anglais/lib/math.ang

PI := 3.14159265358979323
E := 2.718281828459045235360287471352

# abs(x)
# x: number
#   Get the absolute value of a number. If x is negative, the returned
#   value is positive and equal to `-x`. If x is positive or zero, the
#   returned value is x.
fn absf(x: float) -> float {
    # if the number is negative
    if x < 0.0 {
        # negate it so it's positive
        return -x
    }

    return x
}

fn absi(n: int) -> int {
    if n < 0 {
        -n
    } else {
        n
    }
}

DERIVE_DX := 0.00000001
fn derive(f: fn(float) -> float, x: float) -> float {
    return (f(x + DERIVE_DX) - f(x))/DERIVE_DX
}

NEWTONS_ACC := 0.000000000001
fn newtons(f: fn(float) -> float) -> float {
    pg := 0.0
    g := 1.0

    while absf(g - pg) > NEWTONS_ACC {
        pg = g
        g = pg - f(pg) / derive(f, pg)
    }

    return g
}

MAX_SQRT_DX := 0.0000001

# sqrt(x)
# x: number
#   Calculate the approximate square root using newton's method until
#   the accuracy has increased by less than the variable `MAX_SQRT_DX`.
fn sqrt(x: float) -> float {
    ng := x
    g := 1.0

    while absf(g - ng) > MAX_SQRT_DX {
        g = ng

        # create new guess
        ng = (g + x / g) / 2.0
    }

    g
}

# floor(x)
# x: number
#   Return the whole number part of the number. if x is a whole number,
#   the returned value is x. If x is not a whole number, the closest
#   whole number which is less than or equal to x is returned.


# ceil(x)
# x: number
#   Return the whole number part of the number. if x is a whole number,
#   the returned value is x. If x is not a whole number, the closest
#   whole number which is greater than or equal to x is returned.


# round(x)
# x: number
#   Return the closest whole number to the value x.
fn round(x: float) -> float {
    f := floor(x)

    if x - f > 0.5 {
        return f + 1.0
    }

    return f
}

# mod(x, n)
# x: number; any number
# n: number; the number to divide by
#   Return the rest from a division of x by n.
fn mod(x: float, n: float) -> float {
    if x == 0.0 {
        return 0.0
    }

    if x < 0.0 {
        while x + n <= 0.0 {
            x = x + n
        }
    } else {
        while x - n >= 0.0 {
            x = x - n
        }
    }

    return x
}

# sm_exp(x)
# x: number; any number between 0 and 1
#   Get an approximate value of e raised to the power of x.
#   This value is only reasonable if 0<x<1.
#   It is approximated using the taylor series of e**x.
SM_EXP_ACC := 0.00000000001
fn sm_exp(x: float) -> float {
    p_tot := 0.0
    tot := 1.0
    n := 1
    x_pow := x
    f := 1.0

    while absf(tot - p_tot) > SM_EXP_ACC {
        p_tot = tot
        t := x_pow / f
        tot = tot + t
        f = f * float(n+1)
        x_pow = x_pow * x
        n = n + 1
    }

    return tot
}

# exp(x)
# x: number; any number
#   Get an approximate value of e raised to the power of x.
fn exp(x: float) -> float {
    n := absf(x)
    tot := 1.0
    while n >= 1.0 {
        tot = tot * E
        n = n - 1.0
    }

    if n > 0.0 {
        tot = tot * sm_exp(n)
    }

    if x < 0.0 {
        1.0/tot
    } else {
        tot
    }
}

# ln(x)
# x: number; any number
#   Get the approximate value of the natural logarithm
#   This function uses newton's method to approximate.
LN_ACC := 0.0000000001
fn ln(x: float) -> float {
    pg := 0.0
    g := 1.0

    while absf(pg - g) > LN_ACC {
        pg = g
        g = pg + x / exp(pg) - 1.0
    }

    return g
}

# pow(x, p)
# x: number; any number. The base
# p: number; the value of the exponent
#   Raise any number to any power (x^p)
fn pow(x: float, p: float) -> float {
    return exp(p*ln(x))
}

# log(x, b)
# x: number; any number greater than 0
# b: number; any number as the base
#   Calculate the approximate value of the logarithm
#   of a with b as base.
LOG_ACC := 0.0000001
fn log(a: float, b: float) -> float {
    ln_b := ln(b)

    pg := 0.0
    g := 1.0

    while absf(g - pg) > LOG_ACC {
        pg = g
        g = pg - 1.0/ln_b - a/(ln_b*pow(b, pg))
    }

    return g
}

# sin(x)
# x: number; an angle in radians
#   Get the sine of an angle (in radians). https://en.wikipedia.org/wiki/Sine_and_cosine
#   TODO: use hashmap with precomputed values and linear interpolation
fn sin(x: float) -> float {
    f := 1.0
    x = mod(x, 2.0*PI)
    if x > PI {
        x = PI - x
        f = -1.0
    }

    # compute sine with a taylor series mock function of sine (valid between -pi and +pi)
    tot := x
    l := 1.0
    i := 1.0
    s := -1.0

    while i <= 19.0 {
        i = i + 2.0
        l = s * l * x / i / (i-1.0)

        tot = tot + l

        s = -s
    }

    return tot*f
}

# cos(x)
# x: number; an angle in radians
#   Get the cosine of an angle (in radians). https://en.wikipedia.org/wiki/Sine_and_cosine
fn cos(x: float) -> float {
    # todo
    0.0
}

# tan(x)
# x: number; an angle in radians
#   Get the tangent of an angle. https://en.wikipedia.org/wiki/Tangent
fn tan(x: float) -> float {
    # todo
    0.0
}

(E:, PI:, sqrt:, log:, ln:, exp:, pow:)