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36 .\" @(#)bc.1 6.8 (Berkeley) 8/8/91
37 .\"
38 .Dd October 19, 2004
39 .Dt BC 1
40 .Sh NAME
41 .Nm bc
42 .Nd arbitrary-precision arithmetic language and calculator
43 .Sh SYNOPSIS
44 .Nm
45 .Op Fl cl
46 .Op Fl e Ar expression
47 .Op Ar file ...
48 .Sh DESCRIPTION
49 .Nm
50 is an interactive processor for a language which resembles
51 C but provides unlimited precision arithmetic.
52 It takes input from any expressions on the command line and
53 any files given, then reads the standard input.
54 .Pp
55 Options available:
56 .Bl -tag -width Ds
57 .It Fl c
58 .Nm
59 is actually a preprocessor for
60 .Xr dc 1 ,
61 which it invokes automatically, unless the
62 .Fl c
63 .Pq compile only
64 option is present.
65 In this case the generated
66 .Xr dc 1
67 instructions are sent to the standard output,
68 instead of being interpreted by a running
69 .Xr dc 1
70 process.
71 .It Fl e Ar expression
72 Evaluate
73 .Ar expression .
74 If multiple
75 .Fl e
76 options are specified, they are processed in the order given,
77 separated by newlines.
78 .It Fl l
79 Allow specification of an arbitrary precision math library.
80 The definitions in the library are available to command line
81 expressions.
82 .El
83 .Pp
84 The syntax for
85 .Nm
86 programs is as follows:
87 .Sq L
88 means letter a-z;
89 .Sq E
90 means expression;
91 .Sq S
92 means statement.
93 As a non-portable extension, it is possible to use long names
94 in addition to single letter names.
95 A long name is a sequence starting with a lowercase letter
96 followed by any number of lowercase letters and digits.
97 The underscore character
98 .Pq Sq _
99 counts as a letter.
100 .Pp
101 Comments
102 .Bd -unfilled -offset indent -compact
103 are enclosed in /* and */
104 are enclosed in # and the next newline
105 .Ed
106 .Pp
107 The newline is not part of the line comment,
108 which in itself is a non-portable extension.
109 .Pp
110 Names
111 .Bd -unfilled -offset indent -compact
112 simple variables: L
113 array elements: L [ E ]
114 The words `ibase', `obase', and `scale'
115 The word `last' or a single dot
116 .Ed
117 .Pp
118 Other operands
119 .Bd -unfilled -offset indent -compact
120 arbitrarily long numbers with optional sign and decimal point
121 ( E )
122 sqrt ( E )
123 length ( E ) number of significant decimal digits
124 scale ( E ) number of digits right of decimal point
125 L ( E , ... , E )
126 .Ed
127 .Pp
128 The sequence
129 .Sq \e<newline><whitespace>
130 is ignored within numbers.
131 .Pp
132 Operators
133 .Pp
134 The following arithmetic and logical operators can be used.
135 The semantics of the operators is the same as in the C language.
136 They are listed in order of decreasing precedence.
137 Operators in the same group have the same precedence.
138 .Bl -column -offset indent "= += \-= *= /= %= ^=" "Associativity" \
139 "multiply, divide, modulus"
140 .It Sy "Operator" Ta Sy "Associativity" Ta Sy "Description"
141 .It "++ \-\-" Ta "none" Ta "increment, decrement"
142 .It "\-" Ta "none" Ta "unary minus"
143 .It "^" Ta "right" Ta "power"
144 .It "* / %" Ta "left" Ta "multiply, divide, modulus"
145 .It "+ \-" Ta "left" Ta "plus, minus"
146 .It "= += -= *= /= %= ^=" Ta "right" Ta "assignment"
147 .It "== <= >= != < >" Ta "none" Ta "relational"
148 .It "!" Ta "none" Ta "boolean not"
149 .It "&&" Ta "left" Ta "boolean and"
150 .It "||" Ta "left" Ta "boolean or"
151 .El
152 .Pp
153 Note the following:
154 .Bl -bullet -offset indent
155 .It
156 The relational operators may appear in any expression.
157 The
158 .St -p1003.2
159 standard only allows them in the conditional expression of an
160 .Sq if ,
161 .Sq while
162 or
163 .Sq for
164 statement.
165 .It
166 The relational operators have a lower precedence than the assignment
167 operators.
168 This has the consequence that the expression
169 .Sy a = b < c
170 is interpreted as
171 .Sy (a = b) < c ,
172 which is probably not what the programmer intended.
173 .It
174 In contrast with the C language, the relational operators all have
175 the same precedence, and are non-associative.
176 The expression
177 .Sy a < b < c
178 will produce a syntax error.
179 .It
180 The boolean operators (!, && and ||) are non-portable extensions.
181 .It
182 The boolean not
183 (!) operator has much lower precedence than the same operator in the
184 C language.
185 This has the consequence that the expression
186 .Sy !a < b
187 is interpreted as
188 .Sy !(a < b) .
189 Prudent programmers use parentheses when writing expressions involving
190 boolean operators.
191 .El
192 .Pp
193 Statements
194 .Bd -unfilled -offset indent -compact
195 E
196 { S ; ... ; S }
197 if ( E ) S
198 if ( E ) S else S
199 while ( E ) S
200 for ( E ; E ; E ) S
201 null statement
202 break
203 continue
204 quit
205 a string of characters, enclosed in double quotes
206 print E ,..., E
207 .Ed
208 .Pp
209 A string may contain any character, except a double quote.
210 The if statement with an else branch is a non-portable extension.
211 All three E's in a for statement may be empty.
212 This is a non-portable extension.
213 The continue and print statements are also non-portable extensions.
214 .Pp
215 The print statement takes a list of comma-separated expressions.
216 Each expression in the list is evaluated and the computed
217 value is printed and assigned to the variable `last'.
218 No trailing newline is printed.
219 The expression may also be a string enclosed in double quotes.
220 Within these strings the following escape sequences may be used:
221 .Sq \ea
222 for bell (alert),
223 .Sq \eb
224 for backspace,
225 .Sq \ef
226 for formfeed,
227 .Sq \en
228 for newline,
229 .Sq \er
230 for carriage return,
231 .Sq \et
232 for tab,
233 .Sq \eq
234 for double quote and
235 .Sq \e\e
236 for backslash.
237 Any other character following a backslash will be ignored.
238 Strings will not be assigned to `last'.
239 .Pp
240 Function definitions
241 .Bd -unfilled -offset indent
242 define L ( L ,..., L ) {
243 auto L, ... , L
244 S; ... S
245 return ( E )
246 }
247 .Ed
248 .Pp
249 As a non-portable extension, the opening brace of the define statement
250 may appear on the next line.
251 The return statement may also appear in the following forms:
252 .Bd -unfilled -offset indent
253 return
254 return ()
255 return E
256 .Ed
257 .Pp
258 The first two are equivalent to the statement
259 .Dq return 0 .
260 The last form is a non-portable extension.
261 Not specifying a return statement is equivalent to writing
262 .Dq return (0) .
263 .Pp
264 Functions available in the math library, which is loaded by specifying the
265 .Fl l
266 flag on the command line
267 .Pp
268 .Bl -tag -width j(n,x) -offset indent -compact
269 .It s(x)
270 sine
271 .It c(x)
272 cosine
273 .It e(x)
274 exponential
275 .It l(x)
276 log
277 .It a(x)
278 arctangent
279 .It j(n,x)
280 Bessel function
281 .El
282 .Pp
283 All function arguments are passed by value.
284 .Pp
285 The value of a statement that is an expression is printed
286 unless the main operator is an assignment.
287 The value printed is assigned to the special variable `last'.
288 This is a non-portable extension.
289 A single dot may be used as a synonym for `last'.
290 Either semicolons or newlines may separate statements.
291 Assignment to
292 .Ar scale
293 influences the number of digits to be retained on arithmetic
294 operations in the manner of
295 .Xr dc 1 .
296 Assignments to
297 .Ar ibase
298 or
299 .Ar obase
300 set the input and output number radix respectively.
301 .Pp
302 The same letter may be used as an array, a function,
303 and a simple variable simultaneously.
304 All variables are global to the program.
305 `Auto' variables are pushed down during function calls.
306 When using arrays as function arguments
307 or defining them as automatic variables,
308 empty square brackets must follow the array name.
309 .Pp
310 For example
311 .Bd -literal -offset indent
312 scale = 20
313 define e(x){
314 auto a, b, c, i, s
315 a = 1
316 b = 1
317 s = 1
318 for(i=1; 1==1; i++){
319 a = a*x
320 b = b*i
321 c = a/b
322 if(c == 0) return(s)
323 s = s+c
324 }
325 }
326 .Ed
327 .Pp
328 defines a function to compute an approximate value of
329 the exponential function and
330 .Pp
331 .Dl for(i=1; i<=10; i++) e(i)
332 .Pp
333 prints approximate values of the exponential function of
334 the first ten integers.
335 .Bd -literal -offset indent
336 $ bc -l -e 'scale = 500; 2 * a(2^10000)' -e quit
337 .Ed
338 .Pp
339 prints an approximation of pi.
340 .Sh FILES
341 .Bl -tag -width /usr/share/misc/bc.library -compact
342 .It Pa /usr/share/misc/bc.library
343 math library, read when the
344 .Fl l
345 option is specified on the command line.
346 .El
347 .Sh SEE ALSO
348 .Xr dc 1
349 .Pp
350 "BC \- An Arbitrary Precision Desk-Calculator Language",
351 .Pa /usr/share/doc/usd/06.bc/ .
352 .Sh STANDARDS
353 The
354 .Nm
355 utility is compliant with the
356 .St -p1003.1-2004
357 specification.
358 .Pp
359 The flags
360 .Op Fl ce
361 are extensions to that specification.
362 .Sh HISTORY
363 The
364 .Nm
365 command first appeared in
366 .At v6 .
367 A complete rewrite of the
368 .Nm
369 command first appeared in
370 .Ox 3.5 .
371 .Sh AUTHORS
372 .An -nosplit
373 The original version of the
374 .Nm
375 command was written by
376 .An Robert Morris
377 and
378 .An Lorinda Cherry .
379 The current version of the
380 .Nm
381 utility was written by
382 .An Otto Moerbeek .
383 .Sh BUGS
384 .Ql Quit
385 is interpreted when read, not when executed.
386 .Pp
387 Some non-portable extensions, as found in the GNU version of the
388 .Nm
389 utility are not implemented (yet).