3 SPDX-License-Identifier: BSD-2-Clause
5 Copyright (c) 2018-2021 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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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 If this option is given on the command-line (i.e., not in **BC_ENV_ARGS**,
183 see the **ENVIRONMENT VARIABLES** section), then after processing all
184 expressions and files, bc(1) will exit, unless **-** (**stdin**) was given
185 as an argument at least once to **-f** or **--file**, whether on the
186 command-line or in **BC_ENV_ARGS**. However, if any other **-e**,
187 **--expression**, **-f**, or **--file** arguments are given after **-f-** or
188 equivalent is given, bc(1) will give a fatal error and exit.
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 If this option is given on the command-line (i.e., not in **BC_ENV_ARGS**,
199 see the **ENVIRONMENT VARIABLES** section), then after processing all
200 expressions and files, bc(1) will exit, unless **-** (**stdin**) was given
201 as an argument at least once to **-f** or **--file**. However, if any other
202 **-e**, **--expression**, **-f**, or **--file** arguments are given after
203 **-f-** or equivalent is given, bc(1) will give a fatal error and exit.
205 This is a **non-portable extension**.
207 All long options are **non-portable extensions**.
211 Any non-error output is written to **stdout**. In addition, if history (see the
212 **HISTORY** section) and the prompt (see the **TTY MODE** section) are enabled,
213 both are output to **stdout**.
215 **Note**: Unlike other bc(1) implementations, this bc(1) will issue a fatal
216 error (see the **EXIT STATUS** section) if it cannot write to **stdout**, so if
217 **stdout** is closed, as in **bc <file> >&-**, it will quit with an error. This
218 is done so that bc(1) can report problems when **stdout** is redirected to a
221 If there are scripts that depend on the behavior of other bc(1) implementations,
222 it is recommended that those scripts be changed to redirect **stdout** to
227 Any error output is written to **stderr**.
229 **Note**: Unlike other bc(1) implementations, this bc(1) will issue a fatal
230 error (see the **EXIT STATUS** section) if it cannot write to **stderr**, so if
231 **stderr** is closed, as in **bc <file> 2>&-**, it will quit with an error. This
232 is done so that bc(1) can exit with an error code when **stderr** is redirected
235 If there are scripts that depend on the behavior of other bc(1) implementations,
236 it is recommended that those scripts be changed to redirect **stderr** to
241 The syntax for bc(1) programs is mostly C-like, with some differences. This
242 bc(1) follows the [POSIX standard][1], which is a much more thorough resource
243 for the language this bc(1) accepts. This section is meant to be a summary and a
244 listing of all the extensions to the standard.
246 In the sections below, **E** means expression, **S** means statement, and **I**
249 Identifiers (**I**) start with a lowercase letter and can be followed by any
250 number (up to **BC_NAME_MAX-1**) of lowercase letters (**a-z**), digits
251 (**0-9**), and underscores (**\_**). The regex is **\[a-z\]\[a-z0-9\_\]\***.
252 Identifiers with more than one character (letter) are a
253 **non-portable extension**.
255 **ibase** is a global variable determining how to interpret constant numbers. It
256 is the "input" base, or the number base used for interpreting input numbers.
257 **ibase** is initially **10**. If the **-s** (**--standard**) and **-w**
258 (**--warn**) flags were not given on the command line, the max allowable value
259 for **ibase** is **36**. Otherwise, it is **16**. The min allowable value for
260 **ibase** is **2**. The max allowable value for **ibase** can be queried in
261 bc(1) programs with the **maxibase()** built-in function.
263 **obase** is a global variable determining how to output results. It is the
264 "output" base, or the number base used for outputting numbers. **obase** is
265 initially **10**. The max allowable value for **obase** is **BC_BASE_MAX** and
266 can be queried in bc(1) programs with the **maxobase()** built-in function. The
267 min allowable value for **obase** is **0**. If **obase** is **0**, values are
268 output in scientific notation, and if **obase** is **1**, values are output in
269 engineering notation. Otherwise, values are output in the specified base.
271 Outputting in scientific and engineering notations are **non-portable
274 The *scale* of an expression is the number of digits in the result of the
275 expression right of the decimal point, and **scale** is a global variable that
276 sets the precision of any operations, with exceptions. **scale** is initially
277 **0**. **scale** cannot be negative. The max allowable value for **scale** is
278 **BC_SCALE_MAX** and can be queried in bc(1) programs with the **maxscale()**
281 bc(1) has both *global* variables and *local* variables. All *local*
282 variables are local to the function; they are parameters or are introduced in
283 the **auto** list of a function (see the **FUNCTIONS** section). If a variable
284 is accessed which is not a parameter or in the **auto** list, it is assumed to
285 be *global*. If a parent function has a *local* variable version of a variable
286 that a child function considers *global*, the value of that *global* variable in
287 the child function is the value of the variable in the parent function, not the
288 value of the actual *global* variable.
290 All of the above applies to arrays as well.
292 The value of a statement that is an expression (i.e., any of the named
293 expressions or operands) is printed unless the lowest precedence operator is an
294 assignment operator *and* the expression is notsurrounded by parentheses.
296 The value that is printed is also assigned to the special variable **last**. A
297 single dot (**.**) may also be used as a synonym for **last**. These are
298 **non-portable extensions**.
300 Either semicolons or newlines may separate statements.
304 There are two kinds of comments:
306 1. Block comments are enclosed in **/\*** and **\*/**.
307 2. Line comments go from **#** until, and not including, the next newline. This
308 is a **non-portable extension**.
312 The following are named expressions in bc(1):
315 2. Array Elements: **I[E]**
320 7. **last** or a single dot (**.**)
322 Numbers 6 and 7 are **non-portable extensions**.
324 The meaning of **seed** is dependent on the current pseudo-random number
325 generator but is guaranteed to not change except for new major versions.
327 The *scale* and sign of the value may be significant.
329 If a previously used **seed** value is assigned to **seed** and used again, the
330 pseudo-random number generator is guaranteed to produce the same sequence of
331 pseudo-random numbers as it did when the **seed** value was previously used.
333 The exact value assigned to **seed** is not guaranteed to be returned if
334 **seed** is queried again immediately. However, if **seed** *does* return a
335 different value, both values, when assigned to **seed**, are guaranteed to
336 produce the same sequence of pseudo-random numbers. This means that certain
337 values assigned to **seed** will *not* produce unique sequences of pseudo-random
338 numbers. The value of **seed** will change after any use of the **rand()** and
339 **irand(E)** operands (see the *Operands* subsection below), except if the
340 parameter passed to **irand(E)** is **0**, **1**, or negative.
342 There is no limit to the length (number of significant decimal digits) or
343 *scale* of the value that can be assigned to **seed**.
345 Variables and arrays do not interfere; users can have arrays named the same as
346 variables. This also applies to functions (see the **FUNCTIONS** section), so a
347 user can have a variable, array, and function that all have the same name, and
348 they will not shadow each other, whether inside of functions or not.
350 Named expressions are required as the operand of **increment**/**decrement**
351 operators and as the left side of **assignment** operators (see the *Operators*
356 The following are valid operands in bc(1):
358 1. Numbers (see the *Numbers* subsection below).
359 2. Array indices (**I[E]**).
360 3. **(E)**: The value of **E** (used to change precedence).
361 4. **sqrt(E)**: The square root of **E**. **E** must be non-negative.
362 5. **length(E)**: The number of significant decimal digits in **E**.
363 6. **length(I[])**: The number of elements in the array **I**. This is a
364 **non-portable extension**.
365 7. **scale(E)**: The *scale* of **E**.
366 8. **abs(E)**: The absolute value of **E**. This is a **non-portable
368 9. **I()**, **I(E)**, **I(E, E)**, and so on, where **I** is an identifier for
369 a non-**void** function (see the *Void Functions* subsection of the
370 **FUNCTIONS** section). The **E** argument(s) may also be arrays of the form
371 **I[]**, which will automatically be turned into array references (see the
372 *Array References* subsection of the **FUNCTIONS** section) if the
373 corresponding parameter in the function definition is an array reference.
374 10. **read()**: Reads a line from **stdin** and uses that as an expression. The
375 result of that expression is the result of the **read()** operand. This is a
376 **non-portable extension**.
377 11. **maxibase()**: The max allowable **ibase**. This is a **non-portable
379 12. **maxobase()**: The max allowable **obase**. This is a **non-portable
381 13. **maxscale()**: The max allowable **scale**. This is a **non-portable
383 14. **rand()**: A pseudo-random integer between **0** (inclusive) and
384 **BC_RAND_MAX** (inclusive). Using this operand will change the value of
385 **seed**. This is a **non-portable extension**.
386 15. **irand(E)**: A pseudo-random integer between **0** (inclusive) and the
387 value of **E** (exclusive). If **E** is negative or is a non-integer
388 (**E**'s *scale* is not **0**), an error is raised, and bc(1) resets (see
389 the **RESET** section) while **seed** remains unchanged. If **E** is larger
390 than **BC_RAND_MAX**, the higher bound is honored by generating several
391 pseudo-random integers, multiplying them by appropriate powers of
392 **BC_RAND_MAX+1**, and adding them together. Thus, the size of integer that
393 can be generated with this operand is unbounded. Using this operand will
394 change the value of **seed**, unless the value of **E** is **0** or **1**.
395 In that case, **0** is returned, and **seed** is *not* changed. This is a
396 **non-portable extension**.
397 16. **maxrand()**: The max integer returned by **rand()**. This is a
398 **non-portable extension**.
400 The integers generated by **rand()** and **irand(E)** are guaranteed to be as
401 unbiased as possible, subject to the limitations of the pseudo-random number
404 **Note**: The values returned by the pseudo-random number generator with
405 **rand()** and **irand(E)** are guaranteed to *NOT* be cryptographically secure.
406 This is a consequence of using a seeded pseudo-random number generator. However,
407 they *are* guaranteed to be reproducible with identical **seed** values. This
408 means that the pseudo-random values from bc(1) should only be used where a
409 reproducible stream of pseudo-random numbers is *ESSENTIAL*. In any other case,
410 use a non-seeded pseudo-random number generator.
414 Numbers are strings made up of digits, uppercase letters, and at most **1**
415 period for a radix. Numbers can have up to **BC_NUM_MAX** digits. Uppercase
416 letters are equal to **9** + their position in the alphabet (i.e., **A** equals
417 **10**, or **9+1**). If a digit or letter makes no sense with the current value
418 of **ibase**, they are set to the value of the highest valid digit in **ibase**.
420 Single-character numbers (i.e., **A** alone) take the value that they would have
421 if they were valid digits, regardless of the value of **ibase**. This means that
422 **A** alone always equals decimal **10** and **Z** alone always equals decimal
425 In addition, bc(1) accepts numbers in scientific notation. These have the form
426 **\<number\>e\<integer\>**. The exponent (the portion after the **e**) must be
427 an integer. An example is **1.89237e9**, which is equal to **1892370000**.
428 Negative exponents are also allowed, so **4.2890e-3** is equal to **0.0042890**.
430 Using scientific notation is an error or warning if the **-s** or **-w**,
431 respectively, command-line options (or equivalents) are given.
433 **WARNING**: Both the number and the exponent in scientific notation are
434 interpreted according to the current **ibase**, but the number is still
435 multiplied by **10\^exponent** regardless of the current **ibase**. For example,
436 if **ibase** is **16** and bc(1) is given the number string **FFeA**, the
437 resulting decimal number will be **2550000000000**, and if bc(1) is given the
438 number string **10e-4**, the resulting decimal number will be **0.0016**.
440 Accepting input as scientific notation is a **non-portable extension**.
444 The following arithmetic and logical operators can be used. They are listed in
445 order of decreasing precedence. Operators in the same group have the same
450 : Type: Prefix and Postfix
454 Description: **increment**, **decrement**
462 Description: **negation**, **boolean not**
470 Description: **truncation**
478 Description: **set precision**
486 Description: **power**
494 Description: **multiply**, **divide**, **modulus**
502 Description: **add**, **subtract**
510 Description: **shift left**, **shift right**
512 **=** **\<\<=** **\>\>=** **+=** **-=** **\*=** **/=** **%=** **\^=** **\@=**
518 Description: **assignment**
520 **==** **\<=** **\>=** **!=** **\<** **\>**
526 Description: **relational**
534 Description: **boolean and**
542 Description: **boolean or**
544 The operators will be described in more detail below.
548 : The prefix and postfix **increment** and **decrement** operators behave
549 exactly like they would in C. They require a named expression (see the
550 *Named Expressions* subsection) as an operand.
552 The prefix versions of these operators are more efficient; use them where
557 : The **negation** operator returns **0** if a user attempts to negate any
558 expression with the value **0**. Otherwise, a copy of the expression with
559 its sign flipped is returned.
563 : The **boolean not** operator returns **1** if the expression is **0**, or
566 This is a **non-portable extension**.
570 : The **truncation** operator returns a copy of the given expression with all
571 of its *scale* removed.
573 This is a **non-portable extension**.
577 : The **set precision** operator takes two expressions and returns a copy of
578 the first with its *scale* equal to the value of the second expression. That
579 could either mean that the number is returned without change (if the
580 *scale* of the first expression matches the value of the second
581 expression), extended (if it is less), or truncated (if it is more).
583 The second expression must be an integer (no *scale*) and non-negative.
585 This is a **non-portable extension**.
589 : The **power** operator (not the **exclusive or** operator, as it would be in
590 C) takes two expressions and raises the first to the power of the value of
591 the second. The *scale* of the result is equal to **scale**.
593 The second expression must be an integer (no *scale*), and if it is
594 negative, the first value must be non-zero.
598 : The **multiply** operator takes two expressions, multiplies them, and
599 returns the product. If **a** is the *scale* of the first expression and
600 **b** is the *scale* of the second expression, the *scale* of the result is
601 equal to **min(a+b,max(scale,a,b))** where **min()** and **max()** return
606 : The **divide** operator takes two expressions, divides them, and returns the
607 quotient. The *scale* of the result shall be the value of **scale**.
609 The second expression must be non-zero.
613 : The **modulus** operator takes two expressions, **a** and **b**, and
614 evaluates them by 1) Computing **a/b** to current **scale** and 2) Using the
615 result of step 1 to calculate **a-(a/b)\*b** to *scale*
616 **max(scale+scale(b),scale(a))**.
618 The second expression must be non-zero.
622 : The **add** operator takes two expressions, **a** and **b**, and returns the
623 sum, with a *scale* equal to the max of the *scale*s of **a** and **b**.
627 : The **subtract** operator takes two expressions, **a** and **b**, and
628 returns the difference, with a *scale* equal to the max of the *scale*s of
633 : The **left shift** operator takes two expressions, **a** and **b**, and
634 returns a copy of the value of **a** with its decimal point moved **b**
637 The second expression must be an integer (no *scale*) and non-negative.
639 This is a **non-portable extension**.
643 : The **right shift** operator takes two expressions, **a** and **b**, and
644 returns a copy of the value of **a** with its decimal point moved **b**
647 The second expression must be an integer (no *scale*) and non-negative.
649 This is a **non-portable extension**.
651 **=** **\<\<=** **\>\>=** **+=** **-=** **\*=** **/=** **%=** **\^=** **\@=**
653 : The **assignment** operators take two expressions, **a** and **b** where
654 **a** is a named expression (see the *Named Expressions* subsection).
656 For **=**, **b** is copied and the result is assigned to **a**. For all
657 others, **a** and **b** are applied as operands to the corresponding
658 arithmetic operator and the result is assigned to **a**.
660 The **assignment** operators that correspond to operators that are
661 extensions are themselves **non-portable extensions**.
663 **==** **\<=** **\>=** **!=** **\<** **\>**
665 : The **relational** operators compare two expressions, **a** and **b**, and
666 if the relation holds, according to C language semantics, the result is
667 **1**. Otherwise, it is **0**.
669 Note that unlike in C, these operators have a lower precedence than the
670 **assignment** operators, which means that **a=b\>c** is interpreted as
673 Also, unlike the [standard][1] requires, these operators can appear anywhere
674 any other expressions can be used. This allowance is a
675 **non-portable extension**.
679 : The **boolean and** operator takes two expressions and returns **1** if both
680 expressions are non-zero, **0** otherwise.
682 This is *not* a short-circuit operator.
684 This is a **non-portable extension**.
688 : The **boolean or** operator takes two expressions and returns **1** if one
689 of the expressions is non-zero, **0** otherwise.
691 This is *not* a short-circuit operator.
693 This is a **non-portable extension**.
697 The following items are statements:
700 2. **{** **S** **;** ... **;** **S** **}**
701 3. **if** **(** **E** **)** **S**
702 4. **if** **(** **E** **)** **S** **else** **S**
703 5. **while** **(** **E** **)** **S**
704 6. **for** **(** **E** **;** **E** **;** **E** **)** **S**
705 7. An empty statement
711 13. A string of characters, enclosed in double quotes
712 14. **print** **E** **,** ... **,** **E**
713 15. **I()**, **I(E)**, **I(E, E)**, and so on, where **I** is an identifier for
714 a **void** function (see the *Void Functions* subsection of the
715 **FUNCTIONS** section). The **E** argument(s) may also be arrays of the form
716 **I[]**, which will automatically be turned into array references (see the
717 *Array References* subsection of the **FUNCTIONS** section) if the
718 corresponding parameter in the function definition is an array reference.
720 Numbers 4, 9, 11, 12, 14, and 15 are **non-portable extensions**.
722 Also, as a **non-portable extension**, any or all of the expressions in the
723 header of a for loop may be omitted. If the condition (second expression) is
724 omitted, it is assumed to be a constant **1**.
726 The **break** statement causes a loop to stop iterating and resume execution
727 immediately following a loop. This is only allowed in loops.
729 The **continue** statement causes a loop iteration to stop early and returns to
730 the start of the loop, including testing the loop condition. This is only
733 The **if** **else** statement does the same thing as in C.
735 The **quit** statement causes bc(1) to quit, even if it is on a branch that will
736 not be executed (it is a compile-time command).
738 The **halt** statement causes bc(1) to quit, if it is executed. (Unlike **quit**
739 if it is on a branch of an **if** statement that is not executed, bc(1) does not
742 The **limits** statement prints the limits that this bc(1) is subject to. This
743 is like the **quit** statement in that it is a compile-time command.
745 An expression by itself is evaluated and printed, followed by a newline.
747 Both scientific notation and engineering notation are available for printing the
748 results of expressions. Scientific notation is activated by assigning **0** to
749 **obase**, and engineering notation is activated by assigning **1** to
750 **obase**. To deactivate them, just assign a different value to **obase**.
752 Scientific notation and engineering notation are disabled if bc(1) is run with
753 either the **-s** or **-w** command-line options (or equivalents).
755 Printing numbers in scientific notation and/or engineering notation is a
756 **non-portable extension**.
760 The "expressions" in a **print** statement may also be strings. If they are, there
761 are backslash escape sequences that are interpreted specially. What those
762 sequences are, and what they cause to be printed, are shown below:
776 Any other character following a backslash causes the backslash and character to
779 Any non-string expression in a print statement shall be assigned to **last**,
780 like any other expression that is printed.
782 ## Order of Evaluation
784 All expressions in a statment are evaluated left to right, except as necessary
785 to maintain order of operations. This means, for example, assuming that **i** is
786 equal to **0**, in the expression
790 the first (or 0th) element of **a** is set to **1**, and **i** is equal to **2**
791 at the end of the expression.
793 This includes function arguments. Thus, assuming **i** is equal to **0**, this
794 means that in the expression
798 the first argument passed to **x()** is **0**, and the second argument is **1**,
799 while **i** is equal to **2** before the function starts executing.
803 Function definitions are as follows:
813 Any **I** in the parameter list or **auto** list may be replaced with **I[]** to
814 make a parameter or **auto** var an array, and any **I** in the parameter list
815 may be replaced with **\*I[]** to make a parameter an array reference. Callers
816 of functions that take array references should not put an asterisk in the call;
817 they must be called with just **I[]** like normal array parameters and will be
818 automatically converted into references.
820 As a **non-portable extension**, the opening brace of a **define** statement may
821 appear on the next line.
823 As a **non-portable extension**, the return statement may also be in one of the
827 2. **return** **(** **)**
830 The first two, or not specifying a **return** statement, is equivalent to
831 **return (0)**, unless the function is a **void** function (see the *Void
832 Functions* subsection below).
836 Functions can also be **void** functions, defined as follows:
839 define void I(I,...,I){
846 They can only be used as standalone expressions, where such an expression would
847 be printed alone, except in a print statement.
849 Void functions can only use the first two **return** statements listed above.
850 They can also omit the return statement entirely.
852 The word "void" is not treated as a keyword; it is still possible to have
853 variables, arrays, and functions named **void**. The word "void" is only
854 treated specially right after the **define** keyword.
856 This is a **non-portable extension**.
860 For any array in the parameter list, if the array is declared in the form
866 it is a **reference**. Any changes to the array in the function are reflected,
867 when the function returns, to the array that was passed in.
869 Other than this, all function arguments are passed by value.
871 This is a **non-portable extension**.
875 All of the functions below, including the functions in the extended math
876 library (see the *Extended Library* subsection below), are available when the
877 **-l** or **--mathlib** command-line flags are given, except that the extended
878 math library is not available when the **-s** option, the **-w** option, or
879 equivalents are given.
883 The [standard][1] defines the following functions for the math library:
887 : Returns the sine of **x**, which is assumed to be in radians.
889 This is a transcendental function (see the *Transcendental Functions*
894 : Returns the cosine of **x**, which is assumed to be in radians.
896 This is a transcendental function (see the *Transcendental Functions*
901 : Returns the arctangent of **x**, in radians.
903 This is a transcendental function (see the *Transcendental Functions*
908 : Returns the natural logarithm of **x**.
910 This is a transcendental function (see the *Transcendental Functions*
915 : Returns the mathematical constant **e** raised to the power of **x**.
917 This is a transcendental function (see the *Transcendental Functions*
922 : Returns the bessel integer order **n** (truncated) of **x**.
924 This is a transcendental function (see the *Transcendental Functions*
929 The extended library is *not* loaded when the **-s**/**--standard** or
930 **-w**/**--warn** options are given since they are not part of the library
931 defined by the [standard][1].
933 The extended library is a **non-portable extension**.
937 : Calculates **x** to the power of **y**, even if **y** is not an integer, and
938 returns the result to the current **scale**.
940 It is an error if **y** is negative and **x** is **0**.
942 This is a transcendental function (see the *Transcendental Functions*
947 : Returns **x** rounded to **p** decimal places according to the rounding mode
948 [round half away from **0**][3].
952 : Returns **x** rounded to **p** decimal places according to the rounding mode
953 [round away from **0**][6].
957 : Returns the factorial of the truncated absolute value of **x**.
961 : Returns the permutation of the truncated absolute value of **n** of the
962 truncated absolute value of **k**, if **k \<= n**. If not, it returns **0**.
966 : Returns the combination of the truncated absolute value of **n** of the
967 truncated absolute value of **k**, if **k \<= n**. If not, it returns **0**.
971 : Returns the logarithm base **2** of **x**.
973 This is a transcendental function (see the *Transcendental Functions*
978 : Returns the logarithm base **10** of **x**.
980 This is a transcendental function (see the *Transcendental Functions*
985 : Returns the logarithm base **b** of **x**.
987 This is a transcendental function (see the *Transcendental Functions*
992 : Returns the cube root of **x**.
996 : Calculates the truncated value of **n**, **r**, and returns the **r**th root
997 of **x** to the current **scale**.
999 If **r** is **0** or negative, this raises an error and causes bc(1) to
1000 reset (see the **RESET** section). It also raises an error and causes bc(1)
1001 to reset if **r** is even and **x** is negative.
1005 : Returns **pi** to **p** decimal places.
1007 This is a transcendental function (see the *Transcendental Functions*
1012 : Returns the tangent of **x**, which is assumed to be in radians.
1014 This is a transcendental function (see the *Transcendental Functions*
1019 : Returns the arctangent of **y/x**, in radians. If both **y** and **x** are
1020 equal to **0**, it raises an error and causes bc(1) to reset (see the
1021 **RESET** section). Otherwise, if **x** is greater than **0**, it returns
1022 **a(y/x)**. If **x** is less than **0**, and **y** is greater than or equal
1023 to **0**, it returns **a(y/x)+pi**. If **x** is less than **0**, and **y**
1024 is less than **0**, it returns **a(y/x)-pi**. If **x** is equal to **0**,
1025 and **y** is greater than **0**, it returns **pi/2**. If **x** is equal to
1026 **0**, and **y** is less than **0**, it returns **-pi/2**.
1028 This function is the same as the **atan2()** function in many programming
1031 This is a transcendental function (see the *Transcendental Functions*
1036 : Returns the sine of **x**, which is assumed to be in radians.
1038 This is an alias of **s(x)**.
1040 This is a transcendental function (see the *Transcendental Functions*
1045 : Returns the cosine of **x**, which is assumed to be in radians.
1047 This is an alias of **c(x)**.
1049 This is a transcendental function (see the *Transcendental Functions*
1054 : Returns the tangent of **x**, which is assumed to be in radians.
1056 If **x** is equal to **1** or **-1**, this raises an error and causes bc(1)
1057 to reset (see the **RESET** section).
1059 This is an alias of **t(x)**.
1061 This is a transcendental function (see the *Transcendental Functions*
1066 : Returns the arctangent of **x**, in radians.
1068 This is an alias of **a(x)**.
1070 This is a transcendental function (see the *Transcendental Functions*
1075 : Returns the arctangent of **y/x**, in radians. If both **y** and **x** are
1076 equal to **0**, it raises an error and causes bc(1) to reset (see the
1077 **RESET** section). Otherwise, if **x** is greater than **0**, it returns
1078 **a(y/x)**. If **x** is less than **0**, and **y** is greater than or equal
1079 to **0**, it returns **a(y/x)+pi**. If **x** is less than **0**, and **y**
1080 is less than **0**, it returns **a(y/x)-pi**. If **x** is equal to **0**,
1081 and **y** is greater than **0**, it returns **pi/2**. If **x** is equal to
1082 **0**, and **y** is less than **0**, it returns **-pi/2**.
1084 This function is the same as the **atan2()** function in many programming
1087 This is an alias of **a2(y, x)**.
1089 This is a transcendental function (see the *Transcendental Functions*
1094 : Converts **x** from radians to degrees and returns the result.
1096 This is a transcendental function (see the *Transcendental Functions*
1101 : Converts **x** from degrees to radians and returns the result.
1103 This is a transcendental function (see the *Transcendental Functions*
1108 : Generates a pseudo-random number between **0** (inclusive) and **1**
1109 (exclusive) with the number of decimal digits after the decimal point equal
1110 to the truncated absolute value of **p**. If **p** is not **0**, then
1111 calling this function will change the value of **seed**. If **p** is **0**,
1112 then **0** is returned, and **seed** is *not* changed.
1116 : Generates a pseudo-random number that is between **0** (inclusive) and the
1117 truncated absolute value of **i** (exclusive) with the number of decimal
1118 digits after the decimal point equal to the truncated absolute value of
1119 **p**. If the absolute value of **i** is greater than or equal to **2**, and
1120 **p** is not **0**, then calling this function will change the value of
1121 **seed**; otherwise, **0** is returned and **seed** is not changed.
1125 : Returns **x** with its sign flipped with probability **0.5**. In other
1126 words, it randomizes the sign of **x**.
1130 : Returns a random boolean value (either **0** or **1**).
1134 : Returns the numbers of unsigned integer bytes required to hold the truncated
1135 absolute value of **x**.
1139 : Returns the numbers of signed, two's-complement integer bytes required to
1140 hold the truncated value of **x**.
1144 : Outputs the hexadecimal (base **16**) representation of **x**.
1146 This is a **void** function (see the *Void Functions* subsection of the
1147 **FUNCTIONS** section).
1151 : Outputs the binary (base **2**) representation of **x**.
1153 This is a **void** function (see the *Void Functions* subsection of the
1154 **FUNCTIONS** section).
1158 : Outputs the base **b** representation of **x**.
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 an
1166 unsigned integer in as few power of two bytes as possible. Both outputs are
1167 split into bytes separated by spaces.
1169 If **x** is not an integer or is negative, an error message is printed
1170 instead, but bc(1) 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 a signed,
1178 two's-complement integer in as few power of two bytes as possible. Both
1179 outputs are split into bytes separated by spaces.
1181 If **x** is not an integer, an error message is printed instead, but bc(1)
1182 is not reset (see the **RESET** section).
1184 This is a **void** function (see the *Void Functions* subsection of the
1185 **FUNCTIONS** section).
1189 : Outputs the representation, in binary and hexadecimal, of **x** as an
1190 unsigned integer in **n** bytes. Both outputs are split into bytes separated
1193 If **x** is not an integer, is negative, or cannot fit into **n** bytes, an
1194 error message is printed instead, but bc(1) is not reset (see the **RESET**
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 a signed,
1203 two's-complement integer in **n** bytes. Both outputs are split into bytes
1204 separated by spaces.
1206 If **x** is not an integer or cannot fit into **n** bytes, an error message
1207 is printed instead, but bc(1) is not reset (see the **RESET** section).
1209 This is a **void** function (see the *Void Functions* subsection of the
1210 **FUNCTIONS** section).
1214 : Outputs the representation, in binary and hexadecimal, of **x** as an
1215 unsigned integer in **1** byte. Both outputs are split into bytes separated
1218 If **x** is not an integer, is negative, or cannot fit into **1** byte, an
1219 error message is printed instead, but bc(1) is not reset (see the **RESET**
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 a signed,
1228 two's-complement integer in **1** byte. Both outputs are split into bytes
1229 separated by spaces.
1231 If **x** is not an integer or cannot fit into **1** byte, an error message
1232 is printed instead, but bc(1) is not reset (see the **RESET** section).
1234 This is a **void** function (see the *Void Functions* subsection of the
1235 **FUNCTIONS** section).
1239 : Outputs the representation, in binary and hexadecimal, of **x** as an
1240 unsigned integer in **2** bytes. Both outputs are split into bytes separated
1243 If **x** is not an integer, is negative, or cannot fit into **2** bytes, an
1244 error message is printed instead, but bc(1) is not reset (see the **RESET**
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 a signed,
1253 two's-complement integer in **2** bytes. Both outputs are split into bytes
1254 separated by spaces.
1256 If **x** is not an integer or cannot fit into **2** bytes, an error message
1257 is printed instead, but bc(1) is not reset (see the **RESET** section).
1259 This is a **void** function (see the *Void Functions* subsection of the
1260 **FUNCTIONS** section).
1264 : Outputs the representation, in binary and hexadecimal, of **x** as an
1265 unsigned integer in **4** bytes. Both outputs are split into bytes separated
1268 If **x** is not an integer, is negative, or cannot fit into **4** bytes, an
1269 error message is printed instead, but bc(1) is not reset (see the **RESET**
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 a signed,
1278 two's-complement integer in **4** bytes. Both outputs are split into bytes
1279 separated by spaces.
1281 If **x** is not an integer or cannot fit into **4** bytes, an error message
1282 is printed instead, but bc(1) is not reset (see the **RESET** section).
1284 This is a **void** function (see the *Void Functions* subsection of the
1285 **FUNCTIONS** section).
1289 : Outputs the representation, in binary and hexadecimal, of **x** as an
1290 unsigned integer in **8** bytes. Both outputs are split into bytes separated
1293 If **x** is not an integer, is negative, or cannot fit into **8** bytes, an
1294 error message is printed instead, but bc(1) is not reset (see the **RESET**
1297 This is a **void** function (see the *Void Functions* subsection of the
1298 **FUNCTIONS** section).
1302 : Outputs the representation, in binary and hexadecimal, of **x** as a signed,
1303 two's-complement integer in **8** bytes. Both outputs are split into bytes
1304 separated by spaces.
1306 If **x** is not an integer or cannot fit into **8** bytes, an error message
1307 is printed instead, but bc(1) is not reset (see the **RESET** section).
1309 This is a **void** function (see the *Void Functions* subsection of the
1310 **FUNCTIONS** section).
1314 : Outputs the representation of the truncated absolute value of **x** as an
1315 unsigned integer in hexadecimal using **n** bytes. Not all of the value will
1316 be output if **n** is too small.
1318 This is a **void** function (see the *Void Functions* subsection of the
1319 **FUNCTIONS** section).
1321 **binary_uint(x, n)**
1323 : Outputs the representation of the truncated absolute value of **x** as an
1324 unsigned integer in binary using **n** bytes. Not all of the value will be
1325 output if **n** is too small.
1327 This is a **void** function (see the *Void Functions* subsection of the
1328 **FUNCTIONS** section).
1330 **output_uint(x, n)**
1332 : Outputs the representation of the truncated absolute value of **x** as an
1333 unsigned integer in the current **obase** (see the **SYNTAX** section) using
1334 **n** bytes. Not all of the value will be output if **n** is too small.
1336 This is a **void** function (see the *Void Functions* subsection of the
1337 **FUNCTIONS** section).
1339 **output_byte(x, i)**
1341 : Outputs byte **i** of the truncated absolute value of **x**, where **0** is
1342 the least significant byte and **number_of_bytes - 1** is the most
1345 This is a **void** function (see the *Void Functions* subsection of the
1346 **FUNCTIONS** section).
1348 ## Transcendental Functions
1350 All transcendental functions can return slightly inaccurate results (up to 1
1351 [ULP][4]). This is unavoidable, and [this article][5] explains why it is
1352 impossible and unnecessary to calculate exact results for the transcendental
1355 Because of the possible inaccuracy, I recommend that users call those functions
1356 with the precision (**scale**) set to at least 1 higher than is necessary. If
1357 exact results are *absolutely* required, users can double the precision
1358 (**scale**) and then truncate.
1360 The transcendental functions in the standard math library are:
1369 The transcendental functions in the extended math library are:
1387 When bc(1) encounters an error or a signal that it has a non-default handler
1388 for, it resets. This means that several things happen.
1390 First, any functions that are executing are stopped and popped off the stack.
1391 The behavior is not unlike that of exceptions in programming languages. Then
1392 the execution point is set so that any code waiting to execute (after all
1393 functions returned) is skipped.
1395 Thus, when bc(1) resets, it skips any remaining code waiting to be executed.
1396 Then, if it is interactive mode, and the error was not a fatal error (see the
1397 **EXIT STATUS** section), it asks for more input; otherwise, it exits with the
1398 appropriate return code.
1400 Note that this reset behavior is different from the GNU bc(1), which attempts to
1401 start executing the statement right after the one that caused an error.
1405 Most bc(1) implementations use **char** types to calculate the value of **1**
1406 decimal digit at a time, but that can be slow. This bc(1) does something
1409 It uses large integers to calculate more than **1** decimal digit at a time. If
1410 built in a environment where **BC_LONG_BIT** (see the **LIMITS** section) is
1411 **64**, then each integer has **9** decimal digits. If built in an environment
1412 where **BC_LONG_BIT** is **32** then each integer has **4** decimal digits. This
1413 value (the number of decimal digits per large integer) is called
1416 The actual values of **BC_LONG_BIT** and **BC_BASE_DIGS** can be queried with
1417 the **limits** statement.
1419 In addition, this bc(1) uses an even larger integer for overflow checking. This
1420 integer type depends on the value of **BC_LONG_BIT**, but is always at least
1421 twice as large as the integer type used to store digits.
1425 The following are the limits on bc(1):
1429 : The number of bits in the **long** type in the environment where bc(1) was
1430 built. This determines how many decimal digits can be stored in a single
1431 large integer (see the **PERFORMANCE** section).
1435 : The number of decimal digits per large integer (see the **PERFORMANCE**
1436 section). Depends on **BC_LONG_BIT**.
1440 : The max decimal number that each large integer can store (see
1441 **BC_BASE_DIGS**) plus **1**. Depends on **BC_BASE_DIGS**.
1445 : The max number that the overflow type (see the **PERFORMANCE** section) can
1446 hold. Depends on **BC_LONG_BIT**.
1450 : The maximum output base. Set at **BC_BASE_POW**.
1454 : The maximum size of arrays. Set at **SIZE_MAX-1**.
1458 : The maximum **scale**. Set at **BC_OVERFLOW_MAX-1**.
1462 : The maximum length of strings. Set at **BC_OVERFLOW_MAX-1**.
1466 : The maximum length of identifiers. Set at **BC_OVERFLOW_MAX-1**.
1470 : The maximum length of a number (in decimal digits), which includes digits
1471 after the decimal point. Set at **BC_OVERFLOW_MAX-1**.
1475 : The maximum integer (inclusive) returned by the **rand()** operand. Set at
1476 **2\^BC_LONG_BIT-1**.
1480 : The maximum allowable exponent (positive or negative). Set at
1481 **BC_OVERFLOW_MAX**.
1485 : The maximum number of vars/arrays. Set at **SIZE_MAX-1**.
1487 The actual values can be queried with the **limits** statement.
1489 These limits are meant to be effectively non-existent; the limits are so large
1490 (at least on 64-bit machines) that there should not be any point at which they
1491 become a problem. In fact, memory should be exhausted before these limits should
1494 # ENVIRONMENT VARIABLES
1496 bc(1) recognizes the following environment variables:
1500 : If this variable exists (no matter the contents), bc(1) behaves as if
1501 the **-s** option was given.
1505 : This is another way to give command-line arguments to bc(1). They should be
1506 in the same format as all other command-line arguments. These are always
1507 processed first, so any files given in **BC_ENV_ARGS** will be processed
1508 before arguments and files given on the command-line. This gives the user
1509 the ability to set up "standard" options and files to be used at every
1510 invocation. The most useful thing for such files to contain would be useful
1511 functions that the user might want every time bc(1) runs.
1513 The code that parses **BC_ENV_ARGS** will correctly handle quoted arguments,
1514 but it does not understand escape sequences. For example, the string
1515 **"/home/gavin/some bc file.bc"** will be correctly parsed, but the string
1516 **"/home/gavin/some \"bc\" file.bc"** will include the backslashes.
1518 The quote parsing will handle either kind of quotes, **'** or **"**. Thus,
1519 if you have a file with any number of single quotes in the name, you can use
1520 double quotes as the outside quotes, as in **"some 'bc' file.bc"**, and vice
1521 versa if you have a file with double quotes. However, handling a file with
1522 both kinds of quotes in **BC_ENV_ARGS** is not supported due to the
1523 complexity of the parsing, though such files are still supported on the
1524 command-line where the parsing is done by the shell.
1528 : If this environment variable exists and contains an integer that is greater
1529 than **1** and is less than **UINT16_MAX** (**2\^16-1**), bc(1) will output
1530 lines to that length, including the backslash (**\\**). The default line
1535 bc(1) returns the following exit statuses:
1543 : A math error occurred. This follows standard practice of using **1** for
1544 expected errors, since math errors will happen in the process of normal
1547 Math errors include divide by **0**, taking the square root of a negative
1548 number, using a negative number as a bound for the pseudo-random number
1549 generator, attempting to convert a negative number to a hardware integer,
1550 overflow when converting a number to a hardware integer, and attempting to
1551 use a non-integer where an integer is required.
1553 Converting to a hardware integer happens for the second operand of the power
1554 (**\^**), places (**\@**), left shift (**\<\<**), and right shift (**\>\>**)
1555 operators and their corresponding assignment operators.
1559 : A parse error occurred.
1561 Parse errors include unexpected **EOF**, using an invalid character, failing
1562 to find the end of a string or comment, using a token where it is invalid,
1563 giving an invalid expression, giving an invalid print statement, giving an
1564 invalid function definition, attempting to assign to an expression that is
1565 not a named expression (see the *Named Expressions* subsection of the
1566 **SYNTAX** section), giving an invalid **auto** list, having a duplicate
1567 **auto**/function parameter, failing to find the end of a code block,
1568 attempting to return a value from a **void** function, attempting to use a
1569 variable as a reference, and using any extensions when the option **-s** or
1570 any equivalents were given.
1574 : A runtime error occurred.
1576 Runtime errors include assigning an invalid number to **ibase**, **obase**,
1577 or **scale**; give a bad expression to a **read()** call, calling **read()**
1578 inside of a **read()** call, type errors, passing the wrong number of
1579 arguments to functions, attempting to call an undefined function, and
1580 attempting to use a **void** function call as a value in an expression.
1584 : A fatal error occurred.
1586 Fatal errors include memory allocation errors, I/O errors, failing to open
1587 files, attempting to use files that do not have only ASCII characters (bc(1)
1588 only accepts ASCII characters), attempting to open a directory as a file,
1589 and giving invalid command-line options.
1591 The exit status **4** is special; when a fatal error occurs, bc(1) always exits
1592 and returns **4**, no matter what mode bc(1) is in.
1594 The other statuses will only be returned when bc(1) is not in interactive mode
1595 (see the **INTERACTIVE MODE** section), since bc(1) resets its state (see the
1596 **RESET** section) and accepts more input when one of those errors occurs in
1597 interactive mode. This is also the case when interactive mode is forced by the
1598 **-i** flag or **--interactive** option.
1600 These exit statuses allow bc(1) to be used in shell scripting with error
1601 checking, and its normal behavior can be forced by using the **-i** flag or
1602 **--interactive** option.
1606 Per the [standard][1], bc(1) has an interactive mode and a non-interactive mode.
1607 Interactive mode is turned on automatically when both **stdin** and **stdout**
1608 are hooked to a terminal, but the **-i** flag and **--interactive** option can
1609 turn it on in other cases.
1611 In interactive mode, bc(1) attempts to recover from errors (see the **RESET**
1612 section), and in normal execution, flushes **stdout** as soon as execution is
1613 done for the current input.
1617 If **stdin**, **stdout**, and **stderr** are all connected to a TTY, bc(1) turns
1620 TTY mode is different from interactive mode because interactive mode is required
1621 in the [bc(1) specification][1], and interactive mode requires only **stdin**
1622 and **stdout** to be connected to a terminal.
1626 Sending a **SIGINT** will cause bc(1) to stop execution of the current input. If
1627 bc(1) is in TTY mode (see the **TTY MODE** section), it will reset (see the
1628 **RESET** section). Otherwise, it will clean up and exit.
1630 Note that "current input" can mean one of two things. If bc(1) is processing
1631 input from **stdin** in TTY mode, it will ask for more input. If bc(1) is
1632 processing input from a file in TTY mode, it will stop processing the file and
1633 start processing the next file, if one exists, or ask for input from **stdin**
1634 if no other file exists.
1636 This means that if a **SIGINT** is sent to bc(1) as it is executing a file, it
1637 can seem as though bc(1) did not respond to the signal since it will immediately
1638 start executing the next file. This is by design; most files that users execute
1639 when interacting with bc(1) have function definitions, which are quick to parse.
1640 If a file takes a long time to execute, there may be a bug in that file. The
1641 rest of the files could still be executed without problem, allowing the user to
1644 **SIGTERM** and **SIGQUIT** cause bc(1) to clean up and exit, and it uses the
1645 default handler for all other signals.
1653 bc(1) is compliant with the [IEEE Std 1003.1-2017 (“POSIX.1-2017”)][1]
1654 specification. The flags **-efghiqsvVw**, all long options, and the extensions
1655 noted above are extensions to that specification.
1657 Note that the specification explicitly says that bc(1) only accepts numbers that
1658 use a period (**.**) as a radix point, regardless of the value of
1663 None are known. Report bugs at https://git.yzena.com/gavin/bc.
1667 Gavin D. Howard <gavin@yzena.com> and contributors.
1669 [1]: https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html
1670 [2]: https://www.gnu.org/software/bc/
1671 [3]: https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero
1672 [4]: https://en.wikipedia.org/wiki/Unit_in_the_last_place
1673 [5]: https://people.eecs.berkeley.edu/~wkahan/LOG10HAF.TXT
1674 [6]: https://en.wikipedia.org/wiki/Rounding#Rounding_away_from_zero