/home/mdboom/Work/builds/cpython/Objects/longobject.c
Line | Count | Source (jump to first uncovered line) |
1 | /* Long (arbitrary precision) integer object implementation */ |
2 | |
3 | /* XXX The functional organization of this file is terrible */ |
4 | |
5 | #include "Python.h" |
6 | #include "pycore_bitutils.h" // _Py_popcount32() |
7 | #include "pycore_initconfig.h" // _PyStatus_OK() |
8 | #include "pycore_long.h" // _Py_SmallInts |
9 | #include "pycore_object.h" // _PyObject_InitVar() |
10 | #include "pycore_pystate.h" // _Py_IsMainInterpreter() |
11 | #include "pycore_runtime.h" // _PY_NSMALLPOSINTS |
12 | #include "pycore_structseq.h" // _PyStructSequence_FiniType() |
13 | |
14 | #include <ctype.h> |
15 | #include <float.h> |
16 | #include <stddef.h> |
17 | #include <stdlib.h> // abs() |
18 | |
19 | #include "clinic/longobject.c.h" |
20 | /*[clinic input] |
21 | class int "PyObject *" "&PyLong_Type" |
22 | [clinic start generated code]*/ |
23 | /*[clinic end generated code: output=da39a3ee5e6b4b0d input=ec0275e3422a36e3]*/ |
24 | |
25 | /* Is this PyLong of size 1, 0 or -1? */ |
26 | #define IS_MEDIUM_VALUE(x) (((size_t)Py_SIZE170M (x)) + 1U < 3U) |
27 | |
28 | /* convert a PyLong of size 1, 0 or -1 to a C integer */ |
29 | static inline stwodigits |
30 | medium_value(PyLongObject *x) |
31 | { |
32 | assert(IS_MEDIUM_VALUE(x)); |
33 | return ((stwodigits)Py_SIZE(x)) * x->ob_digit[0]; |
34 | } |
35 | |
36 | #define IS_SMALL_INT(ival) (-_PY_NSMALLNEGINTS <= (ival) && (ival) < 263M _PY_NSMALLPOSINTS263M ) |
37 | #define IS_SMALL_UINT(ival) ((ival) < _PY_NSMALLPOSINTS) |
38 | |
39 | static inline void |
40 | _Py_DECREF_INT(PyLongObject *op) |
41 | { |
42 | assert(PyLong_CheckExact(op)); |
43 | _Py_DECREF_SPECIALIZED((PyObject *)op, (destructor)PyObject_Free); |
44 | } |
45 | |
46 | static inline int |
47 | is_medium_int(stwodigits x) |
48 | { |
49 | /* Take care that we are comparing unsigned values. */ |
50 | twodigits x_plus_mask = ((twodigits)x) + PyLong_MASK; |
51 | return x_plus_mask < ((twodigits)PyLong_MASK) + PyLong_BASE; |
52 | } |
53 | |
54 | static PyObject * |
55 | get_small_int(sdigit ival) |
56 | { |
57 | assert(IS_SMALL_INT(ival)); |
58 | PyObject *v = (PyObject *)&_PyLong_SMALL_INTS[_PY_NSMALLNEGINTS + ival]; |
59 | Py_INCREF(v); |
60 | return v; |
61 | } |
62 | |
63 | static PyLongObject * |
64 | maybe_small_long(PyLongObject *v) |
65 | { |
66 | if (v && IS_MEDIUM_VALUE(v)) { Branch (66:9): [True: 13.7M, False: 0]
|
67 | stwodigits ival = medium_value(v); |
68 | if (IS_SMALL_INT(ival)) { |
69 | _Py_DECREF_INT(v); |
70 | return (PyLongObject *)get_small_int((sdigit)ival); |
71 | } |
72 | } |
73 | return v; |
74 | } |
75 | |
76 | /* For int multiplication, use the O(N**2) school algorithm unless |
77 | * both operands contain more than KARATSUBA_CUTOFF digits (this |
78 | * being an internal Python int digit, in base BASE). |
79 | */ |
80 | #define KARATSUBA_CUTOFF 70 |
81 | #define KARATSUBA_SQUARE_CUTOFF (2 * KARATSUBA_CUTOFF) |
82 | |
83 | /* For exponentiation, use the binary left-to-right algorithm unless the |
84 | ^ exponent contains more than HUGE_EXP_CUTOFF bits. In that case, do |
85 | * (no more than) EXP_WINDOW_SIZE bits at a time. The potential drawback is |
86 | * that a table of 2**(EXP_WINDOW_SIZE - 1) intermediate results is |
87 | * precomputed. |
88 | */ |
89 | #define EXP_WINDOW_SIZE 5 |
90 | #define EXP_TABLE_LEN (1 << (EXP_WINDOW_SIZE - 1)) |
91 | /* Suppose the exponent has bit length e. All ways of doing this |
92 | * need e squarings. The binary method also needs a multiply for |
93 | * each bit set. In a k-ary method with window width w, a multiply |
94 | * for each non-zero window, so at worst (and likely!) |
95 | * ceiling(e/w). The k-ary sliding window method has the same |
96 | * worst case, but the window slides so it can sometimes skip |
97 | * over an all-zero window that the fixed-window method can't |
98 | * exploit. In addition, the windowing methods need multiplies |
99 | * to precompute a table of small powers. |
100 | * |
101 | * For the sliding window method with width 5, 16 precomputation |
102 | * multiplies are needed. Assuming about half the exponent bits |
103 | * are set, then, the binary method needs about e/2 extra mults |
104 | * and the window method about 16 + e/5. |
105 | * |
106 | * The latter is smaller for e > 53 1/3. We don't have direct |
107 | * access to the bit length, though, so call it 60, which is a |
108 | * multiple of a long digit's max bit length (15 or 30 so far). |
109 | */ |
110 | #define HUGE_EXP_CUTOFF 60 |
111 | |
112 | #define SIGCHECK(PyTryBlock) \ |
113 | do { \ |
114 | if (PyErr_CheckSignals()) PyTryBlock0 \ |
115 | } while(0) |
116 | |
117 | /* Normalize (remove leading zeros from) an int object. |
118 | Doesn't attempt to free the storage--in most cases, due to the nature |
119 | of the algorithms used, this could save at most be one word anyway. */ |
120 | |
121 | static PyLongObject * |
122 | long_normalize(PyLongObject *v) |
123 | { |
124 | Py_ssize_t j = Py_ABS(Py_SIZE(v)); |
125 | Py_ssize_t i = j; |
126 | |
127 | while (i > 0 && v->ob_digit[i-1] == 040.2M ) Branch (127:12): [True: 40.2M, False: 555k]
Branch (127:21): [True: 13.3M, False: 26.9M]
|
128 | --i; |
129 | if (i != j) { Branch (129:9): [True: 9.80M, False: 17.6M]
|
130 | Py_SET_SIZE(v, (Py_SIZE(v) < 0) ? -(i) : i); |
131 | } |
132 | return v; |
133 | } |
134 | |
135 | /* Allocate a new int object with size digits. |
136 | Return NULL and set exception if we run out of memory. */ |
137 | |
138 | #define MAX_LONG_DIGITS \ |
139 | ((PY_SSIZE_T_MAX - offsetof(PyLongObject, ob_digit))/sizeof(digit)) |
140 | |
141 | PyLongObject * |
142 | _PyLong_New(Py_ssize_t size) |
143 | { |
144 | PyLongObject *result; |
145 | if (size > (Py_ssize_t)MAX_LONG_DIGITS) { Branch (145:9): [True: 0, False: 91.2M]
|
146 | PyErr_SetString(PyExc_OverflowError, |
147 | "too many digits in integer"); |
148 | return NULL; |
149 | } |
150 | /* Fast operations for single digit integers (including zero) |
151 | * assume that there is always at least one digit present. */ |
152 | Py_ssize_t ndigits = size ? size91.2M : 111.5k ; Branch (152:26): [True: 91.2M, False: 11.5k]
|
153 | /* Number of bytes needed is: offsetof(PyLongObject, ob_digit) + |
154 | sizeof(digit)*size. Previous incarnations of this code used |
155 | sizeof(PyVarObject) instead of the offsetof, but this risks being |
156 | incorrect in the presence of padding between the PyVarObject header |
157 | and the digits. */ |
158 | result = PyObject_Malloc(offsetof(PyLongObject, ob_digit) + |
159 | ndigits*sizeof(digit)); |
160 | if (!result) { Branch (160:9): [True: 0, False: 91.2M]
|
161 | PyErr_NoMemory(); |
162 | return NULL; |
163 | } |
164 | _PyObject_InitVar((PyVarObject*)result, &PyLong_Type, size); |
165 | return result; |
166 | } |
167 | |
168 | PyObject * |
169 | _PyLong_Copy(PyLongObject *src) |
170 | { |
171 | PyLongObject *result; |
172 | Py_ssize_t i; |
173 | |
174 | assert(src != NULL); |
175 | i = Py_SIZE(src); |
176 | if (i < 0) Branch (176:9): [True: 199k, False: 570k]
|
177 | i = -(i); |
178 | if (i < 2) { Branch (178:9): [True: 545k, False: 223k]
|
179 | stwodigits ival = medium_value(src); |
180 | if (IS_SMALL_INT(ival)) { |
181 | return get_small_int((sdigit)ival); |
182 | } |
183 | } |
184 | result = _PyLong_New(i); |
185 | if (result != NULL) { Branch (185:9): [True: 259k, False: 0]
|
186 | Py_SET_SIZE(result, Py_SIZE(src)); |
187 | while (--i >= 0) { Branch (187:16): [True: 4.11M, False: 259k]
|
188 | result->ob_digit[i] = src->ob_digit[i]; |
189 | } |
190 | } |
191 | return (PyObject *)result; |
192 | } |
193 | |
194 | static PyObject * |
195 | _PyLong_FromMedium(sdigit x) |
196 | { |
197 | assert(!IS_SMALL_INT(x)); |
198 | assert(is_medium_int(x)); |
199 | /* We could use a freelist here */ |
200 | PyLongObject *v = PyObject_Malloc(sizeof(PyLongObject)); |
201 | if (v == NULL) { Branch (201:9): [True: 0, False: 61.1M]
|
202 | PyErr_NoMemory(); |
203 | return NULL; |
204 | } |
205 | Py_ssize_t sign = x < 0 ? -13.22M : 157.9M ; Branch (205:23): [True: 3.22M, False: 57.9M]
|
206 | digit abs_x = x < 0 ? -x3.22M : x57.9M ; Branch (206:19): [True: 3.22M, False: 57.9M]
|
207 | _PyObject_InitVar((PyVarObject*)v, &PyLong_Type, sign); |
208 | v->ob_digit[0] = abs_x; |
209 | return (PyObject*)v; |
210 | } |
211 | |
212 | static PyObject * |
213 | _PyLong_FromLarge(stwodigits ival) |
214 | { |
215 | twodigits abs_ival; |
216 | int sign; |
217 | assert(!is_medium_int(ival)); |
218 | |
219 | if (ival < 0) { Branch (219:9): [True: 13.5k, False: 17.6M]
|
220 | /* negate: can't write this as abs_ival = -ival since that |
221 | invokes undefined behaviour when ival is LONG_MIN */ |
222 | abs_ival = 0U-(twodigits)ival; |
223 | sign = -1; |
224 | } |
225 | else { |
226 | abs_ival = (twodigits)ival; |
227 | sign = 1; |
228 | } |
229 | /* Must be at least two digits */ |
230 | assert(abs_ival >> PyLong_SHIFT != 0); |
231 | twodigits t = abs_ival >> (PyLong_SHIFT * 2); |
232 | Py_ssize_t ndigits = 2; |
233 | while (t) { Branch (233:12): [True: 0, False: 17.6M]
|
234 | ++ndigits; |
235 | t >>= PyLong_SHIFT; |
236 | } |
237 | PyLongObject *v = _PyLong_New(ndigits); |
238 | if (v != NULL) { Branch (238:9): [True: 17.6M, False: 0]
|
239 | digit *p = v->ob_digit; |
240 | Py_SET_SIZE(v, ndigits * sign); |
241 | t = abs_ival; |
242 | while (t) { Branch (242:16): [True: 35.3M, False: 17.6M]
|
243 | *p++ = Py_SAFE_DOWNCAST( |
244 | t & PyLong_MASK, twodigits, digit); |
245 | t >>= PyLong_SHIFT; |
246 | } |
247 | } |
248 | return (PyObject *)v; |
249 | } |
250 | |
251 | /* Create a new int object from a C word-sized int */ |
252 | static inline PyObject * |
253 | _PyLong_FromSTwoDigits(stwodigits x) |
254 | { |
255 | if (IS_SMALL_INT(x)) { |
256 | return get_small_int((sdigit)x); |
257 | } |
258 | assert(x != 0); |
259 | if (is_medium_int(x)) { Branch (259:9): [True: 16.3M, False: 17.6M]
|
260 | return _PyLong_FromMedium((sdigit)x); |
261 | } |
262 | return _PyLong_FromLarge(x); |
263 | } |
264 | |
265 | int |
266 | _PyLong_AssignValue(PyObject **target, Py_ssize_t value) |
267 | { |
268 | PyObject *old = *target; |
269 | if (IS_SMALL_INT(value)) { |
270 | *target = get_small_int(Py_SAFE_DOWNCAST(value, Py_ssize_t, sdigit)); |
271 | Py_XDECREF(old); |
272 | return 0; |
273 | } |
274 | else if (old != NULL && PyLong_CheckExact(old) && Branch (274:14): [True: 25.6M, False: 2.92k]
|
275 | Py_REFCNT23.5M (old) == 123.5M && Py_SIZE22.3M (old) == 122.3M && Branch (275:14): [True: 22.3M, False: 1.21M]
Branch (275:37): [True: 22.1M, False: 127k]
|
276 | (size_t)value <= 22.1M PyLong_MASK22.1M ) Branch (276:14): [True: 22.1M, False: 2]
|
277 | { |
278 | // Mutate in place if there are no other references the old |
279 | // object. This avoids an allocation in a common case. |
280 | // Since the primary use-case is iterating over ranges, which |
281 | // are typically positive, only do this optimization |
282 | // for positive integers (for now). |
283 | ((PyLongObject *)old)->ob_digit[0] = |
284 | Py_SAFE_DOWNCAST(value, Py_ssize_t, digit); |
285 | return 0; |
286 | } |
287 | else { |
288 | *target = PyLong_FromSsize_t(value); |
289 | Py_XDECREF(old); |
290 | if (*target == NULL) { Branch (290:13): [True: 0, False: 3.44M]
|
291 | return -1; |
292 | } |
293 | return 0; |
294 | } |
295 | } |
296 | |
297 | /* If a freshly-allocated int is already shared, it must |
298 | be a small integer, so negating it must go to PyLong_FromLong */ |
299 | Py_LOCAL_INLINE(void) |
300 | _PyLong_Negate(PyLongObject **x_p) |
301 | { |
302 | PyLongObject *x; |
303 | |
304 | x = (PyLongObject *)*x_p; |
305 | if (Py_REFCNT(x) == 1) { Branch (305:9): [True: 227k, False: 42.7k]
|
306 | Py_SET_SIZE(x, -Py_SIZE(x)); |
307 | return; |
308 | } |
309 | |
310 | *x_p = (PyLongObject *)_PyLong_FromSTwoDigits(-medium_value(x)); |
311 | Py_DECREF(x); |
312 | } |
313 | |
314 | /* Create a new int object from a C long int */ |
315 | |
316 | PyObject * |
317 | PyLong_FromLong(long ival) |
318 | { |
319 | PyLongObject *v; |
320 | unsigned long abs_ival, t; |
321 | int ndigits; |
322 | |
323 | /* Handle small and medium cases. */ |
324 | if (IS_SMALL_INT(ival)) { |
325 | return get_small_int((sdigit)ival); |
326 | } |
327 | if (-(long)PyLong_MASK <= ival && ival <= (long)47.8M PyLong_MASK47.8M ) { Branch (327:9): [True: 47.8M, False: 628k]
Branch (327:39): [True: 44.0M, False: 3.79M]
|
328 | return _PyLong_FromMedium((sdigit)ival); |
329 | } |
330 | |
331 | /* Count digits (at least two - smaller cases were handled above). */ |
332 | abs_ival = ival < 0 ? 0U-(unsigned long)ival628k : (unsigned long)ival3.79M ; Branch (332:16): [True: 628k, False: 3.79M]
|
333 | /* Do shift in two steps to avoid possible undefined behavior. */ |
334 | t = abs_ival >> PyLong_SHIFT >> PyLong_SHIFT; |
335 | ndigits = 2; |
336 | while (t) { Branch (336:12): [True: 142k, False: 4.42M]
|
337 | ++ndigits; |
338 | t >>= PyLong_SHIFT; |
339 | } |
340 | |
341 | /* Construct output value. */ |
342 | v = _PyLong_New(ndigits); |
343 | if (v != NULL) { Branch (343:9): [True: 4.42M, False: 0]
|
344 | digit *p = v->ob_digit; |
345 | Py_SET_SIZE(v, ival < 0 ? -ndigits : ndigits); |
346 | t = abs_ival; |
347 | while (t) { Branch (347:16): [True: 8.99M, False: 4.42M]
|
348 | *p++ = (digit)(t & PyLong_MASK); |
349 | t >>= PyLong_SHIFT; |
350 | } |
351 | } |
352 | return (PyObject *)v; |
353 | } |
354 | |
355 | #define PYLONG_FROM_UINT(INT_TYPE, ival) \ |
356 | do { \ |
357 | if (IS_SMALL_UINT(ival)) { \ |
358 | return get_small_int((sdigit)(ival)); \ |
359 | } \ |
360 | /* Count the number of Python digits. */ \ |
361 | Py_ssize_t ndigits = 0; \ |
362 | INT_TYPE t = (ival); \ |
363 | while (t) { \ |
364 | ++ndigits; \ |
365 | t >>= PyLong_SHIFT; \ |
366 | } \ |
367 | PyLongObject *v = _PyLong_New(ndigits); \ |
368 | if (v == NULL) { \ |
369 | return NULL; \ |
370 | } \ |
371 | digit *p = v->ob_digit; \ |
372 | while ((ival)) { \ |
373 | *p++ = (digit)((ival) & PyLong_MASK); \ |
374 | (ival) >>= PyLong_SHIFT; \ |
375 | } \ |
376 | return (PyObject *)v; \ |
377 | } while(00 ) |
378 | |
379 | /* Create a new int object from a C unsigned long int */ |
380 | |
381 | PyObject * |
382 | PyLong_FromUnsignedLong(unsigned long ival) |
383 | { |
384 | PYLONG_FROM_UINT(unsigned long, ival); |
385 | } |
386 | |
387 | /* Create a new int object from a C unsigned long long int. */ |
388 | |
389 | PyObject * |
390 | PyLong_FromUnsignedLongLong(unsigned long long ival) |
391 | { |
392 | PYLONG_FROM_UINT(unsigned long long, ival); |
393 | } |
394 | |
395 | /* Create a new int object from a C size_t. */ |
396 | |
397 | PyObject * |
398 | PyLong_FromSize_t(size_t ival) |
399 | { |
400 | PYLONG_FROM_UINT(size_t, ival); |
401 | } |
402 | |
403 | /* Create a new int object from a C double */ |
404 | |
405 | PyObject * |
406 | PyLong_FromDouble(double dval) |
407 | { |
408 | /* Try to get out cheap if this fits in a long. When a finite value of real |
409 | * floating type is converted to an integer type, the value is truncated |
410 | * toward zero. If the value of the integral part cannot be represented by |
411 | * the integer type, the behavior is undefined. Thus, we must check that |
412 | * value is in range (LONG_MIN - 1, LONG_MAX + 1). If a long has more bits |
413 | * of precision than a double, casting LONG_MIN - 1 to double may yield an |
414 | * approximation, but LONG_MAX + 1 is a power of two and can be represented |
415 | * as double exactly (assuming FLT_RADIX is 2 or 16), so for simplicity |
416 | * check against [-(LONG_MAX + 1), LONG_MAX + 1). |
417 | */ |
418 | const double int_max = (unsigned long)LONG_MAX + 1; |
419 | if (-int_max < dval && dval < int_max12.2M ) { Branch (419:9): [True: 12.2M, False: 474]
Branch (419:28): [True: 12.2M, False: 1.03k]
|
420 | return PyLong_FromLong((long)dval); |
421 | } |
422 | |
423 | PyLongObject *v; |
424 | double frac; |
425 | int i, ndig, expo, neg; |
426 | neg = 0; |
427 | if (Py_IS_INFINITY(dval)) { |
428 | PyErr_SetString(PyExc_OverflowError, |
429 | "cannot convert float infinity to integer"); |
430 | return NULL; |
431 | } |
432 | if (Py_IS_NAN(dval)) { |
433 | PyErr_SetString(PyExc_ValueError, |
434 | "cannot convert float NaN to integer"); |
435 | return NULL; |
436 | } |
437 | if (dval < 0.0) { Branch (437:9): [True: 464, False: 1.03k]
|
438 | neg = 1; |
439 | dval = -dval; |
440 | } |
441 | frac = frexp(dval, &expo); /* dval = frac*2**expo; 0.0 <= frac < 1.0 */ |
442 | assert(expo > 0); |
443 | ndig = (expo-1) / PyLong_SHIFT + 1; /* Number of 'digits' in result */ |
444 | v = _PyLong_New(ndig); |
445 | if (v == NULL) Branch (445:9): [True: 0, False: 1.49k]
|
446 | return NULL; |
447 | frac = ldexp(frac, (expo-1) % PyLong_SHIFT + 1); |
448 | for (i = ndig; --i >= 0; ) { Branch (448:20): [True: 21.4k, False: 1.49k]
|
449 | digit bits = (digit)frac; |
450 | v->ob_digit[i] = bits; |
451 | frac = frac - (double)bits; |
452 | frac = ldexp(frac, PyLong_SHIFT); |
453 | } |
454 | if (neg) { Branch (454:9): [True: 464, False: 1.03k]
|
455 | Py_SET_SIZE(v, -(Py_SIZE(v))); |
456 | } |
457 | return (PyObject *)v; |
458 | } |
459 | |
460 | /* Checking for overflow in PyLong_AsLong is a PITA since C doesn't define |
461 | * anything about what happens when a signed integer operation overflows, |
462 | * and some compilers think they're doing you a favor by being "clever" |
463 | * then. The bit pattern for the largest positive signed long is |
464 | * (unsigned long)LONG_MAX, and for the smallest negative signed long |
465 | * it is abs(LONG_MIN), which we could write -(unsigned long)LONG_MIN. |
466 | * However, some other compilers warn about applying unary minus to an |
467 | * unsigned operand. Hence the weird "0-". |
468 | */ |
469 | #define PY_ABS_LONG_MIN (0-(unsigned long)LONG_MIN) |
470 | #define PY_ABS_SSIZE_T_MIN (0-(size_t)PY_SSIZE_T_MIN) |
471 | |
472 | /* Get a C long int from an int object or any object that has an __index__ |
473 | method. |
474 | |
475 | On overflow, return -1 and set *overflow to 1 or -1 depending on the sign of |
476 | the result. Otherwise *overflow is 0. |
477 | |
478 | For other errors (e.g., TypeError), return -1 and set an error condition. |
479 | In this case *overflow will be 0. |
480 | */ |
481 | |
482 | long |
483 | PyLong_AsLongAndOverflow(PyObject *vv, int *overflow) |
484 | { |
485 | /* This version by Tim Peters */ |
486 | PyLongObject *v; |
487 | unsigned long x, prev; |
488 | long res; |
489 | Py_ssize_t i; |
490 | int sign; |
491 | int do_decref = 0; /* if PyNumber_Index was called */ |
492 | |
493 | *overflow = 0; |
494 | if (vv == NULL) { Branch (494:9): [True: 0, False: 40.3M]
|
495 | PyErr_BadInternalCall(); |
496 | return -1; |
497 | } |
498 | |
499 | if (PyLong_Check(vv)) { |
500 | v = (PyLongObject *)vv; |
501 | } |
502 | else { |
503 | v = (PyLongObject *)_PyNumber_Index(vv); |
504 | if (v == NULL) Branch (504:13): [True: 76.1k, False: 71]
|
505 | return -1; |
506 | do_decref = 1; |
507 | } |
508 | |
509 | res = -1; |
510 | i = Py_SIZE(v); |
511 | |
512 | switch (i) { |
513 | case -1: Branch (513:5): [True: 539k, False: 39.6M]
|
514 | res = -(sdigit)v->ob_digit[0]; |
515 | break; |
516 | case 0: Branch (516:5): [True: 3.79M, False: 36.4M]
|
517 | res = 0; |
518 | break; |
519 | case 1: Branch (519:5): [True: 35.1M, False: 5.11M]
|
520 | res = v->ob_digit[0]; |
521 | break; |
522 | default: Branch (522:5): [True: 777k, False: 39.4M]
|
523 | sign = 1; |
524 | x = 0; |
525 | if (i < 0) { Branch (525:13): [True: 152k, False: 625k]
|
526 | sign = -1; |
527 | i = -(i); |
528 | } |
529 | while (--i >= 0) { Branch (529:16): [True: 1.61M, False: 770k]
|
530 | prev = x; |
531 | x = (x << PyLong_SHIFT) | v->ob_digit[i]; |
532 | if ((x >> PyLong_SHIFT) != prev) { Branch (532:17): [True: 7.91k, False: 1.61M]
|
533 | *overflow = sign; |
534 | goto exit; |
535 | } |
536 | } |
537 | /* Haven't lost any bits, but casting to long requires extra |
538 | * care (see comment above). |
539 | */ |
540 | if (x <= (unsigned long)LONG_MAX) { Branch (540:13): [True: 755k, False: 14.2k]
|
541 | res = (long)x * sign; |
542 | } |
543 | else if (sign < 0 && x == 8.30k PY_ABS_LONG_MIN8.30k ) { Branch (543:18): [True: 8.30k, False: 5.90k]
Branch (543:30): [True: 3.55k, False: 4.74k]
|
544 | res = LONG_MIN; |
545 | } |
546 | else { |
547 | *overflow = sign; |
548 | /* res is already set to -1 */ |
549 | } |
550 | } |
551 | exit: |
552 | if (do_decref) { Branch (552:9): [True: 71, False: 40.2M]
|
553 | Py_DECREF(v); |
554 | } |
555 | return res; |
556 | } |
557 | |
558 | /* Get a C long int from an int object or any object that has an __index__ |
559 | method. Return -1 and set an error if overflow occurs. */ |
560 | |
561 | long |
562 | PyLong_AsLong(PyObject *obj) |
563 | { |
564 | int overflow; |
565 | long result = PyLong_AsLongAndOverflow(obj, &overflow); |
566 | if (overflow) { Branch (566:9): [True: 16.7k, False: 13.3M]
|
567 | /* XXX: could be cute and give a different |
568 | message for overflow == -1 */ |
569 | PyErr_SetString(PyExc_OverflowError, |
570 | "Python int too large to convert to C long"); |
571 | } |
572 | return result; |
573 | } |
574 | |
575 | /* Get a C int from an int object or any object that has an __index__ |
576 | method. Return -1 and set an error if overflow occurs. */ |
577 | |
578 | int |
579 | _PyLong_AsInt(PyObject *obj) |
580 | { |
581 | int overflow; |
582 | long result = PyLong_AsLongAndOverflow(obj, &overflow); |
583 | if (overflow || result > INT_MAX22.6M || result < INT_MIN22.6M ) { Branch (583:9): [True: 4, False: 22.6M]
Branch (583:21): [True: 23, False: 22.6M]
Branch (583:41): [True: 3, False: 22.6M]
|
584 | /* XXX: could be cute and give a different |
585 | message for overflow == -1 */ |
586 | PyErr_SetString(PyExc_OverflowError, |
587 | "Python int too large to convert to C int"); |
588 | return -1; |
589 | } |
590 | return (int)result; |
591 | } |
592 | |
593 | /* Get a Py_ssize_t from an int object. |
594 | Returns -1 and sets an error condition if overflow occurs. */ |
595 | |
596 | Py_ssize_t |
597 | PyLong_AsSsize_t(PyObject *vv) { |
598 | PyLongObject *v; |
599 | size_t x, prev; |
600 | Py_ssize_t i; |
601 | int sign; |
602 | |
603 | if (vv == NULL) { Branch (603:9): [True: 0, False: 80.5M]
|
604 | PyErr_BadInternalCall(); |
605 | return -1; |
606 | } |
607 | if (!PyLong_Check(vv)) { Branch (607:9): [True: 21, False: 80.5M]
|
608 | PyErr_SetString(PyExc_TypeError, "an integer is required"); |
609 | return -1; |
610 | } |
611 | |
612 | v = (PyLongObject *)vv; |
613 | i = Py_SIZE(v); |
614 | switch (i) { Branch (614:13): [True: 1.05M, False: 79.4M]
|
615 | case -1: return -(sdigit)v->ob_digit[0]; Branch (615:5): [True: 8.49M, False: 72.0M]
|
616 | case 0: return 0; Branch (616:5): [True: 9.44M, False: 71.0M]
|
617 | case 1: return v->ob_digit[0]; Branch (617:5): [True: 61.5M, False: 18.9M]
|
618 | } |
619 | sign = 1; |
620 | x = 0; |
621 | if (i < 0) { Branch (621:9): [True: 337k, False: 715k]
|
622 | sign = -1; |
623 | i = -(i); |
624 | } |
625 | while (--i >= 0) { Branch (625:12): [True: 3.06M, False: 1.04M]
|
626 | prev = x; |
627 | x = (x << PyLong_SHIFT) | v->ob_digit[i]; |
628 | if ((x >> PyLong_SHIFT) != prev) Branch (628:13): [True: 2.61k, False: 3.06M]
|
629 | goto overflow; |
630 | } |
631 | /* Haven't lost any bits, but casting to a signed type requires |
632 | * extra care (see comment above). |
633 | */ |
634 | if (x <= (size_t)PY_SSIZE_T_MAX) { Branch (634:9): [True: 1.04M, False: 1.06k]
|
635 | return (Py_ssize_t)x * sign; |
636 | } |
637 | else if (sign < 0 && x == 482 PY_ABS_SSIZE_T_MIN482 ) { Branch (637:14): [True: 482, False: 581]
Branch (637:26): [True: 24, False: 458]
|
638 | return PY_SSIZE_T_MIN; |
639 | } |
640 | /* else overflow */ |
641 | |
642 | overflow: |
643 | PyErr_SetString(PyExc_OverflowError, |
644 | "Python int too large to convert to C ssize_t"); |
645 | return -1; |
646 | } |
647 | |
648 | /* Get a C unsigned long int from an int object. |
649 | Returns -1 and sets an error condition if overflow occurs. */ |
650 | |
651 | unsigned long |
652 | PyLong_AsUnsignedLong(PyObject *vv) |
653 | { |
654 | PyLongObject *v; |
655 | unsigned long x, prev; |
656 | Py_ssize_t i; |
657 | |
658 | if (vv == NULL) { Branch (658:9): [True: 0, False: 1.39M]
|
659 | PyErr_BadInternalCall(); |
660 | return (unsigned long)-1; |
661 | } |
662 | if (!PyLong_Check(vv)) { Branch (662:9): [True: 12, False: 1.39M]
|
663 | PyErr_SetString(PyExc_TypeError, "an integer is required"); |
664 | return (unsigned long)-1; |
665 | } |
666 | |
667 | v = (PyLongObject *)vv; |
668 | i = Py_SIZE(v); |
669 | x = 0; |
670 | if (i < 0) { Branch (670:9): [True: 3.14k, False: 1.39M]
|
671 | PyErr_SetString(PyExc_OverflowError, |
672 | "can't convert negative value to unsigned int"); |
673 | return (unsigned long) -1; |
674 | } |
675 | switch (i) { Branch (675:13): [True: 208k, False: 1.18M]
|
676 | case 0: return 0; Branch (676:5): [True: 130k, False: 1.26M]
|
677 | case 1: return v->ob_digit[0]; Branch (677:5): [True: 1.05M, False: 338k]
|
678 | } |
679 | while (208k --i >= 0) { Branch (679:12): [True: 510k, False: 208k]
|
680 | prev = x; |
681 | x = (x << PyLong_SHIFT) | v->ob_digit[i]; |
682 | if ((x >> PyLong_SHIFT) != prev) { Branch (682:13): [True: 84, False: 510k]
|
683 | PyErr_SetString(PyExc_OverflowError, |
684 | "Python int too large to convert " |
685 | "to C unsigned long"); |
686 | return (unsigned long) -1; |
687 | } |
688 | } |
689 | return x; |
690 | } |
691 | |
692 | /* Get a C size_t from an int object. Returns (size_t)-1 and sets |
693 | an error condition if overflow occurs. */ |
694 | |
695 | size_t |
696 | PyLong_AsSize_t(PyObject *vv) |
697 | { |
698 | PyLongObject *v; |
699 | size_t x, prev; |
700 | Py_ssize_t i; |
701 | |
702 | if (vv == NULL) { Branch (702:9): [True: 0, False: 40.6k]
|
703 | PyErr_BadInternalCall(); |
704 | return (size_t) -1; |
705 | } |
706 | if (!PyLong_Check(vv)) { Branch (706:9): [True: 1, False: 40.5k]
|
707 | PyErr_SetString(PyExc_TypeError, "an integer is required"); |
708 | return (size_t)-1; |
709 | } |
710 | |
711 | v = (PyLongObject *)vv; |
712 | i = Py_SIZE(v); |
713 | x = 0; |
714 | if (i < 0) { Branch (714:9): [True: 803, False: 39.7k]
|
715 | PyErr_SetString(PyExc_OverflowError, |
716 | "can't convert negative value to size_t"); |
717 | return (size_t) -1; |
718 | } |
719 | switch (i) { Branch (719:13): [True: 38.9k, False: 818]
|
720 | case 0: return 0; Branch (720:5): [True: 24, False: 39.7k]
|
721 | case 1: return v->ob_digit[0]; Branch (721:5): [True: 794, False: 39.0k]
|
722 | } |
723 | while (38.9k --i >= 0) { Branch (723:12): [True: 114k, False: 38.9k]
|
724 | prev = x; |
725 | x = (x << PyLong_SHIFT) | v->ob_digit[i]; |
726 | if ((x >> PyLong_SHIFT) != prev) { Branch (726:13): [True: 25, False: 114k]
|
727 | PyErr_SetString(PyExc_OverflowError, |
728 | "Python int too large to convert to C size_t"); |
729 | return (size_t) -1; |
730 | } |
731 | } |
732 | return x; |
733 | } |
734 | |
735 | /* Get a C unsigned long int from an int object, ignoring the high bits. |
736 | Returns -1 and sets an error condition if an error occurs. */ |
737 | |
738 | static unsigned long |
739 | _PyLong_AsUnsignedLongMask(PyObject *vv) |
740 | { |
741 | PyLongObject *v; |
742 | unsigned long x; |
743 | Py_ssize_t i; |
744 | int sign; |
745 | |
746 | if (vv == NULL || !PyLong_Check(vv)) { Branch (746:9): [True: 0, False: 265k]
Branch (746:23): [True: 0, False: 265k]
|
747 | PyErr_BadInternalCall(); |
748 | return (unsigned long) -1; |
749 | } |
750 | v = (PyLongObject *)vv; |
751 | i = Py_SIZE(v); |
752 | switch (i) { Branch (752:13): [True: 104k, False: 161k]
|
753 | case 0: return 0; Branch (753:5): [True: 14.5k, False: 251k]
|
754 | case 1: return v->ob_digit[0]; Branch (754:5): [True: 146k, False: 119k]
|
755 | } |
756 | sign = 1; |
757 | x = 0; |
758 | if (i < 0) { Branch (758:9): [True: 250, False: 104k]
|
759 | sign = -1; |
760 | i = -i; |
761 | } |
762 | while (--i >= 0) { Branch (762:12): [True: 208k, False: 104k]
|
763 | x = (x << PyLong_SHIFT) | v->ob_digit[i]; |
764 | } |
765 | return x * sign; |
766 | } |
767 | |
768 | unsigned long |
769 | PyLong_AsUnsignedLongMask(PyObject *op) |
770 | { |
771 | PyLongObject *lo; |
772 | unsigned long val; |
773 | |
774 | if (op == NULL) { Branch (774:9): [True: 0, False: 268k]
|
775 | PyErr_BadInternalCall(); |
776 | return (unsigned long)-1; |
777 | } |
778 | |
779 | if (PyLong_Check(op)) { |
780 | return _PyLong_AsUnsignedLongMask(op); |
781 | } |
782 | |
783 | lo = (PyLongObject *)_PyNumber_Index(op); |
784 | if (lo == NULL) Branch (784:9): [True: 2.97k, False: 17]
|
785 | return (unsigned long)-1; |
786 | |
787 | val = _PyLong_AsUnsignedLongMask((PyObject *)lo); |
788 | Py_DECREF(lo); |
789 | return val; |
790 | } |
791 | |
792 | int |
793 | _PyLong_Sign(PyObject *vv) |
794 | { |
795 | PyLongObject *v = (PyLongObject *)vv; |
796 | |
797 | assert(v != NULL); |
798 | assert(PyLong_Check(v)); |
799 | |
800 | return Py_SIZE(v) == 0 ? 01.84M : (1.05M Py_SIZE1.05M (v) < 01.05M ? -1143k : 1909k ); Branch (800:12): [True: 1.84M, False: 1.05M]
Branch (800:35): [True: 143k, False: 909k]
|
801 | } |
802 | |
803 | static int |
804 | bit_length_digit(digit x) |
805 | { |
806 | // digit can be larger than unsigned long, but only PyLong_SHIFT bits |
807 | // of it will be ever used. |
808 | static_assert(PyLong_SHIFT <= sizeof(unsigned long) * 8, |
809 | "digit is larger than unsigned long"); |
810 | return _Py_bit_length((unsigned long)x); |
811 | } |
812 | |
813 | size_t |
814 | _PyLong_NumBits(PyObject *vv) |
815 | { |
816 | PyLongObject *v = (PyLongObject *)vv; |
817 | size_t result = 0; |
818 | Py_ssize_t ndigits; |
819 | int msd_bits; |
820 | |
821 | assert(v != NULL); |
822 | assert(PyLong_Check(v)); |
823 | ndigits = Py_ABS(Py_SIZE(v)); |
824 | assert(ndigits == 0 || v->ob_digit[ndigits - 1] != 0); |
825 | if (ndigits > 0) { Branch (825:9): [True: 534k, False: 1.23M]
|
826 | digit msd = v->ob_digit[ndigits - 1]; |
827 | if ((size_t)(ndigits - 1) > SIZE_MAX / (size_t)PyLong_SHIFT) Branch (827:13): [True: 0, False: 534k]
|
828 | goto Overflow; |
829 | result = (size_t)(ndigits - 1) * (size_t)PyLong_SHIFT; |
830 | msd_bits = bit_length_digit(msd); |
831 | if (SIZE_MAX - msd_bits < result) Branch (831:13): [True: 0, False: 534k]
|
832 | goto Overflow; |
833 | result += msd_bits; |
834 | } |
835 | return result; |
836 | |
837 | Overflow: |
838 | PyErr_SetString(PyExc_OverflowError, "int has too many bits " |
839 | "to express in a platform size_t"); |
840 | return (size_t)-1; |
841 | } |
842 | |
843 | PyObject * |
844 | _PyLong_FromByteArray(const unsigned char* bytes, size_t n, |
845 | int little_endian, int is_signed) |
846 | { |
847 | const unsigned char* pstartbyte; /* LSB of bytes */ |
848 | int incr; /* direction to move pstartbyte */ |
849 | const unsigned char* pendbyte; /* MSB of bytes */ |
850 | size_t numsignificantbytes; /* number of bytes that matter */ |
851 | Py_ssize_t ndigits; /* number of Python int digits */ |
852 | PyLongObject* v; /* result */ |
853 | Py_ssize_t idigit = 0; /* next free index in v->ob_digit */ |
854 | |
855 | if (n == 0) Branch (855:9): [True: 12, False: 3.66M]
|
856 | return PyLong_FromLong(0L); |
857 | |
858 | if (little_endian) { Branch (858:9): [True: 3.50M, False: 166k]
|
859 | pstartbyte = bytes; |
860 | pendbyte = bytes + n - 1; |
861 | incr = 1; |
862 | } |
863 | else { |
864 | pstartbyte = bytes + n - 1; |
865 | pendbyte = bytes; |
866 | incr = -1; |
867 | } |
868 | |
869 | if (is_signed) Branch (869:9): [True: 7.52k, False: 3.66M]
|
870 | is_signed = *pendbyte >= 0x80; |
871 | |
872 | /* Compute numsignificantbytes. This consists of finding the most |
873 | significant byte. Leading 0 bytes are insignificant if the number |
874 | is positive, and leading 0xff bytes if negative. */ |
875 | { |
876 | size_t i; |
877 | const unsigned char* p = pendbyte; |
878 | const int pincr = -incr; /* search MSB to LSB */ |
879 | const unsigned char insignificant = is_signed ? 0xff1.96k : 0x003.66M ; Branch (879:45): [True: 1.96k, False: 3.66M]
|
880 | |
881 | for (i = 0; i < n; ++i, p += pincr1.64M ) { Branch (881:21): [True: 5.30M, False: 7.95k]
|
882 | if (*p != insignificant) Branch (882:17): [True: 3.66M, False: 1.64M]
|
883 | break; |
884 | } |
885 | numsignificantbytes = n - i; |
886 | /* 2's-comp is a bit tricky here, e.g. 0xff00 == -0x0100, so |
887 | actually has 2 significant bytes. OTOH, 0xff0001 == |
888 | -0x00ffff, so we wouldn't *need* to bump it there; but we |
889 | do for 0xffff = -0x0001. To be safe without bothering to |
890 | check every case, bump it regardless. */ |
891 | if (is_signed && numsignificantbytes < n1.96k ) Branch (891:13): [True: 1.96k, False: 3.66M]
Branch (891:26): [True: 781, False: 1.18k]
|
892 | ++numsignificantbytes; |
893 | } |
894 | |
895 | /* How many Python int digits do we need? We have |
896 | 8*numsignificantbytes bits, and each Python int digit has |
897 | PyLong_SHIFT bits, so it's the ceiling of the quotient. */ |
898 | /* catch overflow before it happens */ |
899 | if (numsignificantbytes > (PY_SSIZE_T_MAX - PyLong_SHIFT) / 8) { Branch (899:9): [True: 0, False: 3.66M]
|
900 | PyErr_SetString(PyExc_OverflowError, |
901 | "byte array too long to convert to int"); |
902 | return NULL; |
903 | } |
904 | ndigits = (numsignificantbytes * 8 + PyLong_SHIFT - 1) / PyLong_SHIFT; |
905 | v = _PyLong_New(ndigits); |
906 | if (v == NULL) Branch (906:9): [True: 0, False: 3.66M]
|
907 | return NULL; |
908 | |
909 | /* Copy the bits over. The tricky parts are computing 2's-comp on |
910 | the fly for signed numbers, and dealing with the mismatch between |
911 | 8-bit bytes and (probably) 15-bit Python digits.*/ |
912 | { |
913 | size_t i; |
914 | twodigits carry = 1; /* for 2's-comp calculation */ |
915 | twodigits accum = 0; /* sliding register */ |
916 | unsigned int accumbits = 0; /* number of bits in accum */ |
917 | const unsigned char* p = pstartbyte; |
918 | |
919 | for (i = 0; i < numsignificantbytes; ++i, p += incr81.4M ) { Branch (919:21): [True: 81.4M, False: 3.66M]
|
920 | twodigits thisbyte = *p; |
921 | /* Compute correction for 2's comp, if needed. */ |
922 | if (is_signed) { Branch (922:17): [True: 972k, False: 80.4M]
|
923 | thisbyte = (0xff ^ thisbyte) + carry; |
924 | carry = thisbyte >> 8; |
925 | thisbyte &= 0xff; |
926 | } |
927 | /* Because we're going LSB to MSB, thisbyte is |
928 | more significant than what's already in accum, |
929 | so needs to be prepended to accum. */ |
930 | accum |= thisbyte << accumbits; |
931 | accumbits += 8; |
932 | if (accumbits >= PyLong_SHIFT) { Branch (932:17): [True: 20.9M, False: 60.5M]
|
933 | /* There's enough to fill a Python digit. */ |
934 | assert(idigit < ndigits); |
935 | v->ob_digit[idigit] = (digit)(accum & PyLong_MASK); |
936 | ++idigit; |
937 | accum >>= PyLong_SHIFT; |
938 | accumbits -= PyLong_SHIFT; |
939 | assert(accumbits < PyLong_SHIFT); |
940 | } |
941 | } |
942 | assert(accumbits < PyLong_SHIFT); |
943 | if (accumbits) { Branch (943:13): [True: 3.64M, False: 19.2k]
|
944 | assert(idigit < ndigits); |
945 | v->ob_digit[idigit] = (digit)accum; |
946 | ++idigit; |
947 | } |
948 | } |
949 | |
950 | Py_SET_SIZE(v, is_signed ? -idigit : idigit); |
951 | return (PyObject *)maybe_small_long(long_normalize(v)); |
952 | } |
953 | |
954 | int |
955 | _PyLong_AsByteArray(PyLongObject* v, |
956 | unsigned char* bytes, size_t n, |
957 | int little_endian, int is_signed) |
958 | { |
959 | Py_ssize_t i; /* index into v->ob_digit */ |
960 | Py_ssize_t ndigits; /* |v->ob_size| */ |
961 | twodigits accum; /* sliding register */ |
962 | unsigned int accumbits; /* # bits in accum */ |
963 | int do_twos_comp; /* store 2's-comp? is_signed and v < 0 */ |
964 | digit carry; /* for computing 2's-comp */ |
965 | size_t j; /* # bytes filled */ |
966 | unsigned char* p; /* pointer to next byte in bytes */ |
967 | int pincr; /* direction to move p */ |
968 | |
969 | assert(v != NULL && PyLong_Check(v)); |
970 | |
971 | if (Py_SIZE(v) < 0) { Branch (971:9): [True: 77.6k, False: 462k]
|
972 | ndigits = -(Py_SIZE(v)); |
973 | if (!is_signed) { Branch (973:13): [True: 2.42k, False: 75.1k]
|
974 | PyErr_SetString(PyExc_OverflowError, |
975 | "can't convert negative int to unsigned"); |
976 | return -1; |
977 | } |
978 | do_twos_comp = 1; |
979 | } |
980 | else { |
981 | ndigits = Py_SIZE(v); |
982 | do_twos_comp = 0; |
983 | } |
984 | |
985 | if (little_endian) { Branch (985:9): [True: 303k, False: 234k]
|
986 | p = bytes; |
987 | pincr = 1; |
988 | } |
989 | else { |
990 | p = bytes + n - 1; |
991 | pincr = -1; |
992 | } |
993 | |
994 | /* Copy over all the Python digits. |
995 | It's crucial that every Python digit except for the MSD contribute |
996 | exactly PyLong_SHIFT bits to the total, so first assert that the int is |
997 | normalized. */ |
998 | assert(ndigits == 0 || v->ob_digit[ndigits - 1] != 0); |
999 | j = 0; |
1000 | accum = 0; |
1001 | accumbits = 0; |
1002 | carry = do_twos_comp ? 175.1k : 0462k ; Branch (1002:13): [True: 75.1k, False: 462k]
|
1003 | for (i = 0; i < ndigits; ++i12.7M ) { Branch (1003:17): [True: 12.7M, False: 537k]
|
1004 | digit thisdigit = v->ob_digit[i]; |
1005 | if (do_twos_comp) { Branch (1005:13): [True: 428k, False: 12.3M]
|
1006 | thisdigit = (thisdigit ^ PyLong_MASK) + carry; |
1007 | carry = thisdigit >> PyLong_SHIFT; |
1008 | thisdigit &= PyLong_MASK; |
1009 | } |
1010 | /* Because we're going LSB to MSB, thisdigit is more |
1011 | significant than what's already in accum, so needs to be |
1012 | prepended to accum. */ |
1013 | accum |= (twodigits)thisdigit << accumbits; |
1014 | |
1015 | /* The most-significant digit may be (probably is) at least |
1016 | partly empty. */ |
1017 | if (i == ndigits - 1) { Branch (1017:13): [True: 535k, False: 12.2M]
|
1018 | /* Count # of sign bits -- they needn't be stored, |
1019 | * although for signed conversion we need later to |
1020 | * make sure at least one sign bit gets stored. */ |
1021 | digit s = do_twos_comp ? thisdigit ^ 75.1k PyLong_MASK75.1k : thisdigit460k ; Branch (1021:23): [True: 75.1k, False: 460k]
|
1022 | while (s != 0) { Branch (1022:20): [True: 4.93M, False: 535k]
|
1023 | s >>= 1; |
1024 | accumbits++; |
1025 | } |
1026 | } |
1027 | else |
1028 | accumbits += PyLong_SHIFT; |
1029 | |
1030 | /* Store as many bytes as possible. */ |
1031 | while (accumbits >= 8) { Branch (1031:16): [True: 46.3M, False: 12.7M]
|
1032 | if (j >= n) Branch (1032:17): [True: 10, False: 46.3M]
|
1033 | goto Overflow; |
1034 | ++j; |
1035 | *p = (unsigned char)(accum & 0xff); |
1036 | p += pincr; |
1037 | accumbits -= 8; |
1038 | accum >>= 8; |
1039 | } |
1040 | } |
1041 | |
1042 | /* Store the straggler (if any). */ |
1043 | assert(accumbits < 8); |
1044 | assert(carry == 0); /* else do_twos_comp and *every* digit was 0 */ |
1045 | if (accumbits > 0) { Branch (1045:9): [True: 414k, False: 122k]
|
1046 | if (j >= n) Branch (1046:13): [True: 209, False: 414k]
|
1047 | goto Overflow; |
1048 | ++j; |
1049 | if (do_twos_comp) { Branch (1049:13): [True: 73.3k, False: 341k]
|
1050 | /* Fill leading bits of the byte with sign bits |
1051 | (appropriately pretending that the int had an |
1052 | infinite supply of sign bits). */ |
1053 | accum |= (~(twodigits)0) << accumbits; |
1054 | } |
1055 | *p = (unsigned char)(accum & 0xff); |
1056 | p += pincr; |
1057 | } |
1058 | else if (j == n && n > 075.1k && is_signed75.1k ) { Branch (1058:14): [True: 75.1k, False: 47.7k]
Branch (1058:24): [True: 75.1k, False: 5]
Branch (1058:33): [True: 1.20k, False: 73.9k]
|
1059 | /* The main loop filled the byte array exactly, so the code |
1060 | just above didn't get to ensure there's a sign bit, and the |
1061 | loop below wouldn't add one either. Make sure a sign bit |
1062 | exists. */ |
1063 | unsigned char msb = *(p - pincr); |
1064 | int sign_bit_set = msb >= 0x80; |
1065 | assert(accumbits == 0); |
1066 | if (sign_bit_set == do_twos_comp) Branch (1066:13): [True: 0, False: 1.20k]
|
1067 | return 0; |
1068 | else |
1069 | goto Overflow; |
1070 | } |
1071 | |
1072 | /* Fill remaining bytes with copies of the sign bit. */ |
1073 | { |
1074 | unsigned char signbyte = do_twos_comp ? 0xffU74.5k : 0U461k ; Branch (1074:34): [True: 74.5k, False: 461k]
|
1075 | for ( ; j < n; ++j, p += pincr506k ) Branch (1075:17): [True: 506k, False: 536k]
|
1076 | *p = signbyte; |
1077 | } |
1078 | |
1079 | return 0; |
1080 | |
1081 | Overflow: |
1082 | PyErr_SetString(PyExc_OverflowError, "int too big to convert"); |
1083 | return -1; |
1084 | |
1085 | } |
1086 | |
1087 | /* Create a new int object from a C pointer */ |
1088 | |
1089 | PyObject * |
1090 | PyLong_FromVoidPtr(void *p) |
1091 | { |
1092 | #if SIZEOF_VOID_P <= SIZEOF_LONG |
1093 | return PyLong_FromUnsignedLong((unsigned long)(uintptr_t)p); |
1094 | #else |
1095 | |
1096 | #if SIZEOF_LONG_LONG < SIZEOF_VOID_P |
1097 | # error "PyLong_FromVoidPtr: sizeof(long long) < sizeof(void*)" |
1098 | #endif |
1099 | return PyLong_FromUnsignedLongLong((unsigned long long)(uintptr_t)p); |
1100 | #endif /* SIZEOF_VOID_P <= SIZEOF_LONG */ |
1101 | |
1102 | } |
1103 | |
1104 | /* Get a C pointer from an int object. */ |
1105 | |
1106 | void * |
1107 | PyLong_AsVoidPtr(PyObject *vv) |
1108 | { |
1109 | #if SIZEOF_VOID_P <= SIZEOF_LONG |
1110 | long x; |
1111 | |
1112 | if (PyLong_Check(vv) && _PyLong_Sign(vv) < 0) Branch (1112:29): [True: 0, False: 58.8k]
|
1113 | x = PyLong_AsLong(vv); |
1114 | else |
1115 | x = PyLong_AsUnsignedLong(vv); |
1116 | #else |
1117 | |
1118 | #if SIZEOF_LONG_LONG < SIZEOF_VOID_P |
1119 | # error "PyLong_AsVoidPtr: sizeof(long long) < sizeof(void*)" |
1120 | #endif |
1121 | long long x; |
1122 | |
1123 | if (PyLong_Check(vv) && _PyLong_Sign(vv) < 0) |
1124 | x = PyLong_AsLongLong(vv); |
1125 | else |
1126 | x = PyLong_AsUnsignedLongLong(vv); |
1127 | |
1128 | #endif /* SIZEOF_VOID_P <= SIZEOF_LONG */ |
1129 | |
1130 | if (x == -1 && PyErr_Occurred()4 ) Branch (1130:9): [True: 4, False: 58.8k]
Branch (1130:20): [True: 3, False: 1]
|
1131 | return NULL; |
1132 | return (void *)x; |
1133 | } |
1134 | |
1135 | /* Initial long long support by Chris Herborth (chrish@qnx.com), later |
1136 | * rewritten to use the newer PyLong_{As,From}ByteArray API. |
1137 | */ |
1138 | |
1139 | #define PY_ABS_LLONG_MIN (0-(unsigned long long)LLONG_MIN) |
1140 | |
1141 | /* Create a new int object from a C long long int. */ |
1142 | |
1143 | PyObject * |
1144 | PyLong_FromLongLong(long long ival) |
1145 | { |
1146 | PyLongObject *v; |
1147 | unsigned long long abs_ival, t; |
1148 | int ndigits; |
1149 | |
1150 | /* Handle small and medium cases. */ |
1151 | if (IS_SMALL_INT(ival)) { |
1152 | return get_small_int((sdigit)ival); |
1153 | } |
1154 | if (-(long long)PyLong_MASK <= ival && ival <= (long long)1.83M PyLong_MASK1.83M ) { Branch (1154:9): [True: 1.83M, False: 146k]
Branch (1154:44): [True: 689k, False: 1.14M]
|
1155 | return _PyLong_FromMedium((sdigit)ival); |
1156 | } |
1157 | |
1158 | /* Count digits (at least two - smaller cases were handled above). */ |
1159 | abs_ival = ival < 0 ? 0U-(unsigned long long)ival146k : (unsigned long long)ival1.14M ; Branch (1159:16): [True: 146k, False: 1.14M]
|
1160 | /* Do shift in two steps to avoid possible undefined behavior. */ |
1161 | t = abs_ival >> PyLong_SHIFT >> PyLong_SHIFT; |
1162 | ndigits = 2; |
1163 | while (t) { Branch (1163:12): [True: 225k, False: 1.29M]
|
1164 | ++ndigits; |
1165 | t >>= PyLong_SHIFT; |
1166 | } |
1167 | |
1168 | /* Construct output value. */ |
1169 | v = _PyLong_New(ndigits); |
1170 | if (v != NULL) { Branch (1170:9): [True: 1.29M, False: 0]
|
1171 | digit *p = v->ob_digit; |
1172 | Py_SET_SIZE(v, ival < 0 ? -ndigits : ndigits); |
1173 | t = abs_ival; |
1174 | while (t) { Branch (1174:16): [True: 2.80M, False: 1.29M]
|
1175 | *p++ = (digit)(t & PyLong_MASK); |
1176 | t >>= PyLong_SHIFT; |
1177 | } |
1178 | } |
1179 | return (PyObject *)v; |
1180 | } |
1181 | |
1182 | /* Create a new int object from a C Py_ssize_t. */ |
1183 | |
1184 | PyObject * |
1185 | PyLong_FromSsize_t(Py_ssize_t ival) |
1186 | { |
1187 | PyLongObject *v; |
1188 | size_t abs_ival; |
1189 | size_t t; /* unsigned so >> doesn't propagate sign bit */ |
1190 | int ndigits = 0; |
1191 | int negative = 0; |
1192 | |
1193 | if (IS_SMALL_INT(ival)) { |
1194 | return get_small_int((sdigit)ival); |
1195 | } |
1196 | |
1197 | if (ival < 0) { Branch (1197:9): [True: 1.05M, False: 14.0M]
|
1198 | /* avoid signed overflow when ival = SIZE_T_MIN */ |
1199 | abs_ival = (size_t)(-1-ival)+1; |
1200 | negative = 1; |
1201 | } |
1202 | else { |
1203 | abs_ival = (size_t)ival; |
1204 | } |
1205 | |
1206 | /* Count the number of Python digits. */ |
1207 | t = abs_ival; |
1208 | while (t) { Branch (1208:12): [True: 18.5M, False: 15.1M]
|
1209 | ++ndigits; |
1210 | t >>= PyLong_SHIFT; |
1211 | } |
1212 | v = _PyLong_New(ndigits); |
1213 | if (v != NULL) { Branch (1213:9): [True: 15.1M, False: 0]
|
1214 | digit *p = v->ob_digit; |
1215 | Py_SET_SIZE(v, negative ? -ndigits : ndigits); |
1216 | t = abs_ival; |
1217 | while (t) { Branch (1217:16): [True: 18.5M, False: 15.1M]
|
1218 | *p++ = (digit)(t & PyLong_MASK); |
1219 | t >>= PyLong_SHIFT; |
1220 | } |
1221 | } |
1222 | return (PyObject *)v; |
1223 | } |
1224 | |
1225 | /* Get a C long long int from an int object or any object that has an |
1226 | __index__ method. Return -1 and set an error if overflow occurs. */ |
1227 | |
1228 | long long |
1229 | PyLong_AsLongLong(PyObject *vv) |
1230 | { |
1231 | PyLongObject *v; |
1232 | long long bytes; |
1233 | int res; |
1234 | int do_decref = 0; /* if PyNumber_Index was called */ |
1235 | |
1236 | if (vv == NULL) { Branch (1236:9): [True: 0, False: 280k]
|
1237 | PyErr_BadInternalCall(); |
1238 | return -1; |
1239 | } |
1240 | |
1241 | if (PyLong_Check(vv)) { |
1242 | v = (PyLongObject *)vv; |
1243 | } |
1244 | else { |
1245 | v = (PyLongObject *)_PyNumber_Index(vv); |
1246 | if (v == NULL) Branch (1246:13): [True: 35, False: 12]
|
1247 | return -1; |
1248 | do_decref = 1; |
1249 | } |
1250 | |
1251 | res = 0; |
1252 | switch(Py_SIZE(v)) { |
1253 | case -1: Branch (1253:5): [True: 20.8k, False: 259k]
|
1254 | bytes = -(sdigit)v->ob_digit[0]; |
1255 | break; |
1256 | case 0: Branch (1256:5): [True: 54.2k, False: 226k]
|
1257 | bytes = 0; |
1258 | break; |
1259 | case 1: Branch (1259:5): [True: 48.1k, False: 232k]
|
1260 | bytes = v->ob_digit[0]; |
1261 | break; |
1262 | default: Branch (1262:5): [True: 157k, False: 123k]
|
1263 | res = _PyLong_AsByteArray((PyLongObject *)v, (unsigned char *)&bytes, |
1264 | SIZEOF_LONG_LONG, PY_LITTLE_ENDIAN, 1); |
1265 | } |
1266 | if (do_decref) { Branch (1266:9): [True: 12, False: 280k]
|
1267 | Py_DECREF(v); |
1268 | } |
1269 | |
1270 | /* Plan 9 can't handle long long in ? : expressions */ |
1271 | if (res < 0) Branch (1271:9): [True: 891, False: 279k]
|
1272 | return (long long)-1; |
1273 | else |
1274 | return bytes; |
1275 | } |
1276 | |
1277 | /* Get a C unsigned long long int from an int object. |
1278 | Return -1 and set an error if overflow occurs. */ |
1279 | |
1280 | unsigned long long |
1281 | PyLong_AsUnsignedLongLong(PyObject *vv) |
1282 | { |
1283 | PyLongObject *v; |
1284 | unsigned long long bytes; |
1285 | int res; |
1286 | |
1287 | if (vv == NULL) { Branch (1287:9): [True: 0, False: 172k]
|
1288 | PyErr_BadInternalCall(); |
1289 | return (unsigned long long)-1; |
1290 | } |
1291 | if (!PyLong_Check(vv)) { Branch (1291:9): [True: 9, False: 172k]
|
1292 | PyErr_SetString(PyExc_TypeError, "an integer is required"); |
1293 | return (unsigned long long)-1; |
1294 | } |
1295 | |
1296 | v = (PyLongObject*)vv; |
1297 | switch(Py_SIZE(v)) { |
1298 | case 0: return 0; Branch (1298:5): [True: 4.41k, False: 168k]
|
1299 | case 1: return v->ob_digit[0]; Branch (1299:5): [True: 36.5k, False: 136k]
|
1300 | } |
1301 | |
1302 | res = _PyLong_AsByteArray((PyLongObject *)vv, (unsigned char *)&bytes, |
1303 | SIZEOF_LONG_LONG, PY_LITTLE_ENDIAN, 0); |
1304 | |
1305 | /* Plan 9 can't handle long long in ? : expressions */ |
1306 | if (res < 0) Branch (1306:9): [True: 1.66k, False: 130k]
|
1307 | return (unsigned long long)res; |
1308 | else |
1309 | return bytes; |
1310 | } |
1311 | |
1312 | /* Get a C unsigned long int from an int object, ignoring the high bits. |
1313 | Returns -1 and sets an error condition if an error occurs. */ |
1314 | |
1315 | static unsigned long long |
1316 | _PyLong_AsUnsignedLongLongMask(PyObject *vv) |
1317 | { |
1318 | PyLongObject *v; |
1319 | unsigned long long x; |
1320 | Py_ssize_t i; |
1321 | int sign; |
1322 | |
1323 | if (vv == NULL || !PyLong_Check(vv)) { Branch (1323:9): [True: 0, False: 37.1k]
Branch (1323:23): [True: 0, False: 37.1k]
|
1324 | PyErr_BadInternalCall(); |
1325 | return (unsigned long long) -1; |
1326 | } |
1327 | v = (PyLongObject *)vv; |
1328 | switch(Py_SIZE(v)) { |
1329 | case 0: return 0; Branch (1329:5): [True: 16.4k, False: 20.7k]
|
1330 | case 1: return v->ob_digit[0]; Branch (1330:5): [True: 20.7k, False: 16.4k]
|
1331 | } |
1332 | i = Py_SIZE(v); |
1333 | sign = 1; |
1334 | x = 0; |
1335 | if (i < 0) { Branch (1335:9): [True: 0, False: 4]
|
1336 | sign = -1; |
1337 | i = -i; |
1338 | } |
1339 | while (--i >= 0) { Branch (1339:12): [True: 13, False: 4]
|
1340 | x = (x << PyLong_SHIFT) | v->ob_digit[i]; |
1341 | } |
1342 | return x * sign; |
1343 | } |
1344 | |
1345 | unsigned long long |
1346 | PyLong_AsUnsignedLongLongMask(PyObject *op) |
1347 | { |
1348 | PyLongObject *lo; |
1349 | unsigned long long val; |
1350 | |
1351 | if (op == NULL) { Branch (1351:9): [True: 1, False: 37.1k]
|
1352 | PyErr_BadInternalCall(); |
1353 | return (unsigned long long)-1; |
1354 | } |
1355 | |
1356 | if (PyLong_Check(op)) { |
1357 | return _PyLong_AsUnsignedLongLongMask(op); |
1358 | } |
1359 | |
1360 | lo = (PyLongObject *)_PyNumber_Index(op); |
1361 | if (lo == NULL) Branch (1361:9): [True: 0, False: 0]
|
1362 | return (unsigned long long)-1; |
1363 | |
1364 | val = _PyLong_AsUnsignedLongLongMask((PyObject *)lo); |
1365 | Py_DECREF(lo); |
1366 | return val; |
1367 | } |
1368 | |
1369 | /* Get a C long long int from an int object or any object that has an |
1370 | __index__ method. |
1371 | |
1372 | On overflow, return -1 and set *overflow to 1 or -1 depending on the sign of |
1373 | the result. Otherwise *overflow is 0. |
1374 | |
1375 | For other errors (e.g., TypeError), return -1 and set an error condition. |
1376 | In this case *overflow will be 0. |
1377 | */ |
1378 | |
1379 | long long |
1380 | PyLong_AsLongLongAndOverflow(PyObject *vv, int *overflow) |
1381 | { |
1382 | /* This version by Tim Peters */ |
1383 | PyLongObject *v; |
1384 | unsigned long long x, prev; |
1385 | long long res; |
1386 | Py_ssize_t i; |
1387 | int sign; |
1388 | int do_decref = 0; /* if PyNumber_Index was called */ |
1389 | |
1390 | *overflow = 0; |
1391 | if (vv == NULL) { Branch (1391:9): [True: 0, False: 114k]
|
1392 | PyErr_BadInternalCall(); |
1393 | return -1; |
1394 | } |
1395 | |
1396 | if (PyLong_Check(vv)) { |
1397 | v = (PyLongObject *)vv; |
1398 | } |
1399 | else { |
1400 | v = (PyLongObject *)_PyNumber_Index(vv); |
1401 | if (v == NULL) Branch (1401:13): [True: 0, False: 0]
|
1402 | return -1; |
1403 | do_decref = 1; |
1404 | } |
1405 | |
1406 | res = -1; |
1407 | i = Py_SIZE(v); |
1408 | |
1409 | switch (i) { |
1410 | case -1: Branch (1410:5): [True: 2, False: 114k]
|
1411 | res = -(sdigit)v->ob_digit[0]; |
1412 | break; |
1413 | case 0: Branch (1413:5): [True: 1.73k, False: 112k]
|
1414 | res = 0; |
1415 | break; |
1416 | case 1: Branch (1416:5): [True: 112k, False: 1.77k]
|
1417 | res = v->ob_digit[0]; |
1418 | break; |
1419 | default: Branch (1419:5): [True: 37, False: 114k]
|
1420 | sign = 1; |
1421 | x = 0; |
1422 | if (i < 0) { Branch (1422:13): [True: 6, False: 31]
|
1423 | sign = -1; |
1424 | i = -(i); |
1425 | } |
1426 | while (--i >= 0) { Branch (1426:16): [True: 108, False: 15]
|
1427 | prev = x; |
1428 | x = (x << PyLong_SHIFT) + v->ob_digit[i]; |
1429 | if ((x >> PyLong_SHIFT) != prev) { Branch (1429:17): [True: 22, False: 86]
|
1430 | *overflow = sign; |
1431 | goto exit; |
1432 | } |
1433 | } |
1434 | /* Haven't lost any bits, but casting to long requires extra |
1435 | * care (see comment above). |
1436 | */ |
1437 | if (x <= (unsigned long long)LLONG_MAX) { Branch (1437:13): [True: 6, False: 9]
|
1438 | res = (long long)x * sign; |
1439 | } |
1440 | else if (sign < 0 && x == 5 PY_ABS_LLONG_MIN5 ) { Branch (1440:18): [True: 5, False: 4]
Branch (1440:30): [True: 1, False: 4]
|
1441 | res = LLONG_MIN; |
1442 | } |
1443 | else { |
1444 | *overflow = sign; |
1445 | /* res is already set to -1 */ |
1446 | } |
1447 | } |
1448 | exit: |
1449 | if (do_decref) { Branch (1449:9): [True: 0, False: 114k]
|
1450 | Py_DECREF(v); |
1451 | } |
1452 | return res; |
1453 | } |
1454 | |
1455 | int |
1456 | _PyLong_UnsignedShort_Converter(PyObject *obj, void *ptr) |
1457 | { |
1458 | unsigned long uval; |
1459 | |
1460 | if (PyLong_Check(obj) && _PyLong_Sign(obj) < 0) { Branch (1460:30): [True: 2, False: 145k]
|
1461 | PyErr_SetString(PyExc_ValueError, "value must be positive"); |
1462 | return 0; |
1463 | } |
1464 | uval = PyLong_AsUnsignedLong(obj); |
1465 | if (uval == (unsigned long)-1 && PyErr_Occurred()2 ) Branch (1465:9): [True: 2, False: 145k]
Branch (1465:38): [True: 2, False: 0]
|
1466 | return 0; |
1467 | if (uval > USHRT_MAX) { Branch (1467:9): [True: 2, False: 145k]
|
1468 | PyErr_SetString(PyExc_OverflowError, |
1469 | "Python int too large for C unsigned short"); |
1470 | return 0; |
1471 | } |
1472 | |
1473 | *(unsigned short *)ptr = Py_SAFE_DOWNCAST(uval, unsigned long, unsigned short); |
1474 | return 1; |
1475 | } |
1476 | |
1477 | int |
1478 | _PyLong_UnsignedInt_Converter(PyObject *obj, void *ptr) |
1479 | { |
1480 | unsigned long uval; |
1481 | |
1482 | if (PyLong_Check(obj) && _PyLong_Sign(obj) < 0) { Branch (1482:30): [True: 0, False: 4]
|
1483 | PyErr_SetString(PyExc_ValueError, "value must be positive"); |
1484 | return 0; |
1485 | } |
1486 | uval = PyLong_AsUnsignedLong(obj); |
1487 | if (uval == (unsigned long)-1 && PyErr_Occurred()0 ) Branch (1487:9): [True: 0, False: 4]
Branch (1487:38): [True: 0, False: 0]
|
1488 | return 0; |
1489 | if (uval > UINT_MAX) { Branch (1489:9): [True: 0, False: 4]
|
1490 | PyErr_SetString(PyExc_OverflowError, |
1491 | "Python int too large for C unsigned int"); |
1492 | return 0; |
1493 | } |
1494 | |
1495 | *(unsigned int *)ptr = Py_SAFE_DOWNCAST(uval, unsigned long, unsigned int); |
1496 | return 1; |
1497 | } |
1498 | |
1499 | int |
1500 | _PyLong_UnsignedLong_Converter(PyObject *obj, void *ptr) |
1501 | { |
1502 | unsigned long uval; |
1503 | |
1504 | if (PyLong_Check(obj) && _PyLong_Sign(obj) < 0) { Branch (1504:30): [True: 6, False: 72]
|
1505 | PyErr_SetString(PyExc_ValueError, "value must be positive"); |
1506 | return 0; |
1507 | } |
1508 | uval = PyLong_AsUnsignedLong(obj); |
1509 | if (uval == (unsigned long)-1 && PyErr_Occurred()4 ) Branch (1509:9): [True: 4, False: 68]
Branch (1509:38): [True: 4, False: 0]
|
1510 | return 0; |
1511 | |
1512 | *(unsigned long *)ptr = uval; |
1513 | return 1; |
1514 | } |
1515 | |
1516 | int |
1517 | _PyLong_UnsignedLongLong_Converter(PyObject *obj, void *ptr) |
1518 | { |
1519 | unsigned long long uval; |
1520 | |
1521 | if (PyLong_Check(obj) && _PyLong_Sign(obj) < 0) { Branch (1521:30): [True: 2, False: 17]
|
1522 | PyErr_SetString(PyExc_ValueError, "value must be positive"); |
1523 | return 0; |
1524 | } |
1525 | uval = PyLong_AsUnsignedLongLong(obj); |
1526 | if (uval == (unsigned long long)-1 && PyErr_Occurred()2 ) Branch (1526:9): [True: 2, False: 15]
Branch (1526:43): [True: 1, False: 1]
|
1527 | return 0; |
1528 | |
1529 | *(unsigned long long *)ptr = uval; |
1530 | return 1; |
1531 | } |
1532 | |
1533 | int |
1534 | _PyLong_Size_t_Converter(PyObject *obj, void *ptr) |
1535 | { |
1536 | size_t uval; |
1537 |
|
1538 | if (PyLong_Check(obj) && _PyLong_Sign(obj) < 0) { Branch (1538:30): [True: 0, False: 0]
|
1539 | PyErr_SetString(PyExc_ValueError, "value must be positive"); |
1540 | return 0; |
1541 | } |
1542 | uval = PyLong_AsSize_t(obj); |
1543 | if (uval == (size_t)-1 && PyErr_Occurred()) Branch (1543:9): [True: 0, False: 0]
Branch (1543:31): [True: 0, False: 0]
|
1544 | return 0; |
1545 | |
1546 | *(size_t *)ptr = uval; |
1547 | return 1; |
1548 | } |
1549 | |
1550 | |
1551 | #define CHECK_BINOP(v,w) \ |
1552 | do { \ |
1553 | if (!PyLong_Check(v) || !108M PyLong_Check108M (w)) \ |
1554 | Py_RETURN_NOTIMPLEMENTED2.18M ; \ |
1555 | } while(0107M ) |
1556 | |
1557 | /* x[0:m] and y[0:n] are digit vectors, LSD first, m >= n required. x[0:n] |
1558 | * is modified in place, by adding y to it. Carries are propagated as far as |
1559 | * x[m-1], and the remaining carry (0 or 1) is returned. |
1560 | */ |
1561 | static digit |
1562 | v_iadd(digit *x, Py_ssize_t m, digit *y, Py_ssize_t n) |
1563 | { |
1564 | Py_ssize_t i; |
1565 | digit carry = 0; |
1566 | |
1567 | assert(m >= n); |
1568 | for (i = 0; i < n; ++i1.53M ) { Branch (1568:17): [True: 1.53M, False: 8.62k]
|
1569 | carry += x[i] + y[i]; |
1570 | x[i] = carry & PyLong_MASK; |
1571 | carry >>= PyLong_SHIFT; |
1572 | assert((carry & 1) == carry); |
1573 | } |
1574 | for (; carry && i < m272k ; ++i272k ) { Branch (1574:12): [True: 272k, False: 8.62k]
Branch (1574:21): [True: 272k, False: 0]
|
1575 | carry += x[i]; |
1576 | x[i] = carry & PyLong_MASK; |
1577 | carry >>= PyLong_SHIFT; |
1578 | assert((carry & 1) == carry); |
1579 | } |
1580 | return carry; |
1581 | } |
1582 | |
1583 | /* x[0:m] and y[0:n] are digit vectors, LSD first, m >= n required. x[0:n] |
1584 | * is modified in place, by subtracting y from it. Borrows are propagated as |
1585 | * far as x[m-1], and the remaining borrow (0 or 1) is returned. |
1586 | */ |
1587 | static digit |
1588 | v_isub(digit *x, Py_ssize_t m, digit *y, Py_ssize_t n) |
1589 | { |
1590 | Py_ssize_t i; |
1591 | digit borrow = 0; |
1592 | |
1593 | assert(m >= n); |
1594 | for (i = 0; i < n; ++i2.13M ) { Branch (1594:17): [True: 2.13M, False: 15.0k]
|
1595 | borrow = x[i] - y[i] - borrow; |
1596 | x[i] = borrow & PyLong_MASK; |
1597 | borrow >>= PyLong_SHIFT; |
1598 | borrow &= 1; /* keep only 1 sign bit */ |
1599 | } |
1600 | for (; borrow && i < m278k ; ++i278k ) { Branch (1600:12): [True: 278k, False: 15.0k]
Branch (1600:22): [True: 278k, False: 0]
|
1601 | borrow = x[i] - borrow; |
1602 | x[i] = borrow & PyLong_MASK; |
1603 | borrow >>= PyLong_SHIFT; |
1604 | borrow &= 1; |
1605 | } |
1606 | return borrow; |
1607 | } |
1608 | |
1609 | /* Shift digit vector a[0:m] d bits left, with 0 <= d < PyLong_SHIFT. Put |
1610 | * result in z[0:m], and return the d bits shifted out of the top. |
1611 | */ |
1612 | static digit |
1613 | v_lshift(digit *z, digit *a, Py_ssize_t m, int d) |
1614 | { |
1615 | Py_ssize_t i; |
1616 | digit carry = 0; |
1617 | |
1618 | assert(0 <= d && d < PyLong_SHIFT); |
1619 | for (i=0; i < m; i++30.5M ) { Branch (1619:15): [True: 30.5M, False: 7.21M]
|
1620 | twodigits acc = (twodigits)a[i] << d | carry; |
1621 | z[i] = (digit)acc & PyLong_MASK; |
1622 | carry = (digit)(acc >> PyLong_SHIFT); |
1623 | } |
1624 | return carry; |
1625 | } |
1626 | |
1627 | /* Shift digit vector a[0:m] d bits right, with 0 <= d < PyLong_SHIFT. Put |
1628 | * result in z[0:m], and return the d bits shifted out of the bottom. |
1629 | */ |
1630 | static digit |
1631 | v_rshift(digit *z, digit *a, Py_ssize_t m, int d) |
1632 | { |
1633 | Py_ssize_t i; |
1634 | digit carry = 0; |
1635 | digit mask = ((digit)1 << d) - 1U; |
1636 | |
1637 | assert(0 <= d && d < PyLong_SHIFT); |
1638 | for (i=m; i-- > 0;) { Branch (1638:15): [True: 13.2M, False: 3.59M]
|
1639 | twodigits acc = (twodigits)carry << PyLong_SHIFT | a[i]; |
1640 | carry = (digit)acc & mask; |
1641 | z[i] = (digit)(acc >> d); |
1642 | } |
1643 | return carry; |
1644 | } |
1645 | |
1646 | /* Divide long pin, w/ size digits, by non-zero digit n, storing quotient |
1647 | in pout, and returning the remainder. pin and pout point at the LSD. |
1648 | It's OK for pin == pout on entry, which saves oodles of mallocs/frees in |
1649 | _PyLong_Format, but that should be done with great care since ints are |
1650 | immutable. |
1651 | |
1652 | This version of the code can be 20% faster than the pre-2022 version |
1653 | on todays compilers on architectures like amd64. It evolved from Mark |
1654 | Dickinson observing that a 128:64 divide instruction was always being |
1655 | generated by the compiler despite us working with 30-bit digit values. |
1656 | See the thread for full context: |
1657 | |
1658 | https://mail.python.org/archives/list/python-dev@python.org/thread/ZICIMX5VFCX4IOFH5NUPVHCUJCQ4Q7QM/#NEUNFZU3TQU4CPTYZNF3WCN7DOJBBTK5 |
1659 | |
1660 | If you ever want to change this code, pay attention to performance using |
1661 | different compilers, optimization levels, and cpu architectures. Beware of |
1662 | PGO/FDO builds doing value specialization such as a fast path for //10. :) |
1663 | |
1664 | Verify that 17 isn't specialized and this works as a quick test: |
1665 | python -m timeit -s 'x = 10**1000; r=x//10; assert r == 10**999, r' 'x//17' |
1666 | */ |
1667 | static digit |
1668 | inplace_divrem1(digit *pout, digit *pin, Py_ssize_t size, digit n) |
1669 | { |
1670 | digit remainder = 0; |
1671 | |
1672 | assert(n > 0 && n <= PyLong_MASK); |
1673 | while (--size >= 0) { Branch (1673:12): [True: 6.31M, False: 428k]
|
1674 | twodigits dividend; |
1675 | dividend = ((twodigits)remainder << PyLong_SHIFT) | pin[size]; |
1676 | digit quotient; |
1677 | quotient = (digit)(dividend / n); |
1678 | remainder = dividend % n; |
1679 | pout[size] = quotient; |
1680 | } |
1681 | return remainder; |
1682 | } |
1683 | |
1684 | |
1685 | /* Divide an integer by a digit, returning both the quotient |
1686 | (as function result) and the remainder (through *prem). |
1687 | The sign of a is ignored; n should not be zero. */ |
1688 | |
1689 | static PyLongObject * |
1690 | divrem1(PyLongObject *a, digit n, digit *prem) |
1691 | { |
1692 | const Py_ssize_t size = Py_ABS(Py_SIZE(a)); |
1693 | PyLongObject *z; |
1694 | |
1695 | assert(n > 0 && n <= PyLong_MASK); |
1696 | z = _PyLong_New(size); |
1697 | if (z == NULL) Branch (1697:9): [True: 0, False: 412k]
|
1698 | return NULL; |
1699 | *prem = inplace_divrem1(z->ob_digit, a->ob_digit, size, n); |
1700 | return long_normalize(z); |
1701 | } |
1702 | |
1703 | /* Remainder of long pin, w/ size digits, by non-zero digit n, |
1704 | returning the remainder. pin points at the LSD. */ |
1705 | |
1706 | static digit |
1707 | inplace_rem1(digit *pin, Py_ssize_t size, digit n) |
1708 | { |
1709 | twodigits rem = 0; |
1710 | |
1711 | assert(n > 0 && n <= PyLong_MASK); |
1712 | while (--size >= 0) Branch (1712:12): [True: 39.8M, False: 17.3M]
|
1713 | rem = ((rem << PyLong_SHIFT) | pin[size]) % n; |
1714 | return (digit)rem; |
1715 | } |
1716 | |
1717 | /* Get the remainder of an integer divided by a digit, returning |
1718 | the remainder as the result of the function. The sign of a is |
1719 | ignored; n should not be zero. */ |
1720 | |
1721 | static PyLongObject * |
1722 | rem1(PyLongObject *a, digit n) |
1723 | { |
1724 | const Py_ssize_t size = Py_ABS(Py_SIZE(a)); |
1725 | |
1726 | assert(n > 0 && n <= PyLong_MASK); |
1727 | return (PyLongObject *)PyLong_FromLong( |
1728 | (long)inplace_rem1(a->ob_digit, size, n) |
1729 | ); |
1730 | } |
1731 | |
1732 | /* Convert an integer to a base 10 string. Returns a new non-shared |
1733 | string. (Return value is non-shared so that callers can modify the |
1734 | returned value if necessary.) */ |
1735 | |
1736 | static int |
1737 | long_to_decimal_string_internal(PyObject *aa, |
1738 | PyObject **p_output, |
1739 | _PyUnicodeWriter *writer, |
1740 | _PyBytesWriter *bytes_writer, |
1741 | char **bytes_str) |
1742 | { |
1743 | PyLongObject *scratch, *a; |
1744 | PyObject *str = NULL; |
1745 | Py_ssize_t size, strlen, size_a, i, j; |
1746 | digit *pout, *pin, rem, tenpow; |
1747 | int negative; |
1748 | int d; |
1749 | int kind; |
1750 | |
1751 | a = (PyLongObject *)aa; |
1752 | if (a == NULL || !PyLong_Check(a)) { Branch (1752:9): [True: 0, False: 12.8M]
Branch (1752:22): [True: 0, False: 12.8M]
|
1753 | PyErr_BadInternalCall(); |
1754 | return -1; |
1755 | } |
1756 | size_a = Py_ABS(Py_SIZE(a)); |
1757 | negative = Py_SIZE(a) < 0; |
1758 | |
1759 | /* quick and dirty upper bound for the number of digits |
1760 | required to express a in base _PyLong_DECIMAL_BASE: |
1761 | |
1762 | #digits = 1 + floor(log2(a) / log2(_PyLong_DECIMAL_BASE)) |
1763 | |
1764 | But log2(a) < size_a * PyLong_SHIFT, and |
1765 | log2(_PyLong_DECIMAL_BASE) = log2(10) * _PyLong_DECIMAL_SHIFT |
1766 | > 3.3 * _PyLong_DECIMAL_SHIFT |
1767 | |
1768 | size_a * PyLong_SHIFT / (3.3 * _PyLong_DECIMAL_SHIFT) = |
1769 | size_a + size_a / d < size_a + size_a / floor(d), |
1770 | where d = (3.3 * _PyLong_DECIMAL_SHIFT) / |
1771 | (PyLong_SHIFT - 3.3 * _PyLong_DECIMAL_SHIFT) |
1772 | */ |
1773 | d = (33 * _PyLong_DECIMAL_SHIFT) / |
1774 | (10 * PyLong_SHIFT - 33 * _PyLong_DECIMAL_SHIFT); |
1775 | assert(size_a < PY_SSIZE_T_MAX/2); |
1776 | size = 1 + size_a + size_a / d; |
1777 | scratch = _PyLong_New(size); |
1778 | if (scratch == NULL) Branch (1778:9): [True: 0, False: 12.8M]
|
1779 | return -1; |
1780 | |
1781 | /* convert array of base _PyLong_BASE digits in pin to an array of |
1782 | base _PyLong_DECIMAL_BASE digits in pout, following Knuth (TAOCP, |
1783 | Volume 2 (3rd edn), section 4.4, Method 1b). */ |
1784 | pin = a->ob_digit; |
1785 | pout = scratch->ob_digit; |
1786 | size = 0; |
1787 | for (i = size_a; --i >= 0; ) { Branch (1787:22): [True: 22.2M, False: 12.8M]
|
1788 | digit hi = pin[i]; |
1789 | for (j = 0; j < size; j++102M ) { Branch (1789:21): [True: 102M, False: 22.2M]
|
1790 | twodigits z = (twodigits)pout[j] << PyLong_SHIFT | hi; |
1791 | hi = (digit)(z / _PyLong_DECIMAL_BASE); |
1792 | pout[j] = (digit)(z - (twodigits)hi * |
1793 | _PyLong_DECIMAL_BASE); |
1794 | } |
1795 | while (hi) { Branch (1795:16): [True: 22.2M, False: 22.2M]
|
1796 | pout[size++] = hi % _PyLong_DECIMAL_BASE; |
1797 | hi /= _PyLong_DECIMAL_BASE; |
1798 | } |
1799 | /* check for keyboard interrupt */ |
1800 | SIGCHECK({ |
1801 | Py_DECREF(scratch); |
1802 | return -1; |
1803 | }); |
1804 | } |
1805 | /* pout should have at least one digit, so that the case when a = 0 |
1806 | works correctly */ |
1807 | if (size == 0) Branch (1807:9): [True: 2.07M, False: 10.8M]
|
1808 | pout[size++] = 0; |
1809 | |
1810 | /* calculate exact length of output string, and allocate */ |
1811 | strlen = negative + 1 + (size - 1) * _PyLong_DECIMAL_SHIFT; |
1812 | tenpow = 10; |
1813 | rem = pout[size-1]; |
1814 | while (rem >= tenpow) { Branch (1814:12): [True: 24.5M, False: 12.8M]
|
1815 | tenpow *= 10; |
1816 | strlen++; |
1817 | } |
1818 | if (writer) { Branch (1818:9): [True: 9.02M, False: 3.86M]
|
1819 | if (_PyUnicodeWriter_Prepare(writer, strlen, '9') == -1) { Branch (1819:13): [True: 0, False: 9.02M]
|
1820 | Py_DECREF(scratch); |
1821 | return -1; |
1822 | } |
1823 | kind = writer->kind; |
1824 | } |
1825 | else if (bytes_writer) { Branch (1825:14): [True: 88, False: 3.86M]
|
1826 | *bytes_str = _PyBytesWriter_Prepare(bytes_writer, *bytes_str, strlen); |
1827 | if (*bytes_str == NULL) { Branch (1827:13): [True: 0, False: 88]
|
1828 | Py_DECREF(scratch); |
1829 | return -1; |
1830 | } |
1831 | } |
1832 | else { |
1833 | str = PyUnicode_New(strlen, '9'); |
1834 | if (str == NULL) { Branch (1834:13): [True: 0, False: 3.86M]
|
1835 | Py_DECREF(scratch); |
1836 | return -1; |
1837 | } |
1838 | kind = PyUnicode_KIND(str); |
1839 | } |
1840 | |
1841 | #define WRITE_DIGITS(p) \ |
1842 | do { \ |
1843 | /* pout[0] through pout[size-2] contribute exactly \ |
1844 | _PyLong_DECIMAL_SHIFT digits each */ \ |
1845 | for (i=0; i < size - 1; i++11.4M ) { \ |
1846 | rem = pout[i]; \ |
1847 | for (j = 0; j < _PyLong_DECIMAL_SHIFT; j++103M ) { \ |
1848 | *--p = '0' + rem % 10; \ |
1849 | rem /= 10; \ |
1850 | } \ |
1851 | } \ |
1852 | /* pout[size-1]: always produce at least one decimal digit */ \ |
1853 | rem = pout[i]; \ |
1854 | do { \ |
1855 | *--p = '0' + rem % 10; \ |
1856 | rem /= 10; \ |
1857 | } while (rem != 0); \ |
1858 | \ |
1859 | /* and sign */ \ |
1860 | if (negative) \ |
1861 | *--p = '-'155k ; \ |
1862 | } while (0) |
1863 | |
1864 | #define WRITE_UNICODE_DIGITS(TYPE) \ |
1865 | do 12.8M { \ |
1866 | if (writer) \ |
1867 | p = (TYPE*)9.02M PyUnicode_DATA9.02M (writer->buffer) + writer->pos + strlen; \ |
1868 | else \ |
1869 | p = (TYPE*)3.86M PyUnicode_DATA3.86M (str) + strlen; \ |
1870 | \ |
1871 | WRITE_DIGITS(p); \ |
1872 | \ |
1873 | /* check we've counted correctly */ \ |
1874 | if (writer) \ |
1875 | assert(p == ((TYPE*)PyUnicode_DATA(writer->buffer) + writer->pos)); \ |
1876 | else \ |
1877 | assert(p == (TYPE*)PyUnicode_DATA(str)); \ |
1878 | } while (0) |
1879 | |
1880 | /* fill the string right-to-left */ |
1881 | if (bytes_writer) { Branch (1881:9): [True: 88, False: 12.8M]
|
1882 | char *p = *bytes_str + strlen; |
1883 | WRITE_DIGITS(p); |
1884 | assert(p == *bytes_str); |
1885 | } |
1886 | else if (kind == PyUnicode_1BYTE_KIND) { Branch (1886:14): [True: 12.8M, False: 11]
|
1887 | Py_UCS1 *p; |
1888 | WRITE_UNICODE_DIGITS(Py_UCS1); |
1889 | } |
1890 | else if (kind == PyUnicode_2BYTE_KIND) { Branch (1890:14): [True: 11, False: 0]
|
1891 | Py_UCS2 *p; |
1892 | WRITE_UNICODE_DIGITS(Py_UCS2); |
1893 | } |
1894 | else { |
1895 | Py_UCS4 *p; |
1896 | assert (kind == PyUnicode_4BYTE_KIND); |
1897 | WRITE_UNICODE_DIGITS(Py_UCS4); |
1898 | } |
1899 | #undef WRITE_DIGITS |
1900 | #undef WRITE_UNICODE_DIGITS |
1901 | |
1902 | _Py_DECREF_INT(scratch); |
1903 | if (writer) { Branch (1903:9): [True: 9.02M, False: 3.86M]
|
1904 | writer->pos += strlen; |
1905 | } |
1906 | else if (bytes_writer) { Branch (1906:14): [True: 88, False: 3.86M]
|
1907 | (*bytes_str) += strlen; |
1908 | } |
1909 | else { |
1910 | assert(_PyUnicode_CheckConsistency(str, 1)); |
1911 | *p_output = (PyObject *)str; |
1912 | } |
1913 | return 0; |
1914 | } |
1915 | |
1916 | static PyObject * |
1917 | long_to_decimal_string(PyObject *aa) |
1918 | { |
1919 | PyObject *v; |
1920 | if (long_to_decimal_string_internal(aa, &v, NULL, NULL, NULL) == -1) Branch (1920:9): [True: 0, False: 3.78M]
|
1921 | return NULL; |
1922 | return v; |
1923 | } |
1924 | |
1925 | /* Convert an int object to a string, using a given conversion base, |
1926 | which should be one of 2, 8 or 16. Return a string object. |
1927 | If base is 2, 8 or 16, add the proper prefix '0b', '0o' or '0x' |
1928 | if alternate is nonzero. */ |
1929 | |
1930 | static int |
1931 | long_format_binary(PyObject *aa, int base, int alternate, |
1932 | PyObject **p_output, _PyUnicodeWriter *writer, |
1933 | _PyBytesWriter *bytes_writer, char **bytes_str) |
1934 | { |
1935 | PyLongObject *a = (PyLongObject *)aa; |
1936 | PyObject *v = NULL; |
1937 | Py_ssize_t sz; |
1938 | Py_ssize_t size_a; |
1939 | int kind; |
1940 | int negative; |
1941 | int bits; |
1942 | |
1943 | assert(base == 2 || base == 8 || base == 16); |
1944 | if (a == NULL || !PyLong_Check(a)) { Branch (1944:9): [True: 0, False: 767k]
Branch (1944:22): [True: 0, False: 767k]
|
1945 | PyErr_BadInternalCall(); |
1946 | return -1; |
1947 | } |
1948 | size_a = Py_ABS(Py_SIZE(a)); |
1949 | negative = Py_SIZE(a) < 0; |
1950 | |
1951 | /* Compute a rough upper bound for the length of the string */ |
1952 | switch (base) { |
1953 | case 16: Branch (1953:5): [True: 621k, False: 145k]
|
1954 | bits = 4; |
1955 | break; |
1956 | case 8: Branch (1956:5): [True: 10.9k, False: 756k]
|
1957 | bits = 3; |
1958 | break; |
1959 | case 2: Branch (1959:5): [True: 134k, False: 632k]
|
1960 | bits = 1; |
1961 | break; |
1962 | default: Branch (1962:5): [True: 0, False: 767k]
|
1963 | Py_UNREACHABLE(); |
1964 | } |
1965 | |
1966 | /* Compute exact length 'sz' of output string. */ |
1967 | if (size_a == 0) { Branch (1967:9): [True: 69.2k, False: 698k]
|
1968 | sz = 1; |
1969 | } |
1970 | else { |
1971 | Py_ssize_t size_a_in_bits; |
1972 | /* Ensure overflow doesn't occur during computation of sz. */ |
1973 | if (size_a > (PY_SSIZE_T_MAX - 3) / PyLong_SHIFT) { Branch (1973:13): [True: 0, False: 698k]
|
1974 | PyErr_SetString(PyExc_OverflowError, |
1975 | "int too large to format"); |
1976 | return -1; |
1977 | } |
1978 | size_a_in_bits = (size_a - 1) * PyLong_SHIFT + |
1979 | bit_length_digit(a->ob_digit[size_a - 1]); |
1980 | /* Allow 1 character for a '-' sign. */ |
1981 | sz = negative + (size_a_in_bits + (bits - 1)) / bits; |
1982 | } |
1983 | if (alternate) { Branch (1983:9): [True: 717k, False: 49.6k]
|
1984 | /* 2 characters for prefix */ |
1985 | sz += 2; |
1986 | } |
1987 | |
1988 | if (writer) { Branch (1988:9): [True: 49.2k, False: 718k]
|
1989 | if (_PyUnicodeWriter_Prepare(writer, sz, 'x') == -1) Branch (1989:13): [True: 0, False: 49.2k]
|
1990 | return -1; |
1991 | kind = writer->kind; |
1992 | } |
1993 | else if (bytes_writer) { Branch (1993:14): [True: 556, False: 717k]
|
1994 | *bytes_str = _PyBytesWriter_Prepare(bytes_writer, *bytes_str, sz); |
1995 | if (*bytes_str == NULL) Branch (1995:13): [True: 0, False: 556]
|
1996 | return -1; |
1997 | } |
1998 | else { |
1999 | v = PyUnicode_New(sz, 'x'); |
2000 | if (v == NULL) Branch (2000:13): [True: 0, False: 717k]
|
2001 | return -1; |
2002 | kind = PyUnicode_KIND(v); |
2003 | } |
2004 | |
2005 | #define WRITE_DIGITS(p) \ |
2006 | do { \ |
2007 | if (size_a == 0) { \ |
2008 | *--p = '0'; \ |
2009 | } \ |
2010 | else { \ |
2011 | /* JRH: special case for power-of-2 bases */ \ |
2012 | twodigits accum = 0; \ |
2013 | int accumbits = 0; /* # of bits in accum */ \ |
2014 | Py_ssize_t i; \ |
2015 | for (i = 0; i < size_a; ++i744k ) { \ |
2016 | accum |= (twodigits)a->ob_digit[i] << accumbits; \ |
2017 | accumbits += PyLong_SHIFT; \ |
2018 | assert(accumbits >= bits); \ |
2019 | do { \ |
2020 | char cdigit; \ |
2021 | cdigit = (char)(accum & (base - 1)); \ |
2022 | cdigit += (cdigit < 10) ? '0'3.29M : 'a'-10691k ; \ |
2023 | *--p = cdigit; \ |
2024 | accumbits -= bits; \ |
2025 | accum >>= bits; \ |
2026 | } while (i < size_a-1 ? accumbits >= bits496k : accum > 03.49M ); \ |
2027 | } \ |
2028 | } \ |
2029 | \ |
2030 | if (alternate) { \ |
2031 | if (base == 16) \ |
2032 | *--p = 'x'573k ; \ |
2033 | else if (144k base == 8144k ) \ |
2034 | *--p = 'o'9.78k ; \ |
2035 | else /* (base == 2) */ \ |
2036 | *--p = 'b'134k ; \ |
2037 | *--p = '0'; \ |
2038 | } \ |
2039 | if (negative) \ |
2040 | *--p = '-'69.4k ; \ |
2041 | } while (0) |
2042 | |
2043 | #define WRITE_UNICODE_DIGITS(TYPE) \ |
2044 | do 766k { \ |
2045 | if (writer) \ |
2046 | p = (TYPE*)49.2k PyUnicode_DATA49.2k (writer->buffer) + writer->pos + sz; \ |
2047 | else \ |
2048 | p = (TYPE*)717k PyUnicode_DATA717k (v) + sz; \ |
2049 | \ |
2050 | WRITE_DIGITS(p); \ |
2051 | \ |
2052 | if (writer) \ |
2053 | assert(p == ((TYPE*)PyUnicode_DATA(writer->buffer) + writer->pos)); \ |
2054 | else \ |
2055 | assert(p == (TYPE*)PyUnicode_DATA(v)); \ |
2056 | } while (0) |
2057 | |
2058 | if (bytes_writer) { Branch (2058:9): [True: 556, False: 766k]
|
2059 | char *p = *bytes_str + sz; |
2060 | WRITE_DIGITS(p); |
2061 | assert(p == *bytes_str); |
2062 | } |
2063 | else if (kind == PyUnicode_1BYTE_KIND) { Branch (2063:14): [True: 766k, False: 0]
|
2064 | Py_UCS1 *p; |
2065 | WRITE_UNICODE_DIGITS(Py_UCS1); |
2066 | } |
2067 | else if (kind == PyUnicode_2BYTE_KIND) { Branch (2067:14): [True: 0, False: 0]
|
2068 | Py_UCS2 *p; |
2069 | WRITE_UNICODE_DIGITS(Py_UCS2); |
2070 | } |
2071 | else { |
2072 | Py_UCS4 *p; |
2073 | assert (kind == PyUnicode_4BYTE_KIND); |
2074 | WRITE_UNICODE_DIGITS(Py_UCS4); |
2075 | } |
2076 | #undef WRITE_DIGITS |
2077 | #undef WRITE_UNICODE_DIGITS |
2078 | |
2079 | if (writer) { Branch (2079:9): [True: 49.2k, False: 718k]
|
2080 | writer->pos += sz; |
2081 | } |
2082 | else if (bytes_writer) { Branch (2082:14): [True: 556, False: 717k]
|
2083 | (*bytes_str) += sz; |
2084 | } |
2085 | else { |
2086 | assert(_PyUnicode_CheckConsistency(v, 1)); |
2087 | *p_output = v; |
2088 | } |
2089 | return 0; |
2090 | } |
2091 | |
2092 | PyObject * |
2093 | _PyLong_Format(PyObject *obj, int base) |
2094 | { |
2095 | PyObject *str; |
2096 | int err; |
2097 | if (base == 10) Branch (2097:9): [True: 86.5k, False: 717k]
|
2098 | err = long_to_decimal_string_internal(obj, &str, NULL, NULL, NULL); |
2099 | else |
2100 | err = long_format_binary(obj, base, 1, &str, NULL, NULL, NULL); |
2101 | if (err == -1) Branch (2101:9): [True: 0, False: 804k]
|
2102 | return NULL; |
2103 | return str; |
2104 | } |
2105 | |
2106 | int |
2107 | _PyLong_FormatWriter(_PyUnicodeWriter *writer, |
2108 | PyObject *obj, |
2109 | int base, int alternate) |
2110 | { |
2111 | if (base == 10) Branch (2111:9): [True: 9.02M, False: 49.2k]
|
2112 | return long_to_decimal_string_internal(obj, NULL, writer, |
2113 | NULL, NULL); |
2114 | else |
2115 | return long_format_binary(obj, base, alternate, NULL, writer, |
2116 | NULL, NULL); |
2117 | } |
2118 | |
2119 | char* |
2120 | _PyLong_FormatBytesWriter(_PyBytesWriter *writer, char *str, |
2121 | PyObject *obj, |
2122 | int base, int alternate) |
2123 | { |
2124 | char *str2; |
2125 | int res; |
2126 | str2 = str; |
2127 | if (base == 10) Branch (2127:9): [True: 88, False: 556]
|
2128 | res = long_to_decimal_string_internal(obj, NULL, NULL, |
2129 | writer, &str2); |
2130 | else |
2131 | res = long_format_binary(obj, base, alternate, NULL, NULL, |
2132 | writer, &str2); |
2133 | if (res < 0) Branch (2133:9): [True: 0, False: 644]
|
2134 | return NULL; |
2135 | assert(str2 != NULL); |
2136 | return str2; |
2137 | } |
2138 | |
2139 | /* Table of digit values for 8-bit string -> integer conversion. |
2140 | * '0' maps to 0, ..., '9' maps to 9. |
2141 | * 'a' and 'A' map to 10, ..., 'z' and 'Z' map to 35. |
2142 | * All other indices map to 37. |
2143 | * Note that when converting a base B string, a char c is a legitimate |
2144 | * base B digit iff _PyLong_DigitValue[Py_CHARPyLong_MASK(c)] < B. |
2145 | */ |
2146 | unsigned char _PyLong_DigitValue[256] = { |
2147 | 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, |
2148 | 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, |
2149 | 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, |
2150 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 37, 37, 37, 37, 37, 37, |
2151 | 37, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, |
2152 | 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 37, 37, 37, 37, |
2153 | 37, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, |
2154 | 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 37, 37, 37, 37, |
2155 | 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, |
2156 | 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, |
2157 | 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, |
2158 | 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, |
2159 | 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, |
2160 | 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, |
2161 | 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, |
2162 | 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, |
2163 | }; |
2164 | |
2165 | /* *str points to the first digit in a string of base `base` digits. base |
2166 | * is a power of 2 (2, 4, 8, 16, or 32). *str is set to point to the first |
2167 | * non-digit (which may be *str!). A normalized int is returned. |
2168 | * The point to this routine is that it takes time linear in the number of |
2169 | * string characters. |
2170 | * |
2171 | * Return values: |
2172 | * -1 on syntax error (exception needs to be set, *res is untouched) |
2173 | * 0 else (exception may be set, in that case *res is set to NULL) |
2174 | */ |
2175 | static int |
2176 | long_from_binary_base(const char **str, int base, PyLongObject **res) |
2177 | { |
2178 | const char *p = *str; |
2179 | const char *start = p; |
2180 | char prev = 0; |
2181 | Py_ssize_t digits = 0; |
2182 | int bits_per_char; |
2183 | Py_ssize_t n; |
2184 | PyLongObject *z; |
2185 | twodigits accum; |
2186 | int bits_in_accum; |
2187 | digit *pdigit; |
2188 | |
2189 | assert(base >= 2 && base <= 32 && (base & (base - 1)) == 0); |
2190 | n = base; |
2191 | for (bits_per_char = -1; n; ++bits_per_char786k ) { Branch (2191:30): [True: 786k, False: 182k]
|
2192 | n >>= 1; |
2193 | } |
2194 | /* count digits and set p to end-of-string */ |
2195 | while (_PyLong_DigitValue[Py_CHARMASK(*p)] < base || *p == '_'182k ) { Branch (2195:12): [True: 1.35M, False: 182k]
Branch (2195:58): [True: 71, False: 182k]
|
2196 | if (*p == '_') { Branch (2196:13): [True: 71, False: 1.35M]
|
2197 | if (prev == '_') { Branch (2197:17): [True: 3, False: 68]
|
2198 | *str = p - 1; |
2199 | return -1; |
2200 | } |
2201 | } else { |
2202 | ++digits; |
2203 | } |
2204 | prev = *p; |
2205 | ++p; |
2206 | } |
2207 | if (prev == '_') { Branch (2207:9): [True: 3, False: 182k]
|
2208 | /* Trailing underscore not allowed. */ |
2209 | *str = p - 1; |
2210 | return -1; |
2211 | } |
2212 | |
2213 | *str = p; |
2214 | /* n <- the number of Python digits needed, |
2215 | = ceiling((digits * bits_per_char) / PyLong_SHIFT). */ |
2216 | if (digits > (PY_SSIZE_T_MAX - (PyLong_SHIFT - 1)) / bits_per_char) { Branch (2216:9): [True: 0, False: 182k]
|
2217 | PyErr_SetString(PyExc_ValueError, |
2218 | "int string too large to convert"); |
2219 | *res = NULL; |
2220 | return 0; |
2221 | } |
2222 | n = (digits * bits_per_char + PyLong_SHIFT - 1) / PyLong_SHIFT; |
2223 | z = _PyLong_New(n); |
2224 | if (z == NULL) { Branch (2224:9): [True: 0, False: 182k]
|
2225 | *res = NULL; |
2226 | return 0; |
2227 | } |
2228 | /* Read string from right, and fill in int from left; i.e., |
2229 | * from least to most significant in both. |
2230 | */ |
2231 | accum = 0; |
2232 | bits_in_accum = 0; |
2233 | pdigit = z->ob_digit; |
2234 | while (--p >= start) { Branch (2234:12): [True: 1.35M, False: 182k]
|
2235 | int k; |
2236 | if (*p == '_') { Branch (2236:13): [True: 62, False: 1.35M]
|
2237 | continue; |
2238 | } |
2239 | k = (int)_PyLong_DigitValue[Py_CHARMASK(*p)]; |
2240 | assert(k >= 0 && k < base); |
2241 | accum |= (twodigits)k << bits_in_accum; |
2242 | bits_in_accum += bits_per_char; |
2243 | if (bits_in_accum >= PyLong_SHIFT) { Branch (2243:13): [True: 39.1k, False: 1.31M]
|
2244 | *pdigit++ = (digit)(accum & PyLong_MASK); |
2245 | assert(pdigit - z->ob_digit <= n); |
2246 | accum >>= PyLong_SHIFT; |
2247 | bits_in_accum -= PyLong_SHIFT; |
2248 | assert(bits_in_accum < PyLong_SHIFT); |
2249 | } |
2250 | } |
2251 | if (bits_in_accum) { Branch (2251:9): [True: 181k, False: 577]
|
2252 | assert(bits_in_accum <= PyLong_SHIFT); |
2253 | *pdigit++ = (digit)accum; |
2254 | assert(pdigit - z->ob_digit <= n); |
2255 | } |
2256 | while (pdigit - z->ob_digit < n) Branch (2256:12): [True: 0, False: 182k]
|
2257 | *pdigit++ = 0; |
2258 | *res = long_normalize(z); |
2259 | return 0; |
2260 | } |
2261 | |
2262 | /* Parses an int from a bytestring. Leading and trailing whitespace will be |
2263 | * ignored. |
2264 | * |
2265 | * If successful, a PyLong object will be returned and 'pend' will be pointing |
2266 | * to the first unused byte unless it's NULL. |
2267 | * |
2268 | * If unsuccessful, NULL will be returned. |
2269 | */ |
2270 | PyObject * |
2271 | PyLong_FromString(const char *str, char **pend, int base) |
2272 | { |
2273 | int sign = 1, error_if_nonzero = 0; |
2274 | const char *start, *orig_str = str; |
2275 | PyLongObject *z = NULL; |
2276 | PyObject *strobj; |
2277 | Py_ssize_t slen; |
2278 | |
2279 | if ((base != 0 && base < 2787k ) || base > 36) { Branch (2279:10): [True: 787k, False: 52.0k]
Branch (2279:23): [True: 0, False: 787k]
Branch (2279:36): [True: 0, False: 839k]
|
2280 | PyErr_SetString(PyExc_ValueError, |
2281 | "int() arg 2 must be >= 2 and <= 36"); |
2282 | return NULL; |
2283 | } |
2284 | while (839k *str != '\0' && Py_ISSPACE868k (*str)) { Branch (2284:12): [True: 868k, False: 36]
|
2285 | str++; |
2286 | } |
2287 | if (*str == '+') { Branch (2287:9): [True: 2.79k, False: 836k]
|
2288 | ++str; |
2289 | } |
2290 | else if (*str == '-') { Branch (2290:14): [True: 22.8k, False: 814k]
|
2291 | ++str; |
2292 | sign = -1; |
2293 | } |
2294 | if (base == 0) { Branch (2294:9): [True: 52.0k, False: 787k]
|
2295 | if (str[0] != '0') { Branch (2295:13): [True: 50.7k, False: 1.23k]
|
2296 | base = 10; |
2297 | } |
2298 | else if (str[1] == 'x' || str[1] == 'X'846 ) { Branch (2298:18): [True: 392, False: 846]
Branch (2298:35): [True: 8, False: 838]
|
2299 | base = 16; |
2300 | } |
2301 | else if (str[1] == 'o' || str[1] == 'O'463 ) { Branch (2301:18): [True: 375, False: 463]
Branch (2301:35): [True: 2, False: 461]
|
2302 | base = 8; |
2303 | } |
2304 | else if (str[1] == 'b' || str[1] == 'B'92 ) { Branch (2304:18): [True: 369, False: 92]
Branch (2304:35): [True: 8, False: 84]
|
2305 | base = 2; |
2306 | } |
2307 | else { |
2308 | /* "old" (C-style) octal literal, now invalid. |
2309 | it might still be zero though */ |
2310 | error_if_nonzero = 1; |
2311 | base = 10; |
2312 | } |
2313 | } |
2314 | if (str[0] == '0' && Branch (2314:9): [True: 180k, False: 658k]
|
2315 | (180k (180k base == 16180k && (18.0k str[1] == 'x'18.0k || str[1] == 'X'17.6k )) || Branch (2315:11): [True: 18.0k, False: 162k]
Branch (2315:26): [True: 403, False: 17.6k]
Branch (2315:43): [True: 12, False: 17.6k]
|
2316 | (180k base == 8180k && (87.7k str[1] == 'o'87.7k || str[1] == 'O'87.3k )) || Branch (2316:11): [True: 87.7k, False: 92.6k]
Branch (2316:26): [True: 379, False: 87.3k]
Branch (2316:43): [True: 5, False: 87.3k]
|
2317 | (180k base == 2180k && (10.4k str[1] == 'b'10.4k || str[1] == 'B'10.1k )))) { Branch (2317:11): [True: 10.4k, False: 169k]
Branch (2317:26): [True: 373, False: 10.1k]
Branch (2317:43): [True: 11, False: 10.0k]
|
2318 | str += 2; |
2319 | /* One underscore allowed here. */ |
2320 | if (*str == '_') { Branch (2320:13): [True: 8, False: 1.17k]
|
2321 | ++str; |
2322 | } |
2323 | } |
2324 | if (str[0] == '_') { Branch (2324:9): [True: 3, False: 839k]
|
2325 | /* May not start with underscores. */ |
2326 | goto onError; |
2327 | } |
2328 | |
2329 | start = str; |
2330 | if ((base & (base - 1)) == 0) { Branch (2330:9): [True: 182k, False: 657k]
|
2331 | int res = long_from_binary_base(&str, base, &z); |
2332 | if (res < 0) { Branch (2332:13): [True: 6, False: 182k]
|
2333 | /* Syntax error. */ |
2334 | goto onError; |
2335 | } |
2336 | } |
2337 | else { |
2338 | /*** |
2339 | Binary bases can be converted in time linear in the number of digits, because |
2340 | Python's representation base is binary. Other bases (including decimal!) use |
2341 | the simple quadratic-time algorithm below, complicated by some speed tricks. |
2342 | |
2343 | First some math: the largest integer that can be expressed in N base-B digits |
2344 | is B**N-1. Consequently, if we have an N-digit input in base B, the worst- |
2345 | case number of Python digits needed to hold it is the smallest integer n s.t. |
2346 | |
2347 | BASE**n-1 >= B**N-1 [or, adding 1 to both sides] |
2348 | BASE**n >= B**N [taking logs to base BASE] |
2349 | n >= log(B**N)/log(BASE) = N * log(B)/log(BASE) |
2350 | |
2351 | The static array log_base_BASE[base] == log(base)/log(BASE) so we can compute |
2352 | this quickly. A Python int with that much space is reserved near the start, |
2353 | and the result is computed into it. |
2354 | |
2355 | The input string is actually treated as being in base base**i (i.e., i digits |
2356 | are processed at a time), where two more static arrays hold: |
2357 | |
2358 | convwidth_base[base] = the largest integer i such that base**i <= BASE |
2359 | convmultmax_base[base] = base ** convwidth_base[base] |
2360 | |
2361 | The first of these is the largest i such that i consecutive input digits |
2362 | must fit in a single Python digit. The second is effectively the input |
2363 | base we're really using. |
2364 | |
2365 | Viewing the input as a sequence <c0, c1, ..., c_n-1> of digits in base |
2366 | convmultmax_base[base], the result is "simply" |
2367 | |
2368 | (((c0*B + c1)*B + c2)*B + c3)*B + ... ))) + c_n-1 |
2369 | |
2370 | where B = convmultmax_base[base]. |
2371 | |
2372 | Error analysis: as above, the number of Python digits `n` needed is worst- |
2373 | case |
2374 | |
2375 | n >= N * log(B)/log(BASE) |
2376 | |
2377 | where `N` is the number of input digits in base `B`. This is computed via |
2378 | |
2379 | size_z = (Py_ssize_t)((scan - str) * log_base_BASE[base]) + 1; |
2380 | |
2381 | below. Two numeric concerns are how much space this can waste, and whether |
2382 | the computed result can be too small. To be concrete, assume BASE = 2**15, |
2383 | which is the default (and it's unlikely anyone changes that). |
2384 | |
2385 | Waste isn't a problem: provided the first input digit isn't 0, the difference |
2386 | between the worst-case input with N digits and the smallest input with N |
2387 | digits is about a factor of B, but B is small compared to BASE so at most |
2388 | one allocated Python digit can remain unused on that count. If |
2389 | N*log(B)/log(BASE) is mathematically an exact integer, then truncating that |
2390 | and adding 1 returns a result 1 larger than necessary. However, that can't |
2391 | happen: whenever B is a power of 2, long_from_binary_base() is called |
2392 | instead, and it's impossible for B**i to be an integer power of 2**15 when |
2393 | B is not a power of 2 (i.e., it's impossible for N*log(B)/log(BASE) to be |
2394 | an exact integer when B is not a power of 2, since B**i has a prime factor |
2395 | other than 2 in that case, but (2**15)**j's only prime factor is 2). |
2396 | |
2397 | The computed result can be too small if the true value of N*log(B)/log(BASE) |
2398 | is a little bit larger than an exact integer, but due to roundoff errors (in |
2399 | computing log(B), log(BASE), their quotient, and/or multiplying that by N) |
2400 | yields a numeric result a little less than that integer. Unfortunately, "how |
2401 | close can a transcendental function get to an integer over some range?" |
2402 | questions are generally theoretically intractable. Computer analysis via |
2403 | continued fractions is practical: expand log(B)/log(BASE) via continued |
2404 | fractions, giving a sequence i/j of "the best" rational approximations. Then |
2405 | j*log(B)/log(BASE) is approximately equal to (the integer) i. This shows that |
2406 | we can get very close to being in trouble, but very rarely. For example, |
2407 | 76573 is a denominator in one of the continued-fraction approximations to |
2408 | log(10)/log(2**15), and indeed: |
2409 | |
2410 | >>> log(10)/log(2**15)*76573 |
2411 | 16958.000000654003 |
2412 | |
2413 | is very close to an integer. If we were working with IEEE single-precision, |
2414 | rounding errors could kill us. Finding worst cases in IEEE double-precision |
2415 | requires better-than-double-precision log() functions, and Tim didn't bother. |
2416 | Instead the code checks to see whether the allocated space is enough as each |
2417 | new Python digit is added, and copies the whole thing to a larger int if not. |
2418 | This should happen extremely rarely, and in fact I don't have a test case |
2419 | that triggers it(!). Instead the code was tested by artificially allocating |
2420 | just 1 digit at the start, so that the copying code was exercised for every |
2421 | digit beyond the first. |
2422 | ***/ |
2423 | twodigits c; /* current input character */ |
2424 | Py_ssize_t size_z; |
2425 | Py_ssize_t digits = 0; |
2426 | int i; |
2427 | int convwidth; |
2428 | twodigits convmultmax, convmult; |
2429 | digit *pz, *pzstop; |
2430 | const char *scan, *lastdigit; |
2431 | char prev = 0; |
2432 | |
2433 | static double log_base_BASE[37] = {0.0e0,}; |
2434 | static int convwidth_base[37] = {0,}; |
2435 | static twodigits convmultmax_base[37] = {0,}; |
2436 | |
2437 | if (log_base_BASE[base] == 0.0) { Branch (2437:13): [True: 31, False: 657k]
|
2438 | twodigits convmax = base; |
2439 | int i = 1; |
2440 | |
2441 | log_base_BASE[base] = (log((double)base) / |
2442 | log((double)PyLong_BASE)); |
2443 | for (;;) { |
2444 | twodigits next = convmax * base; |
2445 | if (next > PyLong_BASE) { Branch (2445:21): [True: 31, False: 198]
|
2446 | break; |
2447 | } |
2448 | convmax = next; |
2449 | ++i; |
2450 | } |
2451 | convmultmax_base[base] = convmax; |
2452 | assert(i > 0); |
2453 | convwidth_base[base] = i; |
2454 | } |
2455 | |
2456 | /* Find length of the string of numeric characters. */ |
2457 | scan = str; |
2458 | lastdigit = str; |
2459 | |
2460 | while (_PyLong_DigitValue[Py_CHARMASK(*scan)] < base || *scan == '_'657k ) { Branch (2460:16): [True: 4.73M, False: 657k]
Branch (2460:65): [True: 32, False: 657k]
|
2461 | if (*scan == '_') { Branch (2461:17): [True: 32, False: 4.73M]
|
2462 | if (prev == '_') { Branch (2462:21): [True: 2, False: 30]
|
2463 | /* Only one underscore allowed. */ |
2464 | str = lastdigit + 1; |
2465 | goto onError; |
2466 | } |
2467 | } |
2468 | else { |
2469 | ++digits; |
2470 | lastdigit = scan; |
2471 | } |
2472 | prev = *scan; |
2473 | ++scan; |
2474 | } |
2475 | if (prev == '_') { Branch (2475:13): [True: 6, False: 657k]
|
2476 | /* Trailing underscore not allowed. */ |
2477 | /* Set error pointer to first underscore. */ |
2478 | str = lastdigit + 1; |
2479 | goto onError; |
2480 | } |
2481 | |
2482 | /* Create an int object that can contain the largest possible |
2483 | * integer with this base and length. Note that there's no |
2484 | * need to initialize z->ob_digit -- no slot is read up before |
2485 | * being stored into. |
2486 | */ |
2487 | double fsize_z = (double)digits * log_base_BASE[base] + 1.0; |
2488 | if (fsize_z > (double)MAX_LONG_DIGITS) { Branch (2488:13): [True: 0, False: 657k]
|
2489 | /* The same exception as in _PyLong_New(). */ |
2490 | PyErr_SetString(PyExc_OverflowError, |
2491 | "too many digits in integer"); |
2492 | return NULL; |
2493 | } |
2494 | size_z = (Py_ssize_t)fsize_z; |
2495 | /* Uncomment next line to test exceedingly rare copy code */ |
2496 | /* size_z = 1; */ |
2497 | assert(size_z > 0); |
2498 | z = _PyLong_New(size_z); |
2499 | if (z == NULL) { Branch (2499:13): [True: 0, False: 657k]
|
2500 | return NULL; |
2501 | } |
2502 | Py_SET_SIZE(z, 0); |
2503 | |
2504 | /* `convwidth` consecutive input digits are treated as a single |
2505 | * digit in base `convmultmax`. |
2506 | */ |
2507 | convwidth = convwidth_base[base]; |
2508 | convmultmax = convmultmax_base[base]; |
2509 | |
2510 | /* Work ;-) */ |
2511 | while (str < scan) { Branch (2511:16): [True: 986k, False: 657k]
|
2512 | if (*str == '_') { Branch (2512:17): [True: 0, False: 986k]
|
2513 | str++; |
2514 | continue; |
2515 | } |
2516 | /* grab up to convwidth digits from the input string */ |
2517 | c = (digit)_PyLong_DigitValue[Py_CHARMASK(*str++)]; |
2518 | for (i = 1; i < convwidth && str != scan4.39M ; ++str3.74M ) { Branch (2518:25): [True: 4.39M, False: 333k]
Branch (2518:42): [True: 3.74M, False: 652k]
|
2519 | if (*str == '_') { Branch (2519:21): [True: 22, False: 3.74M]
|
2520 | continue; |
2521 | } |
2522 | i++; |
2523 | c = (twodigits)(c * base + |
2524 | (int)_PyLong_DigitValue[Py_CHARMASK(*str)]); |
2525 | assert(c < PyLong_BASE); |
2526 | } |
2527 | |
2528 | convmult = convmultmax; |
2529 | /* Calculate the shift only if we couldn't get |
2530 | * convwidth digits. |
2531 | */ |
2532 | if (i != convwidth) { Branch (2532:17): [True: 652k, False: 333k]
|
2533 | convmult = base; |
2534 | for ( ; i > 1; --i1.07M ) { Branch (2534:25): [True: 1.07M, False: 652k]
|
2535 | convmult *= base; |
2536 | } |
2537 | } |
2538 | |
2539 | /* Multiply z by convmult, and add c. */ |
2540 | pz = z->ob_digit; |
2541 | pzstop = pz + Py_SIZE(z); |
2542 | for (; pz < pzstop; ++pz11.7M ) { Branch (2542:20): [True: 11.7M, False: 986k]
|
2543 | c += (twodigits)*pz * convmult; |
2544 | *pz = (digit)(c & PyLong_MASK); |
2545 | c >>= PyLong_SHIFT; |
2546 | } |
2547 | /* carry off the current end? */ |
2548 | if (c) { Branch (2548:17): [True: 932k, False: 53.3k]
|
2549 | assert(c < PyLong_BASE); |
2550 | if (Py_SIZE(z) < size_z) { Branch (2550:21): [True: 932k, False: 0]
|
2551 | *pz = (digit)c; |
2552 | Py_SET_SIZE(z, Py_SIZE(z) + 1); |
2553 | } |
2554 | else { |
2555 | PyLongObject *tmp; |
2556 | /* Extremely rare. Get more space. */ |
2557 | assert(Py_SIZE(z) == size_z); |
2558 | tmp = _PyLong_New(size_z + 1); |
2559 | if (tmp == NULL) { Branch (2559:25): [True: 0, False: 0]
|
2560 | Py_DECREF(z); |
2561 | return NULL; |
2562 | } |
2563 | memcpy(tmp->ob_digit, |
2564 | z->ob_digit, |
2565 | sizeof(digit) * size_z); |
2566 | Py_DECREF(z); |
2567 | z = tmp; |
2568 | z->ob_digit[size_z] = (digit)c; |
2569 | ++size_z; |
2570 | } |
2571 | } |
2572 | } |
2573 | } |
2574 | if (z == NULL) { Branch (2574:9): [True: 0, False: 839k]
|
2575 | return NULL; |
2576 | } |
2577 | if (error_if_nonzero) { Branch (2577:9): [True: 80, False: 839k]
|
2578 | /* reset the base to 0, else the exception message |
2579 | doesn't make too much sense */ |
2580 | base = 0; |
2581 | if (Py_SIZE(z) != 0) { Branch (2581:13): [True: 4, False: 76]
|
2582 | goto onError; |
2583 | } |
2584 | /* there might still be other problems, therefore base |
2585 | remains zero here for the same reason */ |
2586 | } |
2587 | if (str == start) { Branch (2587:9): [True: 726, False: 839k]
|
2588 | goto onError; |
2589 | } |
2590 | if (sign < 0) { Branch (2590:9): [True: 22.7k, False: 816k]
|
2591 | Py_SET_SIZE(z, -(Py_SIZE(z))); |
2592 | } |
2593 | while (*str && Py_ISSPACE180k (*str)) { Branch (2593:12): [True: 180k, False: 838k]
|
2594 | str++; |
2595 | } |
2596 | if (*str != '\0') { Branch (2596:9): [True: 376, False: 838k]
|
2597 | goto onError; |
2598 | } |
2599 | long_normalize(z); |
2600 | z = maybe_small_long(z); |
2601 | if (z == NULL) { Branch (2601:9): [True: 0, False: 838k]
|
2602 | return NULL; |
2603 | } |
2604 | if (pend != NULL) { Branch (2604:9): [True: 699k, False: 139k]
|
2605 | *pend = (char *)str; |
2606 | } |
2607 | return (PyObject *) z; |
2608 | |
2609 | onError: |
2610 | if (pend != NULL) { Branch (2610:9): [True: 1.12k, False: 2]
|
2611 | *pend = (char *)str; |
2612 | } |
2613 | Py_XDECREF(z); |
2614 | slen = strlen(orig_str) < 200 ? strlen(orig_str) : 2000 ; Branch (2614:12): [True: 1.12k, False: 0]
|
2615 | strobj = PyUnicode_FromStringAndSize(orig_str, slen); |
2616 | if (strobj == NULL) { Branch (2616:9): [True: 2, False: 1.12k]
|
2617 | return NULL; |
2618 | } |
2619 | PyErr_Format(PyExc_ValueError, |
2620 | "invalid literal for int() with base %d: %.200R", |
2621 | base, strobj); |
2622 | Py_DECREF(strobj); |
2623 | return NULL; |
2624 | } |
2625 | |
2626 | /* Since PyLong_FromString doesn't have a length parameter, |
2627 | * check here for possible NULs in the string. |
2628 | * |
2629 | * Reports an invalid literal as a bytes object. |
2630 | */ |
2631 | PyObject * |
2632 | _PyLong_FromBytes(const char *s, Py_ssize_t len, int base) |
2633 | { |
2634 | PyObject *result, *strobj; |
2635 | char *end = NULL; |
2636 | |
2637 | result = PyLong_FromString(s, &end, base); |
2638 | if (end == NULL || (result != NULL && end == s + len238k )) Branch (2638:9): [True: 0, False: 238k]
Branch (2638:25): [True: 238k, False: 33]
Branch (2638:43): [True: 238k, False: 2]
|
2639 | return result; |
2640 | Py_XDECREF(result); |
2641 | strobj = PyBytes_FromStringAndSize(s, Py_MIN(len, 200)); |
2642 | if (strobj != NULL) { Branch (2642:9): [True: 35, False: 0]
|
2643 | PyErr_Format(PyExc_ValueError, |
2644 | "invalid literal for int() with base %d: %.200R", |
2645 | base, strobj); |
2646 | Py_DECREF(strobj); |
2647 | } |
2648 | return NULL; |
2649 | } |
2650 | |
2651 | PyObject * |
2652 | PyLong_FromUnicodeObject(PyObject *u, int base) |
2653 | { |
2654 | PyObject *result, *asciidig; |
2655 | const char *buffer; |
2656 | char *end = NULL; |
2657 | Py_ssize_t buflen; |
2658 | |
2659 | asciidig = _PyUnicode_TransformDecimalAndSpaceToASCII(u); |
2660 | if (asciidig == NULL) Branch (2660:9): [True: 0, False: 461k]
|
2661 | return NULL; |
2662 | assert(PyUnicode_IS_ASCII(asciidig)); |
2663 | /* Simply get a pointer to existing ASCII characters. */ |
2664 | buffer = PyUnicode_AsUTF8AndSize(asciidig, &buflen); |
2665 | assert(buffer != NULL); |
2666 | |
2667 | result = PyLong_FromString(buffer, &end, base); |
2668 | if (end == NULL || (result != NULL && end == buffer + buflen460k )) { Branch (2668:9): [True: 0, False: 461k]
Branch (2668:25): [True: 460k, False: 1.08k]
Branch (2668:43): [True: 460k, False: 7]
|
2669 | Py_DECREF(asciidig); |
2670 | return result; |
2671 | } |
2672 | Py_DECREF(asciidig); |
2673 | Py_XDECREF(result); |
2674 | PyErr_Format(PyExc_ValueError, |
2675 | "invalid literal for int() with base %d: %.200R", |
2676 | base, u); |
2677 | return NULL; |
2678 | } |
2679 | |
2680 | /* forward */ |
2681 | static PyLongObject *x_divrem |
2682 | (PyLongObject *, PyLongObject *, PyLongObject **); |
2683 | static PyObject *long_long(PyObject *v); |
2684 | |
2685 | /* Int division with remainder, top-level routine */ |
2686 | |
2687 | static int |
2688 | long_divrem(PyLongObject *a, PyLongObject *b, |
2689 | PyLongObject **pdiv, PyLongObject **prem) |
2690 | { |
2691 | Py_ssize_t size_a = Py_ABS(Py_SIZE(a)), size_b = Py_ABS(Py_SIZE(b)); |
2692 | PyLongObject *z; |
2693 | |
2694 | if (size_b == 0) { Branch (2694:9): [True: 259, False: 1.61M]
|
2695 | PyErr_SetString(PyExc_ZeroDivisionError, |
2696 | "integer division or modulo by zero"); |
2697 | return -1; |
2698 | } |
2699 | if (size_a < size_b || Branch (2699:9): [True: 794k, False: 824k]
|
2700 | (824k size_a == size_b824k && Branch (2700:10): [True: 239k, False: 585k]
|
2701 | a->ob_digit[size_a-1] < b->ob_digit[size_b-1]239k )) { Branch (2701:10): [True: 4.51k, False: 234k]
|
2702 | /* |a| < |b|. */ |
2703 | *prem = (PyLongObject *)long_long((PyObject *)a); |
2704 | if (*prem == NULL) { Branch (2704:13): [True: 0, False: 799k]
|
2705 | return -1; |
2706 | } |
2707 | PyObject *zero = _PyLong_GetZero(); |
2708 | Py_INCREF(zero); |
2709 | *pdiv = (PyLongObject*)zero; |
2710 | return 0; |
2711 | } |
2712 | if (size_b == 1) { Branch (2712:9): [True: 411k, False: 408k]
|
2713 | digit rem = 0; |
2714 | z = divrem1(a, b->ob_digit[0], &rem); |
2715 | if (z == NULL) Branch (2715:13): [True: 0, False: 411k]
|
2716 | return -1; |
2717 | *prem = (PyLongObject *) PyLong_FromLong((long)rem); |
2718 | if (*prem == NULL) { Branch (2718:13): [True: 0, False: 411k]
|
2719 | Py_DECREF(z); |
2720 | return -1; |
2721 | } |
2722 | } |
2723 | else { |
2724 | z = x_divrem(a, b, prem); |
2725 | *prem = maybe_small_long(*prem); |
2726 | if (z == NULL) Branch (2726:13): [True: 0, False: 408k]
|
2727 | return -1; |
2728 | } |
2729 | /* Set the signs. |
2730 | The quotient z has the sign of a*b; |
2731 | the remainder r has the sign of a, |
2732 | so a = b*z + r. */ |
2733 | if ((Py_SIZE(a) < 0) != (Py_SIZE(b) < 0)) { Branch (2733:9): [True: 45.0k, False: 775k]
|
2734 | _PyLong_Negate(&z); |
2735 | if (z == NULL) { Branch (2735:13): [True: 0, False: 45.0k]
|
2736 | Py_CLEAR(*prem); |
2737 | return -1; |
2738 | } |
2739 | } |
2740 | if (Py_SIZE(a) < 0 && Py_SIZE45.0k (*prem) != 045.0k ) { Branch (2740:9): [True: 45.0k, False: 775k]
Branch (2740:27): [True: 25.4k, False: 19.6k]
|
2741 | _PyLong_Negate(prem); |
2742 | if (*prem == NULL) { Branch (2742:13): [True: 0, False: 25.4k]
|
2743 | Py_DECREF(z); |
2744 | Py_CLEAR(*prem); |
2745 | return -1; |
2746 | } |
2747 | } |
2748 | *pdiv = maybe_small_long(z); |
2749 | return 0; |
2750 | } |
2751 | |
2752 | /* Int remainder, top-level routine */ |
2753 | |
2754 | static int |
2755 | long_rem(PyLongObject *a, PyLongObject *b, PyLongObject **prem) |
2756 | { |
2757 | Py_ssize_t size_a = Py_ABS(Py_SIZE(a)), size_b = Py_ABS(Py_SIZE(b)); |
2758 | |
2759 | if (size_b == 0) { Branch (2759:9): [True: 4, False: 20.4M]
|
2760 | PyErr_SetString(PyExc_ZeroDivisionError, |
2761 | "integer modulo by zero"); |
2762 | return -1; |
2763 | } |
2764 | if (size_a < size_b || Branch (2764:9): [True: 49.0k, False: 20.4M]
|
2765 | (20.4M size_a == size_b20.4M && Branch (2765:10): [True: 111k, False: 20.2M]
|
2766 | a->ob_digit[size_a-1] < b->ob_digit[size_b-1]111k )) { Branch (2766:10): [True: 3.24k, False: 108k]
|
2767 | /* |a| < |b|. */ |
2768 | *prem = (PyLongObject *)long_long((PyObject *)a); |
2769 | return -(*prem == NULL); |
2770 | } |
2771 | if (size_b == 1) { Branch (2771:9): [True: 17.3M, False: 3.01M]
|
2772 | *prem = rem1(a, b->ob_digit[0]); |
2773 | if (*prem == NULL) Branch (2773:13): [True: 0, False: 17.3M]
|
2774 | return -1; |
2775 | } |
2776 | else { |
2777 | /* Slow path using divrem. */ |
2778 | Py_XDECREF(x_divrem(a, b, prem)); |
2779 | *prem = maybe_small_long(*prem); |
2780 | if (*prem == NULL) Branch (2780:13): [True: 0, False: 3.01M]
|
2781 | return -1; |
2782 | } |
2783 | /* Set the sign. */ |
2784 | if (Py_SIZE(a) < 0 && Py_SIZE13.1k (*prem) != 013.1k ) { Branch (2784:9): [True: 13.1k, False: 20.3M]
Branch (2784:27): [True: 3.15k, False: 9.94k]
|
2785 | _PyLong_Negate(prem); |
2786 | if (*prem == NULL) { Branch (2786:13): [True: 0, False: 3.15k]
|
2787 | Py_CLEAR(*prem); |
2788 | return -1; |
2789 | } |
2790 | } |
2791 | return 0; |
2792 | } |
2793 | |
2794 | /* Unsigned int division with remainder -- the algorithm. The arguments v1 |
2795 | and w1 should satisfy 2 <= Py_ABS(Py_SIZE(w1)) <= Py_ABS(Py_SIZE(v1)). */ |
2796 | |
2797 | static PyLongObject * |
2798 | x_divrem(PyLongObject *v1, PyLongObject *w1, PyLongObject **prem) |
2799 | { |
2800 | PyLongObject *v, *w, *a; |
2801 | Py_ssize_t i, k, size_v, size_w; |
2802 | int d; |
2803 | digit wm1, wm2, carry, q, r, vtop, *v0, *vk, *w0, *ak; |
2804 | twodigits vv; |
2805 | sdigit zhi; |
2806 | stwodigits z; |
2807 | |
2808 | /* We follow Knuth [The Art of Computer Programming, Vol. 2 (3rd |
2809 | edn.), section 4.3.1, Algorithm D], except that we don't explicitly |
2810 | handle the special case when the initial estimate q for a quotient |
2811 | digit is >= PyLong_BASE: the max value for q is PyLong_BASE+1, and |
2812 | that won't overflow a digit. */ |
2813 | |
2814 | /* allocate space; w will also be used to hold the final remainder */ |
2815 | size_v = Py_ABS(Py_SIZE(v1)); |
2816 | size_w = Py_ABS(Py_SIZE(w1)); |
2817 | assert(size_v >= size_w && size_w >= 2); /* Assert checks by div() */ |
2818 | v = _PyLong_New(size_v+1); |
2819 | if (v == NULL) { Branch (2819:9): [True: 0, False: 3.51M]
|
2820 | *prem = NULL; |
2821 | return NULL; |
2822 | } |
2823 | w = _PyLong_New(size_w); |
2824 | if (w == NULL) { Branch (2824:9): [True: 0, False: 3.51M]
|
2825 | Py_DECREF(v); |
2826 | *prem = NULL; |
2827 | return NULL; |
2828 | } |
2829 | |
2830 | /* normalize: shift w1 left so that its top digit is >= PyLong_BASE/2. |
2831 | shift v1 left by the same amount. Results go into w and v. */ |
2832 | d = PyLong_SHIFT - bit_length_digit(w1->ob_digit[size_w-1]); |
2833 | carry = v_lshift(w->ob_digit, w1->ob_digit, size_w, d); |
2834 | assert(carry == 0); |
2835 | carry = v_lshift(v->ob_digit, v1->ob_digit, size_v, d); |
2836 | if (carry != 0 || v->ob_digit[size_v-1] >= w->ob_digit[size_w-1]462k ) { Branch (2836:9): [True: 3.05M, False: 462k]
Branch (2836:23): [True: 169k, False: 293k]
|
2837 | v->ob_digit[size_v] = carry; |
2838 | size_v++; |
2839 | } |
2840 | |
2841 | /* Now v->ob_digit[size_v-1] < w->ob_digit[size_w-1], so quotient has |
2842 | at most (and usually exactly) k = size_v - size_w digits. */ |
2843 | k = size_v - size_w; |
2844 | assert(k >= 0); |
2845 | a = _PyLong_New(k); |
2846 | if (a == NULL) { Branch (2846:9): [True: 0, False: 3.51M]
|
2847 | Py_DECREF(w); |
2848 | Py_DECREF(v); |
2849 | *prem = NULL; |
2850 | return NULL; |
2851 | } |
2852 | v0 = v->ob_digit; |
2853 | w0 = w->ob_digit; |
2854 | wm1 = w0[size_w-1]; |
2855 | wm2 = w0[size_w-2]; |
2856 | for (vk = v0+k, ak = a->ob_digit + k; vk-- > v0;) { Branch (2856:43): [True: 6.85M, False: 3.51M]
|
2857 | /* inner loop: divide vk[0:size_w+1] by w0[0:size_w], giving |
2858 | single-digit quotient q, remainder in vk[0:size_w]. */ |
2859 | |
2860 | SIGCHECK({ |
2861 | Py_DECREF(a); |
2862 | Py_DECREF(w); |
2863 | Py_DECREF(v); |
2864 | *prem = NULL; |
2865 | return NULL; |
2866 | }); |
2867 | |
2868 | /* estimate quotient digit q; may overestimate by 1 (rare) */ |
2869 | vtop = vk[size_w]; |
2870 | assert(vtop <= wm1); |
2871 | vv = ((twodigits)vtop << PyLong_SHIFT) | vk[size_w-1]; |
2872 | /* The code used to compute the remainder via |
2873 | * r = (digit)(vv - (twodigits)wm1 * q); |
2874 | * and compilers generally generated code to do the * and -. |
2875 | * But modern processors generally compute q and r with a single |
2876 | * instruction, and modern optimizing compilers exploit that if we |
2877 | * _don't_ try to optimize it. |
2878 | */ |
2879 | q = (digit)(vv / wm1); |
2880 | r = (digit)(vv % wm1); |
2881 | while ((twodigits)wm2 * q > (((twodigits)r << PyLong_SHIFT) Branch (2881:16): [True: 224k, False: 6.78M]
|
2882 | | vk[size_w-2])) { |
2883 | --q; |
2884 | r += wm1; |
2885 | if (r >= PyLong_BASE) Branch (2885:17): [True: 68.0k, False: 156k]
|
2886 | break; |
2887 | } |
2888 | assert(q <= PyLong_BASE); |
2889 | |
2890 | /* subtract q*w0[0:size_w] from vk[0:size_w+1] */ |
2891 | zhi = 0; |
2892 | for (i = 0; i < size_w; ++i25.2M ) { Branch (2892:21): [True: 25.2M, False: 6.85M]
|
2893 | /* invariants: -PyLong_BASE <= -q <= zhi <= 0; |
2894 | -PyLong_BASE * q <= z < PyLong_BASE */ |
2895 | z = (sdigit)vk[i] + zhi - |
2896 | (stwodigits)q * (stwodigits)w0[i]; |
2897 | vk[i] = (digit)z & PyLong_MASK; |
2898 | zhi = (sdigit)Py_ARITHMETIC_RIGHT_SHIFT(stwodigits, |
2899 | z, PyLong_SHIFT); |
2900 | } |
2901 | |
2902 | /* add w back if q was too large (this branch taken rarely) */ |
2903 | assert((sdigit)vtop + zhi == -1 || (sdigit)vtop + zhi == 0); |
2904 | if ((sdigit)vtop + zhi < 0) { Branch (2904:13): [True: 405, False: 6.85M]
|
2905 | carry = 0; |
2906 | for (i = 0; i < size_w; ++i3.62k ) { Branch (2906:25): [True: 3.62k, False: 405]
|
2907 | carry += vk[i] + w0[i]; |
2908 | vk[i] = carry & PyLong_MASK; |
2909 | carry >>= PyLong_SHIFT; |
2910 | } |
2911 | --q; |
2912 | } |
2913 | |
2914 | /* store quotient digit */ |
2915 | assert(q < PyLong_BASE); |
2916 | *--ak = q; |
2917 | } |
2918 | |
2919 | /* unshift remainder; we reuse w to store the result */ |
2920 | carry = v_rshift(w0, v0, size_w, d); |
2921 | assert(carry==0); |
2922 | Py_DECREF(v); |
2923 | |
2924 | *prem = long_normalize(w); |
2925 | return long_normalize(a); |
2926 | } |
2927 | |
2928 | /* For a nonzero PyLong a, express a in the form x * 2**e, with 0.5 <= |
2929 | abs(x) < 1.0 and e >= 0; return x and put e in *e. Here x is |
2930 | rounded to DBL_MANT_DIG significant bits using round-half-to-even. |
2931 | If a == 0, return 0.0 and set *e = 0. If the resulting exponent |
2932 | e is larger than PY_SSIZE_T_MAX, raise OverflowError and return |
2933 | -1.0. */ |
2934 | |
2935 | /* attempt to define 2.0**DBL_MANT_DIG as a compile-time constant */ |
2936 | #if DBL_MANT_DIG == 53 |
2937 | #define EXP2_DBL_MANT_DIG 9007199254740992.0 |
2938 | #else |
2939 | #define EXP2_DBL_MANT_DIG (ldexp(1.0, DBL_MANT_DIG)) |
2940 | #endif |
2941 | |
2942 | double |
2943 | _PyLong_Frexp(PyLongObject *a, Py_ssize_t *e) |
2944 | { |
2945 | Py_ssize_t a_size, a_bits, shift_digits, shift_bits, x_size; |
2946 | /* See below for why x_digits is always large enough. */ |
2947 | digit rem; |
2948 | digit x_digits[2 + (DBL_MANT_DIG + 1) / PyLong_SHIFT] = {0,}; |
2949 | double dx; |
2950 | /* Correction term for round-half-to-even rounding. For a digit x, |
2951 | "x + half_even_correction[x & 7]" gives x rounded to the nearest |
2952 | multiple of 4, rounding ties to a multiple of 8. */ |
2953 | static const int half_even_correction[8] = {0, -1, -2, 1, 0, -1, 2, 1}; |
2954 | |
2955 | a_size = Py_ABS(Py_SIZE(a)); |
2956 | if (a_size == 0) { Branch (2956:9): [True: 0, False: 149k]
|
2957 | /* Special case for 0: significand 0.0, exponent 0. */ |
2958 | *e = 0; |
2959 | return 0.0; |
2960 | } |
2961 | a_bits = bit_length_digit(a->ob_digit[a_size-1]); |
2962 | /* The following is an overflow-free version of the check |
2963 | "if ((a_size - 1) * PyLong_SHIFT + a_bits > PY_SSIZE_T_MAX) ..." */ |
2964 | if (a_size >= (PY_SSIZE_T_MAX - 1) / PyLong_SHIFT + 1 && Branch (2964:9): [True: 0, False: 149k]
|
2965 | (0 a_size > (0 PY_SSIZE_T_MAX0 - 1) / PyLong_SHIFT0 + 1 || Branch (2965:10): [True: 0, False: 0]
|
2966 | a_bits > (PY_SSIZE_T_MAX - 1) % PyLong_SHIFT + 1)) Branch (2966:10): [True: 0, False: 0]
|
2967 | goto overflow; |
2968 | a_bits = (a_size - 1) * PyLong_SHIFT + a_bits; |
2969 | |
2970 | /* Shift the first DBL_MANT_DIG + 2 bits of a into x_digits[0:x_size] |
2971 | (shifting left if a_bits <= DBL_MANT_DIG + 2). |
2972 | |
2973 | Number of digits needed for result: write // for floor division. |
2974 | Then if shifting left, we end up using |
2975 | |
2976 | 1 + a_size + (DBL_MANT_DIG + 2 - a_bits) // PyLong_SHIFT |
2977 | |
2978 | digits. If shifting right, we use |
2979 | |
2980 | a_size - (a_bits - DBL_MANT_DIG - 2) // PyLong_SHIFT |
2981 | |
2982 | digits. Using a_size = 1 + (a_bits - 1) // PyLong_SHIFT along with |
2983 | the inequalities |
2984 | |
2985 | m // PyLong_SHIFT + n // PyLong_SHIFT <= (m + n) // PyLong_SHIFT |
2986 | m // PyLong_SHIFT - n // PyLong_SHIFT <= |
2987 | 1 + (m - n - 1) // PyLong_SHIFT, |
2988 | |
2989 | valid for any integers m and n, we find that x_size satisfies |
2990 | |
2991 | x_size <= 2 + (DBL_MANT_DIG + 1) // PyLong_SHIFT |
2992 | |
2993 | in both cases. |
2994 | */ |
2995 | if (a_bits <= DBL_MANT_DIG + 2) { Branch (2995:9): [True: 94.3k, False: 55.4k]
|
2996 | shift_digits = (DBL_MANT_DIG + 2 - a_bits) / PyLong_SHIFT; |
2997 | shift_bits = (DBL_MANT_DIG + 2 - a_bits) % PyLong_SHIFT; |
2998 | x_size = shift_digits; |
2999 | rem = v_lshift(x_digits + x_size, a->ob_digit, a_size, |
3000 | (int)shift_bits); |
3001 | x_size += a_size; |
3002 | x_digits[x_size++] = rem; |
3003 | } |
3004 | else { |
3005 | shift_digits = (a_bits - DBL_MANT_DIG - 2) / PyLong_SHIFT; |
3006 | shift_bits = (a_bits - DBL_MANT_DIG - 2) % PyLong_SHIFT; |
3007 | rem = v_rshift(x_digits, a->ob_digit + shift_digits, |
3008 | a_size - shift_digits, (int)shift_bits); |
3009 | x_size = a_size - shift_digits; |
3010 | /* For correct rounding below, we need the least significant |
3011 | bit of x to be 'sticky' for this shift: if any of the bits |
3012 | shifted out was nonzero, we set the least significant bit |
3013 | of x. */ |
3014 | if (rem) Branch (3014:13): [True: 36.8k, False: 18.6k]
|
3015 | x_digits[0] |= 1; |
3016 | else |
3017 | while (18.6k shift_digits > 0) Branch (3017:20): [True: 145k, False: 17.9k]
|
3018 | if (a->ob_digit[--shift_digits]) { Branch (3018:21): [True: 646, False: 144k]
|
3019 | x_digits[0] |= 1; |
3020 | break; |
3021 | } |
3022 | } |
3023 | assert(1 <= x_size && x_size <= (Py_ssize_t)Py_ARRAY_LENGTH(x_digits)); |
3024 | |
3025 | /* Round, and convert to double. */ |
3026 | x_digits[0] += half_even_correction[x_digits[0] & 7]; |
3027 | dx = x_digits[--x_size]; |
3028 | while (x_size > 0) Branch (3028:12): [True: 286k, False: 149k]
|
3029 | dx = dx * PyLong_BASE + x_digits[--x_size]; |
3030 | |
3031 | /* Rescale; make correction if result is 1.0. */ |
3032 | dx /= 4.0 * EXP2_DBL_MANT_DIG; |
3033 | if (dx == 1.0) { Branch (3033:9): [True: 2.29k, False: 147k]
|
3034 | if (a_bits == PY_SSIZE_T_MAX) Branch (3034:13): [True: 0, False: 2.29k]
|
3035 | goto overflow; |
3036 | dx = 0.5; |
3037 | a_bits += 1; |
3038 | } |
3039 | |
3040 | *e = a_bits; |
3041 | return Py_SIZE(a) < 0 ? -dx20.8k : dx129k ; Branch (3041:12): [True: 20.8k, False: 129k]
|
3042 | |
3043 | overflow: |
3044 | /* exponent > PY_SSIZE_T_MAX */ |
3045 | PyErr_SetString(PyExc_OverflowError, |
3046 | "huge integer: number of bits overflows a Py_ssize_t"); |
3047 | *e = 0; |
3048 | return -1.0; |
3049 | } |
3050 | |
3051 | /* Get a C double from an int object. Rounds to the nearest double, |
3052 | using the round-half-to-even rule in the case of a tie. */ |
3053 | |
3054 | double |
3055 | PyLong_AsDouble(PyObject *v) |
3056 | { |
3057 | Py_ssize_t exponent; |
3058 | double x; |
3059 | |
3060 | if (v == NULL) { Branch (3060:9): [True: 0, False: 6.63M]
|
3061 | PyErr_BadInternalCall(); |
3062 | return -1.0; |
3063 | } |
3064 | if (!PyLong_Check(v)) { Branch (3064:9): [True: 1, False: 6.63M]
|
3065 | PyErr_SetString(PyExc_TypeError, "an integer is required"); |
3066 | return -1.0; |
3067 | } |
3068 | if (IS_MEDIUM_VALUE(v)) { |
3069 | /* Fast path; single digit long (31 bits) will cast safely |
3070 | to double. This improves performance of FP/long operations |
3071 | by 20%. |
3072 | */ |
3073 | return (double)medium_value((PyLongObject *)v); |
3074 | } |
3075 | x = _PyLong_Frexp((PyLongObject *)v, &exponent); |
3076 | if ((x == -1.0 && PyErr_Occurred()0 ) || exponent > DBL_MAX_EXP) { Branch (3076:10): [True: 0, False: 149k]
Branch (3076:23): [True: 0, False: 0]
Branch (3076:44): [True: 90, False: 149k]
|
3077 | PyErr_SetString(PyExc_OverflowError, |
3078 | "int too large to convert to float"); |
3079 | return -1.0; |
3080 | } |
3081 | return ldexp(x, (int)exponent); |
3082 | } |
3083 | |
3084 | /* Methods */ |
3085 | |
3086 | /* if a < b, return a negative number |
3087 | if a == b, return 0 |
3088 | if a > b, return a positive number */ |
3089 | |
3090 | static Py_ssize_t |
3091 | long_compare(PyLongObject *a, PyLongObject *b) |
3092 | { |
3093 | Py_ssize_t sign = Py_SIZE(a) - Py_SIZE(b); |
3094 | if (sign == 0) { Branch (3094:9): [True: 35.0M, False: 10.9M]
|
3095 | Py_ssize_t i = Py_ABS(Py_SIZE(a)); |
3096 | sdigit diff = 0; |
3097 | while (--i >= 0) { Branch (3097:16): [True: 41.1M, False: 11.4M]
|
3098 | diff = (sdigit) a->ob_digit[i] - (sdigit) b->ob_digit[i]; |
3099 | if (diff) { Branch (3099:17): [True: 23.6M, False: 17.5M]
|
3100 | break; |
3101 | } |
3102 | } |
3103 | sign = Py_SIZE(a) < 0 ? -diff1.67M : diff33.4M ; Branch (3103:16): [True: 1.67M, False: 33.4M]
|
3104 | } |
3105 | return sign; |
3106 | } |
3107 | |
3108 | static PyObject * |
3109 | long_richcompare(PyObject *self, PyObject *other, int op) |
3110 | { |
3111 | Py_ssize_t result; |
3112 | CHECK_BINOP(self, other); |
3113 | if (self == other) Branch (3113:9): [True: 3.93M, False: 45.7M]
|
3114 | result = 0; |
3115 | else |
3116 | result = long_compare((PyLongObject*)self, (PyLongObject*)other); |
3117 | Py_RETURN_RICHCOMPARE(result, 0, op); |
3118 | } |
3119 | |
3120 | static Py_hash_t |
3121 | long_hash(PyLongObject *v) |
3122 | { |
3123 | Py_uhash_t x; |
3124 | Py_ssize_t i; |
3125 | int sign; |
3126 | |
3127 | i = Py_SIZE(v); |
3128 | switch(i) { Branch (3128:12): [True: 2.89M, False: 34.1M]
|
3129 | case -1: return v->ob_digit[0]==1 ? -211.4k : -(sdigit)v->ob_digit[0]40.0k ; Branch (3129:5): [True: 51.5k, False: 37.0M]
Branch (3129:21): [True: 11.4k, False: 40.0k]
|
3130 | case 0: return 0; Branch (3130:5): [True: 1.08M, False: 35.9M]
|
3131 | case 1: return v->ob_digit[0]; Branch (3131:5): [True: 33.0M, False: 4.03M]
|
3132 | } |
3133 | sign = 1; |
3134 | x = 0; |
3135 | if (i < 0) { Branch (3135:9): [True: 10.8k, False: 2.88M]
|
3136 | sign = -1; |
3137 | i = -(i); |
3138 | } |
3139 | while (--i >= 0) { Branch (3139:12): [True: 6.33M, False: 2.89M]
|
3140 | /* Here x is a quantity in the range [0, _PyHASH_MODULUS); we |
3141 | want to compute x * 2**PyLong_SHIFT + v->ob_digit[i] modulo |
3142 | _PyHASH_MODULUS. |
3143 | |
3144 | The computation of x * 2**PyLong_SHIFT % _PyHASH_MODULUS |
3145 | amounts to a rotation of the bits of x. To see this, write |
3146 | |
3147 | x * 2**PyLong_SHIFT = y * 2**_PyHASH_BITS + z |
3148 | |
3149 | where y = x >> (_PyHASH_BITS - PyLong_SHIFT) gives the top |
3150 | PyLong_SHIFT bits of x (those that are shifted out of the |
3151 | original _PyHASH_BITS bits, and z = (x << PyLong_SHIFT) & |
3152 | _PyHASH_MODULUS gives the bottom _PyHASH_BITS - PyLong_SHIFT |
3153 | bits of x, shifted up. Then since 2**_PyHASH_BITS is |
3154 | congruent to 1 modulo _PyHASH_MODULUS, y*2**_PyHASH_BITS is |
3155 | congruent to y modulo _PyHASH_MODULUS. So |
3156 | |
3157 | x * 2**PyLong_SHIFT = y + z (mod _PyHASH_MODULUS). |
3158 | |
3159 | The right-hand side is just the result of rotating the |
3160 | _PyHASH_BITS bits of x left by PyLong_SHIFT places; since |
3161 | not all _PyHASH_BITS bits of x are 1s, the same is true |
3162 | after rotation, so 0 <= y+z < _PyHASH_MODULUS and y + z is |
3163 | the reduction of x*2**PyLong_SHIFT modulo |
3164 | _PyHASH_MODULUS. */ |
3165 | x = ((x << PyLong_SHIFT) & _PyHASH_MODULUS) | |
3166 | (x >> (_PyHASH_BITS - PyLong_SHIFT)); |
3167 | x += v->ob_digit[i]; |
3168 | if (x >= _PyHASH_MODULUS) Branch (3168:13): [True: 834, False: 6.33M]
|
3169 | x -= _PyHASH_MODULUS; |
3170 | } |
3171 | x = x * sign; |
3172 | if (x == (Py_uhash_t)-1) Branch (3172:9): [True: 13, False: 2.89M]
|
3173 | x = (Py_uhash_t)-2; |
3174 | return (Py_hash_t)x; |
3175 | } |
3176 | |
3177 | |
3178 | /* Add the absolute values of two integers. */ |
3179 | |
3180 | static PyLongObject * |
3181 | x_add(PyLongObject *a, PyLongObject *b) |
3182 | { |
3183 | Py_ssize_t size_a = Py_ABS(Py_SIZE(a)), size_b = Py_ABS(Py_SIZE(b)); |
3184 | PyLongObject *z; |
3185 | Py_ssize_t i; |
3186 | digit carry = 0; |
3187 | |
3188 | /* Ensure a is the larger of the two: */ |
3189 | if (size_a < size_b) { Branch (3189:9): [True: 162k, False: 2.38M]
|
3190 | { PyLongObject *temp = a; a = b; b = temp; } |
3191 | { Py_ssize_t size_temp = size_a; |
3192 | size_a = size_b; |
3193 | size_b = size_temp; } |
3194 | } |
3195 | z = _PyLong_New(size_a+1); |
3196 | if (z == NULL) Branch (3196:9): [True: 0, False: 2.54M]
|
3197 | return NULL; |
3198 | for (i = 0; 2.54M i < size_b; ++i5.73M ) { Branch (3198:17): [True: 5.73M, False: 2.54M]
|
3199 | carry += a->ob_digit[i] + b->ob_digit[i]; |
3200 | z->ob_digit[i] = carry & PyLong_MASK; |
3201 | carry >>= PyLong_SHIFT; |
3202 | } |
3203 | for (; i < size_a; ++i6.96M ) { Branch (3203:12): [True: 6.96M, False: 2.54M]
|
3204 | carry += a->ob_digit[i]; |
3205 | z->ob_digit[i] = carry & PyLong_MASK; |
3206 | carry >>= PyLong_SHIFT; |
3207 | } |
3208 | z->ob_digit[i] = carry; |
3209 | return long_normalize(z); |
3210 | } |
3211 | |
3212 | /* Subtract the absolute values of two integers. */ |
3213 | |
3214 | static PyLongObject * |
3215 | x_sub(PyLongObject *a, PyLongObject *b) |
3216 | { |
3217 | Py_ssize_t size_a = Py_ABS(Py_SIZE(a)), size_b = Py_ABS(Py_SIZE(b)); |
3218 | PyLongObject *z; |
3219 | Py_ssize_t i; |
3220 | int sign = 1; |
3221 | digit borrow = 0; |
3222 | |
3223 | /* Ensure a is the larger of the two: */ |
3224 | if (size_a < size_b) { Branch (3224:9): [True: 765k, False: 1.13M]
|
3225 | sign = -1; |
3226 | { PyLongObject *temp = a; a = b; b = temp; } |
3227 | { Py_ssize_t size_temp = size_a; |
3228 | size_a = size_b; |
3229 | size_b = size_temp; } |
3230 | } |
3231 | else if (size_a == size_b) { Branch (3231:14): [True: 218k, False: 916k]
|
3232 | /* Find highest digit where a and b differ: */ |
3233 | i = size_a; |
3234 | while (--i >= 0 && a->ob_digit[i] == b->ob_digit[i]538k ) Branch (3234:16): [True: 538k, False: 5.91k]
Branch (3234:28): [True: 325k, False: 212k]
|
3235 | ; |
3236 | if (i < 0) Branch (3236:13): [True: 5.91k, False: 212k]
|
3237 | return (PyLongObject *)PyLong_FromLong(0); |
3238 | if (a->ob_digit[i] < b->ob_digit[i]) { Branch (3238:13): [True: 80.9k, False: 131k]
|
3239 | sign = -1; |
3240 | { PyLongObject *temp = a; a = b; b = temp; } |
3241 | } |
3242 | size_a = size_b = i+1; |
3243 | } |
3244 | z = _PyLong_New(size_a); |
3245 | if (z == NULL) Branch (3245:9): [True: 0, False: 1.89M]
|
3246 | return NULL; |
3247 | for (i = 0; 1.89M i < size_b; ++i4.28M ) { Branch (3247:17): [True: 4.28M, False: 1.89M]
|
3248 | /* The following assumes unsigned arithmetic |
3249 | works module 2**N for some N>PyLong_SHIFT. */ |
3250 | borrow = a->ob_digit[i] - b->ob_digit[i] - borrow; |
3251 | z->ob_digit[i] = borrow & PyLong_MASK; |
3252 | borrow >>= PyLong_SHIFT; |
3253 | borrow &= 1; /* Keep only one sign bit */ |
3254 | } |
3255 | for (; i < size_a; ++i5.23M ) { Branch (3255:12): [True: 5.23M, False: 1.89M]
|
3256 | borrow = a->ob_digit[i] - borrow; |
3257 | z->ob_digit[i] = borrow & PyLong_MASK; |
3258 | borrow >>= PyLong_SHIFT; |
3259 | borrow &= 1; /* Keep only one sign bit */ |
3260 | } |
3261 | assert(borrow == 0); |
3262 | if (sign < 0) { Branch (3262:9): [True: 846k, False: 1.04M]
|
3263 | Py_SET_SIZE(z, -Py_SIZE(z)); |
3264 | } |
3265 | return maybe_small_long(long_normalize(z)); |
3266 | } |
3267 | |
3268 | PyObject * |
3269 | _PyLong_Add(PyLongObject *a, PyLongObject *b) |
3270 | { |
3271 | if (IS_MEDIUM_VALUE(a) && IS_MEDIUM_VALUE19.2M (b)) { |
3272 | return _PyLong_FromSTwoDigits(medium_value(a) + medium_value(b)); |
3273 | } |
3274 | |
3275 | PyLongObject *z; |
3276 | if (Py_SIZE(a) < 0) { Branch (3276:9): [True: 1.17M, False: 2.85M]
|
3277 | if (Py_SIZE(b) < 0) { Branch (3277:13): [True: 292k, False: 879k]
|
3278 | z = x_add(a, b); |
3279 | if (z != NULL) { Branch (3279:17): [True: 292k, False: 0]
|
3280 | /* x_add received at least one multiple-digit int, |
3281 | and thus z must be a multiple-digit int. |
3282 | That also means z is not an element of |
3283 | small_ints, so negating it in-place is safe. */ |
3284 | assert(Py_REFCNT(z) == 1); |
3285 | Py_SET_SIZE(z, -(Py_SIZE(z))); |
3286 | } |
3287 | } |
3288 | else |
3289 | z = x_sub(b, a); |
3290 | } |
3291 | else { |
3292 | if (Py_SIZE(b) < 0) Branch (3292:13): [True: 776k, False: 2.07M]
|
3293 | z = x_sub(a, b); |
3294 | else |
3295 | z = x_add(a, b); |
3296 | } |
3297 | return (PyObject *)z; |
3298 | } |
3299 | |
3300 | static PyObject * |
3301 | long_add(PyLongObject *a, PyLongObject *b) |
3302 | { |
3303 | CHECK_BINOP(a, b); |
3304 | return _PyLong_Add(a, b); |
3305 | } |
3306 | |
3307 | PyObject * |
3308 | _PyLong_Subtract(PyLongObject *a, PyLongObject *b) |
3309 | { |
3310 | PyLongObject *z; |
3311 | |
3312 | if (IS_MEDIUM_VALUE(a) && IS_MEDIUM_VALUE12.8M (b)) { |
3313 | return _PyLong_FromSTwoDigits(medium_value(a) - medium_value(b)); |
3314 | } |
3315 | if (Py_SIZE(a) < 0) { Branch (3315:9): [True: 59.1k, False: 349k]
|
3316 | if (Py_SIZE(b) < 0) { Branch (3316:13): [True: 26.1k, False: 33.0k]
|
3317 | z = x_sub(b, a); |
3318 | } |
3319 | else { |
3320 | z = x_add(a, b); |
3321 | if (z != NULL) { Branch (3321:17): [True: 33.0k, False: 0]
|
3322 | assert(Py_SIZE(z) == 0 || Py_REFCNT(z) == 1); |
3323 | Py_SET_SIZE(z, -(Py_SIZE(z))); |
3324 | } |
3325 | } |
3326 | } |
3327 | else { |
3328 | if (Py_SIZE(b) < 0) Branch (3328:13): [True: 131k, False: 217k]
|
3329 | z = x_add(a, b); |
3330 | else |
3331 | z = x_sub(a, b); |
3332 | } |
3333 | return (PyObject *)z; |
3334 | } |
3335 | |
3336 | static PyObject * |
3337 | long_sub(PyLongObject *a, PyLongObject *b) |
3338 | { |
3339 | CHECK_BINOP(a, b); |
3340 | return _PyLong_Subtract(a, b); |
3341 | } |
3342 | |
3343 | /* Grade school multiplication, ignoring the signs. |
3344 | * Returns the absolute value of the product, or NULL if error. |
3345 | */ |
3346 | static PyLongObject * |
3347 | x_mul(PyLongObject *a, PyLongObject *b) |
3348 | { |
3349 | PyLongObject *z; |
3350 | Py_ssize_t size_a = Py_ABS(Py_SIZE(a)); |
3351 | Py_ssize_t size_b = Py_ABS(Py_SIZE(b)); |
3352 | Py_ssize_t i; |
3353 | |
3354 | z = _PyLong_New(size_a + size_b); |
3355 | if (z == NULL) Branch (3355:9): [True: 0, False: 7.49M]
|
3356 | return NULL; |
3357 | |
3358 | memset(z->ob_digit, 0, Py_SIZE(z) * sizeof(digit)); |
3359 | if (a == b) { Branch (3359:9): [True: 3.34M, False: 4.15M]
|
3360 | /* Efficient squaring per HAC, Algorithm 14.16: |
3361 | * http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf |
3362 | * Gives slightly less than a 2x speedup when a == b, |
3363 | * via exploiting that each entry in the multiplication |
3364 | * pyramid appears twice (except for the size_a squares). |
3365 | */ |
3366 | digit *paend = a->ob_digit + size_a; |
3367 | for (i = 0; i < size_a; ++i9.72M ) { Branch (3367:21): [True: 9.72M, False: 3.34M]
|
3368 | twodigits carry; |
3369 | twodigits f = a->ob_digit[i]; |
3370 | digit *pz = z->ob_digit + (i << 1); |
3371 | digit *pa = a->ob_digit + i + 1; |
3372 | |
3373 | SIGCHECK({ |
3374 | Py_DECREF(z); |
3375 | return NULL; |
3376 | }); |
3377 | |
3378 | carry = *pz + f * f; |
3379 | *pz++ = (digit)(carry & PyLong_MASK); |
3380 | carry >>= PyLong_SHIFT; |
3381 | assert(carry <= PyLong_MASK); |
3382 | |
3383 | /* Now f is added in twice in each column of the |
3384 | * pyramid it appears. Same as adding f<<1 once. |
3385 | */ |
3386 | f <<= 1; |
3387 | while (pa < paend) { Branch (3387:20): [True: 75.1M, False: 9.72M]
|
3388 | carry += *pz + *pa++ * f; |
3389 | *pz++ = (digit)(carry & PyLong_MASK); |
3390 | carry >>= PyLong_SHIFT; |
3391 | assert(carry <= (PyLong_MASK << 1)); |
3392 | } |
3393 | if (carry) { Branch (3393:17): [True: 4.04M, False: 5.67M]
|
3394 | /* See comment below. pz points at the highest possible |
3395 | * carry position from the last outer loop iteration, so |
3396 | * *pz is at most 1. |
3397 | */ |
3398 | assert(*pz <= 1); |
3399 | carry += *pz; |
3400 | *pz = (digit)(carry & PyLong_MASK); |
3401 | carry >>= PyLong_SHIFT; |
3402 | if (carry) { Branch (3402:21): [True: 26.1k, False: 4.01M]
|
3403 | /* If there's still a carry, it must be into a position |
3404 | * that still holds a 0. Where the base |
3405 | ^ B is 1 << PyLong_SHIFT, the last add was of a carry no |
3406 | * more than 2*B - 2 to a stored digit no more than 1. |
3407 | * So the sum was no more than 2*B - 1, so the current |
3408 | * carry no more than floor((2*B - 1)/B) = 1. |
3409 | */ |
3410 | assert(carry == 1); |
3411 | assert(pz[1] == 0); |
3412 | pz[1] = (digit)carry; |
3413 | } |
3414 | } |
3415 | } |
3416 | } |
3417 | else { /* a is not the same as b -- gradeschool int mult */ |
3418 | for (i = 0; i < size_a; ++i9.42M ) { Branch (3418:21): [True: 9.42M, False: 4.15M]
|
3419 | twodigits carry = 0; |
3420 | twodigits f = a->ob_digit[i]; |
3421 | digit *pz = z->ob_digit + i; |
3422 | digit *pb = b->ob_digit; |
3423 | digit *pbend = b->ob_digit + size_b; |
3424 | |
3425 | SIGCHECK({ |
3426 | Py_DECREF(z); |
3427 | return NULL; |
3428 | }); |
3429 | |
3430 | while (9.42M pb < pbend) { Branch (3430:20): [True: 250M, False: 9.42M]
|
3431 | carry += *pz + *pb++ * f; |
3432 | *pz++ = (digit)(carry & PyLong_MASK); |
3433 | carry >>= PyLong_SHIFT; |
3434 | assert(carry <= PyLong_MASK); |
3435 | } |
3436 | if (carry) Branch (3436:17): [True: 6.26M, False: 3.16M]
|
3437 | *pz += (digit)(carry & PyLong_MASK); |
3438 | assert((carry >> PyLong_SHIFT) == 0); |
3439 | } |
3440 | } |
3441 | return long_normalize(z); |
3442 | } |
3443 | |
3444 | /* A helper for Karatsuba multiplication (k_mul). |
3445 | Takes an int "n" and an integer "size" representing the place to |
3446 | split, and sets low and high such that abs(n) == (high << size) + low, |
3447 | viewing the shift as being by digits. The sign bit is ignored, and |
3448 | the return values are >= 0. |
3449 | Returns 0 on success, -1 on failure. |
3450 | */ |
3451 | static int |
3452 | kmul_split(PyLongObject *n, |
3453 | Py_ssize_t size, |
3454 | PyLongObject **high, |
3455 | PyLongObject **low) |
3456 | { |
3457 | PyLongObject *hi, *lo; |
3458 | Py_ssize_t size_lo, size_hi; |
3459 | const Py_ssize_t size_n = Py_ABS(Py_SIZE(n)); |
3460 | |
3461 | size_lo = Py_MIN(size_n, size); |
3462 | size_hi = size_n - size_lo; |
3463 | |
3464 | if ((hi = _PyLong_New(size_hi)) == NULL) Branch (3464:9): [True: 0, False: 12.4k]
|
3465 | return -1; |
3466 | if ((lo = _PyLong_New(size_lo)) == NULL) { Branch (3466:9): [True: 0, False: 12.4k]
|
3467 | Py_DECREF(hi); |
3468 | return -1; |
3469 | } |
3470 | |
3471 | memcpy(lo->ob_digit, n->ob_digit, size_lo * sizeof(digit)); |
3472 | memcpy(hi->ob_digit, n->ob_digit + size_lo, size_hi * sizeof(digit)); |
3473 | |
3474 | *high = long_normalize(hi); |
3475 | *low = long_normalize(lo); |
3476 | return 0; |
3477 | } |
3478 | |
3479 | static PyLongObject *k_lopsided_mul(PyLongObject *a, PyLongObject *b); |
3480 | |
3481 | /* Karatsuba multiplication. Ignores the input signs, and returns the |
3482 | * absolute value of the product (or NULL if error). |
3483 | * See Knuth Vol. 2 Chapter 4.3.3 (Pp. 294-295). |
3484 | */ |
3485 | static PyLongObject * |
3486 | k_mul(PyLongObject *a, PyLongObject *b) |
3487 | { |
3488 | Py_ssize_t asize = Py_ABS(Py_SIZE(a)); |
3489 | Py_ssize_t bsize = Py_ABS(Py_SIZE(b)); |
3490 | PyLongObject *ah = NULL; |
3491 | PyLongObject *al = NULL; |
3492 | PyLongObject *bh = NULL; |
3493 | PyLongObject *bl = NULL; |
3494 | PyLongObject *ret = NULL; |
3495 | PyLongObject *t1, *t2, *t3; |
3496 | Py_ssize_t shift; /* the number of digits we split off */ |
3497 | Py_ssize_t i; |
3498 | |
3499 | /* (ah*X+al)(bh*X+bl) = ah*bh*X*X + (ah*bl + al*bh)*X + al*bl |
3500 | * Let k = (ah+al)*(bh+bl) = ah*bl + al*bh + ah*bh + al*bl |
3501 | * Then the original product is |
3502 | * ah*bh*X*X + (k - ah*bh - al*bl)*X + al*bl |
3503 | * By picking X to be a power of 2, "*X" is just shifting, and it's |
3504 | * been reduced to 3 multiplies on numbers half the size. |
3505 | */ |
3506 | |
3507 | /* We want to split based on the larger number; fiddle so that b |
3508 | * is largest. |
3509 | */ |
3510 | if (asize > bsize) { Branch (3510:9): [True: 2.22M, False: 5.29M]
|
3511 | t1 = a; |
3512 | a = b; |
3513 | b = t1; |
3514 | |
3515 | i = asize; |
3516 | asize = bsize; |
3517 | bsize = i; |
3518 | } |
3519 | |
3520 | /* Use gradeschool math when either number is too small. */ |
3521 | i = a == b ? KARATSUBA_SQUARE_CUTOFF3.34M : KARATSUBA_CUTOFF4.16M ; Branch (3521:9): [True: 3.34M, False: 4.16M]
|
3522 | if (asize <= i) { Branch (3522:9): [True: 7.50M, False: 7.59k]
|
3523 | if (asize == 0) Branch (3523:13): [True: 16.3k, False: 7.49M]
|
3524 | return (PyLongObject *)PyLong_FromLong(0); |
3525 | else |
3526 | return x_mul(a, b); |
3527 | } |
3528 | |
3529 | /* If a is small compared to b, splitting on b gives a degenerate |
3530 | * case with ah==0, and Karatsuba may be (even much) less efficient |
3531 | * than "grade school" then. However, we can still win, by viewing |
3532 | * b as a string of "big digits", each of width a->ob_size. That |
3533 | * leads to a sequence of balanced calls to k_mul. |
3534 | */ |
3535 | if (2 * asize <= bsize) Branch (3535:9): [True: 72, False: 7.52k]
|
3536 | return k_lopsided_mul(a, b); |
3537 | |
3538 | /* Split a & b into hi & lo pieces. */ |
3539 | shift = bsize >> 1; |
3540 | if (kmul_split(a, shift, &ah, &al) < 0) goto fail0 ; Branch (3540:9): [True: 0, False: 7.52k]
|
3541 | assert(Py_SIZE(ah) > 0); /* the split isn't degenerate */ |
3542 | |
3543 | if (a == b) { Branch (3543:9): [True: 2.58k, False: 4.94k]
|
3544 | bh = ah; |
3545 | bl = al; |
3546 | Py_INCREF(bh); |
3547 | Py_INCREF(bl); |
3548 | } |
3549 | else if (kmul_split(b, shift, &bh, &bl) < 0) goto fail0 ; Branch (3549:14): [True: 0, False: 4.94k]
|
3550 | |
3551 | /* The plan: |
3552 | * 1. Allocate result space (asize + bsize digits: that's always |
3553 | * enough). |
3554 | * 2. Compute ah*bh, and copy into result at 2*shift. |
3555 | * 3. Compute al*bl, and copy into result at 0. Note that this |
3556 | * can't overlap with #2. |
3557 | * 4. Subtract al*bl from the result, starting at shift. This may |
3558 | * underflow (borrow out of the high digit), but we don't care: |
3559 | * we're effectively doing unsigned arithmetic mod |
3560 | * BASE**(sizea + sizeb), and so long as the *final* result fits, |
3561 | * borrows and carries out of the high digit can be ignored. |
3562 | * 5. Subtract ah*bh from the result, starting at shift. |
3563 | * 6. Compute (ah+al)*(bh+bl), and add it into the result starting |
3564 | * at shift. |
3565 | */ |
3566 | |
3567 | /* 1. Allocate result space. */ |
3568 | ret = _PyLong_New(asize + bsize); |
3569 | if (ret == NULL) goto fail0 ; Branch (3569:9): [True: 0, False: 7.52k]
|
3570 | #ifdef Py_DEBUG |
3571 | /* Fill with trash, to catch reference to uninitialized digits. */ |
3572 | memset(ret->ob_digit, 0xDF, Py_SIZE(ret) * sizeof(digit)); |
3573 | #endif |
3574 | |
3575 | /* 2. t1 <- ah*bh, and copy into high digits of result. */ |
3576 | if ((t1 = k_mul(ah, bh)) == NULL) goto fail0 ; Branch (3576:9): [True: 0, False: 7.52k]
|
3577 | assert(Py_SIZE(t1) >= 0); |
3578 | assert(2*shift + Py_SIZE(t1) <= Py_SIZE(ret)); |
3579 | memcpy(ret->ob_digit + 2*shift, t1->ob_digit, |
3580 | Py_SIZE(t1) * sizeof(digit)); |
3581 | |
3582 | /* Zero-out the digits higher than the ah*bh copy. */ |
3583 | i = Py_SIZE(ret) - 2*shift - Py_SIZE(t1); |
3584 | if (i) Branch (3584:9): [True: 3.06k, False: 4.46k]
|
3585 | memset(ret->ob_digit + 2*shift + Py_SIZE(t1), 0, |
3586 | i * sizeof(digit)); |
3587 | |
3588 | /* 3. t2 <- al*bl, and copy into the low digits. */ |
3589 | if ((t2 = k_mul(al, bl)) == NULL) { Branch (3589:9): [True: 0, False: 7.52k]
|
3590 | Py_DECREF(t1); |
3591 | goto fail; |
3592 | } |
3593 | assert(Py_SIZE(t2) >= 0); |
3594 | assert(Py_SIZE(t2) <= 2*shift); /* no overlap with high digits */ |
3595 | memcpy(ret->ob_digit, t2->ob_digit, Py_SIZE(t2) * sizeof(digit)); |
3596 | |
3597 | /* Zero out remaining digits. */ |
3598 | i = 2*shift - Py_SIZE(t2); /* number of uninitialized digits */ |
3599 | if (i) Branch (3599:9): [True: 2.29k, False: 5.22k]
|
3600 | memset(ret->ob_digit + Py_SIZE(t2), 0, i * sizeof(digit)); |
3601 | |
3602 | /* 4 & 5. Subtract ah*bh (t1) and al*bl (t2). We do al*bl first |
3603 | * because it's fresher in cache. |
3604 | */ |
3605 | i = Py_SIZE(ret) - shift; /* # digits after shift */ |
3606 | (void)v_isub(ret->ob_digit + shift, i, t2->ob_digit, Py_SIZE(t2)); |
3607 | _Py_DECREF_INT(t2); |
3608 | |
3609 | (void)v_isub(ret->ob_digit + shift, i, t1->ob_digit, Py_SIZE(t1)); |
3610 | _Py_DECREF_INT(t1); |
3611 | |
3612 | /* 6. t3 <- (ah+al)(bh+bl), and add into result. */ |
3613 | if ((t1 = x_add(ah, al)) == NULL) goto fail0 ; Branch (3613:9): [True: 0, False: 7.52k]
|
3614 | _Py_DECREF_INT(ah); |
3615 | _Py_DECREF_INT(al); |
3616 | ah = al = NULL; |
3617 | |
3618 | if (a == b) { Branch (3618:9): [True: 2.58k, False: 4.94k]
|
3619 | t2 = t1; |
3620 | Py_INCREF(t2); |
3621 | } |
3622 | else if ((t2 = x_add(bh, bl)) == NULL) { Branch (3622:14): [True: 0, False: 4.94k]
|
3623 | Py_DECREF(t1); |
3624 | goto fail; |
3625 | } |
3626 | _Py_DECREF_INT(bh); |
3627 | _Py_DECREF_INT(bl); |
3628 | bh = bl = NULL; |
3629 | |
3630 | t3 = k_mul(t1, t2); |
3631 | _Py_DECREF_INT(t1); |
3632 | _Py_DECREF_INT(t2); |
3633 | if (t3 == NULL) goto fail0 ; Branch (3633:9): [True: 0, False: 7.52k]
|
3634 | assert(Py_SIZE(t3) >= 0); |
3635 | |
3636 | /* Add t3. It's not obvious why we can't run out of room here. |
3637 | * See the (*) comment after this function. |
3638 | */ |
3639 | (void)v_iadd(ret->ob_digit + shift, i, t3->ob_digit, Py_SIZE(t3)); |
3640 | _Py_DECREF_INT(t3); |
3641 | |
3642 | return long_normalize(ret); |
3643 | |
3644 | fail: |
3645 | Py_XDECREF(ret); |
3646 | Py_XDECREF(ah); |
3647 | Py_XDECREF(al); |
3648 | Py_XDECREF(bh); |
3649 | Py_XDECREF(bl); |
3650 | return NULL; |
3651 | } |
3652 | |
3653 | /* (*) Why adding t3 can't "run out of room" above. |
3654 | |
3655 | Let f(x) mean the floor of x and c(x) mean the ceiling of x. Some facts |
3656 | to start with: |
3657 | |
3658 | 1. For any integer i, i = c(i/2) + f(i/2). In particular, |
3659 | bsize = c(bsize/2) + f(bsize/2). |
3660 | 2. shift = f(bsize/2) |
3661 | 3. asize <= bsize |
3662 | 4. Since we call k_lopsided_mul if asize*2 <= bsize, asize*2 > bsize in this |
3663 | routine, so asize > bsize/2 >= f(bsize/2) in this routine. |
3664 | |
3665 | We allocated asize + bsize result digits, and add t3 into them at an offset |
3666 | of shift. This leaves asize+bsize-shift allocated digit positions for t3 |
3667 | to fit into, = (by #1 and #2) asize + f(bsize/2) + c(bsize/2) - f(bsize/2) = |
3668 | asize + c(bsize/2) available digit positions. |
3669 | |
3670 | bh has c(bsize/2) digits, and bl at most f(size/2) digits. So bh+hl has |
3671 | at most c(bsize/2) digits + 1 bit. |
3672 | |
3673 | If asize == bsize, ah has c(bsize/2) digits, else ah has at most f(bsize/2) |
3674 | digits, and al has at most f(bsize/2) digits in any case. So ah+al has at |
3675 | most (asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 1 bit. |
3676 | |
3677 | The product (ah+al)*(bh+bl) therefore has at most |
3678 | |
3679 | c(bsize/2) + (asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 2 bits |
3680 | |
3681 | and we have asize + c(bsize/2) available digit positions. We need to show |
3682 | this is always enough. An instance of c(bsize/2) cancels out in both, so |
3683 | the question reduces to whether asize digits is enough to hold |
3684 | (asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 2 bits. If asize < bsize, |
3685 | then we're asking whether asize digits >= f(bsize/2) digits + 2 bits. By #4, |
3686 | asize is at least f(bsize/2)+1 digits, so this in turn reduces to whether 1 |
3687 | digit is enough to hold 2 bits. This is so since PyLong_SHIFT=15 >= 2. If |
3688 | asize == bsize, then we're asking whether bsize digits is enough to hold |
3689 | c(bsize/2) digits + 2 bits, or equivalently (by #1) whether f(bsize/2) digits |
3690 | is enough to hold 2 bits. This is so if bsize >= 2, which holds because |
3691 | bsize >= KARATSUBA_CUTOFF >= 2. |
3692 | |
3693 | Note that since there's always enough room for (ah+al)*(bh+bl), and that's |
3694 | clearly >= each of ah*bh and al*bl, there's always enough room to subtract |
3695 | ah*bh and al*bl too. |
3696 | */ |
3697 | |
3698 | /* b has at least twice the digits of a, and a is big enough that Karatsuba |
3699 | * would pay off *if* the inputs had balanced sizes. View b as a sequence |
3700 | * of slices, each with a->ob_size digits, and multiply the slices by a, |
3701 | * one at a time. This gives k_mul balanced inputs to work with, and is |
3702 | * also cache-friendly (we compute one double-width slice of the result |
3703 | * at a time, then move on, never backtracking except for the helpful |
3704 | * single-width slice overlap between successive partial sums). |
3705 | */ |
3706 | static PyLongObject * |
3707 | k_lopsided_mul(PyLongObject *a, PyLongObject *b) |
3708 | { |
3709 | const Py_ssize_t asize = Py_ABS(Py_SIZE(a)); |
3710 | Py_ssize_t bsize = Py_ABS(Py_SIZE(b)); |
3711 | Py_ssize_t nbdone; /* # of b digits already multiplied */ |
3712 | PyLongObject *ret; |
3713 | PyLongObject *bslice = NULL; |
3714 | |
3715 | assert(asize > KARATSUBA_CUTOFF); |
3716 | assert(2 * asize <= bsize); |
3717 | |
3718 | /* Allocate result space, and zero it out. */ |
3719 | ret = _PyLong_New(asize + bsize); |
3720 | if (ret == NULL) Branch (3720:9): [True: 0, False: 72]
|
3721 | return NULL; |
3722 | memset(ret->ob_digit, 0, Py_SIZE(ret) * sizeof(digit)); |
3723 | |
3724 | /* Successive slices of b are copied into bslice. */ |
3725 | bslice = _PyLong_New(asize); |
3726 | if (bslice == NULL) Branch (3726:9): [True: 0, False: 72]
|
3727 | goto fail; |
3728 | |
3729 | nbdone = 0; |
3730 | while (bsize > 0) { Branch (3730:12): [True: 1.10k, False: 72]
|
3731 | PyLongObject *product; |
3732 | const Py_ssize_t nbtouse = Py_MIN(bsize, asize); |
3733 | |
3734 | /* Multiply the next slice of b by a. */ |
3735 | memcpy(bslice->ob_digit, b->ob_digit + nbdone, |
3736 | nbtouse * sizeof(digit)); |
3737 | Py_SET_SIZE(bslice, nbtouse); |
3738 | product = k_mul(a, bslice); |
3739 | if (product == NULL) Branch (3739:13): [True: 0, False: 1.10k]
|
3740 | goto fail; |
3741 | |
3742 | /* Add into result. */ |
3743 | (void)v_iadd(ret->ob_digit + nbdone, Py_SIZE(ret) - nbdone, |
3744 | product->ob_digit, Py_SIZE(product)); |
3745 | _Py_DECREF_INT(product); |
3746 | |
3747 | bsize -= nbtouse; |
3748 | nbdone += nbtouse; |
3749 | } |
3750 | |
3751 | _Py_DECREF_INT(bslice); |
3752 | return long_normalize(ret); |
3753 | |
3754 | fail: |
3755 | Py_DECREF(ret); |
3756 | Py_XDECREF(bslice); |
3757 | return NULL; |
3758 | } |
3759 | |
3760 | PyObject * |
3761 | _PyLong_Multiply(PyLongObject *a, PyLongObject *b) |
3762 | { |
3763 | PyLongObject *z; |
3764 | |
3765 | /* fast path for single-digit multiplication */ |
3766 | if (IS_MEDIUM_VALUE(a) && IS_MEDIUM_VALUE28.7M (b)) { |
3767 | stwodigits v = medium_value(a) * medium_value(b); |
3768 | return _PyLong_FromSTwoDigits(v); |
3769 | } |
3770 | |
3771 | z = k_mul(a, b); |
3772 | /* Negate if exactly one of the inputs is negative. */ |
3773 | if (((Py_SIZE(a) ^ Py_SIZE(b)) < 0) && z114k ) { Branch (3773:9): [True: 114k, False: 7.37M]
Branch (3773:44): [True: 114k, False: 0]
|
3774 | _PyLong_Negate(&z); |
3775 | if (z == NULL) Branch (3775:13): [True: 0, False: 114k]
|
3776 | return NULL; |
3777 | } |
3778 | return (PyObject *)z; |
3779 | } |
3780 | |
3781 | static PyObject * |
3782 | long_mul(PyLongObject *a, PyLongObject *b) |
3783 | { |
3784 | CHECK_BINOP(a, b); |
3785 | return _PyLong_Multiply(a, b); |
3786 | } |
3787 | |
3788 | /* Fast modulo division for single-digit longs. */ |
3789 | static PyObject * |
3790 | fast_mod(PyLongObject *a, PyLongObject *b) |
3791 | { |
3792 | sdigit left = a->ob_digit[0]; |
3793 | sdigit right = b->ob_digit[0]; |
3794 | sdigit mod; |
3795 | |
3796 | assert(Py_ABS(Py_SIZE(a)) == 1); |
3797 | assert(Py_ABS(Py_SIZE(b)) == 1); |
3798 | |
3799 | if (Py_SIZE(a) == Py_SIZE(b)) { Branch (3799:9): [True: 2.55M, False: 64.2k]
|
3800 | /* 'a' and 'b' have the same sign. */ |
3801 | mod = left % right; |
3802 | } |
3803 | else { |
3804 | /* Either 'a' or 'b' is negative. */ |
3805 | mod = right - 1 - (left - 1) % right; |
3806 | } |
3807 | |
3808 | return PyLong_FromLong(mod * (sdigit)Py_SIZE(b)); |
3809 | } |
3810 | |
3811 | /* Fast floor division for single-digit longs. */ |
3812 | static PyObject * |
3813 | fast_floor_div(PyLongObject *a, PyLongObject *b) |
3814 | { |
3815 | sdigit left = a->ob_digit[0]; |
3816 | sdigit right = b->ob_digit[0]; |
3817 | sdigit div; |
3818 | |
3819 | assert(Py_ABS(Py_SIZE(a)) == 1); |
3820 | assert(Py_ABS(Py_SIZE(b)) == 1); |
3821 | |
3822 | if (Py_SIZE(a) == Py_SIZE(b)) { Branch (3822:9): [True: 1.99M, False: 101k]
|
3823 | /* 'a' and 'b' have the same sign. */ |
3824 | div = left / right; |
3825 | } |
3826 | else { |
3827 | /* Either 'a' or 'b' is negative. */ |
3828 | div = -1 - (left - 1) / right; |
3829 | } |
3830 | |
3831 | return PyLong_FromLong(div); |
3832 | } |
3833 | |
3834 | /* The / and % operators are now defined in terms of divmod(). |
3835 | The expression a mod b has the value a - b*floor(a/b). |
3836 | The long_divrem function gives the remainder after division of |
3837 | |a| by |b|, with the sign of a. This is also expressed |
3838 | as a - b*trunc(a/b), if trunc truncates towards zero. |
3839 | Some examples: |
3840 | a b a rem b a mod b |
3841 | 13 10 3 3 |
3842 | -13 10 -3 7 |
3843 | 13 -10 3 -7 |
3844 | -13 -10 -3 -3 |
3845 | So, to get from rem to mod, we have to add b if a and b |
3846 | have different signs. We then subtract one from the 'div' |
3847 | part of the outcome to keep the invariant intact. */ |
3848 | |
3849 | /* Compute |
3850 | * *pdiv, *pmod = divmod(v, w) |
3851 | * NULL can be passed for pdiv or pmod, in which case that part of |
3852 | * the result is simply thrown away. The caller owns a reference to |
3853 | * each of these it requests (does not pass NULL for). |
3854 | */ |
3855 | static int |
3856 | l_divmod(PyLongObject *v, PyLongObject *w, |
3857 | PyLongObject **pdiv, PyLongObject **pmod) |
3858 | { |
3859 | PyLongObject *div, *mod; |
3860 | |
3861 | if (Py_ABS(Py_SIZE(v)) == 1 && Py_ABS567k (Py_SIZE(w)) == 1567k ) { Branch (3861:9): [True: 567k, False: 1.60M]
Branch (3861:36): [True: 555k, False: 12.2k]
|
3862 | /* Fast path for single-digit longs */ |
3863 | div = NULL; |
3864 | if (pdiv != NULL) { Branch (3864:13): [True: 555k, False: 0]
|
3865 | div = (PyLongObject *)fast_floor_div(v, w); |
3866 | if (div == NULL) { Branch (3866:17): [True: 0, False: 555k]
|
3867 | return -1; |
3868 | } |
3869 | } |
3870 | if (pmod != NULL) { Branch (3870:13): [True: 555k, False: 0]
|
3871 | mod = (PyLongObject *)fast_mod(v, w); |
3872 | if (mod == NULL) { Branch (3872:17): [True: 0, False: 555k]
|
3873 | Py_XDECREF(div); |
3874 | return -1; |
3875 | } |
3876 | *pmod = mod; |
3877 | } |
3878 | if (pdiv != NULL) { Branch (3878:13): [True: 555k, False: 0]
|
3879 | /* We only want to set `*pdiv` when `*pmod` is |
3880 | set successfully. */ |
3881 | *pdiv = div; |
3882 | } |
3883 | return 0; |
3884 | } |
3885 | if (long_divrem(v, w, &div, &mod) < 0) Branch (3885:9): [True: 257, False: 1.61M]
|
3886 | return -1; |
3887 | if ((Py_SIZE(mod) < 0 && Py_SIZE29.3k (w) > 029.3k ) || Branch (3887:10): [True: 29.3k, False: 1.58M]
Branch (3887:30): [True: 26.2k, False: 3.12k]
|
3888 | (1.59M Py_SIZE1.59M (mod) > 01.59M && Py_SIZE318k (w) < 0318k )) { Branch (3888:10): [True: 318k, False: 1.27M]
Branch (3888:30): [True: 3.17k, False: 315k]
|
3889 | PyLongObject *temp; |
3890 | temp = (PyLongObject *) long_add(mod, w); |
3891 | Py_DECREF(mod); |
3892 | mod = temp; |
3893 | if (mod == NULL) { Branch (3893:13): [True: 0, False: 29.4k]
|
3894 | Py_DECREF(div); |
3895 | return -1; |
3896 | } |
3897 | temp = (PyLongObject *) long_sub(div, (PyLongObject *)_PyLong_GetOne()); |
3898 | if (temp == NULL) { Branch (3898:13): [True: 0, False: 29.4k]
|
3899 | Py_DECREF(mod); |
3900 | Py_DECREF(div); |
3901 | return -1; |
3902 | } |
3903 | Py_DECREF(div); |
3904 | div = temp; |
3905 | } |
3906 | if (pdiv != NULL) Branch (3906:9): [True: 1.61M, False: 0]
|
3907 | *pdiv = div; |
3908 | else |
3909 | Py_DECREF(div); |
3910 | |
3911 | if (pmod != NULL) Branch (3911:9): [True: 789k, False: 828k]
|
3912 | *pmod = mod; |
3913 | else |
3914 | Py_DECREF(mod); |
3915 | |
3916 | return 0; |
3917 | } |
3918 | |
3919 | /* Compute |
3920 | * *pmod = v % w |
3921 | * pmod cannot be NULL. The caller owns a reference to pmod. |
3922 | */ |
3923 | static int |
3924 | l_mod(PyLongObject *v, PyLongObject *w, PyLongObject **pmod) |
3925 | { |
3926 | PyLongObject *mod; |
3927 | |
3928 | assert(pmod); |
3929 | if (Py_ABS(Py_SIZE(v)) == 1 && Py_ABS2.07M (Py_SIZE(w)) == 12.07M ) { Branch (3929:9): [True: 2.07M, False: 20.4M]
Branch (3929:36): [True: 2.05M, False: 13.9k]
|
3930 | /* Fast path for single-digit longs */ |
3931 | *pmod = (PyLongObject *)fast_mod(v, w); |
3932 | return -(*pmod == NULL); |
3933 | } |
3934 | if (long_rem(v, w, &mod) < 0) Branch (3934:9): [True: 4, False: 20.4M]
|
3935 | return -1; |
3936 | if ((Py_SIZE(mod) < 0 && Py_SIZE4.83k (w) > 04.83k ) || Branch (3936:10): [True: 4.83k, False: 20.4M]
Branch (3936:30): [True: 1.93k, False: 2.90k]
|
3937 | (20.4M Py_SIZE20.4M (mod) > 020.4M && Py_SIZE20.2M (w) < 020.2M )) { Branch (3937:10): [True: 20.2M, False: 237k]
Branch (3937:30): [True: 5.60k, False: 20.2M]
|
3938 | PyLongObject *temp; |
3939 | temp = (PyLongObject *) long_add(mod, w); |
3940 | Py_DECREF(mod); |
3941 | mod = temp; |
3942 | if (mod == NULL) Branch (3942:13): [True: 0, False: 7.53k]
|
3943 | return -1; |
3944 | } |
3945 | *pmod = mod; |
3946 | |
3947 | return 0; |
3948 | } |
3949 | |
3950 | static PyObject * |
3951 | long_div(PyObject *a, PyObject *b) |
3952 | { |
3953 | PyLongObject *div; |
3954 | |
3955 | CHECK_BINOP(a, b); |
3956 | |
3957 | if (Py_ABS(Py_SIZE(a)) == 1 && Py_ABS1.55M (Py_SIZE(b)) == 11.55M ) { Branch (3957:9): [True: 1.55M, False: 822k]
Branch (3957:36): [True: 1.54M, False: 6.75k]
|
3958 | return fast_floor_div((PyLongObject*)a, (PyLongObject*)b); |
3959 | } |
3960 | |
3961 | if (l_divmod((PyLongObject*)a, (PyLongObject*)b, &div, NULL) < 0) Branch (3961:9): [True: 250, False: 828k]
|
3962 | div = NULL; |
3963 | return (PyObject *)div; |
3964 | } |
3965 | |
3966 | /* PyLong/PyLong -> float, with correctly rounded result. */ |
3967 | |
3968 | #define MANT_DIG_DIGITS (DBL_MANT_DIG / PyLong_SHIFT4.74M ) |
3969 | #define MANT_DIG_BITS (DBL_MANT_DIG % PyLong_SHIFT) |
3970 | |
3971 | static PyObject * |
3972 | long_true_divide(PyObject *v, PyObject *w) |
3973 | { |
3974 | PyLongObject *a, *b, *x; |
3975 | Py_ssize_t a_size, b_size, shift, extra_bits, diff, x_size, x_bits; |
3976 | digit mask, low; |
3977 | int inexact, negate, a_is_small, b_is_small; |
3978 | double dx, result; |
3979 | |
3980 | CHECK_BINOP(v, w); |
3981 | a = (PyLongObject *)v; |
3982 | b = (PyLongObject *)w; |
3983 | |
3984 | /* |
3985 | Method in a nutshell: |
3986 | |
3987 | 0. reduce to case a, b > 0; filter out obvious underflow/overflow |
3988 | 1. choose a suitable integer 'shift' |
3989 | 2. use integer arithmetic to compute x = floor(2**-shift*a/b) |
3990 | 3. adjust x for correct rounding |
3991 | 4. convert x to a double dx with the same value |
3992 | 5. return ldexp(dx, shift). |
3993 | |
3994 | In more detail: |
3995 | |
3996 | 0. For any a, a/0 raises ZeroDivisionError; for nonzero b, 0/b |
3997 | returns either 0.0 or -0.0, depending on the sign of b. For a and |
3998 | b both nonzero, ignore signs of a and b, and add the sign back in |
3999 | at the end. Now write a_bits and b_bits for the bit lengths of a |
4000 | and b respectively (that is, a_bits = 1 + floor(log_2(a)); likewise |
4001 | for b). Then |
4002 | |
4003 | 2**(a_bits - b_bits - 1) < a/b < 2**(a_bits - b_bits + 1). |
4004 | |
4005 | So if a_bits - b_bits > DBL_MAX_EXP then a/b > 2**DBL_MAX_EXP and |
4006 | so overflows. Similarly, if a_bits - b_bits < DBL_MIN_EXP - |
4007 | DBL_MANT_DIG - 1 then a/b underflows to 0. With these cases out of |
4008 | the way, we can assume that |
4009 | |
4010 | DBL_MIN_EXP - DBL_MANT_DIG - 1 <= a_bits - b_bits <= DBL_MAX_EXP. |
4011 | |
4012 | 1. The integer 'shift' is chosen so that x has the right number of |
4013 | bits for a double, plus two or three extra bits that will be used |
4014 | in the rounding decisions. Writing a_bits and b_bits for the |
4015 | number of significant bits in a and b respectively, a |
4016 | straightforward formula for shift is: |
4017 | |
4018 | shift = a_bits - b_bits - DBL_MANT_DIG - 2 |
4019 | |
4020 | This is fine in the usual case, but if a/b is smaller than the |
4021 | smallest normal float then it can lead to double rounding on an |
4022 | IEEE 754 platform, giving incorrectly rounded results. So we |
4023 | adjust the formula slightly. The actual formula used is: |
4024 | |
4025 | shift = MAX(a_bits - b_bits, DBL_MIN_EXP) - DBL_MANT_DIG - 2 |
4026 | |
4027 | 2. The quantity x is computed by first shifting a (left -shift bits |
4028 | if shift <= 0, right shift bits if shift > 0) and then dividing by |
4029 | b. For both the shift and the division, we keep track of whether |
4030 | the result is inexact, in a flag 'inexact'; this information is |
4031 | needed at the rounding stage. |
4032 | |
4033 | With the choice of shift above, together with our assumption that |
4034 | a_bits - b_bits >= DBL_MIN_EXP - DBL_MANT_DIG - 1, it follows |
4035 | that x >= 1. |
4036 | |
4037 | 3. Now x * 2**shift <= a/b < (x+1) * 2**shift. We want to replace |
4038 | this with an exactly representable float of the form |
4039 | |
4040 | round(x/2**extra_bits) * 2**(extra_bits+shift). |
4041 | |
4042 | For float representability, we need x/2**extra_bits < |
4043 | 2**DBL_MANT_DIG and extra_bits + shift >= DBL_MIN_EXP - |
4044 | DBL_MANT_DIG. This translates to the condition: |
4045 | |
4046 | extra_bits >= MAX(x_bits, DBL_MIN_EXP - shift) - DBL_MANT_DIG |
4047 | |
4048 | To round, we just modify the bottom digit of x in-place; this can |
4049 | end up giving a digit with value > PyLONG_MASK, but that's not a |
4050 | problem since digits can hold values up to 2*PyLONG_MASK+1. |
4051 | |
4052 | With the original choices for shift above, extra_bits will always |
4053 | be 2 or 3. Then rounding under the round-half-to-even rule, we |
4054 | round up iff the most significant of the extra bits is 1, and |
4055 | either: (a) the computation of x in step 2 had an inexact result, |
4056 | or (b) at least one other of the extra bits is 1, or (c) the least |
4057 | significant bit of x (above those to be rounded) is 1. |
4058 | |
4059 | 4. Conversion to a double is straightforward; all floating-point |
4060 | operations involved in the conversion are exact, so there's no |
4061 | danger of rounding errors. |
4062 | |
4063 | 5. Use ldexp(x, shift) to compute x*2**shift, the final result. |
4064 | The result will always be exactly representable as a double, except |
4065 | in the case that it overflows. To avoid dependence on the exact |
4066 | behaviour of ldexp on overflow, we check for overflow before |
4067 | applying ldexp. The result of ldexp is adjusted for sign before |
4068 | returning. |
4069 | */ |
4070 | |
4071 | /* Reduce to case where a and b are both positive. */ |
4072 | a_size = Py_ABS(Py_SIZE(a)); |
4073 | b_size = Py_ABS(Py_SIZE(b)); |
4074 | negate = (Py_SIZE(a) < 0) ^ (Py_SIZE(b) < 0); |
4075 | if (b_size == 0) { Branch (4075:9): [True: 2.49k, False: 2.23M]
|
4076 | PyErr_SetString(PyExc_ZeroDivisionError, |
4077 | "division by zero"); |
4078 | goto error; |
4079 | } |
4080 | if (a_size == 0) Branch (4080:9): [True: 2.21k, False: 2.23M]
|
4081 | goto underflow_or_zero; |
4082 | |
4083 | /* Fast path for a and b small (exactly representable in a double). |
4084 | Relies on floating-point division being correctly rounded; results |
4085 | may be subject to double rounding on x86 machines that operate with |
4086 | the x87 FPU set to 64-bit precision. */ |
4087 | a_is_small = a_size <= MANT_DIG_DIGITS || Branch (4087:18): [True: 2.12M, False: 109k]
|
4088 | (109k a_size == 109k MANT_DIG_DIGITS109k +1 && Branch (4088:10): [True: 58.4k, False: 50.8k]
|
4089 | a->ob_digit[58.4k MANT_DIG_DIGITS58.4k ] >> MANT_DIG_BITS58.4k == 0); Branch (4089:10): [True: 1.38k, False: 57.0k]
|
4090 | b_is_small = b_size <= MANT_DIG_DIGITS || Branch (4090:18): [True: 2.14M, False: 93.5k]
|
4091 | (93.5k b_size == 93.5k MANT_DIG_DIGITS93.5k +1 && Branch (4091:10): [True: 20.0k, False: 73.5k]
|
4092 | b->ob_digit[20.0k MANT_DIG_DIGITS20.0k ] >> MANT_DIG_BITS20.0k == 0); Branch (4092:10): [True: 14.7k, False: 5.24k]
|
4093 | if (a_is_small && b_is_small2.12M ) { Branch (4093:9): [True: 2.12M, False: 107k]
Branch (4093:23): [True: 2.12M, False: 2.08k]
|
4094 | double da, db; |
4095 | da = a->ob_digit[--a_size]; |
4096 | while (a_size > 0) Branch (4096:16): [True: 571, False: 2.12M]
|
4097 | da = da * PyLong_BASE + a->ob_digit[--a_size]; |
4098 | db = b->ob_digit[--b_size]; |
4099 | while (b_size > 0) Branch (4099:16): [True: 130, False: 2.12M]
|
4100 | db = db * PyLong_BASE + b->ob_digit[--b_size]; |
4101 | result = da / db; |
4102 | goto success; |
4103 | } |
4104 | |
4105 | /* Catch obvious cases of underflow and overflow */ |
4106 | diff = a_size - b_size; |
4107 | if (diff > PY_SSIZE_T_MAX/PyLong_SHIFT - 1) Branch (4107:9): [True: 0, False: 110k]
|
4108 | /* Extreme overflow */ |
4109 | goto overflow; |
4110 | else if (diff < 1 - PY_SSIZE_T_MAX/PyLong_SHIFT) Branch (4110:14): [True: 0, False: 110k]
|
4111 | /* Extreme underflow */ |
4112 | goto underflow_or_zero; |
4113 | /* Next line is now safe from overflowing a Py_ssize_t */ |
4114 | diff = diff * PyLong_SHIFT + bit_length_digit(a->ob_digit[a_size - 1]) - |
4115 | bit_length_digit(b->ob_digit[b_size - 1]); |
4116 | /* Now diff = a_bits - b_bits. */ |
4117 | if (diff > DBL_MAX_EXP) Branch (4117:9): [True: 35, False: 109k]
|
4118 | goto overflow; |
4119 | else if (diff < DBL_MIN_EXP - DBL_MANT_DIG - 1) Branch (4119:14): [True: 41, False: 109k]
|
4120 | goto underflow_or_zero; |
4121 | |
4122 | /* Choose value for shift; see comments for step 1 above. */ |
4123 | shift = Py_MAX(diff, DBL_MIN_EXP) - DBL_MANT_DIG - 2; |
4124 | |
4125 | inexact = 0; |
4126 | |
4127 | /* x = abs(a * 2**-shift) */ |
4128 | if (shift <= 0) { Branch (4128:9): [True: 88.0k, False: 21.8k]
|
4129 | Py_ssize_t i, shift_digits = -shift / PyLong_SHIFT; |
4130 | digit rem; |
4131 | /* x = a << -shift */ |
4132 | if (a_size >= PY_SSIZE_T_MAX - 1 - shift_digits) { Branch (4132:13): [True: 0, False: 88.0k]
|
4133 | /* In practice, it's probably impossible to end up |
4134 | here. Both a and b would have to be enormous, |
4135 | using close to SIZE_T_MAX bytes of memory each. */ |
4136 | PyErr_SetString(PyExc_OverflowError, |
4137 | "intermediate overflow during division"); |
4138 | goto error; |
4139 | } |
4140 | x = _PyLong_New(a_size + shift_digits + 1); |
4141 | if (x == NULL) Branch (4141:13): [True: 0, False: 88.0k]
|
4142 | goto error; |
4143 | for (i = 0; 88.0k i < shift_digits; i++345k ) Branch (4143:21): [True: 345k, False: 88.0k]
|
4144 | x->ob_digit[i] = 0; |
4145 | rem = v_lshift(x->ob_digit + shift_digits, a->ob_digit, |
4146 | a_size, -shift % PyLong_SHIFT); |
4147 | x->ob_digit[a_size + shift_digits] = rem; |
4148 | } |
4149 | else { |
4150 | Py_ssize_t shift_digits = shift / PyLong_SHIFT; |
4151 | digit rem; |
4152 | /* x = a >> shift */ |
4153 | assert(a_size >= shift_digits); |
4154 | x = _PyLong_New(a_size - shift_digits); |
4155 | if (x == NULL) Branch (4155:13): [True: 0, False: 21.8k]
|
4156 | goto error; |
4157 | rem = v_rshift(x->ob_digit, a->ob_digit + shift_digits, |
4158 | a_size - shift_digits, shift % PyLong_SHIFT); |
4159 | /* set inexact if any of the bits shifted out is nonzero */ |
4160 | if (rem) Branch (4160:13): [True: 17.0k, False: 4.85k]
|
4161 | inexact = 1; |
4162 | while (!inexact && shift_digits > 014.4k ) Branch (4162:16): [True: 14.4k, False: 18.4k]
Branch (4162:28): [True: 11.0k, False: 3.42k]
|
4163 | if (a->ob_digit[--shift_digits]) Branch (4163:17): [True: 1.42k, False: 9.60k]
|
4164 | inexact = 1; |
4165 | } |
4166 | long_normalize(x); |
4167 | x_size = Py_SIZE(x); |
4168 | |
4169 | /* x //= b. If the remainder is nonzero, set inexact. We own the only |
4170 | reference to x, so it's safe to modify it in-place. */ |
4171 | if (b_size == 1) { Branch (4171:9): [True: 16.5k, False: 93.4k]
|
4172 | digit rem = inplace_divrem1(x->ob_digit, x->ob_digit, x_size, |
4173 | b->ob_digit[0]); |
4174 | long_normalize(x); |
4175 | if (rem) Branch (4175:13): [True: 1.51k, False: 15.0k]
|
4176 | inexact = 1; |
4177 | } |
4178 | else { |
4179 | PyLongObject *div, *rem; |
4180 | div = x_divrem(x, b, &rem); |
4181 | Py_DECREF(x); |
4182 | x = div; |
4183 | if (x == NULL) Branch (4183:13): [True: 0, False: 93.4k]
|
4184 | goto error; |
4185 | if (Py_SIZE(rem)) |
4186 | inexact = 1; |
4187 | Py_DECREF(rem); |
4188 | } |
4189 | x_size = Py_ABS(Py_SIZE(x)); |
4190 | assert(x_size > 0); /* result of division is never zero */ |
4191 | x_bits = (x_size-1)*PyLong_SHIFT+bit_length_digit(x->ob_digit[x_size-1]); |
4192 | |
4193 | /* The number of extra bits that have to be rounded away. */ |
4194 | extra_bits = Py_MAX(x_bits, DBL_MIN_EXP - shift) - DBL_MANT_DIG; |
4195 | assert(extra_bits == 2 || extra_bits == 3); |
4196 | |
4197 | /* Round by directly modifying the low digit of x. */ |
4198 | mask = (digit)1 << (extra_bits - 1); |
4199 | low = x->ob_digit[0] | inexact; |
4200 | if ((low & mask) && (low & (3U*mask-1U))55.0k ) Branch (4200:9): [True: 55.0k, False: 54.8k]
Branch (4200:25): [True: 55.0k, False: 24]
|
4201 | low += mask; |
4202 | x->ob_digit[0] = low & ~(2U*mask-1U); |
4203 | |
4204 | /* Convert x to a double dx; the conversion is exact. */ |
4205 | dx = x->ob_digit[--x_size]; |
4206 | while (x_size > 0) Branch (4206:12): [True: 109k, False: 109k]
|
4207 | dx = dx * PyLong_BASE + x->ob_digit[--x_size]; |
4208 | Py_DECREF(x); |
4209 | |
4210 | /* Check whether ldexp result will overflow a double. */ |
4211 | if (shift + x_bits >= DBL_MAX_EXP && Branch (4211:9): [True: 487, False: 109k]
|
4212 | (487 shift + x_bits > DBL_MAX_EXP487 || dx == ldexp(1.0, (int)x_bits)486 )) Branch (4212:10): [True: 1, False: 486]
Branch (4212:42): [True: 252, False: 234]
|
4213 | goto overflow; |
4214 | result = ldexp(dx, (int)shift); |
4215 | |
4216 | success: |
4217 | return PyFloat_FromDouble(negate ? -result24.7k : result2.20M ); Branch (4217:31): [True: 24.7k, False: 2.20M]
|
4218 | |
4219 | underflow_or_zero: |
4220 | return PyFloat_FromDouble(negate ? -0.033 : 0.02.21k ); Branch (4220:31): [True: 33, False: 2.21k]
|
4221 | |
4222 | overflow: |
4223 | PyErr_SetString(PyExc_OverflowError, |
4224 | "integer division result too large for a float"); |
4225 | error: |
4226 | return NULL; |
4227 | } |
4228 | |
4229 | static PyObject * |
4230 | long_mod(PyObject *a, PyObject *b) |
4231 | { |
4232 | PyLongObject *mod; |
4233 | |
4234 | CHECK_BINOP(a, b); |
4235 | |
4236 | if (l_mod((PyLongObject*)a, (PyLongObject*)b, &mod) < 0) Branch (4236:9): [True: 4, False: 1.33M]
|
4237 | mod = NULL; |
4238 | return (PyObject *)mod; |
4239 | } |
4240 | |
4241 | static PyObject * |
4242 | long_divmod(PyObject *a, PyObject *b) |
4243 | { |
4244 | PyLongObject *div, *mod; |
4245 | PyObject *z; |
4246 | |
4247 | CHECK_BINOP(a, b); |
4248 | |
4249 | if (l_divmod((PyLongObject*)a, (PyLongObject*)b, &div, &mod) < 0) { Branch (4249:9): [True: 7, False: 1.20M]
|
4250 | return NULL; |
4251 | } |
4252 | z = PyTuple_New(2); |
4253 | if (z != NULL) { Branch (4253:9): [True: 1.20M, False: 0]
|
4254 | PyTuple_SET_ITEM(z, 0, (PyObject *) div); |
4255 | PyTuple_SET_ITEM(z, 1, (PyObject *) mod); |
4256 | } |
4257 | else { |
4258 | Py_DECREF(div); |
4259 | Py_DECREF(mod); |
4260 | } |
4261 | return z; |
4262 | } |
4263 | |
4264 | |
4265 | /* Compute an inverse to a modulo n, or raise ValueError if a is not |
4266 | invertible modulo n. Assumes n is positive. The inverse returned |
4267 | is whatever falls out of the extended Euclidean algorithm: it may |
4268 | be either positive or negative, but will be smaller than n in |
4269 | absolute value. |
4270 | |
4271 | Pure Python equivalent for long_invmod: |
4272 | |
4273 | def invmod(a, n): |
4274 | b, c = 1, 0 |
4275 | while n: |
4276 | q, r = divmod(a, n) |
4277 | a, b, c, n = n, c, b - q*c, r |
4278 | |
4279 | # at this point a is the gcd of the original inputs |
4280 | if a == 1: |
4281 | return b |
4282 | raise ValueError("Not invertible") |
4283 | */ |
4284 | |
4285 | static PyLongObject * |
4286 | long_invmod(PyLongObject *a, PyLongObject *n) |
4287 | { |
4288 | PyLongObject *b, *c; |
4289 | |
4290 | /* Should only ever be called for positive n */ |
4291 | assert(Py_SIZE(n) > 0); |
4292 | |
4293 | b = (PyLongObject *)PyLong_FromLong(1L); |
4294 | if (b == NULL) { Branch (4294:9): [True: 0, False: 39.4k]
|
4295 | return NULL; |
4296 | } |
4297 | c = (PyLongObject *)PyLong_FromLong(0L); |
4298 | if (c == NULL) { Branch (4298:9): [True: 0, False: 39.4k]
|
4299 | Py_DECREF(b); |
4300 | return NULL; |
4301 | } |
4302 | Py_INCREF(a); |
4303 | Py_INCREF(n); |
4304 | |
4305 | /* references now owned: a, b, c, n */ |
4306 | while (Py_SIZE(n) != 0) { Branch (4306:12): [True: 136k, False: 39.4k]
|
4307 | PyLongObject *q, *r, *s, *t; |
4308 | |
4309 | if (l_divmod(a, n, &q, &r) == -1) { Branch (4309:13): [True: 0, False: 136k]
|
4310 | goto Error; |
4311 | } |
4312 | Py_DECREF(a); |
4313 | a = n; |
4314 | n = r; |
4315 | t = (PyLongObject *)long_mul(q, c); |
4316 | Py_DECREF(q); |
4317 | if (t == NULL) { Branch (4317:13): [True: 0, False: 136k]
|
4318 | goto Error; |
4319 | } |
4320 | s = (PyLongObject *)long_sub(b, t); |
4321 | Py_DECREF(t); |
4322 | if (s == NULL) { Branch (4322:13): [True: 0, False: 136k]
|
4323 | goto Error; |
4324 | } |
4325 | Py_DECREF(b); |
4326 | b = c; |
4327 | c = s; |
4328 | } |
4329 | /* references now owned: a, b, c, n */ |
4330 | |
4331 | Py_DECREF(c); |
4332 | Py_DECREF(n); |
4333 | if (long_compare(a, (PyLongObject *)_PyLong_GetOne())) { Branch (4333:9): [True: 11.3k, False: 28.1k]
|
4334 | /* a != 1; we don't have an inverse. */ |
4335 | Py_DECREF(a); |
4336 | Py_DECREF(b); |
4337 | PyErr_SetString(PyExc_ValueError, |
4338 | "base is not invertible for the given modulus"); |
4339 | return NULL; |
4340 | } |
4341 | else { |
4342 | /* a == 1; b gives an inverse modulo n */ |
4343 | Py_DECREF(a); |
4344 | return b; |
4345 | } |
4346 | |
4347 | Error: |
4348 | Py_DECREF(a); |
4349 | Py_DECREF(b); |
4350 | Py_DECREF(c); |
4351 | Py_DECREF(n); |
4352 | return NULL; |
4353 | } |
4354 | |
4355 | |
4356 | /* pow(v, w, x) */ |
4357 | static PyObject * |
4358 | long_pow(PyObject *v, PyObject *w, PyObject *x) |
4359 | { |
4360 | PyLongObject *a, *b, *c; /* a,b,c = v,w,x */ |
4361 | int negativeOutput = 0; /* if x<0 return negative output */ |
4362 | |
4363 | PyLongObject *z = NULL; /* accumulated result */ |
4364 | Py_ssize_t i, j; /* counters */ |
4365 | PyLongObject *temp = NULL; |
4366 | PyLongObject *a2 = NULL; /* may temporarily hold a**2 % c */ |
4367 | |
4368 | /* k-ary values. If the exponent is large enough, table is |
4369 | * precomputed so that table[i] == a**(2*i+1) % c for i in |
4370 | * range(EXP_TABLE_LEN). |
4371 | * Note: this is uninitialzed stack trash: don't pay to set it to known |
4372 | * values unless it's needed. Instead ensure that num_table_entries is |
4373 | * set to the number of entries actually filled whenever a branch to the |
4374 | * Error or Done labels is possible. |
4375 | */ |
4376 | PyLongObject *table[EXP_TABLE_LEN]; |
4377 | Py_ssize_t num_table_entries = 0; |
4378 | |
4379 | /* a, b, c = v, w, x */ |
4380 | CHECK_BINOP(v, w); |
4381 | a = (PyLongObject*)v; Py_INCREF(a); |
4382 | b = (PyLongObject*)w; Py_INCREF(b); |
4383 | if (PyLong_Check(x)) { |
4384 | c = (PyLongObject *)x; |
4385 | Py_INCREF(x); |
4386 | } |
4387 | else if (x == Py_None) Branch (4387:14): [True: 1.26M, False: 1]
|
4388 | c = NULL; |
4389 | else { |
4390 | Py_DECREF(a); |
4391 | Py_DECREF(b); |
4392 | Py_RETURN_NOTIMPLEMENTED; |
4393 | } |
4394 | |
4395 | if (Py_SIZE(b) < 0 && c == NULL48.7k ) { Branch (4395:9): [True: 48.7k, False: 2.13M]
Branch (4395:27): [True: 8.16k, False: 40.5k]
|
4396 | /* if exponent is negative and there's no modulus: |
4397 | return a float. This works because we know |
4398 | that this calls float_pow() which converts its |
4399 | arguments to double. */ |
4400 | Py_DECREF(a); |
4401 | Py_DECREF(b); |
4402 | return PyFloat_Type.tp_as_number->nb_power(v, w, x); |
4403 | } |
4404 | |
4405 | if (c) { Branch (4405:9): [True: 921k, False: 1.25M]
|
4406 | /* if modulus == 0: |
4407 | raise ValueError() */ |
4408 | if (Py_SIZE(c) == 0) { Branch (4408:13): [True: 301, False: 921k]
|
4409 | PyErr_SetString(PyExc_ValueError, |
4410 | "pow() 3rd argument cannot be 0"); |
4411 | goto Error; |
4412 | } |
4413 | |
4414 | /* if modulus < 0: |
4415 | negativeOutput = True |
4416 | modulus = -modulus */ |
4417 | if (Py_SIZE(c) < 0) { Branch (4417:13): [True: 31.5k, False: 889k]
|
4418 | negativeOutput = 1; |
4419 | temp = (PyLongObject *)_PyLong_Copy(c); |
4420 | if (temp == NULL) Branch (4420:17): [True: 0, False: 31.5k]
|
4421 | goto Error; |
4422 | Py_DECREF(c); |
4423 | c = temp; |
4424 | temp = NULL; |
4425 | _PyLong_Negate(&c); |
4426 | if (c == NULL) Branch (4426:17): [True: 0, False: 31.5k]
|
4427 | goto Error; |
4428 | } |
4429 | |
4430 | /* if modulus == 1: |
4431 | return 0 */ |
4432 | if ((Py_SIZE(c) == 1) && (c->ob_digit[0] == 1)915k ) { Branch (4432:13): [True: 915k, False: 5.89k]
Branch (4432:34): [True: 2.41k, False: 913k]
|
4433 | z = (PyLongObject *)PyLong_FromLong(0L); |
4434 | goto Done; |
4435 | } |
4436 | |
4437 | /* if exponent is negative, negate the exponent and |
4438 | replace the base with a modular inverse */ |
4439 | if (Py_SIZE(b) < 0) { Branch (4439:13): [True: 39.4k, False: 879k]
|
4440 | temp = (PyLongObject *)_PyLong_Copy(b); |
4441 | if (temp == NULL) Branch (4441:17): [True: 0, False: 39.4k]
|
4442 | goto Error; |
4443 | Py_DECREF(b); |
4444 | b = temp; |
4445 | temp = NULL; |
4446 | _PyLong_Negate(&b); |
4447 | if (b == NULL) Branch (4447:17): [True: 0, False: 39.4k]
|
4448 | goto Error; |
4449 | |
4450 | temp = long_invmod(a, c); |
4451 | if (temp == NULL) Branch (4451:17): [True: 11.3k, False: 28.1k]
|
4452 | goto Error; |
4453 | Py_DECREF(a); |
4454 | a = temp; |
4455 | temp = NULL; |
4456 | } |
4457 | |
4458 | /* Reduce base by modulus in some cases: |
4459 | 1. If base < 0. Forcing the base non-negative makes things easier. |
4460 | 2. If base is obviously larger than the modulus. The "small |
4461 | exponent" case later can multiply directly by base repeatedly, |
4462 | while the "large exponent" case multiplies directly by base 31 |
4463 | times. It can be unboundedly faster to multiply by |
4464 | base % modulus instead. |
4465 | We could _always_ do this reduction, but l_mod() isn't cheap, |
4466 | so we only do it when it buys something. */ |
4467 | if (Py_SIZE(a) < 0 || Py_SIZE883k (a) > 883k Py_SIZE883k (c)) { Branch (4467:13): [True: 24.5k, False: 883k]
Branch (4467:31): [True: 0, False: 883k]
|
4468 | if (l_mod(a, c, &temp) < 0) Branch (4468:17): [True: 0, False: 24.5k]
|
4469 | goto Error; |
4470 | Py_DECREF(a); |
4471 | a = temp; |
4472 | temp = NULL; |
4473 | } |
4474 | } |
4475 | |
4476 | /* At this point a, b, and c are guaranteed non-negative UNLESS |
4477 | c is NULL, in which case a may be negative. */ |
4478 | |
4479 | z = (PyLongObject *)PyLong_FromLong(1L); |
4480 | if (z == NULL) Branch (4480:9): [True: 0, False: 2.16M]
|
4481 | goto Error; |
4482 | |
4483 | /* Perform a modular reduction, X = X % c, but leave X alone if c |
4484 | * is NULL. |
4485 | */ |
4486 | #define REDUCE(X) \ |
4487 | do { \ |
4488 | if (c != NULL) { \ |
4489 | if (l_mod(X, c, &temp) < 0) \ |
4490 | goto Error0 ; \ |
4491 | Py_XDECREF(X); \ |
4492 | X = temp; \ |
4493 | temp = NULL; \ |
4494 | } \ |
4495 | } while(0) |
4496 | |
4497 | /* Multiply two values, then reduce the result: |
4498 | result = X*Y % c. If c is NULL, skip the mod. */ |
4499 | #define MULT(X, Y, result) \ |
4500 | do { \ |
4501 | temp = (PyLongObject *)long_mul(X, Y); \ |
4502 | if (temp == NULL) \ |
4503 | goto Error0 ; \ |
4504 | Py_XDECREF(result); \ |
4505 | result = temp; \ |
4506 | temp = NULL; \ |
4507 | REDUCE(result); \ |
4508 | } while(0) |
4509 | |
4510 | i = Py_SIZE(b); |
4511 | digit bi = i ? b->ob_digit[i-1]2.11M : 051.8k ; Branch (4511:16): [True: 2.11M, False: 51.8k]
|
4512 | digit bit; |
4513 | if (i <= 1 && bi <= 32.16M ) { Branch (4513:9): [True: 2.16M, False: 161]
Branch (4513:19): [True: 644k, False: 1.51M]
|
4514 | /* aim for minimal overhead */ |
4515 | if (bi >= 2) { Branch (4515:13): [True: 549k, False: 94.4k]
|
4516 | MULT(a, a, z); |
4517 | if (bi == 3) { Branch (4517:17): [True: 92.1k, False: 457k]
|
4518 | MULT(z, a, z); |
4519 | } |
4520 | } |
4521 | else if (bi == 1) { Branch (4521:18): [True: 42.6k, False: 51.8k]
|
4522 | /* Multiplying by 1 serves two purposes: if `a` is of an int |
4523 | * subclass, makes the result an int (e.g., pow(False, 1) returns |
4524 | * 0 instead of False), and potentially reduces `a` by the modulus. |
4525 | */ |
4526 | MULT(a, z, z); |
4527 | } |
4528 | /* else bi is 0, and z==1 is correct */ |
4529 | } |
4530 | else if (i <= HUGE_EXP_CUTOFF / PyLong_SHIFT ) { Branch (4530:14): [True: 1.51M, False: 160]
|
4531 | /* Left-to-right binary exponentiation (HAC Algorithm 14.79) */ |
4532 | /* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf */ |
4533 | |
4534 | /* Find the first significant exponent bit. Search right to left |
4535 | * because we're primarily trying to cut overhead for small powers. |
4536 | */ |
4537 | assert(bi); /* else there is no significant bit */ |
4538 | Py_INCREF(a); |
4539 | Py_DECREF(z); |
4540 | z = a; |
4541 | for (bit = 2; ; bit <<= 116.5M ) { |
4542 | if (bit > bi) { /* found the first bit */ Branch (4542:17): [True: 1.51M, False: 16.5M]
|
4543 | assert((bi & bit) == 0); |
4544 | bit >>= 1; |
4545 | assert(bi & bit); |
4546 | break; |
4547 | } |
4548 | } |
4549 | for (--i, bit >>= 1;;) { |
4550 | for (; bit != 0; bit >>= 116.5M ) { Branch (4550:20): [True: 16.5M, False: 1.51M]
|
4551 | MULT(z, z, z); |
4552 | if (bi & bit) { Branch (4552:21): [True: 5.78M, False: 10.7M]
|
4553 | MULT(z, a, z); |
4554 | } |
4555 | } |
4556 | if (--i < 0) { Branch (4556:17): [True: 1.51M, False: 1]
|
4557 | break; |
4558 | } |
4559 | bi = b->ob_digit[i]; |
4560 | bit = (digit)1 << (PyLong_SHIFT-1); |
4561 | } |
4562 | } |
4563 | else { |
4564 | /* Left-to-right k-ary sliding window exponentiation |
4565 | * (Handbook of Applied Cryptography (HAC) Algorithm 14.85) |
4566 | */ |
4567 | Py_INCREF(a); |
4568 | table[0] = a; |
4569 | num_table_entries = 1; |
4570 | MULT(a, a, a2); |
4571 | /* table[i] == a**(2*i + 1) % c */ |
4572 | for (i = 1; 160 i < EXP_TABLE_LEN; ++i2.40k ) { Branch (4572:21): [True: 2.40k, False: 160]
|
4573 | table[i] = NULL; /* must set to known value for MULT */ |
4574 | MULT(table[i-1], a2, table[i]); |
4575 | ++num_table_entries; /* incremented iff MULT succeeded */ |
4576 | } |
4577 | Py_CLEAR(a2); |
4578 | |
4579 | /* Repeatedly extract the next (no more than) EXP_WINDOW_SIZE bits |
4580 | * into `pending`, starting with the next 1 bit. The current bit |
4581 | * length of `pending` is `blen`. |
4582 | */ |
4583 | int pending = 0, blen = 0; |
4584 | #define ABSORB_PENDING do { \ |
4585 | int ntz = 0; /* number of trailing zeroes in `pending` */ \ |
4586 | assert(pending && blen); \ |
4587 | assert(pending >> (blen - 1)); \ |
4588 | assert(pending >> blen == 0); \ |
4589 | while ((pending & 1) == 0) { \ |
4590 | ++ntz; \ |
4591 | pending >>= 1; \ |
4592 | } \ |
4593 | assert(ntz < blen); \ |
4594 | blen -= ntz; \ |
4595 | do { \ |
4596 | MULT(z, z, z); \ |
4597 | } while (--blen); \ |
4598 | MULT(z, table[pending >> 1], z); \ |
4599 | while (411k ntz-- > 0) \ |
4600 | MULT385k (z, z, z); \ |
4601 | assert(blen == 0); \ |
4602 | pending = 0; \ |
4603 | } while(0) |
4604 | |
4605 | for (i = Py_SIZE160 (b) - 1; i >= 0; --i82.4k ) { Branch (4605:34): [True: 82.4k, False: 160]
|
4606 | const digit bi = b->ob_digit[i]; |
4607 | for (j = PyLong_SHIFT82.4k - 1; j >= 0; --j2.47M ) { Branch (4607:40): [True: 2.47M, False: 82.4k]
|
4608 | const int bit = (bi >> j) & 1; |
4609 | pending = (pending << 1) | bit; |
4610 | if (pending) { Branch (4610:21): [True: 2.05M, False: 414k]
|
4611 | ++blen; |
4612 | if (blen == EXP_WINDOW_SIZE) Branch (4612:25): [True: 411k, False: 1.64M]
|
4613 | ABSORB_PENDING; |
4614 | } |
4615 | else /* absorb strings of 0 bits */ |
4616 | MULT(z, z, z); |
4617 | } |
4618 | } |
4619 | if (pending) Branch (4619:13): [True: 34, False: 126]
|
4620 | ABSORB_PENDING; |
4621 | } |
4622 | |
4623 | if (negativeOutput && (24.5k Py_SIZE24.5k (z) != 0)) { Branch (4623:9): [True: 24.5k, False: 2.13M]
Branch (4623:27): [True: 23.6k, False: 919]
|
4624 | temp = (PyLongObject *)long_sub(z, c); |
4625 | if (temp == NULL) Branch (4625:13): [True: 0, False: 23.6k]
|
4626 | goto Error; |
4627 | Py_DECREF(z); |
4628 | z = temp; |
4629 | temp = NULL; |
4630 | } |
4631 | goto Done; |
4632 | |
4633 | Error: |
4634 | Py_CLEAR(z); |
4635 | /* fall through */ |
4636 | Done: |
4637 | for (i = 0; i < num_table_entries; ++i2.56k ) Branch (4637:17): [True: 2.56k, False: 2.17M]
|
4638 | Py_DECREF(table[i]); |
4639 | Py_DECREF(a); |
4640 | Py_DECREF(b); |
4641 | Py_XDECREF(c); |
4642 | Py_XDECREF(a2); |
4643 | Py_XDECREF(temp); |
4644 | return (PyObject *)z; |
4645 | } |
4646 | |
4647 | static PyObject * |
4648 | long_invert(PyLongObject *v) |
4649 | { |
4650 | /* Implement ~x as -(x+1) */ |
4651 | PyLongObject *x; |
4652 | if (IS_MEDIUM_VALUE(v)) |
4653 | return _PyLong_FromSTwoDigits(~medium_value(v)); |
4654 | x = (PyLongObject *) long_add(v, (PyLongObject *)_PyLong_GetOne()); |
4655 | if (x == NULL) Branch (4655:9): [True: 0, False: 11.5k]
|
4656 | return NULL; |
4657 | _PyLong_Negate(&x); |
4658 | /* No need for maybe_small_long here, since any small |
4659 | longs will have been caught in the Py_SIZE <= 1 fast path. */ |
4660 | return (PyObject *)x; |
4661 | } |
4662 | |
4663 | static PyObject * |
4664 | long_neg(PyLongObject *v) |
4665 | { |
4666 | PyLongObject *z; |
4667 | if (IS_MEDIUM_VALUE(v)) |
4668 | return _PyLong_FromSTwoDigits(-medium_value(v)); |
4669 | z = (PyLongObject *)_PyLong_Copy(v); |
4670 | if (z != NULL) Branch (4670:9): [True: 223k, False: 0]
|
4671 | Py_SET_SIZE(z, -(Py_SIZE(v))); |
4672 | return (PyObject *)z; |
4673 | } |
4674 | |
4675 | static PyObject * |
4676 | long_abs(PyLongObject *v) |
4677 | { |
4678 | if (Py_SIZE(v) < 0) Branch (4678:9): [True: 283k, False: 1.04M]
|
4679 | return long_neg(v); |
4680 | else |
4681 | return long_long((PyObject *)v); |
4682 | } |
4683 | |
4684 | static int |
4685 | long_bool(PyLongObject *v) |
4686 | { |
4687 | return Py_SIZE(v) != 0; |
4688 | } |
4689 | |
4690 | /* wordshift, remshift = divmod(shiftby, PyLong_SHIFT) */ |
4691 | static int |
4692 | divmod_shift(PyObject *shiftby, Py_ssize_t *wordshift, digit *remshift) |
4693 | { |
4694 | assert(PyLong_Check(shiftby)); |
4695 | assert(Py_SIZE(shiftby) >= 0); |
4696 | Py_ssize_t lshiftby = PyLong_AsSsize_t((PyObject *)shiftby); |
4697 | if (lshiftby >= 0) { Branch (4697:9): [True: 2.72M, False: 6]
|
4698 | *wordshift = lshiftby / PyLong_SHIFT; |
4699 | *remshift = lshiftby % PyLong_SHIFT; |
4700 | return 0; |
4701 | } |
4702 | /* PyLong_Check(shiftby) is true and Py_SIZE(shiftby) >= 0, so it must |
4703 | be that PyLong_AsSsize_t raised an OverflowError. */ |
4704 | assert(PyErr_ExceptionMatches(PyExc_OverflowError)); |
4705 | PyErr_Clear(); |
4706 | PyLongObject *wordshift_obj = divrem1((PyLongObject *)shiftby, PyLong_SHIFT, remshift); |
4707 | if (wordshift_obj == NULL) { Branch (4707:9): [True: 0, False: 6]
|
4708 | return -1; |
4709 | } |
4710 | *wordshift = PyLong_AsSsize_t((PyObject *)wordshift_obj); |
4711 | Py_DECREF(wordshift_obj); |
4712 | if (*wordshift >= 0 && *wordshift < 0 PY_SSIZE_T_MAX0 / (Py_ssize_t)sizeof(digit)) { Branch (4712:9): [True: 0, False: 6]
Branch (4712:28): [True: 0, False: 0]
|
4713 | return 0; |
4714 | } |
4715 | PyErr_Clear(); |
4716 | /* Clip the value. With such large wordshift the right shift |
4717 | returns 0 and the left shift raises an error in _PyLong_New(). */ |
4718 | *wordshift = PY_SSIZE_T_MAX / sizeof(digit); |
4719 | *remshift = 0; |
4720 | return 0; |
4721 | } |
4722 | |
4723 | /* Inner function for both long_rshift and _PyLong_Rshift, shifting an |
4724 | integer right by PyLong_SHIFT*wordshift + remshift bits. |
4725 | wordshift should be nonnegative. */ |
4726 | |
4727 | static PyObject * |
4728 | long_rshift1(PyLongObject *a, Py_ssize_t wordshift, digit remshift) |
4729 | { |
4730 | PyLongObject *z = NULL; |
4731 | Py_ssize_t newsize, hishift, size_a; |
4732 | twodigits accum; |
4733 | int a_negative; |
4734 | |
4735 | /* Total number of bits shifted must be nonnegative. */ |
4736 | assert(wordshift >= 0); |
4737 | assert(remshift < PyLong_SHIFT); |
4738 | |
4739 | /* Fast path for small a. */ |
4740 | if (IS_MEDIUM_VALUE(a)) { |
4741 | stwodigits m, x; |
4742 | digit shift; |
4743 | m = medium_value(a); |
4744 | shift = wordshift == 0 ? remshift930k : PyLong_SHIFT5.82k ; Branch (4744:17): [True: 930k, False: 5.82k]
|
4745 | x = m < 0 ? ~(~m >> shift)10.8k : m >> shift925k ; Branch (4745:13): [True: 10.8k, False: 925k]
|
4746 | return _PyLong_FromSTwoDigits(x); |
4747 | } |
4748 | |
4749 | a_negative = Py_SIZE(a) < 0; |
4750 | size_a = Py_ABS(Py_SIZE(a)); |
4751 | |
4752 | if (a_negative) { Branch (4752:9): [True: 17.9k, False: 346k]
|
4753 | /* For negative 'a', adjust so that 0 < remshift <= PyLong_SHIFT, |
4754 | while keeping PyLong_SHIFT*wordshift + remshift the same. This |
4755 | ensures that 'newsize' is computed correctly below. */ |
4756 | if (remshift == 0) { Branch (4756:13): [True: 600, False: 17.3k]
|
4757 | if (wordshift == 0) { Branch (4757:17): [True: 301, False: 299]
|
4758 | /* Can only happen if the original shift was 0. */ |
4759 | return long_long((PyObject *)a); |
4760 | } |
4761 | remshift = PyLong_SHIFT; |
4762 | --wordshift; |
4763 | } |
4764 | } |
4765 | |
4766 | assert(wordshift >= 0); |
4767 | newsize = size_a - wordshift; |
4768 | if (newsize <= 0) { Branch (4768:9): [True: 2, False: 363k]
|
4769 | /* Shifting all the bits of 'a' out gives either -1 or 0. */ |
4770 | return PyLong_FromLong(-a_negative); |
4771 | } |
4772 | z = _PyLong_New(newsize); |
4773 | if (z == NULL) { Branch (4773:9): [True: 0, False: 363k]
|
4774 | return NULL; |
4775 | } |
4776 | hishift = PyLong_SHIFT - remshift; |
4777 | |
4778 | accum = a->ob_digit[wordshift]; |
4779 | if (a_negative) { Branch (4779:9): [True: 17.6k, False: 346k]
|
4780 | /* |
4781 | For a positive integer a and nonnegative shift, we have: |
4782 | |
4783 | (-a) >> shift == -((a + 2**shift - 1) >> shift). |
4784 | |
4785 | In the addition `a + (2**shift - 1)`, the low `wordshift` digits of |
4786 | `2**shift - 1` all have value `PyLong_MASK`, so we get a carry out |
4787 | from the bottom `wordshift` digits when at least one of the least |
4788 | significant `wordshift` digits of `a` is nonzero. Digit `wordshift` |
4789 | of `2**shift - 1` has value `PyLong_MASK >> hishift`. |
4790 | */ |
4791 | Py_SET_SIZE(z, -newsize); |
4792 | |
4793 | digit sticky = 0; |
4794 | for (Py_ssize_t j = 0; j < wordshift; j++8.58k ) { Branch (4794:32): [True: 8.58k, False: 17.6k]
|
4795 | sticky |= a->ob_digit[j]; |
4796 | } |
4797 | accum += (PyLong_MASK >> hishift) + (digit)(sticky != 0); |
4798 | } |
4799 | |
4800 | accum >>= remshift; |
4801 | for (Py_ssize_t i = 0, j = wordshift + 1; j < size_a; i++, j++757k ) { Branch (4801:47): [True: 757k, False: 363k]
|
4802 | accum += (twodigits)a->ob_digit[j] << hishift; |
4803 | z->ob_digit[i] = (digit)(accum & PyLong_MASK); |
4804 | accum >>= PyLong_SHIFT; |
4805 | } |
4806 | assert(accum <= PyLong_MASK); |
4807 | z->ob_digit[newsize - 1] = (digit)accum; |
4808 | |
4809 | z = maybe_small_long(long_normalize(z)); |
4810 | return (PyObject *)z; |
4811 | } |
4812 | |
4813 | static PyObject * |
4814 | long_rshift(PyObject *a, PyObject *b) |
4815 | { |
4816 | Py_ssize_t wordshift; |
4817 | digit remshift; |
4818 | |
4819 | CHECK_BINOP(a, b); |
4820 | |
4821 | if (Py_SIZE(b) < 0) { Branch (4821:9): [True: 5, False: 1.18M]
|
4822 | PyErr_SetString(PyExc_ValueError, "negative shift count"); |
4823 | return NULL; |
4824 | } |
4825 | if (Py_SIZE(a) == 0) { Branch (4825:9): [True: 33.3k, False: 1.15M]
|
4826 | return PyLong_FromLong(0); |
4827 | } |
4828 | if (divmod_shift(b, &wordshift, &remshift) < 0) Branch (4828:9): [True: 0, False: 1.15M]
|
4829 | return NULL; |
4830 | return long_rshift1((PyLongObject *)a, wordshift, remshift); |
4831 | } |
4832 | |
4833 | /* Return a >> shiftby. */ |
4834 | PyObject * |
4835 | _PyLong_Rshift(PyObject *a, size_t shiftby) |
4836 | { |
4837 | Py_ssize_t wordshift; |
4838 | digit remshift; |
4839 | |
4840 | assert(PyLong_Check(a)); |
4841 | if (Py_SIZE(a) == 0) { Branch (4841:9): [True: 0, False: 144k]
|
4842 | return PyLong_FromLong(0); |
4843 | } |
4844 | wordshift = shiftby / PyLong_SHIFT; |
4845 | remshift = shiftby % PyLong_SHIFT; |
4846 | return long_rshift1((PyLongObject *)a, wordshift, remshift); |
4847 | } |
4848 | |
4849 | static PyObject * |
4850 | long_lshift1(PyLongObject *a, Py_ssize_t wordshift, digit remshift) |
4851 | { |
4852 | PyLongObject *z = NULL; |
4853 | Py_ssize_t oldsize, newsize, i, j; |
4854 | twodigits accum; |
4855 | |
4856 | if (wordshift == 0 && IS_MEDIUM_VALUE657k (a)) { Branch (4856:9): [True: 657k, False: 1.03M]
|
4857 | stwodigits m = medium_value(a); |
4858 | // bypass undefined shift operator behavior |
4859 | stwodigits x = m < 0 ? -(-m << remshift)10.6k : m << remshift359k ; Branch (4859:24): [True: 10.6k, False: 359k]
|
4860 | return _PyLong_FromSTwoDigits(x); |
4861 | } |
4862 | |
4863 | oldsize = Py_ABS(Py_SIZE(a)); |
4864 | newsize = oldsize + wordshift; |
4865 | if (remshift) Branch (4865:9): [True: 1.16M, False: 160k]
|
4866 | ++newsize; |
4867 | z = _PyLong_New(newsize); |
4868 | if (z == NULL) Branch (4868:9): [True: 0, False: 1.32M]
|
4869 | return NULL; |
4870 | if (Py_SIZE(a) < 0) { Branch (4870:9): [True: 301k, False: 1.02M]
|
4871 | assert(Py_REFCNT(z) == 1); |
4872 | Py_SET_SIZE(z, -Py_SIZE(z)); |
4873 | } |
4874 | for (i = 0; i < wordshift; i++5.24M ) Branch (4874:17): [True: 5.24M, False: 1.32M]
|
4875 | z->ob_digit[i] = 0; |
4876 | accum = 0; |
4877 | for (j = 0; j < oldsize; i++, j++10.7M ) { Branch (4877:17): [True: 10.7M, False: 1.32M]
|
4878 | accum |= (twodigits)a->ob_digit[j] << remshift; |
4879 | z->ob_digit[i] = (digit)(accum & PyLong_MASK); |
4880 | accum >>= PyLong_SHIFT; |
4881 | } |
4882 | if (remshift) Branch (4882:9): [True: 1.16M, False: 160k]
|
4883 | z->ob_digit[newsize-1] = (digit)accum; |
4884 | else |
4885 | assert(!accum); |
4886 | z = long_normalize(z); |
4887 | return (PyObject *) maybe_small_long(z); |
4888 | } |
4889 | |
4890 | static PyObject * |
4891 | long_lshift(PyObject *a, PyObject *b) |
4892 | { |
4893 | Py_ssize_t wordshift; |
4894 | digit remshift; |
4895 | |
4896 | CHECK_BINOP(a, b); |
4897 | |
4898 | if (Py_SIZE(b) < 0) { Branch (4898:9): [True: 7, False: 1.61M]
|
4899 | PyErr_SetString(PyExc_ValueError, "negative shift count"); |
4900 | return NULL; |
4901 | } |
4902 | if (Py_SIZE(a) == 0) { Branch (4902:9): [True: 39.2k, False: 1.57M]
|
4903 | return PyLong_FromLong(0); |
4904 | } |
4905 | if (divmod_shift(b, &wordshift, &remshift) < 0) Branch (4905:9): [True: 0, False: 1.57M]
|
4906 | return NULL; |
4907 | return long_lshift1((PyLongObject *)a, wordshift, remshift); |
4908 | } |
4909 | |
4910 | /* Return a << shiftby. */ |
4911 | PyObject * |
4912 | _PyLong_Lshift(PyObject *a, size_t shiftby) |
4913 | { |
4914 | Py_ssize_t wordshift; |
4915 | digit remshift; |
4916 | |
4917 | assert(PyLong_Check(a)); |
4918 | if (Py_SIZE(a) == 0) { Branch (4918:9): [True: 0, False: 121k]
|
4919 | return PyLong_FromLong(0); |
4920 | } |
4921 | wordshift = shiftby / PyLong_SHIFT; |
4922 | remshift = shiftby % PyLong_SHIFT; |
4923 | return long_lshift1((PyLongObject *)a, wordshift, remshift); |
4924 | } |
4925 | |
4926 | /* Compute two's complement of digit vector a[0:m], writing result to |
4927 | z[0:m]. The digit vector a need not be normalized, but should not |
4928 | be entirely zero. a and z may point to the same digit vector. */ |
4929 | |
4930 | static void |
4931 | v_complement(digit *z, digit *a, Py_ssize_t m) |
4932 | { |
4933 | Py_ssize_t i; |
4934 | digit carry = 1; |
4935 | for (i = 0; i < m; ++i3.77M ) { Branch (4935:17): [True: 3.77M, False: 701k]
|
4936 | carry += a[i] ^ PyLong_MASK; |
4937 | z[i] = carry & PyLong_MASK; |
4938 | carry >>= PyLong_SHIFT; |
4939 | } |
4940 | assert(carry == 0); |
4941 | } |
4942 | |
4943 | /* Bitwise and/xor/or operations */ |
4944 | |
4945 | static PyObject * |
4946 | long_bitwise(PyLongObject *a, |
4947 | char op, /* '&', '|', '^' */ |
4948 | PyLongObject *b) |
4949 | { |
4950 | int nega, negb, negz; |
4951 | Py_ssize_t size_a, size_b, size_z, i; |
4952 | PyLongObject *z; |
4953 | |
4954 | /* Bitwise operations for negative numbers operate as though |
4955 | on a two's complement representation. So convert arguments |
4956 | from sign-magnitude to two's complement, and convert the |
4957 | result back to sign-magnitude at the end. */ |
4958 | |
4959 | /* If a is negative, replace it by its two's complement. */ |
4960 | size_a = Py_ABS(Py_SIZE(a)); |
4961 | nega = Py_SIZE(a) < 0; |
4962 | if (nega) { Branch (4962:9): [True: 583k, False: 817k]
|
4963 | z = _PyLong_New(size_a); |
4964 | if (z == NULL) Branch (4964:13): [True: 0, False: 583k]
|
4965 | return NULL; |
4966 | v_complement(z->ob_digit, a->ob_digit, size_a); |
4967 | a = z; |
4968 | } |
4969 | else |
4970 | /* Keep reference count consistent. */ |
4971 | Py_INCREF(a); |
4972 | |
4973 | /* Same for b. */ |
4974 | size_b = Py_ABS(Py_SIZE(b)); |
4975 | negb = Py_SIZE(b) < 0; |
4976 | if (negb) { Branch (4976:9): [True: 68.6k, False: 1.33M]
|
4977 | z = _PyLong_New(size_b); |
4978 | if (z == NULL) { Branch (4978:13): [True: 0, False: 68.6k]
|
4979 | Py_DECREF(a); |
4980 | return NULL; |
4981 | } |
4982 | v_complement(z->ob_digit, b->ob_digit, size_b); |
4983 | b = z; |
4984 | } |
4985 | else |
4986 | Py_INCREF(b); |
4987 | |
4988 | /* Swap a and b if necessary to ensure size_a >= size_b. */ |
4989 | if (size_a < size_b) { Branch (4989:9): [True: 54.7k, False: 1.34M]
|
4990 | z = a; a = b; b = z; |
4991 | size_z = size_a; size_a = size_b; size_b = size_z; |
4992 | negz = nega; nega = negb; negb = negz; |
4993 | } |
4994 | |
4995 | /* JRH: The original logic here was to allocate the result value (z) |
4996 | as the longer of the two operands. However, there are some cases |
4997 | where the result is guaranteed to be shorter than that: AND of two |
4998 | positives, OR of two negatives: use the shorter number. AND with |
4999 | mixed signs: use the positive number. OR with mixed signs: use the |
5000 | negative number. |
5001 | */ |
5002 | switch (op) { |
5003 | case '^': Branch (5003:5): [True: 61.0k, False: 1.33M]
|
5004 | negz = nega ^ negb; |
5005 | size_z = size_a; |
5006 | break; |
5007 | case '&': Branch (5007:5): [True: 1.19M, False: 209k]
|
5008 | negz = nega & negb; |
5009 | size_z = negb ? size_a37.9k : size_b1.15M ; Branch (5009:18): [True: 37.9k, False: 1.15M]
|
5010 | break; |
5011 | case '|': Branch (5011:5): [True: 148k, False: 1.25M]
|
5012 | negz = nega | negb; |
5013 | size_z = negb ? size_b2.24k : size_a146k ; Branch (5013:18): [True: 2.24k, False: 146k]
|
5014 | break; |
5015 | default: Branch (5015:5): [True: 0, False: 1.40M]
|
5016 | Py_UNREACHABLE(); |
5017 | } |
5018 | |
5019 | /* We allow an extra digit if z is negative, to make sure that |
5020 | the final two's complement of z doesn't overflow. */ |
5021 | z = _PyLong_New(size_z + negz); |
5022 | if (z == NULL) { Branch (5022:9): [True: 0, False: 1.40M]
|
5023 | Py_DECREF(a); |
5024 | Py_DECREF(b); |
5025 | return NULL; |
5026 | } |
5027 | |
5028 | /* Compute digits for overlap of a and b. */ |
5029 | switch(op) { |
5030 | case '&': Branch (5030:5): [True: 1.19M, False: 209k]
|
5031 | for (i = 0; i < size_b; ++i1.27M ) Branch (5031:21): [True: 1.27M, False: 1.19M]
|
5032 | z->ob_digit[i] = a->ob_digit[i] & b->ob_digit[i]; |
5033 | break; |
5034 | case '|': Branch (5034:5): [True: 148k, False: 1.25M]
|
5035 | for (i = 0; i < size_b; ++i206k ) Branch (5035:21): [True: 206k, False: 148k]
|
5036 | z->ob_digit[i] = a->ob_digit[i] | b->ob_digit[i]; |
5037 | break; |
5038 | case '^': Branch (5038:5): [True: 61.0k, False: 1.33M]
|
5039 | for (i = 0; i < size_b; ++i1.09M ) Branch (5039:21): [True: 1.09M, False: 61.0k]
|
5040 | z->ob_digit[i] = a->ob_digit[i] ^ b->ob_digit[i]; |
5041 | break; |
5042 | default: Branch (5042:5): [True: 0, False: 1.40M]
|
5043 | Py_UNREACHABLE(); |
5044 | } |
5045 | |
5046 | /* Copy any remaining digits of a, inverting if necessary. */ |
5047 | if (op == '^' && negb61.0k ) Branch (5047:9): [True: 61.0k, False: 1.33M]
Branch (5047:22): [True: 26.0k, False: 34.9k]
|
5048 | for (; 26.0k i < size_z; ++i240k ) Branch (5048:16): [True: 240k, False: 26.0k]
|
5049 | z->ob_digit[i] = a->ob_digit[i] ^ PyLong_MASK; |
5050 | else if (i < size_z) Branch (5050:14): [True: 191k, False: 1.18M]
|
5051 | memcpy(&z->ob_digit[i], &a->ob_digit[i], |
5052 | (size_z-i)*sizeof(digit)); |
5053 | |
5054 | /* Complement result if negative. */ |
5055 | if (negz) { Branch (5055:9): [True: 49.8k, False: 1.35M]
|
5056 | Py_SET_SIZE(z, -(Py_SIZE(z))); |
5057 | z->ob_digit[size_z] = PyLong_MASK; |
5058 | v_complement(z->ob_digit, z->ob_digit, size_z+1); |
5059 | } |
5060 | |
5061 | Py_DECREF(a); |
5062 | Py_DECREF(b); |
5063 | return (PyObject *)maybe_small_long(long_normalize(z)); |
5064 | } |
5065 | |
5066 | static PyObject * |
5067 | long_and(PyObject *a, PyObject *b) |
5068 | { |
5069 | CHECK_BINOP(a, b); |
5070 | PyLongObject *x = (PyLongObject*)a; |
5071 | PyLongObject *y = (PyLongObject*)b; |
5072 | if (IS_MEDIUM_VALUE(x) && IS_MEDIUM_VALUE3.96M (y)) { |
5073 | return _PyLong_FromSTwoDigits(medium_value(x) & medium_value(y)); |
5074 | } |
5075 | return long_bitwise(x, '&', y); |
5076 | } |
5077 | |
5078 | static PyObject * |
5079 | long_xor(PyObject *a, PyObject *b) |
5080 | { |
5081 | CHECK_BINOP(a, b); |
5082 | PyLongObject *x = (PyLongObject*)a; |
5083 | PyLongObject *y = (PyLongObject*)b; |
5084 | if (IS_MEDIUM_VALUE(x) && IS_MEDIUM_VALUE131k (y)) { |
5085 | return _PyLong_FromSTwoDigits(medium_value(x) ^ medium_value(y)); |
5086 | } |
5087 | return long_bitwise(x, '^', y); |
5088 | } |
5089 | |
5090 | static PyObject * |
5091 | long_or(PyObject *a, PyObject *b) |
5092 | { |
5093 | CHECK_BINOP(a, b); |
5094 | PyLongObject *x = (PyLongObject*)a; |
5095 | PyLongObject *y = (PyLongObject*)b; |
5096 | if (IS_MEDIUM_VALUE(x) && IS_MEDIUM_VALUE1.95M (y)) { |
5097 | return _PyLong_FromSTwoDigits(medium_value(x) | medium_value(y)); |
5098 | } |
5099 | return long_bitwise(x, '|', y); |
5100 | } |
5101 | |
5102 | static PyObject * |
5103 | long_long(PyObject *v) |
5104 | { |
5105 | if (PyLong_CheckExact(v)) |
5106 | Py_INCREF(v); |
5107 | else |
5108 | v = _PyLong_Copy((PyLongObject *)v); |
5109 | return v; |
5110 | } |
5111 | |
5112 | PyObject * |
5113 | _PyLong_GCD(PyObject *aarg, PyObject *barg) |
5114 | { |
5115 | PyLongObject *a, *b, *c = NULL, *d = NULL, *r; |
5116 | stwodigits x, y, q, s, t, c_carry, d_carry; |
5117 | stwodigits A, B, C, D, T; |
5118 | int nbits, k; |
5119 | Py_ssize_t size_a, size_b, alloc_a, alloc_b; |
5120 | digit *a_digit, *b_digit, *c_digit, *d_digit, *a_end, *b_end; |
5121 | |
5122 | a = (PyLongObject *)aarg; |
5123 | b = (PyLongObject *)barg; |
5124 | size_a = Py_SIZE(a); |
5125 | size_b = Py_SIZE(b); |
5126 | if (-2 <= size_a && size_a <= 2500k && -2 <= size_b390k && size_b <= 2390k ) { Branch (5126:9): [True: 500k, False: 40]
Branch (5126:25): [True: 390k, False: 109k]
Branch (5126:40): [True: 390k, False: 0]
Branch (5126:56): [True: 320k, False: 70.0k]
|
5127 | Py_INCREF(a); |
5128 | Py_INCREF(b); |
5129 | goto simple; |
5130 | } |
5131 | |
5132 | /* Initial reduction: make sure that 0 <= b <= a. */ |
5133 | a = (PyLongObject *)long_abs(a); |
5134 | if (a == NULL) Branch (5134:9): [True: 0, False: 179k]
|
5135 | return NULL; |
5136 | b = (PyLongObject *)long_abs(b); |
5137 | if (b == NULL) { Branch (5137:9): [True: 0, False: 179k]
|
5138 | Py_DECREF(a); |
5139 | return NULL; |
5140 | } |
5141 | if (long_compare(a, b) < 0) { Branch (5141:9): [True: 106k, False: 73.4k]
|
5142 | r = a; |
5143 | a = b; |
5144 | b = r; |
5145 | } |
5146 | /* We now own references to a and b */ |
5147 | |
5148 | alloc_a = Py_SIZE(a); |
5149 | alloc_b = Py_SIZE(b); |
5150 | /* reduce until a fits into 2 digits */ |
5151 | while ((size_a = Py_SIZE(a)) > 2) { Branch (5151:12): [True: 279k, False: 115k]
|
5152 | nbits = bit_length_digit(a->ob_digit[size_a-1]); |
5153 | /* extract top 2*PyLong_SHIFT bits of a into x, along with |
5154 | corresponding bits of b into y */ |
5155 | size_b = Py_SIZE(b); |
5156 | assert(size_b <= size_a); |
5157 | if (size_b == 0) { Branch (5157:13): [True: 64.3k, False: 214k]
|
5158 | if (size_a < alloc_a) { Branch (5158:17): [True: 16, False: 64.3k]
|
5159 | r = (PyLongObject *)_PyLong_Copy(a); |
5160 | Py_DECREF(a); |
5161 | } |
5162 | else |
5163 | r = a; |
5164 | Py_DECREF(b); |
5165 | Py_XDECREF(c); |
5166 | Py_XDECREF(d); |
5167 | return (PyObject *)r; |
5168 | } |
5169 | x = (((twodigits)a->ob_digit[size_a-1] << (2*PyLong_SHIFT-nbits)) | |
5170 | ((twodigits)a->ob_digit[size_a-2] << (PyLong_SHIFT-nbits)) | |
5171 | (a->ob_digit[size_a-3] >> nbits)); |
5172 | |
5173 | y = ((size_b >= size_a - 2 ? b->ob_digit[size_a-3] >> nbits185k : 029.3k ) | Branch (5173:15): [True: 185k, False: 29.3k]
|
5174 | (size_b >= size_a - 1 ? (twodigits)b->ob_digit[size_a-2] << (152k PyLong_SHIFT152k -nbits) : 062.5k ) | Branch (5174:15): [True: 152k, False: 62.5k]
|
5175 | (size_b >= size_a ? (twodigits)b->ob_digit[size_a-1] << (2*99.9k PyLong_SHIFT99.9k -nbits) : 0114k )); Branch (5175:15): [True: 99.9k, False: 114k]
|
5176 | |
5177 | /* inner loop of Lehmer's algorithm; A, B, C, D never grow |
5178 | larger than PyLong_MASK during the algorithm. */ |
5179 | A = 1; B = 0; C = 0; D = 1; |
5180 | for (k=0;; k++908k ) { |
5181 | if (y-C == 0) Branch (5181:17): [True: 42.8k, False: 1.08M]
|
5182 | break; |
5183 | q = (x+(A-1))/(y-C); |
5184 | s = B+q*D; |
5185 | t = x-q*y; |
5186 | if (s > t) Branch (5186:17): [True: 172k, False: 908k]
|
5187 | break; |
5188 | x = y; y = t; |
5189 | t = A+q*C; A = D; B = C; C = s; D = t; |
5190 | } |
5191 | |
5192 | if (k == 0) { Branch (5192:13): [True: 140k, False: 74.4k]
|
5193 | /* no progress; do a Euclidean step */ |
5194 | if (l_mod(a, b, &r) < 0) Branch (5194:17): [True: 0, False: 140k]
|
5195 | goto error; |
5196 | Py_DECREF(a); |
5197 | a = b; |
5198 | b = r; |
5199 | alloc_a = alloc_b; |
5200 | alloc_b = Py_SIZE(b); |
5201 | continue; |
5202 | } |
5203 | |
5204 | /* |
5205 | a, b = A*b-B*a, D*a-C*b if k is odd |
5206 | a, b = A*a-B*b, D*b-C*a if k is even |
5207 | */ |
5208 | if (k&1) { Branch (5208:13): [True: 37.5k, False: 36.8k]
|
5209 | T = -A; A = -B; B = T; |
5210 | T = -C; C = -D; D = T; |
5211 | } |
5212 | if (c != NULL) { Branch (5212:13): [True: 24.4k, False: 49.9k]
|
5213 | Py_SET_SIZE(c, size_a); |
5214 | } |
5215 | else if (Py_REFCNT(a) == 1) { Branch (5215:18): [True: 16, False: 49.9k]
|
5216 | Py_INCREF(a); |
5217 | c = a; |
5218 | } |
5219 | else { |
5220 | alloc_a = size_a; |
5221 | c = _PyLong_New(size_a); |
5222 | if (c == NULL) Branch (5222:17): [True: 0, False: 49.9k]
|
5223 | goto error; |
5224 | } |
5225 | |
5226 | if (d != NULL) { Branch (5226:13): [True: 24.4k, False: 49.9k]
|
5227 | Py_SET_SIZE(d, size_a); |
5228 | } |
5229 | else if (Py_REFCNT(b) == 1 && size_a <= alloc_b11.7k ) { Branch (5229:18): [True: 11.7k, False: 38.2k]
Branch (5229:39): [True: 11.1k, False: 621]
|
5230 | Py_INCREF(b); |
5231 | d = b; |
5232 | Py_SET_SIZE(d, size_a); |
5233 | } |
5234 | else { |
5235 | alloc_b = size_a; |
5236 | d = _PyLong_New(size_a); |
5237 | if (d == NULL) Branch (5237:17): [True: 0, False: 38.8k]
|
5238 | goto error; |
5239 | } |
5240 | a_end = a->ob_digit + size_a; |
5241 | b_end = b->ob_digit + size_b; |
5242 | |
5243 | /* compute new a and new b in parallel */ |
5244 | a_digit = a->ob_digit; |
5245 | b_digit = b->ob_digit; |
5246 | c_digit = c->ob_digit; |
5247 | d_digit = d->ob_digit; |
5248 | c_carry = 0; |
5249 | d_carry = 0; |
5250 | while (b_digit < b_end) { Branch (5250:16): [True: 220k, False: 74.4k]
|
5251 | c_carry += (A * *a_digit) - (B * *b_digit); |
5252 | d_carry += (D * *b_digit++) - (C * *a_digit++); |
5253 | *c_digit++ = (digit)(c_carry & PyLong_MASK); |
5254 | *d_digit++ = (digit)(d_carry & PyLong_MASK); |
5255 | c_carry >>= PyLong_SHIFT; |
5256 | d_carry >>= PyLong_SHIFT; |
5257 | } |
5258 | while (a_digit < a_end) { Branch (5258:16): [True: 35.5k, False: 74.4k]
|
5259 | c_carry += A * *a_digit; |
5260 | d_carry -= C * *a_digit++; |
5261 | *c_digit++ = (digit)(c_carry & PyLong_MASK); |
5262 | *d_digit++ = (digit)(d_carry & PyLong_MASK); |
5263 | c_carry >>= PyLong_SHIFT; |
5264 | d_carry >>= PyLong_SHIFT; |
5265 | } |
5266 | assert(c_carry == 0); |
5267 | assert(d_carry == 0); |
5268 | |
5269 | Py_INCREF(c); |
5270 | Py_INCREF(d); |
5271 | Py_DECREF(a); |
5272 | Py_DECREF(b); |
5273 | a = long_normalize(c); |
5274 | b = long_normalize(d); |
5275 | } |
5276 | Py_XDECREF(c); |
5277 | Py_XDECREF(d); |
5278 | |
5279 | simple: |
5280 | assert(Py_REFCNT(a) > 0); |
5281 | assert(Py_REFCNT(b) > 0); |
5282 | /* Issue #24999: use two shifts instead of ">> 2*PyLong_SHIFT" to avoid |
5283 | undefined behaviour when LONG_MAX type is smaller than 60 bits */ |
5284 | #if LONG_MAX >> PyLong_SHIFT >> PyLong_SHIFT |
5285 | /* a fits into a long, so b must too */ |
5286 | x = PyLong_AsLong((PyObject *)a); |
5287 | y = PyLong_AsLong((PyObject *)b); |
5288 | #elif LLONG_MAX >> PyLong_SHIFT >> PyLong_SHIFT |
5289 | x = PyLong_AsLongLong((PyObject *)a); |
5290 | y = PyLong_AsLongLong((PyObject *)b); |
5291 | #else |
5292 | # error "_PyLong_GCD" |
5293 | #endif |
5294 | x = Py_ABS(x); |
5295 | y = Py_ABS(y); |
5296 | Py_DECREF(a); |
5297 | Py_DECREF(b); |
5298 | |
5299 | /* usual Euclidean algorithm for longs */ |
5300 | while (y != 0) { Branch (5300:12): [True: 4.37M, False: 435k]
|
5301 | t = y; |
5302 | y = x % y; |
5303 | x = t; |
5304 | } |
5305 | #if LONG_MAX >> PyLong_SHIFT >> PyLong_SHIFT |
5306 | return PyLong_FromLong(x); |
5307 | #elif LLONG_MAX >> PyLong_SHIFT >> PyLong_SHIFT |
5308 | return PyLong_FromLongLong(x); |
5309 | #else |
5310 | # error "_PyLong_GCD" |
5311 | #endif |
5312 | |
5313 | error: |
5314 | Py_DECREF(a); |
5315 | Py_DECREF(b); |
5316 | Py_XDECREF(c); |
5317 | Py_XDECREF(d); |
5318 | return NULL; |
5319 | } |
5320 | |
5321 | static PyObject * |
5322 | long_float(PyObject *v) |
5323 | { |
5324 | double result; |
5325 | result = PyLong_AsDouble(v); |
5326 | if (result == -1.0 && PyErr_Occurred()65.6k ) Branch (5326:9): [True: 65.6k, False: 183k]
Branch (5326:27): [True: 52, False: 65.6k]
|
5327 | return NULL; |
5328 | return PyFloat_FromDouble(result); |
5329 | } |
5330 | |
5331 | static PyObject * |
5332 | long_subtype_new(PyTypeObject *type, PyObject *x, PyObject *obase); |
5333 | |
5334 | /*[clinic input] |
5335 | @classmethod |
5336 | int.__new__ as long_new |
5337 | x: object(c_default="NULL") = 0 |
5338 | / |
5339 | base as obase: object(c_default="NULL") = 10 |
5340 | [clinic start generated code]*/ |
5341 | |
5342 | static PyObject * |
5343 | long_new_impl(PyTypeObject *type, PyObject *x, PyObject *obase) |
5344 | /*[clinic end generated code: output=e47cfe777ab0f24c input=81c98f418af9eb6f]*/ |
5345 | { |
5346 | Py_ssize_t base; |
5347 | |
5348 | if (type != &PyLong_Type) Branch (5348:9): [True: 50.6k, False: 5.36M]
|
5349 | return long_subtype_new(type, x, obase); /* Wimp out */ |
5350 | if (x == NULL) { Branch (5350:9): [True: 21.0k, False: 5.34M]
|
5351 | if (obase != NULL) { Branch (5351:13): [True: 2, False: 21.0k]
|
5352 | PyErr_SetString(PyExc_TypeError, |
5353 | "int() missing string argument"); |
5354 | return NULL; |
5355 | } |
5356 | return PyLong_FromLong(0L); |
5357 | } |
5358 | if (obase == NULL) Branch (5358:9): [True: 5.10M, False: 237k]
|
5359 | return PyNumber_Long(x); |
5360 | |
5361 | base = PyNumber_AsSsize_t(obase, NULL); |
5362 | if (base == -1 && PyErr_Occurred()2 ) Branch (5362:9): [True: 2, False: 237k]
Branch (5362:23): [True: 2, False: 0]
|
5363 | return NULL; |
5364 | if ((base != 0 && base < 2188k ) || base > 36237k ) { Branch (5364:10): [True: 188k, False: 48.5k]
Branch (5364:23): [True: 11, False: 188k]
Branch (5364:36): [True: 9, False: 237k]
|
5365 | PyErr_SetString(PyExc_ValueError, |
5366 | "int() base must be >= 2 and <= 36, or 0"); |
5367 | return NULL; |
5368 | } |
5369 | |
5370 | if (PyUnicode_Check(x)) |
5371 | return PyLong_FromUnicodeObject(x, (int)base); |
5372 | else if (PyByteArray_Check(x) || PyBytes_Check47.0k (x)) { |
5373 | const char *string; |
5374 | if (PyByteArray_Check(x)) |
5375 | string = PyByteArray_AS_STRING(x); |
5376 | else |
5377 | string = PyBytes_AS_STRING(x); |
5378 | return _PyLong_FromBytes(string, Py_SIZE(x), (int)base); |
5379 | } |
5380 | else { |
5381 | PyErr_SetString(PyExc_TypeError, |
5382 | "int() can't convert non-string with explicit base"); |
5383 | return NULL; |
5384 | } |
5385 | } |
5386 | |
5387 | /* Wimpy, slow approach to tp_new calls for subtypes of int: |
5388 | first create a regular int from whatever arguments we got, |
5389 | then allocate a subtype instance and initialize it from |
5390 | the regular int. The regular int is then thrown away. |
5391 | */ |
5392 | static PyObject * |
5393 | long_subtype_new(PyTypeObject *type, PyObject *x, PyObject *obase) |
5394 | { |
5395 | PyLongObject *tmp, *newobj; |
5396 | Py_ssize_t i, n; |
5397 | |
5398 | assert(PyType_IsSubtype(type, &PyLong_Type)); |
5399 | tmp = (PyLongObject *)long_new_impl(&PyLong_Type, x, obase); |
5400 | if (tmp == NULL) Branch (5400:9): [True: 0, False: 50.6k]
|
5401 | return NULL; |
5402 | assert(PyLong_Check(tmp)); |
5403 | n = Py_SIZE(tmp); |
5404 | if (n < 0) Branch (5404:9): [True: 7, False: 50.6k]
|
5405 | n = -n; |
5406 | newobj = (PyLongObject *)type->tp_alloc(type, n); |
5407 | if (newobj == NULL) { Branch (5407:9): [True: 0, False: 50.6k]
|
5408 | Py_DECREF(tmp); |
5409 | return NULL; |
5410 | } |
5411 | assert(PyLong_Check(newobj)); |
5412 | Py_SET_SIZE(newobj, Py_SIZE(tmp)); |
5413 | for (i = 0; i < n; i++49.3k ) { Branch (5413:17): [True: 49.3k, False: 50.6k]
|
5414 | newobj->ob_digit[i] = tmp->ob_digit[i]; |
5415 | } |
5416 | Py_DECREF(tmp); |
5417 | return (PyObject *)newobj; |
5418 | } |
5419 | |
5420 | /*[clinic input] |
5421 | int.__getnewargs__ |
5422 | [clinic start generated code]*/ |
5423 | |
5424 | static PyObject * |
5425 | int___getnewargs___impl(PyObject *self) |
5426 | /*[clinic end generated code: output=839a49de3f00b61b input=5904770ab1fb8c75]*/ |
5427 | { |
5428 | return Py_BuildValue("(N)", _PyLong_Copy((PyLongObject *)self)); |
5429 | } |
5430 | |
5431 | static PyObject * |
5432 | long_get0(PyObject *Py_UNUSED(self), void *Py_UNUSED(context)) |
5433 | { |
5434 | return PyLong_FromLong(0L); |
5435 | } |
5436 | |
5437 | static PyObject * |
5438 | long_get1(PyObject *Py_UNUSED(self), void *Py_UNUSED(ignored)) |
5439 | { |
5440 | return PyLong_FromLong(1L); |
5441 | } |
5442 | |
5443 | /*[clinic input] |
5444 | int.__format__ |
5445 | |
5446 | format_spec: unicode |
5447 | / |
5448 | [clinic start generated code]*/ |
5449 | |
5450 | static PyObject * |
5451 | int___format___impl(PyObject *self, PyObject *format_spec) |
5452 | /*[clinic end generated code: output=b4929dee9ae18689 input=e31944a9b3e428b7]*/ |
5453 | { |
5454 | _PyUnicodeWriter writer; |
5455 | int ret; |
5456 | |
5457 | _PyUnicodeWriter_Init(&writer); |
5458 | ret = _PyLong_FormatAdvancedWriter( |
5459 | &writer, |
5460 | self, |
5461 | format_spec, 0, PyUnicode_GET_LENGTH(format_spec)); |
5462 | if (ret == -1) { Branch (5462:9): [True: 350, False: 1.76k]
|
5463 | _PyUnicodeWriter_Dealloc(&writer); |
5464 | return NULL; |
5465 | } |
5466 | return _PyUnicodeWriter_Finish(&writer); |
5467 | } |
5468 | |
5469 | /* Return a pair (q, r) such that a = b * q + r, and |
5470 | abs(r) <= abs(b)/2, with equality possible only if q is even. |
5471 | In other words, q == a / b, rounded to the nearest integer using |
5472 | round-half-to-even. */ |
5473 | |
5474 | PyObject * |
5475 | _PyLong_DivmodNear(PyObject *a, PyObject *b) |
5476 | { |
5477 | PyLongObject *quo = NULL, *rem = NULL; |
5478 | PyObject *twice_rem, *result, *temp; |
5479 | int quo_is_odd, quo_is_neg; |
5480 | Py_ssize_t cmp; |
5481 | |
5482 | /* Equivalent Python code: |
5483 | |
5484 | def divmod_near(a, b): |
5485 | q, r = divmod(a, b) |
5486 | # round up if either r / b > 0.5, or r / b == 0.5 and q is odd. |
5487 | # The expression r / b > 0.5 is equivalent to 2 * r > b if b is |
5488 | # positive, 2 * r < b if b negative. |
5489 | greater_than_half = 2*r > b if b > 0 else 2*r < b |
5490 | exactly_half = 2*r == b |
5491 | if greater_than_half or exactly_half and q % 2 == 1: |
5492 | q += 1 |
5493 | r -= b |
5494 | return q, r |
5495 | |
5496 | */ |
5497 | if (!PyLong_Check(a) || !PyLong_Check(b)) { Branch (5497:9): [True: 0, False: 1.56k]
Branch (5497:29): [True: 0, False: 1.56k]
|
5498 | PyErr_SetString(PyExc_TypeError, |
5499 | "non-integer arguments in division"); |
5500 | return NULL; |
5501 | } |
5502 | |
5503 | /* Do a and b have different signs? If so, quotient is negative. */ |
5504 | quo_is_neg = (Py_SIZE(a) < 0) != (Py_SIZE(b) < 0); |
5505 | |
5506 | if (long_divrem((PyLongObject*)a, (PyLongObject*)b, &quo, &rem) < 0) Branch (5506:9): [True: 2, False: 1.56k]
|
5507 | goto error; |
5508 | |
5509 | /* compare twice the remainder with the divisor, to see |
5510 | if we need to adjust the quotient and remainder */ |
5511 | PyObject *one = _PyLong_GetOne(); // borrowed reference |
5512 | twice_rem = long_lshift((PyObject *)rem, one); |
5513 | if (twice_rem == NULL) Branch (5513:9): [True: 0, False: 1.56k]
|
5514 | goto error; |
5515 | if (quo_is_neg) { Branch (5515:9): [True: 555, False: 1.01k]
|
5516 | temp = long_neg((PyLongObject*)twice_rem); |
5517 | Py_DECREF(twice_rem); |
5518 | twice_rem = temp; |
5519 | if (twice_rem == NULL) Branch (5519:13): [True: 0, False: 555]
|
5520 | goto error; |
5521 | } |
5522 | cmp = long_compare((PyLongObject *)twice_rem, (PyLongObject *)b); |
5523 | Py_DECREF(twice_rem); |
5524 | |
5525 | quo_is_odd = Py_SIZE(quo) != 0 && ((quo->ob_digit[0] & 1) != 0)1.52k ; Branch (5525:18): [True: 1.52k, False: 44]
Branch (5525:39): [True: 562, False: 960]
|
5526 | if ((Py_SIZE(b) < 0 ? cmp < 024 : cmp > 01.54k ) || (1.03k cmp == 01.03k && quo_is_odd128 )) { Branch (5526:9): [True: 528, False: 1.03k]
Branch (5526:10): [True: 24, False: 1.54k]
Branch (5526:50): [True: 128, False: 910]
Branch (5526:62): [True: 63, False: 65]
|
5527 | /* fix up quotient */ |
5528 | if (quo_is_neg) Branch (5528:13): [True: 247, False: 344]
|
5529 | temp = long_sub(quo, (PyLongObject *)one); |
5530 | else |
5531 | temp = long_add(quo, (PyLongObject *)one); |
5532 | Py_DECREF(quo); |
5533 | quo = (PyLongObject *)temp; |
5534 | if (quo == NULL) Branch (5534:13): [True: 0, False: 591]
|
5535 | goto error; |
5536 | /* and remainder */ |
5537 | if (quo_is_neg) Branch (5537:13): [True: 247, False: 344]
|
5538 | temp = long_add(rem, (PyLongObject *)b); |
5539 | else |
5540 | temp = long_sub(rem, (PyLongObject *)b); |
5541 | Py_DECREF(rem); |
5542 | rem = (PyLongObject *)temp; |
5543 | if (rem == NULL) Branch (5543:13): [True: 0, False: 591]
|
5544 | goto error; |
5545 | } |
5546 | |
5547 | result = PyTuple_New(2); |
5548 | if (result == NULL) Branch (5548:9): [True: 0, False: 1.56k]
|
5549 | goto error; |
5550 | |
5551 | /* PyTuple_SET_ITEM steals references */ |
5552 | PyTuple_SET_ITEM(result, 0, (PyObject *)quo); |
5553 | PyTuple_SET_ITEM(result, 1, (PyObject *)rem); |
5554 | return result; |
5555 | |
5556 | error: |
5557 | Py_XDECREF(quo); |
5558 | Py_XDECREF(rem); |
5559 | return NULL; |
5560 | } |
5561 | |
5562 | /*[clinic input] |
5563 | int.__round__ |
5564 | |
5565 | ndigits as o_ndigits: object = NULL |
5566 | / |
5567 | |
5568 | Rounding an Integral returns itself. |
5569 | |
5570 | Rounding with an ndigits argument also returns an integer. |
5571 | [clinic start generated code]*/ |
5572 | |
5573 | static PyObject * |
5574 | int___round___impl(PyObject *self, PyObject *o_ndigits) |
5575 | /*[clinic end generated code: output=954fda6b18875998 input=1614cf23ec9e18c3]*/ |
5576 | { |
5577 | PyObject *temp, *result, *ndigits; |
5578 | |
5579 | /* To round an integer m to the nearest 10**n (n positive), we make use of |
5580 | * the divmod_near operation, defined by: |
5581 | * |
5582 | * divmod_near(a, b) = (q, r) |
5583 | * |
5584 | * where q is the nearest integer to the quotient a / b (the |
5585 | * nearest even integer in the case of a tie) and r == a - q * b. |
5586 | * Hence q * b = a - r is the nearest multiple of b to a, |
5587 | * preferring even multiples in the case of a tie. |
5588 | * |
5589 | * So the nearest multiple of 10**n to m is: |
5590 | * |
5591 | * m - divmod_near(m, 10**n)[1]. |
5592 | */ |
5593 | if (o_ndigits == NULL) Branch (5593:9): [True: 168, False: 1.67k]
|
5594 | return long_long(self); |
5595 | |
5596 | ndigits = _PyNumber_Index(o_ndigits); |
5597 | if (ndigits == NULL) Branch (5597:9): [True: 3, False: 1.67k]
|
5598 | return NULL; |
5599 | |
5600 | /* if ndigits >= 0 then no rounding is necessary; return self unchanged */ |
5601 | if (Py_SIZE(ndigits) >= 0) { Branch (5601:9): [True: 512, False: 1.16k]
|
5602 | Py_DECREF(ndigits); |
5603 | return long_long(self); |
5604 | } |
5605 | |
5606 | /* result = self - divmod_near(self, 10 ** -ndigits)[1] */ |
5607 | temp = long_neg((PyLongObject*)ndigits); |
5608 | Py_DECREF(ndigits); |
5609 | ndigits = temp; |
5610 | if (ndigits == NULL) Branch (5610:9): [True: 0, False: 1.16k]
|
5611 | return NULL; |
5612 | |
5613 | result = PyLong_FromLong(10L); |
5614 | if (result == NULL) { Branch (5614:9): [True: 0, False: 1.16k]
|
5615 | Py_DECREF(ndigits); |
5616 | return NULL; |
5617 | } |
5618 | |
5619 | temp = long_pow(result, ndigits, Py_None); |
5620 | Py_DECREF(ndigits); |
5621 | Py_DECREF(result); |
5622 | result = temp; |
5623 | if (result == NULL) Branch (5623:9): [True: 0, False: 1.16k]
|
5624 | return NULL; |
5625 | |
5626 | temp = _PyLong_DivmodNear(self, result); |
5627 | Py_DECREF(result); |
5628 | result = temp; |
5629 | if (result == NULL) Branch (5629:9): [True: 0, False: 1.16k]
|
5630 | return NULL; |
5631 | |
5632 | temp = long_sub((PyLongObject *)self, |
5633 | (PyLongObject *)PyTuple_GET_ITEM(result, 1)); |
5634 | Py_DECREF(result); |
5635 | result = temp; |
5636 | |
5637 | return result; |
5638 | } |
5639 | |
5640 | /*[clinic input] |
5641 | int.__sizeof__ -> Py_ssize_t |
5642 | |
5643 | Returns size in memory, in bytes. |
5644 | [clinic start generated code]*/ |
5645 | |
5646 | static Py_ssize_t |
5647 | int___sizeof___impl(PyObject *self) |
5648 | /*[clinic end generated code: output=3303f008eaa6a0a5 input=9b51620c76fc4507]*/ |
5649 | { |
5650 | Py_ssize_t res; |
5651 | |
5652 | res = offsetof(PyLongObject, ob_digit) + Py_ABS(Py_SIZE(self))*sizeof(digit); |
5653 | return res; |
5654 | } |
5655 | |
5656 | /*[clinic input] |
5657 | int.bit_length |
5658 | |
5659 | Number of bits necessary to represent self in binary. |
5660 | |
5661 | >>> bin(37) |
5662 | '0b100101' |
5663 | >>> (37).bit_length() |
5664 | 6 |
5665 | [clinic start generated code]*/ |
5666 | |
5667 | static PyObject * |
5668 | int_bit_length_impl(PyObject *self) |
5669 | /*[clinic end generated code: output=fc1977c9353d6a59 input=e4eb7a587e849a32]*/ |
5670 | { |
5671 | PyLongObject *result, *x, *y; |
5672 | Py_ssize_t ndigits; |
5673 | int msd_bits; |
5674 | digit msd; |
5675 | |
5676 | assert(self != NULL); |
5677 | assert(PyLong_Check(self)); |
5678 | |
5679 | ndigits = Py_ABS(Py_SIZE(self)); |
5680 | if (ndigits == 0) Branch (5680:9): [True: 6.14k, False: 5.04M]
|
5681 | return PyLong_FromLong(0); |
5682 | |
5683 | msd = ((PyLongObject *)self)->ob_digit[ndigits-1]; |
5684 | msd_bits = bit_length_digit(msd); |
5685 | |
5686 | if (ndigits <= PY_SSIZE_T_MAX/PyLong_SHIFT) Branch (5686:9): [True: 5.04M, False: 0]
|
5687 | return PyLong_FromSsize_t((ndigits-1)*PyLong_SHIFT + msd_bits); |
5688 | |
5689 | /* expression above may overflow; use Python integers instead */ |
5690 | result = (PyLongObject *)PyLong_FromSsize_t(ndigits - 1); |
5691 | if (result == NULL) Branch (5691:9): [True: 0, False: 0]
|
5692 | return NULL; |
5693 | x = (PyLongObject *)PyLong_FromLong(PyLong_SHIFT); |
5694 | if (x == NULL) Branch (5694:9): [True: 0, False: 0]
|
5695 | goto error; |
5696 | y = (PyLongObject *)long_mul(result, x); |
5697 | Py_DECREF(x); |
5698 | if (y == NULL) Branch (5698:9): [True: 0, False: 0]
|
5699 | goto error; |
5700 | Py_DECREF(result); |
5701 | result = y; |
5702 |
|
5703 | x = (PyLongObject *)PyLong_FromLong((long)msd_bits); |
5704 | if (x == NULL) Branch (5704:9): [True: 0, False: 0]
|
5705 | goto error; |
5706 | y = (PyLongObject *)long_add(result, x); |
5707 | Py_DECREF(x); |
5708 | if (y == NULL) Branch (5708:9): [True: 0, False: 0]
|
5709 | goto error; |
5710 | Py_DECREF(result); |
5711 | result = y; |
5712 |
|
5713 | return (PyObject *)result; |
5714 | |
5715 | error: |
5716 | Py_DECREF(result); |
5717 | return NULL; |
5718 | } |
5719 | |
5720 | static int |
5721 | popcount_digit(digit d) |
5722 | { |
5723 | // digit can be larger than uint32_t, but only PyLong_SHIFT bits |
5724 | // of it will be ever used. |
5725 | static_assert(PyLong_SHIFT <= 32, "digit is larger than uint32_t"); |
5726 | return _Py_popcount32((uint32_t)d); |
5727 | } |
5728 | |
5729 | /*[clinic input] |
5730 | int.bit_count |
5731 | |
5732 | Number of ones in the binary representation of the absolute value of self. |
5733 | |
5734 | Also known as the population count. |
5735 | |
5736 | >>> bin(13) |
5737 | '0b1101' |
5738 | >>> (13).bit_count() |
5739 | 3 |
5740 | [clinic start generated code]*/ |
5741 | |
5742 | static PyObject * |
5743 | int_bit_count_impl(PyObject *self) |
5744 | /*[clinic end generated code: output=2e571970daf1e5c3 input=7e0adef8e8ccdf2e]*/ |
5745 | { |
5746 | assert(self != NULL); |
5747 | assert(PyLong_Check(self)); |
5748 | |
5749 | PyLongObject *z = (PyLongObject *)self; |
5750 | Py_ssize_t ndigits = Py_ABS(Py_SIZE(z)); |
5751 | Py_ssize_t bit_count = 0; |
5752 | |
5753 | /* Each digit has up to PyLong_SHIFT ones, so the accumulated bit count |
5754 | from the first PY_SSIZE_T_MAX/PyLong_SHIFT digits can't overflow a |
5755 | Py_ssize_t. */ |
5756 | Py_ssize_t ndigits_fast = Py_MIN(ndigits, PY_SSIZE_T_MAX/PyLong_SHIFT); |
5757 | for (Py_ssize_t i = 0; i < ndigits_fast; i++176k ) { Branch (5757:28): [True: 176k, False: 2.05k]
|
5758 | bit_count += popcount_digit(z->ob_digit[i]); |
5759 | } |
5760 | |
5761 | PyObject *result = PyLong_FromSsize_t(bit_count); |
5762 | if (result == NULL) { Branch (5762:9): [True: 0, False: 2.05k]
|
5763 | return NULL; |
5764 | } |
5765 | |
5766 | /* Use Python integers if bit_count would overflow. */ |
5767 | for (Py_ssize_t i = ndigits_fast; i < ndigits; i++0 ) { Branch (5767:39): [True: 0, False: 2.05k]
|
5768 | PyObject *x = PyLong_FromLong(popcount_digit(z->ob_digit[i])); |
5769 | if (x == NULL) { Branch (5769:13): [True: 0, False: 0]
|
5770 | goto error; |
5771 | } |
5772 | PyObject *y = long_add((PyLongObject *)result, (PyLongObject *)x); |
5773 | Py_DECREF(x); |
5774 | if (y == NULL) { Branch (5774:13): [True: 0, False: 0]
|
5775 | goto error; |
5776 | } |
5777 | Py_DECREF(result); |
5778 | result = y; |
5779 | } |
5780 | |
5781 | return result; |
5782 | |
5783 | error: |
5784 | Py_DECREF(result); |
5785 | return NULL; |
5786 | } |
5787 | |
5788 | /*[clinic input] |
5789 | int.as_integer_ratio |
5790 | |
5791 | Return integer ratio. |
5792 | |
5793 | Return a pair of integers, whose ratio is exactly equal to the original int |
5794 | and with a positive denominator. |
5795 | |
5796 | >>> (10).as_integer_ratio() |
5797 | (10, 1) |
5798 | >>> (-10).as_integer_ratio() |
5799 | (-10, 1) |
5800 | >>> (0).as_integer_ratio() |
5801 | (0, 1) |
5802 | [clinic start generated code]*/ |
5803 | |
5804 | static PyObject * |
5805 | int_as_integer_ratio_impl(PyObject *self) |
5806 | /*[clinic end generated code: output=e60803ae1cc8621a input=55ce3058e15de393]*/ |
5807 | { |
5808 | PyObject *ratio_tuple; |
5809 | PyObject *numerator = long_long(self); |
5810 | if (numerator == NULL) { Branch (5810:9): [True: 0, False: 79.9k]
|
5811 | return NULL; |
5812 | } |
5813 | ratio_tuple = PyTuple_Pack(2, numerator, _PyLong_GetOne()); |
5814 | Py_DECREF(numerator); |
5815 | return ratio_tuple; |
5816 | } |
5817 | |
5818 | /*[clinic input] |
5819 | int.to_bytes |
5820 | |
5821 | length: Py_ssize_t = 1 |
5822 | Length of bytes object to use. An OverflowError is raised if the |
5823 | integer is not representable with the given number of bytes. Default |
5824 | is length 1. |
5825 | byteorder: unicode(c_default="NULL") = "big" |
5826 | The byte order used to represent the integer. If byteorder is 'big', |
5827 | the most significant byte is at the beginning of the byte array. If |
5828 | byteorder is 'little', the most significant byte is at the end of the |
5829 | byte array. To request the native byte order of the host system, use |
5830 | `sys.byteorder' as the byte order value. Default is to use 'big'. |
5831 | * |
5832 | signed as is_signed: bool = False |
5833 | Determines whether two's complement is used to represent the integer. |
5834 | If signed is False and a negative integer is given, an OverflowError |
5835 | is raised. |
5836 | |
5837 | Return an array of bytes representing an integer. |
5838 | [clinic start generated code]*/ |
5839 | |
5840 | static PyObject * |
5841 | int_to_bytes_impl(PyObject *self, Py_ssize_t length, PyObject *byteorder, |
5842 | int is_signed) |
5843 | /*[clinic end generated code: output=89c801df114050a3 input=d42ecfb545039d71]*/ |
5844 | { |
5845 | int little_endian; |
5846 | PyObject *bytes; |
5847 | |
5848 | if (byteorder == NULL) Branch (5848:9): [True: 967, False: 207k]
|
5849 | little_endian = 0; |
5850 | else if (_PyUnicode_Equal(byteorder, &_Py_ID(little))) Branch (5850:14): [True: 6.08k, False: 201k]
|
5851 | little_endian = 1; |
5852 | else if (_PyUnicode_Equal(byteorder, &_Py_ID(big))) Branch (5852:14): [True: 201k, False: 0]
|
5853 | little_endian = 0; |
5854 | else { |
5855 | PyErr_SetString(PyExc_ValueError, |
5856 | "byteorder must be either 'little' or 'big'"); |
5857 | return NULL; |
5858 | } |
5859 | |
5860 | if (length < 0) { Branch (5860:9): [True: 0, False: 208k]
|
5861 | PyErr_SetString(PyExc_ValueError, |
5862 | "length argument must be non-negative"); |
5863 | return NULL; |
5864 | } |
5865 | |
5866 | bytes = PyBytes_FromStringAndSize(NULL, length); |
5867 | if (bytes == NULL) Branch (5867:9): [True: 0, False: 208k]
|
5868 | return NULL; |
5869 | |
5870 | if (_PyLong_AsByteArray((PyLongObject *)self, Branch (5870:9): [True: 11, False: 208k]
|
5871 | (unsigned char *)PyBytes_AS_STRING(bytes), |
5872 | length, little_endian, is_signed) < 0) { |
5873 | Py_DECREF(bytes); |
5874 | return NULL; |
5875 | } |
5876 | |
5877 | return bytes; |
5878 | } |
5879 | |
5880 | /*[clinic input] |
5881 | @classmethod |
5882 | int.from_bytes |
5883 | |
5884 | bytes as bytes_obj: object |
5885 | Holds the array of bytes to convert. The argument must either |
5886 | support the buffer protocol or be an iterable object producing bytes. |
5887 | Bytes and bytearray are examples of built-in objects that support the |
5888 | buffer protocol. |
5889 | byteorder: unicode(c_default="NULL") = "big" |
5890 | The byte order used to represent the integer. If byteorder is 'big', |
5891 | the most significant byte is at the beginning of the byte array. If |
5892 | byteorder is 'little', the most significant byte is at the end of the |
5893 | byte array. To request the native byte order of the host system, use |
5894 | `sys.byteorder' as the byte order value. Default is to use 'big'. |
5895 | * |
5896 | signed as is_signed: bool = False |
5897 | Indicates whether two's complement is used to represent the integer. |
5898 | |
5899 | Return the integer represented by the given array of bytes. |
5900 | [clinic start generated code]*/ |
5901 | |
5902 | static PyObject * |
5903 | int_from_bytes_impl(PyTypeObject *type, PyObject *bytes_obj, |
5904 | PyObject *byteorder, int is_signed) |
5905 | /*[clinic end generated code: output=efc5d68e31f9314f input=33326dccdd655553]*/ |
5906 | { |
5907 | int little_endian; |
5908 | PyObject *long_obj, *bytes; |
5909 | |
5910 | if (byteorder == NULL) Branch (5910:9): [True: 165k, False: 23.3k]
|
5911 | little_endian = 0; |
5912 | else if (_PyUnicode_Equal(byteorder, &_Py_ID(little))) Branch (5912:14): [True: 21.7k, False: 1.57k]
|
5913 | little_endian = 1; |
5914 | else if (_PyUnicode_Equal(byteorder, &_Py_ID(big))) Branch (5914:14): [True: 1.57k, False: 2]
|
5915 | little_endian = 0; |
5916 | else { |
5917 | PyErr_SetString(PyExc_ValueError, |
5918 | "byteorder must be either 'little' or 'big'"); |
5919 | return NULL; |
5920 | } |
5921 | |
5922 | bytes = PyObject_Bytes(bytes_obj); |
5923 | if (bytes == NULL) Branch (5923:9): [True: 71, False: 188k]
|
5924 | return NULL; |
5925 | |
5926 | long_obj = _PyLong_FromByteArray( |
5927 | (unsigned char *)PyBytes_AS_STRING(bytes), Py_SIZE(bytes), |
5928 | little_endian, is_signed); |
5929 | Py_DECREF(bytes); |
5930 | |
5931 | if (long_obj != NULL && type != &PyLong_Type) { Branch (5931:9): [True: 188k, False: 0]
Branch (5931:29): [True: 14, False: 188k]
|
5932 | Py_SETREF(long_obj, PyObject_CallOneArg((PyObject *)type, long_obj)); |
5933 | } |
5934 | |
5935 | return long_obj; |
5936 | } |
5937 | |
5938 | static PyObject * |
5939 | long_long_meth(PyObject *self, PyObject *Py_UNUSED(ignored)) |
5940 | { |
5941 | return long_long(self); |
5942 | } |
5943 | |
5944 | static PyMethodDef long_methods[] = { |
5945 | {"conjugate", long_long_meth, METH_NOARGS, |
5946 | "Returns self, the complex conjugate of any int."}, |
5947 | INT_BIT_LENGTH_METHODDEF |
5948 | INT_BIT_COUNT_METHODDEF |
5949 | INT_TO_BYTES_METHODDEF |
5950 | INT_FROM_BYTES_METHODDEF |
5951 | INT_AS_INTEGER_RATIO_METHODDEF |
5952 | {"__trunc__", long_long_meth, METH_NOARGS, |
5953 | "Truncating an Integral returns itself."}, |
5954 | {"__floor__", long_long_meth, METH_NOARGS, |
5955 | "Flooring an Integral returns itself."}, |
5956 | {"__ceil__", long_long_meth, METH_NOARGS, |
5957 | "Ceiling of an Integral returns itself."}, |
5958 | INT___ROUND___METHODDEF |
5959 | INT___GETNEWARGS___METHODDEF |
5960 | INT___FORMAT___METHODDEF |
5961 | INT___SIZEOF___METHODDEF |
5962 | {NULL, NULL} /* sentinel */ |
5963 | }; |
5964 | |
5965 | static PyGetSetDef long_getset[] = { |
5966 | {"real", |
5967 | (getter)long_long_meth, (setter)NULL, |
5968 | "the real part of a complex number", |
5969 | NULL}, |
5970 | {"imag", |
5971 | long_get0, (setter)NULL, |
5972 | "the imaginary part of a complex number", |
5973 | NULL}, |
5974 | {"numerator", |
5975 | (getter)long_long_meth, (setter)NULL, |
5976 | "the numerator of a rational number in lowest terms", |
5977 | NULL}, |
5978 | {"denominator", |
5979 | long_get1, (setter)NULL, |
5980 | "the denominator of a rational number in lowest terms", |
5981 | NULL}, |
5982 | {NULL} /* Sentinel */ |
5983 | }; |
5984 | |
5985 | PyDoc_STRVAR(long_doc, |
5986 | "int([x]) -> integer\n\ |
5987 | int(x, base=10) -> integer\n\ |
5988 | \n\ |
5989 | Convert a number or string to an integer, or return 0 if no arguments\n\ |
5990 | are given. If x is a number, return x.__int__(). For floating point\n\ |
5991 | numbers, this truncates towards zero.\n\ |
5992 | \n\ |
5993 | If x is not a number or if base is given, then x must be a string,\n\ |
5994 | bytes, or bytearray instance representing an integer literal in the\n\ |
5995 | given base. The literal can be preceded by '+' or '-' and be surrounded\n\ |
5996 | by whitespace. The base defaults to 10. Valid bases are 0 and 2-36.\n\ |
5997 | Base 0 means to interpret the base from the string as an integer literal.\n\ |
5998 | >>> int('0b100', base=0)\n\ |
5999 | 4"); |
6000 | |
6001 | static PyNumberMethods long_as_number = { |
6002 | (binaryfunc)long_add, /*nb_add*/ |
6003 | (binaryfunc)long_sub, /*nb_subtract*/ |
6004 | (binaryfunc)long_mul, /*nb_multiply*/ |
6005 | long_mod, /*nb_remainder*/ |
6006 | long_divmod, /*nb_divmod*/ |
6007 | long_pow, /*nb_power*/ |
6008 | (unaryfunc)long_neg, /*nb_negative*/ |
6009 | long_long, /*tp_positive*/ |
6010 | (unaryfunc)long_abs, /*tp_absolute*/ |
6011 | (inquiry)long_bool, /*tp_bool*/ |
6012 | (unaryfunc)long_invert, /*nb_invert*/ |
6013 | long_lshift, /*nb_lshift*/ |
6014 | long_rshift, /*nb_rshift*/ |
6015 | long_and, /*nb_and*/ |
6016 | long_xor, /*nb_xor*/ |
6017 | long_or, /*nb_or*/ |
6018 | long_long, /*nb_int*/ |
6019 | 0, /*nb_reserved*/ |
6020 | long_float, /*nb_float*/ |
6021 | 0, /* nb_inplace_add */ |
6022 | 0, /* nb_inplace_subtract */ |
6023 | 0, /* nb_inplace_multiply */ |
6024 | 0, /* nb_inplace_remainder */ |
6025 | 0, /* nb_inplace_power */ |
6026 | 0, /* nb_inplace_lshift */ |
6027 | 0, /* nb_inplace_rshift */ |
6028 | 0, /* nb_inplace_and */ |
6029 | 0, /* nb_inplace_xor */ |
6030 | 0, /* nb_inplace_or */ |
6031 | long_div, /* nb_floor_divide */ |
6032 | long_true_divide, /* nb_true_divide */ |
6033 | 0, /* nb_inplace_floor_divide */ |
6034 | 0, /* nb_inplace_true_divide */ |
6035 | long_long, /* nb_index */ |
6036 | }; |
6037 | |
6038 | PyTypeObject PyLong_Type = { |
6039 | PyVarObject_HEAD_INIT(&PyType_Type, 0) |
6040 | "int", /* tp_name */ |
6041 | offsetof(PyLongObject, ob_digit), /* tp_basicsize */ |
6042 | sizeof(digit), /* tp_itemsize */ |
6043 | 0, /* tp_dealloc */ |
6044 | 0, /* tp_vectorcall_offset */ |
6045 | 0, /* tp_getattr */ |
6046 | 0, /* tp_setattr */ |
6047 | 0, /* tp_as_async */ |
6048 | long_to_decimal_string, /* tp_repr */ |
6049 | &long_as_number, /* tp_as_number */ |
6050 | 0, /* tp_as_sequence */ |
6051 | 0, /* tp_as_mapping */ |
6052 | (hashfunc)long_hash, /* tp_hash */ |
6053 | 0, /* tp_call */ |
6054 | 0, /* tp_str */ |
6055 | PyObject_GenericGetAttr, /* tp_getattro */ |
6056 | 0, /* tp_setattro */ |
6057 | 0, /* tp_as_buffer */ |
6058 | Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE | |
6059 | Py_TPFLAGS_LONG_SUBCLASS | |
6060 | _Py_TPFLAGS_MATCH_SELF, /* tp_flags */ |
6061 | long_doc, /* tp_doc */ |
6062 | 0, /* tp_traverse */ |
6063 | 0, /* tp_clear */ |
6064 | long_richcompare, /* tp_richcompare */ |
6065 | 0, /* tp_weaklistoffset */ |
6066 | 0, /* tp_iter */ |
6067 | 0, /* tp_iternext */ |
6068 | long_methods, /* tp_methods */ |
6069 | 0, /* tp_members */ |
6070 | long_getset, /* tp_getset */ |
6071 | 0, /* tp_base */ |
6072 | 0, /* tp_dict */ |
6073 | 0, /* tp_descr_get */ |
6074 | 0, /* tp_descr_set */ |
6075 | 0, /* tp_dictoffset */ |
6076 | 0, /* tp_init */ |
6077 | 0, /* tp_alloc */ |
6078 | long_new, /* tp_new */ |
6079 | PyObject_Free, /* tp_free */ |
6080 | }; |
6081 | |
6082 | static PyTypeObject Int_InfoType; |
6083 | |
6084 | PyDoc_STRVAR(int_info__doc__, |
6085 | "sys.int_info\n\ |
6086 | \n\ |
6087 | A named tuple that holds information about Python's\n\ |
6088 | internal representation of integers. The attributes are read only."); |
6089 | |
6090 | static PyStructSequence_Field int_info_fields[] = { |
6091 | {"bits_per_digit", "size of a digit in bits"}, |
6092 | {"sizeof_digit", "size in bytes of the C type used to represent a digit"}, |
6093 | {NULL, NULL} |
6094 | }; |
6095 | |
6096 | static PyStructSequence_Desc int_info_desc = { |
6097 | "sys.int_info", /* name */ |
6098 | int_info__doc__, /* doc */ |
6099 | int_info_fields, /* fields */ |
6100 | 2 /* number of fields */ |
6101 | }; |
6102 | |
6103 | PyObject * |
6104 | PyLong_GetInfo(void) |
6105 | { |
6106 | PyObject* int_info; |
6107 | int field = 0; |
6108 | int_info = PyStructSequence_New(&Int_InfoType); |
6109 | if (int_info == NULL) Branch (6109:9): [True: 0, False: 278]
|
6110 | return NULL; |
6111 | PyStructSequence_SET_ITEM(int_info, field++, |
6112 | PyLong_FromLong(PyLong_SHIFT)); |
6113 | PyStructSequence_SET_ITEM(int_info, field++, |
6114 | PyLong_FromLong(sizeof(digit))); |
6115 | if (PyErr_Occurred()) { Branch (6115:9): [True: 0, False: 278]
|
6116 | Py_CLEAR(int_info); |
6117 | return NULL; |
6118 | } |
6119 | return int_info; |
6120 | } |
6121 | |
6122 | |
6123 | /* runtime lifecycle */ |
6124 | |
6125 | PyStatus |
6126 | _PyLong_InitTypes(PyInterpreterState *interp) |
6127 | { |
6128 | if (!_Py_IsMainInterpreter(interp)) { Branch (6128:9): [True: 171, False: 107]
|
6129 | return _PyStatus_OK(); |
6130 | } |
6131 | |
6132 | if (PyType_Ready(&PyLong_Type) < 0) { Branch (6132:9): [True: 0, False: 107]
|
6133 | return _PyStatus_ERR("Can't initialize int type"); |
6134 | } |
6135 | |
6136 | /* initialize int_info */ |
6137 | if (Int_InfoType.tp_name == NULL) { Branch (6137:9): [True: 107, False: 0]
|
6138 | if (PyStructSequence_InitType2(&Int_InfoType, &int_info_desc) < 0) { Branch (6138:13): [True: 0, False: 107]
|
6139 | return _PyStatus_ERR("can't init int info type"); |
6140 | } |
6141 | } |
6142 | |
6143 | return _PyStatus_OK(); |
6144 | } |
6145 | |
6146 | |
6147 | void |
6148 | _PyLong_FiniTypes(PyInterpreterState *interp) |
6149 | { |
6150 | if (!_Py_IsMainInterpreter(interp)) { Branch (6150:9): [True: 169, False: 103]
|
6151 | return; |
6152 | } |
6153 | |
6154 | _PyStructSequence_FiniType(&Int_InfoType); |
6155 | } |