Opaque type that represents floating point number with 32 exponent bits and 52 significand bits.

Record type that represents inner content of WideFloat.

WideFloat representing 0.

zero == fromFloat 0 --> True

WideFloat representing 1.

one == fromFloat 1 --> True

Creates a WideFloat value from specified exponent and significand. If the absolute value of given significand is greater 2 or less than 1, n is added to the exponent and 2^(-n) is multiplied to the significand where n denote floor (logBase 2 (abs significand))

create { base2toThe1024exponent = 0, significand = 10 }
    == create { base2toThe1024exponent = 3, significand = 1.25 }
    --> True

Creates a WideFloat value from specified float

fromFloat (1024.0 * 1024.0 * 1024.0 * 1024.0)
    == create { base2toThe1024exponent = 40, significand = 1 }
    --> True

Returns True if the parameter is recognized as zero in floating point precision.

fromFloat 1
    |> add
        ( create
            { base2toThe1024exponent = 100
            , significand = 1
            }
        )
    |> differenceFrom
        ( create
            { base2toThe1024exponent = 100
            , significand = 1
            }
        )
    |> isZero --> True




fromFloat 1
    |> add
        ( create
            { base2toThe1024exponent = 50
            , significand = 1
            }
        )
    |> differenceFrom
        ( create
            { base2toThe1024exponent = 50
            , significand = 1
            }
        )
    |> isZero --> False

Returns True if the second parameter is larger than first one. Reads naturally when used with pipe operator(|>).

w1 : WideFloat
w1 =
    create
        { base2toThe1024exponent = 1000
        , significand = 1
        }


w2 : WideFloat
w2 =
    create
        { base2toThe1024exponent = 999
        , significand = 1.999
        }


w1 |> isLargerThan w2 --> True


w2 |> isLargerThan w1 --> False

Returns True if the second parameter is smaller than first one. Reads naturally when used with pipe operator(|>).

w1 : WideFloat
w1 =
    create
        { base2toThe1024exponent = 1000
        , significand = 1
        }


w2 : WideFloat
w2 =
    create
        { base2toThe1024exponent = 999
        , significand = 1.999
        }


w1 |> isSmallerThan w2 --> False


w2 |> isSmallerThan w1 --> True

Returns True if the value of first parameter is the same as the second parameter.

w1 : WideFloat
w1 =
    create
        { base2toThe1024exponent = 1000
        , significand = 1
        }


w2 : WideFloat
w2 =
    create
        { base2toThe1024exponent = 50
        , significand = 1
        }
        |> add
            (create
                { base2toThe1024exponent = 0
                , significand = 1
                }
            )


w1 |> isEqualTo w1 --> True


w1 |> isEqualTo w2 --> False

adds two WideFloats.

w1 : WideFloat
w1 =
    create
        { base2toThe1024exponent = 100
        , significand = 1
        }


w2 : WideFloat
w2 =
    create
        { base2toThe1024exponent = 99
        , significand = 1
        }


add w1 w2 --> create { base2toThe1024exponent = 100, significand = 1.5 }

Subtracts WideFloat value given as the first parameter from the second. Reads naturally when used with pipe(|>).

w1 : WideFloat
w1 =
    create
        { base2toThe1024exponent = 100
        , significand = 1
        }


w2 : WideFloat
w2 =
    create
        { base2toThe1024exponent = 99
        , significand = 1.75
        }


w1 |> differenceFrom w2 --> create { base2toThe1024exponent = 97, significand = 1.0 }

Multiplies two WideFloats.

w1 : WideFloat
w1 =
    create
        { base2toThe1024exponent = 100
        , significand = 1.5
        }


w2 : WideFloat
w2 =
    create
        { base2toThe1024exponent = 200
        , significand = 1.75
        }


multiply w1 w2 --> create { base2toThe1024exponent = 301, significand = 1.3125 }

multiplies a Float value on a WideFloat value.

w : WideFloat
w =
    create
        { base2toThe1024exponent = 100
        , significand = 1
        }


multiplyFloat 3 w --> create { base2toThe1024exponent = 101, significand = 1.5 }

Returns ratio between to WideFloats. Reads naturally when used with pipe(|>).

w1 : WideFloat
w1 =
    create
        { base2toThe1024exponent = 100
        , significand = 1
        }


w2 : WideFloat
w2 =
    create
        { base2toThe1024exponent = 99
        , significand = 1.6
        }


w1 |> dividedBy w2
    |> differenceFrom ( create { base2toThe1024exponent = 0, significand = 1.25})
    |> isSmallerThan ( create { base2toThe1024exponent = -30, significand = 1})--> True

Returns proportion of the first parameter in the sum of first and second parameters.

w1 : WideFloat
w1 =
    create
        { base2toThe1024exponent = 100
        , significand = 2 ^ (-511)
        }


w2 : WideFloat
w2 =
    create
        { base2toThe1024exponent = 99
        , significand = 1
        }


proportionOf w1 w2 == 2.0 / 3.0 --> True

Returns a record representing the inner content of WideFloat. Inverse function of create (when significand is specified properly).

content : { base2toThe1024exponent : Int, significand : Float}
content =
    { base2toThe1024exponent = 1000, significand = 1.234 }




getInternal (create content)
   == content --> True

Returns a String value representing the base 10 expression of a WideFloat. You can specify how many digits is shown after decimal point as the first parameter. The result may be a little less precise than other calcurations implemented in this module.

create
    { base2toThe1024exponent = 1
    , significand = 1
    }
    |> toString 3 --> "1.798e308"

If you want some other formats, you can make your original toString function using getInternal.