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

3 files changed, 70 insertions, 30 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
diff --git a/Python/dtoa.c b/Python/dtoa.c
index 5dfc0e1..6e3162f 100644
--- a/Python/dtoa.c
+++ b/Python/dtoa.c
@@ -309,7 +309,7 @@ BCinfo {
 // struct Bigint is defined in pycore_dtoa.h.
 typedef struct Bigint Bigint;
 
-#ifndef Py_USING_MEMORY_DEBUGGER
+#if !defined(Py_GIL_DISABLED) && !defined(Py_USING_MEMORY_DEBUGGER)
 
 /* Memory management: memory is allocated from, and returned to, Kmax+1 pools
    of memory, where pool k (0 <= k <= Kmax) is for Bigints b with b->maxwds ==
@@ -428,7 +428,7 @@ Bfree(Bigint *v)
     }
 }
 
-#endif /* Py_USING_MEMORY_DEBUGGER */
+#endif /* !defined(Py_GIL_DISABLED) && !defined(Py_USING_MEMORY_DEBUGGER) */
 
 #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign,   \
                           y->wds*sizeof(Long) + 2*sizeof(int))
@@ -673,10 +673,17 @@ mult(Bigint *a, Bigint *b)
 static Bigint *
 pow5mult(Bigint *b, int k)
 {
-    Bigint *b1, *p5, *p51;
+    Bigint *b1, *p5, **p5s;
     int i;
     static const int p05[3] = { 5, 25, 125 };
 
+    // For double-to-string conversion, the maximum value of k is limited by
+    // DBL_MAX_10_EXP (308), the maximum decimal base-10 exponent for binary64.
+    // For string-to-double conversion, the extreme case is constrained by our
+    // hardcoded exponent limit before we underflow of -512, adjusted by
+    // STRTOD_DIGLIM-DBL_DIG-1, giving a maximum of k=535.
+    assert(0 <= k && k < 1024);
+
     if ((i = k & 3)) {
         b = multadd(b, p05[i-1], 0);
         if (b == NULL)
@@ -686,18 +693,11 @@ pow5mult(Bigint *b, int k)
     if (!(k >>= 2))
         return b;
     PyInterpreterState *interp = _PyInterpreterState_GET();
-    p5 = interp->dtoa.p5s;
-    if (!p5) {
-        /* first time */
-        p5 = i2b(625);
-        if (p5 == NULL) {
-            Bfree(b);
-            return NULL;
-        }
-        interp->dtoa.p5s = p5;
-        p5->next = 0;
-    }
+    p5s = interp->dtoa.p5s;
     for(;;) {
+        assert(p5s != interp->dtoa.p5s + Bigint_Pow5size);
+        p5 = *p5s;
+        p5s++;
         if (k & 1) {
             b1 = mult(b, p5);
             Bfree(b);
@@ -707,17 +707,6 @@ pow5mult(Bigint *b, int k)
         }
         if (!(k >>= 1))
             break;
-        p51 = p5->next;
-        if (!p51) {
-            p51 = mult(p5,p5);
-            if (p51 == NULL) {
-                Bfree(b);
-                return NULL;
-            }
-            p51->next = 0;
-            p5->next = p51;
-        }
-        p5 = p51;
     }
     return b;
 }
@@ -2811,3 +2800,42 @@ _Py_dg_dtoa(double dd, int mode, int ndigits,
 }
 
 #endif  // _PY_SHORT_FLOAT_REPR == 1
+
+PyStatus
+_PyDtoa_Init(PyInterpreterState *interp)
+{
+#if _PY_SHORT_FLOAT_REPR == 1 && !defined(Py_USING_MEMORY_DEBUGGER)
+    Bigint **p5s = interp->dtoa.p5s;
+
+    // 5**4 = 625
+    Bigint *p5 = i2b(625);
+    if (p5 == NULL) {
+        return PyStatus_NoMemory();
+    }
+    p5s[0] = p5;
+
+    // compute 5**8, 5**16, 5**32, ..., 5**512
+    for (Py_ssize_t i = 1; i < Bigint_Pow5size; i++) {
+        p5 = mult(p5, p5);
+        if (p5 == NULL) {
+            return PyStatus_NoMemory();
+        }
+        p5s[i] = p5;
+    }
+
+#endif
+    return PyStatus_Ok();
+}
+
+void
+_PyDtoa_Fini(PyInterpreterState *interp)
+{
+#if _PY_SHORT_FLOAT_REPR == 1 && !defined(Py_USING_MEMORY_DEBUGGER)
+    Bigint **p5s = interp->dtoa.p5s;
+    for (Py_ssize_t i = 0; i < Bigint_Pow5size; i++) {
+        Bigint *p5 = p5s[i];
+        p5s[i] = NULL;
+        Bfree(p5);
+    }
+#endif
+}
diff --git a/Python/pylifecycle.c b/Python/pylifecycle.c
index 95a72eb..20bfe1a 100644
--- a/Python/pylifecycle.c
+++ b/Python/pylifecycle.c
@@ -820,6 +820,11 @@ pycore_interp_init(PyThreadState *tstate)
         return status;
     }
 
+    status = _PyDtoa_Init(interp);
+    if (_PyStatus_EXCEPTION(status)) {
+        return status;
+    }
+
     // The GC must be initialized before the first GC collection.
     status = _PyGC_Init(interp);
     if (_PyStatus_EXCEPTION(status)) {
@@ -1776,6 +1781,7 @@ finalize_interp_clear(PyThreadState *tstate)
     _PyXI_Fini(tstate->interp);
     _PyExc_ClearExceptionGroupType(tstate->interp);
     _Py_clear_generic_types(tstate->interp);
+    _PyDtoa_Fini(tstate->interp);
 
     /* Clear interpreter state and all thread states */
     _PyInterpreterState_Clear(tstate);