module Math

Extended Modules

• Math

Defined in:

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 : BigFloat, value2 : BigFloat) : BigFloat

  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.

• #fma(value1 : Float32, value2 : Float32, value3 : Float32) : Float32

  Fused multiply-add; returns value1 * value2 + value3, performing a single rounding instead of two.

• #fma(value1 : Float64, value2 : Float64, value3 : Float64) : Float64

  Fused multiply-add; returns value1 * value2 + value3, performing a single rounding instead of two.

• #fma(value1, value2, value3)

  Fused multiply-add; returns value1 * value2 + value3, performing a single rounding instead of two.

• #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 : BigFloat) : Int64

  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 : BigFloat, exp : Int) : BigFloat

  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 : BigFloat) : BigFloat

  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 : Int::Primitive)

  Computes the smallest nonnegative power of 2 that is greater than or equal to v.

• #pw2ceil(v : BigInt) : BigInt

  Computes the smallest nonnegative power of 2 that is greater than or equal to v.

• #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 : BigFloat, exp : Int) : BigFloat

  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 : BigFloat, exp : Int) : BigFloat

  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

require "complex"

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

Math.fma(0.1, 10.0, -1.0) # => 5.551115123125783e-17
1.0 * 10.0 - 1.0          # => 0.0

Math.fma(0.1, 10.0, -1.0) # => 5.551115123125783e-17
1.0 * 10.0 - 1.0          # => 0.0

Math.fma(0.1, 10.0, -1.0) # => 5.551115123125783e-17
1.0 * 10.0 - 1.0          # => 0.0

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

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

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

Math.lgamma(2.96)

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

Math.lgamma(2.96)

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

Math.lgamma(2.96)

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

require "complex"

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

require "complex"

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

require "complex"

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

Math.pw2ceil(33) # => 64
Math.pw2ceil(64) # => 64
Math.pw2ceil(-5) # => 1

Math.pw2ceil(33) # => 64
Math.pw2ceil(64) # => 64
Math.pw2ceil(-5) # => 1

require "big"

Math.sqrt(1_000_000_000_000.to_big_i * 1_000_000_000_000.to_big_i) # => 1000000000000.0

require "big"

Math.sqrt(1_000_000_000_000.to_big_f * 1_000_000_000_000.to_big_f) # => 1000000000000.0

require "big"

Math.sqrt(1_000_000_000_000.to_big_r * 1_000_000_000_000.to_big_r) # => 1000000000000.0

require "complex"

Math.sqrt(4 + 2.i) # => 2.0581710272714924 + 0.48586827175664565.i

Math.sqrt(-1.0)         # => -NaN
Math.sqrt(-1.0 + 0.0.i) # => 0.0 + 1.0.i