Merge branch 'main' into sandbox

CMakeLists.txt

@@ -1,4 +1,4 @@
-cmake_minimum_required(VERSION 3.10)
+cmake_minimum_required(VERSION 3.20)
 
 project(pocketpy)
 

amalgamate.py

@@ -1,11 +1,12 @@
 import re
 import shutil
 import os
+import subprocess
 import sys
 import time
 from typing import List, Dict
 
-assert os.system("python prebuild.py") == 0
+assert subprocess.call([sys.executable, "prebuild.py"]) == 0
 
 ROOT = 'include/pocketpy'
 PUBLIC_HEADERS = ['config.h', 'export.h', 'vmath.h', 'sandbox.h', 'pocketpy.h']

cmake_build.py

@@ -2,7 +2,7 @@ import os
 import sys
 import shutil
 
-assert os.system("python prebuild.py") == 0
+assert os.system(f'"{sys.executable}" prebuild.py') == 0
 
 if not os.path.exists("build"):
     os.mkdir("build")

docs/features/ub.md

@@ -5,7 +5,9 @@ title: Undefined Behaviour
 
 These are the undefined behaviours of pkpy. The behaviour of pkpy is undefined if you do the following things.
 
-1. Delete a builtin object. For example, `del int.__add__`.
+1. Modify or delete an attribute of a builtin type. For example, `int.__add__ = f` or
+   `del int.__add__`. The interpreter takes fast paths that assume the arithmetic and
+   comparison methods of `int` and `float` are the original ones.
 2. Call an unbound method with the wrong type of `self`. For example, `int.__add__('1', 2)`.
 3. Type `T`'s `__new__` returns an object that is not an instance of `T`.
 4. Call `__new__` with a type that is not a subclass of `type`.

docs/modules/pickle.md

@@ -24,6 +24,12 @@ The following types can be pickled:
 - [x] classes accessible from the top level of a module;
 - [x] instances of such classes
 
+Cyclic and shared references are preserved: `list`, `dict` and instances of
+python classes are memoized before their contents are written, so an object
+graph containing reference cycles round-trips correctly and object identity
+is retained. A cycle that passes only through a `tuple` or through a
+`__reduce__` result is not supported.
+
 The following magic methods are available:
 
 - [ ] `__getnewargs__`

docs/modules/random.md

@@ -30,3 +30,28 @@ Shuffle a sequence inplace.
 ### `random.choices(population, weights=None, k=1)`
 
 Return a k sized list of elements chosen from the population with replacement.
+
+### `random.getstate()`
+
+Return the internal state of the generator as a `bytes` object.
+
+### `random.setstate(state)`
+
+Restore the internal state of the generator from a `bytes` object
+returned by a previous call to `getstate()`.
+
+### `random.Random(x=None)`
+
+Create a new generator. `x` may be an `int` seed, `None` (seeded lazily from the
+system clock on first use), or a state returned by `getstate()`.
+
+A `Random` object supports `pickle`, so its state can be saved and restored:
+
+```python
+import pickle, random
+
+r = random.Random(7)
+data = pickle.dumps(r)
+r2 = pickle.loads(data)
+assert r.random() == r2.random()
+```

include/pocketpy/common/floatconv.h

@@ -0,0 +1,47 @@
+#pragma once
+
+#include <stdbool.h>
+
+/* Deterministic conversions between `double` and its decimal text form.
+ *
+ * The C library's `strtod`, `snprintf("%g")` and friends are not usable when
+ * bit-identical results across platforms are required: they are affected by
+ * the current locale, and several libc implementations are not correctly
+ * rounded. The routines below are ported from Wuffs and only use integer
+ * arithmetic, so they produce the same bits on every IEEE-754 platform.
+ *
+ * See `src/common/floatconv.c` for provenance and license.
+ */
+
+/* Buffer size that `c11__f64_to_shortest` never exceeds. */
+#define C11_F64_SHORTEST_BUF_SIZE 32
+
+/* The largest precision `c11__f64_to_fixed` honours. Anything larger is
+ * clamped, matching the upstream Wuffs limit. */
+#define C11_F64_MAX_PRECISION 4095
+
+/* Buffer size that `c11__f64_to_fixed` never exceeds for a given precision:
+ * a sign, up to 309 integral digits, a '.', `precision` fractional digits and
+ * a byte of slack. */
+#define C11_F64_FIXED_BUF_SIZE(precision) (312 + (precision))
+
+/* A drop-in replacement for `strtod`, minus hexadecimal floats and minus any
+ * locale sensitivity. Skips leading whitespace, parses the longest prefix of
+ * `s` that forms a decimal float (including `inf`, `infinity` and `nan`, case
+ * insensitive) and, if `p_end` is non-NULL, stores the first unconsumed
+ * character there. Returns 0.0 and sets `*p_end` to `s` if nothing parses. */
+double strtod1(const char* s, char** p_end);
+
+/* Parses the whole of `[data, data + size)` as a decimal float. Returns false
+ * without touching `*out` unless every byte is consumed. */
+bool c11__parse_f64(const char* data, int size, double* out);
+
+/* Writes `x` using the fewest digits that still round-trip back to `x`, in the
+ * notation CPython's `repr()` picks. `x` must be finite. Returns the number of
+ * bytes written, or 0 if `dst_size` is too small. */
+int c11__f64_to_shortest(char* dst, int dst_size, double x);
+
+/* Writes `x` with exactly `precision` digits after the decimal point, i.e.
+ * `"%.*f"`. `x` must be finite. Returns the number of bytes written, or 0 if
+ * `dst_size` is too small. */
+int c11__f64_to_fixed(char* dst, int dst_size, double x, int precision);

include/pocketpy/interpreter/bindings.h

@@ -2,10 +2,32 @@
 
 #include "pocketpy/pocketpy.h"
 
-bool generator__next__(int argc, py_Ref argv);
-bool array2d_like_iterator__next__(int argc, py_Ref argv);
-bool list_iterator__next__(int argc, py_Ref argv);
-bool tuple_iterator__next__(int argc, py_Ref argv);
-bool dict_items__next__(int argc, py_Ref argv);
-bool range_iterator__next__(int argc, py_Ref argv);
-bool str_iterator__next__(int argc, py_Ref argv);
+/* Exception-free `__next__` of the builtin iterators. `py_next()` calls these
+ * directly so that exhausting a builtin iterator does not construct a
+ * `StopIteration` object.
+ *   1: a value was produced into `py_retval()`
+ *   0: the iterator is exhausted; `py_retval()` holds the `StopIteration`
+ *      value, or `nil` if there is none
+ *  -1: an error occurred and an exception was set */
+int generator__iternext(py_Ref self);
+int array2d_like_iterator__iternext(py_Ref self);
+int list_iterator__iternext(py_Ref self);
+int tuple_iterator__iternext(py_Ref self);
+int dict_items__iternext(py_Ref self);
+int range_iterator__iternext(py_Ref self);
+int str_iterator__iternext(py_Ref self);
+
+/// Raise `StopIteration` for an `__iternext` result of `0`.
+/// `py_retval()` must hold the value to carry, or `nil` for no value.
+bool pk__raise_stopiteration() PY_RAISE;
+
+/// Define the `__next__` magic method as the exception-based wrapper of
+/// `name##__iternext`. Only the owning type binds it, so it stays file-local.
+#define PK_DEFINE_NEXT_WRAPPER(name)                                                               \
+    static bool name##__next__(int argc, py_Ref argv) {                                            \
+        PY_CHECK_ARGC(1);                                                                          \
+        int res = name##__iternext(argv);                                                          \
+        if(res == -1) return false;                                                                \
+        if(res == 0) return pk__raise_stopiteration();                                             \
+        return true;                                                                               \
+    }

include/pocketpy/interpreter/typeinfo.h

@@ -21,6 +21,12 @@ typedef struct py_TypeInfo {
     bool (*delattribute)(py_Ref self, py_Name name) PY_RAISE;
     bool (*getunboundmethod)(py_Ref self, py_Name name) PY_RETURN;
 
+    // Resolved `__new__`/`__init__`, valid while `magics_version` matches
+    // `vm->type_version`. `cached_init` is nil when the type has no `__init__`.
+    py_TValue cached_new;
+    py_TValue cached_init;
+    uint64_t magics_version;
+
     py_TValue annotations;
     py_Dtor dtor;  // destructor for this type, NULL if no dtor
     void (*on_end_subclass)(struct py_TypeInfo*);  // backdoor for enum module
@@ -28,6 +34,8 @@ typedef struct py_TypeInfo {
 
 py_TypeInfo* pk_typeinfo(py_Type type);
 py_ItemRef pk_tpfindname(py_TypeInfo* ti, py_Name name);
+/// Re-resolve `cached_new`/`cached_init` against the current `type_version`.
+void pk_tpresolvemagics(py_TypeInfo* ti);
 #define pk_tpfindmagic pk_tpfindname
 
 py_Type pk_newtype(const char* name,

include/pocketpy/interpreter/vm.h

@@ -47,6 +47,9 @@ typedef struct VM {
 
     BinTree modules;
     c11_vector /*TypePointer*/ types;
+    // Bumped on every write to a type's `__dict__`. `py_TypeInfo` caches the
+    // resolution of `__new__`/`__init__` and re-resolves when this moves.
+    uint64_t type_version;
 
     py_GlobalRef builtins;  // builtins module
     py_GlobalRef main;      // __main__ module

include/pocketpy/pocketpy.h

@@ -590,7 +590,10 @@ PK_API bool py_hash(py_Ref, py_i64* out) PY_RAISE;
 /// Get the iterator of the object.
 PK_API bool py_iter(py_Ref) PY_RAISE PY_RETURN;
 /// Get the next element from the iterator.
-/// 1: success, 0: StopIteration, -1: error
+/// 1: a value was produced into `py_retval()`
+/// 0: the iterator is exhausted; `py_retval()` holds the `StopIteration` value,
+///    or `nil` if there is none
+/// -1: error
 PK_API int py_next(py_Ref) PY_RAISE PY_RETURN;
 /// Python equivalent to `str(val)`.
 PK_API bool py_str(py_Ref val) PY_RAISE PY_RETURN;

scripts/format.py

@@ -1,22 +0,0 @@
-import os
-import subprocess
-
-def get_all_files(root: str):
-    for path, _, files in os.walk(root):
-        for file in files:
-            fullpath = os.path.join(path, file)
-            # ignore some files
-            if fullpath.startswith('include/pybind11'):
-                continue
-            if file.startswith('_'):
-                continue
-            if not file.endswith('.c') and not file.endswith('.h') and not file.endswith('.hpp'):
-                continue
-            yield fullpath
-
-if __name__ == '__main__':
-    files = []
-    files.extend(get_all_files('include'))
-    files.extend(get_all_files('src'))
-    files.extend(get_all_files('src2'))
-    subprocess.run(['clang-format', '-i'] + files, check=True)

scripts/run_tests.py

@@ -7,7 +7,7 @@ pkpy_exe = 'main.exe' if sys.platform == 'win32' else './main'
 
 def test_file(filepath, cpython=False):
     if cpython:
-        return os.system("python " + filepath) == 0
+        return os.system(f'"{sys.executable}" {filepath}') == 0
     code = os.system(pkpy_exe + ' ' + filepath)
     if code != 0:
         print('Return code:', code)
@@ -74,7 +74,7 @@ exit()
             print(res.stdout)
             exit(1)
 
-code = os.system(f'python compileall.py {pkpy_exe} tests tmp/tests')
+code = os.system(f'"{sys.executable}" compileall.py {pkpy_exe} tests tmp/tests')
 assert code == 0
 
 if len(sys.argv) == 2:

src/bindings/py_array.c

@@ -1,6 +1,7 @@
 #include "pocketpy/pocketpy.h"
 #include "pocketpy/objects/object.h"
 #include "pocketpy/objects/iterator.h"
+#include "pocketpy/interpreter/bindings.h"
 #include "pocketpy/interpreter/vm.h"
 
 int pk_arrayview(py_Ref self, py_TValue** p) {
@@ -57,27 +58,31 @@ bool pk_arraycontains(py_Ref self, py_Ref val) {
     return true;
 }
 
-bool list_iterator__next__(int argc, py_Ref argv) {
-    PY_CHECK_ARGC(1);
-    list_iterator* ud = py_touserdata(argv);
+PK_DEFINE_NEXT_WRAPPER(list_iterator)
+
+int list_iterator__iternext(py_Ref self) {
+    list_iterator* ud = py_touserdata(self);
     if(ud->index < ud->vec->length) {
         py_TValue* res = c11__at(py_TValue, ud->vec, ud->index);
         py_assign(py_retval(), res);
         ud->index++;
-        return true;
+        return 1;
     }
-    return StopIteration();
+    py_newnil(py_retval());
+    return 0;
 }
 
-bool tuple_iterator__next__(int argc, py_Ref argv) {
-    PY_CHECK_ARGC(1);
-    tuple_iterator* ud = py_touserdata(argv);
+PK_DEFINE_NEXT_WRAPPER(tuple_iterator)
+
+int tuple_iterator__iternext(py_Ref self) {
+    tuple_iterator* ud = py_touserdata(self);
     if(ud->index < ud->length) {
         py_assign(py_retval(), ud->p + ud->index);
         ud->index++;
-        return true;
+        return 1;
     }
-    return StopIteration();
+    py_newnil(py_retval());
+    return 0;
 }
 
 py_Type pk_list_iterator__register() {

src/bindings/py_mappingproxy.c

@@ -75,8 +75,7 @@ static bool namedict_items(int argc, py_Ref argv) {
 static bool namedict_clear(int argc, py_Ref argv) {
     PY_CHECK_ARGC(1);
     py_Ref object = py_getslot(argv, 0);
-    NameDict* dict = PyObject__dict(object->_obj);
-    NameDict__clear(dict);
+    py_cleardict(object);
     py_newnone(py_retval());
     return true;
 }

src/bindings/py_number.c

@@ -1,6 +1,7 @@
 #include "pocketpy/interpreter/vm.h"
 #include "pocketpy/common/sstream.h"
 #include "pocketpy/common/dmath.h"
+#include "pocketpy/common/floatconv.h"
 #include "pocketpy/pocketpy.h"
 
 
@@ -480,7 +481,7 @@ static bool float__new__(int argc, py_Ref argv) {
             }
 
             char* p_end;
-            py_f64 float_out = strtod(sv.data, &p_end);
+            py_f64 float_out = strtod1(sv.data, &p_end);
             if(p_end != sv.data + sv.size) return ValueError("invalid literal for float(): %q", sv);
             py_newfloat(py_retval(), float_out);
             return true;
@@ -519,11 +520,23 @@ static bool bool__repr__(int argc, py_Ref argv) {
     return true;
 }
 
+static bool bool_try_cast_i64(py_Ref arg, py_i64* out) {
+    if (arg->type == tp_int) {
+        *out = py_toint(arg);
+        return true;
+    } else if (arg->type == tp_bool) {
+        *out = py_tobool(arg);
+        return true;
+    } else {
+        return false;
+    }
+}
+
 static bool bool__eq__(int argc, py_Ref argv) {
     PY_CHECK_ARGC(2);
-    bool lhs = py_tobool(&argv[0]);
-    if(argv[1].type == tp_bool) {
-        bool rhs = py_tobool(&argv[1]);
+    py_i64 lhs = (py_i64)py_tobool(&argv[0]);
+    py_i64 rhs;
+    if(bool_try_cast_i64(py_arg(1), &rhs)) {
         py_newbool(py_retval(), lhs == rhs);
     } else {
         py_newnotimplemented(py_retval());
@@ -533,9 +546,9 @@ static bool bool__eq__(int argc, py_Ref argv) {
 
 static bool bool__ne__(int argc, py_Ref argv) {
     PY_CHECK_ARGC(2);
-    bool lhs = py_tobool(&argv[0]);
-    if(argv[1].type == tp_bool) {
-        bool rhs = py_tobool(&argv[1]);
+    py_i64 lhs = (py_i64)py_tobool(&argv[0]);
+    py_i64 rhs;
+    if(bool_try_cast_i64(py_arg(1), &rhs)) {
         py_newbool(py_retval(), lhs != rhs);
     } else {
         py_newnotimplemented(py_retval());
@@ -560,25 +573,6 @@ DEF_BOOL_BITWISE(__and__, &&)
 DEF_BOOL_BITWISE(__or__, ||)
 DEF_BOOL_BITWISE(__xor__, !=)
 
-static bool bool__invert__(int argc, py_Ref argv) {
-    PY_CHECK_ARGC(1);
-    bool val = py_tobool(&argv[0]);
-    py_newbool(py_retval(), !val);
-    return true;
-}
-
-static bool bool_try_cast_i64(py_Ref arg, py_i64* out) {
-    if (arg->type == tp_int) {
-        *out = py_toint(arg);
-        return true;
-    } else if (arg->type == tp_bool) {
-        *out = py_tobool(arg);
-        return true;
-    } else {
-        return false;
-    }
-}
-
 static bool bool__add__(int argc, py_Ref argv) {
     PY_CHECK_ARGC(2);
     py_i64 lhs = py_tobool(py_arg(0));
@@ -710,7 +704,6 @@ void pk_number__register() {
     py_bindmagic(tp_bool, __and__, bool__and__);
     py_bindmagic(tp_bool, __or__, bool__or__);
     py_bindmagic(tp_bool, __xor__, bool__xor__);
-    py_bindmagic(tp_bool, __invert__, bool__invert__);
     py_bindmagic(tp_bool, __add__, bool__add__);
     py_bindmagic(tp_bool, __sub__, bool__sub__);
     py_bindmagic(tp_bool, __mul__, bool__mul__);

src/bindings/py_range.c

@@ -3,6 +3,7 @@
 #include "pocketpy/common/utils.h"
 #include "pocketpy/objects/object.h"
 #include "pocketpy/interpreter/vm.h"
+#include "pocketpy/interpreter/bindings.h"
 
 typedef struct Range {
     py_i64 start;
@@ -41,9 +42,17 @@ static bool range__new__(int argc, py_Ref argv) {
     return true;
 }
 
+typedef struct RangeIterator {
+    Range range;
+    py_i64 current;
+} RangeIterator;
+
 static bool range__iter__(int argc, py_Ref argv) {
     PY_CHECK_ARGC(1);
-    return py_tpcall(tp_range_iterator, 1, argv);
+    RangeIterator* ud = py_newobject(py_retval(), tp_range_iterator, 0, sizeof(RangeIterator));
+    ud->range = *(Range*)py_touserdata(argv);
+    ud->current = ud->range.start;
+    return true;
 }
 
 py_Type pk_range__register() {
@@ -54,11 +63,6 @@ py_Type pk_range__register() {
     return type;
 }
 
-typedef struct RangeIterator {
-    Range range;
-    py_i64 current;
-} RangeIterator;
-
 static bool range_iterator__new__(int argc, py_Ref argv) {
     PY_CHECK_ARGC(2);
     PY_CHECK_ARG_TYPE(1, tp_range);
@@ -68,17 +72,19 @@ static bool range_iterator__new__(int argc, py_Ref argv) {
     return true;
 }
 
-bool range_iterator__next__(int argc, py_Ref argv) {
-    PY_CHECK_ARGC(1);
-    RangeIterator* ud = py_touserdata(argv);
-    if(ud->range.step > 0) {
-        if(ud->current >= ud->range.stop) return StopIteration();
-    } else {
-        if(ud->current <= ud->range.stop) return StopIteration();
+PK_DEFINE_NEXT_WRAPPER(range_iterator)
+
+int range_iterator__iternext(py_Ref self) {
+    RangeIterator* ud = py_touserdata(self);
+    bool exhausted = ud->range.step > 0 ? ud->current >= ud->range.stop
+                                        : ud->current <= ud->range.stop;
+    if(exhausted) {
+        py_newnil(py_retval());
+        return 0;
     }
     py_newint(py_retval(), ud->current);
     ud->current += ud->range.step;
-    return true;
+    return 1;
 }
 
 py_Type pk_range_iterator__register() {

src/bindings/py_str.c

@@ -5,6 +5,7 @@
 #include "pocketpy/objects/object.h"
 #include "pocketpy/interpreter/vm.h"
 #include "pocketpy/common/sstream.h"
+#include "pocketpy/interpreter/bindings.h"
 #include <stdbool.h>
 
 c11_string* pk_tostr(py_Ref self) {
@@ -680,17 +681,21 @@ py_Type pk_str__register() {
     return type;
 }
 
-bool str_iterator__next__(int argc, py_Ref argv) {
-    PY_CHECK_ARGC(1);
-    int* ud = py_touserdata(&argv[0]);
+PK_DEFINE_NEXT_WRAPPER(str_iterator)
+
+int str_iterator__iternext(py_Ref self) {
+    int* ud = py_touserdata(self);
     int size;
-    const char* data = py_tostrn(py_getslot(argv, 0), &size);
-    if(*ud == size) return StopIteration();
+    const char* data = py_tostrn(py_getslot(self, 0), &size);
+    if(*ud == size) {
+        py_newnil(py_retval());
+        return 0;
+    }
     int start = *ud;
     int len = c11__u8_header(data[*ud], false);
     *ud += len;
     py_newstrv(py_retval(), (c11_sv){data + start, len});
-    return true;
+    return 1;
 }
 
 py_Type pk_str_iterator__register() {

src/common/floatconv.c

@@ -0,0 +1,2949 @@
+/* Deterministic conversion between `double` and its decimal text form.
+ *
+ * The bulk of this file is vendored verbatim from Wuffs so that it stays cheap
+ * to diff against upstream when picking up fixes:
+ *
+ *   https://github.com/google/wuffs
+ *     internal/cgen/base/floatconv-submodule-data.c
+ *     internal/cgen/base/floatconv-submodule-code.c
+ *
+ * Copyright 2020 The Wuffs Authors.
+ * SPDX-License-Identifier: Apache-2.0 OR MIT
+ *
+ * Parsing is Eisel-Lemire with an exact high-precision-decimal fallback;
+ * rendering runs the same decimal machinery backwards. Both are correctly
+ * rounded, locale independent and (with the one exception guarded below) use
+ * integer arithmetic only, which is what makes them deterministic.
+ *
+ * Deviations from upstream are tagged `[pocketpy]`:
+ *   1. the f16/f32 entry points are dropped, as is the wuffs_base__ machinery
+ *      they need; what little remains is reimplemented in the shim below;
+ *   2. every entry point is `static`, since pocketpy exposes its own API at
+ *      the bottom of this file;
+ *   3. the shortest-round-trip renderer switches to exponent notation on
+ *      CPython's threshold rather than C's "%g" one;
+ *   4. the sole floating-point fast path is compiled out on targets with
+ *      excess intermediate precision.
+ *
+ * Do not run clang-format over the vendored region; `scripts/format.py` skips
+ * this file on purpose.
+ */
+
+#include "pocketpy/common/floatconv.h"
+
+#include <float.h>
+#include <stddef.h>
+#include <stdint.h>
+#include <string.h>
+
+/* ---------------- [pocketpy] wuffs_base__ shim ----------------
+ *
+ * Just enough of Wuffs' base module for the vendored code to compile. These
+ * are copied from internal/cgen/base/fundamental-public.h and
+ * internal/cgen/base/strconv-public.h.
+ */
+
+#define WUFFS_BASE__MAYBE_STATIC static
+
+typedef struct wuffs_base__slice_u8__struct {
+  uint8_t* ptr;
+  size_t len;
+} wuffs_base__slice_u8;
+
+typedef struct wuffs_base__status__struct {
+  const char* repr;
+} wuffs_base__status;
+
+typedef struct wuffs_base__result_f64__struct {
+  wuffs_base__status status;
+  double value;
+} wuffs_base__result_f64;
+
+static const char wuffs_base__error__bad_argument[] = "#base: bad argument";
+static const char wuffs_base__error__bad_receiver[] = "#base: bad receiver";
+
+static inline wuffs_base__status  //
+wuffs_base__make_status(const char* repr) {
+  wuffs_base__status z;
+  z.repr = repr;
+  return z;
+}
+
+static inline int32_t  //
+wuffs_base__i32__max(int32_t x, int32_t y) {
+  return x > y ? x : y;
+}
+
+static inline uint32_t  //
+wuffs_base__u32__min(uint32_t x, uint32_t y) {
+  return x < y ? x : y;
+}
+
+#if (defined(__GNUC__) || defined(__clang__)) && (__SIZEOF_LONG__ == 8)
+
+static inline uint32_t  //
+wuffs_base__count_leading_zeroes_u64(uint64_t u) {
+  return u ? ((uint32_t)(__builtin_clzl(u))) : 64u;
+}
+
+#else
+
+static inline uint32_t  //
+wuffs_base__count_leading_zeroes_u64(uint64_t u) {
+  if (u == 0) {
+    return 64;
+  }
+
+  uint32_t n = 0;
+  if ((u >> 32) == 0) {
+    n |= 32;
+    u <<= 32;
+  }
+  if ((u >> 48) == 0) {
+    n |= 16;
+    u <<= 16;
+  }
+  if ((u >> 56) == 0) {
+    n |= 8;
+    u <<= 8;
+  }
+  if ((u >> 60) == 0) {
+    n |= 4;
+    u <<= 4;
+  }
+  if ((u >> 62) == 0) {
+    n |= 2;
+    u <<= 2;
+  }
+  if ((u >> 63) == 0) {
+    n |= 1;
+    u <<= 1;
+  }
+  return n;
+}
+
+#endif
+
+typedef struct wuffs_base__multiply_u64__output__struct {
+  uint64_t lo;
+  uint64_t hi;
+} wuffs_base__multiply_u64__output;
+
+static inline wuffs_base__multiply_u64__output  //
+wuffs_base__multiply_u64(uint64_t x, uint64_t y) {
+#if defined(__SIZEOF_INT128__)
+  __uint128_t z = ((__uint128_t)x) * ((__uint128_t)y);
+  wuffs_base__multiply_u64__output o;
+  o.lo = ((uint64_t)(z));
+  o.hi = ((uint64_t)(z >> 64));
+  return o;
+#else
+  uint64_t x0 = x & 0xFFFFFFFF;
+  uint64_t x1 = x >> 32;
+  uint64_t y0 = y & 0xFFFFFFFF;
+  uint64_t y1 = y >> 32;
+  uint64_t w0 = x0 * y0;
+  uint64_t t = (x1 * y0) + (w0 >> 32);
+  uint64_t w1 = t & 0xFFFFFFFF;
+  uint64_t w2 = t >> 32;
+  w1 += x0 * y1;
+  wuffs_base__multiply_u64__output o;
+  o.lo = x * y;
+  o.hi = (x1 * y1) + w2 + (w1 >> 32);
+  return o;
+#endif
+}
+
+static inline void  //
+wuffs_base__poke_u24le__no_bounds_check(uint8_t* p, uint32_t x) {
+  p[0] = (uint8_t)(x >> 0);
+  p[1] = (uint8_t)(x >> 8);
+  p[2] = (uint8_t)(x >> 16);
+}
+
+static inline void  //
+wuffs_base__poke_u32le__no_bounds_check(uint8_t* p, uint32_t x) {
+  p[0] = (uint8_t)(x >> 0);
+  p[1] = (uint8_t)(x >> 8);
+  p[2] = (uint8_t)(x >> 16);
+  p[3] = (uint8_t)(x >> 24);
+}
+
+static inline uint64_t  //
+wuffs_base__ieee_754_bit_representation__from_f64_to_u64(double f) {
+  uint64_t u = 0;
+  if (sizeof(uint64_t) == sizeof(double)) {
+    memcpy(&u, &f, sizeof(uint64_t));
+  }
+  return u;
+}
+
+static inline double  //
+wuffs_base__ieee_754_bit_representation__from_u64_to_f64(uint64_t u) {
+  double f = 0;
+  if (sizeof(uint64_t) == sizeof(double)) {
+    memcpy(&f, &u, sizeof(uint64_t));
+  }
+  return f;
+}
+
+// Options for wuffs_base__parse_number_f64.
+#define WUFFS_BASE__PARSE_NUMBER_XXX__DEFAULT_OPTIONS ((uint32_t)0x00000000)
+#define WUFFS_BASE__PARSE_NUMBER_XXX__ALLOW_MULTIPLE_LEADING_ZEROES \
+  ((uint32_t)0x00000001)
+#define WUFFS_BASE__PARSE_NUMBER_XXX__ALLOW_UNDERSCORES ((uint32_t)0x00000002)
+#define WUFFS_BASE__PARSE_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA \
+  ((uint32_t)0x00000010)
+#define WUFFS_BASE__PARSE_NUMBER_FXX__REJECT_INF_AND_NAN ((uint32_t)0x00000020)
+
+// Options for wuffs_base__render_number_f64.
+#define WUFFS_BASE__RENDER_NUMBER_XXX__DEFAULT_OPTIONS ((uint32_t)0x00000000)
+#define WUFFS_BASE__RENDER_NUMBER_XXX__ALIGN_RIGHT ((uint32_t)0x00000100)
+#define WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN ((uint32_t)0x00000200)
+#define WUFFS_BASE__RENDER_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA \
+  ((uint32_t)0x00001000)
+#define WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_ABSENT ((uint32_t)0x00002000)
+#define WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_PRESENT ((uint32_t)0x00004000)
+#define WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION \
+  ((uint32_t)0x00008000)
+
+/* [pocketpy] Deviation 3.
+ *
+ * Wuffs' "%g" notation follows C and switches to an exponent once the decimal
+ * point moves past 6 digits, so 1e6 would render as "1e+06". CPython's repr()
+ * instead switches once `decimal_point > 16`, which is what
+ * `wuffs_private_impl__high_prec_dec__render_*` calls an `e_threshold` of 16.
+ * See `format_float_short` in CPython's Python/pystrtod.c.
+ */
+#define PK_FLOATCONV_REPR_E_THRESHOLD 16
+
+/* [pocketpy] Deviation 4.
+ *
+ * Everything below is integer arithmetic except for one `d *= power_of_10`
+ * fast path in wuffs_base__parse_number_f64. That multiply is exact and
+ * correctly rounded on an IEEE-754 target, but on a target that evaluates
+ * doubles in a wider format -- 32-bit x86 using the x87 stack is the one that
+ * still matters -- it rounds twice and can land one ulp away from what the
+ * integer path computes. Compile it out there and let Eisel-Lemire handle
+ * those inputs instead; the answer is the same, just a few ns slower.
+ */
+#if !defined(FLT_EVAL_METHOD) || (FLT_EVAL_METHOD == 0)
+#define PK_FLOATCONV_HAS_EXACT_DOUBLE_ARITHMETIC 1
+#else
+#define PK_FLOATCONV_HAS_EXACT_DOUBLE_ARITHMETIC 0
+#endif
+
+/* ---------------- end of the [pocketpy] shim ---------------- */
+
+// ---------------- IEEE 754 Floating Point
+
+// The etc__hpd_left_shift and etc__powers_of_5 tables were printed by
+// script/print-hpd-left-shift.go. That script has an optional -comments flag,
+// whose output is not copied here, which prints further detail.
+//
+// These tables are used in
+// wuffs_private_impl__high_prec_dec__lshift_num_new_digits.
+
+// wuffs_private_impl__hpd_left_shift[i] encodes the number of new digits
+// created after multiplying a positive integer by (1 << i): the additional
+// length in the decimal representation. For example, shifting "234" by 3
+// (equivalent to multiplying by 8) will produce "1872". Going from a 3-length
+// string to a 4-length string means that 1 new digit was added (and existing
+// digits may have changed).
+//
+// Shifting by i can add either N or N-1 new digits, depending on whether the
+// original positive integer compares >= or < to the i'th power of 5 (as 10
+// equals 2 * 5). Comparison is lexicographic, not numerical.
+//
+// For example, shifting by 4 (i.e. multiplying by 16) can add 1 or 2 new
+// digits, depending on a lexicographic comparison to (5 ** 4), i.e. "625":
+//  - ("1"      << 4) is "16",       which adds 1 new digit.
+//  - ("5678"   << 4) is "90848",    which adds 1 new digit.
+//  - ("624"    << 4) is "9984",     which adds 1 new digit.
+//  - ("62498"  << 4) is "999968",   which adds 1 new digit.
+//  - ("625"    << 4) is "10000",    which adds 2 new digits.
+//  - ("625001" << 4) is "10000016", which adds 2 new digits.
+//  - ("7008"   << 4) is "112128",   which adds 2 new digits.
+//  - ("99"     << 4) is "1584",     which adds 2 new digits.
+//
+// Thus, when i is 4, N is 2 and (5 ** i) is "625". This etc__hpd_left_shift
+// array encodes this as:
+//  - etc__hpd_left_shift[4] is 0x1006 = (2 << 11) | 0x0006.
+//  - etc__hpd_left_shift[5] is 0x1009 = (? << 11) | 0x0009.
+// where the ? isn't relevant for i == 4.
+//
+// The high 5 bits of etc__hpd_left_shift[i] is N, the higher of the two
+// possible number of new digits. The low 11 bits are an offset into the
+// etc__powers_of_5 array (of length 0x051C, so offsets fit in 11 bits). When i
+// is 4, its offset and the next one is 6 and 9, and etc__powers_of_5[6 .. 9]
+// is the string "\x06\x02\x05", so the relevant power of 5 is "625".
+//
+// Thanks to Ken Thompson for the original idea.
+static const uint16_t wuffs_private_impl__hpd_left_shift[65] = {
+    0x0000, 0x0800, 0x0801, 0x0803, 0x1006, 0x1009, 0x100D, 0x1812, 0x1817,
+    0x181D, 0x2024, 0x202B, 0x2033, 0x203C, 0x2846, 0x2850, 0x285B, 0x3067,
+    0x3073, 0x3080, 0x388E, 0x389C, 0x38AB, 0x38BB, 0x40CC, 0x40DD, 0x40EF,
+    0x4902, 0x4915, 0x4929, 0x513E, 0x5153, 0x5169, 0x5180, 0x5998, 0x59B0,
+    0x59C9, 0x61E3, 0x61FD, 0x6218, 0x6A34, 0x6A50, 0x6A6D, 0x6A8B, 0x72AA,
+    0x72C9, 0x72E9, 0x7B0A, 0x7B2B, 0x7B4D, 0x8370, 0x8393, 0x83B7, 0x83DC,
+    0x8C02, 0x8C28, 0x8C4F, 0x9477, 0x949F, 0x94C8, 0x9CF2, 0x051C, 0x051C,
+    0x051C, 0x051C,
+};
+
+// wuffs_private_impl__powers_of_5 contains the powers of 5, concatenated
+// together: "5", "25", "125", "625", "3125", etc.
+static const uint8_t wuffs_private_impl__powers_of_5[0x051C] = {
+    5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5, 3, 9,
+    0, 6, 2, 5, 1, 9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8, 2, 8, 1, 2,
+    5, 2, 4, 4, 1, 4, 0, 6, 2, 5, 1, 2, 2, 0, 7, 0, 3, 1, 2, 5, 6, 1, 0, 3, 5,
+    1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2, 5, 1, 5, 2, 5, 8, 7, 8, 9, 0,
+    6, 2, 5, 7, 6, 2, 9, 3, 9, 4, 5, 3, 1, 2, 5, 3, 8, 1, 4, 6, 9, 7, 2, 6, 5,
+    6, 2, 5, 1, 9, 0, 7, 3, 4, 8, 6, 3, 2, 8, 1, 2, 5, 9, 5, 3, 6, 7, 4, 3, 1,
+    6, 4, 0, 6, 2, 5, 4, 7, 6, 8, 3, 7, 1, 5, 8, 2, 0, 3, 1, 2, 5, 2, 3, 8, 4,
+    1, 8, 5, 7, 9, 1, 0, 1, 5, 6, 2, 5, 1, 1, 9, 2, 0, 9, 2, 8, 9, 5, 5, 0, 7,
+    8, 1, 2, 5, 5, 9, 6, 0, 4, 6, 4, 4, 7, 7, 5, 3, 9, 0, 6, 2, 5, 2, 9, 8, 0,
+    2, 3, 2, 2, 3, 8, 7, 6, 9, 5, 3, 1, 2, 5, 1, 4, 9, 0, 1, 1, 6, 1, 1, 9, 3,
+    8, 4, 7, 6, 5, 6, 2, 5, 7, 4, 5, 0, 5, 8, 0, 5, 9, 6, 9, 2, 3, 8, 2, 8, 1,
+    2, 5, 3, 7, 2, 5, 2, 9, 0, 2, 9, 8, 4, 6, 1, 9, 1, 4, 0, 6, 2, 5, 1, 8, 6,
+    2, 6, 4, 5, 1, 4, 9, 2, 3, 0, 9, 5, 7, 0, 3, 1, 2, 5, 9, 3, 1, 3, 2, 2, 5,
+    7, 4, 6, 1, 5, 4, 7, 8, 5, 1, 5, 6, 2, 5, 4, 6, 5, 6, 6, 1, 2, 8, 7, 3, 0,
+    7, 7, 3, 9, 2, 5, 7, 8, 1, 2, 5, 2, 3, 2, 8, 3, 0, 6, 4, 3, 6, 5, 3, 8, 6,
+    9, 6, 2, 8, 9, 0, 6, 2, 5, 1, 1, 6, 4, 1, 5, 3, 2, 1, 8, 2, 6, 9, 3, 4, 8,
+    1, 4, 4, 5, 3, 1, 2, 5, 5, 8, 2, 0, 7, 6, 6, 0, 9, 1, 3, 4, 6, 7, 4, 0, 7,
+    2, 2, 6, 5, 6, 2, 5, 2, 9, 1, 0, 3, 8, 3, 0, 4, 5, 6, 7, 3, 3, 7, 0, 3, 6,
+    1, 3, 2, 8, 1, 2, 5, 1, 4, 5, 5, 1, 9, 1, 5, 2, 2, 8, 3, 6, 6, 8, 5, 1, 8,
+    0, 6, 6, 4, 0, 6, 2, 5, 7, 2, 7, 5, 9, 5, 7, 6, 1, 4, 1, 8, 3, 4, 2, 5, 9,
+    0, 3, 3, 2, 0, 3, 1, 2, 5, 3, 6, 3, 7, 9, 7, 8, 8, 0, 7, 0, 9, 1, 7, 1, 2,
+    9, 5, 1, 6, 6, 0, 1, 5, 6, 2, 5, 1, 8, 1, 8, 9, 8, 9, 4, 0, 3, 5, 4, 5, 8,
+    5, 6, 4, 7, 5, 8, 3, 0, 0, 7, 8, 1, 2, 5, 9, 0, 9, 4, 9, 4, 7, 0, 1, 7, 7,
+    2, 9, 2, 8, 2, 3, 7, 9, 1, 5, 0, 3, 9, 0, 6, 2, 5, 4, 5, 4, 7, 4, 7, 3, 5,
+    0, 8, 8, 6, 4, 6, 4, 1, 1, 8, 9, 5, 7, 5, 1, 9, 5, 3, 1, 2, 5, 2, 2, 7, 3,
+    7, 3, 6, 7, 5, 4, 4, 3, 2, 3, 2, 0, 5, 9, 4, 7, 8, 7, 5, 9, 7, 6, 5, 6, 2,
+    5, 1, 1, 3, 6, 8, 6, 8, 3, 7, 7, 2, 1, 6, 1, 6, 0, 2, 9, 7, 3, 9, 3, 7, 9,
+    8, 8, 2, 8, 1, 2, 5, 5, 6, 8, 4, 3, 4, 1, 8, 8, 6, 0, 8, 0, 8, 0, 1, 4, 8,
+    6, 9, 6, 8, 9, 9, 4, 1, 4, 0, 6, 2, 5, 2, 8, 4, 2, 1, 7, 0, 9, 4, 3, 0, 4,
+    0, 4, 0, 0, 7, 4, 3, 4, 8, 4, 4, 9, 7, 0, 7, 0, 3, 1, 2, 5, 1, 4, 2, 1, 0,
+    8, 5, 4, 7, 1, 5, 2, 0, 2, 0, 0, 3, 7, 1, 7, 4, 2, 2, 4, 8, 5, 3, 5, 1, 5,
+    6, 2, 5, 7, 1, 0, 5, 4, 2, 7, 3, 5, 7, 6, 0, 1, 0, 0, 1, 8, 5, 8, 7, 1, 1,
+    2, 4, 2, 6, 7, 5, 7, 8, 1, 2, 5, 3, 5, 5, 2, 7, 1, 3, 6, 7, 8, 8, 0, 0, 5,
+    0, 0, 9, 2, 9, 3, 5, 5, 6, 2, 1, 3, 3, 7, 8, 9, 0, 6, 2, 5, 1, 7, 7, 6, 3,
+    5, 6, 8, 3, 9, 4, 0, 0, 2, 5, 0, 4, 6, 4, 6, 7, 7, 8, 1, 0, 6, 6, 8, 9, 4,
+    5, 3, 1, 2, 5, 8, 8, 8, 1, 7, 8, 4, 1, 9, 7, 0, 0, 1, 2, 5, 2, 3, 2, 3, 3,
+    8, 9, 0, 5, 3, 3, 4, 4, 7, 2, 6, 5, 6, 2, 5, 4, 4, 4, 0, 8, 9, 2, 0, 9, 8,
+    5, 0, 0, 6, 2, 6, 1, 6, 1, 6, 9, 4, 5, 2, 6, 6, 7, 2, 3, 6, 3, 2, 8, 1, 2,
+    5, 2, 2, 2, 0, 4, 4, 6, 0, 4, 9, 2, 5, 0, 3, 1, 3, 0, 8, 0, 8, 4, 7, 2, 6,
+    3, 3, 3, 6, 1, 8, 1, 6, 4, 0, 6, 2, 5, 1, 1, 1, 0, 2, 2, 3, 0, 2, 4, 6, 2,
+    5, 1, 5, 6, 5, 4, 0, 4, 2, 3, 6, 3, 1, 6, 6, 8, 0, 9, 0, 8, 2, 0, 3, 1, 2,
+    5, 5, 5, 5, 1, 1, 1, 5, 1, 2, 3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 1, 1, 8, 1, 5,
+    8, 3, 4, 0, 4, 5, 4, 1, 0, 1, 5, 6, 2, 5, 2, 7, 7, 5, 5, 5, 7, 5, 6, 1, 5,
+    6, 2, 8, 9, 1, 3, 5, 1, 0, 5, 9, 0, 7, 9, 1, 7, 0, 2, 2, 7, 0, 5, 0, 7, 8,
+    1, 2, 5, 1, 3, 8, 7, 7, 7, 8, 7, 8, 0, 7, 8, 1, 4, 4, 5, 6, 7, 5, 5, 2, 9,
+    5, 3, 9, 5, 8, 5, 1, 1, 3, 5, 2, 5, 3, 9, 0, 6, 2, 5, 6, 9, 3, 8, 8, 9, 3,
+    9, 0, 3, 9, 0, 7, 2, 2, 8, 3, 7, 7, 6, 4, 7, 6, 9, 7, 9, 2, 5, 5, 6, 7, 6,
+    2, 6, 9, 5, 3, 1, 2, 5, 3, 4, 6, 9, 4, 4, 6, 9, 5, 1, 9, 5, 3, 6, 1, 4, 1,
+    8, 8, 8, 2, 3, 8, 4, 8, 9, 6, 2, 7, 8, 3, 8, 1, 3, 4, 7, 6, 5, 6, 2, 5, 1,
+    7, 3, 4, 7, 2, 3, 4, 7, 5, 9, 7, 6, 8, 0, 7, 0, 9, 4, 4, 1, 1, 9, 2, 4, 4,
+    8, 1, 3, 9, 1, 9, 0, 6, 7, 3, 8, 2, 8, 1, 2, 5, 8, 6, 7, 3, 6, 1, 7, 3, 7,
+    9, 8, 8, 4, 0, 3, 5, 4, 7, 2, 0, 5, 9, 6, 2, 2, 4, 0, 6, 9, 5, 9, 5, 3, 3,
+    6, 9, 1, 4, 0, 6, 2, 5,
+};
+
+// --------
+
+// wuffs_private_impl__powers_of_10 contains truncated approximations to the
+// powers of 10, ranging from 1e-307 to 1e+288 inclusive, as 596 pairs of
+// uint64_t values (a 128-bit mantissa).
+//
+// There's also an implicit third column (implied by a linear formula involving
+// the base-10 exponent) that is the base-2 exponent, biased by a magic
+// constant. That constant (1214 or 0x04BE) equals 1023 + 191. 1023 is the bias
+// for IEEE 754 double-precision floating point. 191 is ((3 * 64) - 1) and
+// wuffs_private_impl__parse_number_f64_eisel_lemire works with
+// multiples-of-64-bit mantissas.
+//
+// For example, the third row holds the approximation to 1e-305:
+//   0xE0B62E29_29ABA83C_331ACDAB_FE94DE87 * (2 ** (0x0049 - 0x04BE))
+//
+// Similarly, 1e+4 is approximated by:
+//   0x9C400000_00000000_00000000_00000000 * (2 ** (0x044C - 0x04BE))
+//
+// Similarly, 1e+68 is approximated by:
+//   0xED63A231_D4C4FB27_4CA7AAA8_63EE4BDD * (2 ** (0x0520 - 0x04BE))
+//
+// This table was generated by by script/print-mpb-powers-of-10.go
+static const uint64_t wuffs_private_impl__powers_of_10[596][2] = {
+    {0xA5D3B6D479F8E056, 0x8FD0C16206306BAB},  // 1e-307
+    {0x8F48A4899877186C, 0xB3C4F1BA87BC8696},  // 1e-306
+    {0x331ACDABFE94DE87, 0xE0B62E2929ABA83C},  // 1e-305
+    {0x9FF0C08B7F1D0B14, 0x8C71DCD9BA0B4925},  // 1e-304
+    {0x07ECF0AE5EE44DD9, 0xAF8E5410288E1B6F},  // 1e-303
+    {0xC9E82CD9F69D6150, 0xDB71E91432B1A24A},  // 1e-302
+    {0xBE311C083A225CD2, 0x892731AC9FAF056E},  // 1e-301
+    {0x6DBD630A48AAF406, 0xAB70FE17C79AC6CA},  // 1e-300
+    {0x092CBBCCDAD5B108, 0xD64D3D9DB981787D},  // 1e-299
+    {0x25BBF56008C58EA5, 0x85F0468293F0EB4E},  // 1e-298
+    {0xAF2AF2B80AF6F24E, 0xA76C582338ED2621},  // 1e-297
+    {0x1AF5AF660DB4AEE1, 0xD1476E2C07286FAA},  // 1e-296
+    {0x50D98D9FC890ED4D, 0x82CCA4DB847945CA},  // 1e-295
+    {0xE50FF107BAB528A0, 0xA37FCE126597973C},  // 1e-294
+    {0x1E53ED49A96272C8, 0xCC5FC196FEFD7D0C},  // 1e-293
+    {0x25E8E89C13BB0F7A, 0xFF77B1FCBEBCDC4F},  // 1e-292
+    {0x77B191618C54E9AC, 0x9FAACF3DF73609B1},  // 1e-291
+    {0xD59DF5B9EF6A2417, 0xC795830D75038C1D},  // 1e-290
+    {0x4B0573286B44AD1D, 0xF97AE3D0D2446F25},  // 1e-289
+    {0x4EE367F9430AEC32, 0x9BECCE62836AC577},  // 1e-288
+    {0x229C41F793CDA73F, 0xC2E801FB244576D5},  // 1e-287
+    {0x6B43527578C1110F, 0xF3A20279ED56D48A},  // 1e-286
+    {0x830A13896B78AAA9, 0x9845418C345644D6},  // 1e-285
+    {0x23CC986BC656D553, 0xBE5691EF416BD60C},  // 1e-284
+    {0x2CBFBE86B7EC8AA8, 0xEDEC366B11C6CB8F},  // 1e-283
+    {0x7BF7D71432F3D6A9, 0x94B3A202EB1C3F39},  // 1e-282
+    {0xDAF5CCD93FB0CC53, 0xB9E08A83A5E34F07},  // 1e-281
+    {0xD1B3400F8F9CFF68, 0xE858AD248F5C22C9},  // 1e-280
+    {0x23100809B9C21FA1, 0x91376C36D99995BE},  // 1e-279
+    {0xABD40A0C2832A78A, 0xB58547448FFFFB2D},  // 1e-278
+    {0x16C90C8F323F516C, 0xE2E69915B3FFF9F9},  // 1e-277
+    {0xAE3DA7D97F6792E3, 0x8DD01FAD907FFC3B},  // 1e-276
+    {0x99CD11CFDF41779C, 0xB1442798F49FFB4A},  // 1e-275
+    {0x40405643D711D583, 0xDD95317F31C7FA1D},  // 1e-274
+    {0x482835EA666B2572, 0x8A7D3EEF7F1CFC52},  // 1e-273
+    {0xDA3243650005EECF, 0xAD1C8EAB5EE43B66},  // 1e-272
+    {0x90BED43E40076A82, 0xD863B256369D4A40},  // 1e-271
+    {0x5A7744A6E804A291, 0x873E4F75E2224E68},  // 1e-270
+    {0x711515D0A205CB36, 0xA90DE3535AAAE202},  // 1e-269
+    {0x0D5A5B44CA873E03, 0xD3515C2831559A83},  // 1e-268
+    {0xE858790AFE9486C2, 0x8412D9991ED58091},  // 1e-267
+    {0x626E974DBE39A872, 0xA5178FFF668AE0B6},  // 1e-266
+    {0xFB0A3D212DC8128F, 0xCE5D73FF402D98E3},  // 1e-265
+    {0x7CE66634BC9D0B99, 0x80FA687F881C7F8E},  // 1e-264
+    {0x1C1FFFC1EBC44E80, 0xA139029F6A239F72},  // 1e-263
+    {0xA327FFB266B56220, 0xC987434744AC874E},  // 1e-262
+    {0x4BF1FF9F0062BAA8, 0xFBE9141915D7A922},  // 1e-261
+    {0x6F773FC3603DB4A9, 0x9D71AC8FADA6C9B5},  // 1e-260
+    {0xCB550FB4384D21D3, 0xC4CE17B399107C22},  // 1e-259
+    {0x7E2A53A146606A48, 0xF6019DA07F549B2B},  // 1e-258
+    {0x2EDA7444CBFC426D, 0x99C102844F94E0FB},  // 1e-257
+    {0xFA911155FEFB5308, 0xC0314325637A1939},  // 1e-256
+    {0x793555AB7EBA27CA, 0xF03D93EEBC589F88},  // 1e-255
+    {0x4BC1558B2F3458DE, 0x96267C7535B763B5},  // 1e-254
+    {0x9EB1AAEDFB016F16, 0xBBB01B9283253CA2},  // 1e-253
+    {0x465E15A979C1CADC, 0xEA9C227723EE8BCB},  // 1e-252
+    {0x0BFACD89EC191EC9, 0x92A1958A7675175F},  // 1e-251
+    {0xCEF980EC671F667B, 0xB749FAED14125D36},  // 1e-250
+    {0x82B7E12780E7401A, 0xE51C79A85916F484},  // 1e-249
+    {0xD1B2ECB8B0908810, 0x8F31CC0937AE58D2},  // 1e-248
+    {0x861FA7E6DCB4AA15, 0xB2FE3F0B8599EF07},  // 1e-247
+    {0x67A791E093E1D49A, 0xDFBDCECE67006AC9},  // 1e-246
+    {0xE0C8BB2C5C6D24E0, 0x8BD6A141006042BD},  // 1e-245
+    {0x58FAE9F773886E18, 0xAECC49914078536D},  // 1e-244
+    {0xAF39A475506A899E, 0xDA7F5BF590966848},  // 1e-243
+    {0x6D8406C952429603, 0x888F99797A5E012D},  // 1e-242
+    {0xC8E5087BA6D33B83, 0xAAB37FD7D8F58178},  // 1e-241
+    {0xFB1E4A9A90880A64, 0xD5605FCDCF32E1D6},  // 1e-240
+    {0x5CF2EEA09A55067F, 0x855C3BE0A17FCD26},  // 1e-239
+    {0xF42FAA48C0EA481E, 0xA6B34AD8C9DFC06F},  // 1e-238
+    {0xF13B94DAF124DA26, 0xD0601D8EFC57B08B},  // 1e-237
+    {0x76C53D08D6B70858, 0x823C12795DB6CE57},  // 1e-236
+    {0x54768C4B0C64CA6E, 0xA2CB1717B52481ED},  // 1e-235
+    {0xA9942F5DCF7DFD09, 0xCB7DDCDDA26DA268},  // 1e-234
+    {0xD3F93B35435D7C4C, 0xFE5D54150B090B02},  // 1e-233
+    {0xC47BC5014A1A6DAF, 0x9EFA548D26E5A6E1},  // 1e-232
+    {0x359AB6419CA1091B, 0xC6B8E9B0709F109A},  // 1e-231
+    {0xC30163D203C94B62, 0xF867241C8CC6D4C0},  // 1e-230
+    {0x79E0DE63425DCF1D, 0x9B407691D7FC44F8},  // 1e-229
+    {0x985915FC12F542E4, 0xC21094364DFB5636},  // 1e-228
+    {0x3E6F5B7B17B2939D, 0xF294B943E17A2BC4},  // 1e-227
+    {0xA705992CEECF9C42, 0x979CF3CA6CEC5B5A},  // 1e-226
+    {0x50C6FF782A838353, 0xBD8430BD08277231},  // 1e-225
+    {0xA4F8BF5635246428, 0xECE53CEC4A314EBD},  // 1e-224
+    {0x871B7795E136BE99, 0x940F4613AE5ED136},  // 1e-223
+    {0x28E2557B59846E3F, 0xB913179899F68584},  // 1e-222
+    {0x331AEADA2FE589CF, 0xE757DD7EC07426E5},  // 1e-221
+    {0x3FF0D2C85DEF7621, 0x9096EA6F3848984F},  // 1e-220
+    {0x0FED077A756B53A9, 0xB4BCA50B065ABE63},  // 1e-219
+    {0xD3E8495912C62894, 0xE1EBCE4DC7F16DFB},  // 1e-218
+    {0x64712DD7ABBBD95C, 0x8D3360F09CF6E4BD},  // 1e-217
+    {0xBD8D794D96AACFB3, 0xB080392CC4349DEC},  // 1e-216
+    {0xECF0D7A0FC5583A0, 0xDCA04777F541C567},  // 1e-215
+    {0xF41686C49DB57244, 0x89E42CAAF9491B60},  // 1e-214
+    {0x311C2875C522CED5, 0xAC5D37D5B79B6239},  // 1e-213
+    {0x7D633293366B828B, 0xD77485CB25823AC7},  // 1e-212
+    {0xAE5DFF9C02033197, 0x86A8D39EF77164BC},  // 1e-211
+    {0xD9F57F830283FDFC, 0xA8530886B54DBDEB},  // 1e-210
+    {0xD072DF63C324FD7B, 0xD267CAA862A12D66},  // 1e-209
+    {0x4247CB9E59F71E6D, 0x8380DEA93DA4BC60},  // 1e-208
+    {0x52D9BE85F074E608, 0xA46116538D0DEB78},  // 1e-207
+    {0x67902E276C921F8B, 0xCD795BE870516656},  // 1e-206
+    {0x00BA1CD8A3DB53B6, 0x806BD9714632DFF6},  // 1e-205
+    {0x80E8A40ECCD228A4, 0xA086CFCD97BF97F3},  // 1e-204
+    {0x6122CD128006B2CD, 0xC8A883C0FDAF7DF0},  // 1e-203
+    {0x796B805720085F81, 0xFAD2A4B13D1B5D6C},  // 1e-202
+    {0xCBE3303674053BB0, 0x9CC3A6EEC6311A63},  // 1e-201
+    {0xBEDBFC4411068A9C, 0xC3F490AA77BD60FC},  // 1e-200
+    {0xEE92FB5515482D44, 0xF4F1B4D515ACB93B},  // 1e-199
+    {0x751BDD152D4D1C4A, 0x991711052D8BF3C5},  // 1e-198
+    {0xD262D45A78A0635D, 0xBF5CD54678EEF0B6},  // 1e-197
+    {0x86FB897116C87C34, 0xEF340A98172AACE4},  // 1e-196
+    {0xD45D35E6AE3D4DA0, 0x9580869F0E7AAC0E},  // 1e-195
+    {0x8974836059CCA109, 0xBAE0A846D2195712},  // 1e-194
+    {0x2BD1A438703FC94B, 0xE998D258869FACD7},  // 1e-193
+    {0x7B6306A34627DDCF, 0x91FF83775423CC06},  // 1e-192
+    {0x1A3BC84C17B1D542, 0xB67F6455292CBF08},  // 1e-191
+    {0x20CABA5F1D9E4A93, 0xE41F3D6A7377EECA},  // 1e-190
+    {0x547EB47B7282EE9C, 0x8E938662882AF53E},  // 1e-189
+    {0xE99E619A4F23AA43, 0xB23867FB2A35B28D},  // 1e-188
+    {0x6405FA00E2EC94D4, 0xDEC681F9F4C31F31},  // 1e-187
+    {0xDE83BC408DD3DD04, 0x8B3C113C38F9F37E},  // 1e-186
+    {0x9624AB50B148D445, 0xAE0B158B4738705E},  // 1e-185
+    {0x3BADD624DD9B0957, 0xD98DDAEE19068C76},  // 1e-184
+    {0xE54CA5D70A80E5D6, 0x87F8A8D4CFA417C9},  // 1e-183
+    {0x5E9FCF4CCD211F4C, 0xA9F6D30A038D1DBC},  // 1e-182
+    {0x7647C3200069671F, 0xD47487CC8470652B},  // 1e-181
+    {0x29ECD9F40041E073, 0x84C8D4DFD2C63F3B},  // 1e-180
+    {0xF468107100525890, 0xA5FB0A17C777CF09},  // 1e-179
+    {0x7182148D4066EEB4, 0xCF79CC9DB955C2CC},  // 1e-178
+    {0xC6F14CD848405530, 0x81AC1FE293D599BF},  // 1e-177
+    {0xB8ADA00E5A506A7C, 0xA21727DB38CB002F},  // 1e-176
+    {0xA6D90811F0E4851C, 0xCA9CF1D206FDC03B},  // 1e-175
+    {0x908F4A166D1DA663, 0xFD442E4688BD304A},  // 1e-174
+    {0x9A598E4E043287FE, 0x9E4A9CEC15763E2E},  // 1e-173
+    {0x40EFF1E1853F29FD, 0xC5DD44271AD3CDBA},  // 1e-172
+    {0xD12BEE59E68EF47C, 0xF7549530E188C128},  // 1e-171
+    {0x82BB74F8301958CE, 0x9A94DD3E8CF578B9},  // 1e-170
+    {0xE36A52363C1FAF01, 0xC13A148E3032D6E7},  // 1e-169
+    {0xDC44E6C3CB279AC1, 0xF18899B1BC3F8CA1},  // 1e-168
+    {0x29AB103A5EF8C0B9, 0x96F5600F15A7B7E5},  // 1e-167
+    {0x7415D448F6B6F0E7, 0xBCB2B812DB11A5DE},  // 1e-166
+    {0x111B495B3464AD21, 0xEBDF661791D60F56},  // 1e-165
+    {0xCAB10DD900BEEC34, 0x936B9FCEBB25C995},  // 1e-164
+    {0x3D5D514F40EEA742, 0xB84687C269EF3BFB},  // 1e-163
+    {0x0CB4A5A3112A5112, 0xE65829B3046B0AFA},  // 1e-162
+    {0x47F0E785EABA72AB, 0x8FF71A0FE2C2E6DC},  // 1e-161
+    {0x59ED216765690F56, 0xB3F4E093DB73A093},  // 1e-160
+    {0x306869C13EC3532C, 0xE0F218B8D25088B8},  // 1e-159
+    {0x1E414218C73A13FB, 0x8C974F7383725573},  // 1e-158
+    {0xE5D1929EF90898FA, 0xAFBD2350644EEACF},  // 1e-157
+    {0xDF45F746B74ABF39, 0xDBAC6C247D62A583},  // 1e-156
+    {0x6B8BBA8C328EB783, 0x894BC396CE5DA772},  // 1e-155
+    {0x066EA92F3F326564, 0xAB9EB47C81F5114F},  // 1e-154
+    {0xC80A537B0EFEFEBD, 0xD686619BA27255A2},  // 1e-153
+    {0xBD06742CE95F5F36, 0x8613FD0145877585},  // 1e-152
+    {0x2C48113823B73704, 0xA798FC4196E952E7},  // 1e-151
+    {0xF75A15862CA504C5, 0xD17F3B51FCA3A7A0},  // 1e-150
+    {0x9A984D73DBE722FB, 0x82EF85133DE648C4},  // 1e-149
+    {0xC13E60D0D2E0EBBA, 0xA3AB66580D5FDAF5},  // 1e-148
+    {0x318DF905079926A8, 0xCC963FEE10B7D1B3},  // 1e-147
+    {0xFDF17746497F7052, 0xFFBBCFE994E5C61F},  // 1e-146
+    {0xFEB6EA8BEDEFA633, 0x9FD561F1FD0F9BD3},  // 1e-145
+    {0xFE64A52EE96B8FC0, 0xC7CABA6E7C5382C8},  // 1e-144
+    {0x3DFDCE7AA3C673B0, 0xF9BD690A1B68637B},  // 1e-143
+    {0x06BEA10CA65C084E, 0x9C1661A651213E2D},  // 1e-142
+    {0x486E494FCFF30A62, 0xC31BFA0FE5698DB8},  // 1e-141
+    {0x5A89DBA3C3EFCCFA, 0xF3E2F893DEC3F126},  // 1e-140
+    {0xF89629465A75E01C, 0x986DDB5C6B3A76B7},  // 1e-139
+    {0xF6BBB397F1135823, 0xBE89523386091465},  // 1e-138
+    {0x746AA07DED582E2C, 0xEE2BA6C0678B597F},  // 1e-137
+    {0xA8C2A44EB4571CDC, 0x94DB483840B717EF},  // 1e-136
+    {0x92F34D62616CE413, 0xBA121A4650E4DDEB},  // 1e-135
+    {0x77B020BAF9C81D17, 0xE896A0D7E51E1566},  // 1e-134
+    {0x0ACE1474DC1D122E, 0x915E2486EF32CD60},  // 1e-133
+    {0x0D819992132456BA, 0xB5B5ADA8AAFF80B8},  // 1e-132
+    {0x10E1FFF697ED6C69, 0xE3231912D5BF60E6},  // 1e-131
+    {0xCA8D3FFA1EF463C1, 0x8DF5EFABC5979C8F},  // 1e-130
+    {0xBD308FF8A6B17CB2, 0xB1736B96B6FD83B3},  // 1e-129
+    {0xAC7CB3F6D05DDBDE, 0xDDD0467C64BCE4A0},  // 1e-128
+    {0x6BCDF07A423AA96B, 0x8AA22C0DBEF60EE4},  // 1e-127
+    {0x86C16C98D2C953C6, 0xAD4AB7112EB3929D},  // 1e-126
+    {0xE871C7BF077BA8B7, 0xD89D64D57A607744},  // 1e-125
+    {0x11471CD764AD4972, 0x87625F056C7C4A8B},  // 1e-124
+    {0xD598E40D3DD89BCF, 0xA93AF6C6C79B5D2D},  // 1e-123
+    {0x4AFF1D108D4EC2C3, 0xD389B47879823479},  // 1e-122
+    {0xCEDF722A585139BA, 0x843610CB4BF160CB},  // 1e-121
+    {0xC2974EB4EE658828, 0xA54394FE1EEDB8FE},  // 1e-120
+    {0x733D226229FEEA32, 0xCE947A3DA6A9273E},  // 1e-119
+    {0x0806357D5A3F525F, 0x811CCC668829B887},  // 1e-118
+    {0xCA07C2DCB0CF26F7, 0xA163FF802A3426A8},  // 1e-117
+    {0xFC89B393DD02F0B5, 0xC9BCFF6034C13052},  // 1e-116
+    {0xBBAC2078D443ACE2, 0xFC2C3F3841F17C67},  // 1e-115
+    {0xD54B944B84AA4C0D, 0x9D9BA7832936EDC0},  // 1e-114
+    {0x0A9E795E65D4DF11, 0xC5029163F384A931},  // 1e-113
+    {0x4D4617B5FF4A16D5, 0xF64335BCF065D37D},  // 1e-112
+    {0x504BCED1BF8E4E45, 0x99EA0196163FA42E},  // 1e-111
+    {0xE45EC2862F71E1D6, 0xC06481FB9BCF8D39},  // 1e-110
+    {0x5D767327BB4E5A4C, 0xF07DA27A82C37088},  // 1e-109
+    {0x3A6A07F8D510F86F, 0x964E858C91BA2655},  // 1e-108
+    {0x890489F70A55368B, 0xBBE226EFB628AFEA},  // 1e-107
+    {0x2B45AC74CCEA842E, 0xEADAB0ABA3B2DBE5},  // 1e-106
+    {0x3B0B8BC90012929D, 0x92C8AE6B464FC96F},  // 1e-105
+    {0x09CE6EBB40173744, 0xB77ADA0617E3BBCB},  // 1e-104
+    {0xCC420A6A101D0515, 0xE55990879DDCAABD},  // 1e-103
+    {0x9FA946824A12232D, 0x8F57FA54C2A9EAB6},  // 1e-102
+    {0x47939822DC96ABF9, 0xB32DF8E9F3546564},  // 1e-101
+    {0x59787E2B93BC56F7, 0xDFF9772470297EBD},  // 1e-100
+    {0x57EB4EDB3C55B65A, 0x8BFBEA76C619EF36},  // 1e-99
+    {0xEDE622920B6B23F1, 0xAEFAE51477A06B03},  // 1e-98
+    {0xE95FAB368E45ECED, 0xDAB99E59958885C4},  // 1e-97
+    {0x11DBCB0218EBB414, 0x88B402F7FD75539B},  // 1e-96
+    {0xD652BDC29F26A119, 0xAAE103B5FCD2A881},  // 1e-95
+    {0x4BE76D3346F0495F, 0xD59944A37C0752A2},  // 1e-94
+    {0x6F70A4400C562DDB, 0x857FCAE62D8493A5},  // 1e-93
+    {0xCB4CCD500F6BB952, 0xA6DFBD9FB8E5B88E},  // 1e-92
+    {0x7E2000A41346A7A7, 0xD097AD07A71F26B2},  // 1e-91
+    {0x8ED400668C0C28C8, 0x825ECC24C873782F},  // 1e-90
+    {0x728900802F0F32FA, 0xA2F67F2DFA90563B},  // 1e-89
+    {0x4F2B40A03AD2FFB9, 0xCBB41EF979346BCA},  // 1e-88
+    {0xE2F610C84987BFA8, 0xFEA126B7D78186BC},  // 1e-87
+    {0x0DD9CA7D2DF4D7C9, 0x9F24B832E6B0F436},  // 1e-86
+    {0x91503D1C79720DBB, 0xC6EDE63FA05D3143},  // 1e-85
+    {0x75A44C6397CE912A, 0xF8A95FCF88747D94},  // 1e-84
+    {0xC986AFBE3EE11ABA, 0x9B69DBE1B548CE7C},  // 1e-83
+    {0xFBE85BADCE996168, 0xC24452DA229B021B},  // 1e-82
+    {0xFAE27299423FB9C3, 0xF2D56790AB41C2A2},  // 1e-81
+    {0xDCCD879FC967D41A, 0x97C560BA6B0919A5},  // 1e-80
+    {0x5400E987BBC1C920, 0xBDB6B8E905CB600F},  // 1e-79
+    {0x290123E9AAB23B68, 0xED246723473E3813},  // 1e-78
+    {0xF9A0B6720AAF6521, 0x9436C0760C86E30B},  // 1e-77
+    {0xF808E40E8D5B3E69, 0xB94470938FA89BCE},  // 1e-76
+    {0xB60B1D1230B20E04, 0xE7958CB87392C2C2},  // 1e-75
+    {0xB1C6F22B5E6F48C2, 0x90BD77F3483BB9B9},  // 1e-74
+    {0x1E38AEB6360B1AF3, 0xB4ECD5F01A4AA828},  // 1e-73
+    {0x25C6DA63C38DE1B0, 0xE2280B6C20DD5232},  // 1e-72
+    {0x579C487E5A38AD0E, 0x8D590723948A535F},  // 1e-71
+    {0x2D835A9DF0C6D851, 0xB0AF48EC79ACE837},  // 1e-70
+    {0xF8E431456CF88E65, 0xDCDB1B2798182244},  // 1e-69
+    {0x1B8E9ECB641B58FF, 0x8A08F0F8BF0F156B},  // 1e-68
+    {0xE272467E3D222F3F, 0xAC8B2D36EED2DAC5},  // 1e-67
+    {0x5B0ED81DCC6ABB0F, 0xD7ADF884AA879177},  // 1e-66
+    {0x98E947129FC2B4E9, 0x86CCBB52EA94BAEA},  // 1e-65
+    {0x3F2398D747B36224, 0xA87FEA27A539E9A5},  // 1e-64
+    {0x8EEC7F0D19A03AAD, 0xD29FE4B18E88640E},  // 1e-63
+    {0x1953CF68300424AC, 0x83A3EEEEF9153E89},  // 1e-62
+    {0x5FA8C3423C052DD7, 0xA48CEAAAB75A8E2B},  // 1e-61
+    {0x3792F412CB06794D, 0xCDB02555653131B6},  // 1e-60
+    {0xE2BBD88BBEE40BD0, 0x808E17555F3EBF11},  // 1e-59
+    {0x5B6ACEAEAE9D0EC4, 0xA0B19D2AB70E6ED6},  // 1e-58
+    {0xF245825A5A445275, 0xC8DE047564D20A8B},  // 1e-57
+    {0xEED6E2F0F0D56712, 0xFB158592BE068D2E},  // 1e-56
+    {0x55464DD69685606B, 0x9CED737BB6C4183D},  // 1e-55
+    {0xAA97E14C3C26B886, 0xC428D05AA4751E4C},  // 1e-54
+    {0xD53DD99F4B3066A8, 0xF53304714D9265DF},  // 1e-53
+    {0xE546A8038EFE4029, 0x993FE2C6D07B7FAB},  // 1e-52
+    {0xDE98520472BDD033, 0xBF8FDB78849A5F96},  // 1e-51
+    {0x963E66858F6D4440, 0xEF73D256A5C0F77C},  // 1e-50
+    {0xDDE7001379A44AA8, 0x95A8637627989AAD},  // 1e-49
+    {0x5560C018580D5D52, 0xBB127C53B17EC159},  // 1e-48
+    {0xAAB8F01E6E10B4A6, 0xE9D71B689DDE71AF},  // 1e-47
+    {0xCAB3961304CA70E8, 0x9226712162AB070D},  // 1e-46
+    {0x3D607B97C5FD0D22, 0xB6B00D69BB55C8D1},  // 1e-45
+    {0x8CB89A7DB77C506A, 0xE45C10C42A2B3B05},  // 1e-44
+    {0x77F3608E92ADB242, 0x8EB98A7A9A5B04E3},  // 1e-43
+    {0x55F038B237591ED3, 0xB267ED1940F1C61C},  // 1e-42
+    {0x6B6C46DEC52F6688, 0xDF01E85F912E37A3},  // 1e-41
+    {0x2323AC4B3B3DA015, 0x8B61313BBABCE2C6},  // 1e-40
+    {0xABEC975E0A0D081A, 0xAE397D8AA96C1B77},  // 1e-39
+    {0x96E7BD358C904A21, 0xD9C7DCED53C72255},  // 1e-38
+    {0x7E50D64177DA2E54, 0x881CEA14545C7575},  // 1e-37
+    {0xDDE50BD1D5D0B9E9, 0xAA242499697392D2},  // 1e-36
+    {0x955E4EC64B44E864, 0xD4AD2DBFC3D07787},  // 1e-35
+    {0xBD5AF13BEF0B113E, 0x84EC3C97DA624AB4},  // 1e-34
+    {0xECB1AD8AEACDD58E, 0xA6274BBDD0FADD61},  // 1e-33
+    {0x67DE18EDA5814AF2, 0xCFB11EAD453994BA},  // 1e-32
+    {0x80EACF948770CED7, 0x81CEB32C4B43FCF4},  // 1e-31
+    {0xA1258379A94D028D, 0xA2425FF75E14FC31},  // 1e-30
+    {0x096EE45813A04330, 0xCAD2F7F5359A3B3E},  // 1e-29
+    {0x8BCA9D6E188853FC, 0xFD87B5F28300CA0D},  // 1e-28
+    {0x775EA264CF55347D, 0x9E74D1B791E07E48},  // 1e-27
+    {0x95364AFE032A819D, 0xC612062576589DDA},  // 1e-26
+    {0x3A83DDBD83F52204, 0xF79687AED3EEC551},  // 1e-25
+    {0xC4926A9672793542, 0x9ABE14CD44753B52},  // 1e-24
+    {0x75B7053C0F178293, 0xC16D9A0095928A27},  // 1e-23
+    {0x5324C68B12DD6338, 0xF1C90080BAF72CB1},  // 1e-22
+    {0xD3F6FC16EBCA5E03, 0x971DA05074DA7BEE},  // 1e-21
+    {0x88F4BB1CA6BCF584, 0xBCE5086492111AEA},  // 1e-20
+    {0x2B31E9E3D06C32E5, 0xEC1E4A7DB69561A5},  // 1e-19
+    {0x3AFF322E62439FCF, 0x9392EE8E921D5D07},  // 1e-18
+    {0x09BEFEB9FAD487C2, 0xB877AA3236A4B449},  // 1e-17
+    {0x4C2EBE687989A9B3, 0xE69594BEC44DE15B},  // 1e-16
+    {0x0F9D37014BF60A10, 0x901D7CF73AB0ACD9},  // 1e-15
+    {0x538484C19EF38C94, 0xB424DC35095CD80F},  // 1e-14
+    {0x2865A5F206B06FB9, 0xE12E13424BB40E13},  // 1e-13
+    {0xF93F87B7442E45D3, 0x8CBCCC096F5088CB},  // 1e-12
+    {0xF78F69A51539D748, 0xAFEBFF0BCB24AAFE},  // 1e-11
+    {0xB573440E5A884D1B, 0xDBE6FECEBDEDD5BE},  // 1e-10
+    {0x31680A88F8953030, 0x89705F4136B4A597},  // 1e-9
+    {0xFDC20D2B36BA7C3D, 0xABCC77118461CEFC},  // 1e-8
+    {0x3D32907604691B4C, 0xD6BF94D5E57A42BC},  // 1e-7
+    {0xA63F9A49C2C1B10F, 0x8637BD05AF6C69B5},  // 1e-6
+    {0x0FCF80DC33721D53, 0xA7C5AC471B478423},  // 1e-5
+    {0xD3C36113404EA4A8, 0xD1B71758E219652B},  // 1e-4
+    {0x645A1CAC083126E9, 0x83126E978D4FDF3B},  // 1e-3
+    {0x3D70A3D70A3D70A3, 0xA3D70A3D70A3D70A},  // 1e-2
+    {0xCCCCCCCCCCCCCCCC, 0xCCCCCCCCCCCCCCCC},  // 1e-1
+    {0x0000000000000000, 0x8000000000000000},  // 1e0
+    {0x0000000000000000, 0xA000000000000000},  // 1e1
+    {0x0000000000000000, 0xC800000000000000},  // 1e2
+    {0x0000000000000000, 0xFA00000000000000},  // 1e3
+    {0x0000000000000000, 0x9C40000000000000},  // 1e4
+    {0x0000000000000000, 0xC350000000000000},  // 1e5
+    {0x0000000000000000, 0xF424000000000000},  // 1e6
+    {0x0000000000000000, 0x9896800000000000},  // 1e7
+    {0x0000000000000000, 0xBEBC200000000000},  // 1e8
+    {0x0000000000000000, 0xEE6B280000000000},  // 1e9
+    {0x0000000000000000, 0x9502F90000000000},  // 1e10
+    {0x0000000000000000, 0xBA43B74000000000},  // 1e11
+    {0x0000000000000000, 0xE8D4A51000000000},  // 1e12
+    {0x0000000000000000, 0x9184E72A00000000},  // 1e13
+    {0x0000000000000000, 0xB5E620F480000000},  // 1e14
+    {0x0000000000000000, 0xE35FA931A0000000},  // 1e15
+    {0x0000000000000000, 0x8E1BC9BF04000000},  // 1e16
+    {0x0000000000000000, 0xB1A2BC2EC5000000},  // 1e17
+    {0x0000000000000000, 0xDE0B6B3A76400000},  // 1e18
+    {0x0000000000000000, 0x8AC7230489E80000},  // 1e19
+    {0x0000000000000000, 0xAD78EBC5AC620000},  // 1e20
+    {0x0000000000000000, 0xD8D726B7177A8000},  // 1e21
+    {0x0000000000000000, 0x878678326EAC9000},  // 1e22
+    {0x0000000000000000, 0xA968163F0A57B400},  // 1e23
+    {0x0000000000000000, 0xD3C21BCECCEDA100},  // 1e24
+    {0x0000000000000000, 0x84595161401484A0},  // 1e25
+    {0x0000000000000000, 0xA56FA5B99019A5C8},  // 1e26
+    {0x0000000000000000, 0xCECB8F27F4200F3A},  // 1e27
+    {0x4000000000000000, 0x813F3978F8940984},  // 1e28
+    {0x5000000000000000, 0xA18F07D736B90BE5},  // 1e29
+    {0xA400000000000000, 0xC9F2C9CD04674EDE},  // 1e30
+    {0x4D00000000000000, 0xFC6F7C4045812296},  // 1e31
+    {0xF020000000000000, 0x9DC5ADA82B70B59D},  // 1e32
+    {0x6C28000000000000, 0xC5371912364CE305},  // 1e33
+    {0xC732000000000000, 0xF684DF56C3E01BC6},  // 1e34
+    {0x3C7F400000000000, 0x9A130B963A6C115C},  // 1e35
+    {0x4B9F100000000000, 0xC097CE7BC90715B3},  // 1e36
+    {0x1E86D40000000000, 0xF0BDC21ABB48DB20},  // 1e37
+    {0x1314448000000000, 0x96769950B50D88F4},  // 1e38
+    {0x17D955A000000000, 0xBC143FA4E250EB31},  // 1e39
+    {0x5DCFAB0800000000, 0xEB194F8E1AE525FD},  // 1e40
+    {0x5AA1CAE500000000, 0x92EFD1B8D0CF37BE},  // 1e41
+    {0xF14A3D9E40000000, 0xB7ABC627050305AD},  // 1e42
+    {0x6D9CCD05D0000000, 0xE596B7B0C643C719},  // 1e43
+    {0xE4820023A2000000, 0x8F7E32CE7BEA5C6F},  // 1e44
+    {0xDDA2802C8A800000, 0xB35DBF821AE4F38B},  // 1e45
+    {0xD50B2037AD200000, 0xE0352F62A19E306E},  // 1e46
+    {0x4526F422CC340000, 0x8C213D9DA502DE45},  // 1e47
+    {0x9670B12B7F410000, 0xAF298D050E4395D6},  // 1e48
+    {0x3C0CDD765F114000, 0xDAF3F04651D47B4C},  // 1e49
+    {0xA5880A69FB6AC800, 0x88D8762BF324CD0F},  // 1e50
+    {0x8EEA0D047A457A00, 0xAB0E93B6EFEE0053},  // 1e51
+    {0x72A4904598D6D880, 0xD5D238A4ABE98068},  // 1e52
+    {0x47A6DA2B7F864750, 0x85A36366EB71F041},  // 1e53
+    {0x999090B65F67D924, 0xA70C3C40A64E6C51},  // 1e54
+    {0xFFF4B4E3F741CF6D, 0xD0CF4B50CFE20765},  // 1e55
+    {0xBFF8F10E7A8921A4, 0x82818F1281ED449F},  // 1e56
+    {0xAFF72D52192B6A0D, 0xA321F2D7226895C7},  // 1e57
+    {0x9BF4F8A69F764490, 0xCBEA6F8CEB02BB39},  // 1e58
+    {0x02F236D04753D5B4, 0xFEE50B7025C36A08},  // 1e59
+    {0x01D762422C946590, 0x9F4F2726179A2245},  // 1e60
+    {0x424D3AD2B7B97EF5, 0xC722F0EF9D80AAD6},  // 1e61
+    {0xD2E0898765A7DEB2, 0xF8EBAD2B84E0D58B},  // 1e62
+    {0x63CC55F49F88EB2F, 0x9B934C3B330C8577},  // 1e63
+    {0x3CBF6B71C76B25FB, 0xC2781F49FFCFA6D5},  // 1e64
+    {0x8BEF464E3945EF7A, 0xF316271C7FC3908A},  // 1e65
+    {0x97758BF0E3CBB5AC, 0x97EDD871CFDA3A56},  // 1e66
+    {0x3D52EEED1CBEA317, 0xBDE94E8E43D0C8EC},  // 1e67
+    {0x4CA7AAA863EE4BDD, 0xED63A231D4C4FB27},  // 1e68
+    {0x8FE8CAA93E74EF6A, 0x945E455F24FB1CF8},  // 1e69
+    {0xB3E2FD538E122B44, 0xB975D6B6EE39E436},  // 1e70
+    {0x60DBBCA87196B616, 0xE7D34C64A9C85D44},  // 1e71
+    {0xBC8955E946FE31CD, 0x90E40FBEEA1D3A4A},  // 1e72
+    {0x6BABAB6398BDBE41, 0xB51D13AEA4A488DD},  // 1e73
+    {0xC696963C7EED2DD1, 0xE264589A4DCDAB14},  // 1e74
+    {0xFC1E1DE5CF543CA2, 0x8D7EB76070A08AEC},  // 1e75
+    {0x3B25A55F43294BCB, 0xB0DE65388CC8ADA8},  // 1e76
+    {0x49EF0EB713F39EBE, 0xDD15FE86AFFAD912},  // 1e77
+    {0x6E3569326C784337, 0x8A2DBF142DFCC7AB},  // 1e78
+    {0x49C2C37F07965404, 0xACB92ED9397BF996},  // 1e79
+    {0xDC33745EC97BE906, 0xD7E77A8F87DAF7FB},  // 1e80
+    {0x69A028BB3DED71A3, 0x86F0AC99B4E8DAFD},  // 1e81
+    {0xC40832EA0D68CE0C, 0xA8ACD7C0222311BC},  // 1e82
+    {0xF50A3FA490C30190, 0xD2D80DB02AABD62B},  // 1e83
+    {0x792667C6DA79E0FA, 0x83C7088E1AAB65DB},  // 1e84
+    {0x577001B891185938, 0xA4B8CAB1A1563F52},  // 1e85
+    {0xED4C0226B55E6F86, 0xCDE6FD5E09ABCF26},  // 1e86
+    {0x544F8158315B05B4, 0x80B05E5AC60B6178},  // 1e87
+    {0x696361AE3DB1C721, 0xA0DC75F1778E39D6},  // 1e88
+    {0x03BC3A19CD1E38E9, 0xC913936DD571C84C},  // 1e89
+    {0x04AB48A04065C723, 0xFB5878494ACE3A5F},  // 1e90
+    {0x62EB0D64283F9C76, 0x9D174B2DCEC0E47B},  // 1e91
+    {0x3BA5D0BD324F8394, 0xC45D1DF942711D9A},  // 1e92
+    {0xCA8F44EC7EE36479, 0xF5746577930D6500},  // 1e93
+    {0x7E998B13CF4E1ECB, 0x9968BF6ABBE85F20},  // 1e94
+    {0x9E3FEDD8C321A67E, 0xBFC2EF456AE276E8},  // 1e95
+    {0xC5CFE94EF3EA101E, 0xEFB3AB16C59B14A2},  // 1e96
+    {0xBBA1F1D158724A12, 0x95D04AEE3B80ECE5},  // 1e97
+    {0x2A8A6E45AE8EDC97, 0xBB445DA9CA61281F},  // 1e98
+    {0xF52D09D71A3293BD, 0xEA1575143CF97226},  // 1e99
+    {0x593C2626705F9C56, 0x924D692CA61BE758},  // 1e100
+    {0x6F8B2FB00C77836C, 0xB6E0C377CFA2E12E},  // 1e101
+    {0x0B6DFB9C0F956447, 0xE498F455C38B997A},  // 1e102
+    {0x4724BD4189BD5EAC, 0x8EDF98B59A373FEC},  // 1e103
+    {0x58EDEC91EC2CB657, 0xB2977EE300C50FE7},  // 1e104
+    {0x2F2967B66737E3ED, 0xDF3D5E9BC0F653E1},  // 1e105
+    {0xBD79E0D20082EE74, 0x8B865B215899F46C},  // 1e106
+    {0xECD8590680A3AA11, 0xAE67F1E9AEC07187},  // 1e107
+    {0xE80E6F4820CC9495, 0xDA01EE641A708DE9},  // 1e108
+    {0x3109058D147FDCDD, 0x884134FE908658B2},  // 1e109
+    {0xBD4B46F0599FD415, 0xAA51823E34A7EEDE},  // 1e110
+    {0x6C9E18AC7007C91A, 0xD4E5E2CDC1D1EA96},  // 1e111
+    {0x03E2CF6BC604DDB0, 0x850FADC09923329E},  // 1e112
+    {0x84DB8346B786151C, 0xA6539930BF6BFF45},  // 1e113
+    {0xE612641865679A63, 0xCFE87F7CEF46FF16},  // 1e114
+    {0x4FCB7E8F3F60C07E, 0x81F14FAE158C5F6E},  // 1e115
+    {0xE3BE5E330F38F09D, 0xA26DA3999AEF7749},  // 1e116
+    {0x5CADF5BFD3072CC5, 0xCB090C8001AB551C},  // 1e117
+    {0x73D9732FC7C8F7F6, 0xFDCB4FA002162A63},  // 1e118
+    {0x2867E7FDDCDD9AFA, 0x9E9F11C4014DDA7E},  // 1e119
+    {0xB281E1FD541501B8, 0xC646D63501A1511D},  // 1e120
+    {0x1F225A7CA91A4226, 0xF7D88BC24209A565},  // 1e121
+    {0x3375788DE9B06958, 0x9AE757596946075F},  // 1e122
+    {0x0052D6B1641C83AE, 0xC1A12D2FC3978937},  // 1e123
+    {0xC0678C5DBD23A49A, 0xF209787BB47D6B84},  // 1e124
+    {0xF840B7BA963646E0, 0x9745EB4D50CE6332},  // 1e125
+    {0xB650E5A93BC3D898, 0xBD176620A501FBFF},  // 1e126
+    {0xA3E51F138AB4CEBE, 0xEC5D3FA8CE427AFF},  // 1e127
+    {0xC66F336C36B10137, 0x93BA47C980E98CDF},  // 1e128
+    {0xB80B0047445D4184, 0xB8A8D9BBE123F017},  // 1e129
+    {0xA60DC059157491E5, 0xE6D3102AD96CEC1D},  // 1e130
+    {0x87C89837AD68DB2F, 0x9043EA1AC7E41392},  // 1e131
+    {0x29BABE4598C311FB, 0xB454E4A179DD1877},  // 1e132
+    {0xF4296DD6FEF3D67A, 0xE16A1DC9D8545E94},  // 1e133
+    {0x1899E4A65F58660C, 0x8CE2529E2734BB1D},  // 1e134
+    {0x5EC05DCFF72E7F8F, 0xB01AE745B101E9E4},  // 1e135
+    {0x76707543F4FA1F73, 0xDC21A1171D42645D},  // 1e136
+    {0x6A06494A791C53A8, 0x899504AE72497EBA},  // 1e137
+    {0x0487DB9D17636892, 0xABFA45DA0EDBDE69},  // 1e138
+    {0x45A9D2845D3C42B6, 0xD6F8D7509292D603},  // 1e139
+    {0x0B8A2392BA45A9B2, 0x865B86925B9BC5C2},  // 1e140
+    {0x8E6CAC7768D7141E, 0xA7F26836F282B732},  // 1e141
+    {0x3207D795430CD926, 0xD1EF0244AF2364FF},  // 1e142
+    {0x7F44E6BD49E807B8, 0x8335616AED761F1F},  // 1e143
+    {0x5F16206C9C6209A6, 0xA402B9C5A8D3A6E7},  // 1e144
+    {0x36DBA887C37A8C0F, 0xCD036837130890A1},  // 1e145
+    {0xC2494954DA2C9789, 0x802221226BE55A64},  // 1e146
+    {0xF2DB9BAA10B7BD6C, 0xA02AA96B06DEB0FD},  // 1e147
+    {0x6F92829494E5ACC7, 0xC83553C5C8965D3D},  // 1e148
+    {0xCB772339BA1F17F9, 0xFA42A8B73ABBF48C},  // 1e149
+    {0xFF2A760414536EFB, 0x9C69A97284B578D7},  // 1e150
+    {0xFEF5138519684ABA, 0xC38413CF25E2D70D},  // 1e151
+    {0x7EB258665FC25D69, 0xF46518C2EF5B8CD1},  // 1e152
+    {0xEF2F773FFBD97A61, 0x98BF2F79D5993802},  // 1e153
+    {0xAAFB550FFACFD8FA, 0xBEEEFB584AFF8603},  // 1e154
+    {0x95BA2A53F983CF38, 0xEEAABA2E5DBF6784},  // 1e155
+    {0xDD945A747BF26183, 0x952AB45CFA97A0B2},  // 1e156
+    {0x94F971119AEEF9E4, 0xBA756174393D88DF},  // 1e157
+    {0x7A37CD5601AAB85D, 0xE912B9D1478CEB17},  // 1e158
+    {0xAC62E055C10AB33A, 0x91ABB422CCB812EE},  // 1e159
+    {0x577B986B314D6009, 0xB616A12B7FE617AA},  // 1e160
+    {0xED5A7E85FDA0B80B, 0xE39C49765FDF9D94},  // 1e161
+    {0x14588F13BE847307, 0x8E41ADE9FBEBC27D},  // 1e162
+    {0x596EB2D8AE258FC8, 0xB1D219647AE6B31C},  // 1e163
+    {0x6FCA5F8ED9AEF3BB, 0xDE469FBD99A05FE3},  // 1e164
+    {0x25DE7BB9480D5854, 0x8AEC23D680043BEE},  // 1e165
+    {0xAF561AA79A10AE6A, 0xADA72CCC20054AE9},  // 1e166
+    {0x1B2BA1518094DA04, 0xD910F7FF28069DA4},  // 1e167
+    {0x90FB44D2F05D0842, 0x87AA9AFF79042286},  // 1e168
+    {0x353A1607AC744A53, 0xA99541BF57452B28},  // 1e169
+    {0x42889B8997915CE8, 0xD3FA922F2D1675F2},  // 1e170
+    {0x69956135FEBADA11, 0x847C9B5D7C2E09B7},  // 1e171
+    {0x43FAB9837E699095, 0xA59BC234DB398C25},  // 1e172
+    {0x94F967E45E03F4BB, 0xCF02B2C21207EF2E},  // 1e173
+    {0x1D1BE0EEBAC278F5, 0x8161AFB94B44F57D},  // 1e174
+    {0x6462D92A69731732, 0xA1BA1BA79E1632DC},  // 1e175
+    {0x7D7B8F7503CFDCFE, 0xCA28A291859BBF93},  // 1e176
+    {0x5CDA735244C3D43E, 0xFCB2CB35E702AF78},  // 1e177
+    {0x3A0888136AFA64A7, 0x9DEFBF01B061ADAB},  // 1e178
+    {0x088AAA1845B8FDD0, 0xC56BAEC21C7A1916},  // 1e179
+    {0x8AAD549E57273D45, 0xF6C69A72A3989F5B},  // 1e180
+    {0x36AC54E2F678864B, 0x9A3C2087A63F6399},  // 1e181
+    {0x84576A1BB416A7DD, 0xC0CB28A98FCF3C7F},  // 1e182
+    {0x656D44A2A11C51D5, 0xF0FDF2D3F3C30B9F},  // 1e183
+    {0x9F644AE5A4B1B325, 0x969EB7C47859E743},  // 1e184
+    {0x873D5D9F0DDE1FEE, 0xBC4665B596706114},  // 1e185
+    {0xA90CB506D155A7EA, 0xEB57FF22FC0C7959},  // 1e186
+    {0x09A7F12442D588F2, 0x9316FF75DD87CBD8},  // 1e187
+    {0x0C11ED6D538AEB2F, 0xB7DCBF5354E9BECE},  // 1e188
+    {0x8F1668C8A86DA5FA, 0xE5D3EF282A242E81},  // 1e189
+    {0xF96E017D694487BC, 0x8FA475791A569D10},  // 1e190
+    {0x37C981DCC395A9AC, 0xB38D92D760EC4455},  // 1e191
+    {0x85BBE253F47B1417, 0xE070F78D3927556A},  // 1e192
+    {0x93956D7478CCEC8E, 0x8C469AB843B89562},  // 1e193
+    {0x387AC8D1970027B2, 0xAF58416654A6BABB},  // 1e194
+    {0x06997B05FCC0319E, 0xDB2E51BFE9D0696A},  // 1e195
+    {0x441FECE3BDF81F03, 0x88FCF317F22241E2},  // 1e196
+    {0xD527E81CAD7626C3, 0xAB3C2FDDEEAAD25A},  // 1e197
+    {0x8A71E223D8D3B074, 0xD60B3BD56A5586F1},  // 1e198
+    {0xF6872D5667844E49, 0x85C7056562757456},  // 1e199
+    {0xB428F8AC016561DB, 0xA738C6BEBB12D16C},  // 1e200
+    {0xE13336D701BEBA52, 0xD106F86E69D785C7},  // 1e201
+    {0xECC0024661173473, 0x82A45B450226B39C},  // 1e202
+    {0x27F002D7F95D0190, 0xA34D721642B06084},  // 1e203
+    {0x31EC038DF7B441F4, 0xCC20CE9BD35C78A5},  // 1e204
+    {0x7E67047175A15271, 0xFF290242C83396CE},  // 1e205
+    {0x0F0062C6E984D386, 0x9F79A169BD203E41},  // 1e206
+    {0x52C07B78A3E60868, 0xC75809C42C684DD1},  // 1e207
+    {0xA7709A56CCDF8A82, 0xF92E0C3537826145},  // 1e208
+    {0x88A66076400BB691, 0x9BBCC7A142B17CCB},  // 1e209
+    {0x6ACFF893D00EA435, 0xC2ABF989935DDBFE},  // 1e210
+    {0x0583F6B8C4124D43, 0xF356F7EBF83552FE},  // 1e211
+    {0xC3727A337A8B704A, 0x98165AF37B2153DE},  // 1e212
+    {0x744F18C0592E4C5C, 0xBE1BF1B059E9A8D6},  // 1e213
+    {0x1162DEF06F79DF73, 0xEDA2EE1C7064130C},  // 1e214
+    {0x8ADDCB5645AC2BA8, 0x9485D4D1C63E8BE7},  // 1e215
+    {0x6D953E2BD7173692, 0xB9A74A0637CE2EE1},  // 1e216
+    {0xC8FA8DB6CCDD0437, 0xE8111C87C5C1BA99},  // 1e217
+    {0x1D9C9892400A22A2, 0x910AB1D4DB9914A0},  // 1e218
+    {0x2503BEB6D00CAB4B, 0xB54D5E4A127F59C8},  // 1e219
+    {0x2E44AE64840FD61D, 0xE2A0B5DC971F303A},  // 1e220
+    {0x5CEAECFED289E5D2, 0x8DA471A9DE737E24},  // 1e221
+    {0x7425A83E872C5F47, 0xB10D8E1456105DAD},  // 1e222
+    {0xD12F124E28F77719, 0xDD50F1996B947518},  // 1e223
+    {0x82BD6B70D99AAA6F, 0x8A5296FFE33CC92F},  // 1e224
+    {0x636CC64D1001550B, 0xACE73CBFDC0BFB7B},  // 1e225
+    {0x3C47F7E05401AA4E, 0xD8210BEFD30EFA5A},  // 1e226
+    {0x65ACFAEC34810A71, 0x8714A775E3E95C78},  // 1e227
+    {0x7F1839A741A14D0D, 0xA8D9D1535CE3B396},  // 1e228
+    {0x1EDE48111209A050, 0xD31045A8341CA07C},  // 1e229
+    {0x934AED0AAB460432, 0x83EA2B892091E44D},  // 1e230
+    {0xF81DA84D5617853F, 0xA4E4B66B68B65D60},  // 1e231
+    {0x36251260AB9D668E, 0xCE1DE40642E3F4B9},  // 1e232
+    {0xC1D72B7C6B426019, 0x80D2AE83E9CE78F3},  // 1e233
+    {0xB24CF65B8612F81F, 0xA1075A24E4421730},  // 1e234
+    {0xDEE033F26797B627, 0xC94930AE1D529CFC},  // 1e235
+    {0x169840EF017DA3B1, 0xFB9B7CD9A4A7443C},  // 1e236
+    {0x8E1F289560EE864E, 0x9D412E0806E88AA5},  // 1e237
+    {0xF1A6F2BAB92A27E2, 0xC491798A08A2AD4E},  // 1e238
+    {0xAE10AF696774B1DB, 0xF5B5D7EC8ACB58A2},  // 1e239
+    {0xACCA6DA1E0A8EF29, 0x9991A6F3D6BF1765},  // 1e240
+    {0x17FD090A58D32AF3, 0xBFF610B0CC6EDD3F},  // 1e241
+    {0xDDFC4B4CEF07F5B0, 0xEFF394DCFF8A948E},  // 1e242
+    {0x4ABDAF101564F98E, 0x95F83D0A1FB69CD9},  // 1e243
+    {0x9D6D1AD41ABE37F1, 0xBB764C4CA7A4440F},  // 1e244
+    {0x84C86189216DC5ED, 0xEA53DF5FD18D5513},  // 1e245
+    {0x32FD3CF5B4E49BB4, 0x92746B9BE2F8552C},  // 1e246
+    {0x3FBC8C33221DC2A1, 0xB7118682DBB66A77},  // 1e247
+    {0x0FABAF3FEAA5334A, 0xE4D5E82392A40515},  // 1e248
+    {0x29CB4D87F2A7400E, 0x8F05B1163BA6832D},  // 1e249
+    {0x743E20E9EF511012, 0xB2C71D5BCA9023F8},  // 1e250
+    {0x914DA9246B255416, 0xDF78E4B2BD342CF6},  // 1e251
+    {0x1AD089B6C2F7548E, 0x8BAB8EEFB6409C1A},  // 1e252
+    {0xA184AC2473B529B1, 0xAE9672ABA3D0C320},  // 1e253
+    {0xC9E5D72D90A2741E, 0xDA3C0F568CC4F3E8},  // 1e254
+    {0x7E2FA67C7A658892, 0x8865899617FB1871},  // 1e255
+    {0xDDBB901B98FEEAB7, 0xAA7EEBFB9DF9DE8D},  // 1e256
+    {0x552A74227F3EA565, 0xD51EA6FA85785631},  // 1e257
+    {0xD53A88958F87275F, 0x8533285C936B35DE},  // 1e258
+    {0x8A892ABAF368F137, 0xA67FF273B8460356},  // 1e259
+    {0x2D2B7569B0432D85, 0xD01FEF10A657842C},  // 1e260
+    {0x9C3B29620E29FC73, 0x8213F56A67F6B29B},  // 1e261
+    {0x8349F3BA91B47B8F, 0xA298F2C501F45F42},  // 1e262
+    {0x241C70A936219A73, 0xCB3F2F7642717713},  // 1e263
+    {0xED238CD383AA0110, 0xFE0EFB53D30DD4D7},  // 1e264
+    {0xF4363804324A40AA, 0x9EC95D1463E8A506},  // 1e265
+    {0xB143C6053EDCD0D5, 0xC67BB4597CE2CE48},  // 1e266
+    {0xDD94B7868E94050A, 0xF81AA16FDC1B81DA},  // 1e267
+    {0xCA7CF2B4191C8326, 0x9B10A4E5E9913128},  // 1e268
+    {0xFD1C2F611F63A3F0, 0xC1D4CE1F63F57D72},  // 1e269
+    {0xBC633B39673C8CEC, 0xF24A01A73CF2DCCF},  // 1e270
+    {0xD5BE0503E085D813, 0x976E41088617CA01},  // 1e271
+    {0x4B2D8644D8A74E18, 0xBD49D14AA79DBC82},  // 1e272
+    {0xDDF8E7D60ED1219E, 0xEC9C459D51852BA2},  // 1e273
+    {0xCABB90E5C942B503, 0x93E1AB8252F33B45},  // 1e274
+    {0x3D6A751F3B936243, 0xB8DA1662E7B00A17},  // 1e275
+    {0x0CC512670A783AD4, 0xE7109BFBA19C0C9D},  // 1e276
+    {0x27FB2B80668B24C5, 0x906A617D450187E2},  // 1e277
+    {0xB1F9F660802DEDF6, 0xB484F9DC9641E9DA},  // 1e278
+    {0x5E7873F8A0396973, 0xE1A63853BBD26451},  // 1e279
+    {0xDB0B487B6423E1E8, 0x8D07E33455637EB2},  // 1e280
+    {0x91CE1A9A3D2CDA62, 0xB049DC016ABC5E5F},  // 1e281
+    {0x7641A140CC7810FB, 0xDC5C5301C56B75F7},  // 1e282
+    {0xA9E904C87FCB0A9D, 0x89B9B3E11B6329BA},  // 1e283
+    {0x546345FA9FBDCD44, 0xAC2820D9623BF429},  // 1e284
+    {0xA97C177947AD4095, 0xD732290FBACAF133},  // 1e285
+    {0x49ED8EABCCCC485D, 0x867F59A9D4BED6C0},  // 1e286
+    {0x5C68F256BFFF5A74, 0xA81F301449EE8C70},  // 1e287
+    {0x73832EEC6FFF3111, 0xD226FC195C6A2F8C},  // 1e288
+};
+
+#if PK_FLOATCONV_HAS_EXACT_DOUBLE_ARITHMETIC  // [pocketpy] Deviation 4.
+// wuffs_private_impl__f64_powers_of_10 holds powers of 10 that can be exactly
+// represented by a float64 (what C calls a double).
+static const double wuffs_private_impl__f64_powers_of_10[23] = {
+    1e0,  1e1,  1e2,  1e3,  1e4,  1e5,  1e6,  1e7,  1e8,  1e9,  1e10, 1e11,
+    1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22,
+};
+#endif
+
+// --------
+
+#define WUFFS_PRIVATE_IMPL__HPD__DECIMAL_POINT__RANGE 2047
+#define WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION 800
+
+// WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL is the largest N such that
+// ((10 << N) < (1 << 64)).
+#define WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL 60
+
+// wuffs_private_impl__high_prec_dec (abbreviated as HPD) is a fixed precision
+// floating point decimal number, augmented with ±infinity values, but it
+// cannot represent NaN (Not a Number).
+//
+// "High precision" means that the mantissa holds 800 decimal digits. 800 is
+// WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION.
+//
+// An HPD isn't for general purpose arithmetic, only for conversions to and
+// from IEEE 754 double-precision floating point, where the largest and
+// smallest positive, finite values are approximately 1.8e+308 and 4.9e-324.
+// HPD exponents above +2047 mean infinity, below -2047 mean zero. The ±2047
+// bounds are further away from zero than ±(324 + 800), where 800 and 2047 is
+// WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION and
+// WUFFS_PRIVATE_IMPL__HPD__DECIMAL_POINT__RANGE.
+//
+// digits[.. num_digits] are the number's digits in big-endian order. The
+// uint8_t values are in the range [0 ..= 9], not ['0' ..= '9'], where e.g. '7'
+// is the ASCII value 0x37.
+//
+// decimal_point is the index (within digits) of the decimal point. It may be
+// negative or be larger than num_digits, in which case the explicit digits are
+// padded with implicit zeroes.
+//
+// For example, if num_digits is 3 and digits is "\x07\x08\x09":
+//  - A decimal_point of -2 means ".00789"
+//  - A decimal_point of -1 means ".0789"
+//  - A decimal_point of +0 means ".789"
+//  - A decimal_point of +1 means "7.89"
+//  - A decimal_point of +2 means "78.9"
+//  - A decimal_point of +3 means "789."
+//  - A decimal_point of +4 means "7890."
+//  - A decimal_point of +5 means "78900."
+//
+// As above, a decimal_point higher than +2047 means that the overall value is
+// infinity, lower than -2047 means zero.
+//
+// negative is a sign bit. An HPD can distinguish positive and negative zero.
+//
+// truncated is whether there are more than
+// WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION digits, and at least one of those
+// extra digits are non-zero. The existence of long-tail digits can affect
+// rounding.
+//
+// The "all fields are zero" value is valid, and represents the number +0.
+typedef struct wuffs_private_impl__high_prec_dec__struct {
+  uint32_t num_digits;
+  int32_t decimal_point;
+  bool negative;
+  bool truncated;
+  uint8_t digits[WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION];
+} wuffs_private_impl__high_prec_dec;
+
+// wuffs_private_impl__high_prec_dec__trim trims trailing zeroes from the
+// h->digits[.. h->num_digits] slice. They have no benefit, since we explicitly
+// track h->decimal_point.
+//
+// Preconditions:
+//  - h is non-NULL.
+static inline void  //
+wuffs_private_impl__high_prec_dec__trim(wuffs_private_impl__high_prec_dec* h) {
+  while ((h->num_digits > 0) && (h->digits[h->num_digits - 1] == 0)) {
+    h->num_digits--;
+  }
+}
+
+// wuffs_private_impl__high_prec_dec__assign sets h to represent the number x.
+//
+// Preconditions:
+//  - h is non-NULL.
+static void  //
+wuffs_private_impl__high_prec_dec__assign(wuffs_private_impl__high_prec_dec* h,
+                                          uint64_t x,
+                                          bool negative) {
+  uint32_t n = 0;
+
+  // Set h->digits.
+  if (x > 0) {
+    // Calculate the digits, working right-to-left. After we determine n (how
+    // many digits there are), copy from buf to h->digits.
+    //
+    // UINT64_MAX, 18446744073709551615, is 20 digits long. It can be faster to
+    // copy a constant number of bytes than a variable number (20 instead of
+    // n). Make buf large enough (and start writing to it from the middle) so
+    // that can we always copy 20 bytes: the slice buf[(20-n) .. (40-n)].
+    uint8_t buf[40] = {0};
+    uint8_t* ptr = &buf[20];
+    do {
+      uint64_t remaining = x / 10;
+      x -= remaining * 10;
+      ptr--;
+      *ptr = (uint8_t)x;
+      n++;
+      x = remaining;
+    } while (x > 0);
+    memcpy(h->digits, ptr, 20);
+  }
+
+  // Set h's other fields.
+  h->num_digits = n;
+  h->decimal_point = (int32_t)n;
+  h->negative = negative;
+  h->truncated = false;
+  wuffs_private_impl__high_prec_dec__trim(h);
+}
+
+static wuffs_base__status  //
+wuffs_private_impl__high_prec_dec__parse(wuffs_private_impl__high_prec_dec* h,
+                                         wuffs_base__slice_u8 s,
+                                         uint32_t options) {
+  if (!h) {
+    return wuffs_base__make_status(wuffs_base__error__bad_receiver);
+  }
+  h->num_digits = 0;
+  h->decimal_point = 0;
+  h->negative = false;
+  h->truncated = false;
+
+  uint8_t* p = s.ptr;
+  uint8_t* q = s.ptr + s.len;
+
+  if (options & WUFFS_BASE__PARSE_NUMBER_XXX__ALLOW_UNDERSCORES) {
+    for (;; p++) {
+      if (p >= q) {
+        return wuffs_base__make_status(wuffs_base__error__bad_argument);
+      } else if (*p != '_') {
+        break;
+      }
+    }
+  }
+
+  // Parse sign.
+  do {
+    if (*p == '+') {
+      p++;
+    } else if (*p == '-') {
+      h->negative = true;
+      p++;
+    } else {
+      break;
+    }
+    if (options & WUFFS_BASE__PARSE_NUMBER_XXX__ALLOW_UNDERSCORES) {
+      for (;; p++) {
+        if (p >= q) {
+          return wuffs_base__make_status(wuffs_base__error__bad_argument);
+        } else if (*p != '_') {
+          break;
+        }
+      }
+    }
+  } while (0);
+
+  // Parse digits, up to (and including) a '.', 'E' or 'e'. Examples for each
+  // limb in this if-else chain:
+  //  - "0.789"
+  //  - "1002.789"
+  //  - ".789"
+  //  - Other (invalid input).
+  uint32_t nd = 0;
+  int32_t dp = 0;
+  bool no_digits_before_separator = false;
+  if (('0' == *p) &&
+      !(options &
+        WUFFS_BASE__PARSE_NUMBER_XXX__ALLOW_MULTIPLE_LEADING_ZEROES)) {
+    p++;
+    for (;; p++) {
+      if (p >= q) {
+        goto after_all;
+      } else if (*p ==
+                 ((options &
+                   WUFFS_BASE__PARSE_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA)
+                      ? ','
+                      : '.')) {
+        p++;
+        goto after_sep;
+      } else if ((*p == 'E') || (*p == 'e')) {
+        p++;
+        goto after_exp;
+      } else if ((*p != '_') ||
+                 !(options & WUFFS_BASE__PARSE_NUMBER_XXX__ALLOW_UNDERSCORES)) {
+        return wuffs_base__make_status(wuffs_base__error__bad_argument);
+      }
+    }
+
+  } else if (('0' <= *p) && (*p <= '9')) {
+    if (*p == '0') {
+      for (; (p < q) && (*p == '0'); p++) {
+      }
+    } else {
+      h->digits[nd++] = (uint8_t)(*p - '0');
+      dp = (int32_t)nd;
+      p++;
+    }
+
+    for (;; p++) {
+      if (p >= q) {
+        goto after_all;
+      } else if (('0' <= *p) && (*p <= '9')) {
+        if (nd < WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION) {
+          h->digits[nd++] = (uint8_t)(*p - '0');
+          dp = (int32_t)nd;
+        } else if ('0' != *p) {
+          // Long-tail non-zeroes set the truncated bit.
+          h->truncated = true;
+        }
+      } else if (*p ==
+                 ((options &
+                   WUFFS_BASE__PARSE_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA)
+                      ? ','
+                      : '.')) {
+        p++;
+        goto after_sep;
+      } else if ((*p == 'E') || (*p == 'e')) {
+        p++;
+        goto after_exp;
+      } else if ((*p != '_') ||
+                 !(options & WUFFS_BASE__PARSE_NUMBER_XXX__ALLOW_UNDERSCORES)) {
+        return wuffs_base__make_status(wuffs_base__error__bad_argument);
+      }
+    }
+
+  } else if (*p == ((options &
+                     WUFFS_BASE__PARSE_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA)
+                        ? ','
+                        : '.')) {
+    p++;
+    no_digits_before_separator = true;
+
+  } else {
+    return wuffs_base__make_status(wuffs_base__error__bad_argument);
+  }
+
+after_sep:
+  for (;; p++) {
+    if (p >= q) {
+      goto after_all;
+    } else if ('0' == *p) {
+      if (nd == 0) {
+        // Track leading zeroes implicitly.
+        dp--;
+      } else if (nd < WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION) {
+        h->digits[nd++] = (uint8_t)(*p - '0');
+      }
+    } else if (('0' < *p) && (*p <= '9')) {
+      if (nd < WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION) {
+        h->digits[nd++] = (uint8_t)(*p - '0');
+      } else {
+        // Long-tail non-zeroes set the truncated bit.
+        h->truncated = true;
+      }
+    } else if ((*p == 'E') || (*p == 'e')) {
+      p++;
+      goto after_exp;
+    } else if ((*p != '_') ||
+               !(options & WUFFS_BASE__PARSE_NUMBER_XXX__ALLOW_UNDERSCORES)) {
+      return wuffs_base__make_status(wuffs_base__error__bad_argument);
+    }
+  }
+
+after_exp:
+  do {
+    if (options & WUFFS_BASE__PARSE_NUMBER_XXX__ALLOW_UNDERSCORES) {
+      for (;; p++) {
+        if (p >= q) {
+          return wuffs_base__make_status(wuffs_base__error__bad_argument);
+        } else if (*p != '_') {
+          break;
+        }
+      }
+    }
+
+    int32_t exp_sign = +1;
+    if (*p == '+') {
+      p++;
+    } else if (*p == '-') {
+      exp_sign = -1;
+      p++;
+    }
+
+    int32_t exp = 0;
+    const int32_t exp_large = WUFFS_PRIVATE_IMPL__HPD__DECIMAL_POINT__RANGE +
+                              WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION;
+    bool saw_exp_digits = false;
+    for (; p < q; p++) {
+      if ((*p == '_') &&
+          (options & WUFFS_BASE__PARSE_NUMBER_XXX__ALLOW_UNDERSCORES)) {
+        // No-op.
+      } else if (('0' <= *p) && (*p <= '9')) {
+        saw_exp_digits = true;
+        if (exp < exp_large) {
+          exp = (10 * exp) + ((int32_t)(*p - '0'));
+        }
+      } else {
+        break;
+      }
+    }
+    if (!saw_exp_digits) {
+      return wuffs_base__make_status(wuffs_base__error__bad_argument);
+    }
+    dp += exp_sign * exp;
+  } while (0);
+
+after_all:
+  if (p != q) {
+    return wuffs_base__make_status(wuffs_base__error__bad_argument);
+  }
+  h->num_digits = nd;
+  if (nd == 0) {
+    if (no_digits_before_separator) {
+      return wuffs_base__make_status(wuffs_base__error__bad_argument);
+    }
+    h->decimal_point = 0;
+  } else if (dp < -WUFFS_PRIVATE_IMPL__HPD__DECIMAL_POINT__RANGE) {
+    h->decimal_point = -WUFFS_PRIVATE_IMPL__HPD__DECIMAL_POINT__RANGE - 1;
+  } else if (dp > +WUFFS_PRIVATE_IMPL__HPD__DECIMAL_POINT__RANGE) {
+    h->decimal_point = +WUFFS_PRIVATE_IMPL__HPD__DECIMAL_POINT__RANGE + 1;
+  } else {
+    h->decimal_point = dp;
+  }
+  wuffs_private_impl__high_prec_dec__trim(h);
+  return wuffs_base__make_status(NULL);
+}
+
+// --------
+
+// wuffs_private_impl__high_prec_dec__lshift_num_new_digits returns the number
+// of additional decimal digits when left-shifting by shift.
+//
+// See below for preconditions.
+static uint32_t  //
+wuffs_private_impl__high_prec_dec__lshift_num_new_digits(
+    wuffs_private_impl__high_prec_dec* h,
+    uint32_t shift) {
+  // Masking with 0x3F should be unnecessary (assuming the preconditions) but
+  // it's cheap and ensures that we don't overflow the
+  // wuffs_private_impl__hpd_left_shift array.
+  shift &= 63;
+
+  uint32_t x_a = wuffs_private_impl__hpd_left_shift[shift];
+  uint32_t x_b = wuffs_private_impl__hpd_left_shift[shift + 1];
+  uint32_t num_new_digits = x_a >> 11;
+  uint32_t pow5_a = 0x7FF & x_a;
+  uint32_t pow5_b = 0x7FF & x_b;
+
+  const uint8_t* pow5 = &wuffs_private_impl__powers_of_5[pow5_a];
+  uint32_t i = 0;
+  uint32_t n = pow5_b - pow5_a;
+  for (; i < n; i++) {
+    if (i >= h->num_digits) {
+      return num_new_digits - 1;
+    } else if (h->digits[i] == pow5[i]) {
+      continue;
+    } else if (h->digits[i] < pow5[i]) {
+      return num_new_digits - 1;
+    } else {
+      return num_new_digits;
+    }
+  }
+  return num_new_digits;
+}
+
+// --------
+
+// wuffs_private_impl__high_prec_dec__rounded_integer returns the integral
+// (non-fractional) part of h, provided that it is 18 or fewer decimal digits.
+// For 19 or more digits, it returns UINT64_MAX. Note that:
+//  - (1 << 53) is    9007199254740992, which has 16 decimal digits.
+//  - (1 << 56) is   72057594037927936, which has 17 decimal digits.
+//  - (1 << 59) is  576460752303423488, which has 18 decimal digits.
+//  - (1 << 63) is 9223372036854775808, which has 19 decimal digits.
+// and that IEEE 754 double precision has 52 mantissa bits.
+//
+// That integral part is rounded-to-even: rounding 7.5 or 8.5 both give 8.
+//
+// h's negative bit is ignored: rounding -8.6 returns 9.
+//
+// See below for preconditions.
+static uint64_t  //
+wuffs_private_impl__high_prec_dec__rounded_integer(
+    wuffs_private_impl__high_prec_dec* h) {
+  if ((h->num_digits == 0) || (h->decimal_point < 0)) {
+    return 0;
+  } else if (h->decimal_point > 18) {
+    return UINT64_MAX;
+  }
+
+  uint32_t dp = (uint32_t)(h->decimal_point);
+  uint64_t n = 0;
+  uint32_t i = 0;
+  for (; i < dp; i++) {
+    n = (10 * n) + ((i < h->num_digits) ? h->digits[i] : 0);
+  }
+
+  bool round_up = false;
+  if (dp < h->num_digits) {
+    round_up = h->digits[dp] >= 5;
+    if ((h->digits[dp] == 5) && (dp + 1 == h->num_digits)) {
+      // We are exactly halfway. If we're truncated, round up, otherwise round
+      // to even.
+      round_up = h->truncated ||  //
+                 ((dp > 0) && (1 & h->digits[dp - 1]));
+    }
+  }
+  if (round_up) {
+    n++;
+  }
+
+  return n;
+}
+
+// wuffs_private_impl__high_prec_dec__small_xshift shifts h's number (where 'x'
+// is 'l' or 'r' for left or right) by a small shift value.
+//
+// Preconditions:
+//  - h is non-NULL.
+//  - h->decimal_point is "not extreme".
+//  - shift is non-zero.
+//  - shift is "a small shift".
+//
+// "Not extreme" means within ±WUFFS_PRIVATE_IMPL__HPD__DECIMAL_POINT__RANGE.
+//
+// "A small shift" means not more than
+// WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL.
+//
+// wuffs_private_impl__high_prec_dec__rounded_integer and
+// wuffs_private_impl__high_prec_dec__lshift_num_new_digits have the same
+// preconditions.
+//
+// wuffs_private_impl__high_prec_dec__lshift keeps the first two preconditions
+// but not the last two. Its shift argument is signed and does not need to be
+// "small": zero is a no-op, positive means left shift and negative means right
+// shift.
+
+static void  //
+wuffs_private_impl__high_prec_dec__small_lshift(
+    wuffs_private_impl__high_prec_dec* h,
+    uint32_t shift) {
+  if (h->num_digits == 0) {
+    return;
+  }
+  uint32_t num_new_digits =
+      wuffs_private_impl__high_prec_dec__lshift_num_new_digits(h, shift);
+  uint32_t rx = h->num_digits - 1;                   // Read  index.
+  uint32_t wx = h->num_digits - 1 + num_new_digits;  // Write index.
+  uint64_t n = 0;
+
+  // Repeat: pick up a digit, put down a digit, right to left.
+  while (((int32_t)rx) >= 0) {
+    n += ((uint64_t)(h->digits[rx])) << shift;
+    uint64_t quo = n / 10;
+    uint64_t rem = n - (10 * quo);
+    if (wx < WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION) {
+      h->digits[wx] = (uint8_t)rem;
+    } else if (rem > 0) {
+      h->truncated = true;
+    }
+    n = quo;
+    wx--;
+    rx--;
+  }
+
+  // Put down leading digits, right to left.
+  while (n > 0) {
+    uint64_t quo = n / 10;
+    uint64_t rem = n - (10 * quo);
+    if (wx < WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION) {
+      h->digits[wx] = (uint8_t)rem;
+    } else if (rem > 0) {
+      h->truncated = true;
+    }
+    n = quo;
+    wx--;
+  }
+
+  // Finish.
+  h->num_digits += num_new_digits;
+  if (h->num_digits > WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION) {
+    h->num_digits = WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION;
+  }
+  h->decimal_point += (int32_t)num_new_digits;
+  wuffs_private_impl__high_prec_dec__trim(h);
+}
+
+static void  //
+wuffs_private_impl__high_prec_dec__small_rshift(
+    wuffs_private_impl__high_prec_dec* h,
+    uint32_t shift) {
+  uint32_t rx = 0;  // Read  index.
+  uint32_t wx = 0;  // Write index.
+  uint64_t n = 0;
+
+  // Pick up enough leading digits to cover the first shift.
+  while ((n >> shift) == 0) {
+    if (rx < h->num_digits) {
+      // Read a digit.
+      n = (10 * n) + h->digits[rx++];
+    } else if (n == 0) {
+      // h's number used to be zero and remains zero.
+      return;
+    } else {
+      // Read sufficient implicit trailing zeroes.
+      while ((n >> shift) == 0) {
+        n = 10 * n;
+        rx++;
+      }
+      break;
+    }
+  }
+  h->decimal_point -= ((int32_t)(rx - 1));
+  if (h->decimal_point < -WUFFS_PRIVATE_IMPL__HPD__DECIMAL_POINT__RANGE) {
+    // After the shift, h's number is effectively zero.
+    h->num_digits = 0;
+    h->decimal_point = 0;
+    h->truncated = false;
+    return;
+  }
+
+  // Repeat: pick up a digit, put down a digit, left to right.
+  uint64_t mask = (((uint64_t)(1)) << shift) - 1;
+  while (rx < h->num_digits) {
+    uint8_t new_digit = ((uint8_t)(n >> shift));
+    n = (10 * (n & mask)) + h->digits[rx++];
+    h->digits[wx++] = new_digit;
+  }
+
+  // Put down trailing digits, left to right.
+  while (n > 0) {
+    uint8_t new_digit = ((uint8_t)(n >> shift));
+    n = 10 * (n & mask);
+    if (wx < WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION) {
+      h->digits[wx++] = new_digit;
+    } else if (new_digit > 0) {
+      h->truncated = true;
+    }
+  }
+
+  // Finish.
+  h->num_digits = wx;
+  wuffs_private_impl__high_prec_dec__trim(h);
+}
+
+static void  //
+wuffs_private_impl__high_prec_dec__lshift(wuffs_private_impl__high_prec_dec* h,
+                                          int32_t shift) {
+  if (shift > 0) {
+    while (shift > +WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL) {
+      wuffs_private_impl__high_prec_dec__small_lshift(
+          h, WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL);
+      shift -= WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL;
+    }
+    wuffs_private_impl__high_prec_dec__small_lshift(h, ((uint32_t)(+shift)));
+  } else if (shift < 0) {
+    while (shift < -WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL) {
+      wuffs_private_impl__high_prec_dec__small_rshift(
+          h, WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL);
+      shift += WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL;
+    }
+    wuffs_private_impl__high_prec_dec__small_rshift(h, ((uint32_t)(-shift)));
+  }
+}
+
+// --------
+
+// wuffs_private_impl__high_prec_dec__round_etc rounds h's number. For those
+// functions that take an n argument, rounding produces at most n digits (which
+// is not necessarily at most n decimal places). Negative n values are ignored,
+// as well as any n greater than or equal to h's number of digits. The
+// etc__round_just_enough function implicitly chooses an n to implement
+// WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION.
+//
+// Preconditions:
+//  - h is non-NULL.
+//  - h->decimal_point is "not extreme".
+//
+// "Not extreme" means within ±WUFFS_PRIVATE_IMPL__HPD__DECIMAL_POINT__RANGE.
+
+static void  //
+wuffs_private_impl__high_prec_dec__round_down(
+    wuffs_private_impl__high_prec_dec* h,
+    int32_t n) {
+  if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
+    return;
+  }
+  h->num_digits = (uint32_t)(n);
+  wuffs_private_impl__high_prec_dec__trim(h);
+}
+
+static void  //
+wuffs_private_impl__high_prec_dec__round_up(
+    wuffs_private_impl__high_prec_dec* h,
+    int32_t n) {
+  if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
+    return;
+  }
+
+  for (n--; n >= 0; n--) {
+    if (h->digits[n] < 9) {
+      h->digits[n]++;
+      h->num_digits = (uint32_t)(n + 1);
+      return;
+    }
+  }
+
+  // The number is all 9s. Change to a single 1 and adjust the decimal point.
+  h->digits[0] = 1;
+  h->num_digits = 1;
+  h->decimal_point++;
+}
+
+static void  //
+wuffs_private_impl__high_prec_dec__round_nearest(
+    wuffs_private_impl__high_prec_dec* h,
+    int32_t n) {
+  if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
+    return;
+  }
+  bool up = h->digits[n] >= 5;
+  if ((h->digits[n] == 5) && ((n + 1) == ((int32_t)(h->num_digits)))) {
+    up = h->truncated ||  //
+         ((n > 0) && ((h->digits[n - 1] & 1) != 0));
+  }
+
+  if (up) {
+    wuffs_private_impl__high_prec_dec__round_up(h, n);
+  } else {
+    wuffs_private_impl__high_prec_dec__round_down(h, n);
+  }
+}
+
+static void  //
+wuffs_private_impl__high_prec_dec__round_just_enough(
+    wuffs_private_impl__high_prec_dec* h,
+    int32_t exp2,
+    uint64_t mantissa) {
+  // The magic numbers 52 and 53 in this function are because IEEE 754 double
+  // precision has 52 mantissa bits.
+  //
+  // Let f be the floating point number represented by exp2 and mantissa (and
+  // also the number in h): the number (mantissa * (2 ** (exp2 - 52))).
+  //
+  // If f is zero or a small integer, we can return early.
+  if ((mantissa == 0) ||
+      ((exp2 < 53) && (h->decimal_point >= ((int32_t)(h->num_digits))))) {
+    return;
+  }
+
+  // The smallest normal f has an exp2 of -1022 and a mantissa of (1 << 52).
+  // Subnormal numbers have the same exp2 but a smaller mantissa.
+  static const int32_t min_incl_normal_exp2 = -1022;
+  static const uint64_t min_incl_normal_mantissa = 0x0010000000000000ul;
+
+  // Compute lower and upper bounds such that any number between them (possibly
+  // inclusive) will round to f. First, the lower bound. Our number f is:
+  //   ((mantissa + 0)         * (2 ** (  exp2 - 52)))
+  //
+  // The next lowest floating point number is:
+  //   ((mantissa - 1)         * (2 ** (  exp2 - 52)))
+  // unless (mantissa - 1) drops the (1 << 52) bit and exp2 is not the
+  // min_incl_normal_exp2. Either way, call it:
+  //   ((l_mantissa)           * (2 ** (l_exp2 - 52)))
+  //
+  // The lower bound is halfway between them (noting that 52 became 53):
+  //   (((2 * l_mantissa) + 1) * (2 ** (l_exp2 - 53)))
+  int32_t l_exp2 = exp2;
+  uint64_t l_mantissa = mantissa - 1;
+  if ((exp2 > min_incl_normal_exp2) && (mantissa <= min_incl_normal_mantissa)) {
+    l_exp2 = exp2 - 1;
+    l_mantissa = (2 * mantissa) - 1;
+  }
+  wuffs_private_impl__high_prec_dec lower;
+  wuffs_private_impl__high_prec_dec__assign(&lower, (2 * l_mantissa) + 1,
+                                            false);
+  wuffs_private_impl__high_prec_dec__lshift(&lower, l_exp2 - 53);
+
+  // Next, the upper bound. Our number f is:
+  //   ((mantissa + 0)       * (2 ** (exp2 - 52)))
+  //
+  // The next highest floating point number is:
+  //   ((mantissa + 1)       * (2 ** (exp2 - 52)))
+  //
+  // The upper bound is halfway between them (noting that 52 became 53):
+  //   (((2 * mantissa) + 1) * (2 ** (exp2 - 53)))
+  wuffs_private_impl__high_prec_dec upper;
+  wuffs_private_impl__high_prec_dec__assign(&upper, (2 * mantissa) + 1, false);
+  wuffs_private_impl__high_prec_dec__lshift(&upper, exp2 - 53);
+
+  // The lower and upper bounds are possible outputs only if the original
+  // mantissa is even, so that IEEE round-to-even would round to the original
+  // mantissa and not its neighbors.
+  bool inclusive = (mantissa & 1) == 0;
+
+  // As we walk the digits, we want to know whether rounding up would fall
+  // within the upper bound. This is tracked by upper_delta:
+  //  - When -1, the digits of h and upper are the same so far.
+  //  - When +0, we saw a difference of 1 between h and upper on a previous
+  //    digit and subsequently only 9s for h and 0s for upper. Thus, rounding
+  //    up may fall outside of the bound if !inclusive.
+  //  - When +1, the difference is greater than 1 and we know that rounding up
+  //    falls within the bound.
+  //
+  // This is a state machine with three states. The numerical value for each
+  // state (-1, +0 or +1) isn't important, other than their order.
+  int upper_delta = -1;
+
+  // We can now figure out the shortest number of digits required. Walk the
+  // digits until h has distinguished itself from lower or upper.
+  //
+  // The zi and zd variables are indexes and digits, for z in l (lower), h (the
+  // number) and u (upper).
+  //
+  // The lower, h and upper numbers may have their decimal points at different
+  // places. In this case, upper is the longest, so we iterate ui starting from
+  // 0 and iterate li and hi starting from either 0 or -1.
+  int32_t ui = 0;
+  for (;; ui++) {
+    // Calculate hd, the middle number's digit.
+    int32_t hi = ui - upper.decimal_point + h->decimal_point;
+    if (hi >= ((int32_t)(h->num_digits))) {
+      break;
+    }
+    uint8_t hd = (((uint32_t)hi) < h->num_digits) ? h->digits[hi] : 0;
+
+    // Calculate ld, the lower bound's digit.
+    int32_t li = ui - upper.decimal_point + lower.decimal_point;
+    uint8_t ld = (((uint32_t)li) < lower.num_digits) ? lower.digits[li] : 0;
+
+    // We can round down (truncate) if lower has a different digit than h or if
+    // lower is inclusive and is exactly the result of rounding down (i.e. we
+    // have reached the final digit of lower).
+    bool can_round_down =
+        (ld != hd) ||  //
+        (inclusive && ((li + 1) == ((int32_t)(lower.num_digits))));
+
+    // Calculate ud, the upper bound's digit, and update upper_delta.
+    uint8_t ud = (((uint32_t)ui) < upper.num_digits) ? upper.digits[ui] : 0;
+    if (upper_delta < 0) {
+      if ((hd + 1) < ud) {
+        // For example:
+        // h     = 12345???
+        // upper = 12347???
+        upper_delta = +1;
+      } else if (hd != ud) {
+        // For example:
+        // h     = 12345???
+        // upper = 12346???
+        upper_delta = +0;
+      }
+    } else if (upper_delta == 0) {
+      if ((hd != 9) || (ud != 0)) {
+        // For example:
+        // h     = 1234598?
+        // upper = 1234600?
+        upper_delta = +1;
+      }
+    }
+
+    // We can round up if upper has a different digit than h and either upper
+    // is inclusive or upper is bigger than the result of rounding up.
+    bool can_round_up =
+        (upper_delta > 0) ||    //
+        ((upper_delta == 0) &&  //
+         (inclusive || ((ui + 1) < ((int32_t)(upper.num_digits)))));
+
+    // If we can round either way, round to nearest. If we can round only one
+    // way, do it. If we can't round, continue the loop.
+    if (can_round_down) {
+      if (can_round_up) {
+        wuffs_private_impl__high_prec_dec__round_nearest(h, hi + 1);
+        return;
+      } else {
+        wuffs_private_impl__high_prec_dec__round_down(h, hi + 1);
+        return;
+      }
+    } else {
+      if (can_round_up) {
+        wuffs_private_impl__high_prec_dec__round_up(h, hi + 1);
+        return;
+      }
+    }
+  }
+}
+
+// --------
+
+// wuffs_private_impl__parse_number_f64_eisel_lemire produces the IEEE 754
+// double-precision value for an exact mantissa and base-10 exponent. For
+// example:
+//  - when parsing "12345.678e+02", man is 12345678 and exp10 is -1.
+//  - when parsing "-12", man is 12 and exp10 is 0. Processing the leading
+//    minus sign is the responsibility of the caller, not this function.
+//
+// On success, it returns a non-negative int64_t such that the low 63 bits hold
+// the 11-bit exponent and 52-bit mantissa.
+//
+// On failure, it returns a negative value.
+//
+// The algorithm is based on an original idea by Michael Eisel that was refined
+// by Daniel Lemire. See
+// https://lemire.me/blog/2020/03/10/fast-float-parsing-in-practice/
+// and
+// https://nigeltao.github.io/blog/2020/eisel-lemire.html
+//
+// Preconditions:
+//  - man is non-zero.
+//  - exp10 is in the range [-307 ..= 288], the same range of the
+//    wuffs_private_impl__powers_of_10 array.
+//
+// The exp10 range (and the fact that man is in the range [1 ..= UINT64_MAX],
+// approximately [1 ..= 1.85e+19]) means that (man * (10 ** exp10)) is in the
+// range [1e-307 ..= 1.85e+307]. This is entirely within the range of normal
+// (neither subnormal nor non-finite) f64 values: DBL_MIN and DBL_MAX are
+// approximately 2.23e–308 and 1.80e+308.
+static int64_t  //
+wuffs_private_impl__parse_number_f64_eisel_lemire(uint64_t man, int32_t exp10) {
+  // Look up the (possibly truncated) base-2 representation of (10 ** exp10).
+  // The look-up table was constructed so that it is already normalized: the
+  // table entry's mantissa's MSB (most significant bit) is on.
+  const uint64_t* po10 = &wuffs_private_impl__powers_of_10[exp10 + 307][0];
+
+  // Normalize the man argument. The (man != 0) precondition means that a
+  // non-zero bit exists.
+  uint32_t clz = wuffs_base__count_leading_zeroes_u64(man);
+  man <<= clz;
+
+  // Calculate the return value's base-2 exponent. We might tweak it by ±1
+  // later, but its initial value comes from a linear scaling of exp10,
+  // converting from power-of-10 to power-of-2, and adjusting by clz.
+  //
+  // The magic constants are:
+  //  - 1087 = 1023 + 64. The 1023 is the f64 exponent bias. The 64 is because
+  //    the look-up table uses 64-bit mantissas.
+  //  - 217706 is such that the ratio 217706 / 65536 ≈ 3.321930 is close enough
+  //    (over the practical range of exp10) to log(10) / log(2) ≈ 3.321928.
+  //  - 65536 = 1<<16 is arbitrary but a power of 2, so division is a shift.
+  //
+  // Equality of the linearly-scaled value and the actual power-of-2, over the
+  // range of exp10 arguments that this function accepts, is confirmed by
+  // script/print-mpb-powers-of-10.go
+  uint64_t ret_exp2 =
+      ((uint64_t)(((217706 * exp10) >> 16) + 1087)) - ((uint64_t)clz);
+
+  // Multiply the two mantissas. Normalization means that both mantissas are at
+  // least (1<<63), so the 128-bit product must be at least (1<<126). The high
+  // 64 bits of the product, x_hi, must therefore be at least (1<<62).
+  //
+  // As a consequence, x_hi has either 0 or 1 leading zeroes. Shifting x_hi
+  // right by either 9 or 10 bits (depending on x_hi's MSB) will therefore
+  // leave the top 10 MSBs (bits 54 ..= 63) off and the 11th MSB (bit 53) on.
+  wuffs_base__multiply_u64__output x = wuffs_base__multiply_u64(man, po10[1]);
+  uint64_t x_hi = x.hi;
+  uint64_t x_lo = x.lo;
+
+  // Before we shift right by at least 9 bits, recall that the look-up table
+  // entry was possibly truncated. We have so far only calculated a lower bound
+  // for the product (man * e), where e is (10 ** exp10). The upper bound would
+  // add a further (man * 1) to the 128-bit product, which overflows the lower
+  // 64-bit limb if ((x_lo + man) < man).
+  //
+  // If overflow occurs, that adds 1 to x_hi. Since we're about to shift right
+  // by at least 9 bits, that carried 1 can be ignored unless the higher 64-bit
+  // limb's low 9 bits are all on.
+  //
+  // For example, parsing "9999999999999999999" will take the if-true branch
+  // here, since:
+  //  - x_hi = 0x4563918244F3FFFF
+  //  - x_lo = 0x8000000000000000
+  //  - man  = 0x8AC7230489E7FFFF
+  if (((x_hi & 0x1FF) == 0x1FF) && ((x_lo + man) < man)) {
+    // Refine our calculation of (man * e). Before, our approximation of e used
+    // a "low resolution" 64-bit mantissa. Now use a "high resolution" 128-bit
+    // mantissa. We've already calculated x = (man * bits_0_to_63_incl_of_e).
+    // Now calculate y = (man * bits_64_to_127_incl_of_e).
+    wuffs_base__multiply_u64__output y = wuffs_base__multiply_u64(man, po10[0]);
+    uint64_t y_hi = y.hi;
+    uint64_t y_lo = y.lo;
+
+    // Merge the 128-bit x and 128-bit y, which overlap by 64 bits, to
+    // calculate the 192-bit product of the 64-bit man by the 128-bit e.
+    // As we exit this if-block, we only care about the high 128 bits
+    // (merged_hi and merged_lo) of that 192-bit product.
+    //
+    // For example, parsing "1.234e-45" will take the if-true branch here,
+    // since:
+    //  - x_hi = 0x70B7E3696DB29FFF
+    //  - x_lo = 0xE040000000000000
+    //  - y_hi = 0x33718BBEAB0E0D7A
+    //  - y_lo = 0xA880000000000000
+    uint64_t merged_hi = x_hi;
+    uint64_t merged_lo = x_lo + y_hi;
+    if (merged_lo < x_lo) {
+      merged_hi++;  // Carry the overflow bit.
+    }
+
+    // The "high resolution" approximation of e is still a lower bound. Once
+    // again, see if the upper bound is large enough to produce a different
+    // result. This time, if it does, give up instead of reaching for an even
+    // more precise approximation to e.
+    //
+    // This three-part check is similar to the two-part check that guarded the
+    // if block that we're now in, but it has an extra term for the middle 64
+    // bits (checking that adding 1 to merged_lo would overflow).
+    //
+    // For example, parsing "5.9604644775390625e-8" will take the if-true
+    // branch here, since:
+    //  - merged_hi = 0x7FFFFFFFFFFFFFFF
+    //  - merged_lo = 0xFFFFFFFFFFFFFFFF
+    //  - y_lo      = 0x4DB3FFC120988200
+    //  - man       = 0xD3C21BCECCEDA100
+    if (((merged_hi & 0x1FF) == 0x1FF) && ((merged_lo + 1) == 0) &&
+        (y_lo + man < man)) {
+      return -1;
+    }
+
+    // Replace the 128-bit x with merged.
+    x_hi = merged_hi;
+    x_lo = merged_lo;
+  }
+
+  // As mentioned above, shifting x_hi right by either 9 or 10 bits will leave
+  // the top 10 MSBs (bits 54 ..= 63) off and the 11th MSB (bit 53) on. If the
+  // MSB (before shifting) was on, adjust ret_exp2 for the larger shift.
+  //
+  // Having bit 53 on (and higher bits off) means that ret_mantissa is a 54-bit
+  // number.
+  uint64_t msb = x_hi >> 63;
+  uint64_t ret_mantissa = x_hi >> (msb + 9);
+  ret_exp2 -= 1 ^ msb;
+
+  // IEEE 754 rounds to-nearest with ties rounded to-even. Rounding to-even can
+  // be tricky. If we're half-way between two exactly representable numbers
+  // (x's low 73 bits are zero and the next 2 bits that matter are "01"), give
+  // up instead of trying to pick the winner.
+  //
+  // Technically, we could tighten the condition by changing "73" to "73 or 74,
+  // depending on msb", but a flat "73" is simpler.
+  //
+  // For example, parsing "1e+23" will take the if-true branch here, since:
+  //  - x_hi          = 0x54B40B1F852BDA00
+  //  - ret_mantissa  = 0x002A5A058FC295ED
+  if ((x_lo == 0) && ((x_hi & 0x1FF) == 0) && ((ret_mantissa & 3) == 1)) {
+    return -1;
+  }
+
+  // If we're not halfway then it's rounding to-nearest. Starting with a 54-bit
+  // number, carry the lowest bit (bit 0) up if it's on. Regardless of whether
+  // it was on or off, shifting right by one then produces a 53-bit number. If
+  // carrying up overflowed, shift again.
+  ret_mantissa += ret_mantissa & 1;
+  ret_mantissa >>= 1;
+  // This if block is equivalent to (but benchmarks slightly faster than) the
+  // following branchless form:
+  //    uint64_t overflow_adjustment = ret_mantissa >> 53;
+  //    ret_mantissa >>= overflow_adjustment;
+  //    ret_exp2 += overflow_adjustment;
+  //
+  // For example, parsing "7.2057594037927933e+16" will take the if-true
+  // branch here, since:
+  //  - x_hi          = 0x7FFFFFFFFFFFFE80
+  //  - ret_mantissa  = 0x0020000000000000
+  if ((ret_mantissa >> 53) > 0) {
+    ret_mantissa >>= 1;
+    ret_exp2++;
+  }
+
+  // Starting with a 53-bit number, IEEE 754 double-precision normal numbers
+  // have an implicit mantissa bit. Mask that away and keep the low 52 bits.
+  ret_mantissa &= 0x000FFFFFFFFFFFFF;
+
+  // Pack the bits and return.
+  return ((int64_t)(ret_mantissa | (ret_exp2 << 52)));
+}
+
+// --------
+
+static wuffs_base__result_f64  //
+wuffs_private_impl__parse_number_f64_special(wuffs_base__slice_u8 s,
+                                             uint32_t options) {
+  do {
+    if (options & WUFFS_BASE__PARSE_NUMBER_FXX__REJECT_INF_AND_NAN) {
+      goto fail;
+    }
+
+    uint8_t* p = s.ptr;
+    uint8_t* q = s.ptr + s.len;
+
+    for (; (p < q) && (*p == '_'); p++) {
+    }
+    if (p >= q) {
+      goto fail;
+    }
+
+    // Parse sign.
+    bool negative = false;
+    do {
+      if (*p == '+') {
+        p++;
+      } else if (*p == '-') {
+        negative = true;
+        p++;
+      } else {
+        break;
+      }
+      for (; (p < q) && (*p == '_'); p++) {
+      }
+    } while (0);
+    if (p >= q) {
+      goto fail;
+    }
+
+    bool nan = false;
+    switch (p[0]) {
+      case 'I':
+      case 'i':
+        if (((q - p) < 3) ||                     //
+            ((p[1] != 'N') && (p[1] != 'n')) ||  //
+            ((p[2] != 'F') && (p[2] != 'f'))) {
+          goto fail;
+        }
+        p += 3;
+
+        if ((p >= q) || (*p == '_')) {
+          break;
+        } else if (((q - p) < 5) ||                     //
+                   ((p[0] != 'I') && (p[0] != 'i')) ||  //
+                   ((p[1] != 'N') && (p[1] != 'n')) ||  //
+                   ((p[2] != 'I') && (p[2] != 'i')) ||  //
+                   ((p[3] != 'T') && (p[3] != 't')) ||  //
+                   ((p[4] != 'Y') && (p[4] != 'y'))) {
+          goto fail;
+        }
+        p += 5;
+
+        if ((p >= q) || (*p == '_')) {
+          break;
+        }
+        goto fail;
+
+      case 'N':
+      case 'n':
+        if (((q - p) < 3) ||                     //
+            ((p[1] != 'A') && (p[1] != 'a')) ||  //
+            ((p[2] != 'N') && (p[2] != 'n'))) {
+          goto fail;
+        }
+        p += 3;
+
+        if ((p >= q) || (*p == '_')) {
+          nan = true;
+          break;
+        }
+        goto fail;
+
+      default:
+        goto fail;
+    }
+
+    // Finish.
+    for (; (p < q) && (*p == '_'); p++) {
+    }
+    if (p != q) {
+      goto fail;
+    }
+    wuffs_base__result_f64 ret;
+    ret.status.repr = NULL;
+    ret.value = wuffs_base__ieee_754_bit_representation__from_u64_to_f64(
+        (nan ? 0x7FFFFFFFFFFFFFFF : 0x7FF0000000000000) |
+        (negative ? 0x8000000000000000 : 0));
+    return ret;
+  } while (0);
+
+fail:
+  do {
+    wuffs_base__result_f64 ret;
+    ret.status.repr = wuffs_base__error__bad_argument;
+    ret.value = 0;
+    return ret;
+  } while (0);
+}
+
+WUFFS_BASE__MAYBE_STATIC wuffs_base__result_f64  //
+wuffs_private_impl__high_prec_dec__to_f64(wuffs_private_impl__high_prec_dec* h,
+                                          uint32_t options) {
+  do {
+    // powers converts decimal powers of 10 to binary powers of 2. For example,
+    // (10000 >> 13) is 1. It stops before the elements exceed 60, also known
+    // as WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL.
+    //
+    // This rounds down (1<<13 is a lower bound for 1e4). Adding 1 to the array
+    // element value rounds up (1<<14 is an upper bound for 1e4) while staying
+    // at or below WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL.
+    //
+    // When starting in the range [1e+1 .. 1e+2] (i.e. h->decimal_point == +2),
+    // powers[2] == 6 and so:
+    //  - Right shifting by 6+0 produces the range [10/64 .. 100/64] =
+    //    [0.156250 .. 1.56250]. The resultant h->decimal_point is +0 or +1.
+    //  - Right shifting by 6+1 produces the range [10/128 .. 100/128] =
+    //    [0.078125 .. 0.78125]. The resultant h->decimal_point is -1 or -0.
+    //
+    // When starting in the range [1e-3 .. 1e-2] (i.e. h->decimal_point == -2),
+    // powers[2] == 6 and so:
+    //  - Left shifting by 6+0 produces the range [0.001*64 .. 0.01*64] =
+    //    [0.064 .. 0.64]. The resultant h->decimal_point is -1 or -0.
+    //  - Left shifting by 6+1 produces the range [0.001*128 .. 0.01*128] =
+    //    [0.128 .. 1.28]. The resultant h->decimal_point is +0 or +1.
+    //
+    // Thus, when targeting h->decimal_point being +0 or +1, use (powers[n]+0)
+    // when right shifting but (powers[n]+1) when left shifting.
+    static const uint32_t num_powers = 19;
+    static const uint8_t powers[19] = {
+        0,  3,  6,  9,  13, 16, 19, 23, 26, 29,  //
+        33, 36, 39, 43, 46, 49, 53, 56, 59,      //
+    };
+
+    // Handle zero and obvious extremes. The largest and smallest positive
+    // finite f64 values are approximately 1.8e+308 and 4.9e-324.
+    if ((h->num_digits == 0) || (h->decimal_point < -326)) {
+      goto zero;
+    } else if (h->decimal_point > 310) {
+      goto infinity;
+    }
+
+    // Try the fast Eisel-Lemire algorithm again. Calculating the (man, exp10)
+    // pair from the high_prec_dec h is more correct but slower than the
+    // approach taken in wuffs_base__parse_number_f64. The latter is optimized
+    // for the common cases (e.g. assuming no underscores or a leading '+'
+    // sign) rather than the full set of cases allowed by the Wuffs API.
+    //
+    // When we have 19 or fewer mantissa digits, run Eisel-Lemire once (trying
+    // for an exact result). When we have more than 19 mantissa digits, run it
+    // twice to get a lower and upper bound. We still have an exact result
+    // (within f64's rounding margin) if both bounds are equal (and valid).
+    uint32_t i_max = h->num_digits;
+    if (i_max > 19) {
+      i_max = 19;
+    }
+    int32_t exp10 = h->decimal_point - ((int32_t)i_max);
+    if ((-307 <= exp10) && (exp10 <= 288)) {
+      uint64_t man = 0;
+      uint32_t i;
+      for (i = 0; i < i_max; i++) {
+        man = (10 * man) + h->digits[i];
+      }
+      while (man != 0) {  // The 'while' is just an 'if' that we can 'break'.
+        int64_t r0 =
+            wuffs_private_impl__parse_number_f64_eisel_lemire(man + 0, exp10);
+        if (r0 < 0) {
+          break;
+        } else if (h->num_digits > 19) {
+          int64_t r1 =
+              wuffs_private_impl__parse_number_f64_eisel_lemire(man + 1, exp10);
+          if (r1 != r0) {
+            break;
+          }
+        }
+        wuffs_base__result_f64 ret;
+        ret.status.repr = NULL;
+        ret.value = wuffs_base__ieee_754_bit_representation__from_u64_to_f64(
+            ((uint64_t)r0) | (((uint64_t)(h->negative)) << 63));
+        return ret;
+      }
+    }
+
+    // When Eisel-Lemire fails, fall back to Simple Decimal Conversion. See
+    // https://nigeltao.github.io/blog/2020/parse-number-f64-simple.html
+    //
+    // Scale by powers of 2 until we're in the range [0.1 .. 10]. Equivalently,
+    // that h->decimal_point is +0 or +1.
+    //
+    // First we shift right while at or above 10...
+    const int32_t f64_bias = -1023;
+    int32_t exp2 = 0;
+    while (h->decimal_point > 1) {
+      uint32_t n = (uint32_t)(+h->decimal_point);
+      uint32_t shift = (n < num_powers)
+                           ? powers[n]
+                           : WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL;
+
+      wuffs_private_impl__high_prec_dec__small_rshift(h, shift);
+      if (h->decimal_point < -WUFFS_PRIVATE_IMPL__HPD__DECIMAL_POINT__RANGE) {
+        goto zero;
+      }
+      exp2 += (int32_t)shift;
+    }
+    // ...then we shift left while below 0.1.
+    while (h->decimal_point < 0) {
+      uint32_t shift;
+      uint32_t n = (uint32_t)(-h->decimal_point);
+      shift = (n < num_powers)
+                  // The +1 is per "when targeting h->decimal_point being +0 or
+                  // +1... when left shifting" in the powers comment above.
+                  ? (powers[n] + 1u)
+                  : WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL;
+
+      wuffs_private_impl__high_prec_dec__small_lshift(h, shift);
+      if (h->decimal_point > +WUFFS_PRIVATE_IMPL__HPD__DECIMAL_POINT__RANGE) {
+        goto infinity;
+      }
+      exp2 -= (int32_t)shift;
+    }
+
+    // To get from "in the range [0.1 .. 10]" to "in the range [1 .. 2]" (which
+    // will give us our exponent in base-2), the mantissa's first 3 digits will
+    // determine the final left shift, equal to 52 (the number of explicit f64
+    // bits) plus an additional adjustment.
+    int man3 = (100 * h->digits[0]) +
+               ((h->num_digits > 1) ? (10 * h->digits[1]) : 0) +
+               ((h->num_digits > 2) ? h->digits[2] : 0);
+    int32_t additional_lshift = 0;
+    if (h->decimal_point == 0) {  // The value is in [0.1 .. 1].
+      if (man3 < 125) {
+        additional_lshift = +4;
+      } else if (man3 < 250) {
+        additional_lshift = +3;
+      } else if (man3 < 500) {
+        additional_lshift = +2;
+      } else {
+        additional_lshift = +1;
+      }
+    } else {  // The value is in [1 .. 10].
+      if (man3 < 200) {
+        additional_lshift = -0;
+      } else if (man3 < 400) {
+        additional_lshift = -1;
+      } else if (man3 < 800) {
+        additional_lshift = -2;
+      } else {
+        additional_lshift = -3;
+      }
+    }
+    exp2 -= additional_lshift;
+    uint32_t final_lshift = (uint32_t)(52 + additional_lshift);
+
+    // The minimum normal exponent is (f64_bias + 1).
+    while ((f64_bias + 1) > exp2) {
+      uint32_t n = (uint32_t)((f64_bias + 1) - exp2);
+      if (n > WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL) {
+        n = WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL;
+      }
+      wuffs_private_impl__high_prec_dec__small_rshift(h, n);
+      exp2 += (int32_t)n;
+    }
+
+    // Check for overflow.
+    if ((exp2 - f64_bias) >= 0x07FF) {  // (1 << 11) - 1.
+      goto infinity;
+    }
+
+    // Extract 53 bits for the mantissa (in base-2).
+    wuffs_private_impl__high_prec_dec__small_lshift(h, final_lshift);
+    uint64_t man2 = wuffs_private_impl__high_prec_dec__rounded_integer(h);
+
+    // Rounding might have added one bit. If so, shift and re-check overflow.
+    if ((man2 >> 53) != 0) {
+      man2 >>= 1;
+      exp2++;
+      if ((exp2 - f64_bias) >= 0x07FF) {  // (1 << 11) - 1.
+        goto infinity;
+      }
+    }
+
+    // Handle subnormal numbers.
+    if ((man2 >> 52) == 0) {
+      exp2 = f64_bias;
+    }
+
+    // Pack the bits and return.
+    uint64_t exp2_bits =
+        (uint64_t)((exp2 - f64_bias) & 0x07FF);              // (1 << 11) - 1.
+    uint64_t bits = (man2 & 0x000FFFFFFFFFFFFF) |            // (1 << 52) - 1.
+                    (exp2_bits << 52) |                      //
+                    (h->negative ? 0x8000000000000000 : 0);  // (1 << 63).
+
+    wuffs_base__result_f64 ret;
+    ret.status.repr = NULL;
+    ret.value = wuffs_base__ieee_754_bit_representation__from_u64_to_f64(bits);
+    return ret;
+  } while (0);
+
+zero:
+  do {
+    uint64_t bits = h->negative ? 0x8000000000000000 : 0;
+
+    wuffs_base__result_f64 ret;
+    ret.status.repr = NULL;
+    ret.value = wuffs_base__ieee_754_bit_representation__from_u64_to_f64(bits);
+    return ret;
+  } while (0);
+
+infinity:
+  do {
+    if (options & WUFFS_BASE__PARSE_NUMBER_FXX__REJECT_INF_AND_NAN) {
+      wuffs_base__result_f64 ret;
+      ret.status.repr = wuffs_base__error__bad_argument;
+      ret.value = 0;
+      return ret;
+    }
+
+    uint64_t bits = h->negative ? 0xFFF0000000000000 : 0x7FF0000000000000;
+
+    wuffs_base__result_f64 ret;
+    ret.status.repr = NULL;
+    ret.value = wuffs_base__ieee_754_bit_representation__from_u64_to_f64(bits);
+    return ret;
+  } while (0);
+}
+
+static inline bool  //
+wuffs_private_impl__is_decimal_digit(uint8_t c) {
+  return ('0' <= c) && (c <= '9');
+}
+
+WUFFS_BASE__MAYBE_STATIC wuffs_base__result_f64  //
+wuffs_base__parse_number_f64(wuffs_base__slice_u8 s, uint32_t options) {
+  // In practice, almost all "dd.ddddE±xxx" numbers can be represented
+  // losslessly by a uint64_t mantissa "dddddd" and an int32_t base-10
+  // exponent, adjusting "xxx" for the position (if present) of the decimal
+  // separator '.' or ','.
+  //
+  // This (u64 man, i32 exp10) data structure is superficially similar to the
+  // "Do It Yourself Floating Point" type from Loitsch (†), but the exponent
+  // here is base-10, not base-2.
+  //
+  // If s's number fits in a (man, exp10), parse that pair with the
+  // Eisel-Lemire algorithm. If not, or if Eisel-Lemire fails, parsing s with
+  // the fallback algorithm is slower but comprehensive.
+  //
+  // † "Printing Floating-Point Numbers Quickly and Accurately with Integers"
+  // (https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf).
+  // Florian Loitsch is also the primary contributor to
+  // https://github.com/google/double-conversion
+  do {
+    // Calculating that (man, exp10) pair needs to stay within s's bounds.
+    // Provided that s isn't extremely long, work on a NUL-terminated copy of
+    // s's contents. The NUL byte isn't a valid part of "±dd.ddddE±xxx".
+    //
+    // As the pointer p walks the contents, it's faster to repeatedly check "is
+    // *p a valid digit" than "is p within bounds and *p a valid digit".
+    if (s.len >= 256) {
+      goto fallback;
+    }
+    uint8_t z[256];
+    memcpy(&z[0], s.ptr, s.len);
+    z[s.len] = 0;
+    const uint8_t* p = &z[0];
+
+    // Look for a leading minus sign. Technically, we could also look for an
+    // optional plus sign, but the "script/process-json-numbers.c with -p"
+    // benchmark is noticably slower if we do. It's optional and, in practice,
+    // usually absent. Let the fallback catch it.
+    bool negative = (*p == '-');
+    if (negative) {
+      p++;
+    }
+
+    // After walking "dd.dddd", comparing p later with p now will produce the
+    // number of "d"s and "."s.
+    const uint8_t* const start_of_digits_ptr = p;
+
+    // Walk the "d"s before a '.', 'E', NUL byte, etc. If it starts with '0',
+    // it must be a single '0'. If it starts with a non-zero decimal digit, it
+    // can be a sequence of decimal digits.
+    //
+    // Update the man variable during the walk. It's OK if man overflows now.
+    // We'll detect that later.
+    uint64_t man;
+    if (*p == '0') {
+      man = 0;
+      p++;
+      if (wuffs_private_impl__is_decimal_digit(*p)) {
+        goto fallback;
+      }
+    } else if (wuffs_private_impl__is_decimal_digit(*p)) {
+      man = ((uint8_t)(*p - '0'));
+      p++;
+      for (; wuffs_private_impl__is_decimal_digit(*p); p++) {
+        man = (10 * man) + ((uint8_t)(*p - '0'));
+      }
+    } else {
+      goto fallback;
+    }
+
+    // Walk the "d"s after the optional decimal separator ('.' or ','),
+    // updating the man and exp10 variables.
+    int32_t exp10 = 0;
+    if (*p ==
+        ((options & WUFFS_BASE__PARSE_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA)
+             ? ','
+             : '.')) {
+      p++;
+      const uint8_t* first_after_separator_ptr = p;
+      if (!wuffs_private_impl__is_decimal_digit(*p)) {
+        goto fallback;
+      }
+      man = (10 * man) + ((uint8_t)(*p - '0'));
+      p++;
+      for (; wuffs_private_impl__is_decimal_digit(*p); p++) {
+        man = (10 * man) + ((uint8_t)(*p - '0'));
+      }
+      exp10 = ((int32_t)(first_after_separator_ptr - p));
+    }
+
+    // Count the number of digits:
+    //  - for an input of "314159",  digit_count is 6.
+    //  - for an input of "3.14159", digit_count is 7.
+    //
+    // This is off-by-one if there is a decimal separator. That's OK for now.
+    // We'll correct for that later. The "script/process-json-numbers.c with
+    // -p" benchmark is noticably slower if we try to correct for that now.
+    uint32_t digit_count = (uint32_t)(p - start_of_digits_ptr);
+
+    // Update exp10 for the optional exponent, starting with 'E' or 'e'.
+    if ((*p | 0x20) == 'e') {
+      p++;
+      int32_t exp_sign = +1;
+      if (*p == '-') {
+        p++;
+        exp_sign = -1;
+      } else if (*p == '+') {
+        p++;
+      }
+      if (!wuffs_private_impl__is_decimal_digit(*p)) {
+        goto fallback;
+      }
+      int32_t exp_num = ((uint8_t)(*p - '0'));
+      p++;
+      // The rest of the exp_num walking has a peculiar control flow but, once
+      // again, the "script/process-json-numbers.c with -p" benchmark is
+      // sensitive to alternative formulations.
+      if (wuffs_private_impl__is_decimal_digit(*p)) {
+        exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));
+        p++;
+      }
+      if (wuffs_private_impl__is_decimal_digit(*p)) {
+        exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));
+        p++;
+      }
+      while (wuffs_private_impl__is_decimal_digit(*p)) {
+        if (exp_num > 0x1000000) {
+          goto fallback;
+        }
+        exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));
+        p++;
+      }
+      exp10 += exp_sign * exp_num;
+    }
+
+    // The Wuffs API is that the original slice has no trailing data. It also
+    // allows underscores, which we don't catch here but the fallback should.
+    if (p != &z[s.len]) {
+      goto fallback;
+    }
+
+    // Check that the uint64_t typed man variable has not overflowed, based on
+    // digit_count.
+    //
+    // For reference:
+    //   - (1 << 63) is  9223372036854775808, which has 19 decimal digits.
+    //   - (1 << 64) is 18446744073709551616, which has 20 decimal digits.
+    //   - 19 nines,  9999999999999999999, is  0x8AC7230489E7FFFF, which has 64
+    //     bits and 16 hexadecimal digits.
+    //   - 20 nines, 99999999999999999999, is 0x56BC75E2D630FFFFF, which has 67
+    //     bits and 17 hexadecimal digits.
+    if (digit_count > 19) {
+      // Even if we have more than 19 pseudo-digits, it's not yet definitely an
+      // overflow. Recall that digit_count might be off-by-one (too large) if
+      // there's a decimal separator. It will also over-report the number of
+      // meaningful digits if the input looks something like "0.000dddExxx".
+      //
+      // We adjust by the number of leading '0's and '.'s and re-compare to 19.
+      // Once again, technically, we could skip ','s too, but that perturbs the
+      // "script/process-json-numbers.c with -p" benchmark.
+      const uint8_t* q = start_of_digits_ptr;
+      for (; (*q == '0') || (*q == '.'); q++) {
+      }
+      digit_count -= (uint32_t)(q - start_of_digits_ptr);
+      if (digit_count > 19) {
+        goto fallback;
+      }
+    }
+
+    // The wuffs_private_impl__parse_number_f64_eisel_lemire preconditions
+    // include that exp10 is in the range [-307 ..= 288].
+    if ((exp10 < -307) || (288 < exp10)) {
+      goto fallback;
+    }
+
+#if PK_FLOATCONV_HAS_EXACT_DOUBLE_ARITHMETIC  // [pocketpy] Deviation 4.
+    // If both man and (10 ** exp10) are exactly representable by a double, we
+    // don't need to run the Eisel-Lemire algorithm.
+    if ((-22 <= exp10) && (exp10 <= 22) && ((man >> 53) == 0)) {
+      double d = (double)man;
+      if (exp10 >= 0) {
+        d *= wuffs_private_impl__f64_powers_of_10[+exp10];
+      } else {
+        d /= wuffs_private_impl__f64_powers_of_10[-exp10];
+      }
+      wuffs_base__result_f64 ret;
+      ret.status.repr = NULL;
+      ret.value = negative ? -d : +d;
+      return ret;
+    }
+#endif
+
+    // The wuffs_private_impl__parse_number_f64_eisel_lemire preconditions
+    // include that man is non-zero. Parsing "0" should be caught by the "If
+    // both man and (10 ** exp10)" above, but "0e99" might not.
+    if (man == 0) {
+      goto fallback;
+    }
+
+    // Our man and exp10 are in range. Run the Eisel-Lemire algorithm.
+    int64_t r = wuffs_private_impl__parse_number_f64_eisel_lemire(man, exp10);
+    if (r < 0) {
+      goto fallback;
+    }
+    wuffs_base__result_f64 ret;
+    ret.status.repr = NULL;
+    ret.value = wuffs_base__ieee_754_bit_representation__from_u64_to_f64(
+        ((uint64_t)r) | (((uint64_t)negative) << 63));
+    return ret;
+  } while (0);
+
+fallback:
+  do {
+    wuffs_private_impl__high_prec_dec h;
+    wuffs_base__status status =
+        wuffs_private_impl__high_prec_dec__parse(&h, s, options);
+    if (status.repr) {
+      return wuffs_private_impl__parse_number_f64_special(s, options);
+    }
+    return wuffs_private_impl__high_prec_dec__to_f64(&h, options);
+  } while (0);
+}
+
+// --------
+
+static inline size_t  //
+wuffs_private_impl__render_inf(wuffs_base__slice_u8 dst,
+                               bool neg,
+                               uint32_t options) {
+  if (neg) {
+    if (dst.len < 4) {
+      return 0;
+    }
+    wuffs_base__poke_u32le__no_bounds_check(dst.ptr, 0x666E492D);  // '-Inf'le.
+    return 4;
+  }
+
+  if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {
+    if (dst.len < 4) {
+      return 0;
+    }
+    wuffs_base__poke_u32le__no_bounds_check(dst.ptr, 0x666E492B);  // '+Inf'le.
+    return 4;
+  }
+
+  if (dst.len < 3) {
+    return 0;
+  }
+  wuffs_base__poke_u24le__no_bounds_check(dst.ptr, 0x666E49);  // 'Inf'le.
+  return 3;
+}
+
+static inline size_t  //
+wuffs_private_impl__render_nan(wuffs_base__slice_u8 dst) {
+  if (dst.len < 3) {
+    return 0;
+  }
+  wuffs_base__poke_u24le__no_bounds_check(dst.ptr, 0x4E614E);  // 'NaN'le.
+  return 3;
+}
+
+static size_t  //
+wuffs_private_impl__high_prec_dec__render_exponent_absent(
+    wuffs_base__slice_u8 dst,
+    wuffs_private_impl__high_prec_dec* h,
+    uint32_t precision,
+    uint32_t options) {
+  size_t n = (h->negative ||
+              (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN))
+                 ? 1
+                 : 0;
+  if (h->decimal_point <= 0) {
+    n += 1;
+  } else {
+    n += (size_t)(h->decimal_point);
+  }
+  if (precision > 0) {
+    n += precision + 1;  // +1 for the '.'.
+  }
+
+  // Don't modify dst if the formatted number won't fit.
+  if (n > dst.len) {
+    return 0;
+  }
+
+  // Align-left or align-right.
+  uint8_t* ptr = (options & WUFFS_BASE__RENDER_NUMBER_XXX__ALIGN_RIGHT)
+                     ? &dst.ptr[dst.len - n]
+                     : &dst.ptr[0];
+
+  // Leading "±".
+  if (h->negative) {
+    *ptr++ = '-';
+  } else if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {
+    *ptr++ = '+';
+  }
+
+  // Integral digits.
+  if (h->decimal_point <= 0) {
+    *ptr++ = '0';
+  } else {
+    uint32_t m =
+        wuffs_base__u32__min(h->num_digits, (uint32_t)(h->decimal_point));
+    uint32_t i = 0;
+    for (; i < m; i++) {
+      *ptr++ = (uint8_t)('0' | h->digits[i]);
+    }
+    for (; i < (uint32_t)(h->decimal_point); i++) {
+      *ptr++ = '0';
+    }
+  }
+
+  // Separator and then fractional digits.
+  if (precision > 0) {
+    *ptr++ =
+        (options & WUFFS_BASE__RENDER_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA)
+            ? ','
+            : '.';
+    uint32_t i = 0;
+    for (; i < precision; i++) {
+      uint32_t j = ((uint32_t)(h->decimal_point)) + i;
+      *ptr++ = (uint8_t)('0' | ((j < h->num_digits) ? h->digits[j] : 0));
+    }
+  }
+
+  return n;
+}
+
+static size_t  //
+wuffs_private_impl__high_prec_dec__render_exponent_present(
+    wuffs_base__slice_u8 dst,
+    wuffs_private_impl__high_prec_dec* h,
+    uint32_t precision,
+    uint32_t options) {
+  int32_t exp = 0;
+  if (h->num_digits > 0) {
+    exp = h->decimal_point - 1;
+  }
+  bool negative_exp = exp < 0;
+  if (negative_exp) {
+    exp = -exp;
+  }
+
+  size_t n = (h->negative ||
+              (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN))
+                 ? 4
+                 : 3;  // Mininum 3 bytes: first digit and then "e±".
+  if (precision > 0) {
+    n += precision + 1;  // +1 for the '.'.
+  }
+  n += (exp < 100) ? 2 : 3;
+
+  // Don't modify dst if the formatted number won't fit.
+  if (n > dst.len) {
+    return 0;
+  }
+
+  // Align-left or align-right.
+  uint8_t* ptr = (options & WUFFS_BASE__RENDER_NUMBER_XXX__ALIGN_RIGHT)
+                     ? &dst.ptr[dst.len - n]
+                     : &dst.ptr[0];
+
+  // Leading "±".
+  if (h->negative) {
+    *ptr++ = '-';
+  } else if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {
+    *ptr++ = '+';
+  }
+
+  // Integral digit.
+  if (h->num_digits > 0) {
+    *ptr++ = (uint8_t)('0' | h->digits[0]);
+  } else {
+    *ptr++ = '0';
+  }
+
+  // Separator and then fractional digits.
+  if (precision > 0) {
+    *ptr++ =
+        (options & WUFFS_BASE__RENDER_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA)
+            ? ','
+            : '.';
+    uint32_t i = 1;
+    uint32_t j = wuffs_base__u32__min(h->num_digits, precision + 1);
+    for (; i < j; i++) {
+      *ptr++ = (uint8_t)('0' | h->digits[i]);
+    }
+    for (; i <= precision; i++) {
+      *ptr++ = '0';
+    }
+  }
+
+  // Exponent: "e±" and then 2 or 3 digits.
+  *ptr++ = 'e';
+  *ptr++ = negative_exp ? '-' : '+';
+  if (exp < 10) {
+    *ptr++ = '0';
+    *ptr++ = (uint8_t)('0' | exp);
+  } else if (exp < 100) {
+    *ptr++ = (uint8_t)('0' | (exp / 10));
+    *ptr++ = (uint8_t)('0' | (exp % 10));
+  } else {
+    int32_t e = exp / 100;
+    exp -= e * 100;
+    *ptr++ = (uint8_t)('0' | e);
+    *ptr++ = (uint8_t)('0' | (exp / 10));
+    *ptr++ = (uint8_t)('0' | (exp % 10));
+  }
+
+  return n;
+}
+
+WUFFS_BASE__MAYBE_STATIC size_t  //
+wuffs_base__render_number_f64(wuffs_base__slice_u8 dst,
+                              double x,
+                              uint32_t precision,
+                              uint32_t options) {
+  // Decompose x (64 bits) into negativity (1 bit), base-2 exponent (11 bits
+  // with a -1023 bias) and mantissa (52 bits).
+  uint64_t bits = wuffs_base__ieee_754_bit_representation__from_f64_to_u64(x);
+  bool neg = (bits >> 63) != 0;
+  int32_t exp2 = ((int32_t)(bits >> 52)) & 0x7FF;
+  uint64_t man = bits & 0x000FFFFFFFFFFFFFul;
+
+  // Apply the exponent bias and set the implicit top bit of the mantissa,
+  // unless x is subnormal. Also take care of Inf and NaN.
+  if (exp2 == 0x7FF) {
+    if (man != 0) {
+      return wuffs_private_impl__render_nan(dst);
+    }
+    return wuffs_private_impl__render_inf(dst, neg, options);
+  } else if (exp2 == 0) {
+    exp2 = -1022;
+  } else {
+    exp2 -= 1023;
+    man |= 0x0010000000000000ul;
+  }
+
+  // Ensure that precision isn't too large.
+  if (precision > 4095) {
+    precision = 4095;
+  }
+
+  // Convert from the (neg, exp2, man) tuple to an HPD.
+  wuffs_private_impl__high_prec_dec h;
+  wuffs_private_impl__high_prec_dec__assign(&h, man, neg);
+  if (h.num_digits > 0) {
+    wuffs_private_impl__high_prec_dec__lshift(&h,
+                                              exp2 - 52);  // 52 mantissa bits.
+  }
+
+  // Handle the "%e" and "%f" formats.
+  switch (options & (WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_ABSENT |
+                     WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_PRESENT)) {
+    case WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_ABSENT:  // The "%"f" format.
+      if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {
+        wuffs_private_impl__high_prec_dec__round_just_enough(&h, exp2, man);
+        int32_t p = ((int32_t)(h.num_digits)) - h.decimal_point;
+        precision = ((uint32_t)(wuffs_base__i32__max(0, p)));
+      } else {
+        wuffs_private_impl__high_prec_dec__round_nearest(
+            &h, ((int32_t)precision) + h.decimal_point);
+      }
+      return wuffs_private_impl__high_prec_dec__render_exponent_absent(
+          dst, &h, precision, options);
+
+    case WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_PRESENT:  // The "%e" format.
+      if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {
+        wuffs_private_impl__high_prec_dec__round_just_enough(&h, exp2, man);
+        precision = (h.num_digits > 0) ? (h.num_digits - 1) : 0;
+      } else {
+        wuffs_private_impl__high_prec_dec__round_nearest(
+            &h, ((int32_t)precision) + 1);
+      }
+      return wuffs_private_impl__high_prec_dec__render_exponent_present(
+          dst, &h, precision, options);
+  }
+
+  // We have the "%g" format and so precision means the number of significant
+  // digits, not the number of digits after the decimal separator. Perform
+  // rounding and determine whether to use "%e" or "%f".
+  int32_t e_threshold = 0;
+  if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {
+    wuffs_private_impl__high_prec_dec__round_just_enough(&h, exp2, man);
+    precision = h.num_digits;
+    e_threshold = PK_FLOATCONV_REPR_E_THRESHOLD;  // [pocketpy] Deviation 3; was 6.
+  } else {
+    if (precision == 0) {
+      precision = 1;
+    }
+    wuffs_private_impl__high_prec_dec__round_nearest(&h, ((int32_t)precision));
+    e_threshold = ((int32_t)precision);
+    int32_t nd = ((int32_t)(h.num_digits));
+    if ((e_threshold > nd) && (nd >= h.decimal_point)) {
+      e_threshold = nd;
+    }
+  }
+
+  // Use the "%e" format if the exponent is large.
+  int32_t e = h.decimal_point - 1;
+  if ((e < -4) || (e_threshold <= e)) {
+    uint32_t p = wuffs_base__u32__min(precision, h.num_digits);
+    return wuffs_private_impl__high_prec_dec__render_exponent_present(
+        dst, &h, (p > 0) ? (p - 1) : 0, options);
+  }
+
+  // Use the "%f" format otherwise.
+  int32_t p = ((int32_t)precision);
+  if (p > h.decimal_point) {
+    p = ((int32_t)(h.num_digits));
+  }
+  precision = ((uint32_t)(wuffs_base__i32__max(0, p - h.decimal_point)));
+  return wuffs_private_impl__high_prec_dec__render_exponent_absent(
+      dst, &h, precision, options);
+}
+
+/* ---------------- [pocketpy] public API ----------------
+ *
+ * Parse options. Wuffs' defaults are stricter than C's `strtod`, so we opt
+ * back in to redundant leading zeroes: `float("007")` and the literal `00.7`
+ * both have to keep working.
+ *
+ * Underscores stay rejected. The lexer never puts one inside a number token,
+ * `float("1_0")` was already an error under `strtod`, and Wuffs' rule is looser
+ * than PEP 515's anyway (it would accept a leading `_`).
+ *
+ * Infinities and NaNs stay accepted, so `float("nan")` keeps working and
+ * `1e999` keeps overflowing to `inf` the way CPython does, rather than raising.
+ */
+#define PK_FLOATCONV_PARSE_OPTIONS (WUFFS_BASE__PARSE_NUMBER_XXX__ALLOW_MULTIPLE_LEADING_ZEROES)
+
+static bool pk_floatconv__is_digit(char c) { return ('0' <= c) && (c <= '9'); }
+
+// Whether the NUL-terminated `p` starts with `word`, which must be lowercase
+// ASCII. Case insensitive.
+static bool pk_floatconv__starts_with(const char* p, const char* word) {
+    for(; *word != '\0'; word++, p++) {
+        if((*p | 0x20) != *word) return false;
+    }
+    return true;
+}
+
+bool c11__parse_f64(const char* data, int size, double* out) {
+    if(size <= 0) return false;
+    wuffs_base__slice_u8 s;
+    s.ptr = (uint8_t*)data;  // The vendored parser only reads through this.
+    s.len = (size_t)size;
+    wuffs_base__result_f64 res = wuffs_base__parse_number_f64(s, PK_FLOATCONV_PARSE_OPTIONS);
+    if(res.status.repr != NULL) return false;
+    *out = res.value;
+    return true;
+}
+
+double strtod1(const char* s, char** p_end) {
+    const char* p = s;
+    // strtod() skips leading whitespace. Spelled out rather than via isspace()
+    // so that it cannot pick up a locale's extra space characters.
+    while(*p == ' ' || (*p >= '\t' && *p <= '\r'))
+        p++;
+
+    const char* start = p;
+    if(*p == '+' || *p == '-') p++;
+
+    // Find the longest prefix that c11__parse_f64 will accept. It only takes
+    // whole slices, so the scanning strtod() does implicitly happens here.
+    const char* end;
+    if((*p | 0x20) == 'i') {
+        if(!pk_floatconv__starts_with(p, "inf")) goto fail;
+        end = p + 3;
+        if(pk_floatconv__starts_with(end, "inity")) end += 5;
+    } else if((*p | 0x20) == 'n') {
+        if(!pk_floatconv__starts_with(p, "nan")) goto fail;
+        end = p + 3;
+    } else {
+        int digits = 0;
+        for(; pk_floatconv__is_digit(*p); p++)
+            digits++;
+        if(*p == '.') {
+            p++;
+            for(; pk_floatconv__is_digit(*p); p++)
+                digits++;
+        }
+        if(digits == 0) goto fail;
+        end = p;
+        // Like strtod(), only consume the exponent if it is well formed. In
+        // "1e+" the 'e' belongs to whatever comes after the number.
+        if((*p | 0x20) == 'e') {
+            const char* q = p + 1;
+            if(*q == '+' || *q == '-') q++;
+            if(pk_floatconv__is_digit(*q)) {
+                for(; pk_floatconv__is_digit(*q); q++) {}
+                end = q;
+            }
+        }
+    }
+
+    double out;
+    if(!c11__parse_f64(start, (int)(end - start), &out)) goto fail;
+    if(p_end != NULL) *p_end = (char*)end;
+    return out;
+
+fail:
+    if(p_end != NULL) *p_end = (char*)s;
+    return 0.0;
+}
+
+int c11__f64_to_shortest(char* dst, int dst_size, double x) {
+    if(dst_size <= 0) return 0;
+    wuffs_base__slice_u8 s;
+    s.ptr = (uint8_t*)dst;
+    s.len = (size_t)dst_size;
+    // Neither EXPONENT_ABSENT nor EXPONENT_PRESENT means "%g", which with
+    // PK_FLOATCONV_REPR_E_THRESHOLD is CPython's repr() notation.
+    return (int)wuffs_base__render_number_f64(s, x, 0,
+                                              WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION);
+}
+
+int c11__f64_to_fixed(char* dst, int dst_size, double x, int precision) {
+    if(dst_size <= 0) return 0;
+    if(precision < 0) precision = 0;
+    if(precision > C11_F64_MAX_PRECISION) precision = C11_F64_MAX_PRECISION;
+    wuffs_base__slice_u8 s;
+    s.ptr = (uint8_t*)dst;
+    s.len = (size_t)dst_size;
+    return (int)wuffs_base__render_number_f64(s, x, (uint32_t)precision,
+                                              WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_ABSENT);
+}
+
+
+
+#undef WUFFS_BASE__PARSE_NUMBER_XXX__ALLOW_MULTIPLE_LEADING_ZEROES
+#undef WUFFS_BASE__PARSE_NUMBER_XXX__ALLOW_UNDERSCORES
+#undef WUFFS_PRIVATE_IMPL__HPD__DECIMAL_POINT__RANGE
+#undef WUFFS_BASE__PARSE_NUMBER_XXX__DEFAULT_OPTIONS
+#undef WUFFS_BASE__RENDER_NUMBER_XXX__DEFAULT_OPTIONS
+#undef WUFFS_BASE__PARSE_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA
+#undef WUFFS_PRIVATE_IMPL__HPD__DIGITS_PRECISION
+#undef WUFFS_PRIVATE_IMPL__HPD__SHIFT__MAX_INCL
+#undef WUFFS_BASE__RENDER_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA
+#undef WUFFS_BASE__PARSE_NUMBER_FXX__REJECT_INF_AND_NAN
+#undef WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_ABSENT
+#undef PK_FLOATCONV_PARSE_OPTIONS
+#undef WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_PRESENT
+#undef WUFFS_BASE__RENDER_NUMBER_XXX__ALIGN_RIGHT
+#undef PK_FLOATCONV_REPR_E_THRESHOLD
+#undef PK_FLOATCONV_HAS_EXACT_DOUBLE_ARITHMETIC
+#undef WUFFS_BASE__MAYBE_STATIC
+#undef WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION
+#undef WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN

src/common/sstream.c

@@ -2,6 +2,7 @@
 #include "pocketpy/common/str.h"
 #include "pocketpy/common/utils.h"
 #include "pocketpy/common/dmath.h"
+#include "pocketpy/common/floatconv.h"
 #include "pocketpy/pocketpy.h"
 
 #include <stdarg.h>
@@ -51,25 +52,28 @@ void c11_sbuf__write_f64(c11_sbuf* self, double val, int precision) {
         c11_sbuf__write_cstr(self, "nan");
         return;
     }
-    char b[32];
-    int size;
     if(precision < 0) {
-        for(int g = 15; g <= 17; g++) {
-            size = snprintf(b, sizeof(b), "%.*g", g, val);
-            if(strtod(b, NULL) == val) break;
-        }
-        c11_sbuf__write_cstr(self, b);
+        char b[C11_F64_SHORTEST_BUF_SIZE];
+        int size = c11__f64_to_shortest(b, sizeof(b), val);
+        assert(size > 0);  // C11_F64_SHORTEST_BUF_SIZE is always enough
+        c11_sbuf__write_cstrn(self, b, size);
+        // a float should still look like a float once rendered
         bool all_is_digit = true;
-        for(int i = 1; i < size; i++) {
-            if(!isdigit(b[i])) {
+        for(int i = 0; i < size; i++) {
+            if(b[i] == '.' || b[i] == 'e') {
                 all_is_digit = false;
                 break;
             }
         }
         if(all_is_digit) c11_sbuf__write_cstr(self, ".0");
     } else {
-        size = snprintf(b, sizeof(b), "%.*f", precision, val);
-        c11_sbuf__write_cstr(self, b);
+        if(precision > C11_F64_MAX_PRECISION) precision = C11_F64_MAX_PRECISION;
+        // "%.*f" of a large value needs a lot of room, so render into the
+        // buffer itself instead of a fixed-size scratch array
+        int capacity = C11_F64_FIXED_BUF_SIZE(precision);
+        c11_vector__reserve(&self->data, self->data.length + capacity);
+        char* p = (char*)self->data.data + self->data.length;
+        self->data.length += c11__f64_to_fixed(p, capacity, val, precision);
     }
 }
 

src/compiler/compiler.c

@@ -2697,6 +2697,12 @@ static Error* compile_try_except(Compiler* self) {
     patches[patches_length++] = Ctx__emit_(ctx(), OP_JUMP_FORWARD, BC_NOARG, BC_KEEPLINE);
     Ctx__exit_block(ctx());
 
+    // Take the exception out of flight here, at the handler entry, before any
+    // `except <expr>` is evaluated. Otherwise an expression that raises (an
+    // undefined name, a call that fails) would raise while the original
+    // exception is still pending.
+    Ctx__emit_(ctx(), OP_HANDLE_EXCEPTION, BC_NOARG, BC_KEEPLINE);
+
     do {
         if(patches_length == 8) {
             return SyntaxError(self, "maximum number of except clauses reached");
@@ -2719,7 +2725,6 @@ static Error* compile_try_except(Compiler* self) {
         }
         int patch = Ctx__emit_(ctx(), OP_POP_JUMP_IF_FALSE, BC_NOARG, BC_KEEPLINE);
         // on match
-        Ctx__emit_(ctx(), OP_HANDLE_EXCEPTION, BC_NOARG, BC_KEEPLINE);
         if(as_name) {
             Ctx__emit_(ctx(), OP_PUSH_EXCEPTION, BC_NOARG, BC_KEEPLINE);
             Ctx__emit_store_name(ctx(), name_scope(self), as_name, BC_KEEPLINE);

src/compiler/lexer.c

@@ -1,4 +1,5 @@
 #include "pocketpy/common/sstream.h"
+#include "pocketpy/common/floatconv.h"
 #include "pocketpy/common/vector.h"
 #include "pocketpy/compiler/lexer.h"
 #include "pocketpy/objects/sourcedata.h"
@@ -416,7 +417,7 @@ static Error* eat_number(Lexer* self) {
     // try float
     double float_out;
     char* p_end;
-    float_out = strtod(text.data, &p_end);
+    float_out = strtod1(text.data, &p_end);
 
     if(p_end == text.data + text.size) {
         TokenValue value = {.index = TokenValue_F64, ._f64 = float_out};

src/interpreter/ceval.c

@@ -81,6 +81,14 @@ static bool unpack_dict_to_buffer(py_Ref key, py_Ref val, void* ctx) {
     return TypeError("keywords must be strings, not '%t'", key->type);
 }
 
+static bool binaryop_isnum(const py_TValue* v) {
+    return v->type == tp_int || v->type == tp_float;
+}
+
+static py_f64 binaryop_tof64(const py_TValue* v) {
+    return v->type == tp_int ? (py_f64)v->_i64 : v->_f64;
+}
+
 FrameResult VM__run_top_frame(VM* self) {
     py_Frame* frame = self->top_frame;
     Bytecode* co_codes;
@@ -664,9 +672,34 @@ __NEXT_STEP:
         *TOP() = self->last_retval;                                                                \
         DISPATCH();                                                                                \
     }
-            CASE_BINARY_OP(OP_BINARY_ADD, __add__, __radd__)
-            CASE_BINARY_OP(OP_BINARY_SUB, __sub__, __rsub__)
-            CASE_BINARY_OP(OP_BINARY_MUL, __mul__, __rmul__)
+// Fast paths for `int`/`float` operands. These mirror `DEF_NUM_BINARY_OP` in
+// `py_number.c`, including the promotion of a mixed `int`/`float` pair. Modifying a
+// builtin type's magic methods is undefined behaviour (docs/features/ub.md), so the
+// type is never consulted here.
+#define CASE_BINARY_OP_NUM(label, op, rop, c_op, mk_i, mk_f)                                       \
+    case label: {                                                                                  \
+        if(SECOND()->type == tp_int && TOP()->type == tp_int) {                                    \
+            py_i64 lhs = SECOND()->_i64;                                                           \
+            py_i64 rhs = TOP()->_i64;                                                              \
+            POP();                                                                                 \
+            mk_i(TOP(), lhs c_op rhs);                                                             \
+            DISPATCH();                                                                            \
+        }                                                                                          \
+        if(binaryop_isnum(SECOND()) && binaryop_isnum(TOP())) {                                    \
+            py_f64 lhs = binaryop_tof64(SECOND());                                                 \
+            py_f64 rhs = binaryop_tof64(TOP());                                                    \
+            POP();                                                                                 \
+            mk_f(TOP(), lhs c_op rhs);                                                             \
+            DISPATCH();                                                                            \
+        }                                                                                          \
+        if(!pk_stack_binaryop(self, op, rop)) goto __ERROR;                                        \
+        POP();                                                                                     \
+        *TOP() = self->last_retval;                                                                \
+        DISPATCH();                                                                                \
+    }
+            CASE_BINARY_OP_NUM(OP_BINARY_ADD, __add__, __radd__, +, py_newint, py_newfloat)
+            CASE_BINARY_OP_NUM(OP_BINARY_SUB, __sub__, __rsub__, -, py_newint, py_newfloat)
+            CASE_BINARY_OP_NUM(OP_BINARY_MUL, __mul__, __rmul__, *, py_newint, py_newfloat)
             CASE_BINARY_OP(OP_BINARY_TRUEDIV, __truediv__, __rtruediv__)
             CASE_BINARY_OP(OP_BINARY_FLOORDIV, __floordiv__, __rfloordiv__)
             CASE_BINARY_OP(OP_BINARY_MOD, __mod__, __rmod__)
@@ -677,13 +710,14 @@ __NEXT_STEP:
             CASE_BINARY_OP(OP_BINARY_OR, __or__, 0)
             CASE_BINARY_OP(OP_BINARY_XOR, __xor__, 0)
             CASE_BINARY_OP(OP_BINARY_MATMUL, __matmul__, 0)
-            CASE_BINARY_OP(OP_COMPARE_LT, __lt__, __gt__)
-            CASE_BINARY_OP(OP_COMPARE_LE, __le__, __ge__)
-            CASE_BINARY_OP(OP_COMPARE_EQ, __eq__, __eq__)
-            CASE_BINARY_OP(OP_COMPARE_NE, __ne__, __ne__)
-            CASE_BINARY_OP(OP_COMPARE_GT, __gt__, __lt__)
-            CASE_BINARY_OP(OP_COMPARE_GE, __ge__, __le__)
+            CASE_BINARY_OP_NUM(OP_COMPARE_LT, __lt__, __gt__, <, py_newbool, py_newbool)
+            CASE_BINARY_OP_NUM(OP_COMPARE_LE, __le__, __ge__, <=, py_newbool, py_newbool)
+            CASE_BINARY_OP_NUM(OP_COMPARE_EQ, __eq__, __eq__, ==, py_newbool, py_newbool)
+            CASE_BINARY_OP_NUM(OP_COMPARE_NE, __ne__, __ne__, !=, py_newbool, py_newbool)
+            CASE_BINARY_OP_NUM(OP_COMPARE_GT, __gt__, __lt__, >, py_newbool, py_newbool)
+            CASE_BINARY_OP_NUM(OP_COMPARE_GE, __ge__, __le__, >=, py_newbool, py_newbool)
 #undef CASE_BINARY_OP
+#undef CASE_BINARY_OP_NUM
         case OP_IS_OP: {
             bool res = py_isidentical(SECOND(), TOP());
             POP();
@@ -774,7 +808,8 @@ __NEXT_STEP:
         }
         /*****************************************/
         case OP_CALL: {
-            if(self->heap.gc_enabled) ManagedHeap__collect_hint(&self->heap);
+            if(self->heap.gc_enabled && self->heap.gc_counter >= self->heap.gc_threshold)
+                ManagedHeap__collect_hint(&self->heap);
             vectorcall_opcall(byte.arg & 0xFF, byte.arg >> 8);
             DISPATCH();
         }
@@ -864,9 +899,8 @@ __NEXT_STEP:
             if(res) {
                 return RES_YIELD;
             } else {
-                assert(self->last_retval.type == tp_StopIteration);
-                BaseException* ud = py_touserdata(py_retval());
-                py_ObjectRef value = &ud->args;
+                // `py_next` leaves the StopIteration value in `py_retval()`
+                py_Ref value = py_retval();
                 if(py_isnil(value)) value = py_None();
                 *TOP() = *value;  // [iter] -> [retval]
                 DISPATCH_JUMP((int16_t)byte.arg);
@@ -934,7 +968,6 @@ __NEXT_STEP:
                 PUSH(py_retval());
                 DISPATCH();
             } else {
-                assert(self->last_retval.type == tp_StopIteration);
                 POP();  // [iter] -> []
                 DISPATCH_JUMP((int16_t)byte.arg);
             }
@@ -990,6 +1023,11 @@ __NEXT_STEP:
             py_TValue* p;
             int length;
 
+            if(SP() + byte.arg > self->stack.end) {
+                py_exception(tp_RecursionError, "value stack overflow");
+                goto __ERROR;
+            }
+
             switch(TOP()->type) {
                 case tp_tuple: {
                     length = py_tuple_len(TOP());
@@ -1055,6 +1093,10 @@ __NEXT_STEP:
             DISPATCH();
         }
         case OP_UNPACK_EX: {
+            if(SP() + byte.arg + 1 > self->stack.end) {
+                py_exception(tp_RecursionError, "value stack overflow");
+                goto __ERROR;
+            }
             py_TValue* p;
             int length = pk_arrayview(TOP(), &p);
             if(length == -1) {
@@ -1182,10 +1224,14 @@ __NEXT_STEP:
             DISPATCH();
         }
         case OP_EXCEPTION_MATCH: {
+            // OP_HANDLE_EXCEPTION at the handler entry already moved the
+            // exception into the frame, so nothing is in flight here
+            FrameExcInfo* info = Frame__top_exc_info(frame);
+            assert(info != NULL && !py_isnil(&info->exc));
             bool ok = false;
             bool has_invalid = false;
             if(TOP()->type == tp_type) {
-                ok = py_isinstance(&self->unhandled_exc, py_totype(TOP()));
+                ok = py_isinstance(&info->exc, py_totype(TOP()));
             } else if(TOP()->type == tp_tuple) {
                 int len = py_tuple_len(TOP());
                 py_ObjectRef data = py_tuple_data(TOP());
@@ -1197,7 +1243,7 @@ __NEXT_STEP:
                 }
                 if(!has_invalid) {
                     for(int i = 0; i < len; i++) {
-                        if(py_isinstance(&self->unhandled_exc, py_totype(data + i))) {
+                        if(py_isinstance(&info->exc, py_totype(data + i))) {
                             ok = true;
                             break;
                         }
@@ -1207,7 +1253,7 @@ __NEXT_STEP:
                 has_invalid = true;
             }
             if(has_invalid) {
-                py_newnil(&self->unhandled_exc);
+                // raise first, so `py_raise` can chain `info->exc`, then drop it
                 TypeError("catching classes that do not inherit from BaseException is not allowed");
                 c11_vector__pop(&frame->exc_stack);
                 goto __ERROR;
@@ -1247,11 +1293,12 @@ __NEXT_STEP:
             goto __ERROR;
         }
         case OP_RE_RAISE: {
-            if(py_isnil(&self->unhandled_exc)) {
-                FrameExcInfo* info = Frame__top_exc_info(frame);
-                assert(info != NULL && !py_isnil(&info->exc));
-                self->unhandled_exc = info->exc;
-            }
+            // OP_HANDLE_EXCEPTION at the handler entry took the exception out of
+            // flight, so the frame is the one holding it and we put it back
+            assert(py_isnil(&self->unhandled_exc));
+            FrameExcInfo* info = Frame__top_exc_info(frame);
+            assert(info != NULL && !py_isnil(&info->exc));
+            self->unhandled_exc = info->exc;
             c11_vector__pop(&frame->exc_stack);
             goto __ERROR_RE_RAISE;
         }

src/interpreter/frame.c

@@ -63,9 +63,18 @@ void Frame__delete(py_Frame* self) {
 int Frame__goto_exception_handler(py_Frame* self, ValueStack* value_stack, py_Ref exc) {
     FrameExcInfo* p = self->exc_stack.data;
     for(int i = self->exc_stack.length - 1; i >= 0; i--) {
+        CodeBlock* block = c11__at(CodeBlock, &self->co->blocks, p[i].iblock);
         if(py_isnil(&p[i].exc)) {
+            // A nil `exc` means OP_HANDLE_EXCEPTION has not run for this block,
+            // i.e. we are still inside its `try` body, so it can take over.
+            // Anything raised from an `except <expr>` or from a handler body
+            // finds `exc` already set and falls through to the outer block.
+            // `ip == block->end` is the handler entry itself, which is still
+            // reachable: the watchdog checks for a timeout on the instruction
+            // boundary right before OP_HANDLE_EXCEPTION gets to run.
+            assert(self->ip >= block->start && self->ip <= block->end);
             value_stack->sp = (self->p0 + p[i].offset);  // unwind the stack
-            return c11__at(CodeBlock, &self->co->blocks, p[i].iblock)->end;
+            return block->end;
         } else {
             self->exc_stack.length--;
         }

src/interpreter/generator.c

@@ -1,7 +1,9 @@
 #include "pocketpy/interpreter/generator.h"
 #include "pocketpy/interpreter/frame.h"
 #include "pocketpy/interpreter/vm.h"
+#include "pocketpy/interpreter/bindings.h"
 #include "pocketpy/objects/base.h"
+#include "pocketpy/objects/exception.h"
 #include "pocketpy/pocketpy.h"
 #include <stdbool.h>
 #include <assert.h>
@@ -21,12 +23,16 @@ void Generator__dtor(Generator* ud) {
     if(ud->frame) Frame__delete(ud->frame);
 }
 
-bool generator__next__(int argc, py_Ref argv) {
-    PY_CHECK_ARGC(1);
-    Generator* ud = py_touserdata(argv);
+PK_DEFINE_NEXT_WRAPPER(generator)
+
+int generator__iternext(py_Ref self) {
+    Generator* ud = py_touserdata(self);
     py_StackRef p0 = py_peek(0);
     VM* vm = pk_current_vm;
-    if(ud->state == 2) return StopIteration();
+    if(ud->state == 2) {
+        py_newnil(py_retval());
+        return 0;
+    }
 
     // reset frame->p0
     assert(!ud->frame->is_locals_special);
@@ -35,7 +41,7 @@ bool generator__next__(int argc, py_Ref argv) {
     ud->frame->locals = ud->frame->p0 + locals_offset;
     
     // restore the context
-    py_Ref backup = py_getslot(argv, 0);
+    py_Ref backup = py_getslot(self, 0);
     int length = py_list_len(backup);
     py_TValue* p = py_list_data(backup);
     for(int i = 0; i < length; i++)
@@ -51,10 +57,19 @@ bool generator__next__(int argc, py_Ref argv) {
     if(res == RES_ERROR) {
         ud->state = 2;  // end this generator immediately on error
         if(py_matchexc(tp_StopIteration)) {
+            // PEP 479: a `StopIteration` escaping the body must not be mistaken
+            // for the generator finishing normally
+            py_TValue stop_iter = *py_retval();  // stashed there by py_matchexc
             py_clearexc(p0);
-            return true;
+            // root it on the stack, `RuntimeError` below allocates
+            py_StackRef inner = py_pushtmp();
+            *inner = stop_iter;
+            RuntimeError("generator raised StopIteration");
+            BaseException* exc = py_touserdata(&vm->unhandled_exc);
+            exc->inner_exc = *inner;
+            py_pop();
         }
-        return false;
+        return -1;
     }
 
     if(res == RES_YIELD) {
@@ -67,14 +82,13 @@ bool generator__next__(int argc, py_Ref argv) {
         vm->top_frame = vm->top_frame->f_back;
         vm->recursion_depth--;
         ud->state = 1;
-        return true;
+        return 1;
     } else {
         assert(res == RES_RETURN);
         ud->state = 2;
-        // raise StopIteration(<retval>)
-        bool ok = py_tpcall(tp_StopIteration, 1, py_retval());
-        if(!ok) return false;
-        return py_raise(py_retval());
+        // `py_retval()` already holds the return value, which the caller turns
+        // into `StopIteration(<retval>)` if it needs a real exception
+        return 0;
     }
 }
 

src/interpreter/typeinfo.c

@@ -1,6 +1,15 @@
 #include "pocketpy/interpreter/vm.h"
 #include <assert.h>
 
+void pk_tpresolvemagics(py_TypeInfo* ti) {
+    py_Ref f = pk_tpfindname(ti, __new__);
+    assert(f != NULL);  // `object.__new__` is always reachable
+    ti->cached_new = *f;
+    py_Ref g = pk_tpfindname(ti, __init__);
+    ti->cached_init = g ? *g : *py_NIL();
+    ti->magics_version = pk_current_vm->type_version;
+}
+
 py_ItemRef pk_tpfindname(py_TypeInfo* ti, py_Name name) {
     assert(ti != NULL);
     do {
@@ -52,6 +61,9 @@ static void py_TypeInfo__common_init(py_Name name,
     self->delattribute = NULL;
     self->getunboundmethod = NULL;
 
+    self->cached_new = *py_NIL();
+    self->cached_init = *py_NIL();
+    self->magics_version = 0;  // never resolved
     self->annotations = *py_NIL();
     self->dtor = dtor;
     self->on_end_subclass = NULL;

src/interpreter/vm.c

@@ -98,6 +98,7 @@ void VM__ctor(VM* self) {
 
     self->last_retval = *py_NIL();
     self->unhandled_exc = *py_NIL();
+    self->type_version = 1;  // 0 means "never resolved" in py_TypeInfo
 
     self->recursion_depth = 0;
     self->max_recursion_depth = 1000;
@@ -509,6 +510,13 @@ FrameResult VM__vectorcall(VM* self, uint16_t argc, uint16_t kwargc, bool opcall
         Function* fn = py_touserdata(p0);
         const CodeObject* co = &fn->decl->code;
 
+        // the callee's locals live on the value stack; make room before any of
+        // the paths below writes there
+        if(argv + co->nlocals > self->stack.end) {
+            py_exception(tp_RecursionError, "value stack overflow");
+            return RES_ERROR;
+        }
+
         switch(fn->decl->type) {
             case FuncType_NORMAL: {
                 bool ok = prepare_py_call(self->vectorcall_buffer, argv, p1, kwargc, fn->decl);
@@ -584,9 +592,11 @@ FrameResult VM__vectorcall(VM* self, uint16_t argc, uint16_t kwargc, bool opcall
 
     if(p0->type == tp_type) {
         py_Type p0_type = py_totype(p0);
+        py_TypeInfo* p0_ti = pk_typeinfo(p0_type);
+        if(p0_ti->magics_version != self->type_version) pk_tpresolvemagics(p0_ti);
         // [cls, NULL, args..., kwargs...]
-        py_Ref new_f = py_tpfindmagic(p0_type, __new__);
-        assert(new_f && py_isnil(p0 + 1));
+        py_Ref new_f = &p0_ti->cached_new;
+        assert(py_isnil(p0 + 1));
         bool is_default_new = new_f->type == tp_nativefunc && new_f->_cfunc == pk__object_new;
 
         // prepare a copy of args and kwargs
@@ -603,7 +613,7 @@ FrameResult VM__vectorcall(VM* self, uint16_t argc, uint16_t kwargc, bool opcall
         // NOTE: previously we use `get_unbound_method` but here we just use `tpfindmagic`
         // >> [cls, NULL, args..., kwargs...]
         // >> py_retval() is the new instance
-        py_Ref init_f = py_tpfindmagic(p0_type, __init__);
+        py_Ref init_f = py_isnil(&p0_ti->cached_init) ? NULL : &p0_ti->cached_init;
         if(init_f) {
             if(py_isinstance(py_retval(), p0_type)) {
                 // do an inplace patch
@@ -684,6 +694,8 @@ void ManagedHeap__mark(ManagedHeap* self) {
     for(py_Type i = 1; i < types_length; i++) {
         py_TypeInfo* ti = c11__getitem(TypePointer, &vm->types, i).ti;
         pk__mark_value(&ti->self);
+        pk__mark_value(&ti->cached_new);
+        pk__mark_value(&ti->cached_init);
         pk__mark_value(&ti->annotations);
     }
     // mark frame

src/modules/array2d.c

@@ -1,5 +1,6 @@
 #include "pocketpy/interpreter/array2d.h"
 #include "pocketpy/interpreter/vm.h"
+#include "pocketpy/interpreter/bindings.h"
 #include "pocketpy/pocketpy.h"
 #include <limits.h>
 
@@ -386,8 +387,13 @@ static bool array2d_like__invert__(int argc, py_Ref argv) {
     for(int j = 0; j < self->n_rows; j++) {
         for(int i = 0; i < self->n_cols; i++) {
             py_Ref item = self->f_get(self, i, j);
-            if(!pk_callmagic(__invert__, 1, item)) return false;
-            c11_array2d__set(res, i, j, py_retval());
+            if(item->type == tp_bool) {
+                py_Ref p_out = c11_array2d__get(res, i, j);
+                py_newbool(p_out, !py_tobool(item));
+            } else {
+                if(!pk_callmagic(__invert__, 1, item)) return false;
+                c11_array2d__set(res, i, j, py_retval());
+            }
         }
     }
     py_assign(py_retval(), py_peek(-1));
@@ -884,10 +890,14 @@ static void register_array2d_like(py_Ref mod) {
     }
 }
 
-bool array2d_like_iterator__next__(int argc, py_Ref argv) {
-    PY_CHECK_ARGC(1);
-    c11_array2d_like_iterator* self = py_touserdata(argv);
-    if(self->j >= self->array->n_rows) return StopIteration();
+PK_DEFINE_NEXT_WRAPPER(array2d_like_iterator)
+
+int array2d_like_iterator__iternext(py_Ref self_) {
+    c11_array2d_like_iterator* self = py_touserdata(self_);
+    if(self->j >= self->array->n_rows) {
+        py_newnil(py_retval());
+        return 0;
+    }
     py_TValue* data = py_newtuple(py_retval(), 2);
     py_newvec2i(&data[0],
                 (c11_vec2i){
@@ -899,7 +909,7 @@ bool array2d_like_iterator__next__(int argc, py_Ref argv) {
         self->i = 0;
         self->j++;
     }
-    return true;
+    return 1;
 }
 
 static void register_array2d_like_iterator(py_Ref mod) {
@@ -1002,7 +1012,8 @@ static void register_array2d_view(py_Ref mod) {
 #include "pocketpy/xmacros/smallmap.h"
 #undef SMALLMAP_T__SOURCE
 
-static py_TValue* c11_chunked_array2d__new_chunk(c11_chunked_array2d* self, c11_vec2i pos, py_Ref context) {
+static py_TValue*
+    c11_chunked_array2d__new_chunk(c11_chunked_array2d* self, c11_vec2i pos, py_Ref context) {
     bool exists = c11_chunked_array2d_chunks__contains(&self->chunks, pos);
     if(exists) {
         ValueError("chunk already exists at pos (%d, %d)", pos.x, pos.y);
@@ -1039,15 +1050,15 @@ static void c11_chunked_array2d__world_to_chunk(c11_chunked_array2d* self,
                                                 c11_vec2i* restrict chunk_pos,
                                                 c11_vec2i* restrict local_pos) {
     cpy312__divmod_int_uint(col,
-                           self->chunk_size_log2,
-                           self->chunk_size_mask,
-                           &chunk_pos->x,
-                           &local_pos->x);
+                            self->chunk_size_log2,
+                            self->chunk_size_mask,
+                            &chunk_pos->x,
+                            &local_pos->x);
     cpy312__divmod_int_uint(row,
-                           self->chunk_size_log2,
-                           self->chunk_size_mask,
-                           &chunk_pos->y,
-                           &local_pos->y);
+                            self->chunk_size_log2,
+                            self->chunk_size_mask,
+                            &chunk_pos->y,
+                            &local_pos->y);
 }
 
 static py_TValue* c11_chunked_array2d__parse_col_row(c11_chunked_array2d* self,

src/modules/builtins.c

@@ -7,6 +7,7 @@
 #include "pocketpy/objects/object.h"
 #include "pocketpy/common/sstream.h"
 #include "pocketpy/interpreter/vm.h"
+#include "pocketpy/interpreter/bindings.h"
 #include "pocketpy/common/_generated.h"
 
 
@@ -123,8 +124,8 @@ static bool builtins_next(int argc, py_Ref argv) {
     if(res == -1) return false;
     if(res) return true;
     if(argc == 1) {
-        // StopIteration stored in py_retval()
-        return py_raise(py_retval());
+        // py_retval() holds the StopIteration value, or nil if there is none
+        return pk__raise_stopiteration();
     } else {
         py_assign(py_retval(), py_arg(1));
         return true;

src/modules/pickle.c

@@ -19,9 +19,12 @@ typedef enum {
     PKL_FLOAT32, PKL_FLOAT64,
     PKL_TRUE, PKL_FALSE,
     PKL_STRING, PKL_BYTES,
-    PKL_BUILD_LIST,
+    // mutable containers are built in two phases so that they can be memoized
+    // *before* their contents are written, which is what makes cyclic references work
+    PKL_NEW_LIST, PKL_FILL_LIST,
+    PKL_NEW_DICT, PKL_FILL_DICT,
+    PKL_NEW_OBJECT, PKL_FILL_OBJECT,
     PKL_BUILD_TUPLE,
-    PKL_BUILD_DICT,
     PKL_VEC2, PKL_VEC3,
     PKL_VEC2I, PKL_VEC3I,
     PKL_TYPE,
@@ -30,7 +33,6 @@ typedef enum {
     PKL_GETATTR,
     PKL_TVALUE,
     PKL_CALL,
-    PKL_OBJECT,
     PKL_EOF,
     // clang-format on
 } PickleOp;
@@ -180,10 +182,16 @@ static bool pkl__write_array(PickleObject* buf, PickleOp op, py_TValue* arr, int
     return true;
 }
 
+typedef struct {
+    PickleObject* buf;
+    int length;
+} pkl__DictCtx;
+
 static bool pkl__write_dict_kv(py_Ref k, py_Ref v, void* ctx) {
-    PickleObject* buf = (PickleObject*)ctx;
-    if(!pkl__write_object(buf, k)) return false;
-    if(!pkl__write_object(buf, v)) return false;
+    pkl__DictCtx* self = (pkl__DictCtx*)ctx;
+    if(!pkl__write_object(self->buf, k)) return false;
+    if(!pkl__write_object(self->buf, v)) return false;
+    self->length++;
     return true;
 }
 
@@ -270,9 +278,19 @@ static bool pkl__write_object(PickleObject* buf, py_TValue* obj) {
         }
         case tp_list: {
             if(pkl__try_memo(buf, obj->_obj)) return true;
-            bool ok = pkl__write_array(buf, PKL_BUILD_LIST, py_list_data(obj), py_list_len(obj));
-            if(!ok) return false;
+            // memoize before writing the items so that a cyclic reference back to
+            // this list resolves to `PKL_MEMO_GET` instead of recursing forever
+            pkl__emit_op(buf, PKL_NEW_LIST);
             pkl__store_memo(buf, obj->_obj);
+            int length = py_list_len(obj);
+            for(int i = 0; i < length; i++) {
+                // re-read `data` each time: writing an item may run python code
+                // (e.g. `__reduce__`) which can reallocate the list
+                if(i >= py_list_len(obj)) return ValueError("list changed size during pickling");
+                if(!pkl__write_object(buf, py_list_data(obj) + i)) return false;
+            }
+            pkl__emit_op(buf, PKL_FILL_LIST);
+            pkl__emit_int(buf, length);
             return true;
         }
         case tp_tuple: {
@@ -284,11 +302,12 @@ static bool pkl__write_object(PickleObject* buf, py_TValue* obj) {
         }
         case tp_dict: {
             if(pkl__try_memo(buf, obj->_obj)) return true;
-            bool ok = py_dict_apply(obj, pkl__write_dict_kv, (void*)buf);
-            if(!ok) return false;
-            pkl__emit_op(buf, PKL_BUILD_DICT);
-            pkl__emit_int(buf, py_dict_len(obj));
+            pkl__emit_op(buf, PKL_NEW_DICT);
             pkl__store_memo(buf, obj->_obj);
+            pkl__DictCtx ctx = {buf, 0};
+            if(!py_dict_apply(obj, pkl__write_dict_kv, &ctx)) return false;
+            pkl__emit_op(buf, PKL_FILL_DICT);
+            pkl__emit_int(buf, ctx.length);
             return true;
         }
         case tp_vec2: {
@@ -428,16 +447,24 @@ static bool pkl__write_object(PickleObject* buf, py_TValue* obj) {
                 return true;
             }
             if(ti->is_python) {
+                // create the (empty) instance and memoize it before writing its fields,
+                // so that a cyclic reference back here resolves to `PKL_MEMO_GET`
+                pkl__emit_op(buf, PKL_NEW_OBJECT);
+                pkl__emit_int(buf, obj->type);
+                buf->used_types[obj->type] = true;
+                pkl__store_memo(buf, obj->_obj);
+
                 NameDict* dict = PyObject__dict(obj->_obj);
-                for(int i = dict->capacity - 1; i >= 0; i--) {
+                int length = dict->length;
+                // values first, in slot order; `PKL_FILL_OBJECT` reads the names in the
+                // same order and pairs them up positionally
+                for(int i = 0; i < dict->capacity; i++) {
                     NameDict_KV* kv = &dict->items[i];
                     if(kv->key == NULL) continue;
                     if(!pkl__write_object(buf, &kv->value)) return false;
                 }
-                pkl__emit_op(buf, PKL_OBJECT);
-                pkl__emit_int(buf, obj->type);
-                buf->used_types[obj->type] = true;
-                pkl__emit_int(buf, dict->length);
+                pkl__emit_op(buf, PKL_FILL_OBJECT);
+                pkl__emit_int(buf, length);
                 for(int i = 0; i < dict->capacity; i++) {
                     NameDict_KV* kv = &dict->items[i];
                     if(kv->key == NULL) continue;
@@ -445,9 +472,6 @@ static bool pkl__write_object(PickleObject* buf, py_TValue* obj) {
                     // include '\0'
                     PickleObject__write_bytes(buf, field.data, field.size + 1);
                 }
-
-                // store memo
-                pkl__store_memo(buf, obj->_obj);
                 return true;
             }
             return TypeError("'%t' object is not picklable", obj->type);
@@ -635,16 +659,18 @@ bool py_pickle_loads_body(const unsigned char* p, int memo_length, c11_smallmap_
                 p += size;
                 break;
             }
-            case PKL_BUILD_LIST: {
+            case PKL_NEW_LIST: {
+                py_newlist(py_pushtmp());
+                break;
+            }
+            case PKL_FILL_LIST: {
                 int length = pkl__read_int(&p);
-                py_Ref val = py_retval();
-                py_newlistn(val, length);
-                for(int i = length - 1; i >= 0; i--) {
-                    py_StackRef item = py_peek(-1);
-                    py_list_setitem(val, i, item);
-                    py_pop();
+                // stack: [list, item_0, ..., item_{length-1}]
+                py_StackRef self = py_peek(-1) - length;
+                for(int i = 0; i < length; i++) {
+                    py_list_append(self, self + 1 + i);
                 }
-                py_push(val);
+                py_shrink(length);
                 break;
             }
             case PKL_BUILD_TUPLE: {
@@ -658,21 +684,19 @@ bool py_pickle_loads_body(const unsigned char* p, int memo_length, c11_smallmap_
                 py_push(val);
                 break;
             }
-            case PKL_BUILD_DICT: {
+            case PKL_NEW_DICT: {
+                py_newdict(py_pushtmp());
+                break;
+            }
+            case PKL_FILL_DICT: {
                 int length = pkl__read_int(&p);
-                py_Ref val = py_pushtmp();
-                py_newdict(val);
-                py_StackRef begin = py_peek(-1) - 2 * length;
-                py_StackRef end = py_peek(-1);
-                for(py_StackRef i = begin; i < end; i += 2) {
-                    py_StackRef k = i;
-                    py_StackRef v = i + 1;
-                    bool ok = py_dict_setitem(val, k, v);
-                    if(!ok) return false;
+                // stack: [dict, k_0, v_0, ..., k_{length-1}, v_{length-1}]
+                py_StackRef self = py_peek(-1) - 2 * length;
+                for(int i = 0; i < length; i++) {
+                    py_StackRef k = self + 1 + 2 * i;
+                    if(!py_dict_setitem(self, k, k + 1)) return false;
                 }
-                py_assign(py_retval(), val);
-                py_shrink(2 * length + 1);
-                py_push(py_retval());
+                py_shrink(2 * length);
                 break;
             }
             case PKL_VEC2: {
@@ -749,20 +773,23 @@ bool py_pickle_loads_body(const unsigned char* p, int memo_length, c11_smallmap_
                 py_push(py_retval());
                 break;
             }
-            case PKL_OBJECT: {
+            case PKL_NEW_OBJECT: {
                 py_Type type = (py_Type)pkl__read_int(&p);
                 type = pkl__fix_type(type, type_mapping);
-                py_newobject(py_retval(), type, -1, 0);
-                NameDict* dict = PyObject__dict(py_retval()->_obj);
-                int dict_length = pkl__read_int(&p);
-                for(int i = 0; i < dict_length; i++) {
-                    py_StackRef value = py_peek(-1);
+                py_newobject(py_pushtmp(), type, -1, 0);
+                break;
+            }
+            case PKL_FILL_OBJECT: {
+                int length = pkl__read_int(&p);
+                // stack: [object, value_0, ..., value_{length-1}]
+                py_StackRef self = py_peek(-1) - length;
+                NameDict* dict = PyObject__dict(self->_obj);
+                for(int i = 0; i < length; i++) {
                     c11_sv field = {(const char*)p, strlen((const char*)p)};
-                    NameDict__set(dict, py_namev(field), value);
-                    py_pop();
+                    NameDict__set(dict, py_namev(field), self + 1 + i);
                     p += field.size + 1;
                 }
-                py_push(py_retval());
+                py_shrink(length);
                 break;
             }
             case PKL_EOF: {

src/modules/random.c

@@ -131,6 +131,25 @@ int64_t mt19937__randint(mt19937* self, int64_t a, int64_t b) {
     }
 }
 
+/* dumps the internal state as `bytes` */
+static void mt19937__getstate(mt19937* self, py_OutRef out) {
+    unsigned char* data = py_newbytes(out, sizeof(mt19937));
+    memcpy(data, self, sizeof(mt19937));
+}
+
+/* restores a state produced by `mt19937__getstate` */
+static bool mt19937__setstate(mt19937* self, py_Ref state) {
+    int size;
+    unsigned char* data = py_tobytes(state, &size);
+    if(size != sizeof(mt19937)) return ValueError("invalid state");
+    mt19937 tmp;
+    memcpy(&tmp, data, sizeof(mt19937));
+    /* `mti == N + 1` means mt[N] is not initialized; anything above `N` is out of range */
+    if(tmp.mti < 0 || tmp.mti > N + 1) return ValueError("invalid state");
+    *self = tmp;
+    return true;
+}
+
 static bool Random__new__(int argc, py_Ref argv) {
     mt19937* ud = py_newobject(py_retval(), py_totype(argv), 0, sizeof(mt19937));
     mt19937__ctor(ud);
@@ -142,13 +161,16 @@ static bool Random__init__(int argc, py_Ref argv) {
         // do nothing
     } else if(argc == 2) {
         mt19937* ud = py_touserdata(py_arg(0));
-        if(!py_isnone(&argv[1])) {
+        if(py_istype(py_arg(1), tp_bytes)) {
+            // a state returned by `getstate()`; this is how `__reduce__` rebuilds the object
+            if(!mt19937__setstate(ud, py_arg(1))) return false;
+        } else if(!py_isnone(&argv[1])) {
             PY_CHECK_ARG_TYPE(1, tp_int);
             py_i64 seed = py_toint(py_arg(1));
             mt19937__seed(ud, (uint32_t)seed);
         }
     } else {
-        return TypeError("Random(): expected 1 or 2 arguments, got %d");
+        return TypeError("Random(): expected 1 or 2 arguments, got %d", argc);
     }
     py_newnone(py_retval());
     return true;
@@ -169,6 +191,33 @@ static bool Random_seed(int argc, py_Ref argv) {
     return true;
 }
 
+static bool Random_getstate(int argc, py_Ref argv) {
+    PY_CHECK_ARGC(1);
+    mt19937* ud = py_touserdata(py_arg(0));
+    mt19937__getstate(ud, py_retval());
+    return true;
+}
+
+static bool Random_setstate(int argc, py_Ref argv) {
+    PY_CHECK_ARGC(2);
+    PY_CHECK_ARG_TYPE(1, tp_bytes);
+    mt19937* ud = py_touserdata(py_arg(0));
+    if(!mt19937__setstate(ud, py_arg(1))) return false;
+    py_newnone(py_retval());
+    return true;
+}
+
+static bool Random__reduce__(int argc, py_Ref argv) {
+    PY_CHECK_ARGC(1);
+    mt19937* ud = py_touserdata(py_arg(0));
+    // `(cls, (state,))`, i.e. `cls(state)` restores the generator
+    py_TValue* p = py_newtuple(py_retval(), 2);
+    py_assign(&p[0], py_tpobject(py_typeof(py_arg(0))));
+    py_TValue* args = py_newtuple(&p[1], 1);
+    mt19937__getstate(ud, &args[0]);
+    return true;
+}
+
 static bool Random_random(int argc, py_Ref argv) {
     PY_CHECK_ARGC(1);
     mt19937* ud = py_touserdata(py_arg(0));
@@ -298,9 +347,15 @@ void pk__add_module_random() {
     py_Ref mod = py_newmodule("random");
     py_Type type = py_newtype("Random", tp_object, mod, NULL);
 
+    // must be 2500 bytes so memcpy() works in `mt19937__getstate()` and `mt19937__setstate()`
+    _Static_assert(sizeof(mt19937) == 2500, "sizeof(mt19937) != 2500");
+
     py_bindmagic(type, __new__, Random__new__);
     py_bindmagic(type, __init__, Random__init__);
+    py_bindmagic(type, __reduce__, Random__reduce__);
     py_bindmethod(type, "seed", Random_seed);
+    py_bindmethod(type, "getstate", Random_getstate);
+    py_bindmethod(type, "setstate", Random_setstate);
     py_bindmethod(type, "random", Random_random);
     py_bindmethod(type, "uniform", Random_uniform);
     py_bindmethod(type, "randint", Random_randint);
@@ -317,6 +372,8 @@ void pk__add_module_random() {
     py_setdict(mod, py_name(name), py_retval());
 
     ADD_INST_BOUNDMETHOD("seed");
+    ADD_INST_BOUNDMETHOD("getstate");
+    ADD_INST_BOUNDMETHOD("setstate");
     ADD_INST_BOUNDMETHOD("random");
     ADD_INST_BOUNDMETHOD("uniform");
     ADD_INST_BOUNDMETHOD("randint");

src/public/DictSlots.c

@@ -13,11 +13,15 @@ PK_INLINE py_Ref py_getdict(py_Ref self, py_Name name) {
 
 PK_INLINE void py_setdict(py_Ref self, py_Name name, py_Ref val) {
     assert(self && self->is_ptr);
+    // writing to a type's dict may change what `__new__`/`__init__` resolve to,
+    // for this type and for every subclass of it
+    if(self->type == tp_type) pk_current_vm->type_version++;
     NameDict__set(PyObject__dict(self->_obj), name, val);
 }
 
 bool py_deldict(py_Ref self, py_Name name) {
     assert(self && self->is_ptr);
+    if(self->type == tp_type) pk_current_vm->type_version++;
     return NameDict__del(PyObject__dict(self->_obj), name);
 }
 
@@ -40,6 +44,7 @@ bool py_applydict(py_Ref self, bool (*f)(py_Name, py_Ref, void*), void* ctx) {
 
 void py_cleardict(py_Ref self) {
     assert(self && self->is_ptr);
+    if(self->type == tp_type) pk_current_vm->type_version++;
     NameDict* dict = PyObject__dict(self->_obj);
     NameDict__clear(dict);
 }

src/public/PyDict.c

@@ -4,6 +4,7 @@
 #include "pocketpy/common/sstream.h"
 #include "pocketpy/interpreter/types.h"
 #include "pocketpy/interpreter/vm.h"
+#include "pocketpy/interpreter/bindings.h"
 
 typedef struct {
     Dict* dict;  // weakref for slot 0
@@ -644,30 +645,35 @@ py_Type pk_dict__register() {
 }
 
 //////////////////////////
-bool dict_items__next__(int argc, py_Ref argv) {
-    PY_CHECK_ARGC(1);
-    DictIterator* iter = py_touserdata(py_arg(0));
-    if(DictIterator__modified(iter)) return RuntimeError("dictionary modified during iteration");
+PK_DEFINE_NEXT_WRAPPER(dict_items)
+
+int dict_items__iternext(py_Ref self) {
+    DictIterator* iter = py_touserdata(self);
+    if(DictIterator__modified(iter)) {
+        RuntimeError("dictionary modified during iteration");
+        return -1;
+    }
     DictEntry* entry = (DictIterator__next(iter));
     if(entry) {
         switch(iter->mode) {
             case 0:  // keys
                 py_assign(py_retval(), &entry->key);
-                return true;
+                return 1;
             case 1:  // values
                 py_assign(py_retval(), &entry->val);
-                return true;
+                return 1;
             case 2:  // items
             {
                 py_Ref p = py_newtuple(py_retval(), 2);
                 p[0] = entry->key;
                 p[1] = entry->val;
-                return true;
+                return 1;
             }
             default: c11__unreachable();
         }
     }
-    return StopIteration();
+    py_newnil(py_retval());
+    return 0;
 }
 
 bool dict_items__len__(int argc, py_Ref argv) {

src/public/PyException.c

@@ -5,6 +5,7 @@
 #include "pocketpy/interpreter/vm.h"
 #include "pocketpy/common/sstream.h"
 #include "pocketpy/objects/exception.h"
+#include "pocketpy/interpreter/bindings.h"
 
 void py_BaseException__stpush(py_Frame* frame,
                               py_Ref self,
@@ -15,6 +16,10 @@ void py_BaseException__stpush(py_Frame* frame,
     int max_frame_dumps = py_debugger_status() == 1 ? 31 : 7;
     if(ud->stacktrace.length >= max_frame_dumps) return;
     BaseExceptionFrame* frame_dump = c11_vector__emplace(&ud->stacktrace);
+    // `locals` and `globals` are only filled in when the debugger is attached, but the GC
+    // walks them unconditionally; nil them out before anything below can allocate
+    py_newnil(&frame_dump->locals);
+    py_newnil(&frame_dump->globals);
     PK_INCREF(src);
     frame_dump->src = src;
     frame_dump->lineno = lineno;
@@ -307,3 +312,10 @@ bool StopIteration() {
     if(!ok) return false;
     return py_raise(py_retval());
 }
+
+bool pk__raise_stopiteration() {
+    if(py_isnil(py_retval())) return StopIteration();
+    // carry the value, e.g. `StopIteration(<generator return value>)`
+    if(!py_tpcall(tp_StopIteration, 1, py_retval())) return false;
+    return py_raise(py_retval());
+}

src/public/PythonOps.c

@@ -2,6 +2,7 @@
 #include "pocketpy/interpreter/bindings.h"
 #include "pocketpy/interpreter/vm.h"
 #include "pocketpy/objects/base.h"
+#include "pocketpy/objects/exception.h"
 #include "pocketpy/pocketpy.h"
 
 bool py_binaryadd(py_Ref lhs, py_Ref rhs) { return py_binaryop(lhs, rhs, __add__, __radd__); }
@@ -142,43 +143,31 @@ bool py_iter(py_Ref val) {
 }
 
 int py_next(py_Ref val) {
-    VM* vm = pk_current_vm;
-
+    // builtin iterators signal exhaustion without constructing a `StopIteration`
     switch(val->type) {
-        case tp_generator:
-            if(generator__next__(1, val)) return 1;
-            break;
-        case tp_array2d_like_iterator:
-            if(array2d_like_iterator__next__(1, val)) return 1;
-            break;
-        case tp_list_iterator:
-            if(list_iterator__next__(1, val)) return 1;
-            break;
-        case tp_tuple_iterator:
-            if(tuple_iterator__next__(1, val)) return 1;
-            break;
-        case tp_dict_iterator:
-            if(dict_items__next__(1, val)) return 1;
-            break;
-        case tp_range_iterator:
-            if(range_iterator__next__(1, val)) return 1;
-            break;
-        case tp_str_iterator:
-            if(str_iterator__next__(1, val)) return 1;
-            break;
-        default: {
-            py_Ref tmp = py_tpfindmagic(val->type, __next__);
-            if(!tmp) {
-                TypeError("'%t' object is not an iterator", val->type);
-                return -1;
-            }
-            if(py_call(tmp, 1, val)) return 1;
-            break;
-        }
+        case tp_generator: return generator__iternext(val);
+        case tp_array2d_like_iterator: return array2d_like_iterator__iternext(val);
+        case tp_list_iterator: return list_iterator__iternext(val);
+        case tp_tuple_iterator: return tuple_iterator__iternext(val);
+        case tp_dict_iterator: return dict_items__iternext(val);
+        case tp_range_iterator: return range_iterator__iternext(val);
+        case tp_str_iterator: return str_iterator__iternext(val);
+        default: break;
+    }
+
+    VM* vm = pk_current_vm;
+    py_Ref tmp = py_tpfindmagic(val->type, __next__);
+    if(!tmp) {
+        TypeError("'%t' object is not an iterator", val->type);
+        return -1;
     }
+    if(py_call(tmp, 1, val)) return 1;
     if(vm->unhandled_exc.type == tp_StopIteration) {
-        vm->last_retval = vm->unhandled_exc;
+        // unwrap the value so callers never have to touch the exception object
+        BaseException* ud = py_touserdata(&vm->unhandled_exc);
+        py_TValue value = ud->args;
         py_clearexc(NULL);
+        *py_retval() = value;
         return 0;
     }
     return -1;

tests/010_int.py

@@ -871,4 +871,83 @@ assert 9 // 7 == 1
 assert 9 % 8 == 1
 assert 9 // 8 == 1
 assert 9 % 9 == 0
-assert 9 // 9 == 1
+assert 9 // 9 == 1
+
+# `+`, `-`, `*` and the comparisons take an inline fast path when both operands
+# are `int` or `float`. Cover every type pairing and every way out of it.
+i, f = 7, 2.5
+
+# int op int -> int
+assert 7 + 2 == 9 and type(7 + 2) is int
+assert 7 - 2 == 5 and type(7 - 2) is int
+assert 7 * 2 == 14 and type(7 * 2) is int
+
+# float op float -> float
+assert 7.5 + 2.5 == 10.0 and type(7.5 + 2.5) is float
+assert 7.5 - 2.5 == 5.0 and type(7.5 - 2.5) is float
+assert 7.5 * 2.0 == 15.0 and type(7.5 * 2.0) is float
+
+# mixed operands promote to float in both directions
+assert i + f == 9.5 and type(i + f) is float
+assert f + i == 9.5 and type(f + i) is float
+assert i - f == 4.5 and type(i - f) is float
+assert f - i == -4.5 and type(f - i) is float
+assert i * f == 17.5 and type(i * f) is float
+assert f * i == 17.5 and type(f * i) is float
+
+# comparisons, all four pairings
+assert (2 < 7) and not (7 < 2)
+assert (2.5 < 7.5) and not (7.5 < 2.5)
+assert (2 < 7.5) and not (7.5 < 2)
+assert (2.5 < 7) and not (7 < 2.5)
+assert (7 >= 7) and (7.0 >= 7) and (7 >= 7.0) and (7.0 >= 7.0)
+assert (7 == 7.0) and (7.0 == 7) and not (7 != 7.0)
+assert (7 <= 7.0) and (7.0 <= 7) and not (7 > 7.0) and not (7.0 > 7)
+
+# `bool` is a separate type here, not a subclass of `int`, so it must fall
+# through to the generic path and reach `bool.__add__` and friends
+assert True + 2 == 3
+assert 2 + True == 3
+assert True - 1 == 0
+assert 2 * True == 2
+
+# non-numbers still reach their own magic methods
+assert 'a' + 'b' == 'ab'
+assert [1] + [2] == [1, 2]
+assert 'a' * 2 == 'aa'
+assert (1, 2) < (1, 3)
+
+class Vec:
+    def __init__(self, v):
+        self.v = v
+    def __add__(self, other):
+        return Vec(self.v + other.v)
+    def __radd__(self, other):
+        return Vec(self.v + other)
+    def __lt__(self, other):
+        return self.v < other.v
+
+assert (Vec(1) + Vec(2)).v == 3
+assert (2 + Vec(1)).v == 3          # int.__add__ returns NotImplemented -> __radd__
+assert Vec(1) < Vec(2)
+
+# unsupported pairings still raise
+try:
+    1 + 'a'
+    exit(1)
+except TypeError:
+    pass
+try:
+    1 < 'a'
+    exit(1)
+except TypeError:
+    pass
+
+# division is deliberately not on the fast path
+assert 7 / 2 == 3.5 and type(7 / 2) is float
+assert 7 // 2 == 3 and 7 % 2 == 1
+try:
+    1 / 0
+    exit(1)
+except ZeroDivisionError:
+    pass

tests/030_bool.py

@@ -3,6 +3,14 @@ assert True == True
 assert True != False
 assert False == False
 assert False != True
+assert True == 1
+assert False == 0
+assert True != 0
+assert False != 1
+assert 1 == True
+assert 0 == False
+assert 1 != False
+assert 0 != True
 
 # test and/or/not
 assert True and True

tests/280_exception.py

@@ -220,6 +220,15 @@ except Exception as e:
     if type(e) != TypeError:
         exit(1)
 
+try:
+    try:
+        x, y = [1]
+        exit(1)
+    except undefinedfoo:
+        exit(1)
+except NameError:
+    pass
+
 """
 # finally, only
 def finally_only():
@@ -299,3 +308,70 @@ def finally_return():
     
 assert finally_return() == 1
 """
+
+# An exception raised while evaluating an `except` clause must propagate to the
+# enclosing block, never be caught by the very handler that is being entered.
+def _boom():
+    raise TypeError('boom')
+
+# the clause expression itself raises
+try:
+    try:
+        x, y = [1]
+        exit(1)
+    except (IndexError, _boom()):
+        exit(1)
+except TypeError as e:
+    assert str(e) == 'boom'
+
+# a later clause is the one that fails
+try:
+    try:
+        x, y = [1]
+        exit(1)
+    except IndexError:
+        exit(1)
+    except undefinedbar:
+        exit(1)
+except NameError:
+    pass
+
+# a handler body that raises is not caught by its own try block either
+try:
+    try:
+        raise KeyError('k')
+    except KeyError:
+        raise IndexError('i')
+except IndexError as e:
+    assert str(e) == 'i'
+
+# a non-type in an `except` tuple is still a TypeError
+try:
+    try:
+        raise KeyError('k')
+    except (IndexError, 1):
+        exit(1)
+except TypeError:
+    pass
+
+# A value stack overflow must raise, not corrupt memory. Recursion with many
+# locals exhausts the value stack well before the recursion-depth limit.
+def _deep(n):
+    a, b, c, d, e = 1, 2, 3, 4, 5
+    f, g, h, i, j = 1, 2, 3, 4, 5
+    k, l, m, o, p = 1, 2, 3, 4, 5
+    q, r, s, t, u = 1, 2, 3, 4, 5
+    if n == 0:
+        return a
+    return _deep(n - 1)
+
+try:
+    _deep(5000)
+    exit(1)
+except RecursionError:
+    pass
+
+# the VM has to stay usable afterwards
+assert sum(range(100)) == 4950
+assert [x * 2 for x in range(4)] == [0, 2, 4, 6]
+

tests/290_iter.py

@@ -50,3 +50,85 @@ try:
 except StopIteration:
     pass
 
+
+# --- StopIteration carries the right value ------------------------------
+# `py_next` reports exhaustion without building a StopIteration object, so the
+# object has to be reconstructed faithfully wherever one is actually observable.
+
+it = iter([1])
+assert next(it) == 1
+try:
+    next(it)
+    exit(1)
+except StopIteration as e:
+    assert e.args == ()
+    assert e.value is None
+    assert repr(e) == 'StopIteration()'
+
+assert next(iter([]), 'dflt') == 'dflt'
+
+def gen_with_return():
+    yield 1
+    return 42
+
+it = iter(gen_with_return())
+assert next(it) == 1
+try:
+    next(it)
+    exit(1)
+except StopIteration as e:
+    assert e.args == (42,)
+    assert e.value == 42
+
+def gen_bare_return():
+    yield 1
+
+it = iter(gen_bare_return())
+assert next(it) == 1
+try:
+    next(it)
+    exit(1)
+except StopIteration as e:
+    assert e.value is None
+
+# `yield from` reads the value out of the exhausted sub-iterator
+def outer_with_return():
+    got = yield from gen_with_return()
+    yield got
+assert list(outer_with_return()) == [1, 42]
+
+def outer_bare_return():
+    got = yield from gen_bare_return()
+    yield got
+assert list(outer_bare_return()) == [1, None]
+
+class RaisesWithValue:
+    def __iter__(self):
+        return self
+    def __next__(self):
+        raise StopIteration('V')
+
+def outer_user_iter():
+    got = yield from RaisesWithValue()
+    yield got
+assert list(outer_user_iter()) == ['V']
+
+# --- every builtin iterator still terminates ---------------------------
+assert list(iter([1, 2])) == [1, 2]
+assert list(iter((1, 2))) == [1, 2]
+assert list(range(3)) == [0, 1, 2]
+assert list('ab') == ['a', 'b']
+assert ''.join(iter(['a', 'b'])) == 'ab'
+
+d = {'x': 1, 'y': 2}
+assert sorted(d.keys()) == ['x', 'y']
+assert sorted(d.values()) == [1, 2]
+assert sorted(d.items()) == [('x', 1), ('y', 2)]
+
+# a dict mutated mid-iteration must still be reported as an error
+try:
+    for k in d:
+        d['z'] = 3
+    exit(1)
+except RuntimeError:
+    pass

tests/400_class.py

@@ -156,3 +156,40 @@ class E1:
 
 e1 = E1(3,4)
 assert e1.sum() == 7
+
+# `__new__`/`__init__` are resolved once and cached on the type, so rebinding
+# them later has to invalidate that cache -- for the type and for its subclasses.
+class CacheA:
+    def __init__(self):
+        self.tag = 'old'
+
+assert CacheA().tag == 'old'
+
+def _new_init(self):
+    self.tag = 'new'
+
+CacheA.__init__ = _new_init
+assert CacheA().tag == 'new'
+
+class CacheBase: pass
+class CacheDerived(CacheBase): pass
+
+CacheDerived()  # populate the cache before the base is touched
+
+def _base_init(self):
+    self.tag = 'base'
+
+CacheBase.__init__ = _base_init
+assert CacheDerived().tag == 'base'
+
+class CacheC:
+    def __init__(self):
+        self.tag = 'c'
+
+assert CacheC().tag == 'c'
+del CacheC.__init__
+try:
+    CacheC().tag
+    exit(1)
+except AttributeError:
+    pass

tests/510_yield.py

@@ -127,4 +127,60 @@ def f():
     a = yield from g()
     yield a
 
-assert list(f()) == [1, 2, 3]
+assert list(f()) == [1, 2, 3]
+# --- PEP 479: a StopIteration escaping a generator body becomes RuntimeError ---
+# NOTE: the builtin `iter` is shadowed above, so build iterators via generators
+def _exhausted():
+    return
+    yield
+
+def raises_stop_iteration():
+    yield 1
+    raise StopIteration
+
+try:
+    list(raises_stop_iteration())
+    exit(1)
+except RuntimeError as e:
+    assert str(e) == 'generator raised StopIteration', str(e)
+
+it = raises_stop_iteration()
+assert next(it) == 1
+try:
+    next(it)
+    exit(1)
+except RuntimeError:
+    pass
+
+# the same applies when it comes from an exhausted inner iterator
+def drains_inner():
+    inner = _exhausted()
+    yield 1
+    next(inner)
+
+try:
+    list(drains_inner())
+    exit(1)
+except RuntimeError:
+    pass
+
+# a generator that catches it itself is unaffected
+def catches_it():
+    try:
+        next(_exhausted())
+        exit(1)
+    except StopIteration:
+        yield 'caught'
+
+assert list(catches_it()) == ['caught']
+
+# `yield from` over a sub-generator that finishes normally is unaffected
+def sub_with_return():
+    yield 'a'
+    return 'R'
+
+def delegates():
+    got = yield from sub_with_return()
+    yield got
+
+assert list(delegates()) == ['a', 'R']

tests/705_random.py

@@ -73,3 +73,70 @@ assert c == randint(50, 100)
 
 import random
 assert random.Random(7).randint(1, 100) == a
+
+# test getstate/setstate
+r = random.Random(7)
+for _ in range(5):
+    r.random()
+
+state = r.getstate()
+assert isinstance(state, bytes)
+a = [r.randint(0, 1000) for _ in range(10)]
+r.setstate(state)
+assert a == [r.randint(0, 1000) for _ in range(10)]
+
+# a state can be moved between generators
+other = random.Random(123)
+other.setstate(r.getstate())
+assert other.random() == r.random()
+
+# `Random(state)` is equivalent to `setstate`
+assert random.Random(other.getstate()).random() == other.random()
+
+for bad in [b'', b'123', state[:-1]]:
+    try:
+        random.Random().setstate(bad)
+        exit(1)
+    except ValueError:
+        pass
+
+try:
+    random.Random().setstate(7)
+    exit(1)
+except TypeError:
+    pass
+
+# `mti` must stay within [0, 624+1]
+tmp = list(state)
+for mti in ([0xFF, 0xFF, 0xFF, 0xFF], [0x72, 0x02, 0, 0]):
+    try:
+        random.Random().setstate(bytes(tmp[:-4] + mti))
+        exit(1)
+    except ValueError:
+        pass
+
+# module-level generator exposes the same api
+random.seed(456)
+state = random.getstate()
+a = [random.random() for _ in range(5)]
+random.setstate(state)
+assert a == [random.random() for _ in range(5)]
+
+# test pickle
+import pickle
+
+r = random.Random(7)
+for _ in range(5):
+    r.random()
+
+r2 = pickle.loads(pickle.dumps(r))
+assert isinstance(r2, random.Random) and r2 is not r
+assert [r.random() for _ in range(10)] == [r2.random() for _ in range(10)]
+
+# an unseeded generator round-trips as unseeded
+fresh = random.Random()
+assert pickle.loads(pickle.dumps(fresh)).getstate() == fresh.getstate()
+
+# shared references are preserved
+res = pickle.loads(pickle.dumps([r, r]))
+assert res[0] is res[1]

tests/905_pickle1.py

@@ -0,0 +1,85 @@
+class ActorCpnt:
+	def __init__(self, actor, id):
+		self.actor = actor
+		self.id = id
+		
+class Actor:
+	def __init__(self, id):
+		self.cpnts = [ActorCpnt(self, id)]
+
+import pickle as pkl
+a = Actor(123)
+x = pkl.dumps(a)
+b = pkl.loads(x)
+
+assert isinstance(b, Actor)
+assert len(b.cpnts) == 1
+assert b.cpnts[0].actor is b
+assert b.cpnts[0].id == 123
+# self-referencing list
+a = [1, 2]
+a.append(a)
+b = pkl.loads(pkl.dumps(a))
+assert b[0] == 1 and b[1] == 2
+assert b[2] is b
+
+# self-referencing dict
+d = {'k': 1}
+d['me'] = d
+e = pkl.loads(pkl.dumps(d))
+assert e['k'] == 1
+assert e['me'] is e
+
+# two objects referencing each other
+class P:
+	def __init__(self):
+		self.q = None
+class Q:
+	def __init__(self):
+		self.p = None
+
+p = P()
+q = Q()
+p.q = q
+q.p = p
+p2 = pkl.loads(pkl.dumps(p))
+assert isinstance(p2, P)
+assert isinstance(p2.q, Q)
+assert p2.q.p is p2
+
+# object -> dict -> object
+class Node:
+	def __init__(self):
+		self.edges = {}
+
+n = Node()
+n.edges['self'] = n
+n2 = pkl.loads(pkl.dumps(n))
+assert n2.edges['self'] is n2
+
+# longer cycle: list -> dict -> list
+L = []
+D = {'L': L}
+L.append(D)
+L2 = pkl.loads(pkl.dumps(L))
+assert L2[0]['L'] is L2
+
+# a shared object appearing both inside and outside a cycle
+class Box:
+	def __init__(self, v):
+		self.v = v
+
+shared = Box(7)
+root = {'a': shared, 'b': [shared]}
+root['self'] = root
+r = pkl.loads(pkl.dumps(root))
+assert r['self'] is r
+assert r['a'] is r['b'][0]
+assert r['a'].v == 7
+
+# empty containers
+assert pkl.loads(pkl.dumps([])) == []
+assert pkl.loads(pkl.dumps({})) == {}
+class Empty:
+	pass
+assert isinstance(pkl.loads(pkl.dumps(Empty())), Empty)