FINITE(X)
@@ -118,7 +137,9 @@
  * Note: PC/pyconfig.h defines Py_IS_FINITE as _finite
  */
 #ifndef Py_IS_FINITE
-#ifdef HAVE_FINITE
+#if defined HAVE_DECL_ISFINITE && HAVE_DECL_ISFINITE == 1
+#define Py_IS_FINITE(X) isfinite(X)
+#elif defined HAVE_FINITE
 #define Py_IS_FINITE(X) finite(X)
 #else
 #define Py_IS_FINITE(X) (!Py_IS_INFINITY(X) && !Py_IS_NAN(X))
diff --git a/Misc/NEWS b/Misc/NEWS
index 1dbc349..03d318d 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,10 @@
 Core and Builtins
 -----------------
 
+- Issue #5724: (See also issue #4575.) Fix Py_IS_INFINITY macro to
+  work correctly on x87 FPUs: it now forces its argument to double
+  before testing for infinity.
+
 - Issue #4971: Fix titlecase for characters that are their own
   titlecase, but not their own uppercase.
 
diff --git a/PC/pyconfig.h b/PC/pyconfig.h
index 112c83b..b81f883 100644
--- a/PC/pyconfig.h
+++ b/PC/pyconfig.h
@@ -405,11 +405,11 @@
 /* Define to 1 if you have the `copysign' function. */
 #define HAVE_COPYSIGN 1
 
-/* Define to 1 if you have the `isinf' function. */
-#define HAVE_ISINF 1
+/* Define to 1 if you have the `isinf' macro. */
+#define HAVE_DECL_ISINF 1
 
 /* Define to 1 if you have the `isnan' function. */
-#define HAVE_ISNAN 1
+#define HAVE_DECL_ISNAN 1
 
 /* Define if on AIX 3.
    System headers sometimes define this.
diff --git a/Python/pymath.c b/Python/pymath.c
index 6b8def9..2749688 100644
--- a/Python/pymath.c
+++ b/Python/pymath.c
@@ -1,5 +1,18 @@
 #include "Python.h"
 
+#ifdef X87_DOUBLE_ROUNDING
+/* On x86 platforms using an x87 FPU, this function is called from the
+   Py_FORCE_DOUBLE macro (defined in pymath.h) to force a floating-point
+   number out of an 80-bit x87 FPU register and into a 64-bit memory location,
+   thus rounding from extended precision to double precision. */
+double _Py_force_double(double x)
+{
+	volatile double y;
+	y = x;
+	return y;
+}
+#endif
+
 #ifndef HAVE_HYPOT
 double hypot(double x, double y)
 {
diff --git a/configure b/configure
index 77be421..67725d7 100755
--- a/configure
+++ b/configure
@@ -1,5 +1,5 @@
 #! /bin/sh
-# From configure.in Revision: 68599 .
+# From configure.in Revision: 70731 .
 # Guess values for system-dependent variables and create Makefiles.
 # Generated by GNU Autoconf 2.61 for python 2.6.
 #
@@ -21525,6 +21525,94 @@
 LIBS_SAVE=$LIBS
 LIBS="$LIBS $LIBM"
 
+# Detect whether system arithmetic is subject to x87-style double
+# rounding issues.  The result of this test has little meaning on non
+# IEEE 754 platforms.  On IEEE 754, test should return 1 if rounding
+# mode is round-to-nearest and double rounding issues are present, and
+# 0 otherwise.  See http://bugs.python.org/issue2937 for more info.
+{ echo "$as_me:$LINENO: checking for x87-style double rounding" >&5
+echo $ECHO_N "checking for x87-style double rounding... $ECHO_C" >&6; }
+if test "${ac_cv_x87_double_rounding+set}" = set; then
+  echo $ECHO_N "(cached) $ECHO_C" >&6
+else
+
+if test "$cross_compiling" = yes; then
+  ac_cv_x87_double_rounding=no
+else
+  cat >conftest.$ac_ext <<_ACEOF
+/* confdefs.h.  */
+_ACEOF
+cat confdefs.h >>conftest.$ac_ext
+cat >>conftest.$ac_ext <<_ACEOF
+/* end confdefs.h.  */
+
+#include <stdlib.h>
+#include <math.h>
+int main() {
+    volatile double x, y, z;
+    /* 1./(1-2**-53) -> 1+2**-52 (correct), 1.0 (double rounding) */
+    x = 0.99999999999999989; /* 1-2**-53 */
+    y = 1./x;
+    if (y != 1.)
+        exit(0);
+    /* 1e16+2.99999 -> 1e16+2. (correct), 1e16+4. (double rounding) */
+    x = 1e16;
+    y = 2.99999;
+    z = x + y;
+    if (z != 1e16+4.)
+        exit(0);
+    /* both tests show evidence of double rounding */
+    exit(1);
+}
+
+_ACEOF
+rm -f conftest$ac_exeext
+if { (ac_try="$ac_link"
+case "(($ac_try" in
+  *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+  *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+  (eval "$ac_link") 2>&5
+  ac_status=$?
+  echo "$as_me:$LINENO: \$? = $ac_status" >&5
+  (exit $ac_status); } && { ac_try='./conftest$ac_exeext'
+  { (case "(($ac_try" in
+  *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+  *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+  (eval "$ac_try") 2>&5
+  ac_status=$?
+  echo "$as_me:$LINENO: \$? = $ac_status" >&5
+  (exit $ac_status); }; }; then
+  ac_cv_x87_double_rounding=no
+else
+  echo "$as_me: program exited with status $ac_status" >&5
+echo "$as_me: failed program was:" >&5
+sed 's/^/| /' conftest.$ac_ext >&5
+
+( exit $ac_status )
+ac_cv_x87_double_rounding=yes
+fi
+rm -f core *.core core.conftest.* gmon.out bb.out conftest$ac_exeext conftest.$ac_objext conftest.$ac_ext
+fi
+
+
+fi
+
+{ echo "$as_me:$LINENO: result: $ac_cv_x87_double_rounding" >&5
+echo "${ECHO_T}$ac_cv_x87_double_rounding" >&6; }
+if test "$ac_cv_x87_double_rounding" = yes
+then
+
+cat >>confdefs.h <<\_ACEOF
+#define X87_DOUBLE_ROUNDING 1
+_ACEOF
+
+fi
+
+
 # On FreeBSD 6.2, it appears that tanh(-0.) returns 0. instead of
 # -0. on some architectures.
 { echo "$as_me:$LINENO: checking whether tanh preserves the sign of zero" >&5
@@ -21609,9 +21697,7 @@
 
 
 
-
-
-for ac_func in acosh asinh atanh copysign expm1 finite hypot isinf isnan log1p
+for ac_func in acosh asinh atanh copysign expm1 finite hypot log1p
 do
 as_ac_var=`echo "ac_cv_func_$ac_func" | $as_tr_sh`
 { echo "$as_me:$LINENO: checking for $ac_func" >&5
@@ -21704,6 +21790,209 @@
 fi
 done
 
+{ echo "$as_me:$LINENO: checking whether isinf is declared" >&5
+echo $ECHO_N "checking whether isinf is declared... $ECHO_C" >&6; }
+if test "${ac_cv_have_decl_isinf+set}" = set; then
+  echo $ECHO_N "(cached) $ECHO_C" >&6
+else
+  cat >conftest.$ac_ext <<_ACEOF
+/* confdefs.h.  */
+_ACEOF
+cat confdefs.h >>conftest.$ac_ext
+cat >>conftest.$ac_ext <<_ACEOF
+/* end confdefs.h.  */
+#include <math.h>
+
+int
+main ()
+{
+#ifndef isinf
+  (void) isinf;
+#endif
+
+  ;
+  return 0;
+}
+_ACEOF
+rm -f conftest.$ac_objext
+if { (ac_try="$ac_compile"
+case "(($ac_try" in
+  *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+  *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+  (eval "$ac_compile") 2>conftest.er1
+  ac_status=$?
+  grep -v '^ *+' conftest.er1 >conftest.err
+  rm -f conftest.er1
+  cat conftest.err >&5
+  echo "$as_me:$LINENO: \$? = $ac_status" >&5
+  (exit $ac_status); } && {
+	 test -z "$ac_c_werror_flag" ||
+	 test ! -s conftest.err
+       } && test -s conftest.$ac_objext; then
+  ac_cv_have_decl_isinf=yes
+else
+  echo "$as_me: failed program was:" >&5
+sed 's/^/| /' conftest.$ac_ext >&5
+
+	ac_cv_have_decl_isinf=no
+fi
+
+rm -f core conftest.err conftest.$ac_objext conftest.$ac_ext
+fi
+{ echo "$as_me:$LINENO: result: $ac_cv_have_decl_isinf" >&5
+echo "${ECHO_T}$ac_cv_have_decl_isinf" >&6; }
+if test $ac_cv_have_decl_isinf = yes; then
+
+cat >>confdefs.h <<_ACEOF
+#define HAVE_DECL_ISINF 1
+_ACEOF
+
+
+else
+  cat >>confdefs.h <<_ACEOF
+#define HAVE_DECL_ISINF 0
+_ACEOF
+
+
+fi
+{ echo "$as_me:$LINENO: checking whether isnan is declared" >&5
+echo $ECHO_N "checking whether isnan is declared... $ECHO_C" >&6; }
+if test "${ac_cv_have_decl_isnan+set}" = set; then
+  echo $ECHO_N "(cached) $ECHO_C" >&6
+else
+  cat >conftest.$ac_ext <<_ACEOF
+/* confdefs.h.  */
+_ACEOF
+cat confdefs.h >>conftest.$ac_ext
+cat >>conftest.$ac_ext <<_ACEOF
+/* end confdefs.h.  */
+#include <math.h>
+
+int
+main ()
+{
+#ifndef isnan
+  (void) isnan;
+#endif
+
+  ;
+  return 0;
+}
+_ACEOF
+rm -f conftest.$ac_objext
+if { (ac_try="$ac_compile"
+case "(($ac_try" in
+  *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+  *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+  (eval "$ac_compile") 2>conftest.er1
+  ac_status=$?
+  grep -v '^ *+' conftest.er1 >conftest.err
+  rm -f conftest.er1
+  cat conftest.err >&5
+  echo "$as_me:$LINENO: \$? = $ac_status" >&5
+  (exit $ac_status); } && {
+	 test -z "$ac_c_werror_flag" ||
+	 test ! -s conftest.err
+       } && test -s conftest.$ac_objext; then
+  ac_cv_have_decl_isnan=yes
+else
+  echo "$as_me: failed program was:" >&5
+sed 's/^/| /' conftest.$ac_ext >&5
+
+	ac_cv_have_decl_isnan=no
+fi
+
+rm -f core conftest.err conftest.$ac_objext conftest.$ac_ext
+fi
+{ echo "$as_me:$LINENO: result: $ac_cv_have_decl_isnan" >&5
+echo "${ECHO_T}$ac_cv_have_decl_isnan" >&6; }
+if test $ac_cv_have_decl_isnan = yes; then
+
+cat >>confdefs.h <<_ACEOF
+#define HAVE_DECL_ISNAN 1
+_ACEOF
+
+
+else
+  cat >>confdefs.h <<_ACEOF
+#define HAVE_DECL_ISNAN 0
+_ACEOF
+
+
+fi
+{ echo "$as_me:$LINENO: checking whether isfinite is declared" >&5
+echo $ECHO_N "checking whether isfinite is declared... $ECHO_C" >&6; }
+if test "${ac_cv_have_decl_isfinite+set}" = set; then
+  echo $ECHO_N "(cached) $ECHO_C" >&6
+else
+  cat >conftest.$ac_ext <<_ACEOF
+/* confdefs.h.  */
+_ACEOF
+cat confdefs.h >>conftest.$ac_ext
+cat >>conftest.$ac_ext <<_ACEOF
+/* end confdefs.h.  */
+#include <math.h>
+
+int
+main ()
+{
+#ifndef isfinite
+  (void) isfinite;
+#endif
+
+  ;
+  return 0;
+}
+_ACEOF
+rm -f conftest.$ac_objext
+if { (ac_try="$ac_compile"
+case "(($ac_try" in
+  *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+  *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+  (eval "$ac_compile") 2>conftest.er1
+  ac_status=$?
+  grep -v '^ *+' conftest.er1 >conftest.err
+  rm -f conftest.er1
+  cat conftest.err >&5
+  echo "$as_me:$LINENO: \$? = $ac_status" >&5
+  (exit $ac_status); } && {
+	 test -z "$ac_c_werror_flag" ||
+	 test ! -s conftest.err
+       } && test -s conftest.$ac_objext; then
+  ac_cv_have_decl_isfinite=yes
+else
+  echo "$as_me: failed program was:" >&5
+sed 's/^/| /' conftest.$ac_ext >&5
+
+	ac_cv_have_decl_isfinite=no
+fi
+
+rm -f core conftest.err conftest.$ac_objext conftest.$ac_ext
+fi
+{ echo "$as_me:$LINENO: result: $ac_cv_have_decl_isfinite" >&5
+echo "${ECHO_T}$ac_cv_have_decl_isfinite" >&6; }
+if test $ac_cv_have_decl_isfinite = yes; then
+
+cat >>confdefs.h <<_ACEOF
+#define HAVE_DECL_ISFINITE 1
+_ACEOF
+
+
+else
+  cat >>confdefs.h <<_ACEOF
+#define HAVE_DECL_ISFINITE 0
+_ACEOF
+
+
+fi
+
+
 
 LIBS=$LIBS_SAVE
 
diff --git a/configure.in b/configure.in
index 1caad53..6730b4c 100644
--- a/configure.in
+++ b/configure.in
@@ -3145,6 +3145,44 @@
 LIBS_SAVE=$LIBS
 LIBS="$LIBS $LIBM"
 
+# Detect whether system arithmetic is subject to x87-style double
+# rounding issues.  The result of this test has little meaning on non
+# IEEE 754 platforms.  On IEEE 754, test should return 1 if rounding
+# mode is round-to-nearest and double rounding issues are present, and
+# 0 otherwise.  See http://bugs.python.org/issue2937 for more info.
+AC_MSG_CHECKING(for x87-style double rounding)
+AC_CACHE_VAL(ac_cv_x87_double_rounding, [
+AC_TRY_RUN([
+#include <stdlib.h>
+#include <math.h>
+int main() {
+    volatile double x, y, z;
+    /* 1./(1-2**-53) -> 1+2**-52 (correct), 1.0 (double rounding) */
+    x = 0.99999999999999989; /* 1-2**-53 */
+    y = 1./x;
+    if (y != 1.)
+        exit(0);
+    /* 1e16+2.99999 -> 1e16+2. (correct), 1e16+4. (double rounding) */
+    x = 1e16;
+    y = 2.99999;
+    z = x + y;
+    if (z != 1e16+4.)
+        exit(0);
+    /* both tests show evidence of double rounding */
+    exit(1);
+}
+],
+ac_cv_x87_double_rounding=no,
+ac_cv_x87_double_rounding=yes,
+ac_cv_x87_double_rounding=no)])
+AC_MSG_RESULT($ac_cv_x87_double_rounding)
+if test "$ac_cv_x87_double_rounding" = yes
+then
+  AC_DEFINE(X87_DOUBLE_ROUNDING, 1,
+  [Define if arithmetic is subject to x87-style double rounding issue])
+fi
+
+
 # On FreeBSD 6.2, it appears that tanh(-0.) returns 0. instead of
 # -0. on some architectures.
 AC_MSG_CHECKING(whether tanh preserves the sign of zero)
@@ -3171,7 +3209,8 @@
   [Define if tanh(-0.) is -0., or if platform doesn't have signed zeros])
 fi
 
-AC_CHECK_FUNCS([acosh asinh atanh copysign expm1 finite hypot isinf isnan log1p])
+AC_CHECK_FUNCS([acosh asinh atanh copysign expm1 finite hypot log1p])
+AC_CHECK_DECLS([isinf, isnan, isfinite], [], [], [[#include <math.h>]])
 
 LIBS=$LIBS_SAVE
 
diff --git a/pyconfig.h.in b/pyconfig.h.in
index 852e671..82285bd 100644
--- a/pyconfig.h.in
+++ b/pyconfig.h.in
@@ -115,6 +115,18 @@
 /* Define if you have the 'resize_term' function. */
 #undef HAVE_CURSES_RESIZE_TERM
 
+/* Define to 1 if you have the declaration of `isfinite', and to 0 if you
+   don't. */
+#undef HAVE_DECL_ISFINITE
+
+/* Define to 1 if you have the declaration of `isinf', and to 0 if you don't.
+   */
+#undef HAVE_DECL_ISINF
+
+/* Define to 1 if you have the declaration of `isnan', and to 0 if you don't.
+   */
+#undef HAVE_DECL_ISNAN
+
 /* Define to 1 if you have the declaration of `tzname', and to 0 if you don't.
    */
 #undef HAVE_DECL_TZNAME
@@ -315,12 +327,6 @@
 /* Define to 1 if you have the <io.h> header file. */
 #undef HAVE_IO_H
 
-/* Define to 1 if you have the `isinf' function. */
-#undef HAVE_ISINF
-
-/* Define to 1 if you have the `isnan' function. */
-#undef HAVE_ISNAN
-
 /* Define to 1 if you have the `kill' function. */
 #undef HAVE_KILL
 
@@ -360,7 +366,7 @@
 /* Define to 1 if you have the <libintl.h> header file. */
 #undef HAVE_LIBINTL_H
 
-/* Define to 1 if you have the `readline' library (-lreadline). */
+/* Define if you have the readline library (-lreadline). */
 #undef HAVE_LIBREADLINE
 
 /* Define to 1 if you have the `resolv' library (-lresolv). */
@@ -983,6 +989,9 @@
    first (like Motorola and SPARC, unlike Intel and VAX). */
 #undef WORDS_BIGENDIAN
 
+/* Define if arithmetic is subject to x87-style double rounding issue */
+#undef X87_DOUBLE_ROUNDING
+
 /* Define to 1 if on AIX 3.
    System headers sometimes define this.
    We just want to avoid a redefinition error message.  */