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