library MathLib
globals
    constant real Ln2 = 0.693147
    constant real Ln10 = 2.302585
endglobals

function SignInt takes integer z returns integer
    if z < 0 then
        return -1
    elseif z > 0 then
        return 1
    endif
    return 0
endfunction

function SignReal takes real z returns integer
    if z < 0. then
        return -1
    elseif z > 0. then
        return 1
    endif
    return 0
endfunction

function AbsInt takes integer z returns integer
    if z < 0 then
        return - z
    endif
    return z
endfunction

function AbsReal takes real z returns real
    if z < 0. then
        return - z
    endif
    return z
endfunction

function MaxInt takes integer z1, integer z2 returns integer
    if z1 > z2 then
        return z1
    endif
    return z2
endfunction

function MaxReal takes real z1, real z2 returns real
    if z1 > z2 then
        return z1
    endif
    return z2
endfunction

function MinInt takes integer z1, integer z2 returns integer
    if z1 < z2 then
        return z1
    endif
    return z2
endfunction

function MinReal takes real z1, real z2 returns real
    if z1 < z2 then
        return z1
    endif
    return z2
endfunction

function IsEven takes integer a returns boolean
    return a / 2 * 2 == a
endfunction

function IsOdd takes integer a returns boolean
    return a / 2 * 2 != a
endfunction

function IsDivisibleByN takes integer a, integer n returns boolean
    return a / n * n == a
endfunction

function IsNotDivisibleByN takes integer a, integer n returns boolean
    return a / n * n != a
endfunction

function ModuloN takes integer a, integer n returns integer
    return a - a / n * n
endfunction

function ModuloNPos takes integer a, integer n returns integer
    if a < 0 then
        return a - a / n * n + n
    endif
    return a - a / n * n
endfunction

function Floor takes real r returns integer
    local integer i = R2I(r)
    if r > 0. or not (i != r) then
        return i
    endif
    return i - 1
endfunction

function Ceil takes real r returns integer
    local integer i = R2I(r)
    if r < 0. or not (i != r) then
        return i
    endif
    return i + 1
endfunction

function R2Idown takes real r returns integer
    local integer i = Floor(r)
    if r - i == 1. then  // operation '==' rounds real numbers, so it helps to reduce imprecision in multiplying
        return i + 1
    endif
    return i
endfunction

function R2Iup takes real r returns integer
    local integer i = Floor(r)
    if r == i then  // operation '==' rounds real numbers, so it helps to reduce imprecision in multiplying
        return i
    endif
    return i + 1
endfunction

function R2Ieven takes real r returns integer
    local integer i = Floor(r)
    local real mid = i + 0.5
    if (r == mid and IsEven(i)) or r < mid then
        return i
    endif
    return i + 1
endfunction

function B2I takes boolean b returns integer
    if b then
        return 1
    endif
    return 0
endfunction

function B2Ineg takes boolean b returns integer
    if b then
        return 1
    endif
    return -1
endfunction

function I2B takes integer i returns boolean
    return i != 0
endfunction

function PowerN takes integer i, integer n returns integer
    local integer c = i
    if i == 0 or n < 0 then
        return 0
    elseif i == 1 or n == 0 then
        return 1
    elseif i == -1 then
        if IsEven(n) then
            return 1
        endif
        return -1
    endif
    loop
        exitwhen n == 1
        set c = c * i
        set n = n - 1
    endloop
    return c
endfunction

function Ln takes real r returns real
    // Source https://www.hiveworkshop.com/threads/snippet-natural-logarithm.108059/
    local real sum = 0.
    local real sign = 1.
    if r < 1. then
        set r = 1. / r
        set sign = -1.
    endif
    loop
        exitwhen r < bj_E
        set r = r / bj_E
        set sum = sum + 1.
    endloop
    return sign * (sum + (r - 1.) * (1. + 9. / (2. + r) + 9. / (1. + r * 2.) + 1. / r) / 8.)
endfunction

function Log2 takes real r returns real
    return Ln(r) / Ln2
endfunction

function Log10 takes real r returns real
    return Ln(r) / Ln10
endfunction

function Log takes real r, real base returns real
    return Ln(r) / Ln(base)
endfunction

endlibrary