The other half of Issue #1580: use short float repr where possible.

Addresses the float -> string conversion, using David Gay's code which
was added in Mark Dickinson's checkin r71663.

Also addresses these, which are intertwined with the short repr
changes:

- Issue #5772: format(1e100, '<') produces '1e+100', not '1.0e+100'
- Issue #5515: 'n' formatting with commas no longer works poorly
    with leading zeros.
- PEP 378 Format Specifier for Thousands Separator: implemented
    for floats.
diff --git a/Include/bytesobject.h b/Include/bytesobject.h
index f5a5085..916e3f7 100644
--- a/Include/bytesobject.h
+++ b/Include/bytesobject.h
@@ -91,24 +91,22 @@
    into the string pointed to by buffer.  For the argument descriptions,
    see Objects/stringlib/localeutil.h */
 
-PyAPI_FUNC(int) _PyBytes_InsertThousandsGroupingLocale(char *buffer,
-						  Py_ssize_t n_buffer,
-						  Py_ssize_t n_digits,
-						  Py_ssize_t buf_size,
-						  Py_ssize_t *count,
-						  int append_zero_char);
+PyAPI_FUNC(Py_ssize_t) _PyBytes_InsertThousandsGroupingLocale(char *buffer,
+                                                   Py_ssize_t n_buffer,
+                                                   char *digits,
+                                                   Py_ssize_t n_digits,
+                                                   Py_ssize_t min_width);
 
 /* Using explicit passed-in values, insert the thousands grouping
    into the string pointed to by buffer.  For the argument descriptions,
    see Objects/stringlib/localeutil.h */
-PyAPI_FUNC(int) _PyBytes_InsertThousandsGrouping(char *buffer,
-						 Py_ssize_t n_buffer,
-						 Py_ssize_t n_digits,
-						 Py_ssize_t buf_size,
-						 Py_ssize_t *count,
-                                                 int append_zero_char,
-                                                 const char *grouping,
-                                                 const char *thousands_sep);
+PyAPI_FUNC(Py_ssize_t) _PyBytes_InsertThousandsGrouping(char *buffer,
+                                                   Py_ssize_t n_buffer,
+                                                   char *digits,
+                                                   Py_ssize_t n_digits,
+                                                   Py_ssize_t min_width,
+                                                   const char *grouping,
+                                                   const char *thousands_sep);
 
 /* Flags used by string formatting */
 #define F_LJUST (1<<0)
diff --git a/Include/pystrtod.h b/Include/pystrtod.h
index c6921da..1caa7ae 100644
--- a/Include/pystrtod.h
+++ b/Include/pystrtod.h
@@ -10,6 +10,25 @@
 PyAPI_FUNC(double) PyOS_ascii_atof(const char *str);
 PyAPI_FUNC(char *) PyOS_ascii_formatd(char *buffer, size_t buf_len,  const char *format, double d);
 
+/* The caller is responsible for calling PyMem_Free to free the buffer
+   that's is returned. */
+PyAPI_FUNC(char *) PyOS_double_to_string(double val,
+                                         char format_code,
+                                         int precision,
+                                         int flags,
+                                         int *type);
+
+
+/* PyOS_double_to_string's "flags" parameter can be set to 0 or more of: */
+#define Py_DTSF_SIGN      0x01 /* always add the sign */
+#define Py_DTSF_ADD_DOT_0 0x02 /* if the result is an integer add ".0" */
+#define Py_DTSF_ALT       0x04 /* "alternate" formatting. it's format_code
+                                  specific */
+
+/* PyOS_double_to_string's "type", if non-NULL, will be set to one of: */
+#define Py_DTST_FINITE 0
+#define Py_DTST_INFINITE 1
+#define Py_DTST_NAN 2
 
 #ifdef __cplusplus
 }
diff --git a/Include/unicodeobject.h b/Include/unicodeobject.h
index 98c0372..696c1c7 100644
--- a/Include/unicodeobject.h
+++ b/Include/unicodeobject.h
@@ -1482,24 +1482,22 @@
    into the string pointed to by buffer.  For the argument descriptions,
    see Objects/stringlib/localeutil.h */
 
-PyAPI_FUNC(int) _PyUnicode_InsertThousandsGroupingLocale(Py_UNICODE *buffer,
-						  Py_ssize_t n_buffer,
-						  Py_ssize_t n_digits,
-						  Py_ssize_t buf_size,
-						  Py_ssize_t *count,
-						  int append_zero_char);
+PyAPI_FUNC(Py_ssize_t) _PyUnicode_InsertThousandsGroupingLocale(Py_UNICODE *buffer,
+                                                   Py_ssize_t n_buffer,
+                                                   Py_UNICODE *digits,
+                                                   Py_ssize_t n_digits,
+                                                   Py_ssize_t min_width);
 
 /* Using explicit passed-in values, insert the thousands grouping
    into the string pointed to by buffer.  For the argument descriptions,
    see Objects/stringlib/localeutil.h */
-PyAPI_FUNC(int) _PyUnicode_InsertThousandsGrouping(Py_UNICODE *buffer,
-						 Py_ssize_t n_buffer,
-						 Py_ssize_t n_digits,
-						 Py_ssize_t buf_size,
-						 Py_ssize_t *count,
-                                                 int append_zero_char,
-                                                 const char *grouping,
-                                                 const char *thousands_sep);
+PyAPI_FUNC(Py_ssize_t) _PyUnicode_InsertThousandsGrouping(Py_UNICODE *buffer,
+                                                   Py_ssize_t n_buffer,
+                                                   Py_UNICODE *digits,
+                                                   Py_ssize_t n_digits,
+                                                   Py_ssize_t min_width,
+                                                   const char *grouping,
+                                                   const char *thousands_sep);
 /* === Characters Type APIs =============================================== */
 
 /* Helper array used by Py_UNICODE_ISSPACE(). */