Issue #1580: use short float repr where possible.

 - incorporate and adapt David Gay's dtoa and strtod
   into the Python core
 - on platforms where we can use Gay's code (almost
   all!), repr(float) is based on the shortest
   sequence of decimal digits that rounds correctly.
 - add sys.float_repr_style attribute to indicate
   whether we're using Gay's code or not
 - add autoconf magic to detect and enable SSE2
   instructions on x86/gcc
 - slight change to repr and str:  repr switches
   to exponential notation at 1e16 instead of
   1e17, str switches at 1e11 instead of 1e12

Doc/library/sys.rst

@@ -266,6 +266,19 @@ always available.
       The information in the table is simplified.
 
 
+.. data:: float_repr_style
+
+   A string indicating how the :func:`repr` function behaves for
+   floats.  If the string has value ``'short'`` then for a finite
+   float ``x``, ``repr(x)`` aims to produce a short string with the
+   property that ``float(repr(x)) == x``.  This is the usual behaviour
+   in Python 3.1 and later.  Otherwise, ``float_repr_style`` has value
+   ``'legacy'`` and ``repr(x)`` behaves in the same way as it did in
+   versions of Python prior to 3.1.
+
+   .. versionadded:: 3.1
+
+
 .. function:: getcheckinterval()
 
    Return the interpreter's "check interval"; see :func:`setcheckinterval`.

Doc/license.rst

@@ -657,3 +657,35 @@ The :mod:`select` and contains the following notice for the kqueue interface::
   LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
   OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
   SUCH DAMAGE.
+
+
+strtod and dtoa
+---------------
+
+The file :file:`Python/dtoa.c`, which supplies C functions dtoa and
+strtod for conversion of C doubles to and from strings, is derived
+from the file of the same name by David M. Gay, currently available
+from http://www.netlib.org/fp/.  The original file, as retrieved on
+March 16, 2009, contains the following copyright and licensing
+notice::
+
+   /****************************************************************
+    *
+    * The author of this software is David M. Gay.
+    *
+    * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
+    *
+    * Permission to use, copy, modify, and distribute this software for any
+    * purpose without fee is hereby granted, provided that this entire notice
+    * is included in all copies of any software which is or includes a copy
+    * or modification of this software and in all copies of the supporting
+    * documentation for such software.
+    *
+    * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
+    * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
+    * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
+    * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
+    *
+    ***************************************************************/
+
+

Include/Python.h

@@ -118,6 +118,7 @@
 
 #include "pystrtod.h"
 #include "pystrcmp.h"
+#include "dtoa.h"
 
 /* _Py_Mangle is defined in compile.c */
 PyAPI_FUNC(PyObject*) _Py_Mangle(PyObject *p, PyObject *name);

Include/dtoa.h

+#ifndef PY_NO_SHORT_FLOAT_REPR
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+PyAPI_FUNC(double) _Py_dg_strtod(const char *str, char **ptr);
+PyAPI_FUNC(char *) _Py_dg_dtoa(double d, int mode, int ndigits,
+                        int *decpt, int *sign, char **rve);
+PyAPI_FUNC(void) _Py_dg_freedtoa(char *s);
+
+
+#ifdef __cplusplus
+}
+#endif
+#endif

Include/pymacconfig.h

@@ -17,6 +17,9 @@
 # undef SIZEOF_VOID_P
 # undef SIZEOF__BOOL
 # undef WORDS_BIGENDIAN
+# undef DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754
+# undef DOUBLE_IS_BIG_ENDIAN_IEEE754
+# undef DOUBLE_IS_LITTLE_ENDIAN_IEEE754
 
 #    undef VA_LIST_IS_ARRAY
 #    if defined(__LP64__) && defined(__x86_64__)
@@ -65,6 +68,9 @@
 
 #ifdef __BIG_ENDIAN__
 #define WORDS_BIGENDIAN 1
+#define DOUBLE_IS_BIG_ENDIAN_IEEE754
+#else
+#define DOUBLE_IS_LITTLE_ENDIAN_IEEE754
 #endif /* __BIG_ENDIAN */
 
 

Include/pymath.h

@@ -92,6 +92,11 @@ PyAPI_FUNC(double) _Py_force_double(double);
 #  endif
 #endif
 
+#ifdef HAVE_GCC_ASM_FOR_X87
+PyAPI_FUNC(unsigned short) _Py_get_387controlword(void);
+PyAPI_FUNC(void) _Py_set_387controlword(unsigned short);
+#endif
+
 /* Py_IS_NAN(X)
  * Return 1 if float or double arg is a NaN, else 0.
  * Caution:

Include/pyport.h

@@ -465,6 +465,53 @@ extern "C" {
 			errno = 0;					\
 	} while(0)
 
+/* The functions _Py_dg_strtod and _Py_dg_dtoa in Python/dtoa.c require that
+   the FPU is using 53-bit precision.  Here are macros that force this.  See
+   Python/pystrtod.c for an example of their use. */
+
+#ifdef USING_X87_FPU
+#define _Py_SET_53BIT_PRECISION_HEADER				\
+	unsigned short old_387controlword, new_387controlword
+#define _Py_SET_53BIT_PRECISION_START					\
+	do {								\
+		old_387controlword = _Py_get_387controlword();		\
+		new_387controlword = (old_387controlword & ~0x0f00) | 0x0200; \
+		if (new_387controlword != old_387controlword)		\
+			_Py_set_387controlword(new_387controlword);	\
+	} while (0)
+#define _Py_SET_53BIT_PRECISION_END				\
+	if (new_387controlword != old_387controlword)		\
+		_Py_set_387controlword(old_387controlword)
+#else
+#define _Py_SET_53BIT_PRECISION_HEADER
+#define _Py_SET_53BIT_PRECISION_START
+#define _Py_SET_53BIT_PRECISION_END
+#endif
+
+/* If we can't guarantee 53-bit precision, don't use the code
+   in Python/dtoa.c, but fall back to standard code.  This
+   means that repr of a float will be long (17 sig digits).
+
+   Realistically, there are two things that could go wrong:
+
+   (1) doubles aren't IEEE 754 doubles, or
+   (2) we're on x86 with the rounding precision set to 64-bits
+       (extended precision), and we don't know how to change
+       the rounding precision.
+ */
+
+#if !defined(DOUBLE_IS_LITTLE_ENDIAN_IEEE754) && \
+    !defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) && \
+    !defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754)
+#define PY_NO_SHORT_FLOAT_REPR
+#endif
+
+/* double rounding is symptomatic of use of extended precision on x86 */
+#ifdef X87_DOUBLE_ROUNDING
+#define PY_NO_SHORT_FLOAT_REPR
+#endif
+
+
 /* Py_DEPRECATED(version)
  * Declare a variable, type, or function deprecated.
  * Usage:

Lib/test/formatfloat_testcases.txt

+-- 'f' code formatting, with explicit precision (>= 0).  Output always
+-- has the given number of places after the point;  zeros are added if
+-- necessary to make this true.
+
+-- zeros
+%.0f 0 -> 0
+%.1f 0 -> 0.0
+%.2f 0 -> 0.00
+%.3f 0 -> 0.000
+%.50f 0 -> 0.00000000000000000000000000000000000000000000000000
+
+-- precision 0;  result should never include a .
+%.0f 1.5 -> 2
+%.0f 2.5 -> 2
+%.0f 3.5 -> 4
+%.0f 0.0 -> 0
+%.0f 0.1 -> 0
+%.0f 0.001 -> 0
+%.0f 10.0 -> 10
+%.0f 10.1 -> 10
+%.0f 10.01 -> 10
+%.0f 123.456 -> 123
+%.0f 1234.56 -> 1235
+%.0f 1e49 -> 9999999999999999464902769475481793196872414789632
+-- %.0f 1e50 -> 100000000000000007629769841091887003294964970946560
+%.0f 9.9999999999999987e+49 -> 99999999999999986860582406952576489172979654066176
+
+-- precision 1
+%.1f 0.0001 -> 0.0
+%.1f 0.001 -> 0.0
+%.1f 0.01 -> 0.0
+%.1f 0.04 -> 0.0
+%.1f 0.06 -> 0.1
+%.1f 0.25 -> 0.2
+%.1f 0.75 -> 0.8
+%.1f 1.4 -> 1.4
+%.1f 1.5 -> 1.5
+%.1f 10.0 -> 10.0
+%.1f 1000.03 -> 1000.0
+%.1f 1234.5678 -> 1234.6
+%.1f 1234.7499 -> 1234.7
+%.1f 1234.75 -> 1234.8
+
+-- precision 2
+%.2f 0.0001 -> 0.00
+%.2f 0.001 -> 0.00
+%.2f 0.004999 -> 0.00
+%.2f 0.005001 -> 0.01
+%.2f 0.01 -> 0.01
+%.2f 0.125 -> 0.12
+%.2f 0.375 -> 0.38
+%.2f 1234500 -> 1234500.00
+%.2f 1234560 -> 1234560.00
+%.2f 1234567 -> 1234567.00
+%.2f 1234567.8 -> 1234567.80
+%.2f 1234567.89 -> 1234567.89
+%.2f 1234567.891 -> 1234567.89
+%.2f 1234567.8912 -> 1234567.89
+
+-- alternate form always includes a decimal point.  This only
+-- makes a difference when the precision is 0.
+%#.0f 0 -> 0.
+%#.1f 0 -> 0.0
+%#.0f 1.5 -> 2.
+%#.0f 2.5 -> 2.
+%#.0f 10.1 -> 10.
+%#.0f 1234.56 -> 1235.
+%#.1f 1.4 -> 1.4
+%#.2f 0.375 -> 0.38
+
+-- if precision is omitted it defaults to 6
+%f 0 -> 0.000000
+%f 1230000 -> 1230000.000000
+%f 1234567 -> 1234567.000000
+%f 123.4567 -> 123.456700
+%f 1.23456789 -> 1.234568
+%f 0.00012 -> 0.000120
+%f 0.000123 -> 0.000123
+%f 0.00012345 -> 0.000123
+%f 0.000001 -> 0.000001
+%f 0.0000005001 -> 0.000001
+%f 0.0000004999 -> 0.000000
+
+-- 'e' code formatting with explicit precision (>= 0). Output should
+-- always have exactly the number of places after the point that were
+-- requested.
+
+-- zeros
+%.0e 0 -> 0e+00
+%.1e 0 -> 0.0e+00
+%.2e 0 -> 0.00e+00
+%.10e 0 -> 0.0000000000e+00
+%.50e 0 -> 0.00000000000000000000000000000000000000000000000000e+00
+
+-- precision 0.  no decimal point in the output
+%.0e 0.01 -> 1e-02
+%.0e 0.1 -> 1e-01
+%.0e 1 -> 1e+00
+%.0e 10 -> 1e+01
+%.0e 100 -> 1e+02
+%.0e 0.012 -> 1e-02
+%.0e 0.12 -> 1e-01
+%.0e 1.2 -> 1e+00
+%.0e 12 -> 1e+01
+%.0e 120 -> 1e+02
+%.0e 123.456 -> 1e+02
+%.0e 0.000123456 -> 1e-04
+%.0e 123456000 -> 1e+08
+%.0e 0.5 -> 5e-01
+%.0e 1.4 -> 1e+00
+%.0e 1.5 -> 2e+00
+%.0e 1.6 -> 2e+00
+%.0e 2.4999999 -> 2e+00
+%.0e 2.5 -> 2e+00
+%.0e 2.5000001 -> 3e+00
+%.0e 3.499999999999 -> 3e+00
+%.0e 3.5 -> 4e+00
+%.0e 4.5 -> 4e+00
+%.0e 5.5 -> 6e+00
+%.0e 6.5 -> 6e+00
+%.0e 7.5 -> 8e+00
+%.0e 8.5 -> 8e+00
+%.0e 9.4999 -> 9e+00
+%.0e 9.5 -> 1e+01
+%.0e 10.5 -> 1e+01
+%.0e 14.999 -> 1e+01
+%.0e 15 -> 2e+01
+
+-- precision 1
+%.1e 0.0001 -> 1.0e-04
+%.1e 0.001 -> 1.0e-03
+%.1e 0.01 -> 1.0e-02
+%.1e 0.1 -> 1.0e-01
+%.1e 1 -> 1.0e+00
+%.1e 10 -> 1.0e+01
+%.1e 100 -> 1.0e+02
+%.1e 120 -> 1.2e+02
+%.1e 123 -> 1.2e+02
+%.1e 123.4 -> 1.2e+02
+
+-- precision 2
+%.2e 0.00013 -> 1.30e-04
+%.2e 0.000135 -> 1.35e-04
+%.2e 0.0001357 -> 1.36e-04
+%.2e 0.0001 -> 1.00e-04
+%.2e 0.001 -> 1.00e-03
+%.2e 0.01 -> 1.00e-02
+%.2e 0.1 -> 1.00e-01
+%.2e 1 -> 1.00e+00
+%.2e 10 -> 1.00e+01
+%.2e 100 -> 1.00e+02
+%.2e 1000 -> 1.00e+03
+%.2e 1500 -> 1.50e+03
+%.2e 1590 -> 1.59e+03
+%.2e 1598 -> 1.60e+03
+%.2e 1598.7 -> 1.60e+03
+%.2e 1598.76 -> 1.60e+03
+%.2e 9999 -> 1.00e+04
+
+-- omitted precision defaults to 6
+%e 0 -> 0.000000e+00
+%e 165 -> 1.650000e+02
+%e 1234567 -> 1.234567e+06
+%e 12345678 -> 1.234568e+07
+%e 1.1 -> 1.100000e+00
+
+-- alternate form always contains a decimal point.  This only makes
+-- a difference when precision is 0.
+
+%#.0e 0.01 -> 1.e-02
+%#.0e 0.1 -> 1.e-01
+%#.0e 1 -> 1.e+00
+%#.0e 10 -> 1.e+01
+%#.0e 100 -> 1.e+02
+%#.0e 0.012 -> 1.e-02
+%#.0e 0.12 -> 1.e-01
+%#.0e 1.2 -> 1.e+00
+%#.0e 12 -> 1.e+01
+%#.0e 120 -> 1.e+02
+%#.0e 123.456 -> 1.e+02
+%#.0e 0.000123456 -> 1.e-04
+%#.0e 123456000 -> 1.e+08
+%#.0e 0.5 -> 5.e-01
+%#.0e 1.4 -> 1.e+00
+%#.0e 1.5 -> 2.e+00
+%#.0e 1.6 -> 2.e+00
+%#.0e 2.4999999 -> 2.e+00
+%#.0e 2.5 -> 2.e+00
+%#.0e 2.5000001 -> 3.e+00
+%#.0e 3.499999999999 -> 3.e+00
+%#.0e 3.5 -> 4.e+00
+%#.0e 4.5 -> 4.e+00
+%#.0e 5.5 -> 6.e+00
+%#.0e 6.5 -> 6.e+00
+%#.0e 7.5 -> 8.e+00
+%#.0e 8.5 -> 8.e+00
+%#.0e 9.4999 -> 9.e+00
+%#.0e 9.5 -> 1.e+01
+%#.0e 10.5 -> 1.e+01
+%#.0e 14.999 -> 1.e+01
+%#.0e 15 -> 2.e+01
+%#.1e 123.4 -> 1.2e+02
+%#.2e 0.0001357 -> 1.36e-04
+
+-- 'g' code formatting.
+
+-- zeros
+%.0g 0 -> 0
+%.1g 0 -> 0
+%.2g 0 -> 0
+%.3g 0 -> 0
+%.4g 0 -> 0
+%.10g 0 -> 0
+%.50g 0 -> 0
+%.100g 0 -> 0
+
+-- precision 0 doesn't make a lot of sense for the 'g' code (what does
+-- it mean to have no significant digits?); in practice, it's interpreted
+-- as identical to precision 1
+%.0g 1000 -> 1e+03
+%.0g 100 -> 1e+02
+%.0g 10 -> 1e+01
+%.0g 1 -> 1
+%.0g 0.1 -> 0.1
+%.0g 0.01 -> 0.01
+%.0g 1e-3 -> 0.001
+%.0g 1e-4 -> 0.0001
+%.0g 1e-5 -> 1e-05
+%.0g 1e-6 -> 1e-06
+%.0g 12 -> 1e+01
+%.0g 120 -> 1e+02
+%.0g 1.2 -> 1
+%.0g 0.12 -> 0.1
+%.0g 0.012 -> 0.01
+%.0g 0.0012 -> 0.001
+%.0g 0.00012 -> 0.0001
+%.0g 0.000012 -> 1e-05
+%.0g 0.0000012 -> 1e-06
+
+-- precision 1 identical to precision 0
+%.1g 1000 -> 1e+03
+%.1g 100 -> 1e+02
+%.1g 10 -> 1e+01
+%.1g 1 -> 1
+%.1g 0.1 -> 0.1
+%.1g 0.01 -> 0.01
+%.1g 1e-3 -> 0.001
+%.1g 1e-4 -> 0.0001
+%.1g 1e-5 -> 1e-05
+%.1g 1e-6 -> 1e-06
+%.1g 12 -> 1e+01
+%.1g 120 -> 1e+02
+%.1g 1.2 -> 1
+%.1g 0.12 -> 0.1
+%.1g 0.012 -> 0.01
+%.1g 0.0012 -> 0.001
+%.1g 0.00012 -> 0.0001
+%.1g 0.000012 -> 1e-05
+%.1g 0.0000012 -> 1e-06
+
+-- precision 2
+%.2g 1000 -> 1e+03
+%.2g 100 -> 1e+02
+%.2g 10 -> 10
+%.2g 1 -> 1
+%.2g 0.1 -> 0.1
+%.2g 0.01 -> 0.01
+%.2g 0.001 -> 0.001
+%.2g 1e-4 -> 0.0001
+%.2g 1e-5 -> 1e-05
+%.2g 1e-6 -> 1e-06
+%.2g 1234 -> 1.2e+03
+%.2g 123 -> 1.2e+02
+%.2g 12.3 -> 12
+%.2g 1.23 -> 1.2
+%.2g 0.123 -> 0.12
+%.2g 0.0123 -> 0.012
+%.2g 0.00123 -> 0.0012
+%.2g 0.000123 -> 0.00012
+%.2g 0.0000123 -> 1.2e-05
+
+-- alternate g formatting:  always include decimal point and
+-- exactly <precision> significant digits.
+%#.0g 0 -> 0.
+%#.1g 0 -> 0.
+%#.2g 0 -> 0.0
+%#.3g 0 -> 0.00
+%#.4g 0 -> 0.000
+
+%#.0g 0.2 -> 0.2
+%#.1g 0.2 -> 0.2
+%#.2g 0.2 -> 0.20
+%#.3g 0.2 -> 0.200
+%#.4g 0.2 -> 0.2000
+%#.10g 0.2 -> 0.2000000000
+
+%#.0g 2 -> 2.
+%#.1g 2 -> 2.
+%#.2g 2 -> 2.0
+%#.3g 2 -> 2.00
+%#.4g 2 -> 2.000
+
+%#.0g 20 -> 2.e+01
+%#.1g 20 -> 2.e+01
+%#.2g 20 -> 20.
+%#.3g 20 -> 20.0
+%#.4g 20 -> 20.00
+
+%#.0g 234.56 -> 2.e+02
+%#.1g 234.56 -> 2.e+02
+%#.2g 234.56 -> 2.3e+02
+%#.3g 234.56 -> 235.
+%#.4g 234.56 -> 234.6
+%#.5g 234.56 -> 234.56
+%#.6g 234.56 -> 234.560
+
+-- for repr formatting see the separate test_short_repr test in
+-- test_float.py.  Not all platforms use short repr for floats.
+
+-- str formatting.  Result always includes decimal point and at
+-- least one digit after the point, or an exponent.
+%s 0 -> 0.0
+%s 1 -> 1.0
+
+%s 0.01 -> 0.01
+%s 0.02 -> 0.02
+%s 0.03 -> 0.03
+%s 0.04 -> 0.04
+%s 0.05 -> 0.05
+
+-- str truncates to 12 significant digits
+%s 1.234123412341 -> 1.23412341234
+%s 1.23412341234 -> 1.23412341234
+%s 1.2341234123 -> 1.2341234123
+
+-- values >= 1e11 get an exponent
+%s 10 -> 10.0
+%s 100 -> 100.0
+%s 1e10 -> 10000000000.0
+%s 9.999e10 -> 99990000000.0
+%s 99999999999 -> 99999999999.0
+%s 1e11 -> 1e+11
+%s 1e12 -> 1e+12
+
+-- as do values < 1e-4
+%s 1e-3 -> 0.001
+%s 1.001e-4 -> 0.0001001
+%s 1.000000000001e-4 -> 0.0001
+%s 1.00000000001e-4 -> 0.000100000000001
+%s 1.0000000001e-4 -> 0.00010000000001
+%s 1e-4 -> 0.0001
+%s 0.999999999999e-4 -> 9.99999999999e-05
+%s 0.999e-4 -> 9.99e-05
+%s 1e-5 -> 1e-05

Makefile.pre.in

@@ -305,6 +305,7 @@ PYTHON_OBJS=	\
 		Python/getopt.o \
 		Python/pystrcmp.o \
 		Python/pystrtod.o \
+		Python/dtoa.o \
 		Python/formatter_unicode.o \
 		Python/$(DYNLOADFILE) \
 		$(LIBOBJS) \
@@ -621,6 +622,7 @@ PYTHON_HEADERS= \
 		Include/complexobject.h \
 		Include/descrobject.h \
 		Include/dictobject.h \
+		Include/dtoa.h \
 		Include/enumobject.h \
 		Include/errcode.h \
 		Include/eval.h \

Misc/ACKS

@@ -160,6 +160,7 @@ Scott David Daniels
 Ben Darnell
 Jonathan Dasteel
 John DeGood
+Ned Deily
 Vincent Delft
 Arnaud Delobelle
 Erik Demaine

Misc/NEWS

@@ -12,6 +12,45 @@ What's New in Python 3.1 beta 1?
 Core and Builtins
 -----------------
 
+- The repr function switches to exponential notation at 1e16, not 1e17
+  as it did before.  This change applies to both 'short' and legacy
+  float repr styles.  For the new repr style, it avoids misleading
+  output in some cases: an example is repr(2e16+8), which gives
+  '2.000000000000001e+16'; without this change it would have produced
+  '20000000000000010.0' instead.
+
+- Similarly, the str function switches to exponential notation at
+  1e11, not 1e12.  This avoids printing 13 significant digits in
+  situations where only 12 of them are correct.  Example problem
+  value: str(1e11 + 0.5).  (This minor issue has existed in 2.x for a
+  long time.)
+
+- On x86, SSE2 instructions for floating-point are automatically
+  detected and, where possible, enabled on platforms using the gcc
+  compiler.  As a consequence, some arithmetic operations may have
+  different (more accurate!) results on some platforms, and
+  cross-platform consistency of Python arithmetic should be improved.
+  This applies particularly to Linux/x86.
+
+- Issue #1580: On most platforms, use a 'short' float repr: for a
+  finite float x, repr(x) now outputs a string based on the shortest
+  sequence of decimal digits that rounds to x.  Previous behaviour was
+  to output 17 significant digits and then strip trailing zeros.
+
+  There's a new sys attribute sys.float_repr_style, which takes
+  the value 'short' to indicate that we're using short float repr,
+  and 'legacy' if the short float repr isn't available for one
+  reason or another.
+
+  The float repr change involves incorporating David Gay's 'perfect
+  rounding' code into the Python core (it's in Python/dtoa.c).  As a
+  secondary consequence, all string-to-float and float-to-string
+  conversions (including all float formatting operations) will be
+  correctly rounded on these platforms.
+
+  See issue 1580 discussions for details of platforms for which
+  this change does not apply.
+
 - Issue #5759: float() didn't call __float__ on str subclasses.
 
 - The string.maketrans() function is deprecated; there is a new static method

PC/pyconfig.h

@@ -752,4 +752,8 @@ Py_NO_ENABLE_SHARED to find out.  Also support MS_NO_COREDLL for b/w compat */
    socket handles greater than FD_SETSIZE */
 #define Py_SOCKET_FD_CAN_BE_GE_FD_SETSIZE
 
+/* Define if C doubles are 64-bit IEEE 754 binary format, stored with the
+   least significant byte first */
+#define DOUBLE_IS_LITTLE_ENDIAN_IEEE754 1
+
 #endif /* !Py_CONFIG_H */

PCbuild/pythoncore.vcproj

@@ -894,6 +894,10 @@
 				RelativePath="..\Include\pystrtod.h"
 				>
 			</File>
+			<File
+				RelativePath="..\Include\dtoa.h"
+				>
+			</File>
 			<File
 				RelativePath="..\Include\Python-ast.h"
 				>
@@ -1746,6 +1750,10 @@
 				RelativePath="..\Python\pystrtod.c"
 				>
 			</File>
+			<File
+				RelativePath="..\Python\dtoa.c"
+				>
+			</File>
 			<File
 				RelativePath="..\Python\Python-ast.c"
 				>

Python/pymath.c

@@ -13,6 +13,28 @@ double _Py_force_double(double x)
 }
 #endif
 
+#ifdef USING_X87_FPU
+#  ifdef HAVE_GCC_ASM_FOR_X87
+
+/* inline assembly for getting and setting the 387 FPU control word on
+   gcc/x86 */
+
+unsigned short _Py_get_387controlword(void) {
+    unsigned short cw;
+    __asm__ __volatile__ ("fnstcw %0" : "=m" (cw));
+    return cw;
+}
+
+void _Py_set_387controlword(unsigned short cw) {
+    __asm__ __volatile__ ("fldcw %0" : : "m" (cw));
+}
+
+#  else
+#    error "Unable to get and set x87 control word"
+#  endif
+#endif
+
+
 #ifndef HAVE_HYPOT
 double hypot(double x, double y)
 {

Python/sysmodule.c

@@ -1025,6 +1025,7 @@ platform -- platform identifier\n\
 executable -- pathname of this Python interpreter\n\
 prefix -- prefix used to find the Python library\n\
 exec_prefix -- prefix used to find the machine-specific Python library\n\
+float_repr_style -- string indicating the style of repr() output for floats\n\
 "
 )
 #ifdef MS_WINDOWS
@@ -1428,6 +1429,15 @@ _PySys_Init(void)
 	FlagsType.tp_init = NULL;
 	FlagsType.tp_new = NULL;
 
+	/* float repr style: 0.03 (short) vs 0.029999999999999999 (legacy) */
+#ifndef PY_NO_SHORT_FLOAT_REPR
+	SET_SYS_FROM_STRING("float_repr_style",
+			    PyUnicode_FromString("short"));
+#else
+	SET_SYS_FROM_STRING("float_repr_style",
+			    PyUnicode_FromString("legacy"));
+#endif
+
 #undef SET_SYS_FROM_STRING
 	if (PyErr_Occurred())
 		return NULL;

configure.in

@@ -3065,12 +3065,176 @@ else AC_MSG_ERROR([proper usage is --with-libc=STRING])
 fi],
 [AC_MSG_RESULT(default LIBC="$LIBC")])
 
-# ************************************
-# * Check for mathematical functions *
-# ************************************
+# **************************************************
+# * Check for various properties of floating point *
+# **************************************************
 
-LIBS_SAVE=$LIBS
-LIBS="$LIBS $LIBM"
+AC_MSG_CHECKING(whether C doubles are little-endian IEEE 754 binary64)
+AC_CACHE_VAL(ac_cv_little_endian_double, [
+AC_TRY_RUN([
+#include <string.h>
+int main() {
+    double x = 9006104071832581.0;
+    if (memcmp(&x, "\x05\x04\x03\x02\x01\xff\x3f\x43", 8) == 0)
+        return 0;
+    else
+        return 1;
+}
+],
+ac_cv_little_endian_double=yes,
+ac_cv_little_endian_double=no,
+ac_cv_little_endian_double=no)])
+AC_MSG_RESULT($ac_cv_little_endian_double)
+if test "$ac_cv_little_endian_double" = yes
+then
+  AC_DEFINE(DOUBLE_IS_LITTLE_ENDIAN_IEEE754, 1,
+  [Define if C doubles are 64-bit IEEE 754 binary format, stored
+   with the least significant byte first])
+fi
+
+AC_MSG_CHECKING(whether C doubles are big-endian IEEE 754 binary64)
+AC_CACHE_VAL(ac_cv_big_endian_double, [
+AC_TRY_RUN([
+#include <string.h>
+int main() {
+    double x = 9006104071832581.0;
+    if (memcmp(&x, "\x43\x3f\xff\x01\x02\x03\x04\x05", 8) == 0)
+        return 0;
+    else
+        return 1;
+}
+],
+ac_cv_big_endian_double=yes,
+ac_cv_big_endian_double=no,
+ac_cv_big_endian_double=no)])
+AC_MSG_RESULT($ac_cv_big_endian_double)
+if test "$ac_cv_big_endian_double" = yes
+then
+  AC_DEFINE(DOUBLE_IS_BIG_ENDIAN_IEEE754, 1,
+  [Define if C doubles are 64-bit IEEE 754 binary format, stored
+   with the most significant byte first])
+fi
+
+# Some ARM platforms use a mixed-endian representation for doubles.
+# While Python doesn't currently have full support for these platforms
+# (see e.g., issue 1762561), we can at least make sure that float <-> string
+# conversions work.
+AC_MSG_CHECKING(whether C doubles are ARM mixed-endian IEEE 754 binary64)
+AC_CACHE_VAL(ac_cv_mixed_endian_double, [
+AC_TRY_RUN([
+#include <string.h>
+int main() {
+    double x = 9006104071832581.0;
+    if (memcmp(&x, "\x01\xff\x3f\x43\x05\x04\x03\x02", 8) == 0)
+        return 0;
+    else
+        return 1;
+}
+],
+ac_cv_mixed_endian_double=yes,
+ac_cv_mixed_endian_double=no,
+ac_cv_mixed_endian_double=no)])
+AC_MSG_RESULT($ac_cv_mixed_endian_double)
+if test "$ac_cv_mixed_endian_double" = yes
+then
+  AC_DEFINE(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754, 1,
+  [Define if C doubles are 64-bit IEEE 754 binary format, stored
+   in ARM mixed-endian order (byte order 45670123)])
+fi
+
+# David Gay's code in Python/dtoa.c requires that the FPU uses 53-bit
+# rounding; this is a particular problem on x86, where the x87 FPU has
+# a default rounding precision of 64 bits.  For gcc/x86, we try to fix
+# this by:
+#
+#   (1) using the SSE2 instruction set when available (it usually is
+#       on modern machines)
+#   (2) using inline assembler to get and set the x87 FPU control word
+#       otherwise.
+#
+# On AMD64 (aka x86-64), gcc automatically enables use of SSE2
+# instructions, so we don't bother trying to detect.
+
+if test "$GCC" = yes && test -n "`$CC -dM -E - </dev/null | grep i386`"
+then
+    # determine whether we're already using the SSE2 instruction set for math
+    # (e.g., this is true by default on OS X/x86)
+    AC_MSG_CHECKING(whether SSE2 instructions are already enabled for math)
+    if test -n "`$CC -dM -E - </dev/null | grep __SSE2_MATH__`"
+    then
+        ac_sse2_enabled=yes
+    else
+        ac_sse2_enabled=no
+    fi
+    AC_MSG_RESULT($ac_sse2_enabled)
+
+    # if we're not using SSE2 already, we need to either enable it
+    # (when available), or use inline assembler to get and set the
+    # 387 control word.
+    if test $ac_sse2_enabled = no
+    then
+        # Check cpuid for SSE2 availability.  Bits 25 and 26 of edx tell
+        # us about SSE and SSE2 respectively.
+        AC_MSG_CHECKING(whether SSE2 instructions are available on this CPU)
+        AC_TRY_RUN([
+            int main() {
+                unsigned int ax, bx, cx, dx, func;
+                func = 1U;
+                __asm__ __volatile__ (
+                    "pushl %%ebx\n\t"  /* don't clobber ebx */
+                    "cpuid\n\t"
+                    "movl %%ebx, %1\n\t"
+                    "popl %%ebx"
+                    : "=a" (ax), "=r" (bx), "=c" (cx), "=d" (dx)
+                    : "a" (func)
+                    : "cc" );
+                if ((dx & (1U << 25)) && (dx & (1U << 26)))
+                    return 0;
+                else
+                    return 1;
+            }
+        ],
+        ac_cv_cpu_has_sse2=yes,
+        ac_cv_cpu_has_sse2=no,
+        ac_cv_cpu_has_sse2=no)
+        AC_MSG_RESULT($ac_cv_cpu_has_sse2)
+
+        # determine whether gcc accepts options to turn on SSE2
+        AC_MSG_CHECKING(whether $CC accepts -msse2 -mfpmath=sse)
+        ac_save_cc="$CC"
+        CC="$CC -msse2 -mfpmath=sse"
+        AC_TRY_RUN([int main() { return 0; }],
+        ac_cv_msse2_ok=yes,
+        ac_cv_msse2_ok=no,
+        ac_cv_msse2_ok=no)
+        CC="$ac_save_cc"
+        AC_MSG_RESULT($ac_cv_msse2_ok)
+
+        if test $ac_cv_cpu_has_sse2 = yes && test $ac_cv_msse2_ok = yes
+        then
+            BASECFLAGS="$BASECFLAGS -msse2 -mfpmath=sse"
+        else
+            # SSE2 doesn't appear to be available.  Check that it's okay
+            # to use gcc inline assembler to get and set x87 control word
+            AC_DEFINE(USING_X87_FPU, 1,
+            [Define on x86 hardware if the x87 FPU is being used
+             for floating-point arithmetic])
+            AC_MSG_CHECKING(whether we can use gcc inline assembler to get and set x87 control word)
+            AC_TRY_COMPILE([], [
+              unsigned short cw;
+              __asm__ __volatile__ ("fnstcw %0" : "=m" (cw));
+              __asm__ __volatile__ ("fldcw %0" : : "m" (cw));
+            ],
+            [have_gcc_asm_for_x87=yes], [have_gcc_asm_for_x87=no])
+            AC_MSG_RESULT($have_gcc_asm_for_x87)
+            if test "$have_gcc_asm_for_x87" = yes
+            then
+                AC_DEFINE(HAVE_GCC_ASM_FOR_X87, 1,
+                [Define if we can use gcc inline assembler to get and set x87 control word])
+            fi
+        fi
+    fi
+fi
 
 # Detect whether system arithmetic is subject to x87-style double
 # rounding issues.  The result of this test has little meaning on non
@@ -3078,7 +3242,9 @@ LIBS="$LIBS $LIBM"
 # 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, [
+# $BASECFLAGS may affect the result
+ac_save_cc="$CC"
+CC="$CC $BASECFLAGS"
 AC_TRY_RUN([
 #include <stdlib.h>
 #include <math.h>
@@ -3101,7 +3267,8 @@ int main() {
 ],
 ac_cv_x87_double_rounding=no,
 ac_cv_x87_double_rounding=yes,
-ac_cv_x87_double_rounding=no)])
+ac_cv_x87_double_rounding=no)
+CC="$ac_save_cc"
 AC_MSG_RESULT($ac_cv_x87_double_rounding)
 if test "$ac_cv_x87_double_rounding" = yes
 then
@@ -3109,6 +3276,13 @@ then
   [Define if arithmetic is subject to x87-style double rounding issue])
 fi
 
+# ************************************
+# * Check for mathematical functions *
+# ************************************
+
+LIBS_SAVE=$LIBS
+LIBS="$LIBS $LIBM"
+
 # Multiprocessing check for broken sem_getvalue
 AC_MSG_CHECKING(for broken sem_getvalue)
 AC_TRY_RUN([

pyconfig.h.in

@@ -15,6 +15,18 @@
 /* Define if you have the Mach cthreads package */
 #undef C_THREADS
 
+/* Define if C doubles are 64-bit IEEE 754 binary format, stored in ARM
+   mixed-endian order (byte order 45670123) */
+#undef DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754
+
+/* Define if C doubles are 64-bit IEEE 754 binary format, stored with the most
+   significant byte first */
+#undef DOUBLE_IS_BIG_ENDIAN_IEEE754
+
+/* Define if C doubles are 64-bit IEEE 754 binary format, stored with the
+   least significant byte first */
+#undef DOUBLE_IS_LITTLE_ENDIAN_IEEE754
+
 /* Define if --enable-ipv6 is specified */
 #undef ENABLE_IPV6
 
@@ -232,6 +244,10 @@
 /* Define to 1 if you have the `gai_strerror' function. */
 #undef HAVE_GAI_STRERROR
 
+/* Define if we can use gcc inline assembler to get and set x87 control word
+   */
+#undef HAVE_GCC_ASM_FOR_X87
+
 /* Define if you have the getaddrinfo function. */
 #undef HAVE_GETADDRINFO
 
@@ -970,6 +986,10 @@
 /* Define if you want to use computed gotos in ceval.c. */
 #undef USE_COMPUTED_GOTOS
 
+/* Define on x86 hardware if the x87 FPU is being used for floating-point
+   arithmetic */
+#undef USING_X87_FPU
+
 /* Define if a va_list is an array of some kind */
 #undef VA_LIST_IS_ARRAY