math
This library provides basic mathematical functions.
It provides all its functions and constants inside the table math
.
Functions with the annotation "integer/float
" give
integer results for integer arguments
and float results for non-integer arguments.
The rounding functions
math.ceil
, math.floor
, and math.modf
return an integer when the result fits in the range of an integer,
or a float otherwise.
math.abs (x)
Returns the maximum value between x
and -x
. (integer/float)
math.acos (x)
Returns the arc cosine of x
(in radians).
math.asin (x)
Returns the arc sine of x
(in radians).
math.atan (y [, x])
Returns the arc tangent of y/x
(in radians),
using the signs of both arguments to find the
quadrant of the result.
It also handles correctly the case of x
being zero.
The default value for x
is 1,
so that the call math.atan(y)
returns the arc tangent of y
.
math.ceil (x)
Returns the smallest integral value greater than or equal to x
.
math.cos (x)
Returns the cosine of x
(assumed to be in radians).
math.deg (x)
Converts the angle x
from radians to degrees.
math.exp (x)
Returns the value ex
(where e
is the base of natural logarithms).
math.floor (x)
Returns the largest integral value less than or equal to x
.
math.fmod (x, y)
Returns the remainder of the division of x
by y
that rounds the quotient towards zero. (integer/float)
math.huge
The float value HUGE_VAL
,
a value greater than any other numeric value.
math.log (x [, base])
Returns the logarithm of x
in the given base.
The default for base
is e
(so that the function returns the natural logarithm of x
).
math.max (x, ...)
Returns the argument with the maximum value,
according to the Lua operator <
.
math.maxinteger
An integer with the maximum value for an integer.
math.min (x, ...)
Returns the argument with the minimum value,
according to the Lua operator <
.
math.mininteger
An integer with the minimum value for an integer.
math.modf (x)
Returns the integral part of x
and the fractional part of x
.
Its second result is always a float.
math.pi
The value of π.
math.rad (x)
Converts the angle x
from degrees to radians.
math.random ([m [, n]])
When called without arguments,
returns a pseudo-random float with uniform distribution
in the range [0,1).
When called with two integers m
and n
,
math.random
returns a pseudo-random integer
with uniform distribution in the range [m, n].
The call math.random(n)
, for a positive n
,
is equivalent to math.random(1,n)
.
The call math.random(0)
produces an integer with
all bits (pseudo)random.
This function uses the xoshiro256**
algorithm to produce
pseudo-random 64-bit integers,
which are the results of calls with argument 0.
Other results (ranges and floats)
are unbiased extracted from these integers.
Lua initializes its pseudo-random generator with the equivalent of
a call to math.randomseed
with no arguments,
so that math.random
should generate
different sequences of results each time the program runs.
math.randomseed ([x [, y]])
When called with at least one argument,
the integer parameters x
and y
are
joined into a 128-bit seed that
is used to reinitialize the pseudo-random generator;
equal seeds produce equal sequences of numbers.
The default for y
is zero.
When called with no arguments, Lua generates a seed with a weak attempt for randomness.
This function returns the two seed components that were effectively used, so that setting them again repeats the sequence.
To ensure a required level of randomness to the initial state
(or contrarily, to have a deterministic sequence,
for instance when debugging a program),
you should call math.randomseed
with explicit arguments.
math.sin (x)
Returns the sine of x
(assumed to be in radians).
math.sqrt (x)
Returns the square root of x
.
(You can also use the expression x^0.5
to compute this value.)
math.tan (x)
Returns the tangent of x
(assumed to be in radians).
math.tointeger (x)
If the value x
is convertible to an integer,
returns that integer.
Otherwise, returns fail.
math.type (x)
Returns "integer
" if x
is an integer,
"float
" if it is a float,
or fail if x
is not a number.
math.ult (m, n)
Returns a boolean,
true if and only if integer m
is below integer n
when
they are compared as unsigned integers.