math - perform mathematics calculations

Synopsis

math [-sN | --scale=N] [-bBASE | --base=BASE] [--] EXPRESSION

Description

math performs mathematical calculations. It supports simple operations such as addition, subtraction, and so on, as well as functions like abs(), sqrt() and ln().

By default, the output is a floating-point number with trailing zeroes trimmed. To get a fixed representation, the --scale option can be used, including --scale=0 for integer output.

Keep in mind that parameter expansion happens before expressions are evaluated. This can be very useful in order to perform calculations involving shell variables or the output of command substitutions, but it also means that parenthesis (()) and the asterisk (*) glob character have to be escaped or quoted. x can also be used to denote multiplication, but it needs to be followed by whitespace to distinguish it from hexadecimal numbers.

Parentheses for functions are optional - math sin pi prints 0. However, a comma will bind to the inner function, so math pow sin 3, 5 is an error because it tries to give sin the arguments 3 and 5. When in doubt, use parentheses.

math ignores whitespace between arguments and takes its input as multiple arguments (internally joined with a space), so math 2 +2 and math "2 +    2" work the same. math 2 2 is an error.

The following options are available:

• -sN or --scale=N sets the scale of the result. N must be an integer or the word "max" for the maximum scale. A scale of zero causes results to be rounded down to the nearest integer. So 3/2 returns 1 rather than 2 which 1.5 would normally round to. This is for compatibility with bc which was the basis for this command prior to fish 3.0.0. Scale values greater than zero causes the result to be rounded using the usual rules to the specified number of decimal places.
• -b BASE or --base BASE sets the numeric base used for output (math always understands hexadecimal numbers as input). It currently understands "hex" or "16" for hexadecimal and "octal" or "8" for octal and implies a scale of 0 (other scales cause an error), so it will truncate the result down to an integer. This might change in the future. Hex numbers will be printed with a 0x prefix. Octal numbers will have a prefix of 0 and aren't understood by math as input.

Return Values

If the expression is successfully evaluated and doesn't over/underflow or return NaN the return status is zero (success) else one.

Syntax

math knows some operators, constants, functions and can (obviously) read numbers.

For numbers, . is always the radix character regardless of locale - 2.5, not 2,5. Scientific notation (10e5) and hexadecimal (0xFF) are also available.

Operators

math knows the following operators:

• + for addition and - for subtraction.
• * or x for multiplication, / for division. (Note that * is the glob character and needs to be quoted or escaped, x needs to be followed by whitespace or it looks like 0x hexadecimal notation.)
• ^ for exponentiation.
• % for modulo.
• ( and ) for grouping. (These need to be quoted or escaped because () denotes a command substitution.)

They are all used in an infix manner - 5 + 2, not + 5 2.

Constants

math knows the following constants:

• e - Euler's number.
• pi - π. You know this one. Half of Tau.
• tau. Equivalent to 2π, or the number of radians in a circle.

Use them without a leading $ - pi - 3 should be about 0.

Functions

math supports the following functions:

• abs - the absolute value, with positive sign
• acos - arc cosine
• asin - arc sine
• atan - arc tangent
• atan2 - arc tangent of two variables
• bitand, bitor and bitxor to perform bitwise operations. These will throw away any non-integer parts and interpret the rest as an int.
• ceil - round number up to nearest integer
• cos - the cosine
• cosh - hyperbolic cosine
• exp - the base-e exponential function
• fac - factorial - also known as x! (x * (x - 1) * (x - 2) * ... * 1)
• floor - round number down to nearest integer
• ln - the base-e logarithm
• log or log10 - the base-10 logarithm
• log2 - the base-2 logarithm
• max - returns the larger of two numbers
• min - returns the smaller of two numbers
• ncr - "from n choose r" combination function - how many subsets of size r can be taken from n (order doesn't matter)
• npr - the number of subsets of size r that can be taken from a set of n elements (including different order)
• pow(x,y) returns x to the y (and can be written as x ^ y)
• round - rounds to the nearest integer, away from 0
• sin - the sine function
• sinh - the hyperbolic sine
• sqrt - the square root - (can also be written as x ^ 0.5)
• tan - the tangent
• tanh - the hyperbolic tangent

All of the trigonometric functions use radians (the pi-based scale, not 360°).

Examples

math 1+1 outputs 2.

math $status - 128 outputs the numerical exit status of the last command minus 128.

math 10 / 6 outputs 1.666667.

math -s0 10.0 / 6.0 outputs 1.

math -s3 10 / 6 outputs 1.666.

math "sin(pi)" outputs 0.

math 5 \* 2 or math "5 * 2" or math 5 "*" 2 all output 10.

math 0xFF outputs 255, math 0 x 3 outputs 0 (because it computes 0 multiplied by 3).

math bitand 0xFE, 0x2e outputs 46.

math "bitor(9,2)" outputs 11.

math --base=hex 192 prints 0xc0.

math 'ncr(49,6)' prints 13983816 - that's the number of possible picks in 6-from-49 lotto.

Compatibility notes

Fish 1.x and 2.x releases relied on the bc command for handling math expressions. Starting with fish 3.0.0 fish uses the tinyexpr library and evaluates the expression without the involvement of any external commands.

You don't need to use -- before the expression, even if it begins with a minus sign which might otherwise be interpreted as an invalid option. If you do insert -- before the expression, it will cause option scanning to stop just like for every other command and it won't be part of the expression.