Math Funcers

+

Adds two numbers.

	Type	Value
Input	`Num`	the first summand
b (param #1)	`Num`	the second summand
Output	`Num`	the sum

Examples

Program	Type	Value
`1 +1`	`Num`	`2`
`1 +2 *3`	`Num`	`9`
`1 +(2 *3)`	`Num`	`7`

-

Subtracts a number from another.

	Type	Value
Input	`Num`	the minuend
b (param #1)	`Num`	the subtrahend
Output	`Num`	the difference

Examples

Program	Type	Value	Error
`5 -3`	`Num`	`2`

-

Returns the additive inverse of a number.

	Type	Value
Input	`Any`	any value (is ignored)
n (param #1)	`Num`	a number
Output	`Num`	the additive inverse (opposite number) of n

Examples

Program	Type	Value
`-1`	`Num`	`-1`
`-(-2.0)`	`Num`	`2`
`-inf`	`Num`	`-inf`
`-nan`	`Num`	`nan`

*

Multiplies two numbers.

	Type	Value
Input	`Num`	the first factor
b (param #1)	`Num`	the second factor
Output	`Num`	the product

Examples

Program	Type	Value	Error
`2 *3`	`Num`	`6`

/

Divides a number by another.

	Type	Value
Input	`Num`	the dividend
b (param #1)	`Num`	the divisor
Output	`Num`	the quotient

Examples

Program	Type	Value	Error
`3 /2`	`Num`	`1.5`
`1 /0`	`Num`	`inf`

%

Remainder

	Type	Value
Input	`Num`	the dividend
b (param #1)	`Num`	the divisor
Output	`Num`	the remainder of integer division (rounded towards zero)

Examples

Program	Type	Value	Error
`3 %2`	`Num`	`1`
`-8.5 %3`	`Num`	`-2.5`

<

Less than

	Type	Value
Input	`Num`	a number
b (param #1)	`Num`	another number
Output	`Bool`	true iff the input is smaller than b

Examples

Program	Type	Value
`2 <1`	`Bool`	`false`
`-inf <inf`	`Bool`	`true`
`0 <0`	`Bool`	`false`

>

Greater than

	Type	Value
Input	`Num`	a number
b (param #1)	`Num`	another number
Output	`Bool`	true iff the input is greater than b

Examples

Program	Type	Value
`2 >1`	`Bool`	`true`
`-inf >inf`	`Bool`	`false`
`0 >0`	`Bool`	`false`

<=

Less than or equal to

	Type	Value
Input	`Num`	a number
b (param #1)	`Num`	another number
Output	`Bool`	true iff the input is less than or equal to b

Examples

Program	Type	Value
`2 <=1`	`Bool`	`false`
`-inf <=inf`	`Bool`	`true`
`0 <=0`	`Bool`	`true`

>=

Greater than or equal to

	Type	Value
Input	`Num`	a number
b (param #1)	`Num`	another number
Output	`Bool`	true iff the input is greater than or equal to b

Examples

Program	Type	Value
`2 >=1`	`Bool`	`true`
`-inf >=inf`	`Bool`	`false`
`0 >=0`	`Bool`	`true`

sum

Computes the sum of several numbers.

	Type	Value
Input	`Arr<Num...>`	an array of numbers
Output	`Num`	their sum

Examples

Program	Type	Value	Error
`[1, 2, 3, 4] sum`	`Num`	`10`
`[] sum`	`Num`	`0`

median

Computes the median of several numbers.

	Type	Value
Input	`Arr<Num...>`	an array of numbers
Output	`Num`	their median

Examples

Program	Type	Value
`[2, 3, 7] median`	`Num`	`3`
`[2, 3, 5, 7] median`	`Num`	`4`
`[1.25] median`	`Num`	`1.25`
`[] median`	`Num`	`nan`

mean

Computes the arithmetic mean (average) of several numbers.

	Type	Value
Input	`Arr<Num...>`	an array of numbers
Output	`Num`	their mean

Examples

Program	Type	Value
`[2, 3, 5, 7] mean`	`Num`	`4.25`
`[1.25] mean`	`Num`	`1.25`
`[] mean`	`Num`	`nan`

inf

Returns infinity.

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	the special number value representing positive infinity

Examples

Program	Type	Value
`inf`	`Num`	`inf`
`-inf`	`Num`	`-inf`
`inf +inf`	`Num`	`inf`
`inf -inf`	`Num`	`nan`

nan

Returns NaN.

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	the special number value representing “not a number”

Examples

Program	Type	Value
`nan`	`Num`	`nan`
`nan ==2`	`Bool`	`false`
`nan ==nan`	`Bool`	`false`
`-nan`	`Num`	`nan`

isFinite

Checks whether a number is finite.

	Type	Value
Input	`Num`	a number
Output	`Bool`	true unless the input is positive or negative infinity

Examples

Program	Type	Value
`1024 isFinite`	`Bool`	`true`
`-1024 isFinite`	`Bool`	`true`
`inf isFinite`	`Bool`	`false`
`-inf isFinite`	`Bool`	`false`
`nan isFinite`	`Bool`	`true`

isNaN

Checks whether a number is NaN.

	Type	Value
Input	`Num`	a number
Output	`Bool`	true iff the input is NaN

Examples

Program	Type	Value	Error
`1024 isNaN`	`Bool`	`false`
`nan isNaN`	`Bool`	`true`

epsilon

Returns the floating point epsilon.

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	the difference between 1 and the smallest floating point number greater than 1

Examples

Program	Type	Value	Error
`epsilon`	`Num`	`2.220446049250313e-16`

largestSafeInteger

Returns the largest safe integer.

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	the largest integer that can be represented as an IEEE-754 double precision number and cannot be the result of rounding another number to fit IEEE-754

Examples

Program	Type	Value
`largestSafeInteger +0`	`Num`	`9007199254740991`
`largestSafeInteger +1`	`Num`	`9007199254740992`
`largestSafeInteger +2`	`Num`	`9007199254740992`

largestNum

Returns the largest representable number.

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	the largest number representable as an IEEE-754 double precision number

Examples

Program	Type	Value	Error
`largestNum`	`Num`	`1.7976931348623157e+308`
`largestNum +largestNum`	`Num`	`inf`

smallestSafeInteger

Returns the smallest safe integer.

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	the smallest integer that can be represented as an IEEE-754 double precision number and cannot be the result of rounding another integer to fit the IEEE-754 double precision representation

Examples

Program	Type	Value
`smallestSafeInteger -0`	`Num`	`-9007199254740991`
`smallestSafeInteger -1`	`Num`	`-9007199254740992`
`smallestSafeInteger -2`	`Num`	`-9007199254740992`

smallestPositiveNum

Returns the smallest representable positive number.

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	the smallest representable positive number

Examples

Program	Type	Value	Error
`smallestPositiveNum`	`Num`	`5e-324`

isInteger

Checks whether a number is integer.

	Type	Value
Input	`Num`	a number
Output	`Bool`	true iff the input represents a whole number

Examples

Program	Type	Value	Error
`1.0 isInteger`	`Bool`	`true`
`1.1 isInteger`	`Bool`	`false`

isSafeInteger

Checks whether a number is a safe integer.

	Type	Value
Input	`Num`	a number
Output	`Bool`	true iff the input is an integer and cannot be the result of rounding another integer to fit the IEEE-754 double precision representation

Examples

Program	Type	Value
`-9007199254740992 isSafeInteger`	`Bool`	`false`
`-9007199254740991 isSafeInteger`	`Bool`	`true`
`0 isSafeInteger`	`Bool`	`true`
`0.1 isSafeInteger`	`Bool`	`false`
`9007199254740991 isSafeInteger`	`Bool`	`true`
`9007199254740992 isSafeInteger`	`Bool`	`false`

toBase

Converts an integer to a specified base.

	Type	Value
Input	`Num`	an integer
base (param #1)	`Num`	an integer between 2 and 36 (inclusive)
Output	`Str`	a string representation of the input in the specified base

Examples

Program	Type	Value	Error
`233 toBase(16)`	`Str`	`"e9"`
`11 toBase(16)`	`Str`	`"b"`

toExponential

Converts a number to exponential notation.

	Type	Value
Input	`Num`	a number
Output	`Str`	a string representation of the input in exponential notation with 6 digits after the decimal point

Examples

Program	Type	Value	Error
`77.1234 toExponential`	`Str`	`"7.712340e+01"`
`77 toExponential`	`Str`	`"7.700000e+01"`

toExponential

Converts a number to exponential notation.

	Type	Value
Input	`Num`	a number
precision (param #1)	`Num`	the number of digits after the decimal point
Output	`Str`	a string representation of the input in exponential notation with the specified number of digits after the decimal point

Examples

Program	Type	Value	Error
`77.1234 toExponential(4)`	`Str`	`"7.7123e+01"`
`77.1234 toExponential(2)`	`Str`	`"7.71e+01"`

toFixed

Converts a number to fixed-point notation.

	Type	Value
Input	`Num`	a number
precision (param #1)	`Num`	the number of digits after the decimal point
Output	`Str`	a rounded string representation of the input with the specified number of digits after the decimal point

Examples

Program	Type	Value
`123.456 toFixed(2)`	`Str`	`"123.46"`
`0.004 toFixed(2)`	`Str`	`"0.00"`
`1.23e+5 toFixed(2)`	`Str`	`"123000.00"`

e

Returns Euler's number.

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	an approximation of Euler's number

Examples

Program	Type	Value	Error
`e`	`Num`	`2.718281828459045`

ln2

Returns the natural logarithm of 2.

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	the approximate natural logarithm of 2

Examples

Program	Type	Value	Error
`ln2`	`Num`	`0.6931471805599453`

ln10

Returns the natural logarithm of 10.

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	the approximate natural logarithm of 10

Examples

Program	Type	Value	Error
`ln10`	`Num`	`2.302585092994046`

log2e

Returns the base-2 logarithm of e

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	the approximate base-2 logarithm of Euler's number

Examples

Program	Type	Value	Error
`log2e`	`Num`	`1.4426950408889634`

log10e

Returns the base-10 logarithm of e

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	the approximate base-10 logarithm of Euler's number

Examples

Program	Type	Value	Error
`log10e`	`Num`	`0.4342944819032518`

pi

Returns pi.

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	an approximation of pi

Examples

Program	Type	Value	Error
`pi`	`Num`	`3.141592653589793`
`for Num def radiusToCircumference Num as 2 pi ok 10 radiusToCircumference`	`Num`	`62.83185307179586`

sqrt1_2

Returns the square root of 1/2.

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	the approximate square root of 1/2

Examples

Program	Type	Value	Error
`sqrt1_2`	`Num`	`0.7071067811865476`

sqrt2

Returns the square root of 2.

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	the approximate square root of 2

Examples

Program	Type	Value	Error
`sqrt2`	`Num`	`1.4142135623730951`

abs

Computes the absolute value.

	Type	Value
Input	`Num`	a number
Output	`Num`	the absolute value of the input

Examples

Program	Type	Value
`3 -5 abs`	`Num`	`2`
`5 -3 abs`	`Num`	`2`
`1.23456 -7.89012 abs`	`Num`	`6.6555599999999995`

acos

Computes the inverse cosine.

	Type	Value
Input	`Num`	a number in the interval [-1, 1]
Output	`Num`	the inverse cosine (in radians) of the input, or `nan` if the input is invalid

Examples

Program	Type	Value
`-2 acos`	`Num`	`nan`
`-1 acos`	`Num`	`3.141592653589793`
`0 acos`	`Num`	`1.5707963267948966`
`1 acos`	`Num`	`0`
`1.1 acos`	`Num`	`nan`

acosh

Computes the inverse hyperbolic cosine.

	Type	Value
Input	`Num`	a number greater than or equal to 1
Output	`Num`	the inverse hyperoblic cosine of the input, or `nan` if the input is invalid

Examples

Program	Type	Value
`0.9 acosh`	`Num`	`nan`
`1 acosh`	`Num`	`0`
`10 acosh`	`Num`	`2.993222846126381`

asin

Computes the inverse sine.

	Type	Value
Input	`Num`	a number in the interval [-1, 1]
Output	`Num`	the inverse sine (in radians) of the input, of nan if the input is invalid

Examples

Program	Type	Value
`-2 asin`	`Num`	`nan`
`-1 asin`	`Num`	`-1.5707963267948966`
`0 asin`	`Num`	`0`
`1 asin`	`Num`	`1.5707963267948966`
`1.1 asin`	`Num`	`nan`

asinh

Computes the inverse hyperbolic sine.

	Type	Value
Input	`Num`	a number
Output	`Num`	the inverse hyperbolic sine of the input

Examples

Program	Type	Value
`-1 asinh`	`Num`	`-0.881373587019543`
`0 asinh`	`Num`	`0`
`1 asinh`	`Num`	`0.881373587019543`
`2 asinh`	`Num`	`1.4436354751788103`

atan

Computes the inverse tangent.

	Type	Value
Input	`Num`	a number
Output	`Num`	the inverse tangent (in radians) of the input

Examples

Program	Type	Value
`-10 atan`	`Num`	`-1.4711276743037345`
`-1 atan`	`Num`	`-0.7853981633974483`
`0 atan`	`Num`	`0`
`1 atan`	`Num`	`0.7853981633974483`

atan2

Computes the angle in the plane.

	Type	Value
Input	`Num`	a number y (y-coordinate)
x (param #1)	`Num`	a number (x-coordinate)
Output	`Num`	the angle in the plane (in radians) between the positive x-axis and the ray from (0, 0) to (x, y)

Examples

Program	Type	Value
`5 atan2(5)`	`Num`	`0.7853981633974483`
`10 atan2(10)`	`Num`	`0.7853981633974483`
`10 atan2(0)`	`Num`	`1.5707963267948966`

atanh

Computes the inverse hyperbolic tangent.

	Type	Value
Input	`Num`	a number in the interval [-1, 1]
Output	`Num`	the inverse hyperbolic tangent of the input, or `nan` if the input is invalid

Examples

Program	Type	Value
`-2 atanh`	`Num`	`nan`
`-1 atanh`	`Num`	`-inf`
`0 atanh`	`Num`	`0`
`0.5 atanh`	`Num`	`0.5493061443340548`
`1 atanh`	`Num`	`inf`

cbrt

Computes the cube root.

	Type	Value
Input	`Num`	a number
Output	`Num`	the cube root of the input

Examples

Program	Type	Value
`-1 cbrt`	`Num`	`-1`
`1 cbrt`	`Num`	`1`
`inf cbrt`	`Num`	`inf`
`64 cbrt`	`Num`	`4`

ceil

Rounds a number up.

	Type	Value
Input	`Num`	a number
Output	`Num`	the smallest integer greater than or equal to the input

Examples

Program	Type	Value
`.95 ceil`	`Num`	`1`
`4 ceil`	`Num`	`4`
`7.004 ceil`	`Num`	`8`
`-7.004 ceil`	`Num`	`-7`

clz32

Count leading zeros.

	Type	Value
Input	`Num`	a number (is truncated to integer)
Output	`Num`	the number of leading zero bits in the 32-bit binary representation of the input

Examples

Program	Type	Value
`-inf clz32`	`Num`	`32`
`-4 clz32`	`Num`	`0`
`-1 clz32`	`Num`	`0`
`0 clz32`	`Num`	`32`
`0.5 clz32`	`Num`	`32`
`1 clz32`	`Num`	`31`
`1.1 clz32`	`Num`	`31`
`4 clz32`	`Num`	`29`
`4.7 clz32`	`Num`	`29`
`1000 clz32`	`Num`	`22`
`inf clz32`	`Num`	`32`

cos

Computes the cosine.

	Type	Value
Input	`Num`	an angle in radians
Output	`Num`	the cosine of the input

Examples

Program	Type	Value
`-inf cos`	`Num`	`nan`
`-0 cos`	`Num`	`1`
`0 cos`	`Num`	`1`
`1 cos`	`Num`	`0.5403023058681398`
`pi cos`	`Num`	`-1`
`pi *2 cos`	`Num`	`1`
`inf cos`	`Num`	`nan`

cosh

Computes the hyperbolic cosine.

	Type	Value
Input	`Num`	a number
Output	`Num`	the hyperbolic cosine of the input

Examples

Program	Type	Value
`0 cosh`	`Num`	`1`
`1 cosh`	`Num`	`1.5430806348152437`
`-1 cosh`	`Num`	`1.5430806348152437`
`2 cosh`	`Num`	`3.7621956910836314`

exp

Computes the exponential function.

	Type	Value
Input	`Num`	the exponent
Output	`Num`	e (Euler's number) raised to the exponent

Examples

Program	Type	Value
`-inf exp`	`Num`	`0`
`-1 exp`	`Num`	`0.36787944117144233`
`0 exp`	`Num`	`1`
`1 exp`	`Num`	`2.718281828459045`
`inf exp`	`Num`	`inf`

expm1

Computes the exponential function, subtracted by one.

	Type	Value
Input	`Num`	the exponent
Output	`Num`

e (Euler's number) raised to the exponent, minus 1

Examples

Program	Type	Value
`-inf expm1`	`Num`	`-1`
`-1 expm1`	`Num`	`-0.6321205588285577`
`-0 expm1`	`Num`	`-0`
`0 expm1`	`Num`	`0`
`1 expm1`	`Num`	`1.718281828459045`
`inf expm1`	`Num`	`inf`

floor

Rounds down.

	Type	Value
Input	`Num`	a number
Output	`Num`	the largest integer less than or equal to the input

Examples

Program	Type	Value
`5.95 floor`	`Num`	`5`
`5.05 floor`	`Num`	`5`
`5 floor`	`Num`	`5`
`-5.05 floor`	`Num`	`-6`

fround

Rounds to 32-bit precision.

	Type	Value
Input	`Num`	a number
Output	`Num`	the nearest 32-bit single precision float representation

Examples

Program	Type	Value
`5.5 fround`	`Num`	`5.5`
`5.05 fround`	`Num`	`5.050000190734863`
`5 fround`	`Num`	`5`
`-5.05 fround`	`Num`	`-5.050000190734863`

hypot

Computes the square root of the sum of squares

	Type	Value
Input	`Arr<Num...>`	an array of numbers
Output	`Num`	the square root of the sum of the squares of the input numbers

Examples

Program	Type	Value
`[3, 4] hypot`	`Num`	`5`
`[5, 12] hypot`	`Num`	`13`
`[3, 4, 5] hypot`	`Num`	`7.0710678118654755`
`[-5] hypot`	`Num`	`5`

imul

32-bit multiplication

	Type	Value
Input	`Num`	the first factor
y (param #1)	`Num`	the second factor
Output	`Num`	the product of the 32-bit versions (cf. fround) of the factors

Examples

Program	Type	Value
`3 imul(4)`	`Num`	`12`
`-5 imul(12)`	`Num`	`-60`
`"ffffffff" parseInt(16) imul(5)`	`Num`	`-5`
`"fffffffe" parseInt(16) imul(5)`	`Num`	`-10`

log

Computes the natural logarithm.

	Type	Value
Input	`Num`	a number
Output	`Num`	the natural (base e) logarithm of the input

Examples

Program	Type	Value
`-1 log`	`Num`	`nan`
`-0 log`	`Num`	`-inf`
`0 log`	`Num`	`-inf`
`1 log`	`Num`	`0`
`10 log`	`Num`	`2.302585092994046`
`inf log`	`Num`	`inf`
`8 log /(2 log)`	`Num`	`3`
`625 log /(5 log)`	`Num`	`4`

log10

Computes the base 10 logarithm.

	Type	Value
Input	`Num`	a number
Output	`Num`	the base 10 logarithm of the input

Examples

Program	Type	Value
`-2 log10`	`Num`	`nan`
`-0 log10`	`Num`	`-inf`
`0 log10`	`Num`	`-inf`
`1 log10`	`Num`	`0`
`2 log10`	`Num`	`0.3010299956639812`
`100000 log10`	`Num`	`5`
`inf log10`	`Num`	`inf`

log1p

Computes the natural logarithm of x + 1.

	Type	Value
Input	`Num`	a number (x)
Output	`Num`

the natural (base e) logarithm of (x + 1)

Examples

Program	Type	Value
`1 log1p`	`Num`	`0.6931471805599453`
`0 log1p`	`Num`	`0`
`-1 log1p`	`Num`	`-inf`
`-2 log1p`	`Num`	`nan`

log2

Computes the base 2 logarithm.

	Type	Value
Input	`Num`	a number
Output	`Num`	the base 2 logarithm of the input

Examples

Program	Type	Value
`3 log2`	`Num`	`1.5849625007211563`
`2 log2`	`Num`	`1`
`1 log2`	`Num`	`0`
`0 log2`	`Num`	`-inf`

max

Finds the largest number

	Type	Value
Input	`Arr<Num...>`	an array of numbers
Output	`Num`	the largest number in the input, or -inf if the input is empty

Examples

Program	Type	Value
`[1, 3, 2] max`	`Num`	`3`
`[-1, -3, -2] max`	`Num`	`-1`
`[] max`	`Num`	`-inf`

min

Finds the smallest number

	Type	Value
Input	`Arr<Num...>`	an array of numbers
Output	`Num`	the smallest number in the input, or inf if the input is empty

Examples

Program	Type	Value
`[1, 3, 2] min`	`Num`	`1`
`[-1, -3, -2] min`	`Num`	`-3`
`[] min`	`Num`	`inf`

**

Computes powers (exponentiation).

	Type	Value
Input	`Num`	the base
y (param #1)	`Num`	the exponent
Output	`Num`	the base taken to the y-th power

Examples

Program	Type	Value
`7 **3`	`Num`	`343`
`4 **.5`	`Num`	`2`
`7 **(-2)`	`Num`	`0.02040816326530612`
`-7 **0.5`	`Num`	`nan`

random

Returns a random number between 0 and 1.

	Type	Value
Input	`Any`	any value (is ignored)
Output	`Num`	a floating-point, pseudo-random number n with 0 <= n < 1 and approximately uniform distribution over that range

Examples

Program	Type	Value	Error
`[null] repeat(1000) each(random) each(>=0) all`	`Bool`	`true`
`[null] repeat(1000) each(random) each(<1) all`	`Bool`	`true`

random

Returns a random integer number in a specified interval.

	Type	Value
Input	`Any`	any value (is ignored)
from (param #1)	`Num`	lower bound (inclusive); rounded towards 0 if not integer
to (param #2)	`Num`	upper bound (exclusive); rounded towards 0 if not integer
Output	`Num`	a integer, pseudorandom number n with from <= n < to and approximately uniform distribution over that range

Examples

Program	Type	Value	Error
`[null] repeat(1000) each(random(2, 7)) each(>=2) all`	`Bool`	`true`
`[null] repeat(1000) each(random(2, 7)) each(<7) all`	`Bool`	`true`
`[null] repeat(1000) each(random(2, 7)) each(=n floor ==n) all`	`Bool`	`true`
`[null] repeat(1000) each(random(2.4, 7.6)) each(>=2) all`	`Bool`	`true`
`[null] repeat(1000) each(random(2.4, 7.6)) each(<7) all`	`Bool`	`true`
`[null] repeat(1000) each(random(2.4, 7.6)) each(=n floor ==n) all`	`Bool`	`true`
`[null] repeat(1000) each(random(-7, -2)) each(>=(-7)) all`	`Bool`	`true`
`[null] repeat(1000) each(random(-7, -2)) each(<(-2)) all`	`Bool`	`true`
`[null] repeat(1000) each(random(-7, -2)) each(=n floor ==n) all`	`Bool`	`true`
`[null] repeat(1000) each(random(-7.6, -2.4)) each(>=(-7)) all`	`Bool`	`true`
`[null] repeat(1000) each(random(-7.6, -2.4)) each(<(-2)) all`	`Bool`	`true`
`[null] repeat(1000) each(random(-7.6, -2.4)) each(=n floor ==n) all`	`Bool`	`true`
`random(7, 2)`	`Bool`		`Value error Code: UnexpectedValue Message: Component got an unexpected input value.`
`random(2, 2)`	`Bool`		`Value error Code: UnexpectedValue Message: Component got an unexpected input value.`

round

Rounds a number to the nearest integer.

	Type	Value
Input	`Num`	a number
Output	`Num`	the nearest integer, or away from zero if there's two nearest integers

Examples

Program	Type	Value
`0.9 round`	`Num`	`1`
`5.95 round`	`Num`	`6`
`5.5 round`	`Num`	`6`
`5.05 round`	`Num`	`5`
`-5.05 round`	`Num`	`-5`
`-5.5 round`	`Num`	`-6`
`-5.95 round`	`Num`	`-6`

sign

Determines the sign of a number.

	Type	Value
Input	`Num`	a number
Output	`Num`	1 if the input is positive, -1 if negative, 0 if it's 0, and -0 if it's -0

Examples

Program	Type	Value
`3 sign`	`Num`	`1`
`0 sign`	`Num`	`0`
`-0 sign`	`Num`	`-0`
`-3`	`Num`	`-3`

sin

Computes the sine.

	Type	Value
Input	`Num`	an angle in radians
Output	`Num`	the sine of the input

Examples

Program	Type	Value
`-inf sin`	`Num`	`nan`
`-0 sin`	`Num`	`-0`
`0 sin`	`Num`	`0`
`1 sin`	`Num`	`0.8414709848078965`
`pi /2 sin`	`Num`	`1`
`inf sin`	`Num`	`nan`

sinh

Computes the hyperbolic sine.

	Type	Value
Input	`Num`	a number
Output	`Num`	the hyperbolic sine of the input

Examples

Program	Type	Value
`0 sinh`	`Num`	`0`
`1 sinh`	`Num`	`1.1752011936438014`
`-1 sinh`	`Num`	`-1.1752011936438014`
`2 sinh`	`Num`	`3.626860407847019`

sqrt

Computes square roots.

	Type	Value
Input	`Num`	a number
Output	`Num`	the square root of the input, or nan if it's negative

Examples

Program	Type	Value
`-1 sqrt`	`Num`	`nan`
`-0 sqrt`	`Num`	`-0`
`0 sqrt`	`Num`	`0`
`1 sqrt`	`Num`	`1`
`2 sqrt`	`Num`	`1.4142135623730951`
`9 sqrt`	`Num`	`3`
`inf sqrt`	`Num`	`inf`

tan

Computes the tangent.

	Type	Value
Input	`Num`	an angle in radians
Output	`Num`	the tangent of the input

Examples

Program	Type	Value
`0 *pi /180 tan`	`Num`	`0`
`45 *pi /180 tan`	`Num`	`1`
`90 *pi /180 tan`	`Num`	`16331239353195392`

tanh

Computes the hyperbolic tangent.

	Type	Value
Input	`Num`	a number
Output	`Num`	the hyperbolic tangent of the input

Examples

Program	Type	Value
`-1 tanh`	`Num`	`-0.7615941559557649`
`0 tanh`	`Num`	`0`
`inf tanh`	`Num`	`1`
`1 tanh`	`Num`	`0.7615941559557649`

trunc

Rounds towards zero.

	Type	Value
Input	`Num`	a number
Output	`Num`	the input without fractional digits

Examples

Program	Type	Value
`13.37 trunc`	`Num`	`13`
`42.84 trunc`	`Num`	`42`
`0.123 trunc`	`Num`	`0`
`-0.123 trunc`	`Num`	`-0`

The Bach Programming Language