3 SPDX-License-Identifier: BSD-2-Clause
5 Copyright (c) 2018-2020 Gavin D. Howard and contributors.
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8 modification, are permitted provided that the following conditions are met:
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 decimal 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 : This option is a no-op.
144 This is a **non-portable extension**.
148 : This option is for compatibility with the [GNU bc(1)][2]; it is a no-op.
149 Without this option, GNU bc(1) prints a copyright header. This bc(1) only
150 prints the copyright header if one or more of the **-v**, **-V**, or
151 **--version** options are given.
153 This is a **non-portable extension**.
155 **-s**, **--standard**
157 : Process exactly the language defined by the [standard][1] and error if any
160 This is a **non-portable extension**.
162 **-v**, **-V**, **--version**
164 : Print the version information (copyright header) and exit.
166 This is a **non-portable extension**.
170 : Like **-s** and **--standard**, except that warnings (and not errors) are
171 printed for non-standard extensions and execution continues normally.
173 This is a **non-portable extension**.
175 **-e** *expr*, **--expression**=*expr*
177 : Evaluates *expr*. If multiple expressions are given, they are evaluated in
178 order. If files are given as well (see below), the expressions and files are
179 evaluated in the order given. This means that if a file is given before an
180 expression, the file is read in and evaluated first.
182 After processing all expressions and files, bc(1) will exit, unless **-**
183 (**stdin**) was given as an argument at least once to **-f** or **--file**.
184 However, if any other **-e**, **--expression**, **-f**, or **--file**
185 arguments are given after that, bc(1) will give a fatal error and exit.
187 This is a **non-portable extension**.
189 **-f** *file*, **--file**=*file*
191 : Reads in *file* and evaluates it, line by line, as though it were read
192 through **stdin**. If expressions are also given (see above), the
193 expressions are evaluated in the order given.
195 After processing all expressions and files, bc(1) will exit, unless **-**
196 (**stdin**) was given as an argument at least once to **-f** or **--file**.
198 This is a **non-portable extension**.
200 All long options are **non-portable extensions**.
204 Any non-error output is written to **stdout**.
206 **Note**: Unlike other bc(1) implementations, this bc(1) will issue a fatal
207 error (see the **EXIT STATUS** section) if it cannot write to **stdout**, so if
208 **stdout** is closed, as in **bc <file> >&-**, it will quit with an error. This
209 is done so that bc(1) can report problems when **stdout** is redirected to a
212 If there are scripts that depend on the behavior of other bc(1) implementations,
213 it is recommended that those scripts be changed to redirect **stdout** to
218 Any error output is written to **stderr**.
220 **Note**: Unlike other bc(1) implementations, this bc(1) will issue a fatal
221 error (see the **EXIT STATUS** section) if it cannot write to **stderr**, so if
222 **stderr** is closed, as in **bc <file> 2>&-**, it will quit with an error. This
223 is done so that bc(1) can exit with an error code when **stderr** is redirected
226 If there are scripts that depend on the behavior of other bc(1) implementations,
227 it is recommended that those scripts be changed to redirect **stderr** to
232 The syntax for bc(1) programs is mostly C-like, with some differences. This
233 bc(1) follows the [POSIX standard][1], which is a much more thorough resource
234 for the language this bc(1) accepts. This section is meant to be a summary and a
235 listing of all the extensions to the standard.
237 In the sections below, **E** means expression, **S** means statement, and **I**
240 Identifiers (**I**) start with a lowercase letter and can be followed by any
241 number (up to **BC_NAME_MAX-1**) of lowercase letters (**a-z**), digits
242 (**0-9**), and underscores (**\_**). The regex is **\[a-z\]\[a-z0-9\_\]\***.
243 Identifiers with more than one character (letter) are a
244 **non-portable extension**.
246 **ibase** is a global variable determining how to interpret constant numbers. It
247 is the "input" base, or the number base used for interpreting input numbers.
248 **ibase** is initially **10**. If the **-s** (**--standard**) and **-w**
249 (**--warn**) flags were not given on the command line, the max allowable value
250 for **ibase** is **36**. Otherwise, it is **16**. The min allowable value for
251 **ibase** is **2**. The max allowable value for **ibase** can be queried in
252 bc(1) programs with the **maxibase()** built-in function.
254 **obase** is a global variable determining how to output results. It is the
255 "output" base, or the number base used for outputting numbers. **obase** is
256 initially **10**. The max allowable value for **obase** is **BC_BASE_MAX** and
257 can be queried in bc(1) programs with the **maxobase()** built-in function. The
258 min allowable value for **obase** is **0**. If **obase** is **0**, values are
259 output in scientific notation, and if **obase** is **1**, values are output in
260 engineering notation. Otherwise, values are output in the specified base.
262 Outputting in scientific and engineering notations are **non-portable
265 The *scale* of an expression is the number of digits in the result of the
266 expression right of the decimal point, and **scale** is a global variable that
267 sets the precision of any operations, with exceptions. **scale** is initially
268 **0**. **scale** cannot be negative. The max allowable value for **scale** is
269 **BC_SCALE_MAX** and can be queried in bc(1) programs with the **maxscale()**
272 bc(1) has both *global* variables and *local* variables. All *local*
273 variables are local to the function; they are parameters or are introduced in
274 the **auto** list of a function (see the **FUNCTIONS** section). If a variable
275 is accessed which is not a parameter or in the **auto** list, it is assumed to
276 be *global*. If a parent function has a *local* variable version of a variable
277 that a child function considers *global*, the value of that *global* variable in
278 the child function is the value of the variable in the parent function, not the
279 value of the actual *global* variable.
281 All of the above applies to arrays as well.
283 The value of a statement that is an expression (i.e., any of the named
284 expressions or operands) is printed unless the lowest precedence operator is an
285 assignment operator *and* the expression is notsurrounded by parentheses.
287 The value that is printed is also assigned to the special variable **last**. A
288 single dot (**.**) may also be used as a synonym for **last**. These are
289 **non-portable extensions**.
291 Either semicolons or newlines may separate statements.
295 There are two kinds of comments:
297 1. Block comments are enclosed in **/\*** and **\*/**.
298 2. Line comments go from **#** until, and not including, the next newline. This
299 is a **non-portable extension**.
303 The following are named expressions in bc(1):
306 2. Array Elements: **I[E]**
311 7. **last** or a single dot (**.**)
313 Numbers 6 and 7 are **non-portable extensions**.
315 The meaning of **seed** is dependent on the current pseudo-random number
316 generator but is guaranteed to not change except for new major versions.
318 The *scale* and sign of the value may be significant.
320 If a previously used **seed** value is assigned to **seed** and used again, the
321 pseudo-random number generator is guaranteed to produce the same sequence of
322 pseudo-random numbers as it did when the **seed** value was previously used.
324 The exact value assigned to **seed** is not guaranteed to be returned if
325 **seed** is queried again immediately. However, if **seed** *does* return a
326 different value, both values, when assigned to **seed**, are guaranteed to
327 produce the same sequence of pseudo-random numbers. This means that certain
328 values assigned to **seed** will *not* produce unique sequences of pseudo-random
329 numbers. The value of **seed** will change after any use of the **rand()** and
330 **irand(E)** operands (see the *Operands* subsection below), except if the
331 parameter passed to **irand(E)** is **0**, **1**, or negative.
333 There is no limit to the length (number of significant decimal digits) or
334 *scale* of the value that can be assigned to **seed**.
336 Variables and arrays do not interfere; users can have arrays named the same as
337 variables. This also applies to functions (see the **FUNCTIONS** section), so a
338 user can have a variable, array, and function that all have the same name, and
339 they will not shadow each other, whether inside of functions or not.
341 Named expressions are required as the operand of **increment**/**decrement**
342 operators and as the left side of **assignment** operators (see the *Operators*
347 The following are valid operands in bc(1):
349 1. Numbers (see the *Numbers* subsection below).
350 2. Array indices (**I[E]**).
351 3. **(E)**: The value of **E** (used to change precedence).
352 4. **sqrt(E)**: The square root of **E**. **E** must be non-negative.
353 5. **length(E)**: The number of significant decimal digits in **E**.
354 6. **length(I[])**: The number of elements in the array **I**. This is a
355 **non-portable extension**.
356 7. **scale(E)**: The *scale* of **E**.
357 8. **abs(E)**: The absolute value of **E**. This is a **non-portable
359 9. **I()**, **I(E)**, **I(E, E)**, and so on, where **I** is an identifier for
360 a non-**void** function (see the *Void Functions* subsection of the
361 **FUNCTIONS** section). The **E** argument(s) may also be arrays of the form
362 **I[]**, which will automatically be turned into array references (see the
363 *Array References* subsection of the **FUNCTIONS** section) if the
364 corresponding parameter in the function definition is an array reference.
365 10. **read()**: Reads a line from **stdin** and uses that as an expression. The
366 result of that expression is the result of the **read()** operand. This is a
367 **non-portable extension**.
368 11. **maxibase()**: The max allowable **ibase**. This is a **non-portable
370 12. **maxobase()**: The max allowable **obase**. This is a **non-portable
372 13. **maxscale()**: The max allowable **scale**. This is a **non-portable
374 14. **rand()**: A pseudo-random integer between **0** (inclusive) and
375 **BC_RAND_MAX** (inclusive). Using this operand will change the value of
376 **seed**. This is a **non-portable extension**.
377 15. **irand(E)**: A pseudo-random integer between **0** (inclusive) and the
378 value of **E** (exclusive). If **E** is negative or is a non-integer
379 (**E**'s *scale* is not **0**), an error is raised, and bc(1) resets (see
380 the **RESET** section) while **seed** remains unchanged. If **E** is larger
381 than **BC_RAND_MAX**, the higher bound is honored by generating several
382 pseudo-random integers, multiplying them by appropriate powers of
383 **BC_RAND_MAX+1**, and adding them together. Thus, the size of integer that
384 can be generated with this operand is unbounded. Using this operand will
385 change the value of **seed**, unless the value of **E** is **0** or **1**.
386 In that case, **0** is returned, and **seed** is *not* changed. This is a
387 **non-portable extension**.
388 16. **maxrand()**: The max integer returned by **rand()**. This is a
389 **non-portable extension**.
391 The integers generated by **rand()** and **irand(E)** are guaranteed to be as
392 unbiased as possible, subject to the limitations of the pseudo-random number
395 **Note**: The values returned by the pseudo-random number generator with
396 **rand()** and **irand(E)** are guaranteed to *NOT* be cryptographically secure.
397 This is a consequence of using a seeded pseudo-random number generator. However,
398 they *are* guaranteed to be reproducible with identical **seed** values.
402 Numbers are strings made up of digits, uppercase letters, and at most **1**
403 period for a radix. Numbers can have up to **BC_NUM_MAX** digits. Uppercase
404 letters are equal to **9** + their position in the alphabet (i.e., **A** equals
405 **10**, or **9+1**). If a digit or letter makes no sense with the current value
406 of **ibase**, they are set to the value of the highest valid digit in **ibase**.
408 Single-character numbers (i.e., **A** alone) take the value that they would have
409 if they were valid digits, regardless of the value of **ibase**. This means that
410 **A** alone always equals decimal **10** and **Z** alone always equals decimal
413 In addition, bc(1) accepts numbers in scientific notation. These have the form
414 **\<number\>e\<integer\>**. The exponent (the portion after the **e**) must be
415 an integer. An example is **1.89237e9**, which is equal to **1892370000**.
416 Negative exponents are also allowed, so **4.2890e-3** is equal to **0.0042890**.
418 Using scientific notation is an error or warning if the **-s** or **-w**,
419 respectively, command-line options (or equivalents) are given.
421 **WARNING**: Both the number and the exponent in scientific notation are
422 interpreted according to the current **ibase**, but the number is still
423 multiplied by **10\^exponent** regardless of the current **ibase**. For example,
424 if **ibase** is **16** and bc(1) is given the number string **FFeA**, the
425 resulting decimal number will be **2550000000000**, and if bc(1) is given the
426 number string **10e-4**, the resulting decimal number will be **0.0016**.
428 Accepting input as scientific notation is a **non-portable extension**.
432 The following arithmetic and logical operators can be used. They are listed in
433 order of decreasing precedence. Operators in the same group have the same
438 : Type: Prefix and Postfix
442 Description: **increment**, **decrement**
450 Description: **negation**, **boolean not**
458 Description: **truncation**
466 Description: **set precision**
474 Description: **power**
482 Description: **multiply**, **divide**, **modulus**
490 Description: **add**, **subtract**
498 Description: **shift left**, **shift right**
500 **=** **\<\<=** **\>\>=** **+=** **-=** **\*=** **/=** **%=** **\^=** **\@=**
506 Description: **assignment**
508 **==** **\<=** **\>=** **!=** **\<** **\>**
514 Description: **relational**
522 Description: **boolean and**
530 Description: **boolean or**
532 The operators will be described in more detail below.
536 : The prefix and postfix **increment** and **decrement** operators behave
537 exactly like they would in C. They require a named expression (see the
538 *Named Expressions* subsection) as an operand.
540 The prefix versions of these operators are more efficient; use them where
545 : The **negation** operator returns **0** if a user attempts to negate any
546 expression with the value **0**. Otherwise, a copy of the expression with
547 its sign flipped is returned.
551 : The **boolean not** operator returns **1** if the expression is **0**, or
554 This is a **non-portable extension**.
558 : The **truncation** operator returns a copy of the given expression with all
559 of its *scale* removed.
561 This is a **non-portable extension**.
565 : The **set precision** operator takes two expressions and returns a copy of
566 the first with its *scale* equal to the value of the second expression. That
567 could either mean that the number is returned without change (if the
568 *scale* of the first expression matches the value of the second
569 expression), extended (if it is less), or truncated (if it is more).
571 The second expression must be an integer (no *scale*) and non-negative.
573 This is a **non-portable extension**.
577 : The **power** operator (not the **exclusive or** operator, as it would be in
578 C) takes two expressions and raises the first to the power of the value of
579 the second. The *scale* of the result is equal to **scale**.
581 The second expression must be an integer (no *scale*), and if it is
582 negative, the first value must be non-zero.
586 : The **multiply** operator takes two expressions, multiplies them, and
587 returns the product. If **a** is the *scale* of the first expression and
588 **b** is the *scale* of the second expression, the *scale* of the result is
589 equal to **min(a+b,max(scale,a,b))** where **min()** and **max()** return
594 : The **divide** operator takes two expressions, divides them, and returns the
595 quotient. The *scale* of the result shall be the value of **scale**.
597 The second expression must be non-zero.
601 : The **modulus** operator takes two expressions, **a** and **b**, and
602 evaluates them by 1) Computing **a/b** to current **scale** and 2) Using the
603 result of step 1 to calculate **a-(a/b)\*b** to *scale*
604 **max(scale+scale(b),scale(a))**.
606 The second expression must be non-zero.
610 : The **add** operator takes two expressions, **a** and **b**, and returns the
611 sum, with a *scale* equal to the max of the *scale*s of **a** and **b**.
615 : The **subtract** operator takes two expressions, **a** and **b**, and
616 returns the difference, with a *scale* equal to the max of the *scale*s of
621 : The **left shift** operator takes two expressions, **a** and **b**, and
622 returns a copy of the value of **a** with its decimal point moved **b**
625 The second expression must be an integer (no *scale*) and non-negative.
627 This is a **non-portable extension**.
631 : The **right shift** operator takes two expressions, **a** and **b**, and
632 returns a copy of the value of **a** with its decimal point moved **b**
635 The second expression must be an integer (no *scale*) and non-negative.
637 This is a **non-portable extension**.
639 **=** **\<\<=** **\>\>=** **+=** **-=** **\*=** **/=** **%=** **\^=** **\@=**
641 : The **assignment** operators take two expressions, **a** and **b** where
642 **a** is a named expression (see the *Named Expressions* subsection).
644 For **=**, **b** is copied and the result is assigned to **a**. For all
645 others, **a** and **b** are applied as operands to the corresponding
646 arithmetic operator and the result is assigned to **a**.
648 The **assignment** operators that correspond to operators that are
649 extensions are themselves **non-portable extensions**.
651 **==** **\<=** **\>=** **!=** **\<** **\>**
653 : The **relational** operators compare two expressions, **a** and **b**, and
654 if the relation holds, according to C language semantics, the result is
655 **1**. Otherwise, it is **0**.
657 Note that unlike in C, these operators have a lower precedence than the
658 **assignment** operators, which means that **a=b\>c** is interpreted as
661 Also, unlike the [standard][1] requires, these operators can appear anywhere
662 any other expressions can be used. This allowance is a
663 **non-portable extension**.
667 : The **boolean and** operator takes two expressions and returns **1** if both
668 expressions are non-zero, **0** otherwise.
670 This is *not* a short-circuit operator.
672 This is a **non-portable extension**.
676 : The **boolean or** operator takes two expressions and returns **1** if one
677 of the expressions is non-zero, **0** otherwise.
679 This is *not* a short-circuit operator.
681 This is a **non-portable extension**.
685 The following items are statements:
688 2. **{** **S** **;** ... **;** **S** **}**
689 3. **if** **(** **E** **)** **S**
690 4. **if** **(** **E** **)** **S** **else** **S**
691 5. **while** **(** **E** **)** **S**
692 6. **for** **(** **E** **;** **E** **;** **E** **)** **S**
693 7. An empty statement
699 13. A string of characters, enclosed in double quotes
700 14. **print** **E** **,** ... **,** **E**
701 15. **I()**, **I(E)**, **I(E, E)**, and so on, where **I** is an identifier for
702 a **void** function (see the *Void Functions* subsection of the
703 **FUNCTIONS** section). The **E** argument(s) may also be arrays of the form
704 **I[]**, which will automatically be turned into array references (see the
705 *Array References* subsection of the **FUNCTIONS** section) if the
706 corresponding parameter in the function definition is an array reference.
708 Numbers 4, 9, 11, 12, 14, and 15 are **non-portable extensions**.
710 Also, as a **non-portable extension**, any or all of the expressions in the
711 header of a for loop may be omitted. If the condition (second expression) is
712 omitted, it is assumed to be a constant **1**.
714 The **break** statement causes a loop to stop iterating and resume execution
715 immediately following a loop. This is only allowed in loops.
717 The **continue** statement causes a loop iteration to stop early and returns to
718 the start of the loop, including testing the loop condition. This is only
721 The **if** **else** statement does the same thing as in C.
723 The **quit** statement causes bc(1) to quit, even if it is on a branch that will
724 not be executed (it is a compile-time command).
726 The **halt** statement causes bc(1) to quit, if it is executed. (Unlike **quit**
727 if it is on a branch of an **if** statement that is not executed, bc(1) does not
730 The **limits** statement prints the limits that this bc(1) is subject to. This
731 is like the **quit** statement in that it is a compile-time command.
733 An expression by itself is evaluated and printed, followed by a newline.
735 Both scientific notation and engineering notation are available for printing the
736 results of expressions. Scientific notation is activated by assigning **0** to
737 **obase**, and engineering notation is activated by assigning **1** to
738 **obase**. To deactivate them, just assign a different value to **obase**.
740 Scientific notation and engineering notation are disabled if bc(1) is run with
741 either the **-s** or **-w** command-line options (or equivalents).
743 Printing numbers in scientific notation and/or engineering notation is a
744 **non-portable extension**.
748 The "expressions" in a **print** statement may also be strings. If they are, there
749 are backslash escape sequences that are interpreted specially. What those
750 sequences are, and what they cause to be printed, are shown below:
764 Any other character following a backslash causes the backslash and character to
767 Any non-string expression in a print statement shall be assigned to **last**,
768 like any other expression that is printed.
770 ## Order of Evaluation
772 All expressions in a statment are evaluated left to right, except as necessary
773 to maintain order of operations. This means, for example, assuming that **i** is
774 equal to **0**, in the expression
778 the first (or 0th) element of **a** is set to **1**, and **i** is equal to **2**
779 at the end of the expression.
781 This includes function arguments. Thus, assuming **i** is equal to **0**, this
782 means that in the expression
786 the first argument passed to **x()** is **0**, and the second argument is **1**,
787 while **i** is equal to **2** before the function starts executing.
791 Function definitions are as follows:
801 Any **I** in the parameter list or **auto** list may be replaced with **I[]** to
802 make a parameter or **auto** var an array, and any **I** in the parameter list
803 may be replaced with **\*I[]** to make a parameter an array reference. Callers
804 of functions that take array references should not put an asterisk in the call;
805 they must be called with just **I[]** like normal array parameters and will be
806 automatically converted into references.
808 As a **non-portable extension**, the opening brace of a **define** statement may
809 appear on the next line.
811 As a **non-portable extension**, the return statement may also be in one of the
815 2. **return** **(** **)**
818 The first two, or not specifying a **return** statement, is equivalent to
819 **return (0)**, unless the function is a **void** function (see the *Void
820 Functions* subsection below).
824 Functions can also be **void** functions, defined as follows:
827 define void I(I,...,I){
834 They can only be used as standalone expressions, where such an expression would
835 be printed alone, except in a print statement.
837 Void functions can only use the first two **return** statements listed above.
838 They can also omit the return statement entirely.
840 The word "void" is not treated as a keyword; it is still possible to have
841 variables, arrays, and functions named **void**. The word "void" is only
842 treated specially right after the **define** keyword.
844 This is a **non-portable extension**.
848 For any array in the parameter list, if the array is declared in the form
854 it is a **reference**. Any changes to the array in the function are reflected,
855 when the function returns, to the array that was passed in.
857 Other than this, all function arguments are passed by value.
859 This is a **non-portable extension**.
863 All of the functions below, including the functions in the extended math
864 library (see the *Extended Library* subsection below), are available when the
865 **-l** or **--mathlib** command-line flags are given, except that the extended
866 math library is not available when the **-s** option, the **-w** option, or
867 equivalents are given.
871 The [standard][1] defines the following functions for the math library:
875 : Returns the sine of **x**, which is assumed to be in radians.
877 This is a transcendental function (see the *Transcendental Functions*
882 : Returns the cosine of **x**, which is assumed to be in radians.
884 This is a transcendental function (see the *Transcendental Functions*
889 : Returns the arctangent of **x**, in radians.
891 This is a transcendental function (see the *Transcendental Functions*
896 : Returns the natural logarithm of **x**.
898 This is a transcendental function (see the *Transcendental Functions*
903 : Returns the mathematical constant **e** raised to the power of **x**.
905 This is a transcendental function (see the *Transcendental Functions*
910 : Returns the bessel integer order **n** (truncated) of **x**.
912 This is a transcendental function (see the *Transcendental Functions*
917 The extended library is *not* loaded when the **-s**/**--standard** or
918 **-w**/**--warn** options are given since they are not part of the library
919 defined by the [standard][1].
921 The extended library is a **non-portable extension**.
925 : Calculates **x** to the power of **y**, even if **y** is not an integer, and
926 returns the result to the current **scale**.
928 It is an error if **y** is negative and **x** is **0**.
930 This is a transcendental function (see the *Transcendental Functions*
935 : Returns **x** rounded to **p** decimal places according to the rounding mode
936 [round half away from **0**][3].
940 : Returns **x** rounded to **p** decimal places according to the rounding mode
941 [round away from **0**][6].
945 : Returns the factorial of the truncated absolute value of **x**.
949 : Returns the permutation of the truncated absolute value of **n** of the
950 truncated absolute value of **k**, if **k \<= n**. If not, it returns **0**.
954 : Returns the combination of the truncated absolute value of **n** of the
955 truncated absolute value of **k**, if **k \<= n**. If not, it returns **0**.
959 : Returns the logarithm base **2** of **x**.
961 This is a transcendental function (see the *Transcendental Functions*
966 : Returns the logarithm base **10** of **x**.
968 This is a transcendental function (see the *Transcendental Functions*
973 : Returns the logarithm base **b** of **x**.
975 This is a transcendental function (see the *Transcendental Functions*
980 : Returns the cube root of **x**.
984 : Calculates the truncated value of **n**, **r**, and returns the **r**th root
985 of **x** to the current **scale**.
987 If **r** is **0** or negative, this raises an error and causes bc(1) to
988 reset (see the **RESET** section). It also raises an error and causes bc(1)
989 to reset if **r** is even and **x** is negative.
993 : Returns **pi** to **p** decimal places.
995 This is a transcendental function (see the *Transcendental Functions*
1000 : Returns the tangent of **x**, which is assumed to be in radians.
1002 This is a transcendental function (see the *Transcendental Functions*
1007 : Returns the arctangent of **y/x**, in radians. If both **y** and **x** are
1008 equal to **0**, it raises an error and causes bc(1) to reset (see the
1009 **RESET** section). Otherwise, if **x** is greater than **0**, it returns
1010 **a(y/x)**. If **x** is less than **0**, and **y** is greater than or equal
1011 to **0**, it returns **a(y/x)+pi**. If **x** is less than **0**, and **y**
1012 is less than **0**, it returns **a(y/x)-pi**. If **x** is equal to **0**,
1013 and **y** is greater than **0**, it returns **pi/2**. If **x** is equal to
1014 **0**, and **y** is less than **0**, it returns **-pi/2**.
1016 This function is the same as the **atan2()** function in many programming
1019 This is a transcendental function (see the *Transcendental Functions*
1024 : Returns the sine of **x**, which is assumed to be in radians.
1026 This is an alias of **s(x)**.
1028 This is a transcendental function (see the *Transcendental Functions*
1033 : Returns the cosine of **x**, which is assumed to be in radians.
1035 This is an alias of **c(x)**.
1037 This is a transcendental function (see the *Transcendental Functions*
1042 : Returns the tangent of **x**, which is assumed to be in radians.
1044 If **x** is equal to **1** or **-1**, this raises an error and causes bc(1)
1045 to reset (see the **RESET** section).
1047 This is an alias of **t(x)**.
1049 This is a transcendental function (see the *Transcendental Functions*
1054 : Returns the arctangent of **x**, in radians.
1056 This is an alias of **a(x)**.
1058 This is a transcendental function (see the *Transcendental Functions*
1063 : Returns the arctangent of **y/x**, in radians. If both **y** and **x** are
1064 equal to **0**, it raises an error and causes bc(1) to reset (see the
1065 **RESET** section). Otherwise, if **x** is greater than **0**, it returns
1066 **a(y/x)**. If **x** is less than **0**, and **y** is greater than or equal
1067 to **0**, it returns **a(y/x)+pi**. If **x** is less than **0**, and **y**
1068 is less than **0**, it returns **a(y/x)-pi**. If **x** is equal to **0**,
1069 and **y** is greater than **0**, it returns **pi/2**. If **x** is equal to
1070 **0**, and **y** is less than **0**, it returns **-pi/2**.
1072 This function is the same as the **atan2()** function in many programming
1075 This is an alias of **a2(y, x)**.
1077 This is a transcendental function (see the *Transcendental Functions*
1082 : Converts **x** from radians to degrees and returns the result.
1084 This is a transcendental function (see the *Transcendental Functions*
1089 : Converts **x** from degrees to radians and returns the result.
1091 This is a transcendental function (see the *Transcendental Functions*
1096 : Generates a pseudo-random number between **0** (inclusive) and **1**
1097 (exclusive) with the number of decimal digits after the decimal point equal
1098 to the truncated absolute value of **p**. If **p** is not **0**, then
1099 calling this function will change the value of **seed**. If **p** is **0**,
1100 then **0** is returned, and **seed** is *not* changed.
1104 : Generates a pseudo-random number that is between **0** (inclusive) and the
1105 truncated absolute value of **i** (exclusive) with the number of decimal
1106 digits after the decimal point equal to the truncated absolute value of
1107 **p**. If the absolute value of **i** is greater than or equal to **2**, and
1108 **p** is not **0**, then calling this function will change the value of
1109 **seed**; otherwise, **0** is returned and **seed** is not changed.
1113 : Returns **x** with its sign flipped with probability **0.5**. In other
1114 words, it randomizes the sign of **x**.
1118 : Returns a random boolean value (either **0** or **1**).
1122 : Returns the numbers of unsigned integer bytes required to hold the truncated
1123 absolute value of **x**.
1127 : Returns the numbers of signed, two's-complement integer bytes required to
1128 hold the truncated value of **x**.
1132 : Outputs the hexadecimal (base **16**) representation of **x**.
1134 This is a **void** function (see the *Void Functions* subsection of the
1135 **FUNCTIONS** section).
1139 : Outputs the binary (base **2**) representation of **x**.
1141 This is a **void** function (see the *Void Functions* subsection of the
1142 **FUNCTIONS** section).
1146 : Outputs the base **b** representation of **x**.
1148 This is a **void** function (see the *Void Functions* subsection of the
1149 **FUNCTIONS** section).
1153 : Outputs the representation, in binary and hexadecimal, of **x** as an
1154 unsigned integer in as few power of two bytes as possible. Both outputs are
1155 split into bytes separated by spaces.
1157 If **x** is not an integer or is negative, an error message is printed
1158 instead, but bc(1) is not reset (see the **RESET** section).
1160 This is a **void** function (see the *Void Functions* subsection of the
1161 **FUNCTIONS** section).
1165 : Outputs the representation, in binary and hexadecimal, of **x** as a signed,
1166 two's-complement integer in as few power of two bytes as possible. Both
1167 outputs are split into bytes separated by spaces.
1169 If **x** is not an integer, an error message is printed instead, but bc(1)
1170 is not reset (see the **RESET** section).
1172 This is a **void** function (see the *Void Functions* subsection of the
1173 **FUNCTIONS** section).
1177 : Outputs the representation, in binary and hexadecimal, of **x** as an
1178 unsigned integer in **n** bytes. Both outputs are split into bytes separated
1181 If **x** is not an integer, is negative, or cannot fit into **n** bytes, an
1182 error message is printed instead, but bc(1) is not reset (see the **RESET**
1185 This is a **void** function (see the *Void Functions* subsection of the
1186 **FUNCTIONS** section).
1190 : Outputs the representation, in binary and hexadecimal, of **x** as a signed,
1191 two's-complement integer in **n** bytes. Both outputs are split into bytes
1192 separated by spaces.
1194 If **x** is not an integer or cannot fit into **n** bytes, an error message
1195 is printed instead, but bc(1) is not reset (see the **RESET** section).
1197 This is a **void** function (see the *Void Functions* subsection of the
1198 **FUNCTIONS** section).
1202 : Outputs the representation, in binary and hexadecimal, of **x** as an
1203 unsigned integer in **1** byte. Both outputs are split into bytes separated
1206 If **x** is not an integer, is negative, or cannot fit into **1** byte, an
1207 error message is printed instead, but bc(1) is not reset (see the **RESET**
1210 This is a **void** function (see the *Void Functions* subsection of the
1211 **FUNCTIONS** section).
1215 : Outputs the representation, in binary and hexadecimal, of **x** as a signed,
1216 two's-complement integer in **1** byte. Both outputs are split into bytes
1217 separated by spaces.
1219 If **x** is not an integer or cannot fit into **1** byte, an error message
1220 is printed instead, but bc(1) is not reset (see the **RESET** section).
1222 This is a **void** function (see the *Void Functions* subsection of the
1223 **FUNCTIONS** section).
1227 : Outputs the representation, in binary and hexadecimal, of **x** as an
1228 unsigned integer in **2** bytes. Both outputs are split into bytes separated
1231 If **x** is not an integer, is negative, or cannot fit into **2** bytes, an
1232 error message is printed instead, but bc(1) is not reset (see the **RESET**
1235 This is a **void** function (see the *Void Functions* subsection of the
1236 **FUNCTIONS** section).
1240 : Outputs the representation, in binary and hexadecimal, of **x** as a signed,
1241 two's-complement integer in **2** bytes. Both outputs are split into bytes
1242 separated by spaces.
1244 If **x** is not an integer or cannot fit into **2** bytes, an error message
1245 is printed instead, but bc(1) is not reset (see the **RESET** section).
1247 This is a **void** function (see the *Void Functions* subsection of the
1248 **FUNCTIONS** section).
1252 : Outputs the representation, in binary and hexadecimal, of **x** as an
1253 unsigned integer in **4** bytes. Both outputs are split into bytes separated
1256 If **x** is not an integer, is negative, or cannot fit into **4** bytes, an
1257 error message is printed instead, but bc(1) is not reset (see the **RESET**
1260 This is a **void** function (see the *Void Functions* subsection of the
1261 **FUNCTIONS** section).
1265 : Outputs the representation, in binary and hexadecimal, of **x** as a signed,
1266 two's-complement integer in **4** bytes. Both outputs are split into bytes
1267 separated by spaces.
1269 If **x** is not an integer or cannot fit into **4** bytes, an error message
1270 is printed instead, but bc(1) is not reset (see the **RESET** section).
1272 This is a **void** function (see the *Void Functions* subsection of the
1273 **FUNCTIONS** section).
1277 : Outputs the representation, in binary and hexadecimal, of **x** as an
1278 unsigned integer in **8** bytes. Both outputs are split into bytes separated
1281 If **x** is not an integer, is negative, or cannot fit into **8** bytes, an
1282 error message is printed instead, but bc(1) is not reset (see the **RESET**
1285 This is a **void** function (see the *Void Functions* subsection of the
1286 **FUNCTIONS** section).
1290 : Outputs the representation, in binary and hexadecimal, of **x** as a signed,
1291 two's-complement integer in **8** bytes. Both outputs are split into bytes
1292 separated by spaces.
1294 If **x** is not an integer or cannot fit into **8** bytes, an error message
1295 is printed instead, but bc(1) is not reset (see the **RESET** section).
1297 This is a **void** function (see the *Void Functions* subsection of the
1298 **FUNCTIONS** section).
1302 : Outputs the representation of the truncated absolute value of **x** as an
1303 unsigned integer in hexadecimal using **n** bytes. Not all of the value will
1304 be output if **n** is too small.
1306 This is a **void** function (see the *Void Functions* subsection of the
1307 **FUNCTIONS** section).
1309 **binary_uint(x, n)**
1311 : Outputs the representation of the truncated absolute value of **x** as an
1312 unsigned integer in binary using **n** bytes. Not all of the value will be
1313 output if **n** is too small.
1315 This is a **void** function (see the *Void Functions* subsection of the
1316 **FUNCTIONS** section).
1318 **output_uint(x, n)**
1320 : Outputs the representation of the truncated absolute value of **x** as an
1321 unsigned integer in the current **obase** (see the **SYNTAX** section) using
1322 **n** bytes. Not all of the value will be output if **n** is too small.
1324 This is a **void** function (see the *Void Functions* subsection of the
1325 **FUNCTIONS** section).
1327 **output_byte(x, i)**
1329 : Outputs byte **i** of the truncated absolute value of **x**, where **0** is
1330 the least significant byte and **number_of_bytes - 1** is the most
1333 This is a **void** function (see the *Void Functions* subsection of the
1334 **FUNCTIONS** section).
1336 ## Transcendental Functions
1338 All transcendental functions can return slightly inaccurate results (up to 1
1339 [ULP][4]). This is unavoidable, and [this article][5] explains why it is
1340 impossible and unnecessary to calculate exact results for the transcendental
1343 Because of the possible inaccuracy, I recommend that users call those functions
1344 with the precision (**scale**) set to at least 1 higher than is necessary. If
1345 exact results are *absolutely* required, users can double the precision
1346 (**scale**) and then truncate.
1348 The transcendental functions in the standard math library are:
1357 The transcendental functions in the extended math library are:
1375 When bc(1) encounters an error or a signal that it has a non-default handler
1376 for, it resets. This means that several things happen.
1378 First, any functions that are executing are stopped and popped off the stack.
1379 The behavior is not unlike that of exceptions in programming languages. Then
1380 the execution point is set so that any code waiting to execute (after all
1381 functions returned) is skipped.
1383 Thus, when bc(1) resets, it skips any remaining code waiting to be executed.
1384 Then, if it is interactive mode, and the error was not a fatal error (see the
1385 **EXIT STATUS** section), it asks for more input; otherwise, it exits with the
1386 appropriate return code.
1388 Note that this reset behavior is different from the GNU bc(1), which attempts to
1389 start executing the statement right after the one that caused an error.
1393 Most bc(1) implementations use **char** types to calculate the value of **1**
1394 decimal digit at a time, but that can be slow. This bc(1) does something
1397 It uses large integers to calculate more than **1** decimal digit at a time. If
1398 built in a environment where **BC_LONG_BIT** (see the **LIMITS** section) is
1399 **64**, then each integer has **9** decimal digits. If built in an environment
1400 where **BC_LONG_BIT** is **32** then each integer has **4** decimal digits. This
1401 value (the number of decimal digits per large integer) is called
1404 The actual values of **BC_LONG_BIT** and **BC_BASE_DIGS** can be queried with
1405 the **limits** statement.
1407 In addition, this bc(1) uses an even larger integer for overflow checking. This
1408 integer type depends on the value of **BC_LONG_BIT**, but is always at least
1409 twice as large as the integer type used to store digits.
1413 The following are the limits on bc(1):
1417 : The number of bits in the **long** type in the environment where bc(1) was
1418 built. This determines how many decimal digits can be stored in a single
1419 large integer (see the **PERFORMANCE** section).
1423 : The number of decimal digits per large integer (see the **PERFORMANCE**
1424 section). Depends on **BC_LONG_BIT**.
1428 : The max decimal number that each large integer can store (see
1429 **BC_BASE_DIGS**) plus **1**. Depends on **BC_BASE_DIGS**.
1433 : The max number that the overflow type (see the **PERFORMANCE** section) can
1434 hold. Depends on **BC_LONG_BIT**.
1438 : The maximum output base. Set at **BC_BASE_POW**.
1442 : The maximum size of arrays. Set at **SIZE_MAX-1**.
1446 : The maximum **scale**. Set at **BC_OVERFLOW_MAX-1**.
1450 : The maximum length of strings. Set at **BC_OVERFLOW_MAX-1**.
1454 : The maximum length of identifiers. Set at **BC_OVERFLOW_MAX-1**.
1458 : The maximum length of a number (in decimal digits), which includes digits
1459 after the decimal point. Set at **BC_OVERFLOW_MAX-1**.
1463 : The maximum integer (inclusive) returned by the **rand()** operand. Set at
1464 **2\^BC_LONG_BIT-1**.
1468 : The maximum allowable exponent (positive or negative). Set at
1469 **BC_OVERFLOW_MAX**.
1473 : The maximum number of vars/arrays. Set at **SIZE_MAX-1**.
1475 The actual values can be queried with the **limits** statement.
1477 These limits are meant to be effectively non-existent; the limits are so large
1478 (at least on 64-bit machines) that there should not be any point at which they
1479 become a problem. In fact, memory should be exhausted before these limits should
1482 # ENVIRONMENT VARIABLES
1484 bc(1) recognizes the following environment variables:
1488 : If this variable exists (no matter the contents), bc(1) behaves as if
1489 the **-s** option was given.
1493 : This is another way to give command-line arguments to bc(1). They should be
1494 in the same format as all other command-line arguments. These are always
1495 processed first, so any files given in **BC_ENV_ARGS** will be processed
1496 before arguments and files given on the command-line. This gives the user
1497 the ability to set up "standard" options and files to be used at every
1498 invocation. The most useful thing for such files to contain would be useful
1499 functions that the user might want every time bc(1) runs.
1501 The code that parses **BC_ENV_ARGS** will correctly handle quoted arguments,
1502 but it does not understand escape sequences. For example, the string
1503 **"/home/gavin/some bc file.bc"** will be correctly parsed, but the string
1504 **"/home/gavin/some \"bc\" file.bc"** will include the backslashes.
1506 The quote parsing will handle either kind of quotes, **'** or **"**. Thus,
1507 if you have a file with any number of single quotes in the name, you can use
1508 double quotes as the outside quotes, as in **"some 'bc' file.bc"**, and vice
1509 versa if you have a file with double quotes. However, handling a file with
1510 both kinds of quotes in **BC_ENV_ARGS** is not supported due to the
1511 complexity of the parsing, though such files are still supported on the
1512 command-line where the parsing is done by the shell.
1516 : If this environment variable exists and contains an integer that is greater
1517 than **1** and is less than **UINT16_MAX** (**2\^16-1**), bc(1) will output
1518 lines to that length, including the backslash (**\\**). The default line
1523 bc(1) returns the following exit statuses:
1531 : A math error occurred. This follows standard practice of using **1** for
1532 expected errors, since math errors will happen in the process of normal
1535 Math errors include divide by **0**, taking the square root of a negative
1536 number, using a negative number as a bound for the pseudo-random number
1537 generator, attempting to convert a negative number to a hardware integer,
1538 overflow when converting a number to a hardware integer, and attempting to
1539 use a non-integer where an integer is required.
1541 Converting to a hardware integer happens for the second operand of the power
1542 (**\^**), places (**\@**), left shift (**\<\<**), and right shift (**\>\>**)
1543 operators and their corresponding assignment operators.
1547 : A parse error occurred.
1549 Parse errors include unexpected **EOF**, using an invalid character, failing
1550 to find the end of a string or comment, using a token where it is invalid,
1551 giving an invalid expression, giving an invalid print statement, giving an
1552 invalid function definition, attempting to assign to an expression that is
1553 not a named expression (see the *Named Expressions* subsection of the
1554 **SYNTAX** section), giving an invalid **auto** list, having a duplicate
1555 **auto**/function parameter, failing to find the end of a code block,
1556 attempting to return a value from a **void** function, attempting to use a
1557 variable as a reference, and using any extensions when the option **-s** or
1558 any equivalents were given.
1562 : A runtime error occurred.
1564 Runtime errors include assigning an invalid number to **ibase**, **obase**,
1565 or **scale**; give a bad expression to a **read()** call, calling **read()**
1566 inside of a **read()** call, type errors, passing the wrong number of
1567 arguments to functions, attempting to call an undefined function, and
1568 attempting to use a **void** function call as a value in an expression.
1572 : A fatal error occurred.
1574 Fatal errors include memory allocation errors, I/O errors, failing to open
1575 files, attempting to use files that do not have only ASCII characters (bc(1)
1576 only accepts ASCII characters), attempting to open a directory as a file,
1577 and giving invalid command-line options.
1579 The exit status **4** is special; when a fatal error occurs, bc(1) always exits
1580 and returns **4**, no matter what mode bc(1) is in.
1582 The other statuses will only be returned when bc(1) is not in interactive mode
1583 (see the **INTERACTIVE MODE** section), since bc(1) resets its state (see the
1584 **RESET** section) and accepts more input when one of those errors occurs in
1585 interactive mode. This is also the case when interactive mode is forced by the
1586 **-i** flag or **--interactive** option.
1588 These exit statuses allow bc(1) to be used in shell scripting with error
1589 checking, and its normal behavior can be forced by using the **-i** flag or
1590 **--interactive** option.
1594 Per the [standard][1], bc(1) has an interactive mode and a non-interactive mode.
1595 Interactive mode is turned on automatically when both **stdin** and **stdout**
1596 are hooked to a terminal, but the **-i** flag and **--interactive** option can
1597 turn it on in other cases.
1599 In interactive mode, bc(1) attempts to recover from errors (see the **RESET**
1600 section), and in normal execution, flushes **stdout** as soon as execution is
1601 done for the current input.
1605 If **stdin**, **stdout**, and **stderr** are all connected to a TTY, bc(1) turns
1608 TTY mode is different from interactive mode because interactive mode is required
1609 in the [bc(1) specification][1], and interactive mode requires only **stdin**
1610 and **stdout** to be connected to a terminal.
1614 Sending a **SIGINT** will cause bc(1) to stop execution of the current input. If
1615 bc(1) is in TTY mode (see the **TTY MODE** section), it will reset (see the
1616 **RESET** section). Otherwise, it will clean up and exit.
1618 Note that "current input" can mean one of two things. If bc(1) is processing
1619 input from **stdin** in TTY mode, it will ask for more input. If bc(1) is
1620 processing input from a file in TTY mode, it will stop processing the file and
1621 start processing the next file, if one exists, or ask for input from **stdin**
1622 if no other file exists.
1624 This means that if a **SIGINT** is sent to bc(1) as it is executing a file, it
1625 can seem as though bc(1) did not respond to the signal since it will immediately
1626 start executing the next file. This is by design; most files that users execute
1627 when interacting with bc(1) have function definitions, which are quick to parse.
1628 If a file takes a long time to execute, there may be a bug in that file. The
1629 rest of the files could still be executed without problem, allowing the user to
1632 **SIGTERM** and **SIGQUIT** cause bc(1) to clean up and exit, and it uses the
1633 default handler for all other signals.
1637 This bc(1) ships with support for adding error messages for different locales
1638 and thus, supports **LC_MESSAGES**.
1646 bc(1) is compliant with the [IEEE Std 1003.1-2017 (“POSIX.1-2017”)][1]
1647 specification. The flags **-efghiqsvVw**, all long options, and the extensions
1648 noted above are extensions to that specification.
1650 Note that the specification explicitly says that bc(1) only accepts numbers that
1651 use a period (**.**) as a radix point, regardless of the value of
1654 This bc(1) supports error messages for different locales, and thus, it supports
1659 None are known. Report bugs at https://git.yzena.com/gavin/bc.
1663 Gavin D. Howard <gavin@yzena.com> and contributors.
1665 [1]: https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html
1666 [2]: https://www.gnu.org/software/bc/
1667 [3]: https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero
1668 [4]: https://en.wikipedia.org/wiki/Unit_in_the_last_place
1669 [5]: https://people.eecs.berkeley.edu/~wkahan/LOG10HAF.TXT
1670 [6]: https://en.wikipedia.org/wiki/Rounding#Rounding_away_from_zero