1math::bignum(n) Tcl Math Library math::bignum(n)
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6
8 math::bignum - Arbitrary precision integer numbers
9
11 package require Tcl ?8.4?
12 package require math::bignum ?3.1?
14 ::math::bignum::fromstr string ?radix?
16 ::math::bignum::tostr bignum ?radix?
18 ::math::bignum::sign bignum
20 ::math::bignum::abs bignum
22 ::math::bignum::cmp a b
24 ::math::bignum::iszero bignum
26 ::math::bignum::lt a b
28 ::math::bignum::le a b
30 ::math::bignum::gt a b
32 ::math::bignum::ge a b
34 ::math::bignum::eq a b
36 ::math::bignum::ne a b
38 ::math::bignum::isodd bignum
40 ::math::bignum::iseven bignum
42 ::math::bignum::add a b
44 ::math::bignum::sub a b
46 ::math::bignum::mul a b
48 ::math::bignum::divqr a b
50 ::math::bignum::div a b
52 ::math::bignum::rem a b
54 ::math::bignum::mod n m
56 ::math::bignum::pow base exp
58 ::math::bignum::powm base exp m
60 ::math::bignum::sqrt bignum
62 ::math::bignum::rand bits
64 ::math::bignum::lshift bignum bits
66 ::math::bignum::rshift bignum bits
68 ::math::bignum::bitand a b
70 ::math::bignum::bitor a b
72 ::math::bignum::bitxor a b
74 ::math::bignum::setbit bignumVar bit
76 ::math::bignum::clearbit bignumVar bit
78 ::math::bignum::testbit bignum bit
80 ::math::bignum::bits bignum
82______________________________________________________________________________
84
86 The bignum package provides arbitrary precision integer math (also
87 known as "big numbers") capabilities to the Tcl language. Big numbers
88 are internally represented at Tcl lists: this package provides a set of
89 procedures operating against the internal representation in order to:
90 • perform math operations
92 • convert bignums from the internal representation to a string in
94 the desired radix and vice versa.
95 But the two constants "0" and "1" are automatically converted to the
97 internal representation, in order to easily compare a number to zero,
98 or increment a big number.
99 The bignum interface is opaque, so operations on bignums that are not
101 returned by procedures in this package (but created by hand) may lead
102 to unspecified behaviours. It's safe to treat bignums as pure values,
103 so there is no need to free a bignum, or to duplicate it via a special
104 operation.
105
107 This section shows some simple example. This library being just a way
108 to perform math operations, examples may be the simplest way to learn
109 how to work with it. Consult the API section of this man page for in‐
110 formation about individual procedures.
111 package require math::bignum
113 # Multiplication of two bignums
115 set a [::math::bignum::fromstr 88888881111111]
116 set b [::math::bignum::fromstr 22222220000000]
117 set c [::math::bignum::mul $a $b]
118 puts [::math::bignum::tostr $c] ; # => will output 1975308271604953086420000000
119 set c [::math::bignum::sqrt $c]
120 puts [::math::bignum::tostr $c] ; # => will output 44444440277777
121 # From/To string conversion in different radix
123 set a [::math::bignum::fromstr 1100010101010111001001111010111 2]
124 puts [::math::bignum::tostr $a 16] ; # => will output 62ab93d7
125 # Factorial example
127 proc fact n {
128 # fromstr is not needed for 0 and 1
129 set z 1
130 for {set i 2} {$i <= $n} {incr i} {
131 set z [::math::bignum::mul $z [::math::bignum::fromstr $i]]
132 }
133 return $z
134 }
135 puts [::math::bignum::tostr [fact 100]]
137
140 ::math::bignum::fromstr string ?radix?
141 Convert string into a bignum. If radix is omitted or zero, the
142 string is interpreted in hex if prefixed with 0x, in octal if
143 prefixed with ox, in binary if it's pefixed with bx, as a number
144 in radix 10 otherwise. If instead the radix argument is speci‐
145 fied in the range 2-36, the string is interpreted in the given
146 radix. Please note that this conversion is not needed for two
147 constants : 0 and 1. (see the example)
148 ::math::bignum::tostr bignum ?radix?
150 Convert bignum into a string representing the number in the
151 specified radix. If radix is omitted, the default is 10.
152 ::math::bignum::sign bignum
154 Return the sign of the bignum. The procedure returns 0 if the
155 number is positive, 1 if it's negative.
156 ::math::bignum::abs bignum
158 Return the absolute value of the bignum.
159 ::math::bignum::cmp a b
161 Compare the two bignums a and b, returning 0 if a == b, 1 if a >
162 b, and -1 if a < b.
163 ::math::bignum::iszero bignum
165 Return true if bignum value is zero, otherwise false is re‐
166 turned.
167 ::math::bignum::lt a b
169 Return true if a < b, otherwise false is returned.
170 ::math::bignum::le a b
172 Return true if a <= b, otherwise false is returned.
173 ::math::bignum::gt a b
175 Return true if a > b, otherwise false is returned.
176 ::math::bignum::ge a b
178 Return true if a >= b, otherwise false is returned.
179 ::math::bignum::eq a b
181 Return true if a == b, otherwise false is returned.
182 ::math::bignum::ne a b
184 Return true if a != b, otherwise false is returned.
185 ::math::bignum::isodd bignum
187 Return true if bignum is odd.
188 ::math::bignum::iseven bignum
190 Return true if bignum is even.
191 ::math::bignum::add a b
193 Return the sum of the two bignums a and b.
194 ::math::bignum::sub a b
196 Return the difference of the two bignums a and b.
197 ::math::bignum::mul a b
199 Return the product of the two bignums a and b. The implementa‐
200 tion uses Karatsuba multiplication if both the numbers are big‐
201 ger than a given threshold, otherwise the direct algorith is
202 used.
203 ::math::bignum::divqr a b
205 Return a two-elements list containing as first element the quo‐
206 tient of the division between the two bignums a and b, and the
207 remainder of the division as second element.
208 ::math::bignum::div a b
210 Return the quotient of the division between the two bignums a
211 and b.
212 ::math::bignum::rem a b
214 Return the remainder of the division between the two bignums a
215 and b.
216 ::math::bignum::mod n m
218 Return n modulo m. This operation is called modular reduction.
219 ::math::bignum::pow base exp
221 Return base raised to the exponent exp.
222 ::math::bignum::powm base exp m
224 Return base raised to the exponent exp, modulo m. This function
225 is often used in the field of cryptography.
226 ::math::bignum::sqrt bignum
228 Return the integer part of the square root of bignum
229 ::math::bignum::rand bits
231 Return a random number of at most bits bits. The returned num‐
232 ber is internally generated using Tcl's expr rand() function and
233 is not suitable where an unguessable and cryptographically se‐
234 cure random number is needed.
235 ::math::bignum::lshift bignum bits
237 Return the result of left shifting bignum's binary representa‐
238 tion of bits positions on the left. This is equivalent to mul‐
239 tiplying by 2^bits but much faster.
240 ::math::bignum::rshift bignum bits
242 Return the result of right shifting bignum's binary representa‐
243 tion of bits positions on the right. This is equivalent to di‐
244 viding by 2^bits but much faster.
245 ::math::bignum::bitand a b
247 Return the result of doing a bitwise AND operation on a and b.
248 The operation is restricted to positive numbers, including zero.
249 When negative numbers are provided as arguments the result is
250 undefined.
251 ::math::bignum::bitor a b
253 Return the result of doing a bitwise OR operation on a and b.
254 The operation is restricted to positive numbers, including zero.
255 When negative numbers are provided as arguments the result is
256 undefined.
257 ::math::bignum::bitxor a b
259 Return the result of doing a bitwise XOR operation on a and b.
260 The operation is restricted to positive numbers, including zero.
261 When negative numbers are provided as arguments the result is
262 undefined.
263 ::math::bignum::setbit bignumVar bit
265 Set the bit at bit position to 1 in the bignum stored in the
266 variable bignumVar. Bit 0 is the least significant.
267 ::math::bignum::clearbit bignumVar bit
269 Set the bit at bit position to 0 in the bignum stored in the
270 variable bignumVar. Bit 0 is the least significant.
271 ::math::bignum::testbit bignum bit
273 Return true if the bit at the bit position of bignum is on, oth‐
274 erwise false is returned. If bit is out of range, it is consid‐
275 ered as set to zero.
276 ::math::bignum::bits bignum
278 Return the number of bits needed to represent bignum in radix 2.
279
281 This document, and the package it describes, will undoubtedly contain
282 bugs and other problems. Please report such in the category math ::
283 bignum of the Tcllib Trackers [http://core.tcl.tk/tcllib/reportlist].
284 Please also report any ideas for enhancements you may have for either
285 package and/or documentation.
286 When proposing code changes, please provide unified diffs, i.e the out‐
288 put of diff -u.
289 Note further that attachments are strongly preferred over inlined
291 patches. Attachments can be made by going to the Edit form of the
292 ticket immediately after its creation, and then using the left-most
293 button in the secondary navigation bar.
294
296 bignums, math, multiprecision, tcl
297
299 Mathematics
300
302 Copyright (c) 2004 Salvatore Sanfilippo <antirez at invece dot org>
303 Copyright (c) 2004 Arjen Markus <arjenmarkus at users dot sourceforge dot net>
304tcllib 3.1 math::bignum(n)