README.md

Mathematics library of the Chaos language. You can install this spell with:

occultist install math

and import it with:

import math

Mathematical Constants

num math.pi()

Returns the mathematical constant $\pi = 3.14159...$

kaos> math.pi()
3.14159

num math.e()

Returns the mathematical constant $e = 2.71828...$

kaos> math.e()
2.71828

num math.golden_ratio()

Returns the mathematical constant $\phi = 1.61803...$

kaos> math.golden_ratio()
1.61803

num math.inf()

Returns the positive infinity inf constant.

kaos> math.inf()
inf

num math.nan()

Returns the not-a-number nan constant.

kaos> math.nan()
nan

Trigonometric Functions

num math.cos(num x)

Returns the cosine of x, in degrees.

kaos> math.cos(60)
0.5

num math.sin(num x)

Returns the sine of x, in degrees.

kaos> math.sin(30)
0.5

num math.tan(num x)

Returns the tangent of x, in degrees.

kaos> math.tan(45)
1

num math.acos(num x)

Returns the arc cosine of x, in degrees.

kaos> math.acos(0.5)
60

num math.asin(num x)

Returns the arc sine of x, in degrees.

kaos> math.asin(0.5)
30

num math.atan(num x)

Returns the arc tangent of x, in degrees.

kaos> math.atan(1.0)
45

num math.atan2(num x, num y)

Returns the arc tangent of x (x-coordinate) and y (y-coordinate) in degrees. Two parameters version of atan()

kaos> math.atan2(-10.0, 10.0)
135

Hyperbolic Functions

num math.cosh(num x)

Returns the hyperbolic cosine of x.

kaos> math.cosh(0.693147)
1.25

num math.sinh(num x)

Returns the hyperbolic sine of x.

kaos> math.sinh(0.693147)
0.75

num math.tanh(num x)

Returns the hyperbolic tangent of x.

kaos> math.tanh(0.693147)
0.6

num math.acosh(num x)

Returns the nonnegative area hyperbolic cosine of x.

kaos> math.acosh(3.762196)
2

num math.asinh(num x)

Returns the nonnegative area hyperbolic sine of x.

kaos> math.asinh(3.626860)
2

num math.atanh(num x)

Returns the nonnegative area hyperbolic tangent of x.

kaos> math.atanh(0.761594)
1

Exponential and Logarithmic Functions

num math.exp(num x)

Returns $e$ raised to the power of x: $e^x$

kaos> math.exp(5)
148.413

num dict math.frexp(num x)

Returns the mantissa and exponent of x: $x = {mantissa} \times 2^{exponent}$

kaos> import math
kaos> dict frexp = math.frexp(8)
kaos> frexp['mantissa']
0.5
kaos> frexp['exponent']
4

num math.ldexp(num x, num exp)

Returns the result of multiplying x by 2 raised to the power of y: $x \times 2 ^{y}$

It's the inverse function of frexp()

kaos> math.ldexp(0.95, 4)
15.2

num math.ln(num x)

Returns the natural logarithm of x: $lnx$ or $log_{e}x$

kaos> math.ln(5.5)
1.70475

num math.log(num x, num b)

Returns the base-b logarithm of x: $log_{b}x$

kaos> math.log(81, 3)
4

num math.log1p(num x)

Returns the natural logarithm of 1 + x: $ln(1 + x)$ or $log_{e}(1 + x)$

The result is more accurate than log(x) when x near zero.

kaos> math.log1p(1.0)
0.693147

num math.log2(num x)

Returns the base-2 logarithm of x: $log_{2}x$

Generally more accurate than log(x, 2).

kaos> math.log2(1024.0)
10

num math.log10(num x)

Returns the base-10 logarithm of x: $log_{10}x$

Generally more accurate than log(x, 10).

kaos> math.log10(1000)
3

num dict math.modf(num x)

Returns the integer and fractional parts of x.

kaos> dict modf = math.modf(3.141593)
kaos> modf['integer']
3
kaos> modf['fraction']
0.141593

num math.expm1(num x)

Returns $e$ raised to the power of x, minus 1: $e^x - 1$

kaos> math.expm1(1.0)
1.71828

Power Functions

num math.pow(num x, num y)

Returns x raised to the power of y: $x^y$

kaos> math.pow(2, 3)
8

num math.sqrt(num x)

Returns the square root of x: $\sqrt{x}$

kaos> math.sqrt(1024)
32

num math.cbrt(num x)

Returns the cubic root of x: $\sqrt[3]{x}$

kaos> math.cbrt(27)
3

num math.hypot(num x, num y)

Returns the hypotenuse of a right-angled triangle whose legs are x and y: $\sqrt{x^2 + y^2}$

kaos> math.hypot(3.0, 4.0)
5

Error and Gamma Functions

num math.erf(num x)

Returns the error function value for x.

kaos> math.erf(1.0)
0.842701

num math.erfc(num x)

Returns the complementary error function value for x.

kaos> math.erfc(1.0)
0.157299

num math.gamma(num x)

Returns the gamma function at x.

kaos> math.gamma(0.5)
1.77245

num math.lgamma(num x)

Returns the natural logarithm of the absolute value of the gamma function (log-gamma) at x.

kaos> math.lgamma(0.5)
0.572365

Rounding and Remainder Functions

num math.ceil(num x)

Rounds x upward, returning the smallest integral value that is not less than x.

kaos> math.ceil(3.8)
4
kaos> math.ceil(-3.8)
-3

num math.floor(num x)

Rounds x downward, returning the largest integral value that is not greater than x.

kaos> math.floor(5.6)
5
kaos> math.floor(-5.6)
-6

num math.mod(num x, num y)

Computes the remainder that results from performing integer division of x by y.

kaos> math.mod(23, 4)
3

num math.fmod(num x, num y)

Computes the remainder that results from performing floating-point division of x by y.

kaos> math.fmod(18.5, 4.2)
1.7

num math.trunc(num x)

Rounds x toward zero, returning the nearest integral value that is not larger in magnitude than x.

kaos> math.trunc(3.8)
3
kaos> math.trunc(-3.8)
-3

num math.round(num x)

Returns the integral value that is nearest to x, with halfway cases rounded away from zero.

kaos> math.round(3.8)
4
kaos> math.round(-3.8)
-4

num math.remainder(num x, num y)

Returns the floating-point remainder of x / y (rounded to nearest).

kaos> math.remainder(18.5, 4.2)
1.7

num dict math.remquo(num x, num y)

Returns the same as remainder(), but also returns the quotient.

kaos> dict remquo = math.remquo(10.3, 4.5)
kaos> remquo['remainder']
1.3
kaos> remquo['quotient']
2

Floating-point Manipulation Functions

num math.copysign(num x, num y)

Returns a value with the magnitude of x and the sign of y.

kaos> math.copysign(-10.0, -1.0)
-10

num math.nextafter(num x, num y)

Returns the next representable value after x in the direction of y.

kaos> math.nextafter(0.0, 1.0)
3.6452e-4951
kaos> math.nextafter(0.0, -1.0)
-3.6452e-4951

Other Functions

num math.abs(num x)

Returns the absolute value of x: $\left | x \right |$

kaos> math.abs(3.1416)
3.1416
kaos> math.abs(-10.6)
10.6

num math.factorial(num x)

Returns the factorial of x. Returns -1 if x is negative.

kaos> math.factorial(5)
120
kaos> math.factorial(-5)
-1

Boolean Functions

bool math.is_finite(num x)

Returns whether x is a finite value.

kaos> math.is_finite(0.0)
true
kaos> math.is_finite(1.0 / 0.0)
false

bool math.is_inf(num x)

Returns whether x is an infinity value (either positive infinity or negative infinity).

kaos> math.is_inf(0.0)
false
kaos> math.is_inf(1.0 / 0.0)
true

bool math.is_nan(num x)

Returns whether x is a nan (not-a-number) value.

kaos> math.is_nan(0.0)
false
kaos> num nan_example = math.sqrt(-1.0)
kaos> nan_example
-nan
kaos> math.is_nan(nan_example)
true

bool math.is_normal(num x)

Returns whether x is a normal value: i.e., whether it is neither inf(infinity), nan(not-a-number), zero or subnormal.

kaos> math.is_normal(1.0)
true
kaos> math.is_normal(0.0)
false
kaos> math.is_normal(1.0 / 0.0)
false

bool math.is_positive(num x)

Returns whether the sign of x is positive.

kaos> math.is_positive(1.0)
true
kaos> math.is_positive(-1.0)
false

bool math.is_negative(num x)

Returns whether the sign of x is negative.

kaos> math.is_negative(1.0)
false
kaos> math.is_negative(-1.0)
true