1Data::Integer(3) User Contributed Perl Documentation Data::Integer(3)
2
6 Data::Integer - details of the native integer data type
7
9 use Data::Integer qw(natint_bits);
10 $n = natint_bits;
12 # and other constants; see text
14 use Data::Integer qw(nint sint uint nint_is_sint nint_is_uint);
16 $ni = nint($ni);
18 $si = sint($si);
19 $ui = uint($ui);
20 if(nint_is_sint($ni)) { ...
21 if(nint_is_uint($ni)) { ...
22 use Data::Integer qw(
24 nint_sgn sint_sgn uint_sgn
25 nint_abs sint_abs uint_abs
26 nint_cmp sint_cmp uint_cmp
27 nint_min sint_min uint_min
28 nint_max sint_max uint_max
29 nint_neg sint_neg uint_neg
30 nint_add sint_add uint_add
31 nint_sub sint_sub uint_sub);
32 $sn = nint_sgn($ni);
34 $sn = sint_sgn($si);
35 $sn = uint_sgn($ui);
36 $ni = nint_abs($ni);
37 $si = sint_abs($si);
38 $ui = uint_abs($ui);
39 @sorted_nints = sort { nint_cmp($a, $b) } @nints;
40 @sorted_sints = sort { sint_cmp($a, $b) } @sints;
41 @sorted_uints = sort { uint_cmp($a, $b) } @uints;
42 $ni = nint_min($na, $nb);
43 $si = sint_min($sa, $sb);
44 $ui = uint_min($ua, $ub);
45 $ni = nint_max($na, $nb);
46 $si = sint_max($sa, $sb);
47 $ui = uint_max($ua, $ub);
48 $ni = nint_neg($ni);
49 $si = sint_neg($si);
50 $ui = uint_neg($ui);
51 $ni = nint_add($na, $nb);
52 $si = sint_add($sa, $sb);
53 $ui = uint_add($ua, $ub);
54 $ni = nint_sub($na, $nb);
55 $si = sint_sub($sa, $sb);
56 $ui = uint_sub($ua, $ub);
57 use Data::Integer qw(
59 sint_shl uint_shl
60 sint_shr uint_shr
61 sint_rol uint_rol
62 sint_ror uint_ror);
63 $si = sint_shl($si, $dist);
65 $ui = uint_shl($ui, $dist);
66 $si = sint_shr($si, $dist);
67 $ui = uint_shr($ui, $dist);
68 $si = sint_rol($si, $dist);
69 $ui = uint_rol($ui, $dist);
70 $si = sint_ror($si, $dist);
71 $ui = uint_ror($ui, $dist);
72 use Data::Integer qw(
74 nint_bits_as_sint nint_bits_as_uint
75 sint_bits_as_uint uint_bits_as_sint);
76 $si = nint_bits_as_sint($ni);
78 $ui = nint_bits_as_uint($ni);
79 $ui = sint_bits_as_uint($si);
80 $si = uint_bits_as_sint($ui);
81 use Data::Integer qw(
83 sint_not uint_not
84 sint_and uint_and
85 sint_nand uint_nand
86 sint_andn uint_andn
87 sint_or uint_or
88 sint_nor uint_nor
89 sint_orn uint_orn
90 sint_xor uint_xor
91 sint_nxor uint_nxor
92 sint_mux uint_mux);
93 $si = sint_not($si);
95 $ui = uint_not($ui);
96 $si = sint_and($sa, $sb);
97 $ui = uint_and($ua, $ub);
98 $si = sint_nand($sa, $sb);
99 $ui = uint_nand($ua, $ub);
100 $si = sint_andn($sa, $sb);
101 $ui = uint_andn($ua, $ub);
102 $si = sint_or($sa, $sb);
103 $ui = uint_or($ua, $ub);
104 $si = sint_nor($sa, $sb);
105 $ui = uint_nor($ua, $ub);
106 $si = sint_orn($sa, $sb);
107 $ui = uint_orn($ua, $ub);
108 $si = sint_xor($sa, $sb);
109 $ui = uint_xor($ua, $ub);
110 $si = sint_nxor($sa, $sb);
111 $ui = uint_nxor($ua, $ub);
112 $si = sint_mux($sa, $sb, $sc);
113 $ui = uint_mux($ua, $ub, $uc);
114 use Data::Integer qw(
116 sint_madd uint_madd
117 sint_msub uint_msub
118 sint_cadd uint_cadd
119 sint_csub uint_csub
120 sint_sadd uint_sadd
121 sint_ssub uint_ssub);
122 $si = sint_madd($sa, $sb);
124 $ui = uint_madd($ua, $ub);
125 $si = sint_msub($sa, $sb);
126 $ui = uint_msub($ua, $ub);
127 ($carry, $si) = sint_cadd($sa, $sb, $carry);
128 ($carry, $ui) = uint_cadd($ua, $ub, $carry);
129 ($carry, $si) = sint_csub($sa, $sb, $carry);
130 ($carry, $ui) = uint_csub($ua, $ub, $carry);
131 $si = sint_sadd($sa, $sb);
132 $ui = uint_sadd($ua, $ub);
133 $si = sint_ssub($sa, $sb);
134 $ui = uint_ssub($ua, $ub);
135 use Data::Integer qw(natint_hex hex_natint);
137 print natint_hex($value);
139 $value = hex_natint($string);
140
142 This module is about the native integer numerical data type. A native
143 integer is one of the types of datum that can appear in the numeric
144 part of a Perl scalar. This module supplies constants describing the
145 native integer type.
146 There are actually two native integer representations: signed and
148 unsigned. Both are handled by this module.
149
151 Each native integer format represents a value using binary place value,
152 with some fixed number of bits. The number of bits is the same for
153 both signed and unsigned representations. In each case the least-
154 significant bit has the value 1, the next 2, the next 4, and so on. In
155 the unsigned representation, this pattern continues up to and including
156 the most-significant bit, which for a 32-bit machine therefore has the
157 value 2^31 (2147483648). The unsigned format cannot represent any
158 negative numbers.
159 In the signed format, the most-significant bit is exceptional, having
161 the negation of the value that it does in the unsigned format. Thus on
162 a 32-bit machine this has the value -2^31 (-2147483648). Values with
163 this bit set are negative, and those with it clear are non-negative;
164 this bit is also known as the "sign bit".
165 It is usual in machine arithmetic to use one of these formats at a
167 time, for example to add two signed numbers yielding a signed result.
168 However, Perl has a trick: a scalar with a native integer value
169 contains an additional flag bit which indicates whether the signed or
170 unsigned format is being used. It is therefore possible to mix signed
171 and unsigned numbers in arithmetic, at some extra expense.
172
174 Each of the extreme-value constants has two names, a short one and a
175 long one. The short names are more convenient to use, but the long
176 names are clearer in a context where other similar constants exist.
177 Due to the risks of Perl changing the behaviour of a native integer
179 value that has been involved in floating point arithmetic (see "BUGS"),
180 the extreme-value constants are actually non-constant functions that
181 always return a fresh copy of the appropriate value. The returned
182 value is always a pure native integer value, unsullied by floating
183 point or string operations.
184 natint_bits
186 The width, in bits, of the native integer data types.
187 min_nint
189 min_natint
190 The minimum representable value in either representation. This is
191 -2^(natint_bits - 1).
192 max_nint
194 max_natint
195 The maximum representable value in either representation. This is
196 2^natint_bits - 1.
197 min_sint
199 min_signed_natint
200 The minimum representable value in the signed representation. This
201 is -2^(natint_bits - 1).
202 max_sint
204 max_signed_natint
205 The maximum representable value in the signed representation. This
206 is 2^(natint_bits - 1) - 1.
207 min_uint
209 min_unsigned_natint
210 The minimum representable value in the unsigned representation.
211 This is zero.
212 max_uint
214 max_unsigned_natint
215 The maximum representable value in the unsigned representation.
216 This is 2^natint_bits - 1.
217
219 Each "nint_", "sint_", or "uint_" function operates on one of the three
220 integer formats. "nint_" functions operate on Perl's union of signed
221 and unsigned; "sint_" functions operate on signed integers; and "uint_"
222 functions operate on unsigned integers. Except where indicated
223 otherwise, the function returns a value of its primary type.
224 Parameters A, B, and C, where present, must be numbers of the
226 appropriate type: specifically, with a numerical value that can be
227 represented in that type. If there are multiple flavours of zero, due
228 to floating point funkiness, all zeroes are treated the same.
229 Parameters with other names have other requirements, explained with
230 each function.
231 The functions attempt to detect unsuitable arguments, and "die" if an
233 invalid argument is detected, but they can't notice some kinds of
234 incorrect argument. Generally, it is the caller's responsibility to
235 provide a sane numerical argument, and supplying an invalid argument
236 will cause mayhem. Only the numeric value of plain scalar arguments is
237 used; the string value is completely ignored, so dualvars are not a
238 problem.
239 Canonicalisation and classification
241 These are basic glue functions.
242 nint(A)
244 sint(A)
245 uint(A)
246 These functions each take an argument in a specific integer format
247 and return its numerical value. This is the argument
248 canonicalisation that is performed by all of the functions in this
249 module, presented in isolation.
250 nint_is_sint(A)
252 Takes a native integer of either type. Returns a truth value
253 indicating whether this value can be exactly represented as a
254 signed native integer.
255 nint_is_uint(A)
257 Takes a native integer of either type. Returns a truth value
258 indicating whether this value can be exactly represented as an
259 unsigned native integer.
260 Arithmetic
262 These functions operate on numerical values rather than just bit
263 patterns. They will all "die" if the true numerical result doesn't fit
264 into the result format, rather than give a wrong answer.
265 nint_sgn(A)
267 sint_sgn(A)
268 uint_sgn(A)
269 Returns +1 if the argument is positive, 0 if the argument is zero,
270 or -1 if the argument is negative.
271 nint_abs(A)
273 sint_abs(A)
274 uint_abs(A)
275 Absolute value (magnitude, discarding sign).
276 nint_cmp(A, B)
278 sint_cmp(A, B)
279 uint_cmp(A, B)
280 Arithmetic comparison. Returns -1, 0, or +1, indicating whether A
281 is less than, equal to, or greater than B.
282 nint_min(A, B)
284 sint_min(A, B)
285 uint_min(A, B)
286 Arithmetic minimum. Returns the arithmetically lesser of the two
287 arguments.
288 nint_max(A, B)
290 sint_max(A, B)
291 uint_max(A, B)
292 Arithmetic maximum. Returns the arithmetically greater of the two
293 arguments.
294 nint_neg(A)
296 sint_neg(A)
297 uint_neg(A)
298 Negation: returns -A.
299 nint_add(A, B)
301 sint_add(A, B)
302 uint_add(A, B)
303 Addition: returns A + B.
304 nint_sub(A, B)
306 sint_sub(A, B)
307 uint_sub(A, B)
308 Subtraction: returns A - B.
309 Bit shifting
311 These functions all operate on the bit patterns representing integers,
312 mostly ignoring the numerical values represented. In most cases the
313 results for particular numerical arguments are influenced by the word
314 size, because that determines where a bit being left-shifted will drop
315 off the end of the word and where a bit will be shifted in during a
316 rightward shift.
317 With the exception of rightward shifts (see below), each pair of
319 functions performs exactly the same operations on the bit sequences.
320 There inevitably can't be any functions here that operate on Perl's
321 union of signed and unsigned; you must choose, by which function you
322 call, which type the result is to be tagged as.
323 sint_shl(A, DIST)
325 uint_shl(A, DIST)
326 Bitwise left shift (towards more-significant bits). DIST is the
327 distance to shift, in bits, and must be an integer in the range [0,
328 natint_bits). Zeroes are shifted in from the right.
329 sint_shr(A, DIST)
331 uint_shr(A, DIST)
332 Bitwise right shift (towards less-significant bits). DIST is the
333 distance to shift, in bits, and must be an integer in the range [0,
334 natint_bits).
335 When performing an unsigned right shift, zeroes are shifted in from
337 the left. A signed right shift is different: the sign bit gets
338 duplicated, so right-shifting a negative number always gives a
339 negative result.
340 sint_rol(A, DIST)
342 uint_rol(A, DIST)
343 Bitwise left rotation (towards more-significant bits, with the
344 most-significant bit wrapping round to the least-significant bit).
345 DIST is the distance to rotate, in bits, and must be an integer in
346 the range [0, natint_bits).
347 sint_ror(A, DIST)
349 uint_ror(A, DIST)
350 Bitwise right rotation (towards less-significant bits, with the
351 least-significant bit wrapping round to the most-significant bit).
352 DIST is the distance to rotate, in bits, and must be an integer in
353 the range [0, natint_bits).
354 Format conversion
356 These functions convert between the various native integer formats by
357 reinterpreting the bit patterns used to represent the integers. The
358 bit pattern remains unchanged; its meaning changes, and so the
359 numerical value changes. Perl scalars preserve the numerical value,
360 rather than just the bit pattern, so from the Perl point of view these
361 are functions that change numbers into other numbers.
362 nint_bits_as_sint(A)
364 Converts a native integer of either type to a signed integer, by
365 reinterpreting the bits. The most-significant bit (whether a sign
366 bit or not) becomes a sign bit.
367 nint_bits_as_uint(A)
369 Converts a native integer of either type to an unsigned integer, by
370 reinterpreting the bits. The most-significant bit (whether a sign
371 bit or not) becomes an ordinary most-significant bit.
372 sint_bits_as_uint(A)
374 Converts a signed integer to an unsigned integer, by reinterpreting
375 the bits. The sign bit becomes an ordinary most-significant bit.
376 uint_bits_as_sint(A)
378 Converts an unsigned integer to a signed integer, by reinterpreting
379 the bits. The most-significant bit becomes a sign bit.
380 Bitwise operations
382 These functions all operate on the bit patterns representing integers,
383 completely ignoring the numerical values represented. They are mostly
384 not influenced by the word size, in the sense that they will produce
385 the same numerical result for the same numerical arguments regardless
386 of word size. However, a few are affected by the word size: those on
387 unsigned operands that return a non-zero result if given zero
388 arguments.
389 Each pair of functions performs exactly the same operations on the bit
391 sequences. There inevitably can't be any functions here that operate
392 on Perl's union of signed and unsigned; you must choose, by which
393 function you call, which type the result is to be tagged as.
394 sint_not(A)
396 uint_not(A)
397 Bitwise complement (NOT).
398 sint_and(A, B)
400 uint_and(A, B)
401 Bitwise conjunction (AND).
402 sint_nand(A, B)
404 uint_nand(A, B)
405 Bitwise inverted conjunction (NAND).
406 sint_andn(A, B)
408 uint_andn(A, B)
409 Bitwise conjunction with inverted argument (A AND (NOT B)).
410 sint_or(A, B)
412 uint_or(A, B)
413 Bitwise disjunction (OR).
414 sint_nor(A, B)
416 uint_nor(A, B)
417 Bitwise inverted disjunction (NOR).
418 sint_orn(A, B)
420 uint_orn(A, B)
421 Bitwise disjunction with inverted argument (A OR (NOT B)).
422 sint_xor(A, B)
424 uint_xor(A, B)
425 Bitwise symmetric difference (XOR).
426 sint_nxor(A, B)
428 uint_nxor(A, B)
429 Bitwise symmetric similarity (NXOR).
430 sint_mux(A, B, C)
432 uint_mux(A, B, C)
433 Bitwise multiplex. The output has a bit from B wherever A has a 1
434 bit, and a bit from C wherever A has a 0 bit. That is, the result
435 is (A AND B) OR ((NOT A) AND C).
436 Machine arithmetic
438 These functions perform arithmetic operations that are inherently
439 influenced by the word size. They always produce a well-defined output
440 if given valid inputs. There inevitably can't be any functions here
441 that operate on Perl's union of signed and unsigned; you must choose,
442 by which function you call, which type the result is to be tagged as.
443 sint_madd(A, B)
445 uint_madd(A, B)
446 Modular addition. The result for unsigned addition is (A + B) mod
447 2^natint_bits. The signed version behaves similarly, but with a
448 different result range.
449 sint_msub(A, B)
451 uint_msub(A, B)
452 Modular subtraction. The result for unsigned subtraction is (A -
453 B) mod 2^natint_bits. The signed version behaves similarly, but
454 with a different result range.
455 sint_cadd(A, B, CARRY_IN)
457 uint_cadd(A, B, CARRY_IN)
458 Addition with carry. Two word arguments (A and B) and an input
459 carry bit (CARRY_IN, which must have the value 0 or 1) are all
460 added together. Returns a list of two items: an output carry and
461 an output word (of the same signedness as the inputs). Precisely,
462 the output list (CARRY_OUT, R) is such that CARRY_OUT*2^natint_bits
463 + R = A + B + CARRY_IN.
464 sint_csub(A, B, CARRY_IN)
466 uint_csub(A, B, CARRY_IN)
467 Subtraction with carry (borrow). The second word argument (B) and
468 an input carry bit (CARRY_IN, which must have the value 0 or 1) are
469 subtracted from the first word argument (A). Returns a list of two
470 items: an output carry and an output word (of the same signedness
471 as the inputs). Precisely, the output list (CARRY_OUT, R) is such
472 that R - CARRY_OUT*2^natint_bits = A - B - CARRY_IN.
473 sint_sadd(A, B)
475 uint_sadd(A, B)
476 Saturating addition. The result is A + B if that will fit into the
477 result format, otherwise the minimum or maximum value of the result
478 format is returned depending on the direction in which the addition
479 overflowed.
480 sint_ssub(A, B)
482 uint_ssub(A, B)
483 Saturating subtraction. The result is A - B if that will fit into
484 the result format, otherwise the minimum or maximum value of the
485 result format is returned depending on the direction in which the
486 subtraction overflowed.
487 String conversion
489 natint_hex(VALUE)
490 VALUE must be a native integer value. The function encodes VALUE
491 in hexadecimal, returning that representation as a string.
492 Specifically, the output is of the form "s0xdddd", where "s" is the
493 sign and "dddd" is a sequence of hexadecimal digits.
494 hex_natint(STRING)
496 Generates and returns a native integer value from a string encoding
497 it in hexadecimal. Specifically, the input format is
498 "[s][0x]dddd", where "s" is the sign and "dddd" is a sequence of
499 one or more hexadecimal digits. The input is interpreted case
500 insensitively. If the value given in the string cannot be exactly
501 represented in the native integer type, the function "die"s.
502 The core Perl function "hex" (see "hex" in perlfunc) does a similar
504 job to this function, but differs in several ways. Principally,
505 "hex" doesn't handle negative values, and it gives the wrong answer
506 for values that don't fit into the native integer type. In Perl
507 5.6 it also gives the wrong answer for values that don't fit into
508 the native floating point type. It also doesn't enforce strict
509 syntax on the input string.
510
512 In Perl 5.6, when a native integer scalar is used in any arithmetic
513 other than specifically integer arithmetic, it gets partially
514 transformed into a floating point scalar. Even if its numerical value
515 can be represented exactly in floating point, so that floating point
516 arithmetic uses the correct numerical value, some operations are
517 affected by the floatness. In particular, the stringification of the
518 scalar doesn't necessarily represent its exact value if it is tagged as
519 floating point.
520 Because of this transforming behaviour, if you need to stringify a
522 native integer it is best to ensure that it doesn't get used in any
523 non-integer arithmetic first. If an integer scalar must be used in
524 standard Perl arithmetic, it may be copied first and the copy operated
525 upon to avoid causing side effects on the original. If an integer
526 scalar might have already been transformed, it can be cleaned by
527 passing it through the canonicalisation function "nint". The functions
528 in this module all avoid modifying their arguments, and always return
529 pristine integers.
530 Perl 5.8+ still internally modifies integer scalars in the same
532 circumstances, but seems to have corrected all the misbehaviour that
533 resulted from it.
534 Also in Perl 5.6, default Perl arithmetic doesn't necessarily work
536 correctly on native integers. (This is part of the motivation for the
537 myriad arithmetic functions in this module.) Default arithmetic here
538 is strictly floating point, so if there are native integers that cannot
539 be exactly represented in floating point then the arithmetic will
540 approximate the values before operating on them. Perl 5.8+ attempts to
541 use native integer operations where possible in its default arithmetic,
542 but as of Perl 5.8.8 it doesn't always succeed. For reliable integer
543 arithmetic, integer operations must still be requested explicitly.
544
546 Data::Float, Scalar::Number, perlnumber(1)
547
549 Andrew Main (Zefram) <zefram@fysh.org>
550
552 Copyright (C) 2007, 2010, 2015, 2017 Andrew Main (Zefram)
553 <zefram@fysh.org>
554
556 This module is free software; you can redistribute it and/or modify it
557 under the same terms as Perl itself.
558perl v5.28.1 2019-02-02 Data::Integer(3)