module Math
Extended Modules
Defined in:
big/big_float.crbig/big_int.cr
big/big_rational.cr
complex.cr
math/math.cr
Constant Summary
- E =
LibM.exp_f64(1.0) -
Euler's number (e).
- LOG10 =
LibM.log_f64(10.0) - LOG2 =
LibM.log_f64(2.0) - PI =
3.14159265358979323846 -
Archimedes' constant (π).
- TAU =
6.283185307179586476925 -
The full circle constant (τ), equal to 2π.
Instance Method Summary
- #acos(value : Float32) : Float32
Calculates the arc cosine of value.
- #acos(value : Float64) : Float64
Calculates the arc cosine of value.
- #acos(value)
Calculates the arc cosine of value.
- #acosh(value : Float32) : Float32
Calculates the inverse hyperbolic cosine of value.
- #acosh(value : Float64) : Float64
Calculates the inverse hyperbolic cosine of value.
- #acosh(value)
Calculates the inverse hyperbolic cosine of value.
- #asin(value : Float32) : Float32
Calculates the arc sine of value.
- #asin(value : Float64) : Float64
Calculates the arc sine of value.
- #asin(value)
Calculates the arc sine of value.
- #asinh(value : Float32) : Float32
Calculates the inverse hyperbolic sine of value.
- #asinh(value : Float64) : Float64
Calculates the inverse hyperbolic sine of value.
- #asinh(value)
Calculates the inverse hyperbolic sine of value.
- #atan(value : Float32) : Float32
Calculates the arc tangent of value.
- #atan(value : Float64) : Float64
Calculates the arc tangent of value.
- #atan(value)
Calculates the arc tangent of value.
- #atan2(y : Float32, x : Float32) : Float32
Calculates the two-argument arc tangent of the ray from (0, 0) to (x, y).
- #atan2(y : Float64, x : Float64) : Float64
Calculates the two-argument arc tangent of the ray from (0, 0) to (x, y).
- #atan2(y, x) : Float64
Calculates the two-argument arc tangent of the ray from (0, 0) to (x, y).
- #atanh(value : Float32) : Float32
Calculates the inverse hyperbolic tangent of value.
- #atanh(value : Float64) : Float64
Calculates the inverse hyperbolic tangent of value.
- #atanh(value)
Calculates the inverse hyperbolic tangent of value.
- #besselj(order : Int32, value : Float32)
Calculates the cylindrical Bessel function of the first kind of value for the given order.
- #besselj(order : Int32, value : Float64) : Float64
Calculates the cylindrical Bessel function of the first kind of value for the given order.
- #besselj(order, value)
Calculates the cylindrical Bessel function of the first kind of value for the given order.
- #besselj0(value : Float32)
Calculates the cylindrical Bessel function of the first kind of value for order 0.
- #besselj0(value : Float64) : Float64
Calculates the cylindrical Bessel function of the first kind of value for order 0.
- #besselj0(value)
Calculates the cylindrical Bessel function of the first kind of value for order 0.
- #besselj1(value : Float32)
Calculates the cylindrical Bessel function of the first kind of value for order 1.
- #besselj1(value : Float64) : Float64
Calculates the cylindrical Bessel function of the first kind of value for order 1.
- #besselj1(value)
Calculates the cylindrical Bessel function of the first kind of value for order 1.
- #bessely(order : Int32, value : Float32)
Calculates the cylindrical Bessel function of the second kind of value for the given order.
- #bessely(order : Int32, value : Float64) : Float64
Calculates the cylindrical Bessel function of the second kind of value for the given order.
- #bessely(order, value)
Calculates the cylindrical Bessel function of the second kind of value for the given order.
- #bessely0(value : Float32)
Calculates the cylindrical Bessel function of the second kind of value for order 0.
- #bessely0(value : Float64) : Float64
Calculates the cylindrical Bessel function of the second kind of value for order 0.
- #bessely0(value)
Calculates the cylindrical Bessel function of the second kind of value for order 0.
- #bessely1(value : Float32)
Calculates the cylindrical Bessel function of the second kind of value for order 1.
- #bessely1(value : Float64) : Float64
Calculates the cylindrical Bessel function of the second kind of value for order 1.
- #bessely1(value)
Calculates the cylindrical Bessel function of the second kind of value for order 1.
- #cbrt(value : Float32) : Float32
Calculates the cubic root of value.
- #cbrt(value : Float64) : Float64
Calculates the cubic root of value.
- #cbrt(value)
Calculates the cubic root of value.
- #copysign(value1 : Float32, value2 : Float32)
Returns the floating-point value with the magnitude of value1 and the sign of value2.
- #copysign(value1 : Float64, value2 : Float64) : Float64
Returns the floating-point value with the magnitude of value1 and the sign of value2.
- #copysign(value1, value2)
Returns the floating-point value with the magnitude of value1 and the sign of value2.
- #cos(value : Float32) : Float32
Calculates the cosine of value, measured in radians.
- #cos(value : Float64) : Float64
Calculates the cosine of value, measured in radians.
- #cos(value)
Calculates the cosine of value, measured in radians.
- #cosh(value : Float32) : Float32
Calculates the hyperbolic cosine of value.
- #cosh(value : Float64) : Float64
Calculates the hyperbolic cosine of value.
- #cosh(value)
Calculates the hyperbolic cosine of value.
- #erf(value : Float32) : Float32
Calculates the error function of value.
- #erf(value : Float64) : Float64
Calculates the error function of value.
- #erf(value)
Calculates the error function of value.
- #erfc(value : Float32) : Float32
Calculates 1 minus the error function of value.
- #erfc(value : Float64) : Float64
Calculates 1 minus the error function of value.
- #erfc(value)
Calculates 1 minus the error function of value.
- #exp(value : Float32) : Float32
Calculates the exponential of value.
- #exp(value : Float64) : Float64
Calculates the exponential of value.
- #exp(value : Complex) : Complex
Calculates the exponential of value.
- #exp(value)
Calculates the exponential of value.
- #exp2(value : Float32) : Float32
Calculates 2 raised to the power value.
- #exp2(value : Float64) : Float64
Calculates 2 raised to the power value.
- #exp2(value)
Calculates 2 raised to the power value.
- #expm1(value : Float32) : Float32
Calculates the exponential of value, minus 1.
- #expm1(value : Float64) : Float64
Calculates the exponential of value, minus 1.
- #expm1(value)
Calculates the exponential of value, minus 1.
- #frexp(value : Float32) : Tuple(Float32, Int32)
Decomposes the given floating-point value into a normalized fraction and an integral power of two.
- #frexp(value : Float64) : Tuple(Float64, Int32)
Decomposes the given floating-point value into a normalized fraction and an integral power of two.
- #frexp(value : BigFloat) : Tuple(BigFloat, Int64)
Decomposes the given floating-point value into a normalized fraction and an integral power of two.
- #frexp(value)
Decomposes the given floating-point value into a normalized fraction and an integral power of two.
- #gamma(value : Float32) : Float32
Calculates the gamma function of value.
- #gamma(value : Float64) : Float64
Calculates the gamma function of value.
- #gamma(value) : Float64
Calculates the gamma function of value.
- #hypot(value1 : Float32, value2 : Float32) : Float32
Calculates the length of the hypotenuse from (0, 0) to (value1, value2).
- #hypot(value1 : Float64, value2 : Float64) : Float64
Calculates the length of the hypotenuse from (0, 0) to (value1, value2).
- #hypot(value1, value2)
Calculates the length of the hypotenuse from (0, 0) to (value1, value2).
- #ilogb(value : Float32) : Int32
Returns the unbiased base 2 exponent of the given floating-point value.
- #ilogb(value : Float64) : Int32
Returns the unbiased base 2 exponent of the given floating-point value.
- #ilogb(value)
Returns the unbiased base 2 exponent of the given floating-point value.
- #isqrt(value : Int::Primitive)
Calculates the integer square root of value.
- #isqrt(value : BigInt)
Calculates the integer square root of value.
- #ldexp(value : Float32, exp : Int32) : Float32
Multiplies the given floating-point value by 2 raised to the power exp.
- #ldexp(value : Float64, exp : Int32) : Float64
Multiplies the given floating-point value by 2 raised to the power exp.
- #ldexp(value, exp)
Multiplies the given floating-point value by 2 raised to the power exp.
- #lgamma(value : Float32)
Calculates the logarithmic gamma of value.
- #lgamma(value : Float64) : Float64
Calculates the logarithmic gamma of value.
- #lgamma(value) : Float64
Calculates the logarithmic gamma of value.
- #log(value, base)
Calculates the logarithm of value to the given base.
- #log(value : Float32) : Float32
Calculates the natural logarithm of value.
- #log(value : Float64) : Float64
Calculates the natural logarithm of value.
- #log(value : Complex) : Complex
Calculates the natural logarithm of value.
- #log(value) : Float64
Calculates the natural logarithm of value.
- #log10(value : Float32) : Float32
Calculates the logarithm of value to base 10.
- #log10(value : Float64) : Float64
Calculates the logarithm of value to base 10.
- #log10(value : Complex) : Complex
Calculates the logarithm of value to base 10.
- #log10(value)
Calculates the logarithm of value to base 10.
- #log1p(value : Float32) : Float32
Calculates the natural logarithm of 1 plus value.
- #log1p(value : Float64) : Float64
Calculates the natural logarithm of 1 plus value.
- #log1p(value)
Calculates the natural logarithm of 1 plus value.
- #log2(value : Float32) : Float32
Calculates the logarithm of value to base 2.
- #log2(value : Float64) : Float64
Calculates the logarithm of value to base 2.
- #log2(value : Complex) : Complex
Calculates the logarithm of value to base 2.
- #log2(value) : Float64
Calculates the logarithm of value to base 2.
- #logb(value : Float32) : Float32
Returns the unbiased radix-independent exponent of the given floating-point value.
- #logb(value : Float64) : Float64
Returns the unbiased radix-independent exponent of the given floating-point value.
- #logb(value)
Returns the unbiased radix-independent exponent of the given floating-point value.
- #max(value1 : Float32, value2 : Float32)
Returns the greater of value1 and value2.
- #max(value1 : Float64, value2 : Float64) : Float64
Returns the greater of value1 and value2.
- #max(value1, value2)
Returns the greater of value1 and value2.
- #min(value1 : Float32, value2 : Float32)
Returns the smaller of value1 and value2.
- #min(value1 : Float64, value2 : Float64) : Float64
Returns the smaller of value1 and value2.
- #min(value1, value2)
Returns the smaller of value1 and value2.
- #pw2ceil(v : Int32)
Computes the next highest power of 2 of v.
- #pw2ceil(v : Int64)
- #scalbln(value : Float32, exp : Int64)
Returns the floating-point value with its exponent raised by exp.
- #scalbln(value : Float64, exp : Int64) : Float64
Returns the floating-point value with its exponent raised by exp.
- #scalbln(value, exp) : Float64
Returns the floating-point value with its exponent raised by exp.
- #scalbn(value : Float32, exp : Int32) : Float32
Returns the floating-point value with its exponent raised by exp.
- #scalbn(value : Float64, exp : Int32) : Float64
Returns the floating-point value with its exponent raised by exp.
- #scalbn(value, exp)
Returns the floating-point value with its exponent raised by exp.
- #sin(value : Float32) : Float32
Calculates the sine of value, measured in radians.
- #sin(value : Float64) : Float64
Calculates the sine of value, measured in radians.
- #sin(value)
Calculates the sine of value, measured in radians.
- #sinh(value : Float32) : Float32
Calculates the hyperbolic sine of value.
- #sinh(value : Float64) : Float64
Calculates the hyperbolic sine of value.
- #sinh(value)
Calculates the hyperbolic sine of value.
- #sqrt(value : Float32) : Float32
Calculates the square root of value.
- #sqrt(value : Float64) : Float64
Calculates the square root of value.
- #sqrt(value : BigInt) : BigFloat
Calculates the square root of value.
- #sqrt(value : BigFloat) : BigFloat
Calculates the square root of value.
- #sqrt(value : BigRational) : BigFloat
Calculates the square root of value.
- #sqrt(value : Complex) : Complex
Calculates the square root of value.
- #sqrt(value) : Float64
Calculates the square root of value.
- #tan(value : Float32) : Float32
Calculates the tangent of value, measured in radians.
- #tan(value : Float64) : Float64
Calculates the tangent of value, measured in radians.
- #tan(value)
Calculates the tangent of value, measured in radians.
- #tanh(value : Float32) : Float32
Calculates the hyperbolic tangent of value.
- #tanh(value : Float64) : Float64
Calculates the hyperbolic tangent of value.
- #tanh(value)
Calculates the hyperbolic tangent of value.
Instance Method Detail
def acos(value)Source
Calculates the arc cosine of value.
def acosh(value)Source
Calculates the inverse hyperbolic cosine of value.
def asin(value)Source
Calculates the arc sine of value.
def asinh(value)Source
Calculates the inverse hyperbolic sine of value.
def atan(value)Source
Calculates the arc tangent of value.
def atan2(y : Float32, x : Float32) : Float32Source
Calculates the two-argument arc tangent of the ray from (0, 0) to (x, y).
def atan2(y : Float64, x : Float64) : Float64Source
Calculates the two-argument arc tangent of the ray from (0, 0) to (x, y).
def atan2(y, x) : Float64Source
Calculates the two-argument arc tangent of the ray from (0, 0) to (x, y).
def atanh(value)Source
Calculates the inverse hyperbolic tangent of value.
def besselj(order : Int32, value : Float32)Source
Calculates the cylindrical Bessel function of the first kind of value for the given order.
def besselj(order : Int32, value : Float64) : Float64Source
Calculates the cylindrical Bessel function of the first kind of value for the given order.
def besselj(order, value)Source
Calculates the cylindrical Bessel function of the first kind of value for the given order.
def besselj0(value : Float32)Source
Calculates the cylindrical Bessel function of the first kind of value for order 0.
def besselj0(value : Float64) : Float64Source
Calculates the cylindrical Bessel function of the first kind of value for order 0.
def besselj0(value)Source
Calculates the cylindrical Bessel function of the first kind of value for order 0.
def besselj1(value : Float32)Source
Calculates the cylindrical Bessel function of the first kind of value for order 1.
def besselj1(value : Float64) : Float64Source
Calculates the cylindrical Bessel function of the first kind of value for order 1.
def besselj1(value)Source
Calculates the cylindrical Bessel function of the first kind of value for order 1.
def bessely(order : Int32, value : Float32)Source
Calculates the cylindrical Bessel function of the second kind of value for the given order.
def bessely(order : Int32, value : Float64) : Float64Source
Calculates the cylindrical Bessel function of the second kind of value for the given order.
def bessely(order, value)Source
Calculates the cylindrical Bessel function of the second kind of value for the given order.
def bessely0(value : Float32)Source
Calculates the cylindrical Bessel function of the second kind of value for order 0.
def bessely0(value : Float64) : Float64Source
Calculates the cylindrical Bessel function of the second kind of value for order 0.
def bessely0(value)Source
Calculates the cylindrical Bessel function of the second kind of value for order 0.
def bessely1(value : Float32)Source
Calculates the cylindrical Bessel function of the second kind of value for order 1.
def bessely1(value : Float64) : Float64Source
Calculates the cylindrical Bessel function of the second kind of value for order 1.
def bessely1(value)Source
Calculates the cylindrical Bessel function of the second kind of value for order 1.
def cbrt(value)Source
Calculates the cubic root of value.
def copysign(value1 : Float32, value2 : Float32)Source
Returns the floating-point value with the magnitude of value1 and the sign of value2.
def copysign(value1 : Float64, value2 : Float64) : Float64Source
Returns the floating-point value with the magnitude of value1 and the sign of value2.
def copysign(value1, value2)Source
Returns the floating-point value with the magnitude of value1 and the sign of value2.
def cos(value)Source
Calculates the cosine of value, measured in radians.
def cosh(value)Source
Calculates the hyperbolic cosine of value.
def erf(value)Source
Calculates the error function of value.
def erfc(value)Source
Calculates 1 minus the error function of value.
def exp(value : Complex) : ComplexSource
Calculates the exponential of value.
require "complex" Math.exp(4 + 2.i) # => -22.720847417619233 + 49.645957334580565i
def exp(value)Source
Calculates the exponential of value.
def exp2(value)Source
Calculates 2 raised to the power value.
def expm1(value)Source
Calculates the exponential of value, minus 1.
def frexp(value : Float32) : Tuple(Float32, Int32)Source
Decomposes the given floating-point value into a normalized fraction and an integral power of two.
def frexp(value : Float64) : Tuple(Float64, Int32)Source
Decomposes the given floating-point value into a normalized fraction and an integral power of two.
def frexp(value : BigFloat) : Tuple(BigFloat, Int64)Source
Decomposes the given floating-point value into a normalized fraction and an integral power of two.
def frexp(value)Source
Decomposes the given floating-point value into a normalized fraction and an integral power of two.
def hypot(value1 : Float32, value2 : Float32) : Float32Source
Calculates the length of the hypotenuse from (0, 0) to (value1, value2).
Equivalent to
Math.sqrt(value1 ** 2 + value2 ** 2)
def hypot(value1 : Float64, value2 : Float64) : Float64Source
Calculates the length of the hypotenuse from (0, 0) to (value1, value2).
Equivalent to
Math.sqrt(value1 ** 2 + value2 ** 2)
def hypot(value1, value2)Source
Calculates the length of the hypotenuse from (0, 0) to (value1, value2).
Equivalent to
Math.sqrt(value1 ** 2 + value2 ** 2)
def ilogb(value : Float32) : Int32Source
Returns the unbiased base 2 exponent of the given floating-point value.
def ilogb(value : Float64) : Int32Source
Returns the unbiased base 2 exponent of the given floating-point value.
def ilogb(value)Source
Returns the unbiased base 2 exponent of the given floating-point value.
def isqrt(value : Int::Primitive)Source
Calculates the integer square root of value.
def ldexp(value : Float32, exp : Int32) : Float32Source
Multiplies the given floating-point value by 2 raised to the power exp.
def ldexp(value : Float64, exp : Int32) : Float64Source
Multiplies the given floating-point value by 2 raised to the power exp.
def ldexp(value, exp)Source
Multiplies the given floating-point value by 2 raised to the power exp.
def lgamma(value : Float32)Source
Calculates the logarithmic gamma of value.
Math.lgamma(2.96)
is equivalent to
Math.log(Math.gamma(2.96).abs)
def lgamma(value : Float64) : Float64Source
Calculates the logarithmic gamma of value.
Math.lgamma(2.96)
is equivalent to
Math.log(Math.gamma(2.96).abs)
def lgamma(value) : Float64Source
Calculates the logarithmic gamma of value.
Math.lgamma(2.96)
is equivalent to
Math.log(Math.gamma(2.96).abs)
def log(value, base)Source
Calculates the logarithm of value to the given base.
def log(value : Complex) : ComplexSource
Calculates the natural logarithm of value.
require "complex" Math.log(4 + 2.i) # => 1.4978661367769956 + 0.4636476090008061i
def log10(value : Complex) : ComplexSource
Calculates the logarithm of value to base 10.
require "complex" Math.log10(4 + 2.i) # => 0.6505149978319906 + 0.20135959813668655i
def log10(value)Source
Calculates the logarithm of value to base 10.
def log1p(value)Source
Calculates the natural logarithm of 1 plus value.
def log2(value : Complex) : ComplexSource
Calculates the logarithm of value to base 2.
require "complex" Math.log2(4 + 2.i) # => 2.1609640474436813 + 0.6689021062254881i
def logb(value)Source
def max(value1 : Float64, value2 : Float64) : Float64Source
Returns the greater of value1 and value2.
def max(value1, value2)Source
Returns the greater of value1 and value2.
def min(value1 : Float64, value2 : Float64) : Float64Source
Returns the smaller of value1 and value2.
def min(value1, value2)Source
Returns the smaller of value1 and value2.
def scalbn(value, exp)Source
def sin(value)Source
Calculates the sine of value, measured in radians.
def sinh(value)Source
Calculates the hyperbolic sine of value.
def sqrt(value : BigInt) : BigFloatSource
Calculates the square root of value.
require "big" Math.sqrt(1_000_000_000_000.to_big_i * 1_000_000_000_000.to_big_i) # => 1000000000000.0
def sqrt(value : BigFloat) : BigFloatSource
Calculates the square root of value.
require "big" Math.sqrt(1_000_000_000_000.to_big_f * 1_000_000_000_000.to_big_f) # => 1000000000000.0
def sqrt(value : BigRational) : BigFloatSource
Calculates the square root of value.
require "big" Math.sqrt(1_000_000_000_000.to_big_r * 1_000_000_000_000.to_big_r) # => 1000000000000.0
def sqrt(value : Complex) : ComplexSource
Calculates the square root of value. Inspired by the following blog post of Pavel Panchekha on floating point precision.
require "complex" Math.sqrt(4 + 2.i) # => 2.0581710272714924 + 0.48586827175664565i
Although the imaginary number is defined as i = sqrt(-1), calling Math.sqrt with a negative number will return -NaN. To obtain the result in the complex plane, Math.sqrt must be called with a complex number.
Math.sqrt(-1.0) # => -NaN Math.sqrt(-1.0 + 0.0.i) # => 0.0 + 1.0i
def tan(value)Source
Calculates the tangent of value, measured in radians.
def tanh(value)Source
Calculates the hyperbolic tangent of value.
© 2012–2021 Manas Technology Solutions.
Licensed under the Apache License, Version 2.0.
https://crystal-lang.org/api/1.2.1/Math.html