gh-111962: Make dtoa thread-safe in `--disable-gil` builds. (#112049)

This updates `dtoa.c` to avoid using the Bigint free-list in --disable-gil builds and
to pre-computes the needed powers of 5 during interpreter initialization.

* gh-111962: Make dtoa thread-safe in `--disable-gil` builds.

This avoids using the Bigint free-list in `--disable-gil` builds
and pre-computes the needed powers of 5 during interpreter initialization.

* Fix size of cached powers of 5 array.

We need the powers of 5 up to 5**512 because we only jump straight to
underflow when the exponent is less than -512 (or larger than 308).

* Rename Py_NOGIL to Py_GIL_DISABLED

* Changes from review

* Fix assertion placement

1 files changed, 11 insertions, 5 deletions

diff --git a/Include/internal/pycore_dtoa.h b/Include/internal/pycore_dtoa.h
index ac62a4d..c5cfdf4 100644
--- a/Include/internal/pycore_dtoa.h
+++ b/Include/internal/pycore_dtoa.h
@@ -35,6 +35,9 @@ struct _dtoa_state {
 /* The size of the Bigint freelist */
 #define Bigint_Kmax 7
 
+/* The size of the cached powers of 5 array */
+#define Bigint_Pow5size 8
+
 #ifndef PRIVATE_MEM
 #define PRIVATE_MEM 2304
 #endif
@@ -42,9 +45,10 @@ struct _dtoa_state {
     ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
 
 struct _dtoa_state {
-    /* p5s is a linked list of powers of 5 of the form 5**(2**i), i >= 2 */
+    // p5s is an array of powers of 5 of the form:
+    // 5**(2**(i+2)) for 0 <= i < Bigint_Pow5size
+    struct Bigint *p5s[Bigint_Pow5size];
     // XXX This should be freed during runtime fini.
-    struct Bigint *p5s;
     struct Bigint *freelist[Bigint_Kmax+1];
     double preallocated[Bigint_PREALLOC_SIZE];
     double *preallocated_next;
@@ -57,9 +61,6 @@ struct _dtoa_state {
 #endif  // !Py_USING_MEMORY_DEBUGGER
 
 
-/* These functions are used by modules compiled as C extension like math:
-   they must be exported. */
-
 extern double _Py_dg_strtod(const char *str, char **ptr);
 extern char* _Py_dg_dtoa(double d, int mode, int ndigits,
                          int *decpt, int *sign, char **rve);
@@ -67,6 +68,11 @@ extern void _Py_dg_freedtoa(char *s);
 
 #endif // _PY_SHORT_FLOAT_REPR == 1
 
+
+extern PyStatus _PyDtoa_Init(PyInterpreterState *interp);
+extern void _PyDtoa_Fini(PyInterpreterState *interp);
+
+
 #ifdef __cplusplus
 }
 #endif