3 SPDX-License-Identifier: BSD-2-Clause
5 Copyright (c) 2018-2020 Gavin D. Howard and contributors.
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10 * Redistributions of source code must retain the above copyright notice, this
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14 this list of conditions and the following disclaimer in the documentation
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33 bc - arbitrary-precision arithmetic language and calculator
37 **bc** [**-ghilPqsvVw**] [**--global-stacks**] [**--help**] [**--interactive**] [**--mathlib**] [**--no-prompt**] [**--quiet**] [**--standard**] [**--warn**] [**--version**] [**-e** *expr*] [**--expression**=*expr*...] [**-f** *file*...] [**-file**=*file*...]
42 bc(1) is an interactive processor for a language first standardized in 1991 by
43 POSIX. (The current standard is [here][1].) The language provides unlimited
44 precision decimal arithmetic and is somewhat C-like, but there are differences.
45 Such differences will be noted in this document.
47 After parsing and handling options, this bc(1) reads any files given on the
48 command line and executes them before reading from **stdin**.
52 The following are the options that bc(1) accepts.
54 **-g**, **--global-stacks**
56 : Turns the globals **ibase**, **obase**, **scale**, and **seed** into stacks.
58 This has the effect that a copy of the current value of all four are pushed
59 onto a stack for every function call, as well as popped when every function
60 returns. This means that functions can assign to any and all of those
61 globals without worrying that the change will affect other functions.
62 Thus, a hypothetical function named **output(x,b)** that simply printed
63 **x** in base **b** could be written like this:
65 define void output(x, b) {
72 define void output(x, b) {
80 This makes writing functions much easier.
82 (**Note**: the function **output(x,b)** exists in the extended math library.
83 See the **LIBRARY** section.)
85 However, since using this flag means that functions cannot set **ibase**,
86 **obase**, **scale**, or **seed** globally, functions that are made to do so
87 cannot work anymore. There are two possible use cases for that, and each has
90 First, if a function is called on startup to turn bc(1) into a number
91 converter, it is possible to replace that capability with various shell
94 alias d2o="bc -e ibase=A -e obase=8"
95 alias h2b="bc -e ibase=G -e obase=2"
97 Second, if the purpose of a function is to set **ibase**, **obase**,
98 **scale**, or **seed** globally for any other purpose, it could be split
99 into one to four functions (based on how many globals it sets) and each of
100 those functions could return the desired value for a global.
102 For functions that set **seed**, the value assigned to **seed** is not
103 propagated to parent functions. This means that the sequence of
104 pseudo-random numbers that they see will not be the same sequence of
105 pseudo-random numbers that any parent sees. This is only the case once
106 **seed** has been set.
108 If a function desires to not affect the sequence of pseudo-random numbers
109 of its parents, but wants to use the same **seed**, it can use the following
114 If the behavior of this option is desired for every run of bc(1), then users
115 could make sure to define **BC_ENV_ARGS** and include this option (see the
116 **ENVIRONMENT VARIABLES** section for more details).
118 If **-s**, **-w**, or any equivalents are used, this option is ignored.
120 This is a **non-portable extension**.
124 : Prints a usage message and quits.
126 **-i**, **--interactive**
128 : Forces interactive mode. (See the **INTERACTIVE MODE** section.)
130 This is a **non-portable extension**.
132 **-l**, **--mathlib**
134 : Sets **scale** (see the **SYNTAX** section) to **20** and loads the included
135 math library and the extended math library before running any code,
136 including any expressions or files specified on the command line.
138 To learn what is in the libraries, see the **LIBRARY** section.
140 **-P**, **--no-prompt**
142 : Disables the prompt in TTY mode. (The prompt is only enabled in TTY mode.
143 See the **TTY MODE** section) This is mostly for those users that do not
144 want a prompt or are not used to having them in bc(1). Most of those users
145 would want to put this option in **BC_ENV_ARGS** (see the
146 **ENVIRONMENT VARIABLES** section).
148 This is a **non-portable extension**.
152 : Do not print copyright header. bc(1) will also suppress the header in
153 non-interactive mode.
155 This is mostly for compatibility with the [GNU bc(1)][2].
157 This is a **non-portable extension**.
159 **-s**, **--standard**
161 : Process exactly the language defined by the [standard][1] and error if any
164 This is a **non-portable extension**.
166 **-v**, **-V**, **--version**
168 : Print the version information (copyright header) and exit.
170 This is a **non-portable extension**.
174 : Like **-s** and **--standard**, except that warnings (and not errors) are
175 printed for non-standard extensions and execution continues normally.
177 This is a **non-portable extension**.
179 **-e** *expr*, **--expression**=*expr*
181 : Evaluates *expr*. If multiple expressions are given, they are evaluated in
182 order. If files are given as well (see below), the expressions and files are
183 evaluated in the order given. This means that if a file is given before an
184 expression, the file is read in and evaluated first.
186 In other bc(1) implementations, this option causes the program to execute
187 the expressions and then exit. This bc(1) does not, unless the
188 **BC_EXPR_EXIT** is defined (see the **ENVIRONMENT VARIABLES** section).
190 This is a **non-portable extension**.
192 **-f** *file*, **--file**=*file*
194 : Reads in *file* and evaluates it, line by line, as though it were read
195 through **stdin**. If expressions are also given (see above), the
196 expressions are evaluated in the order given.
198 In other bc(1) implementations, this option causes the program to execute
199 the files and then exit. This bc(1) does not, unless the
200 **BC_EXPR_EXIT** is defined (see the **ENVIRONMENT VARIABLES** section).
202 This is a **non-portable extension**.
204 All long options are **non-portable extensions**.
208 Any non-error output is written to **stdout**.
210 **Note**: Unlike other bc(1) implementations, this bc(1) will issue a fatal
211 error (see the **EXIT STATUS** section) if it cannot write to **stdout**, so if
212 **stdout** is closed, as in **bc <file> >&-**, it will quit with an error. This
213 is done so that bc(1) can report problems when **stdout** is redirected to a
216 If there are scripts that depend on the behavior of other bc(1) implementations,
217 it is recommended that those scripts be changed to redirect **stdout** to
222 Any error output is written to **stderr**.
224 **Note**: Unlike other bc(1) implementations, this bc(1) will issue a fatal
225 error (see the **EXIT STATUS** section) if it cannot write to **stderr**, so if
226 **stderr** is closed, as in **bc <file> 2>&-**, it will quit with an error. This
227 is done so that bc(1) can exit with an error code when **stderr** is redirected
230 If there are scripts that depend on the behavior of other bc(1) implementations,
231 it is recommended that those scripts be changed to redirect **stderr** to
236 The syntax for bc(1) programs is mostly C-like, with some differences. This
237 bc(1) follows the [POSIX standard][1], which is a much more thorough resource
238 for the language this bc(1) accepts. This section is meant to be a summary and a
239 listing of all the extensions to the standard.
241 In the sections below, **E** means expression, **S** means statement, and **I**
244 Identifiers (**I**) start with a lowercase letter and can be followed by any
245 number (up to **BC_NAME_MAX-1**) of lowercase letters (**a-z**), digits
246 (**0-9**), and underscores (**\_**). The regex is **\[a-z\]\[a-z0-9\_\]\***.
247 Identifiers with more than one character (letter) are a
248 **non-portable extension**.
250 **ibase** is a global variable determining how to interpret constant numbers. It
251 is the "input" base, or the number base used for interpreting input numbers.
252 **ibase** is initially **10**. If the **-s** (**--standard**) and **-w**
253 (**--warn**) flags were not given on the command line, the max allowable value
254 for **ibase** is **36**. Otherwise, it is **16**. The min allowable value for
255 **ibase** is **2**. The max allowable value for **ibase** can be queried in
256 bc(1) programs with the **maxibase()** built-in function.
258 **obase** is a global variable determining how to output results. It is the
259 "output" base, or the number base used for outputting numbers. **obase** is
260 initially **10**. The max allowable value for **obase** is **BC_BASE_MAX** and
261 can be queried in bc(1) programs with the **maxobase()** built-in function. The
262 min allowable value for **obase** is **0**. If **obase** is **0**, values are
263 output in scientific notation, and if **obase** is **1**, values are output in
264 engineering notation. Otherwise, values are output in the specified base.
266 Outputting in scientific and engineering notations are **non-portable
269 The *scale* of an expression is the number of digits in the result of the
270 expression right of the decimal point, and **scale** is a global variable that
271 sets the precision of any operations, with exceptions. **scale** is initially
272 **0**. **scale** cannot be negative. The max allowable value for **scale** is
273 **BC_SCALE_MAX** and can be queried in bc(1) programs with the **maxscale()**
276 bc(1) has both *global* variables and *local* variables. All *local*
277 variables are local to the function; they are parameters or are introduced in
278 the **auto** list of a function (see the **FUNCTIONS** section). If a variable
279 is accessed which is not a parameter or in the **auto** list, it is assumed to
280 be *global*. If a parent function has a *local* variable version of a variable
281 that a child function considers *global*, the value of that *global* variable in
282 the child function is the value of the variable in the parent function, not the
283 value of the actual *global* variable.
285 All of the above applies to arrays as well.
287 The value of a statement that is an expression (i.e., any of the named
288 expressions or operands) is printed unless the lowest precedence operator is an
289 assignment operator *and* the expression is notsurrounded by parentheses.
291 The value that is printed is also assigned to the special variable **last**. A
292 single dot (**.**) may also be used as a synonym for **last**. These are
293 **non-portable extensions**.
295 Either semicolons or newlines may separate statements.
299 There are two kinds of comments:
301 1. Block comments are enclosed in **/\*** and **\*/**.
302 2. Line comments go from **#** until, and not including, the next newline. This
303 is a **non-portable extension**.
307 The following are named expressions in bc(1):
310 2. Array Elements: **I[E]**
315 7. **last** or a single dot (**.**)
317 Numbers 6 and 7 are **non-portable extensions**.
319 The meaning of **seed** is dependent on the current pseudo-random number
320 generator but is guaranteed to not change except for new major versions.
322 The *scale* and sign of the value may be significant.
324 If a previously used **seed** value is assigned to **seed** and used again, the
325 pseudo-random number generator is guaranteed to produce the same sequence of
326 pseudo-random numbers as it did when the **seed** value was previously used.
328 The exact value assigned to **seed** is not guaranteed to be returned if
329 **seed** is queried again immediately. However, if **seed** *does* return a
330 different value, both values, when assigned to **seed**, are guaranteed to
331 produce the same sequence of pseudo-random numbers. This means that certain
332 values assigned to **seed** will *not* produce unique sequences of pseudo-random
333 numbers. The value of **seed** will change after any use of the **rand()** and
334 **irand(E)** operands (see the *Operands* subsection below), except if the
335 parameter passed to **irand(E)** is **0**, **1**, or negative.
337 There is no limit to the length (number of significant decimal digits) or
338 *scale* of the value that can be assigned to **seed**.
340 Variables and arrays do not interfere; users can have arrays named the same as
341 variables. This also applies to functions (see the **FUNCTIONS** section), so a
342 user can have a variable, array, and function that all have the same name, and
343 they will not shadow each other, whether inside of functions or not.
345 Named expressions are required as the operand of **increment**/**decrement**
346 operators and as the left side of **assignment** operators (see the *Operators*
351 The following are valid operands in bc(1):
353 1. Numbers (see the *Numbers* subsection below).
354 2. Array indices (**I[E]**).
355 3. **(E)**: The value of **E** (used to change precedence).
356 4. **sqrt(E)**: The square root of **E**. **E** must be non-negative.
357 5. **length(E)**: The number of significant decimal digits in **E**.
358 6. **length(I[])**: The number of elements in the array **I**. This is a
359 **non-portable extension**.
360 7. **scale(E)**: The *scale* of **E**.
361 8. **abs(E)**: The absolute value of **E**. This is a **non-portable
363 9. **I()**, **I(E)**, **I(E, E)**, and so on, where **I** is an identifier for
364 a non-**void** function (see the *Void Functions* subsection of the
365 **FUNCTIONS** section). The **E** argument(s) may also be arrays of the form
366 **I[]**, which will automatically be turned into array references (see the
367 *Array References* subsection of the **FUNCTIONS** section) if the
368 corresponding parameter in the function definition is an array reference.
369 10. **read()**: Reads a line from **stdin** and uses that as an expression. The
370 result of that expression is the result of the **read()** operand. This is a
371 **non-portable extension**.
372 11. **maxibase()**: The max allowable **ibase**. This is a **non-portable
374 12. **maxobase()**: The max allowable **obase**. This is a **non-portable
376 13. **maxscale()**: The max allowable **scale**. This is a **non-portable
378 14. **rand()**: A pseudo-random integer between **0** (inclusive) and
379 **BC_RAND_MAX** (inclusive). Using this operand will change the value of
380 **seed**. This is a **non-portable extension**.
381 15. **irand(E)**: A pseudo-random integer between **0** (inclusive) and the
382 value of **E** (exclusive). If **E** is negative or is a non-integer
383 (**E**'s *scale* is not **0**), an error is raised, and bc(1) resets (see
384 the **RESET** section) while **seed** remains unchanged. If **E** is larger
385 than **BC_RAND_MAX**, the higher bound is honored by generating several
386 pseudo-random integers, multiplying them by appropriate powers of
387 **BC_RAND_MAX+1**, and adding them together. Thus, the size of integer that
388 can be generated with this operand is unbounded. Using this operand will
389 change the value of **seed**, unless the value of **E** is **0** or **1**.
390 In that case, **0** is returned, and **seed** is *not* changed. This is a
391 **non-portable extension**.
392 16. **maxrand()**: The max integer returned by **rand()**. This is a
393 **non-portable extension**.
395 The integers generated by **rand()** and **irand(E)** are guaranteed to be as
396 unbiased as possible, subject to the limitations of the pseudo-random number
399 **Note**: The values returned by the pseudo-random number generator with
400 **rand()** and **irand(E)** are guaranteed to *NOT* be cryptographically secure.
401 This is a consequence of using a seeded pseudo-random number generator. However,
402 they *are* guaranteed to be reproducible with identical **seed** values.
406 Numbers are strings made up of digits, uppercase letters, and at most **1**
407 period for a radix. Numbers can have up to **BC_NUM_MAX** digits. Uppercase
408 letters are equal to **9** + their position in the alphabet (i.e., **A** equals
409 **10**, or **9+1**). If a digit or letter makes no sense with the current value
410 of **ibase**, they are set to the value of the highest valid digit in **ibase**.
412 Single-character numbers (i.e., **A** alone) take the value that they would have
413 if they were valid digits, regardless of the value of **ibase**. This means that
414 **A** alone always equals decimal **10** and **Z** alone always equals decimal
417 In addition, bc(1) accepts numbers in scientific notation. These have the form
418 **\<number\>e\<integer\>**. The power (the portion after the **e**) must be an
419 integer. An example is **1.89237e9**, which is equal to **1892370000**. Negative
420 exponents are also allowed, so **4.2890e-3** is equal to **0.0042890**.
422 Using scientific notation is an error or warning if the **-s** or **-w**,
423 respectively, command-line options (or equivalents) are given.
425 **WARNING**: Both the number and the exponent in scientific notation are
426 interpreted according to the current **ibase**, but the number is still
427 multiplied by **10\^exponent** regardless of the current **ibase**. For example,
428 if **ibase** is **16** and bc(1) is given the number string **FFeA**, the
429 resulting decimal number will be **2550000000000**, and if bc(1) is given the
430 number string **10e-4**, the resulting decimal number will be **0.0016**.
432 Accepting input as scientific notation is a **non-portable extension**.
436 The following arithmetic and logical operators can be used. They are listed in
437 order of decreasing precedence. Operators in the same group have the same
442 : Type: Prefix and Postfix
446 Description: **increment**, **decrement**
454 Description: **negation**, **boolean not**
462 Description: **truncation**
470 Description: **set precision**
478 Description: **power**
486 Description: **multiply**, **divide**, **modulus**
494 Description: **add**, **subtract**
502 Description: **shift left**, **shift right**
504 **=** **\<\<=** **\>\>=** **+=** **-=** **\*=** **/=** **%=** **\^=** **\@=**
510 Description: **assignment**
512 **==** **\<=** **\>=** **!=** **\<** **\>**
518 Description: **relational**
526 Description: **boolean and**
534 Description: **boolean or**
536 The operators will be described in more detail below.
540 : The prefix and postfix **increment** and **decrement** operators behave
541 exactly like they would in C. They require a named expression (see the
542 *Named Expressions* subsection) as an operand.
544 The prefix versions of these operators are more efficient; use them where
549 : The **negation** operator returns **0** if a user attempts to negate any
550 expression with the value **0**. Otherwise, a copy of the expression with
551 its sign flipped is returned.
555 : The **boolean not** operator returns **1** if the expression is **0**, or
558 This is a **non-portable extension**.
562 : The **truncation** operator returns a copy of the given expression with all
563 of its *scale* removed.
565 This is a **non-portable extension**.
569 : The **set precision** operator takes two expressions and returns a copy of
570 the first with its *scale* equal to the value of the second expression. That
571 could either mean that the number is returned without change (if the
572 *scale* of the first expression matches the value of the second
573 expression), extended (if it is less), or truncated (if it is more).
575 The second expression must be an integer (no *scale*) and non-negative.
577 This is a **non-portable extension**.
581 : The **power** operator (not the **exclusive or** operator, as it would be in
582 C) takes two expressions and raises the first to the power of the value of
585 The second expression must be an integer (no *scale*), and if it is
586 negative, the first value must be non-zero.
590 : The **multiply** operator takes two expressions, multiplies them, and
591 returns the product. If **a** is the *scale* of the first expression and
592 **b** is the *scale* of the second expression, the *scale* of the result is
593 equal to **min(a+b,max(scale,a,b))** where **min()** and **max()** return
598 : The **divide** operator takes two expressions, divides them, and returns the
599 quotient. The *scale* of the result shall be the value of **scale**.
601 The second expression must be non-zero.
605 : The **modulus** operator takes two expressions, **a** and **b**, and
606 evaluates them by 1) Computing **a/b** to current **scale** and 2) Using the
607 result of step 1 to calculate **a-(a/b)\*b** to *scale*
608 **max(scale+scale(b),scale(a))**.
610 The second expression must be non-zero.
614 : The **add** operator takes two expressions, **a** and **b**, and returns the
615 sum, with a *scale* equal to the max of the *scale*s of **a** and **b**.
619 : The **subtract** operator takes two expressions, **a** and **b**, and
620 returns the difference, with a *scale* equal to the max of the *scale*s of
625 : The **left shift** operator takes two expressions, **a** and **b**, and
626 returns a copy of the value of **a** with its decimal point moved **b**
629 The second expression must be an integer (no *scale*) and non-negative.
631 This is a **non-portable extension**.
635 : The **right shift** operator takes two expressions, **a** and **b**, and
636 returns a copy of the value of **a** with its decimal point moved **b**
639 The second expression must be an integer (no *scale*) and non-negative.
641 This is a **non-portable extension**.
643 **=** **\<\<=** **\>\>=** **+=** **-=** **\*=** **/=** **%=** **\^=** **\@=**
645 : The **assignment** operators take two expressions, **a** and **b** where
646 **a** is a named expression (see the *Named Expressions* subsection).
648 For **=**, **b** is copied and the result is assigned to **a**. For all
649 others, **a** and **b** are applied as operands to the corresponding
650 arithmetic operator and the result is assigned to **a**.
652 The **assignment** operators that correspond to operators that are
653 extensions are themselves **non-portable extensions**.
655 **==** **\<=** **\>=** **!=** **\<** **\>**
657 : The **relational** operators compare two expressions, **a** and **b**, and
658 if the relation holds, according to C language semantics, the result is
659 **1**. Otherwise, it is **0**.
661 Note that unlike in C, these operators have a lower precedence than the
662 **assignment** operators, which means that **a=b\>c** is interpreted as
665 Also, unlike the [standard][1] requires, these operators can appear anywhere
666 any other expressions can be used. This allowance is a
667 **non-portable extension**.
671 : The **boolean and** operator takes two expressions and returns **1** if both
672 expressions are non-zero, **0** otherwise.
674 This is *not* a short-circuit operator.
676 This is a **non-portable extension**.
680 : The **boolean or** operator takes two expressions and returns **1** if one
681 of the expressions is non-zero, **0** otherwise.
683 This is *not* a short-circuit operator.
685 This is a **non-portable extension**.
689 The following items are statements:
692 2. **{** **S** **;** ... **;** **S** **}**
693 3. **if** **(** **E** **)** **S**
694 4. **if** **(** **E** **)** **S** **else** **S**
695 5. **while** **(** **E** **)** **S**
696 6. **for** **(** **E** **;** **E** **;** **E** **)** **S**
697 7. An empty statement
703 13. A string of characters, enclosed in double quotes
704 14. **print** **E** **,** ... **,** **E**
705 15. **I()**, **I(E)**, **I(E, E)**, and so on, where **I** is an identifier for
706 a **void** function (see the *Void Functions* subsection of the
707 **FUNCTIONS** section). The **E** argument(s) may also be arrays of the form
708 **I[]**, which will automatically be turned into array references (see the
709 *Array References* subsection of the **FUNCTIONS** section) if the
710 corresponding parameter in the function definition is an array reference.
712 Numbers 4, 9, 11, 12, 14, and 15 are **non-portable extensions**.
714 Also, as a **non-portable extension**, any or all of the expressions in the
715 header of a for loop may be omitted. If the condition (second expression) is
716 omitted, it is assumed to be a constant **1**.
718 The **break** statement causes a loop to stop iterating and resume execution
719 immediately following a loop. This is only allowed in loops.
721 The **continue** statement causes a loop iteration to stop early and returns to
722 the start of the loop, including testing the loop condition. This is only
725 The **if** **else** statement does the same thing as in C.
727 The **quit** statement causes bc(1) to quit, even if it is on a branch that will
728 not be executed (it is a compile-time command).
730 The **halt** statement causes bc(1) to quit, if it is executed. (Unlike **quit**
731 if it is on a branch of an **if** statement that is not executed, bc(1) does not
734 The **limits** statement prints the limits that this bc(1) is subject to. This
735 is like the **quit** statement in that it is a compile-time command.
737 An expression by itself is evaluated and printed, followed by a newline.
739 Both scientific notation and engineering notation are available for printing the
740 results of expressions. Scientific notation is activated by assigning **0** to
741 **obase**, and engineering notation is activated by assigning **1** to
742 **obase**. To deactivate them, just assign a different value to **obase**.
744 Scientific notation and engineering notation are disabled if bc(1) is run with
745 either the **-s** or **-w** command-line options (or equivalents).
747 Printing numbers in scientific notation and/or engineering notation is a
748 **non-portable extension**.
752 The "expressions" in a **print** statement may also be strings. If they are, there
753 are backslash escape sequences that are interpreted specially. What those
754 sequences are, and what they cause to be printed, are shown below:
768 Any other character following a backslash causes the backslash and character to
771 Any non-string expression in a print statement shall be assigned to **last**,
772 like any other expression that is printed.
774 ## Order of Evaluation
776 All expressions in a statment are evaluated left to right, except as necessary
777 to maintain order of operations. This means, for example, assuming that **i** is
778 equal to **0**, in the expression
782 the first (or 0th) element of **a** is set to **1**, and **i** is equal to **2**
783 at the end of the expression.
785 This includes function arguments. Thus, assuming **i** is equal to **0**, this
786 means that in the expression
790 the first argument passed to **x()** is **0**, and the second argument is **1**,
791 while **i** is equal to **2** before the function starts executing.
795 Function definitions are as follows:
805 Any **I** in the parameter list or **auto** list may be replaced with **I[]** to
806 make a parameter or **auto** var an array, and any **I** in the parameter list
807 may be replaced with **\*I[]** to make a parameter an array reference. Callers
808 of functions that take array references should not put an asterisk in the call;
809 they must be called with just **I[]** like normal array parameters and will be
810 automatically converted into references.
812 As a **non-portable extension**, the opening brace of a **define** statement may
813 appear on the next line.
815 As a **non-portable extension**, the return statement may also be in one of the
819 2. **return** **(** **)**
822 The first two, or not specifying a **return** statement, is equivalent to
823 **return (0)**, unless the function is a **void** function (see the *Void
824 Functions* subsection below).
828 Functions can also be **void** functions, defined as follows:
831 define void I(I,...,I){
838 They can only be used as standalone expressions, where such an expression would
839 be printed alone, except in a print statement.
841 Void functions can only use the first two **return** statements listed above.
842 They can also omit the return statement entirely.
844 The word "void" is not treated as a keyword; it is still possible to have
845 variables, arrays, and functions named **void**. The word "void" is only
846 treated specially right after the **define** keyword.
848 This is a **non-portable extension**.
852 For any array in the parameter list, if the array is declared in the form
858 it is a **reference**. Any changes to the array in the function are reflected,
859 when the function returns, to the array that was passed in.
861 Other than this, all function arguments are passed by value.
863 This is a **non-portable extension**.
867 All of the functions below, including the functions in the extended math
868 library (see the *Extended Library* subsection below), are available when the
869 **-l** or **--mathlib** command-line flags are given, except that the extended
870 math library is not available when the **-s** option, the **-w** option, or
871 equivalents are given.
875 The [standard][1] defines the following functions for the math library:
879 : Returns the sine of **x**, which is assumed to be in radians.
881 This is a transcendental function (see the *Transcendental Functions*
886 : Returns the cosine of **x**, which is assumed to be in radians.
888 This is a transcendental function (see the *Transcendental Functions*
893 : Returns the arctangent of **x**, in radians.
895 This is a transcendental function (see the *Transcendental Functions*
900 : Returns the natural logarithm of **x**.
902 This is a transcendental function (see the *Transcendental Functions*
907 : Returns the mathematical constant **e** raised to the power of **x**.
909 This is a transcendental function (see the *Transcendental Functions*
914 : Returns the bessel integer order **n** (truncated) of **x**.
916 This is a transcendental function (see the *Transcendental Functions*
921 The extended library is *not* loaded when the **-s**/**--standard** or
922 **-w**/**--warn** options are given since they are not part of the library
923 defined by the [standard][1].
925 The extended library is a **non-portable extension**.
929 : Calculates **x** to the power of **y**, even if **y** is not an integer, and
930 returns the result to the current **scale**.
932 This is a transcendental function (see the *Transcendental Functions*
937 : Returns **x** rounded to **p** decimal places according to the rounding mode
938 [round half away from **0**][3].
942 : Returns **x** rounded to **p** decimal places according to the rounding mode
943 [round away from **0**][6].
947 : Returns the factorial of the truncated absolute value of **x**.
951 : Returns the permutation of the truncated absolute value of **n** of the
952 truncated absolute value of **k**, if **k \<= n**. If not, it returns **0**.
956 : Returns the combination of the truncated absolute value of **n** of the
957 truncated absolute value of **k**, if **k \<= n**. If not, it returns **0**.
961 : Returns the logarithm base **2** of **x**.
963 This is a transcendental function (see the *Transcendental Functions*
968 : Returns the logarithm base **10** of **x**.
970 This is a transcendental function (see the *Transcendental Functions*
975 : Returns the logarithm base **b** of **x**.
977 This is a transcendental function (see the *Transcendental Functions*
982 : Returns the cube root of **x**.
986 : Calculates the truncated value of **n**, **r**, and returns the **r**th root
987 of **x** to the current **scale**.
989 If **r** is **0** or negative, this raises an error and causes bc(1) to
990 reset (see the **RESET** section). It also raises an error and causes bc(1)
991 to reset if **r** is even and **x** is negative.
995 : Returns **pi** to **p** decimal places.
997 This is a transcendental function (see the *Transcendental Functions*
1002 : Returns the tangent of **x**, which is assumed to be in radians.
1004 This is a transcendental function (see the *Transcendental Functions*
1009 : Returns the arctangent of **y/x**, in radians. If both **y** and **x** are
1010 equal to **0**, it raises an error and causes bc(1) to reset (see the
1011 **RESET** section). Otherwise, if **x** is greater than **0**, it returns
1012 **a(y/x)**. If **x** is less than **0**, and **y** is greater than or equal
1013 to **0**, it returns **a(y/x)+pi**. If **x** is less than **0**, and **y**
1014 is less than **0**, it returns **a(y/x)-pi**. If **x** is equal to **0**,
1015 and **y** is greater than **0**, it returns **pi/2**. If **x** is equal to
1016 **0**, and **y** is less than **0**, it returns **-pi/2**.
1018 This function is the same as the **atan2()** function in many programming
1021 This is a transcendental function (see the *Transcendental Functions*
1026 : Returns the sine of **x**, which is assumed to be in radians.
1028 This is an alias of **s(x)**.
1030 This is a transcendental function (see the *Transcendental Functions*
1035 : Returns the cosine of **x**, which is assumed to be in radians.
1037 This is an alias of **c(x)**.
1039 This is a transcendental function (see the *Transcendental Functions*
1044 : Returns the tangent of **x**, which is assumed to be in radians.
1046 If **x** is equal to **1** or **-1**, this raises an error and causes bc(1)
1047 to reset (see the **RESET** section).
1049 This is an alias of **t(x)**.
1051 This is a transcendental function (see the *Transcendental Functions*
1056 : Returns the arctangent of **x**, in radians.
1058 This is an alias of **a(x)**.
1060 This is a transcendental function (see the *Transcendental Functions*
1065 : Returns the arctangent of **y/x**, in radians. If both **y** and **x** are
1066 equal to **0**, it raises an error and causes bc(1) to reset (see the
1067 **RESET** section). Otherwise, if **x** is greater than **0**, it returns
1068 **a(y/x)**. If **x** is less than **0**, and **y** is greater than or equal
1069 to **0**, it returns **a(y/x)+pi**. If **x** is less than **0**, and **y**
1070 is less than **0**, it returns **a(y/x)-pi**. If **x** is equal to **0**,
1071 and **y** is greater than **0**, it returns **pi/2**. If **x** is equal to
1072 **0**, and **y** is less than **0**, it returns **-pi/2**.
1074 This function is the same as the **atan2()** function in many programming
1077 This is an alias of **a2(y, x)**.
1079 This is a transcendental function (see the *Transcendental Functions*
1084 : Converts **x** from radians to degrees and returns the result.
1086 This is a transcendental function (see the *Transcendental Functions*
1091 : Converts **x** from degrees to radians and returns the result.
1093 This is a transcendental function (see the *Transcendental Functions*
1098 : Generates a pseudo-random number between **0** (inclusive) and **1**
1099 (exclusive) with the number of decimal digits after the decimal point equal
1100 to the truncated absolute value of **p**. If **p** is not **0**, then
1101 calling this function will change the value of **seed**. If **p** is **0**,
1102 then **0** is returned, and **seed** is *not* changed.
1106 : Generates a pseudo-random number that is between **0** (inclusive) and the
1107 truncated absolute value of **i** (exclusive) with the number of decimal
1108 digits after the decimal point equal to the truncated absolute value of
1109 **p**. If the absolute value of **i** is greater than or equal to **2**, and
1110 **p** is not **0**, then calling this function will change the value of
1111 **seed**; otherwise, **0** is returned and **seed** is not changed.
1115 : Returns **x** with its sign flipped with probability **0.5**. In other
1116 words, it randomizes the sign of **x**.
1120 : Returns a random boolean value (either **0** or **1**).
1124 : Returns the numbers of unsigned integer bytes required to hold the truncated
1125 absolute value of **x**.
1129 : Returns the numbers of signed, two's-complement integer bytes required to
1130 hold the truncated value of **x**.
1134 : Outputs the hexadecimal (base **16**) representation of **x**.
1136 This is a **void** function (see the *Void Functions* subsection of the
1137 **FUNCTIONS** section).
1141 : Outputs the binary (base **2**) representation of **x**.
1143 This is a **void** function (see the *Void Functions* subsection of the
1144 **FUNCTIONS** section).
1148 : Outputs the base **b** representation of **x**.
1150 This is a **void** function (see the *Void Functions* subsection of the
1151 **FUNCTIONS** section).
1155 : Outputs the representation, in binary and hexadecimal, of **x** as an
1156 unsigned integer in as few power of two bytes as possible. Both outputs are
1157 split into bytes separated by spaces.
1159 If **x** is not an integer or is negative, an error message is printed
1160 instead, but bc(1) is not reset (see the **RESET** section).
1162 This is a **void** function (see the *Void Functions* subsection of the
1163 **FUNCTIONS** section).
1167 : Outputs the representation, in binary and hexadecimal, of **x** as a signed,
1168 two's-complement integer in as few power of two bytes as possible. Both
1169 outputs are split into bytes separated by spaces.
1171 If **x** is not an integer, an error message is printed instead, but bc(1)
1172 is not reset (see the **RESET** section).
1174 This is a **void** function (see the *Void Functions* subsection of the
1175 **FUNCTIONS** section).
1179 : Outputs the representation, in binary and hexadecimal, of **x** as an
1180 unsigned integer in **n** bytes. Both outputs are split into bytes separated
1183 If **x** is not an integer, is negative, or cannot fit into **n** bytes, an
1184 error message is printed instead, but bc(1) is not reset (see the **RESET**
1187 This is a **void** function (see the *Void Functions* subsection of the
1188 **FUNCTIONS** section).
1192 : Outputs the representation, in binary and hexadecimal, of **x** as a signed,
1193 two's-complement integer in **n** bytes. Both outputs are split into bytes
1194 separated by spaces.
1196 If **x** is not an integer or cannot fit into **n** bytes, an error message
1197 is printed instead, but bc(1) is not reset (see the **RESET** section).
1199 This is a **void** function (see the *Void Functions* subsection of the
1200 **FUNCTIONS** section).
1204 : Outputs the representation, in binary and hexadecimal, of **x** as an
1205 unsigned integer in **1** byte. Both outputs are split into bytes separated
1208 If **x** is not an integer, is negative, or cannot fit into **1** byte, an
1209 error message is printed instead, but bc(1) is not reset (see the **RESET**
1212 This is a **void** function (see the *Void Functions* subsection of the
1213 **FUNCTIONS** section).
1217 : Outputs the representation, in binary and hexadecimal, of **x** as a signed,
1218 two's-complement integer in **1** byte. Both outputs are split into bytes
1219 separated by spaces.
1221 If **x** is not an integer or cannot fit into **1** byte, an error message
1222 is printed instead, but bc(1) is not reset (see the **RESET** section).
1224 This is a **void** function (see the *Void Functions* subsection of the
1225 **FUNCTIONS** section).
1229 : Outputs the representation, in binary and hexadecimal, of **x** as an
1230 unsigned integer in **2** bytes. Both outputs are split into bytes separated
1233 If **x** is not an integer, is negative, or cannot fit into **2** bytes, an
1234 error message is printed instead, but bc(1) is not reset (see the **RESET**
1237 This is a **void** function (see the *Void Functions* subsection of the
1238 **FUNCTIONS** section).
1242 : Outputs the representation, in binary and hexadecimal, of **x** as a signed,
1243 two's-complement integer in **2** bytes. Both outputs are split into bytes
1244 separated by spaces.
1246 If **x** is not an integer or cannot fit into **2** bytes, an error message
1247 is printed instead, but bc(1) is not reset (see the **RESET** section).
1249 This is a **void** function (see the *Void Functions* subsection of the
1250 **FUNCTIONS** section).
1254 : Outputs the representation, in binary and hexadecimal, of **x** as an
1255 unsigned integer in **4** bytes. Both outputs are split into bytes separated
1258 If **x** is not an integer, is negative, or cannot fit into **4** bytes, an
1259 error message is printed instead, but bc(1) is not reset (see the **RESET**
1262 This is a **void** function (see the *Void Functions* subsection of the
1263 **FUNCTIONS** section).
1267 : Outputs the representation, in binary and hexadecimal, of **x** as a signed,
1268 two's-complement integer in **4** bytes. Both outputs are split into bytes
1269 separated by spaces.
1271 If **x** is not an integer or cannot fit into **4** bytes, an error message
1272 is printed instead, but bc(1) is not reset (see the **RESET** section).
1274 This is a **void** function (see the *Void Functions* subsection of the
1275 **FUNCTIONS** section).
1279 : Outputs the representation, in binary and hexadecimal, of **x** as an
1280 unsigned integer in **8** bytes. Both outputs are split into bytes separated
1283 If **x** is not an integer, is negative, or cannot fit into **8** bytes, an
1284 error message is printed instead, but bc(1) is not reset (see the **RESET**
1287 This is a **void** function (see the *Void Functions* subsection of the
1288 **FUNCTIONS** section).
1292 : Outputs the representation, in binary and hexadecimal, of **x** as a signed,
1293 two's-complement integer in **8** bytes. Both outputs are split into bytes
1294 separated by spaces.
1296 If **x** is not an integer or cannot fit into **8** bytes, an error message
1297 is printed instead, but bc(1) is not reset (see the **RESET** section).
1299 This is a **void** function (see the *Void Functions* subsection of the
1300 **FUNCTIONS** section).
1304 : Outputs the representation of the truncated absolute value of **x** as an
1305 unsigned integer in hexadecimal using **n** bytes. Not all of the value will
1306 be output if **n** is too small.
1308 This is a **void** function (see the *Void Functions* subsection of the
1309 **FUNCTIONS** section).
1311 **binary_uint(x, n)**
1313 : Outputs the representation of the truncated absolute value of **x** as an
1314 unsigned integer in binary using **n** bytes. Not all of the value will be
1315 output if **n** is too small.
1317 This is a **void** function (see the *Void Functions* subsection of the
1318 **FUNCTIONS** section).
1320 **output_uint(x, n)**
1322 : Outputs the representation of the truncated absolute value of **x** as an
1323 unsigned integer in the current **obase** (see the **SYNTAX** section) using
1324 **n** bytes. Not all of the value will be output if **n** is too small.
1326 This is a **void** function (see the *Void Functions* subsection of the
1327 **FUNCTIONS** section).
1329 **output_byte(x, i)**
1331 : Outputs byte **i** of the truncated absolute value of **x**, where **0** is
1332 the least significant byte and **number_of_bytes - 1** is the most
1335 This is a **void** function (see the *Void Functions* subsection of the
1336 **FUNCTIONS** section).
1338 ## Transcendental Functions
1340 All transcendental functions can return slightly inaccurate results (up to 1
1341 [ULP][4]). This is unavoidable, and [this article][5] explains why it is
1342 impossible and unnecessary to calculate exact results for the transcendental
1345 Because of the possible inaccuracy, I recommend that users call those functions
1346 with the precision (**scale**) set to at least 1 higher than is necessary. If
1347 exact results are *absolutely* required, users can double the precision
1348 (**scale**) and then truncate.
1350 The transcendental functions in the standard math library are:
1359 The transcendental functions in the extended math library are:
1377 When bc(1) encounters an error or a signal that it has a non-default handler
1378 for, it resets. This means that several things happen.
1380 First, any functions that are executing are stopped and popped off the stack.
1381 The behavior is not unlike that of exceptions in programming languages. Then
1382 the execution point is set so that any code waiting to execute (after all
1383 functions returned) is skipped.
1385 Thus, when bc(1) resets, it skips any remaining code waiting to be executed.
1386 Then, if it is interactive mode, and the error was not a fatal error (see the
1387 **EXIT STATUS** section), it asks for more input; otherwise, it exits with the
1388 appropriate return code.
1390 Note that this reset behavior is different from the GNU bc(1), which attempts to
1391 start executing the statement right after the one that caused an error.
1395 Most bc(1) implementations use **char** types to calculate the value of **1**
1396 decimal digit at a time, but that can be slow. This bc(1) does something
1399 It uses large integers to calculate more than **1** decimal digit at a time. If
1400 built in a environment where **BC_LONG_BIT** (see the **LIMITS** section) is
1401 **64**, then each integer has **9** decimal digits. If built in an environment
1402 where **BC_LONG_BIT** is **32** then each integer has **4** decimal digits. This
1403 value (the number of decimal digits per large integer) is called
1406 The actual values of **BC_LONG_BIT** and **BC_BASE_DIGS** can be queried with
1407 the **limits** statement.
1409 In addition, this bc(1) uses an even larger integer for overflow checking. This
1410 integer type depends on the value of **BC_LONG_BIT**, but is always at least
1411 twice as large as the integer type used to store digits.
1415 The following are the limits on bc(1):
1419 : The number of bits in the **long** type in the environment where bc(1) was
1420 built. This determines how many decimal digits can be stored in a single
1421 large integer (see the **PERFORMANCE** section).
1425 : The number of decimal digits per large integer (see the **PERFORMANCE**
1426 section). Depends on **BC_LONG_BIT**.
1430 : The max decimal number that each large integer can store (see
1431 **BC_BASE_DIGS**) plus **1**. Depends on **BC_BASE_DIGS**.
1435 : The max number that the overflow type (see the **PERFORMANCE** section) can
1436 hold. Depends on **BC_LONG_BIT**.
1440 : The maximum output base. Set at **BC_BASE_POW**.
1444 : The maximum size of arrays. Set at **SIZE_MAX-1**.
1448 : The maximum **scale**. Set at **BC_OVERFLOW_MAX-1**.
1452 : The maximum length of strings. Set at **BC_OVERFLOW_MAX-1**.
1456 : The maximum length of identifiers. Set at **BC_OVERFLOW_MAX-1**.
1460 : The maximum length of a number (in decimal digits), which includes digits
1461 after the decimal point. Set at **BC_OVERFLOW_MAX-1**.
1465 : The maximum integer (inclusive) returned by the **rand()** operand. Set at
1466 **2\^BC_LONG_BIT-1**.
1470 : The maximum allowable exponent (positive or negative). Set at
1471 **BC_OVERFLOW_MAX**.
1475 : The maximum number of vars/arrays. Set at **SIZE_MAX-1**.
1477 The actual values can be queried with the **limits** statement.
1479 These limits are meant to be effectively non-existent; the limits are so large
1480 (at least on 64-bit machines) that there should not be any point at which they
1481 become a problem. In fact, memory should be exhausted before these limits should
1484 # ENVIRONMENT VARIABLES
1486 bc(1) recognizes the following environment variables:
1490 : If this variable exists (no matter the contents), bc(1) behaves as if
1491 the **-s** option was given.
1495 : This is another way to give command-line arguments to bc(1). They should be
1496 in the same format as all other command-line arguments. These are always
1497 processed first, so any files given in **BC_ENV_ARGS** will be processed
1498 before arguments and files given on the command-line. This gives the user
1499 the ability to set up "standard" options and files to be used at every
1500 invocation. The most useful thing for such files to contain would be useful
1501 functions that the user might want every time bc(1) runs.
1503 The code that parses **BC_ENV_ARGS** will correctly handle quoted arguments,
1504 but it does not understand escape sequences. For example, the string
1505 **"/home/gavin/some bc file.bc"** will be correctly parsed, but the string
1506 **"/home/gavin/some \"bc\" file.bc"** will include the backslashes.
1508 The quote parsing will handle either kind of quotes, **'** or **"**. Thus,
1509 if you have a file with any number of single quotes in the name, you can use
1510 double quotes as the outside quotes, as in **"some 'bc' file.bc"**, and vice
1511 versa if you have a file with double quotes. However, handling a file with
1512 both kinds of quotes in **BC_ENV_ARGS** is not supported due to the
1513 complexity of the parsing, though such files are still supported on the
1514 command-line where the parsing is done by the shell.
1518 : If this environment variable exists and contains an integer that is greater
1519 than **1** and is less than **UINT16_MAX** (**2\^16-1**), bc(1) will output
1520 lines to that length, including the backslash (**\\**). The default line
1525 : If this variable exists (no matter the contents), bc(1) will exit
1526 immediately after executing expressions and files given by the **-e** and/or
1527 **-f** command-line options (and any equivalents).
1531 bc(1) returns the following exit statuses:
1539 : A math error occurred. This follows standard practice of using **1** for
1540 expected errors, since math errors will happen in the process of normal
1543 Math errors include divide by **0**, taking the square root of a negative
1544 number, using a negative number as a bound for the pseudo-random number
1545 generator, attempting to convert a negative number to a hardware integer,
1546 overflow when converting a number to a hardware integer, and attempting to
1547 use a non-integer where an integer is required.
1549 Converting to a hardware integer happens for the second operand of the power
1550 (**\^**), places (**\@**), left shift (**\<\<**), and right shift (**\>\>**)
1551 operators and their corresponding assignment operators.
1555 : A parse error occurred.
1557 Parse errors include unexpected **EOF**, using an invalid character, failing
1558 to find the end of a string or comment, using a token where it is invalid,
1559 giving an invalid expression, giving an invalid print statement, giving an
1560 invalid function definition, attempting to assign to an expression that is
1561 not a named expression (see the *Named Expressions* subsection of the
1562 **SYNTAX** section), giving an invalid **auto** list, having a duplicate
1563 **auto**/function parameter, failing to find the end of a code block,
1564 attempting to return a value from a **void** function, attempting to use a
1565 variable as a reference, and using any extensions when the option **-s** or
1566 any equivalents were given.
1570 : A runtime error occurred.
1572 Runtime errors include assigning an invalid number to **ibase**, **obase**,
1573 or **scale**; give a bad expression to a **read()** call, calling **read()**
1574 inside of a **read()** call, type errors, passing the wrong number of
1575 arguments to functions, attempting to call an undefined function, and
1576 attempting to use a **void** function call as a value in an expression.
1580 : A fatal error occurred.
1582 Fatal errors include memory allocation errors, I/O errors, failing to open
1583 files, attempting to use files that do not have only ASCII characters (bc(1)
1584 only accepts ASCII characters), attempting to open a directory as a file,
1585 and giving invalid command-line options.
1587 The exit status **4** is special; when a fatal error occurs, bc(1) always exits
1588 and returns **4**, no matter what mode bc(1) is in.
1590 The other statuses will only be returned when bc(1) is not in interactive mode
1591 (see the **INTERACTIVE MODE** section), since bc(1) resets its state (see the
1592 **RESET** section) and accepts more input when one of those errors occurs in
1593 interactive mode. This is also the case when interactive mode is forced by the
1594 **-i** flag or **--interactive** option.
1596 These exit statuses allow bc(1) to be used in shell scripting with error
1597 checking, and its normal behavior can be forced by using the **-i** flag or
1598 **--interactive** option.
1602 Per the [standard][1], bc(1) has an interactive mode and a non-interactive mode.
1603 Interactive mode is turned on automatically when both **stdin** and **stdout**
1604 are hooked to a terminal, but the **-i** flag and **--interactive** option can
1605 turn it on in other cases.
1607 In interactive mode, bc(1) attempts to recover from errors (see the **RESET**
1608 section), and in normal execution, flushes **stdout** as soon as execution is
1609 done for the current input.
1613 If **stdin**, **stdout**, and **stderr** are all connected to a TTY, bc(1) turns
1616 The prompt is enabled in TTY mode.
1618 TTY mode is different from interactive mode because interactive mode is required
1619 in the [bc(1) specification][1], and interactive mode requires only **stdin**
1620 and **stdout** to be connected to a terminal.
1624 Sending a **SIGINT** will cause bc(1) to stop execution of the current input. If
1625 bc(1) is in TTY mode (see the **TTY MODE** section), it will reset (see the
1626 **RESET** section). Otherwise, it will clean up and exit.
1628 Note that "current input" can mean one of two things. If bc(1) is processing
1629 input from **stdin** in TTY mode, it will ask for more input. If bc(1) is
1630 processing input from a file in TTY mode, it will stop processing the file and
1631 start processing the next file, if one exists, or ask for input from **stdin**
1632 if no other file exists.
1634 This means that if a **SIGINT** is sent to bc(1) as it is executing a file, it
1635 can seem as though bc(1) did not respond to the signal since it will immediately
1636 start executing the next file. This is by design; most files that users execute
1637 when interacting with bc(1) have function definitions, which are quick to parse.
1638 If a file takes a long time to execute, there may be a bug in that file. The
1639 rest of the files could still be executed without problem, allowing the user to
1642 **SIGTERM** and **SIGQUIT** cause bc(1) to clean up and exit, and it uses the
1643 default handler for all other signals.
1651 bc(1) is compliant with the [IEEE Std 1003.1-2017 (“POSIX.1-2017”)][1]
1652 specification. The flags **-efghiqsvVw**, all long options, and the extensions
1653 noted above are extensions to that specification.
1655 Note that the specification explicitly says that bc(1) only accepts numbers that
1656 use a period (**.**) as a radix point, regardless of the value of
1661 None are known. Report bugs at https://git.yzena.com/gavin/bc.
1665 Gavin D. Howard <yzena.tech@gmail.com> and contributors.
1667 [1]: https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html
1668 [2]: https://www.gnu.org/software/bc/
1669 [3]: https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero
1670 [4]: https://en.wikipedia.org/wiki/Unit_in_the_last_place
1671 [5]: https://people.eecs.berkeley.edu/~wkahan/LOG10HAF.TXT
1672 [6]: https://en.wikipedia.org/wiki/Rounding#Rounding_away_from_zero