// runtime/math.el — Float math, integer utilities, and numeric conversions.
//
// Implements the math/float surface from el-compiler/runtime/legacy/el_runtime.c
// (lines 303–305 for el_abs/max/min, lines 4725–4771 for float/format ops)
// in pure El, using seed primitives.
//
// Seed primitives consumed:
//   __sqrt_f(f: Float)             -> Float
//   __log_f(f: Float)              -> Float
//   __ln_f(f: Float)               -> Float
//   __sin_f(f: Float)              -> Float
//   __cos_f(f: Float)              -> Float
//   __pi_f()                       -> Float
//   __float_to_str(f: Float)       -> String
//   __str_to_float(s: String)      -> Float
//   __int_to_str(n: Int)           -> String
//   __str_to_int(s: String)        -> Int

// ---------------------------------------------------------------------------
// Integer math — el_abs, el_max, el_min.
//
// Matches legacy el_abs, el_max, el_min (lines 303–305).
// ---------------------------------------------------------------------------

// el_abs — absolute value of an integer.
fn el_abs(n: Int) -> Int {
    if n < 0 { return -n }
    return n
}

// el_max — larger of two integers.
fn el_max(a: Int, b: Int) -> Int {
    if a > b { return a }
    return b
}

// el_min — smaller of two integers.
fn el_min(a: Int, b: Int) -> Int {
    if a < b { return a }
    return b
}

// ---------------------------------------------------------------------------
// Float math — thin wrappers over seed primitives.
//
// Matches legacy math_sqrt, math_log, math_ln, math_sin, math_cos, math_pi
// (lines 4766–4771).
// ---------------------------------------------------------------------------

// math_sqrt — square root.
fn math_sqrt(f: Float) -> Float {
    return __sqrt_f(f)
}

// math_log — base-10 logarithm.
fn math_log(f: Float) -> Float {
    return __log_f(f)
}

// math_ln — natural logarithm.
fn math_ln(f: Float) -> Float {
    return __ln_f(f)
}

// math_sin — sine (radians).
fn math_sin(f: Float) -> Float {
    return __sin_f(f)
}

// math_cos — cosine (radians).
fn math_cos(f: Float) -> Float {
    return __cos_f(f)
}

// math_pi — the constant π.
fn math_pi() -> Float {
    return __pi_f()
}

// ---------------------------------------------------------------------------
// Float conversions — float_to_str, int_to_float, float_to_int, str_to_float.
//
// Matches legacy float_to_str, int_to_float, float_to_int, str_to_float
// (lines 4725–4762).
// ---------------------------------------------------------------------------

// float_to_str — format a float using %g (shortest exact representation).
// Matches legacy float_to_str() → snprintf "%g".
fn float_to_str(f: Float) -> String {
    return __float_to_str(f)
}

// int_to_float — convert an integer to a float.
// Matches legacy int_to_float() → (double)(int64_t)n.
fn int_to_float(n: Int) -> Float {
    return __int_to_float(n)
}

// float_to_int — truncate a float to an integer (toward zero).
// Matches legacy float_to_int() → (int64_t)el_to_float(f).
fn float_to_int(f: Float) -> Int {
    return __float_to_int(f)
}

// str_to_float — parse a float from a string. Returns 0.0 on failure.
// Matches legacy str_to_float() → strtod(str, NULL).
fn str_to_float(s: String) -> Float {
    return __str_to_float(s)
}

// ---------------------------------------------------------------------------
// format_float — format a float to a fixed number of decimal places.
//
// decimals is clamped to [0, 30]. Matches legacy format_float() → snprintf "%.*f".
// ---------------------------------------------------------------------------

fn format_float(f: Float, decimals: Int) -> String {
    let d: Int = decimals
    if d < 0  { d = 0 }
    if d > 30 { d = 30 }
    // Delegate to seed; the seed exposes __format_float(f, d) -> String.
    // This matches snprintf(buf, 128, "%.*f", d, v) in the legacy runtime.
    return __format_float(f, d)
}

// ---------------------------------------------------------------------------
// decimal_round — round a float to d decimal places (half-away-from-zero).
//
// Matches legacy decimal_round():
//   mul = pow(10, d)
//   r = (v >= 0 ? floor(v*mul + 0.5) : -floor(-v*mul + 0.5)) / mul
//
// We implement pow(10, d) via a loop (d <= 15, so at most 15 multiplications).
// ---------------------------------------------------------------------------

// _pow10 — 10^n as a Float for n in [0, 15].
fn _pow10(n: Int) -> Float {
    let result: Float = 1.0
    let i: Int = 0
    while i < n {
        result = result * 10.0
        i = i + 1
    }
    return result
}

// _floor_f — floor of a float: largest integer <= f.
// Uses __float_to_int (truncation) with correction for negative non-integers.
fn _floor_f(f: Float) -> Float {
    let t: Int = __float_to_int(f)
    let tf: Float = __int_to_float(t)
    // if f was negative and not already an integer, subtract 1
    if f < 0.0 {
        if tf > f {
            return tf - 1.0
        }
    }
    return tf
}

fn decimal_round(f: Float, decimals: Int) -> Float {
    let d: Int = decimals
    if d < 0  { d = 0 }
    if d > 15 { d = 15 }
    let mul: Float = _pow10(d)
    if f >= 0.0 {
        return _floor_f(f * mul + 0.5) / mul
    }
    return 0.0 - _floor_f((0.0 - f) * mul + 0.5) / mul
}