1: /* intprops.h -- properties of integer types
2:
3: Copyright (C) 2001-2019 Free Software Foundation, Inc.
4:
5: This program is free software: you can redistribute it and/or modify it
6: under the terms of the GNU General Public License as published
7: by the Free Software Foundation; either version 3 of the License, or
8: (at your option) any later version.
9:
10: This program is distributed in the hope that it will be useful,
11: but WITHOUT ANY WARRANTY; without even the implied warranty of
12: MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13: GNU General Public License for more details.
14:
15: You should have received a copy of the GNU General Public License
16: along with this program. If not, see <https://www.gnu.org/licenses/>. */
17:
18: /* Written by Paul Eggert. */
19:
20: #ifndef _GL_INTPROPS_H
21: #define _GL_INTPROPS_H
22:
23: #include <limits.h>
24:
25: /* Return a value with the common real type of E and V and the value of V.
26: Do not evaluate E. */
27: #define _GL_INT_CONVERT(e, v) ((1 ? 0 : (e)) + (v))
28:
29: /* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see
30: <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00406.html>. */
31: #define _GL_INT_NEGATE_CONVERT(e, v) ((1 ? 0 : (e)) - (v))
32:
33: /* The extra casts in the following macros work around compiler bugs,
34: e.g., in Cray C 5.0.3.0. */
35:
36: /* True if the arithmetic type T is an integer type. bool counts as
37: an integer. */
38: #define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)
39:
40: /* True if the real type T is signed. */
41: #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))
42:
43: /* Return 1 if the real expression E, after promotion, has a
44: signed or floating type. Do not evaluate E. */
45: #define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)
46:
47:
48: /* Minimum and maximum values for integer types and expressions. */
49:
50: /* The width in bits of the integer type or expression T.
51: Do not evaluate T.
52: Padding bits are not supported; this is checked at compile-time below. */
53: #define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT)
54:
55: /* The maximum and minimum values for the integer type T. */
56: #define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))
57: #define TYPE_MAXIMUM(t) \
58: ((t) (! TYPE_SIGNED (t) \
59: ? (t) -1 \
60: : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))
61:
62: /* The maximum and minimum values for the type of the expression E,
63: after integer promotion. E is not evaluated. */
64: #define _GL_INT_MINIMUM(e) \
65: (EXPR_SIGNED (e) \
66: ? ~ _GL_SIGNED_INT_MAXIMUM (e) \
67: : _GL_INT_CONVERT (e, 0))
68: #define _GL_INT_MAXIMUM(e) \
69: (EXPR_SIGNED (e) \
70: ? _GL_SIGNED_INT_MAXIMUM (e) \
71: : _GL_INT_NEGATE_CONVERT (e, 1))
72: #define _GL_SIGNED_INT_MAXIMUM(e) \
73: (((_GL_INT_CONVERT (e, 1) << (TYPE_WIDTH ((e) + 0) - 2)) - 1) * 2 + 1)
74:
75: /* Work around OpenVMS incompatibility with C99. */
76: #if !defined LLONG_MAX && defined __INT64_MAX
77: # define LLONG_MAX __INT64_MAX
78: # define LLONG_MIN __INT64_MIN
79: #endif
80:
81: /* This include file assumes that signed types are two's complement without
82: padding bits; the above macros have undefined behavior otherwise.
83: If this is a problem for you, please let us know how to fix it for your host.
84: This assumption is tested by the intprops-tests module. */
85:
86: /* Does the __typeof__ keyword work? This could be done by
87: 'configure', but for now it's easier to do it by hand. */
88: #if (2 <= __GNUC__ \
89: || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \
90: || (0x5110 <= __SUNPRO_C && !__STDC__))
91: # define _GL_HAVE___TYPEOF__ 1
92: #else
93: # define _GL_HAVE___TYPEOF__ 0
94: #endif
95:
96: /* Return 1 if the integer type or expression T might be signed. Return 0
97: if it is definitely unsigned. This macro does not evaluate its argument,
98: and expands to an integer constant expression. */
99: #if _GL_HAVE___TYPEOF__
100: # define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))
101: #else
102: # define _GL_SIGNED_TYPE_OR_EXPR(t) 1
103: #endif
104:
105: /* Bound on length of the string representing an unsigned integer
106: value representable in B bits. log10 (2.0) < 146/485. The
107: smallest value of B where this bound is not tight is 2621. */
108: #define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)
109:
110: /* Bound on length of the string representing an integer type or expression T.
111: Subtract 1 for the sign bit if T is signed, and then add 1 more for
112: a minus sign if needed.
113:
114: Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is
115: signed, this macro may overestimate the true bound by one byte when
116: applied to unsigned types of size 2, 4, 16, ... bytes. */
117: #define INT_STRLEN_BOUND(t) \
118: (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \
119: + _GL_SIGNED_TYPE_OR_EXPR (t))
120:
121: /* Bound on buffer size needed to represent an integer type or expression T,
122: including the terminating null. */
123: #define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)
124:
125:
126: /* Range overflow checks.
127:
128: The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C
129: operators might not yield numerically correct answers due to
130: arithmetic overflow. They do not rely on undefined or
131: implementation-defined behavior. Their implementations are simple
132: and straightforward, but they are a bit harder to use than the
133: INT_<op>_OVERFLOW macros described below.
134:
135: Example usage:
136:
137: long int i = ...;
138: long int j = ...;
139: if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))
140: printf ("multiply would overflow");
141: else
142: printf ("product is %ld", i * j);
143:
144: Restrictions on *_RANGE_OVERFLOW macros:
145:
146: These macros do not check for all possible numerical problems or
147: undefined or unspecified behavior: they do not check for division
148: by zero, for bad shift counts, or for shifting negative numbers.
149:
150: These macros may evaluate their arguments zero or multiple times,
151: so the arguments should not have side effects. The arithmetic
152: arguments (including the MIN and MAX arguments) must be of the same
153: integer type after the usual arithmetic conversions, and the type
154: must have minimum value MIN and maximum MAX. Unsigned types should
155: use a zero MIN of the proper type.
156:
157: These macros are tuned for constant MIN and MAX. For commutative
158: operations such as A + B, they are also tuned for constant B. */
159:
160: /* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.
161: See above for restrictions. */
162: #define INT_ADD_RANGE_OVERFLOW(a, b, min, max) \
163: ((b) < 0 \
164: ? (a) < (min) - (b) \
165: : (max) - (b) < (a))
166:
167: /* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.
168: See above for restrictions. */
169: #define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max) \
170: ((b) < 0 \
171: ? (max) + (b) < (a) \
172: : (a) < (min) + (b))
173:
174: /* Return 1 if - A would overflow in [MIN,MAX] arithmetic.
175: See above for restrictions. */
176: #define INT_NEGATE_RANGE_OVERFLOW(a, min, max) \
177: ((min) < 0 \
178: ? (a) < - (max) \
179: : 0 < (a))
180:
181: /* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.
182: See above for restrictions. Avoid && and || as they tickle
183: bugs in Sun C 5.11 2010/08/13 and other compilers; see
184: <https://lists.gnu.org/r/bug-gnulib/2011-05/msg00401.html>. */
185: #define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max) \
186: ((b) < 0 \
187: ? ((a) < 0 \
188: ? (a) < (max) / (b) \
189: : (b) == -1 \
190: ? 0 \
191: : (min) / (b) < (a)) \
192: : (b) == 0 \
193: ? 0 \
194: : ((a) < 0 \
195: ? (a) < (min) / (b) \
196: : (max) / (b) < (a)))
197:
198: /* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.
199: See above for restrictions. Do not check for division by zero. */
200: #define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max) \
201: ((min) < 0 && (b) == -1 && (a) < - (max))
202:
203: /* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.
204: See above for restrictions. Do not check for division by zero.
205: Mathematically, % should never overflow, but on x86-like hosts
206: INT_MIN % -1 traps, and the C standard permits this, so treat this
207: as an overflow too. */
208: #define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max) \
209: INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)
210:
211: /* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.
212: See above for restrictions. Here, MIN and MAX are for A only, and B need
213: not be of the same type as the other arguments. The C standard says that
214: behavior is undefined for shifts unless 0 <= B < wordwidth, and that when
215: A is negative then A << B has undefined behavior and A >> B has
216: implementation-defined behavior, but do not check these other
217: restrictions. */
218: #define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max) \
219: ((a) < 0 \
220: ? (a) < (min) >> (b) \
221: : (max) >> (b) < (a))
222:
223: /* True if __builtin_add_overflow (A, B, P) works when P is non-null. */
224: #if 5 <= __GNUC__ && !defined __ICC
225: # define _GL_HAS_BUILTIN_OVERFLOW 1
226: #else
227: # define _GL_HAS_BUILTIN_OVERFLOW 0
228: #endif
229:
230: /* True if __builtin_add_overflow_p (A, B, C) works. */
231: #define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)
232:
233: /* The _GL*_OVERFLOW macros have the same restrictions as the
234: *_RANGE_OVERFLOW macros, except that they do not assume that operands
235: (e.g., A and B) have the same type as MIN and MAX. Instead, they assume
236: that the result (e.g., A + B) has that type. */
237: #if _GL_HAS_BUILTIN_OVERFLOW_P
238: # define _GL_ADD_OVERFLOW(a, b, min, max) \
239: __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)
240: # define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
241: __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)
242: # define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
243: __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)
244: #else
245: # define _GL_ADD_OVERFLOW(a, b, min, max) \
246: ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max) \
247: : (a) < 0 ? (b) <= (a) + (b) \
248: : (b) < 0 ? (a) <= (a) + (b) \
249: : (a) + (b) < (b))
250: # define _GL_SUBTRACT_OVERFLOW(a, b, min, max) \
251: ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max) \
252: : (a) < 0 ? 1 \
253: : (b) < 0 ? (a) - (b) <= (a) \
254: : (a) < (b))
255: # define _GL_MULTIPLY_OVERFLOW(a, b, min, max) \
256: (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a)))) \
257: || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))
258: #endif
259: #define _GL_DIVIDE_OVERFLOW(a, b, min, max) \
260: ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
261: : (a) < 0 ? (b) <= (a) + (b) - 1 \
262: : (b) < 0 && (a) + (b) <= (a))
263: #define _GL_REMAINDER_OVERFLOW(a, b, min, max) \
264: ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max) \
265: : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b) \
266: : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))
267:
268: /* Return a nonzero value if A is a mathematical multiple of B, where
269: A is unsigned, B is negative, and MAX is the maximum value of A's
270: type. A's type must be the same as (A % B)'s type. Normally (A %
271: -B == 0) suffices, but things get tricky if -B would overflow. */
272: #define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max) \
273: (((b) < -_GL_SIGNED_INT_MAXIMUM (b) \
274: ? (_GL_SIGNED_INT_MAXIMUM (b) == (max) \
275: ? (a) \
276: : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1)) \
277: : (a) % - (b)) \
278: == 0)
279:
280: /* Check for integer overflow, and report low order bits of answer.
281:
282: The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
283: might not yield numerically correct answers due to arithmetic overflow.
284: The INT_<op>_WRAPV macros also store the low-order bits of the answer.
285: These macros work correctly on all known practical hosts, and do not rely
286: on undefined behavior due to signed arithmetic overflow.
287:
288: Example usage, assuming A and B are long int:
289:
290: if (INT_MULTIPLY_OVERFLOW (a, b))
291: printf ("result would overflow\n");
292: else
293: printf ("result is %ld (no overflow)\n", a * b);
294:
295: Example usage with WRAPV flavor:
296:
297: long int result;
298: bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);
299: printf ("result is %ld (%s)\n", result,
300: overflow ? "after overflow" : "no overflow");
301:
302: Restrictions on these macros:
303:
304: These macros do not check for all possible numerical problems or
305: undefined or unspecified behavior: they do not check for division
306: by zero, for bad shift counts, or for shifting negative numbers.
307:
308: These macros may evaluate their arguments zero or multiple times, so the
309: arguments should not have side effects.
310:
311: The WRAPV macros are not constant expressions. They support only
312: +, binary -, and *. The result type must be signed.
313:
314: These macros are tuned for their last argument being a constant.
315:
316: Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,
317: A % B, and A << B would overflow, respectively. */
318:
319: #define INT_ADD_OVERFLOW(a, b) \
320: _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)
321: #define INT_SUBTRACT_OVERFLOW(a, b) \
322: _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)
323: #if _GL_HAS_BUILTIN_OVERFLOW_P
324: # define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)
325: #else
326: # define INT_NEGATE_OVERFLOW(a) \
327: INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
328: #endif
329: #define INT_MULTIPLY_OVERFLOW(a, b) \
330: _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)
331: #define INT_DIVIDE_OVERFLOW(a, b) \
332: _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)
333: #define INT_REMAINDER_OVERFLOW(a, b) \
334: _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)
335: #define INT_LEFT_SHIFT_OVERFLOW(a, b) \
336: INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \
337: _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
338:
339: /* Return 1 if the expression A <op> B would overflow,
340: where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,
341: assuming MIN and MAX are the minimum and maximum for the result type.
342: Arguments should be free of side effects. */
343: #define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow) \
344: op_result_overflow (a, b, \
345: _GL_INT_MINIMUM (_GL_INT_CONVERT (a, b)), \
346: _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
347:
348: /* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.
349: Return 1 if the result overflows. See above for restrictions. */
350: #define INT_ADD_WRAPV(a, b, r) \
351: _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)
352: #define INT_SUBTRACT_WRAPV(a, b, r) \
353: _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)
354: #define INT_MULTIPLY_WRAPV(a, b, r) \
355: _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)
356:
357: /* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390. See:
358: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193
359: https://llvm.org/bugs/show_bug.cgi?id=25390
360: For now, assume all versions of GCC-like compilers generate bogus
361: warnings for _Generic. This matters only for older compilers that
362: lack __builtin_add_overflow. */
363: #if __GNUC__
364: # define _GL__GENERIC_BOGUS 1
365: #else
366: # define _GL__GENERIC_BOGUS 0
367: #endif
368:
369: /* Store the low-order bits of A <op> B into *R, where OP specifies
370: the operation. BUILTIN is the builtin operation, and OVERFLOW the
371: overflow predicate. Return 1 if the result overflows. See above
372: for restrictions. */
373: #if _GL_HAS_BUILTIN_OVERFLOW
374: # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)
375: #elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS
376: # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
377: (_Generic \
378: (*(r), \
379: signed char: \
380: _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
381: signed char, SCHAR_MIN, SCHAR_MAX), \
382: short int: \
383: _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
384: short int, SHRT_MIN, SHRT_MAX), \
385: int: \
386: _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
387: int, INT_MIN, INT_MAX), \
388: long int: \
389: _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
390: long int, LONG_MIN, LONG_MAX), \
391: long long int: \
392: _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
393: long long int, LLONG_MIN, LLONG_MAX)))
394: #else
395: # define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \
396: (sizeof *(r) == sizeof (signed char) \
397: ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
398: signed char, SCHAR_MIN, SCHAR_MAX) \
399: : sizeof *(r) == sizeof (short int) \
400: ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
401: short int, SHRT_MIN, SHRT_MAX) \
402: : sizeof *(r) == sizeof (int) \
403: ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \
404: int, INT_MIN, INT_MAX) \
405: : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))
406: # ifdef LLONG_MAX
407: # define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
408: (sizeof *(r) == sizeof (long int) \
409: ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
410: long int, LONG_MIN, LONG_MAX) \
411: : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \
412: long long int, LLONG_MIN, LLONG_MAX))
413: # else
414: # define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \
415: _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \
416: long int, LONG_MIN, LONG_MAX)
417: # endif
418: #endif
419:
420: /* Store the low-order bits of A <op> B into *R, where the operation
421: is given by OP. Use the unsigned type UT for calculation to avoid
422: overflow problems. *R's type is T, with extrema TMIN and TMAX.
423: T must be a signed integer type. Return 1 if the result overflows. */
424: #define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \
425: (sizeof ((a) op (b)) < sizeof (t) \
426: ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \
427: : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))
428: #define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \
429: ((overflow (a, b) \
430: || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \
431: || (tmax) < ((a) op (b))) \
432: ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \
433: : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))
434:
435: /* Return the low-order bits of A <op> B, where the operation is given
436: by OP. Use the unsigned type UT for calculation to avoid undefined
437: behavior on signed integer overflow, and convert the result to type T.
438: UT is at least as wide as T and is no narrower than unsigned int,
439: T is two's complement, and there is no padding or trap representations.
440: Assume that converting UT to T yields the low-order bits, as is
441: done in all known two's-complement C compilers. E.g., see:
442: https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html
443:
444: According to the C standard, converting UT to T yields an
445: implementation-defined result or signal for values outside T's
446: range. However, code that works around this theoretical problem
447: runs afoul of a compiler bug in Oracle Studio 12.3 x86. See:
448: https://lists.gnu.org/r/bug-gnulib/2017-04/msg00049.html
449: As the compiler bug is real, don't try to work around the
450: theoretical problem. */
451:
452: #define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \
453: ((t) ((ut) (a) op (ut) (b)))
454:
455: #endif /* _GL_INTPROPS_H */
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