number

Numbers in Koto are represented internally as either a signed 64 bit integer or float, switching between the two representations automatically depending on usage.

Example

x = 1        # x is assigned as an integer
y = x + 0.5  # y is assigned as a float
x += 0.99    # x is now a float

Reference

abs
acos
and
asin
atan
ceil
clamp
cos
cosh
degrees
e
exp
exp2
flip_bits
floor
infinity
is_nan
ln
log2
log10
max
min
nan
negative_infinity
or
pi
pow
radians
recip
shift_left
shift_right
sin
sinh
sqrt
tan
tanh
tau
to_float
to_int
xor

abs

|Number| -> Number

Returns the absolute value of the number.

Example

-1.abs()
# 1

1.abs()
# 1

acos

|Number| -> Float

Returns the arc cosine of the number. acos is the inverse function of cos.

Example

0.acos()
# π / 2

1.acos()
# 1

and

|Integer, Integer| -> Integer

Returns the bitwise combination of two integers, where a 1 in both input positions produces a 1 in corresponding output positions.

Example

0b1010.and 0b1100
# 0b1000

asin

|Number| -> Float

Returns the arc sine of the number. asin is the inverse function of sin.

Example

0.asin()
# 0

1.asin()
# π / 2

atan

|Number| -> Float

Returns the arc tangent of the number. atan is the inverse function of tan.

Example

0.atan()
# 0

1.atan()
# π / 4

ceil

|Number| -> Integer

Returns the smallest integer that's greater than or equal to the input.

Example

0.5.ceil()
# 1

2.ceil()
# 2

-0.5.ceil()
# 0

clamp

|Number, Number, Number| -> Number

Returns the first number restricted to the range defined by the second and third numbers.

Example

0.clamp 1, 2
# 1

1.5.clamp 1, 2
# 1.5

3.0.clamp 1, 2
# 2

cos

|Number| -> Float

Returns the cosine of the number.

Example

0.cos()
# 1.0

import number.pi

pi.cos()
# -1.0

cosh

|Number| -> Float

Returns the hyperbolic cosine of the number.

Example

3.cosh()
# (e.pow(3) + e.pow(-3)) / 2

degrees

|Number| -> Float

Converts radians into degrees.

Example

from number import pi, tau

pi.degrees()
# 180.0

tau.degrees()
# 360.0

e

Float

Provides the e constant.

exp

|Number| -> Float

Returns the result of applying the exponential function, equivalent to calling e.pow x.

Example

0.exp()
# 1.0

1.exp()
# number.e

exp2

|Number| -> Float

Returns the result of applying the base-2 exponential function, equivalent to calling 2.pow x.

Example

1.exp2()
# 2.0

3.exp2()
# 8.0

flip_bits

|Integer| -> Integer

Returns the input with its bits 'flipped', i.e. 1 => 0, and 0 => 1.

Example

1.flip_bits()
# -2

floor

|Number| -> Integer

Returns the smallest integer that's less than or equal to the input.

Example

0.5.floor()
# 0

2.floor()
# 2

-0.5.floor()
# -1

infinity

Float

Provides the ∞ constant.

is_nan

|Number| -> Bool

Returns true if the number is NaN.

Example

1.is_nan()
# false

(0 / 0).is_nan()
# true

ln

|Number| -> Float

Returns the natural logarithm of the number.

Example

1.ln()
# 0.0

from number import e

e.ln()
# 1.0

log2

|Number| -> Float

Returns the base-2 logarithm of the number.

Example

2.log2()
# 1.0

4.log2()
# 2.0

log10

|Number| -> Float

Returns the base-10 logarithm of the number.

Example

10.log10()
# 1.0

100.log10()
# 2.0

max

|Number, Number| -> Number

Returns the larger of the two numbers.

Example

1.max 2
# 2

4.5.max 3
# 4.5

min

|Number, Number| -> Number

Returns the smaller of the two numbers.

Example

1.min 2
# 1

4.5.min 3
# 3

nan

Float

Provides the NaN (Not a Number) constant.

negative_infinity

Float

Provides the -∞ constant.

or

|Integer, Integer| -> Integer

Returns the bitwise combination of two integers, where a 1 in either input positions produces a 1 in corresponding output positions.

Example

0b1010.or 0b1100
# 0b1110

pi

Float

Provides the π constant.

pow

|Number, Number| -> Number

Returns the result of raising the first number to the power of the second.

Example

2.pow 3
# 8

radians

|Number| -> Float

Converts degrees into radians.

Example

90.radians()
# π / 2

360.radians()
# π * 2

recip

|Number| -> Float

Returns the reciprocal of the number, i.e. 1 / x.

Example

2.recip()
# 0.5

shift_left

|Integer, Integer| -> Integer

Returns the result of shifting the bits of the first number to the left by the amount specified by the second number.

Note

The shift amount must be greater than or equal to 0.

Example

0b1010.shift_left 2
# 0b101000

0b1010.shift_left 2
# 0b101000

sin

|Number| -> Float

Returns the sine of the number.

Example

import number.pi

(pi * 0.5).sin()
# 1.0

(pi * 1.5).sin()
# -1.0

sinh

|Number| -> Float

Returns the hyperbolic sine of the number.

Example

3.sinh()
# (e.pow(3) - e.pow(-3)) / 2

sqrt

|Number| -> Float

Returns the square root of the number.

Example

64.sqrt()
# 8.0

tan

|Number| -> Float

Returns the tangent of the number.

Example

1.tan()
# 1.sin() / 1.cos()

tanh

|Number| -> Float

Returns the hyperbolic tangent of the number.

Example

1.tanh()
# 1.sinh() / 1.cosh()

1.to_float()
# 1.0

to_int

|Number| -> Integer

Returns the number as an Integer. This is equivalent to calling ceil.

Example

1.5.to_int()
# 2

-0.5.to_int()
# 0

xor

|Integer, Integer| -> Integer

Returns the bitwise combination of two integers, where a 1 in one (and only one) of the input positions produces a 1 in corresponding output positions.

Example

0b1010.xor 0b1100
# 0b0110

Koto Reference