module Math

Extended Modules

Defined in:

big/big_float.cr
big/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

Instance Method Detail

def acos(value : Float32) #

Calculates the arc cosine of value.


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def acos(value : Float64) #

Calculates the arc cosine of value.


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def acos(value) #

Calculates the arc cosine of value.


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def acosh(value : Float32) #

Calculates the inverse hyperbolic cosine of value.


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def acosh(value : Float64) #

Calculates the inverse hyperbolic cosine of value.


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def acosh(value) #

Calculates the inverse hyperbolic cosine of value.


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def asin(value : Float32) #

Calculates the arc sine of value.


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def asin(value : Float64) #

Calculates the arc sine of value.


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def asin(value) #

Calculates the arc sine of value.


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def asinh(value : Float32) #

Calculates the inverse hyperbolic sine of value.


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def asinh(value : Float64) #

Calculates the inverse hyperbolic sine of value.


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def asinh(value) #

Calculates the inverse hyperbolic sine of value.


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def atan(value : Float32) #

Calculates the arc tangent of value.


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def atan(value : Float64) #

Calculates the arc tangent of value.


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def atan(value) #

Calculates the arc tangent of value.


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def atan2(y : Float32, x : Float32) #

Calculates the two-argument arc tangent of the ray from (0, 0) to (x, y).


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def atan2(y : Float64, x : Float64) #

Calculates the two-argument arc tangent of the ray from (0, 0) to (x, y).


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def atan2(y, x) #

Calculates the two-argument arc tangent of the ray from (0, 0) to (x, y).


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def atanh(value : Float32) #

Calculates the inverse hyperbolic tangent of value.


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def atanh(value : Float64) #

Calculates the inverse hyperbolic tangent of value.


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def atanh(value) #

Calculates the inverse hyperbolic tangent of value.


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def besselj(order : Int32, value : Float32) #

Calculates the cylindrical Bessel function of the first kind of value for the given order.


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def besselj(order : Int32, value : Float64) #

Calculates the cylindrical Bessel function of the first kind of value for the given order.


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def besselj(order, value) #

Calculates the cylindrical Bessel function of the first kind of value for the given order.


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def besselj0(value : Float32) #

Calculates the cylindrical Bessel function of the first kind of value for order 0.


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def besselj0(value : Float64) #

Calculates the cylindrical Bessel function of the first kind of value for order 0.


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def besselj0(value) #

Calculates the cylindrical Bessel function of the first kind of value for order 0.


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def besselj1(value : Float32) #

Calculates the cylindrical Bessel function of the first kind of value for order 1.


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def besselj1(value : Float64) #

Calculates the cylindrical Bessel function of the first kind of value for order 1.


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def besselj1(value) #

Calculates the cylindrical Bessel function of the first kind of value for order 1.


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def bessely(order : Int32, value : Float32) #

Calculates the cylindrical Bessel function of the second kind of value for the given order.


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def bessely(order : Int32, value : Float64) #

Calculates the cylindrical Bessel function of the second kind of value for the given order.


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def bessely(order, value) #

Calculates the cylindrical Bessel function of the second kind of value for the given order.


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def bessely0(value : Float32) #

Calculates the cylindrical Bessel function of the second kind of value for order 0.


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def bessely0(value : Float64) #

Calculates the cylindrical Bessel function of the second kind of value for order 0.


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def bessely0(value) #

Calculates the cylindrical Bessel function of the second kind of value for order 0.


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def bessely1(value : Float32) #

Calculates the cylindrical Bessel function of the second kind of value for order 1.


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def bessely1(value : Float64) #

Calculates the cylindrical Bessel function of the second kind of value for order 1.


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def bessely1(value) #

Calculates the cylindrical Bessel function of the second kind of value for order 1.


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def cbrt(value : Float32) #

Calculates the cubic root of value.


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def cbrt(value : Float64) #

Calculates the cubic root of value.


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def cbrt(value) #

Calculates the cubic root of value.


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def copysign(value1 : Float32, value2 : Float32) #

Returns the floating-point value with the magnitude of value1 and the sign of value2.


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def copysign(value1 : Float64, value2 : Float64) #

Returns the floating-point value with the magnitude of value1 and the sign of value2.


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def copysign(value1, value2) #

Returns the floating-point value with the magnitude of value1 and the sign of value2.


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def cos(value : Float32) #

Calculates the cosine of value, measured in radians.


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def cos(value : Float64) #

Calculates the cosine of value, measured in radians.


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def cos(value) #

Calculates the cosine of value, measured in radians.


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def cosh(value : Float32) #

Calculates the hyperbolic cosine of value.


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def cosh(value : Float64) #

Calculates the hyperbolic cosine of value.


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def cosh(value) #

Calculates the hyperbolic cosine of value.


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def erf(value : Float32) #

Calculates the error function of value.


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def erf(value : Float64) #

Calculates the error function of value.


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def erf(value) #

Calculates the error function of value.


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def erfc(value : Float32) #

Calculates 1 minus the error function of value.


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def erfc(value : Float64) #

Calculates 1 minus the error function of value.


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def erfc(value) #

Calculates 1 minus the error function of value.


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def exp(value : Float32) #

Calculates the exponential of value.


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def exp(value : Float64) #

Calculates the exponential of value.


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def exp(value : Complex) #

Calculates the exponential of value.

require "complex"

Math.exp(4 + 2.i) # => -22.720847417619233 + 49.645957334580565i

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def exp(value) #

Calculates the exponential of value.


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def exp2(value : Float32) #

Calculates 2 raised to the power value.


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def exp2(value : Float64) #

Calculates 2 raised to the power value.


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def exp2(value) #

Calculates 2 raised to the power value.


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def expm1(value : Float32) #

Calculates the exponential of value, minus 1.


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def expm1(value : Float64) #

Calculates the exponential of value, minus 1.


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def expm1(value) #

Calculates the exponential of value, minus 1.


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def frexp(value : Float32) #

Decomposes the given floating-point value into a normalized fraction and an integral power of two.


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def frexp(value : Float64) #

Decomposes the given floating-point value into a normalized fraction and an integral power of two.


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def frexp(value : BigFloat) #

Decomposes the given floating-point value into a normalized fraction and an integral power of two.


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def frexp(value) #

Decomposes the given floating-point value into a normalized fraction and an integral power of two.


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def gamma(value : Float32) #

Calculates the gamma function of value.

Note that #gamma(n) is same as fact(n - 1) for integer n > 0. However #gamma(n) returns float and can be an approximation.


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def gamma(value : Float64) #

Calculates the gamma function of value.

Note that #gamma(n) is same as fact(n - 1) for integer n > 0. However #gamma(n) returns float and can be an approximation.


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def gamma(value) #

Calculates the gamma function of value.

Note that #gamma(n) is same as fact(n - 1) for integer n > 0. However #gamma(n) returns float and can be an approximation.


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def hypot(value1 : Float32, value2 : Float32) #

Calculates the length of the hypotenuse from (0, 0) to (value1, value2).

Equivalent to

Math.sqrt(value1 ** 2 + value2 ** 2)

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def hypot(value1 : Float64, value2 : Float64) #

Calculates the length of the hypotenuse from (0, 0) to (value1, value2).

Equivalent to

Math.sqrt(value1 ** 2 + value2 ** 2)

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def hypot(value1, value2) #

Calculates the length of the hypotenuse from (0, 0) to (value1, value2).

Equivalent to

Math.sqrt(value1 ** 2 + value2 ** 2)

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def ilogb(value : Float32) #

Returns the unbiased base 2 exponent of the given floating-point value.


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def ilogb(value : Float64) #

Returns the unbiased base 2 exponent of the given floating-point value.


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def ilogb(value) #

Returns the unbiased base 2 exponent of the given floating-point value.


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def ldexp(value : Float32, exp : Int32) #

Multiplies the given floating-point value by 2 raised to the power exp.


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def ldexp(value : Float64, exp : Int32) #

Multiplies the given floating-point value by 2 raised to the power exp.


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def ldexp(value, exp) #

Multiplies the given floating-point value by 2 raised to the power exp.


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def lgamma(value : Float32) #

Calculates the logarithmic gamma of value.

Math.lgamma(2.96)

is equivalent to

Math.log(Math.gamma(2.96).abs)

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def lgamma(value : Float64) #

Calculates the logarithmic gamma of value.

Math.lgamma(2.96)

is equivalent to

Math.log(Math.gamma(2.96).abs)

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def lgamma(value) #

Calculates the logarithmic gamma of value.

Math.lgamma(2.96)

is equivalent to

Math.log(Math.gamma(2.96).abs)

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def log(value, base) #

Calculates the logarithm of value to the given base.


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def log(value : Float32) #

Calculates the natural logarithm of value.


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def log(value : Float64) #

Calculates the natural logarithm of value.


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def log(value : Complex) #

Calculates the natural logarithm of value.

require "complex"

Math.log(4 + 2.i) # => 1.4978661367769956 + 0.4636476090008061i

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def log(value) #

Calculates the natural logarithm of value.


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def log10(value : Float32) #

Calculates the logarithm of value to base 10.


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def log10(value : Float64) #

Calculates the logarithm of value to base 10.


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def log10(value : Complex) #

Calculates the logarithm of value to base 10.

require "complex"

Math.log10(4 + 2.i) # => 0.6505149978319906 + 0.20135959813668655i

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def log10(value) #

Calculates the logarithm of value to base 10.


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def log1p(value : Float32) #

Calculates the natural logarithm of 1 plus value.


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def log1p(value : Float64) #

Calculates the natural logarithm of 1 plus value.


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def log1p(value) #

Calculates the natural logarithm of 1 plus value.


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def log2(value : Float32) #

Calculates the logarithm of value to base 2.


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def log2(value : Float64) #

Calculates the logarithm of value to base 2.


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def log2(value : Complex) #

Calculates the logarithm of value to base 2.

require "complex"

Math.log2(4 + 2.i) # => 2.1609640474436813 + 0.6689021062254881i

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def log2(value) #

Calculates the logarithm of value to base 2.


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def logb(value : Float32) #

Returns the unbiased radix-independent exponent of the given floating-point value.

For Float32 and Float64 this is equivalent to #ilogb.


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def logb(value : Float64) #

Returns the unbiased radix-independent exponent of the given floating-point value.

For Float32 and Float64 this is equivalent to #ilogb.


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def logb(value) #

Returns the unbiased radix-independent exponent of the given floating-point value.

For Float32 and Float64 this is equivalent to #ilogb.


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def max(value1 : Float32, value2 : Float32) #

Returns the greater of value1 and value2.


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def max(value1 : Float64, value2 : Float64) #

Returns the greater of value1 and value2.


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def max(value1, value2) #

Returns the greater of value1 and value2.


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def min(value1 : Float32, value2 : Float32) #

Returns the smaller of value1 and value2.


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def min(value1 : Float64, value2 : Float64) #

Returns the smaller of value1 and value2.


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def min(value1, value2) #

Returns the smaller of value1 and value2.


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def pw2ceil(v) #

Computes the next highest power of 2 of v.

Math.pw2ceil(33) # => 64

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def scalbln(value : Float32, exp : Int64) #

Returns the floating-point value with its exponent raised by exp.

For Float32 and Float64 this is equivalent to #ldexp.


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def scalbln(value : Float64, exp : Int64) #

Returns the floating-point value with its exponent raised by exp.

For Float32 and Float64 this is equivalent to #ldexp.


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def scalbln(value, exp) #

Returns the floating-point value with its exponent raised by exp.

For Float32 and Float64 this is equivalent to #ldexp.


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def scalbn(value : Float32, exp : Int32) #

Returns the floating-point value with its exponent raised by exp.

For Float32 and Float64 this is equivalent to #ldexp.


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def scalbn(value : Float64, exp : Int32) #

Returns the floating-point value with its exponent raised by exp.

For Float32 and Float64 this is equivalent to #ldexp.


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def scalbn(value, exp) #

Returns the floating-point value with its exponent raised by exp.

For Float32 and Float64 this is equivalent to #ldexp.


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def sin(value : Float32) #

Calculates the sine of value, measured in radians.


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def sin(value : Float64) #

Calculates the sine of value, measured in radians.


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def sin(value) #

Calculates the sine of value, measured in radians.


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def sinh(value : Float32) #

Calculates the hyperbolic sine of value.


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def sinh(value : Float64) #

Calculates the hyperbolic sine of value.


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def sinh(value) #

Calculates the hyperbolic sine of value.


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def sqrt(value : Float32) #

Calculates the square root of value.


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def sqrt(value : Float64) #

Calculates the square root of value.


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def sqrt(value : BigInt) #

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

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def sqrt(value : BigFloat) #

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

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def sqrt(value : BigRational) #

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

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def sqrt(value : Complex) #

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

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def sqrt(value) #

Calculates the square root of value.


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def tan(value : Float32) #

Calculates the tangent of value, measured in radians.


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def tan(value : Float64) #

Calculates the tangent of value, measured in radians.


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def tan(value) #

Calculates the tangent of value, measured in radians.


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def tanh(value : Float32) #

Calculates the hyperbolic tangent of value.


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def tanh(value : Float64) #

Calculates the hyperbolic tangent of value.


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def tanh(value) #

Calculates the hyperbolic tangent of value.


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