Cameron Katri's Manual Page Server

Comments

There are two kinds of comments:

1.

Block comments are enclosed in /* and */.

2.

Line comments go from # until, and not including, the next newline. This is a non-portable extension.

Named Expressions

The following are named expressions in bc(1):

1.

Variables: I

2.

Array Elements: I[E]

3.

ibase

4.

obase

5.

scale

6.

seed

7.

last or a single dot (.)

Numbers 6 and 7 are non-portable extensions.

The meaning of seed is dependent on the current pseudo-random number generator but is guaranteed to not change except for new major versions.

The scale and sign of the value may be significant.

If a previously used seed value is assigned to seed and used again, the pseudo-random number generator is guaranteed to produce the same sequence of pseudo-random numbers as it did when the seed value was previously used.

The exact value assigned to seed is not guaranteed to be returned if seed is queried again immediately. However, if seed does return a different value, both values, when assigned to seed, are guaranteed to produce the same sequence of pseudo-random numbers. This means that certain values assigned to seed will not produce unique sequences of pseudo-random numbers. The value of seed will change after any use of the rand() and irand(E) operands (see the Operands subsection below), except if the parameter passed to irand(E) is 0, 1, or negative.

There is no limit to the length (number of significant decimal digits) or scale of the value that can be assigned to seed.

Variables and arrays do not interfere; users can have arrays named the same as variables. This also applies to functions (see the FUNCTIONS section), so a user can have a variable, array, and function that all have the same name, and they will not shadow each other, whether inside of functions or not.

Named expressions are required as the operand of increment/decrement operators and as the left side of assignment operators (see the Operators subsection).

Operands

The following are valid operands in bc(1):

1.

Numbers (see the Numbers subsection below).

2.

Array indices (I[E]).

3.

(E): The value of E (used to change precedence).

4.

sqrt(E): The square root of E. E must be non-negative.

5.

length(E): The number of significant decimal digits in E.

6.

length(I[]): The number of elements in the array I. This is a non-portable extension.

7.

scale(E): The scale of E.

8.

abs(E): The absolute value of E. This is a non-portable extension.

9.

I(), I(E), I(E, E), and so on, where I is an identifier for a non-void function (see the Void Functions subsection of the FUNCTIONS section). The E argument(s) may also be arrays of the form I[], which will automatically be turned into array references (see the Array References subsection of the FUNCTIONS section) if the corresponding parameter in the function definition is an array reference.

10.

read(): Reads a line from stdin and uses that as an expression. The result of that expression is the result of the read() operand. This is a non-portable extension.

11.

maxibase(): The max allowable ibase. This is a non-portable extension.

12.

maxobase(): The max allowable obase. This is a non-portable extension.

13.

maxscale(): The max allowable scale. This is a non-portable extension.

14.

rand(): A pseudo-random integer between 0 (inclusive) and BC_RAND_MAX (inclusive). Using this operand will change the value of seed. This is a non-portable extension.

15.

irand(E): A pseudo-random integer between 0 (inclusive) and the value of E (exclusive). If E is negative or is a non-integer (E's scale is not 0), an error is raised, and bc(1) resets (see the RESET section) while seed remains unchanged. If E is larger than BC_RAND_MAX, the higher bound is honored by generating several pseudo-random integers, multiplying them by appropriate powers of BC_RAND_MAX+1, and adding them together. Thus, the size of integer that can be generated with this operand is unbounded. Using this operand will change the value of seed, unless the value of E is 0 or 1. In that case, 0 is returned, and seed is not changed. This is a non-portable extension.

16.

maxrand(): The max integer returned by rand(). This is a non-portable extension.

The integers generated by rand() and irand(E) are guaranteed to be as unbiased as possible, subject to the limitations of the pseudo-random number generator.

Note: The values returned by the pseudo-random number generator with rand() and irand(E) are guaranteed to NOT be cryptographically secure. This is a consequence of using a seeded pseudo-random number generator. However, they are guaranteed to be reproducible with identical seed values. This means that the pseudo-random values from bc(1) should only be used where a reproducible stream of pseudo-random numbers is ESSENTIAL. In any other case, use a non-seeded pseudo-random number generator.

Numbers

Numbers are strings made up of digits, uppercase letters, and at most 1 period for a radix. Numbers can have up to BC_NUM_MAX digits. Uppercase letters are equal to 9 + their position in the alphabet (i.e., A equals 10, or 9+1). If a digit or letter makes no sense with the current value of ibase, they are set to the value of the highest valid digit in ibase.

Single-character numbers (i.e., A alone) take the value that they would have if they were valid digits, regardless of the value of ibase. This means that A alone always equals decimal 10 and Z alone always equals decimal 35.

In addition, bc(1) accepts numbers in scientific notation. These have the form <number>e<integer>. The exponent (the portion after the e) must be an integer. An example is 1.89237e9, which is equal to 1892370000. Negative exponents are also allowed, so 4.2890e-3 is equal to 0.0042890.

Using scientific notation is an error or warning if the -s or -w, respectively, command-line options (or equivalents) are given.

WARNING: Both the number and the exponent in scientific notation are interpreted according to the current ibase, but the number is still multiplied by 10^exponent regardless of the current ibase. For example, if ibase is 16 and bc(1) is given the number string FFeA, the resulting decimal number will be 2550000000000, and if bc(1) is given the number string 10e-4, the resulting decimal number will be 0.0016.

Accepting input as scientific notation is a non-portable extension.

Operators

The following arithmetic and logical operators can be used. They are listed in order of decreasing precedence. Operators in the same group have the same precedence.

++ --

: Type: Prefix and Postfix

Associativity: None
Description: **increment**, **decrement**
    

- !

: Type: Prefix

Associativity: None
Description: **negation**, **boolean not**
    

$

: Type: Postfix

Associativity: None
Description: **truncation**
    

@

: Type: Binary

Associativity: Right
Description: **set precision**
    

^

: Type: Binary

Associativity: Right
Description: **power**
    

* / %

: Type: Binary

Associativity: Left
Description: **multiply**, **divide**, **modulus**
    

+ -

: Type: Binary

Associativity: Left
Description: **add**, **subtract**
    

<< >>

: Type: Binary

Associativity: Left
Description: **shift left**, **shift right**
    

= <<= >>= += -= *= /= %= ^= @=

: Type: Binary

Associativity: Right
Description: **assignment**
    

== <= >= != < >

: Type: Binary

Associativity: Left
Description: **relational**
    

&&

: Type: Binary

Associativity: Left
Description: **boolean and**
    

||

: Type: Binary

Associativity: Left
Description: **boolean or**
    

The operators will be described in more detail below.

++ --

: The prefix and postfix increment and decrement operators behave exactly like they would in C. They require a named expression (see the Named Expressions subsection) as an operand.

The prefix versions of these operators are more efficient; use them where
possible.
    

-

: The negation operator returns 0 if a user attempts to negate any expression with the value 0. Otherwise, a copy of the expression with its sign flipped is returned.

!

: The boolean not operator returns 1 if the expression is 0, or 0 otherwise.

This is a **non-portable extension**.
    

$

: The truncation operator returns a copy of the given expression with all of its scale removed.

This is a **non-portable extension**.
    

@

: The set precision operator takes two expressions and returns a copy of the first with its scale equal to the value of the second expression. That could either mean that the number is returned without change (if the scale of the first expression matches the value of the second expression), extended (if it is less), or truncated (if it is more).

The second expression must be an integer (no *scale*) and non-negative.
This is a **non-portable extension**.
    

^

: The power operator (not the exclusive or operator, as it would be in C) takes two expressions and raises the first to the power of the value of the second. The scale of the result is equal to scale.

The second expression must be an integer (no *scale*), and if it is
negative, the first value must be non-zero.
    

*

: The multiply operator takes two expressions, multiplies them, and returns the product. If a is the scale of the first expression and b is the scale of the second expression, the scale of the result is equal to min(a+b,max(scale,a,b)) where min() and max() return the obvious values.

/

: The divide operator takes two expressions, divides them, and returns the quotient. The scale of the result shall be the value of scale.

The second expression must be non-zero.
    

%

: The modulus operator takes two expressions, a and b, and evaluates them by 1) Computing a/b to current scale and 2) Using the result of step 1 to calculate a-(a/b)*b to scale max(scale+scale(b),scale(a)).

The second expression must be non-zero.
    

+

: The add operator takes two expressions, a and b, and returns the sum, with a scale equal to the max of the scales of a and b.

-

: The subtract operator takes two expressions, a and b, and returns the difference, with a scale equal to the max of the scales of a and b.

<<

: The left shift operator takes two expressions, a and b, and returns a copy of the value of a with its decimal point moved b places to the right.

The second expression must be an integer (no *scale*) and non-negative.
This is a **non-portable extension**.
    

>>

: The right shift operator takes two expressions, a and b, and returns a copy of the value of a with its decimal point moved b places to the left.

The second expression must be an integer (no *scale*) and non-negative.
This is a **non-portable extension**.
    

= <<= >>= += -= *= /= %= ^= @=

: The assignment operators take two expressions, a and b where a is a named expression (see the Named Expressions subsection).

For **=**, **b** is copied and the result is assigned to **a**. For all
others, **a** and **b** are applied as operands to the corresponding
arithmetic operator and the result is assigned to **a**.
The **assignment** operators that correspond to operators that are
extensions are themselves **non-portable extensions**.
    

== <= >= != < >

: The relational operators compare two expressions, a and b, and if the relation holds, according to C language semantics, the result is 1. Otherwise, it is 0.

Note that unlike in C, these operators have a lower precedence than the
**assignment** operators, which means that **a=b\>c** is interpreted as
**(a=b)\>c**.
Also, unlike the [standard][1] requires, these operators can appear anywhere
any other expressions can be used. This allowance is a
**non-portable extension**.
    

&&

: The boolean and operator takes two expressions and returns 1 if both expressions are non-zero, 0 otherwise.

This is *not* a short-circuit operator.
This is a **non-portable extension**.
    

||

: The boolean or operator takes two expressions and returns 1 if one of the expressions is non-zero, 0 otherwise.

This is *not* a short-circuit operator.
This is a **non-portable extension**.
    

Statements

The following items are statements:

1.

E

2.

{ S ; ... ; S }

3.

if ( E ) S

4.

if ( E ) S else S

5.

while ( E ) S

6.

for ( E ; E ; E ) S

7.

An empty statement

8.

break

9.

continue

10.

quit

11.

halt

12.

limits

13.

A string of characters, enclosed in double quotes

14.

print E , ... , E

15.

I(), I(E), I(E, E), and so on, where I is an identifier for a void function (see the Void Functions subsection of the FUNCTIONS section). The E argument(s) may also be arrays of the form I[], which will automatically be turned into array references (see the Array References subsection of the FUNCTIONS section) if the corresponding parameter in the function definition is an array reference.

Numbers 4, 9, 11, 12, 14, and 15 are non-portable extensions.

Also, as a non-portable extension, any or all of the expressions in the header of a for loop may be omitted. If the condition (second expression) is omitted, it is assumed to be a constant 1.

The break statement causes a loop to stop iterating and resume execution immediately following a loop. This is only allowed in loops.

The continue statement causes a loop iteration to stop early and returns to the start of the loop, including testing the loop condition. This is only allowed in loops.

The if else statement does the same thing as in C.

The quit statement causes bc(1) to quit, even if it is on a branch that will not be executed (it is a compile-time command).

The halt statement causes bc(1) to quit, if it is executed. (Unlike quit if it is on a branch of an if statement that is not executed, bc(1) does not quit.)

The limits statement prints the limits that this bc(1) is subject to. This is like the quit statement in that it is a compile-time command.

An expression by itself is evaluated and printed, followed by a newline.

Both scientific notation and engineering notation are available for printing the results of expressions. Scientific notation is activated by assigning 0 to obase, and engineering notation is activated by assigning 1 to obase. To deactivate them, just assign a different value to obase.

Scientific notation and engineering notation are disabled if bc(1) is run with either the -s or -w command-line options (or equivalents).

Printing numbers in scientific notation and/or engineering notation is a non-portable extension.

Print Statement

The "expressions" in a print statement may also be strings. If they are, there are backslash escape sequences that are interpreted specially. What those sequences are, and what they cause to be printed, are shown below:

* * * * *

\a \a \b \b \\ \ \e \ \f \f \n \n \q " \r \r \t \t

* * * * *

Any other character following a backslash causes the backslash and character to be printed as-is.

Any non-string expression in a print statement shall be assigned to last, like any other expression that is printed.

Order of Evaluation

All expressions in a statment are evaluated left to right, except as necessary to maintain order of operations. This means, for example, assuming that i is equal to 0, in the expression

a[i++] = i++
    

the first (or 0th) element of a is set to 1, and i is equal to 2 at the end of the expression.

This includes function arguments. Thus, assuming i is equal to 0, this means that in the expression

x(i++, i++)
    

the first argument passed to x() is 0, and the second argument is 1, while i is equal to 2 before the function starts executing.

Void Functions

Functions can also be void functions, defined as follows:

define void I(I,...,I){


    auto I,...,I


    S;...;S


    return
}
    

They can only be used as standalone expressions, where such an expression would be printed alone, except in a print statement.

Void functions can only use the first two return statements listed above. They can also omit the return statement entirely.

The word "void" is not treated as a keyword; it is still possible to have variables, arrays, and functions named void. The word "void" is only treated specially right after the define keyword.

This is a non-portable extension.

Array References

For any array in the parameter list, if the array is declared in the form

*I[]
    

it is a reference. Any changes to the array in the function are reflected, when the function returns, to the array that was passed in.

Other than this, all function arguments are passed by value.

This is a non-portable extension.

Standard Library

The standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html) defines the following functions for the math library:

s(x)

: Returns the sine of x, which is assumed to be in radians.

This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

c(x)

: Returns the cosine of x, which is assumed to be in radians.

This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

a(x)

: Returns the arctangent of x, in radians.

This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

l(x)

: Returns the natural logarithm of x.

This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

e(x)

: Returns the mathematical constant e raised to the power of x.

This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

j(x, n)

: Returns the bessel integer order n (truncated) of x.

This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

Extended Library

The extended library is not loaded when the -s/--standard or -w/--warn options are given since they are not part of the library defined by the standard (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html).

The extended library is a non-portable extension.

p(x, y)

: Calculates x to the power of y, even if y is not an integer, and returns the result to the current scale.

It is an error if **y** is negative and **x** is **0**.
This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

r(x, p)

: Returns x rounded to p decimal places according to the rounding mode round half away from 0 (https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero).

ceil(x, p)

: Returns x rounded to p decimal places according to the rounding mode round away from 0 (https://en.wikipedia.org/wiki/Rounding#Rounding_away_from_zero).

f(x)

: Returns the factorial of the truncated absolute value of x.

perm(n, k)

: Returns the permutation of the truncated absolute value of n of the truncated absolute value of k, if k <= n. If not, it returns 0.

comb(n, k)

: Returns the combination of the truncated absolute value of n of the truncated absolute value of k, if k <= n. If not, it returns 0.

l2(x)

: Returns the logarithm base 2 of x.

This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

l10(x)

: Returns the logarithm base 10 of x.

This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

log(x, b)

: Returns the logarithm base b of x.

This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

cbrt(x)

: Returns the cube root of x.

root(x, n)

: Calculates the truncated value of n, r, and returns the rth root of x to the current scale.

If **r** is **0** or negative, this raises an error and causes bc(1) to
reset (see the **RESET** section). It also raises an error and causes bc(1)
to reset if **r** is even and **x** is negative.
    

pi(p)

: Returns pi to p decimal places.

This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

t(x)

: Returns the tangent of x, which is assumed to be in radians.

This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

a2(y, x)

: Returns the arctangent of y/x, in radians. If both y and x are equal to 0, it raises an error and causes bc(1) to reset (see the RESET section). Otherwise, if x is greater than 0, it returns a(y/x). If x is less than 0, and y is greater than or equal to 0, it returns a(y/x)+pi. If x is less than 0, and y is less than 0, it returns a(y/x)-pi. If x is equal to 0, and y is greater than 0, it returns pi/2. If x is equal to 0, and y is less than 0, it returns -pi/2.

This function is the same as the **atan2()** function in many programming
languages.
This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

sin(x)

: Returns the sine of x, which is assumed to be in radians.

This is an alias of **s(x)**.
This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

cos(x)

: Returns the cosine of x, which is assumed to be in radians.

This is an alias of **c(x)**.
This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

tan(x)

: Returns the tangent of x, which is assumed to be in radians.

If **x** is equal to **1** or **-1**, this raises an error and causes bc(1)
to reset (see the **RESET** section).
This is an alias of **t(x)**.
This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

atan(x)

: Returns the arctangent of x, in radians.

This is an alias of **a(x)**.
This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

atan2(y, x)

: Returns the arctangent of y/x, in radians. If both y and x are equal to 0, it raises an error and causes bc(1) to reset (see the RESET section). Otherwise, if x is greater than 0, it returns a(y/x). If x is less than 0, and y is greater than or equal to 0, it returns a(y/x)+pi. If x is less than 0, and y is less than 0, it returns a(y/x)-pi. If x is equal to 0, and y is greater than 0, it returns pi/2. If x is equal to 0, and y is less than 0, it returns -pi/2.

This function is the same as the **atan2()** function in many programming
languages.
This is an alias of **a2(y, x)**.
This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

r2d(x)

: Converts x from radians to degrees and returns the result.

This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

d2r(x)

: Converts x from degrees to radians and returns the result.

This is a transcendental function (see the *Transcendental Functions*
subsection below).
    

frand(p)

: Generates a pseudo-random number between 0 (inclusive) and 1 (exclusive) with the number of decimal digits after the decimal point equal to the truncated absolute value of p. If p is not 0, then calling this function will change the value of seed. If p is 0, then 0 is returned, and seed is not changed.

ifrand(i, p)

: Generates a pseudo-random number that is between 0 (inclusive) and the truncated absolute value of i (exclusive) with the number of decimal digits after the decimal point equal to the truncated absolute value of p. If the absolute value of i is greater than or equal to 2, and p is not 0, then calling this function will change the value of seed; otherwise, 0 is returned and seed is not changed.

srand(x)

: Returns x with its sign flipped with probability 0.5. In other words, it randomizes the sign of x.

brand()

: Returns a random boolean value (either 0 or 1).

ubytes(x)

: Returns the numbers of unsigned integer bytes required to hold the truncated absolute value of x.

sbytes(x)

: Returns the numbers of signed, two's-complement integer bytes required to hold the truncated value of x.

hex(x)

: Outputs the hexadecimal (base 16) representation of x.

This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

binary(x)

: Outputs the binary (base 2) representation of x.

This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

output(x, b)

: Outputs the base b representation of x.

This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

uint(x)

: Outputs the representation, in binary and hexadecimal, of x as an unsigned integer in as few power of two bytes as possible. Both outputs are split into bytes separated by spaces.

If **x** is not an integer or is negative, an error message is printed
instead, but bc(1) is not reset (see the **RESET** section).
This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

int(x)

: Outputs the representation, in binary and hexadecimal, of x as a signed, two's-complement integer in as few power of two bytes as possible. Both outputs are split into bytes separated by spaces.

If **x** is not an integer, an error message is printed instead, but bc(1)
is not reset (see the **RESET** section).
This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

uintn(x, n)

: Outputs the representation, in binary and hexadecimal, of x as an unsigned integer in n bytes. Both outputs are split into bytes separated by spaces.

If **x** is not an integer, is negative, or cannot fit into **n** bytes, an
error message is printed instead, but bc(1) is not reset (see the **RESET**
section).
This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

intn(x, n)

: Outputs the representation, in binary and hexadecimal, of x as a signed, two's-complement integer in n bytes. Both outputs are split into bytes separated by spaces.

If **x** is not an integer or cannot fit into **n** bytes, an error message
is printed instead, but bc(1) is not reset (see the **RESET** section).
This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

uint8(x)

: Outputs the representation, in binary and hexadecimal, of x as an unsigned integer in 1 byte. Both outputs are split into bytes separated by spaces.

If **x** is not an integer, is negative, or cannot fit into **1** byte, an
error message is printed instead, but bc(1) is not reset (see the **RESET**
section).
This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

int8(x)

: Outputs the representation, in binary and hexadecimal, of x as a signed, two's-complement integer in 1 byte. Both outputs are split into bytes separated by spaces.

If **x** is not an integer or cannot fit into **1** byte, an error message
is printed instead, but bc(1) is not reset (see the **RESET** section).
This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

uint16(x)

: Outputs the representation, in binary and hexadecimal, of x as an unsigned integer in 2 bytes. Both outputs are split into bytes separated by spaces.

If **x** is not an integer, is negative, or cannot fit into **2** bytes, an
error message is printed instead, but bc(1) is not reset (see the **RESET**
section).
This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

int16(x)

: Outputs the representation, in binary and hexadecimal, of x as a signed, two's-complement integer in 2 bytes. Both outputs are split into bytes separated by spaces.

If **x** is not an integer or cannot fit into **2** bytes, an error message
is printed instead, but bc(1) is not reset (see the **RESET** section).
This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

uint32(x)

: Outputs the representation, in binary and hexadecimal, of x as an unsigned integer in 4 bytes. Both outputs are split into bytes separated by spaces.

If **x** is not an integer, is negative, or cannot fit into **4** bytes, an
error message is printed instead, but bc(1) is not reset (see the **RESET**
section).
This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

int32(x)

: Outputs the representation, in binary and hexadecimal, of x as a signed, two's-complement integer in 4 bytes. Both outputs are split into bytes separated by spaces.

If **x** is not an integer or cannot fit into **4** bytes, an error message
is printed instead, but bc(1) is not reset (see the **RESET** section).
This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

uint64(x)

: Outputs the representation, in binary and hexadecimal, of x as an unsigned integer in 8 bytes. Both outputs are split into bytes separated by spaces.

If **x** is not an integer, is negative, or cannot fit into **8** bytes, an
error message is printed instead, but bc(1) is not reset (see the **RESET**
section).
This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

int64(x)

: Outputs the representation, in binary and hexadecimal, of x as a signed, two's-complement integer in 8 bytes. Both outputs are split into bytes separated by spaces.

If **x** is not an integer or cannot fit into **8** bytes, an error message
is printed instead, but bc(1) is not reset (see the **RESET** section).
This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

hex_uint(x, n)

: Outputs the representation of the truncated absolute value of x as an unsigned integer in hexadecimal using n bytes. Not all of the value will be output if n is too small.

This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

binary_uint(x, n)

: Outputs the representation of the truncated absolute value of x as an unsigned integer in binary using n bytes. Not all of the value will be output if n is too small.

This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

output_uint(x, n)

: Outputs the representation of the truncated absolute value of x as an unsigned integer in the current obase (see the SYNTAX section) using n bytes. Not all of the value will be output if n is too small.

This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

output_byte(x, i)

: Outputs byte i of the truncated absolute value of x, where 0 is the least significant byte and number_of_bytes - 1 is the most significant byte.

This is a **void** function (see the *Void Functions* subsection of the
**FUNCTIONS** section).
    

Transcendental Functions

All transcendental functions can return slightly inaccurate results (up to 1 ULP (https://en.wikipedia.org/wiki/Unit_in_the_last_place)). This is unavoidable, and this article (https://people.eecs.berkeley.edu/~wkahan/LOG10HAF.TXT) explains why it is impossible and unnecessary to calculate exact results for the transcendental functions.

Because of the possible inaccuracy, I recommend that users call those functions with the precision (scale) set to at least 1 higher than is necessary. If exact results are absolutely required, users can double the precision (scale) and then truncate.

The transcendental functions in the standard math library are:

•

s(x)

•

c(x)

•

a(x)

•

l(x)

•

e(x)

•

j(x, n)

The transcendental functions in the extended math library are:

•

l2(x)

•

l10(x)

•

log(x, b)

•

pi(p)

•

t(x)

•

a2(y, x)

•

sin(x)

•

cos(x)

•

tan(x)

•

atan(x)

•

atan2(y, x)

•

r2d(x)

•

d2r(x)