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33 bc - arbitrary-precision decimal arithmetic language and calculator
37 **bc** [**-cCghilPqRsvVw**] [**-\-digit-clamp**] [**-\-no-digit-clamp**] [**-\-global-stacks**] [**-\-help**] [**-\-interactive**] [**-\-mathlib**] [**-\-no-prompt**] [**-\-no-read-prompt**] [**-\-quiet**] [**-\-standard**] [**-\-warn**] [**-\-version**] [**-e** *expr*] [**-\-expression**=*expr*...] [**-f** *file*...] [**-\-file**=*file*...] [*file*...]
41 bc(1) is an interactive processor for a language first standardized in 1991 by
42 POSIX. (See the **STANDARDS** section.) The language provides unlimited
43 precision decimal arithmetic and is somewhat C-like, but there are differences.
44 Such differences will be noted in this document.
46 After parsing and handling options, this bc(1) reads any files given on the
47 command line and executes them before reading from **stdin**.
49 This bc(1) is a drop-in replacement for *any* bc(1), including (and
50 especially) the GNU bc(1). It also has many extensions and extra features beyond
51 other implementations.
53 **Note**: If running this bc(1) on *any* script meant for another bc(1) gives a
54 parse error, it is probably because a word this bc(1) reserves as a keyword is
55 used as the name of a function, variable, or array. To fix that, use the
56 command-line option **-r** *keyword*, where *keyword* is the keyword that is
57 used as a name in the script. For more information, see the **OPTIONS** section.
59 If parsing scripts meant for other bc(1) implementations still does not work,
60 that is a bug and should be reported. See the **BUGS** section.
64 The following are the options that bc(1) accepts.
66 **-C**, **-\-no-digit-clamp**
68 : Disables clamping of digits greater than or equal to the current **ibase**
71 This means that the value added to a number from a digit is always that
72 digit's value multiplied by the value of ibase raised to the power of the
73 digit's position, which starts from 0 at the least significant digit.
75 If this and/or the **-c** or **-\-digit-clamp** options are given multiple
76 times, the last one given is used.
78 This option overrides the **BC_DIGIT_CLAMP** environment variable (see the
79 **ENVIRONMENT VARIABLES** section) and the default, which can be queried
80 with the **-h** or **-\-help** options.
82 This is a **non-portable extension**.
84 **-c**, **-\-digit-clamp**
86 : Enables clamping of digits greater than or equal to the current **ibase**
89 This means that digits that the value added to a number from a digit that is
90 greater than or equal to the ibase is the value of ibase minus 1 all
91 multiplied by the value of ibase raised to the power of the digit's
92 position, which starts from 0 at the least significant digit.
94 If this and/or the **-C** or **-\-no-digit-clamp** options are given
95 multiple times, the last one given is used.
97 This option overrides the **BC_DIGIT_CLAMP** environment variable (see the
98 **ENVIRONMENT VARIABLES** section) and the default, which can be queried
99 with the **-h** or **-\-help** options.
101 This is a **non-portable extension**.
103 **-e** *expr*, **-\-expression**=*expr*
105 : Evaluates *expr*. If multiple expressions are given, they are evaluated in
106 order. If files are given as well (see the **-f** and **-\-file** options),
107 the expressions and files are evaluated in the order given. This means that
108 if a file is given before an expression, the file is read in and evaluated
111 If this option is given on the command-line (i.e., not in **BC_ENV_ARGS**,
112 see the **ENVIRONMENT VARIABLES** section), then after processing all
113 expressions and files, bc(1) will exit, unless **-** (**stdin**) was given
114 as an argument at least once to **-f** or **-\-file**, whether on the
115 command-line or in **BC_ENV_ARGS**. However, if any other **-e**,
116 **-\-expression**, **-f**, or **-\-file** arguments are given after **-f-**
117 or equivalent is given, bc(1) will give a fatal error and exit.
119 This is a **non-portable extension**.
121 **-f** *file*, **-\-file**=*file*
123 : Reads in *file* and evaluates it, line by line, as though it were read
124 through **stdin**. If expressions are also given (see the **-e** and
125 **-\-expression** options), the expressions are evaluated in the order
128 If this option is given on the command-line (i.e., not in **BC_ENV_ARGS**,
129 see the **ENVIRONMENT VARIABLES** section), then after processing all
130 expressions and files, bc(1) will exit, unless **-** (**stdin**) was given
131 as an argument at least once to **-f** or **-\-file**. However, if any other
132 **-e**, **-\-expression**, **-f**, or **-\-file** arguments are given after
133 **-f-** or equivalent is given, bc(1) will give a fatal error and exit.
135 This is a **non-portable extension**.
137 **-g**, **-\-global-stacks**
139 : Turns the globals **ibase**, **obase**, and **scale** into stacks.
141 This has the effect that a copy of the current value of all three are pushed
142 onto a stack for every function call, as well as popped when every function
143 returns. This means that functions can assign to any and all of those
144 globals without worrying that the change will affect other functions.
145 Thus, a hypothetical function named **output(x,b)** that simply printed
146 **x** in base **b** could be written like this:
148 define void output(x, b) {
153 instead of like this:
155 define void output(x, b) {
163 This makes writing functions much easier.
165 However, since using this flag means that functions cannot set **ibase**,
166 **obase**, or **scale** globally, functions that are made to do so cannot
167 work anymore. There are two possible use cases for that, and each has a
170 First, if a function is called on startup to turn bc(1) into a number
171 converter, it is possible to replace that capability with various shell
174 alias d2o="bc -e ibase=A -e obase=8"
175 alias h2b="bc -e ibase=G -e obase=2"
177 Second, if the purpose of a function is to set **ibase**, **obase**, or
178 **scale** globally for any other purpose, it could be split into one to
179 three functions (based on how many globals it sets) and each of those
180 functions could return the desired value for a global.
182 If the behavior of this option is desired for every run of bc(1), then users
183 could make sure to define **BC_ENV_ARGS** and include this option (see the
184 **ENVIRONMENT VARIABLES** section for more details).
186 If **-s**, **-w**, or any equivalents are used, this option is ignored.
188 This is a **non-portable extension**.
192 : Prints a usage message and exits.
194 **-I** *ibase*, **-\-ibase**=*ibase*
196 : Sets the builtin variable **ibase** to the value *ibase* assuming that
197 *ibase* is in base 10. It is a fatal error if *ibase* is not a valid number.
199 If multiple instances of this option are given, the last is used.
201 This is a **non-portable extension**.
203 **-i**, **-\-interactive**
205 : Forces interactive mode. (See the **INTERACTIVE MODE** section.)
207 This is a **non-portable extension**.
209 **-L**, **-\-no-line-length**
211 : Disables line length checking and prints numbers without backslashes and
212 newlines. In other words, this option sets **BC_LINE_LENGTH** to **0** (see
213 the **ENVIRONMENT VARIABLES** section).
215 This is a **non-portable extension**.
217 **-l**, **-\-mathlib**
219 : Sets **scale** (see the **SYNTAX** section) to **20** and loads the included
220 math library before running any code, including any expressions or files
221 specified on the command line.
223 To learn what is in the library, see the **LIBRARY** section.
225 **-O** *obase*, **-\-obase**=*obase*
227 : Sets the builtin variable **obase** to the value *obase* assuming that
228 *obase* is in base 10. It is a fatal error if *obase* is not a valid number.
230 If multiple instances of this option are given, the last is used.
232 This is a **non-portable extension**.
234 **-P**, **-\-no-prompt**
236 : Disables the prompt in TTY mode. (The prompt is only enabled in TTY mode.
237 See the **TTY MODE** section.) This is mostly for those users that do not
238 want a prompt or are not used to having them in bc(1). Most of those users
239 would want to put this option in **BC_ENV_ARGS** (see the
240 **ENVIRONMENT VARIABLES** section).
242 These options override the **BC_PROMPT** and **BC_TTY_MODE** environment
243 variables (see the **ENVIRONMENT VARIABLES** section).
245 This is a **non-portable extension**.
249 : This option is for compatibility with the GNU bc(1)
250 (https://www.gnu.org/software/bc/); it is a no-op. Without this option, GNU
251 bc(1) prints a copyright header. This bc(1) only prints the copyright header
252 if one or more of the **-v**, **-V**, or **-\-version** options are given
253 unless the **BC_BANNER** environment variable is set and contains a non-zero
254 integer or if this bc(1) was built with the header displayed by default. If
255 *any* of that is the case, then this option *does* prevent bc(1) from
258 This is a **non-portable extension**.
260 **-R**, **-\-no-read-prompt**
262 : Disables the read prompt in TTY mode. (The read prompt is only enabled in
263 TTY mode. See the **TTY MODE** section.) This is mostly for those users that
264 do not want a read prompt or are not used to having them in bc(1). Most of
265 those users would want to put this option in **BC_ENV_ARGS** (see the
266 **ENVIRONMENT VARIABLES** section). This option is also useful in hash bang
267 lines of bc(1) scripts that prompt for user input.
269 This option does not disable the regular prompt because the read prompt is
270 only used when the **read()** built-in function is called.
272 These options *do* override the **BC_PROMPT** and **BC_TTY_MODE**
273 environment variables (see the **ENVIRONMENT VARIABLES** section), but only
276 This is a **non-portable extension**.
278 **-r** *keyword*, **-\-redefine**=*keyword*
280 : Redefines *keyword* in order to allow it to be used as a function, variable,
281 or array name. This is useful when this bc(1) gives parse errors when
282 parsing scripts meant for other bc(1) implementations.
284 The keywords this bc(1) allows to be redefined are:
302 If any of those keywords are used as a function, variable, or array name in
303 a script, use this option with the keyword as the argument. If multiple are
304 used, use this option for all of them; it can be used multiple times.
306 Keywords are *not* redefined when parsing the builtin math library (see the
307 **LIBRARY** section).
309 It is a fatal error to redefine keywords mandated by the POSIX standard (see
310 the **STANDARDS** section). It is a fatal error to attempt to redefine words
311 that this bc(1) does not reserve as keywords.
313 **-S** *scale*, **-\-scale**=*scale*
315 : Sets the builtin variable **scale** to the value *scale* assuming that
316 *scale* is in base 10. It is a fatal error if *scale* is not a valid number.
318 If multiple instances of this option are given, the last is used.
320 This is a **non-portable extension**.
322 **-s**, **-\-standard**
324 : Process exactly the language defined by the standard (see the **STANDARDS**
325 section) and error if any extensions are used.
327 This is a **non-portable extension**.
329 **-v**, **-V**, **-\-version**
331 : Print the version information (copyright header) and exits.
333 This is a **non-portable extension**.
337 : Like **-s** and **-\-standard**, except that warnings (and not errors) are
338 printed for non-standard extensions and execution continues normally.
340 This is a **non-portable extension**.
342 **-z**, **-\-leading-zeroes**
344 : Makes bc(1) print all numbers greater than **-1** and less than **1**, and
345 not equal to **0**, with a leading zero.
347 This can be set for individual numbers with the **plz(x)**, **plznl(x)**,
348 **pnlz(x)**, and **pnlznl(x)** functions in the extended math library (see
349 the **LIBRARY** section).
351 This is a **non-portable extension**.
353 All long options are **non-portable extensions**.
357 If no files or expressions are given by the **-f**, **-\-file**, **-e**, or
358 **-\-expression** options, then bc(1) reads from **stdin**.
360 However, there are a few caveats to this.
362 First, **stdin** is evaluated a line at a time. The only exception to this is if
363 the parse cannot complete. That means that starting a string without ending it
364 or starting a function, **if** statement, or loop without ending it will also
365 cause bc(1) to not execute.
367 Second, after an **if** statement, bc(1) doesn't know if an **else** statement
368 will follow, so it will not execute until it knows there will not be an **else**
373 Any non-error output is written to **stdout**. In addition, if history (see the
374 **HISTORY** section) and the prompt (see the **TTY MODE** section) are enabled,
375 both are output to **stdout**.
377 **Note**: Unlike other bc(1) implementations, this bc(1) will issue a fatal
378 error (see the **EXIT STATUS** section) if it cannot write to **stdout**, so if
379 **stdout** is closed, as in **bc <file> >&-**, it will quit with an error. This
380 is done so that bc(1) can report problems when **stdout** is redirected to a
383 If there are scripts that depend on the behavior of other bc(1) implementations,
384 it is recommended that those scripts be changed to redirect **stdout** to
389 Any error output is written to **stderr**.
391 **Note**: Unlike other bc(1) implementations, this bc(1) will issue a fatal
392 error (see the **EXIT STATUS** section) if it cannot write to **stderr**, so if
393 **stderr** is closed, as in **bc <file> 2>&-**, it will quit with an error. This
394 is done so that bc(1) can exit with an error code when **stderr** is redirected
397 If there are scripts that depend on the behavior of other bc(1) implementations,
398 it is recommended that those scripts be changed to redirect **stderr** to
403 The syntax for bc(1) programs is mostly C-like, with some differences. This
404 bc(1) follows the POSIX standard (see the **STANDARDS** section), which is a
405 much more thorough resource for the language this bc(1) accepts. This section is
406 meant to be a summary and a listing of all the extensions to the standard.
408 In the sections below, **E** means expression, **S** means statement, and **I**
411 Identifiers (**I**) start with a lowercase letter and can be followed by any
412 number (up to **BC_NAME_MAX-1**) of lowercase letters (**a-z**), digits
413 (**0-9**), and underscores (**\_**). The regex is **\[a-z\]\[a-z0-9\_\]\***.
414 Identifiers with more than one character (letter) are a
415 **non-portable extension**.
417 **ibase** is a global variable determining how to interpret constant numbers. It
418 is the "input" base, or the number base used for interpreting input numbers.
419 **ibase** is initially **10**. If the **-s** (**-\-standard**) and **-w**
420 (**-\-warn**) flags were not given on the command line, the max allowable value
421 for **ibase** is **36**. Otherwise, it is **16**. The min allowable value for
422 **ibase** is **2**. The max allowable value for **ibase** can be queried in
423 bc(1) programs with the **maxibase()** built-in function.
425 **obase** is a global variable determining how to output results. It is the
426 "output" base, or the number base used for outputting numbers. **obase** is
427 initially **10**. The max allowable value for **obase** is **BC_BASE_MAX** and
428 can be queried in bc(1) programs with the **maxobase()** built-in function. The
429 min allowable value for **obase** is **2**. Values are output in the specified
432 The *scale* of an expression is the number of digits in the result of the
433 expression right of the decimal point, and **scale** is a global variable that
434 sets the precision of any operations, with exceptions. **scale** is initially
435 **0**. **scale** cannot be negative. The max allowable value for **scale** is
436 **BC_SCALE_MAX** and can be queried in bc(1) programs with the **maxscale()**
439 bc(1) has both *global* variables and *local* variables. All *local*
440 variables are local to the function; they are parameters or are introduced in
441 the **auto** list of a function (see the **FUNCTIONS** section). If a variable
442 is accessed which is not a parameter or in the **auto** list, it is assumed to
443 be *global*. If a parent function has a *local* variable version of a variable
444 that a child function considers *global*, the value of that *global* variable in
445 the child function is the value of the variable in the parent function, not the
446 value of the actual *global* variable.
448 All of the above applies to arrays as well.
450 The value of a statement that is an expression (i.e., any of the named
451 expressions or operands) is printed unless the lowest precedence operator is an
452 assignment operator *and* the expression is notsurrounded by parentheses.
454 The value that is printed is also assigned to the special variable **last**. A
455 single dot (**.**) may also be used as a synonym for **last**. These are
456 **non-portable extensions**.
458 Either semicolons or newlines may separate statements.
462 There are two kinds of comments:
464 1. Block comments are enclosed in **/\*** and **\*/**.
465 2. Line comments go from **#** until, and not including, the next newline. This
466 is a **non-portable extension**.
470 The following are named expressions in bc(1):
473 2. Array Elements: **I[E]**
477 6. **last** or a single dot (**.**)
479 Number 6 is a **non-portable extension**.
481 Variables and arrays do not interfere; users can have arrays named the same as
482 variables. This also applies to functions (see the **FUNCTIONS** section), so a
483 user can have a variable, array, and function that all have the same name, and
484 they will not shadow each other, whether inside of functions or not.
486 Named expressions are required as the operand of **increment**/**decrement**
487 operators and as the left side of **assignment** operators (see the *Operators*
492 The following are valid operands in bc(1):
494 1. Numbers (see the *Numbers* subsection below).
495 2. Array indices (**I[E]**).
496 3. **(E)**: The value of **E** (used to change precedence).
497 4. **sqrt(E)**: The square root of **E**. **E** must be non-negative.
498 5. **length(E)**: The number of significant decimal digits in **E**. Returns
499 **1** for **0** with no decimal places. If given a string, the length of the
500 string is returned. Passing a string to **length(E)** is a **non-portable
502 6. **length(I[])**: The number of elements in the array **I**. This is a
503 **non-portable extension**.
504 7. **scale(E)**: The *scale* of **E**.
505 8. **abs(E)**: The absolute value of **E**. This is a **non-portable
507 9. **is_number(E)**: **1** if the given argument is a number, **0** if it is a
508 string. This is a **non-portable extension**.
509 10. **is_string(E)**: **1** if the given argument is a string, **0** if it is a
510 number. This is a **non-portable extension**.
511 11. **modexp(E, E, E)**: Modular exponentiation, where the first expression is
512 the base, the second is the exponent, and the third is the modulus. All
513 three values must be integers. The second argument must be non-negative. The
514 third argument must be non-zero. This is a **non-portable extension**.
515 11. **divmod(E, E, I[])**: Division and modulus in one operation. This is for
516 optimization. The first expression is the dividend, and the second is the
517 divisor, which must be non-zero. The return value is the quotient, and the
518 modulus is stored in index **0** of the provided array (the last argument).
519 This is a **non-portable extension**.
520 12. **asciify(E)**: If **E** is a string, returns a string that is the first
521 letter of its argument. If it is a number, calculates the number mod **256**
522 and returns that number as a one-character string. This is a **non-portable
524 13. **asciify(I[])**: A string that is made up of the characters that would
525 result from running **asciify(E)** on each element of the array identified
526 by the argument. This allows creating multi-character strings and storing
527 them. This is a **non-portable extension**.
528 14. **I()**, **I(E)**, **I(E, E)**, and so on, where **I** is an identifier for
529 a non-**void** function (see the *Void Functions* subsection of the
530 **FUNCTIONS** section). The **E** argument(s) may also be arrays of the form
531 **I[]**, which will automatically be turned into array references (see the
532 *Array References* subsection of the **FUNCTIONS** section) if the
533 corresponding parameter in the function definition is an array reference.
534 15. **read()**: Reads a line from **stdin** and uses that as an expression. The
535 result of that expression is the result of the **read()** operand. This is a
536 **non-portable extension**.
537 16. **maxibase()**: The max allowable **ibase**. This is a **non-portable
539 17. **maxobase()**: The max allowable **obase**. This is a **non-portable
541 18. **maxscale()**: The max allowable **scale**. This is a **non-portable
543 19. **line_length()**: The line length set with **BC_LINE_LENGTH** (see the
544 **ENVIRONMENT VARIABLES** section). This is a **non-portable extension**.
545 20. **global_stacks()**: **0** if global stacks are not enabled with the **-g**
546 or **-\-global-stacks** options, non-zero otherwise. See the **OPTIONS**
547 section. This is a **non-portable extension**.
548 21. **leading_zero()**: **0** if leading zeroes are not enabled with the **-z**
549 or **--leading-zeroes** options, non-zero otherwise. See the **OPTIONS**
550 section. This is a **non-portable extension**.
554 Numbers are strings made up of digits, uppercase letters, and at most **1**
555 period for a radix. Numbers can have up to **BC_NUM_MAX** digits. Uppercase
556 letters are equal to **9** plus their position in the alphabet, starting from
557 **1** (i.e., **A** equals **10**, or **9+1**).
559 If a digit or letter makes no sense with the current value of **ibase** (i.e.,
560 they are greater than or equal to the current value of **ibase**), then the
561 behavior depends on the existence of the **-c**/**-\-digit-clamp** or
562 **-C**/**-\-no-digit-clamp** options (see the **OPTIONS** section), the
563 existence and setting of the **BC_DIGIT_CLAMP** environment variable (see the
564 **ENVIRONMENT VARIABLES** section), or the default, which can be queried with
565 the **-h**/**-\-help** option.
567 If clamping is off, then digits or letters that are greater than or equal to the
568 current value of **ibase** are not changed. Instead, their given value is
569 multiplied by the appropriate power of **ibase** and added into the number. This
570 means that, with an **ibase** of **3**, the number **AB** is equal to
571 **3\^1\*A+3\^0\*B**, which is **3** times **10** plus **11**, or **41**.
573 If clamping is on, then digits or letters that are greater than or equal to the
574 current value of **ibase** are set to the value of the highest valid digit in
575 **ibase** before being multiplied by the appropriate power of **ibase** and
576 added into the number. This means that, with an **ibase** of **3**, the number
577 **AB** is equal to **3\^1\*2+3\^0\*2**, which is **3** times **2** plus **2**,
580 There is one exception to clamping: single-character numbers (i.e., **A**
581 alone). Such numbers are never clamped and always take the value they would have
582 in the highest possible **ibase**. This means that **A** alone always equals
583 decimal **10** and **Z** alone always equals decimal **35**. This behavior is
584 mandated by the standard (see the STANDARDS section) and is meant to provide an
585 easy way to set the current **ibase** (with the **i** command) regardless of the
586 current value of **ibase**.
588 If clamping is on, and the clamped value of a character is needed, use a leading
589 zero, i.e., for **A**, use **0A**.
593 The following arithmetic and logical operators can be used. They are listed in
594 order of decreasing precedence. Operators in the same group have the same
599 : Type: Prefix and Postfix
603 Description: **increment**, **decrement**
611 Description: **negation**, **boolean not**
619 Description: **power**
627 Description: **multiply**, **divide**, **modulus**
635 Description: **add**, **subtract**
637 **=** **+=** **-=** **\*=** **/=** **%=** **\^=**
643 Description: **assignment**
645 **==** **\<=** **\>=** **!=** **\<** **\>**
651 Description: **relational**
659 Description: **boolean and**
667 Description: **boolean or**
669 The operators will be described in more detail below.
673 : The prefix and postfix **increment** and **decrement** operators behave
674 exactly like they would in C. They require a named expression (see the
675 *Named Expressions* subsection) as an operand.
677 The prefix versions of these operators are more efficient; use them where
682 : The **negation** operator returns **0** if a user attempts to negate any
683 expression with the value **0**. Otherwise, a copy of the expression with
684 its sign flipped is returned.
688 : The **boolean not** operator returns **1** if the expression is **0**, or
691 This is a **non-portable extension**.
695 : The **power** operator (not the **exclusive or** operator, as it would be in
696 C) takes two expressions and raises the first to the power of the value of
697 the second. The *scale* of the result is equal to **scale**.
699 The second expression must be an integer (no *scale*), and if it is
700 negative, the first value must be non-zero.
704 : The **multiply** operator takes two expressions, multiplies them, and
705 returns the product. If **a** is the *scale* of the first expression and
706 **b** is the *scale* of the second expression, the *scale* of the result is
707 equal to **min(a+b,max(scale,a,b))** where **min()** and **max()** return
712 : The **divide** operator takes two expressions, divides them, and returns the
713 quotient. The *scale* of the result shall be the value of **scale**.
715 The second expression must be non-zero.
719 : The **modulus** operator takes two expressions, **a** and **b**, and
720 evaluates them by 1) Computing **a/b** to current **scale** and 2) Using the
721 result of step 1 to calculate **a-(a/b)\*b** to *scale*
722 **max(scale+scale(b),scale(a))**.
724 The second expression must be non-zero.
728 : The **add** operator takes two expressions, **a** and **b**, and returns the
729 sum, with a *scale* equal to the max of the *scale*s of **a** and **b**.
733 : The **subtract** operator takes two expressions, **a** and **b**, and
734 returns the difference, with a *scale* equal to the max of the *scale*s of
737 **=** **+=** **-=** **\*=** **/=** **%=** **\^=**
739 : The **assignment** operators take two expressions, **a** and **b** where
740 **a** is a named expression (see the *Named Expressions* subsection).
742 For **=**, **b** is copied and the result is assigned to **a**. For all
743 others, **a** and **b** are applied as operands to the corresponding
744 arithmetic operator and the result is assigned to **a**.
746 **==** **\<=** **\>=** **!=** **\<** **\>**
748 : The **relational** operators compare two expressions, **a** and **b**, and
749 if the relation holds, according to C language semantics, the result is
750 **1**. Otherwise, it is **0**.
752 Note that unlike in C, these operators have a lower precedence than the
753 **assignment** operators, which means that **a=b\>c** is interpreted as
756 Also, unlike the standard (see the **STANDARDS** section) requires, these
757 operators can appear anywhere any other expressions can be used. This
758 allowance is a **non-portable extension**.
762 : The **boolean and** operator takes two expressions and returns **1** if both
763 expressions are non-zero, **0** otherwise.
765 This is *not* a short-circuit operator.
767 This is a **non-portable extension**.
771 : The **boolean or** operator takes two expressions and returns **1** if one
772 of the expressions is non-zero, **0** otherwise.
774 This is *not* a short-circuit operator.
776 This is a **non-portable extension**.
780 The following items are statements:
783 2. **{** **S** **;** ... **;** **S** **}**
784 3. **if** **(** **E** **)** **S**
785 4. **if** **(** **E** **)** **S** **else** **S**
786 5. **while** **(** **E** **)** **S**
787 6. **for** **(** **E** **;** **E** **;** **E** **)** **S**
788 7. An empty statement
794 13. A string of characters, enclosed in double quotes
795 14. **print** **E** **,** ... **,** **E**
796 15. **stream** **E** **,** ... **,** **E**
797 16. **I()**, **I(E)**, **I(E, E)**, and so on, where **I** is an identifier for
798 a **void** function (see the *Void Functions* subsection of the
799 **FUNCTIONS** section). The **E** argument(s) may also be arrays of the form
800 **I[]**, which will automatically be turned into array references (see the
801 *Array References* subsection of the **FUNCTIONS** section) if the
802 corresponding parameter in the function definition is an array reference.
804 Numbers 4, 9, 11, 12, 14, 15, and 16 are **non-portable extensions**.
806 Also, as a **non-portable extension**, any or all of the expressions in the
807 header of a for loop may be omitted. If the condition (second expression) is
808 omitted, it is assumed to be a constant **1**.
810 The **break** statement causes a loop to stop iterating and resume execution
811 immediately following a loop. This is only allowed in loops.
813 The **continue** statement causes a loop iteration to stop early and returns to
814 the start of the loop, including testing the loop condition. This is only
817 The **if** **else** statement does the same thing as in C.
819 The **quit** statement causes bc(1) to quit, even if it is on a branch that will
820 not be executed (it is a compile-time command).
822 **Warning**: The behavior of this bc(1) on **quit** is slightly different from
823 other bc(1) implementations. Other bc(1) implementations will exit as soon as
824 they finish parsing the line that a **quit** command is on. This bc(1) will
825 execute any completed and executable statements that occur before the **quit**
826 statement before exiting.
828 In other words, for the bc(1) code below:
830 for (i = 0; i < 3; ++i) i; quit
832 Other bc(1) implementations will print nothing, and this bc(1) will print **0**,
833 **1**, and **2** on successive lines before exiting.
835 The **halt** statement causes bc(1) to quit, if it is executed. (Unlike **quit**
836 if it is on a branch of an **if** statement that is not executed, bc(1) does not
839 The **limits** statement prints the limits that this bc(1) is subject to. This
840 is like the **quit** statement in that it is a compile-time command.
842 An expression by itself is evaluated and printed, followed by a newline.
846 If strings appear as a statement by themselves, they are printed without a
849 In addition to appearing as a lone statement by themselves, strings can be
850 assigned to variables and array elements. They can also be passed to functions
851 in variable parameters.
853 If any statement that expects a string is given a variable that had a string
854 assigned to it, the statement acts as though it had received a string.
856 If any math operation is attempted on a string or a variable or array element
857 that has been assigned a string, an error is raised, and bc(1) resets (see the
860 Assigning strings to variables and array elements and passing them to functions
861 are **non-portable extensions**.
865 The "expressions" in a **print** statement may also be strings. If they are, there
866 are backslash escape sequences that are interpreted specially. What those
867 sequences are, and what they cause to be printed, are shown below:
887 Any other character following a backslash causes the backslash and character to
890 Any non-string expression in a print statement shall be assigned to **last**,
891 like any other expression that is printed.
895 The "expressions in a **stream** statement may also be strings.
897 If a **stream** statement is given a string, it prints the string as though the
898 string had appeared as its own statement. In other words, the **stream**
899 statement prints strings normally, without a newline.
901 If a **stream** statement is given a number, a copy of it is truncated and its
902 absolute value is calculated. The result is then printed as though **obase** is
903 **256** and each digit is interpreted as an 8-bit ASCII character, making it a
906 ## Order of Evaluation
908 All expressions in a statment are evaluated left to right, except as necessary
909 to maintain order of operations. This means, for example, assuming that **i** is
910 equal to **0**, in the expression
914 the first (or 0th) element of **a** is set to **1**, and **i** is equal to **2**
915 at the end of the expression.
917 This includes function arguments. Thus, assuming **i** is equal to **0**, this
918 means that in the expression
922 the first argument passed to **x()** is **0**, and the second argument is **1**,
923 while **i** is equal to **2** before the function starts executing.
927 Function definitions are as follows:
937 Any **I** in the parameter list or **auto** list may be replaced with **I[]** to
938 make a parameter or **auto** var an array, and any **I** in the parameter list
939 may be replaced with **\*I[]** to make a parameter an array reference. Callers
940 of functions that take array references should not put an asterisk in the call;
941 they must be called with just **I[]** like normal array parameters and will be
942 automatically converted into references.
944 As a **non-portable extension**, the opening brace of a **define** statement may
945 appear on the next line.
947 As a **non-portable extension**, the return statement may also be in one of the
951 2. **return** **(** **)**
954 The first two, or not specifying a **return** statement, is equivalent to
955 **return (0)**, unless the function is a **void** function (see the *Void
956 Functions* subsection below).
960 Functions can also be **void** functions, defined as follows:
963 define void I(I,...,I){
970 They can only be used as standalone expressions, where such an expression would
971 be printed alone, except in a print statement.
973 Void functions can only use the first two **return** statements listed above.
974 They can also omit the return statement entirely.
976 The word "void" is not treated as a keyword; it is still possible to have
977 variables, arrays, and functions named **void**. The word "void" is only
978 treated specially right after the **define** keyword.
980 This is a **non-portable extension**.
984 For any array in the parameter list, if the array is declared in the form
990 it is a **reference**. Any changes to the array in the function are reflected,
991 when the function returns, to the array that was passed in.
993 Other than this, all function arguments are passed by value.
995 This is a **non-portable extension**.
999 All of the functions below are available when the **-l** or **-\-mathlib**
1000 command-line flags are given.
1004 The standard (see the **STANDARDS** section) defines the following functions for
1009 : Returns the sine of **x**, which is assumed to be in radians.
1011 This is a transcendental function (see the *Transcendental Functions*
1016 : Returns the cosine of **x**, which is assumed to be in radians.
1018 This is a transcendental function (see the *Transcendental Functions*
1023 : Returns the arctangent of **x**, in radians.
1025 This is a transcendental function (see the *Transcendental Functions*
1030 : Returns the natural logarithm of **x**.
1032 This is a transcendental function (see the *Transcendental Functions*
1037 : Returns the mathematical constant **e** raised to the power of **x**.
1039 This is a transcendental function (see the *Transcendental Functions*
1044 : Returns the bessel integer order **n** (truncated) of **x**.
1046 This is a transcendental function (see the *Transcendental Functions*
1049 ## Transcendental Functions
1051 All transcendental functions can return slightly inaccurate results, up to 1 ULP
1052 (https://en.wikipedia.org/wiki/Unit_in_the_last_place). This is unavoidable, and
1053 the article at https://people.eecs.berkeley.edu/~wkahan/LOG10HAF.TXT explains
1054 why it is impossible and unnecessary to calculate exact results for the
1055 transcendental functions.
1057 Because of the possible inaccuracy, I recommend that users call those functions
1058 with the precision (**scale**) set to at least 1 higher than is necessary. If
1059 exact results are *absolutely* required, users can double the precision
1060 (**scale**) and then truncate.
1062 The transcendental functions in the standard math library are:
1073 When bc(1) encounters an error or a signal that it has a non-default handler
1074 for, it resets. This means that several things happen.
1076 First, any functions that are executing are stopped and popped off the stack.
1077 The behavior is not unlike that of exceptions in programming languages. Then
1078 the execution point is set so that any code waiting to execute (after all
1079 functions returned) is skipped.
1081 Thus, when bc(1) resets, it skips any remaining code waiting to be executed.
1082 Then, if it is interactive mode, and the error was not a fatal error (see the
1083 **EXIT STATUS** section), it asks for more input; otherwise, it exits with the
1084 appropriate return code.
1086 Note that this reset behavior is different from the GNU bc(1), which attempts to
1087 start executing the statement right after the one that caused an error.
1091 Most bc(1) implementations use **char** types to calculate the value of **1**
1092 decimal digit at a time, but that can be slow. This bc(1) does something
1095 It uses large integers to calculate more than **1** decimal digit at a time. If
1096 built in a environment where **BC_LONG_BIT** (see the **LIMITS** section) is
1097 **64**, then each integer has **9** decimal digits. If built in an environment
1098 where **BC_LONG_BIT** is **32** then each integer has **4** decimal digits. This
1099 value (the number of decimal digits per large integer) is called
1102 The actual values of **BC_LONG_BIT** and **BC_BASE_DIGS** can be queried with
1103 the **limits** statement.
1105 In addition, this bc(1) uses an even larger integer for overflow checking. This
1106 integer type depends on the value of **BC_LONG_BIT**, but is always at least
1107 twice as large as the integer type used to store digits.
1111 The following are the limits on bc(1):
1115 : The number of bits in the **long** type in the environment where bc(1) was
1116 built. This determines how many decimal digits can be stored in a single
1117 large integer (see the **PERFORMANCE** section).
1121 : The number of decimal digits per large integer (see the **PERFORMANCE**
1122 section). Depends on **BC_LONG_BIT**.
1126 : The max decimal number that each large integer can store (see
1127 **BC_BASE_DIGS**) plus **1**. Depends on **BC_BASE_DIGS**.
1131 : The max number that the overflow type (see the **PERFORMANCE** section) can
1132 hold. Depends on **BC_LONG_BIT**.
1136 : The maximum output base. Set at **BC_BASE_POW**.
1140 : The maximum size of arrays. Set at **SIZE_MAX-1**.
1144 : The maximum **scale**. Set at **BC_OVERFLOW_MAX-1**.
1148 : The maximum length of strings. Set at **BC_OVERFLOW_MAX-1**.
1152 : The maximum length of identifiers. Set at **BC_OVERFLOW_MAX-1**.
1156 : The maximum length of a number (in decimal digits), which includes digits
1157 after the decimal point. Set at **BC_OVERFLOW_MAX-1**.
1161 : The maximum allowable exponent (positive or negative). Set at
1162 **BC_OVERFLOW_MAX**.
1166 : The maximum number of vars/arrays. Set at **SIZE_MAX-1**.
1168 The actual values can be queried with the **limits** statement.
1170 These limits are meant to be effectively non-existent; the limits are so large
1171 (at least on 64-bit machines) that there should not be any point at which they
1172 become a problem. In fact, memory should be exhausted before these limits should
1175 # ENVIRONMENT VARIABLES
1177 As **non-portable extensions**, bc(1) recognizes the following environment
1182 : If this variable exists (no matter the contents), bc(1) behaves as if
1183 the **-s** option was given.
1187 : This is another way to give command-line arguments to bc(1). They should be
1188 in the same format as all other command-line arguments. These are always
1189 processed first, so any files given in **BC_ENV_ARGS** will be processed
1190 before arguments and files given on the command-line. This gives the user
1191 the ability to set up "standard" options and files to be used at every
1192 invocation. The most useful thing for such files to contain would be useful
1193 functions that the user might want every time bc(1) runs.
1195 The code that parses **BC_ENV_ARGS** will correctly handle quoted arguments,
1196 but it does not understand escape sequences. For example, the string
1197 **"/home/gavin/some bc file.bc"** will be correctly parsed, but the string
1198 **"/home/gavin/some \"bc\" file.bc"** will include the backslashes.
1200 The quote parsing will handle either kind of quotes, **'** or **"**. Thus,
1201 if you have a file with any number of single quotes in the name, you can use
1202 double quotes as the outside quotes, as in **"some 'bc' file.bc"**, and vice
1203 versa if you have a file with double quotes. However, handling a file with
1204 both kinds of quotes in **BC_ENV_ARGS** is not supported due to the
1205 complexity of the parsing, though such files are still supported on the
1206 command-line where the parsing is done by the shell.
1210 : If this environment variable exists and contains an integer that is greater
1211 than **1** and is less than **UINT16_MAX** (**2\^16-1**), bc(1) will output
1212 lines to that length, including the backslash (**\\**). The default line
1215 The special value of **0** will disable line length checking and print
1216 numbers without regard to line length and without backslashes and newlines.
1220 : If this environment variable exists and contains an integer, then a non-zero
1221 value activates the copyright banner when bc(1) is in interactive mode,
1222 while zero deactivates it.
1224 If bc(1) is not in interactive mode (see the **INTERACTIVE MODE** section),
1225 then this environment variable has no effect because bc(1) does not print
1226 the banner when not in interactive mode.
1228 This environment variable overrides the default, which can be queried with
1229 the **-h** or **-\-help** options.
1233 : If bc(1) is not in interactive mode (see the **INTERACTIVE MODE** section),
1234 then this environment variable has no effect because bc(1) exits on
1235 **SIGINT** when not in interactive mode.
1237 However, when bc(1) is in interactive mode, then if this environment
1238 variable exists and contains an integer, a non-zero value makes bc(1) reset
1239 on **SIGINT**, rather than exit, and zero makes bc(1) exit. If this
1240 environment variable exists and is *not* an integer, then bc(1) will exit on
1243 This environment variable overrides the default, which can be queried with
1244 the **-h** or **-\-help** options.
1248 : If TTY mode is *not* available (see the **TTY MODE** section), then this
1249 environment variable has no effect.
1251 However, when TTY mode is available, then if this environment variable
1252 exists and contains an integer, then a non-zero value makes bc(1) use TTY
1253 mode, and zero makes bc(1) not use TTY mode.
1255 This environment variable overrides the default, which can be queried with
1256 the **-h** or **-\-help** options.
1260 : If TTY mode is *not* available (see the **TTY MODE** section), then this
1261 environment variable has no effect.
1263 However, when TTY mode is available, then if this environment variable
1264 exists and contains an integer, a non-zero value makes bc(1) use a prompt,
1265 and zero or a non-integer makes bc(1) not use a prompt. If this environment
1266 variable does not exist and **BC_TTY_MODE** does, then the value of the
1267 **BC_TTY_MODE** environment variable is used.
1269 This environment variable and the **BC_TTY_MODE** environment variable
1270 override the default, which can be queried with the **-h** or **-\-help**
1275 : If any expressions or expression files are given on the command-line with
1276 **-e**, **-\-expression**, **-f**, or **-\-file**, then if this environment
1277 variable exists and contains an integer, a non-zero value makes bc(1) exit
1278 after executing the expressions and expression files, and a zero value makes
1281 This environment variable overrides the default, which can be queried with
1282 the **-h** or **-\-help** options.
1286 : When parsing numbers and if this environment variable exists and contains an
1287 integer, a non-zero value makes bc(1) clamp digits that are greater than or
1288 equal to the current **ibase** so that all such digits are considered equal
1289 to the **ibase** minus 1, and a zero value disables such clamping so that
1290 those digits are always equal to their value, which is multiplied by the
1291 power of the **ibase**.
1293 This never applies to single-digit numbers, as per the standard (see the
1294 **STANDARDS** section).
1296 This environment variable overrides the default, which can be queried with
1297 the **-h** or **-\-help** options.
1301 bc(1) returns the following exit statuses:
1309 : A math error occurred. This follows standard practice of using **1** for
1310 expected errors, since math errors will happen in the process of normal
1313 Math errors include divide by **0**, taking the square root of a negative
1314 number, attempting to convert a negative number to a hardware integer,
1315 overflow when converting a number to a hardware integer, overflow when
1316 calculating the size of a number, and attempting to use a non-integer where
1317 an integer is required.
1319 Converting to a hardware integer happens for the second operand of the power
1320 (**\^**) operator and the corresponding assignment operator.
1324 : A parse error occurred.
1326 Parse errors include unexpected **EOF**, using an invalid character, failing
1327 to find the end of a string or comment, using a token where it is invalid,
1328 giving an invalid expression, giving an invalid print statement, giving an
1329 invalid function definition, attempting to assign to an expression that is
1330 not a named expression (see the *Named Expressions* subsection of the
1331 **SYNTAX** section), giving an invalid **auto** list, having a duplicate
1332 **auto**/function parameter, failing to find the end of a code block,
1333 attempting to return a value from a **void** function, attempting to use a
1334 variable as a reference, and using any extensions when the option **-s** or
1335 any equivalents were given.
1339 : A runtime error occurred.
1341 Runtime errors include assigning an invalid number to any global (**ibase**,
1342 **obase**, or **scale**), giving a bad expression to a **read()** call,
1343 calling **read()** inside of a **read()** call, type errors, passing the
1344 wrong number of arguments to functions, attempting to call an undefined
1345 function, and attempting to use a **void** function call as a value in an
1350 : A fatal error occurred.
1352 Fatal errors include memory allocation errors, I/O errors, failing to open
1353 files, attempting to use files that do not have only ASCII characters (bc(1)
1354 only accepts ASCII characters), attempting to open a directory as a file,
1355 and giving invalid command-line options.
1357 The exit status **4** is special; when a fatal error occurs, bc(1) always exits
1358 and returns **4**, no matter what mode bc(1) is in.
1360 The other statuses will only be returned when bc(1) is not in interactive mode
1361 (see the **INTERACTIVE MODE** section), since bc(1) resets its state (see the
1362 **RESET** section) and accepts more input when one of those errors occurs in
1363 interactive mode. This is also the case when interactive mode is forced by the
1364 **-i** flag or **-\-interactive** option.
1366 These exit statuses allow bc(1) to be used in shell scripting with error
1367 checking, and its normal behavior can be forced by using the **-i** flag or
1368 **-\-interactive** option.
1372 Per the standard (see the **STANDARDS** section), bc(1) has an interactive mode
1373 and a non-interactive mode. Interactive mode is turned on automatically when
1374 both **stdin** and **stdout** are hooked to a terminal, but the **-i** flag and
1375 **-\-interactive** option can turn it on in other situations.
1377 In interactive mode, bc(1) attempts to recover from errors (see the **RESET**
1378 section), and in normal execution, flushes **stdout** as soon as execution is
1379 done for the current input. bc(1) may also reset on **SIGINT** instead of exit,
1380 depending on the contents of, or default for, the **BC_SIGINT_RESET**
1381 environment variable (see the **ENVIRONMENT VARIABLES** section).
1385 If **stdin**, **stdout**, and **stderr** are all connected to a TTY, then "TTY
1386 mode" is considered to be available, and thus, bc(1) can turn on TTY mode,
1387 subject to some settings.
1389 If there is the environment variable **BC_TTY_MODE** in the environment (see the
1390 **ENVIRONMENT VARIABLES** section), then if that environment variable contains a
1391 non-zero integer, bc(1) will turn on TTY mode when **stdin**, **stdout**, and
1392 **stderr** are all connected to a TTY. If the **BC_TTY_MODE** environment
1393 variable exists but is *not* a non-zero integer, then bc(1) will not turn TTY
1396 If the environment variable **BC_TTY_MODE** does *not* exist, the default
1397 setting is used. The default setting can be queried with the **-h** or
1398 **-\-help** options.
1400 TTY mode is different from interactive mode because interactive mode is required
1401 in the bc(1) standard (see the **STANDARDS** section), and interactive mode
1402 requires only **stdin** and **stdout** to be connected to a terminal.
1404 ## Command-Line History
1406 Command-line history is only enabled if TTY mode is, i.e., that **stdin**,
1407 **stdout**, and **stderr** are connected to a TTY and the **BC_TTY_MODE**
1408 environment variable (see the **ENVIRONMENT VARIABLES** section) and its default
1409 do not disable TTY mode. See the **COMMAND LINE HISTORY** section for more
1414 If TTY mode is available, then a prompt can be enabled. Like TTY mode itself, it
1415 can be turned on or off with an environment variable: **BC_PROMPT** (see the
1416 **ENVIRONMENT VARIABLES** section).
1418 If the environment variable **BC_PROMPT** exists and is a non-zero integer, then
1419 the prompt is turned on when **stdin**, **stdout**, and **stderr** are connected
1420 to a TTY and the **-P** and **-\-no-prompt** options were not used. The read
1421 prompt will be turned on under the same conditions, except that the **-R** and
1422 **-\-no-read-prompt** options must also not be used.
1424 However, if **BC_PROMPT** does not exist, the prompt can be enabled or disabled
1425 with the **BC_TTY_MODE** environment variable, the **-P** and **-\-no-prompt**
1426 options, and the **-R** and **-\-no-read-prompt** options. See the **ENVIRONMENT
1427 VARIABLES** and **OPTIONS** sections for more details.
1431 Sending a **SIGINT** will cause bc(1) to do one of two things.
1433 If bc(1) is not in interactive mode (see the **INTERACTIVE MODE** section), or
1434 the **BC_SIGINT_RESET** environment variable (see the **ENVIRONMENT VARIABLES**
1435 section), or its default, is either not an integer or it is zero, bc(1) will
1438 However, if bc(1) is in interactive mode, and the **BC_SIGINT_RESET** or its
1439 default is an integer and non-zero, then bc(1) will stop executing the current
1440 input and reset (see the **RESET** section) upon receiving a **SIGINT**.
1442 Note that "current input" can mean one of two things. If bc(1) is processing
1443 input from **stdin** in interactive mode, it will ask for more input. If bc(1)
1444 is processing input from a file in interactive mode, it will stop processing the
1445 file and start processing the next file, if one exists, or ask for input from
1446 **stdin** if no other file exists.
1448 This means that if a **SIGINT** is sent to bc(1) as it is executing a file, it
1449 can seem as though bc(1) did not respond to the signal since it will immediately
1450 start executing the next file. This is by design; most files that users execute
1451 when interacting with bc(1) have function definitions, which are quick to parse.
1452 If a file takes a long time to execute, there may be a bug in that file. The
1453 rest of the files could still be executed without problem, allowing the user to
1456 **SIGTERM** and **SIGQUIT** cause bc(1) to clean up and exit, and it uses the
1457 default handler for all other signals. The one exception is **SIGHUP**; in that
1458 case, and only when bc(1) is in TTY mode (see the **TTY MODE** section), a
1459 **SIGHUP** will cause bc(1) to clean up and exit.
1461 # COMMAND LINE HISTORY
1463 bc(1) supports interactive command-line editing.
1465 If bc(1) can be in TTY mode (see the **TTY MODE** section), history can be
1466 enabled. This means that command-line history can only be enabled when
1467 **stdin**, **stdout**, and **stderr** are all connected to a TTY.
1469 Like TTY mode itself, it can be turned on or off with the environment variable
1470 **BC_TTY_MODE** (see the **ENVIRONMENT VARIABLES** section).
1472 If history is enabled, previous lines can be recalled and edited with the arrow
1475 **Note**: tabs are converted to 8 spaces.
1483 bc(1) is compliant with the IEEE Std 1003.1-2017 (“POSIX.1-2017”) specification
1484 at https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html . The
1485 flags **-efghiqsvVw**, all long options, and the extensions noted above are
1486 extensions to that specification.
1488 In addition, the behavior of the **quit** implements an interpretation of that
1489 specification that is different from all known implementations. For more
1490 information see the **Statements** subsection of the **SYNTAX** section.
1492 Note that the specification explicitly says that bc(1) only accepts numbers that
1493 use a period (**.**) as a radix point, regardless of the value of
1498 Before version **6.1.0**, this bc(1) had incorrect behavior for the **quit**
1501 No other bugs are known. Report bugs at https://git.gavinhoward.com/gavin/bc .
1505 Gavin D. Howard <gavin@gavinhoward.com> and contributors.