# ============================================================================
# numeric.ludic — three "polish" numeric types, written in Ludic:
#   Huge.*    — idle/incremental big numbers (mantissa x 10^exponent)
#   Angle.*   — an auto-wrapping angle in radians
#   Percent.* — a value clamped to [0, 1]
#
# ludicc splices this file into any program that mentions `Huge.*`, `Angle.*`
# or `Percent.*`. It builds on the deterministic fixed-point `Math.*` namespace
# (spliced inline, no runtime of its own), so it works in a plain tool as well
# as a game. The namespaces (emit_call.ludic) alias each method to the matching
# `huge_*` / `angle_*` / `percent_*` function below.
# ============================================================================

# ---- Huge: mantissa + exponent, for idle-game magnitudes -------------------
#
# A value is m x 10^e with the mantissa m normalized to [1, 10) (or 0 for zero);
# e is an unbounded int, so magnitudes far past 1e308 are representable. The
# mantissa is a Q16.16 `fixed`, giving ~4 significant digits — this is a
# DISPLAY-SCALE number for showing 1.23e45, NOT a lockstep-exact value; keep it
# out of the deterministic simulation and use BigInt/Decimal when exactness
# matters.

const HUGE_ONE: fixed = 1.0
const HUGE_TEN: fixed = 10.0

property Huge { m: fixed = 0.0, e: int = 0 }

# normalize (mantissa, exponent) so the mantissa lands in [1, 10)
function huge_make(m: fixed, e: int) -> Huge {
  let h = new Huge
  if m == 0.0 { h.m = 0.0;  h.e = 0;  return h }
  var neg = false
  var mm = m
  if mm < 0.0 { neg = true;  mm = 0.0 - mm }
  var ee = e
  while mm >= HUGE_TEN { mm = mm / HUGE_TEN;  ee = ee + 1 }
  while mm < HUGE_ONE  { mm = mm * HUGE_TEN;  ee = ee - 1 }
  if neg { mm = 0.0 - mm }
  h.m = mm;  h.e = ee
  return h
}

# an int -> Huge (built via i64 so the whole int range normalizes cleanly)
function huge_from(value: int) -> Huge {
  if value == 0 { return huge_make(0.0, 0) }
  var neg = false
  var v: long = value
  if v < 0 { neg = true;  v = 0 - v }
  var e = 0
  var p: long = 1
  while p * 10 <= v { p = p * 10;  e = e + 1 }
  let raw: long = (v * 65536) / p          # v / 10^e in Q16.16 (in [1,10))
  let rawi: int = raw
  var m: fixed = as_fixed(rawi)
  if neg { m = 0.0 - m }
  return huge_make(m, e)
}

function huge_sign(a: Huge) -> int {
  if a.m > 0.0 { return 1 }
  if a.m < 0.0 { return -1 }
  return 0
}

function huge_neg(a: Huge) -> Huge { return huge_make(0.0 - a.m, a.e) }
function huge_mul(a: Huge, b: Huge) -> Huge {
  if a.m == 0.0 or b.m == 0.0 { return huge_make(0.0, 0) }
  return huge_make(a.m * b.m, a.e + b.e)
}

function huge_add(a: Huge, b: Huge) -> Huge {
  if a.m == 0.0 { return b }
  if b.m == 0.0 { return a }
  var big = a
  var small = b
  if b.e > a.e { big = b;  small = a }
  let diff = big.e - small.e
  if diff > 8 { return big }               # negligible at display precision
  var sm = small.m
  var k = 0
  while k < diff { sm = sm / HUGE_TEN;  k = k + 1 }
  return huge_make(big.m + sm, big.e)
}

function huge_sub(a: Huge, b: Huge) -> Huge { return huge_add(a, huge_neg(b)) }

function huge_cmp(a: Huge, b: Huge) -> int {
  let sa = huge_sign(a)
  let sb = huge_sign(b)
  if sa != sb { if sa > sb { return 1 };  return -1 }
  if sa == 0 { return 0 }
  var c = 0
  if a.e != b.e { if a.e > b.e { c = 1 } else { c = 0 - 1 } }
  else { if a.m > b.m { c = 1 } else { if a.m < b.m { c = 0 - 1 } else { c = 0 } } }
  if sa < 0 { c = 0 - c }
  return c
}

function huge_mantissa(a: Huge) -> fixed { return a.m }
function huge_exp(a: Huge) -> int { return a.e }

# scientific text like "1.23e45" (two-decimal mantissa); plain "0" for zero
function huge_str(a: Huge) -> pointer {
  if a.m == 0.0 { return "0" }
  var neg = ""
  var m = a.m
  if m < 0.0 { neg = "-";  m = 0.0 - m }
  var ip: int = floor(m)                   # 1..9
  let frac: fixed = m - fixed(ip)
  var dd: int = floor(frac * 100.0 + 0.5)  # round the two decimals to nearest
  var ex = a.e
  if dd >= 100 { dd = 0;  ip = ip + 1 }    # rounding carried into the ones place
  if ip >= 10 { ip = 1;  ex = ex + 1 }     # ...and on into the exponent
  var ds = string(dd)
  if dd < 10 { ds = "0" + ds }
  return neg + string(ip) + "." + ds + "e" + string(ex)
}

# ---- Angle: an auto-wrapping radian angle ----------------------------------

const ANGLE_PI:  fixed = 3.14159265
const ANGLE_TAU: fixed = 6.28318531

# wrap any radian value into the half-open range [-pi, pi)
function angle_wrap(a: fixed) -> fixed {
  var x = a
  while x >= ANGLE_PI { x = x - ANGLE_TAU }
  while x < 0.0 - ANGLE_PI { x = x + ANGLE_TAU }
  return x
}

function angle_from_degrees(d: fixed) -> fixed { return angle_wrap(Math.deg_to_rad(d)) }
function angle_to_degrees(a: fixed) -> fixed { return Math.rad_to_deg(a) }
function angle_sin(a: fixed) -> fixed { return Math.sin(a) }
function angle_cos(a: fixed) -> fixed { return Math.cos(a) }
function angle_add(a: fixed, b: fixed) -> fixed { return angle_wrap(a + b) }

# the shortest signed rotation from `a` to `b`, in [-pi, pi)
function angle_diff(a: fixed, b: fixed) -> fixed { return angle_wrap(b - a) }

# interpolate from `a` toward `b` along the shortest arc (t is a fixed 0..1)
function angle_lerp(a: fixed, b: fixed, t: fixed) -> fixed { return angle_wrap(a + angle_diff(a, b) * t) }

# ---- Percent: a value clamped to [0, 1] ------------------------------------

const PCT_ONE: fixed = 1.0

# clamp any fixed into [0, 1]
function percent_clamp(v: fixed) -> fixed {
  if v < 0.0 { return 0.0 }
  if v > PCT_ONE { return PCT_ONE }
  return v
}

# num / den as a clamped ratio (0 when den is 0)
function percent_of(num: fixed, den: fixed) -> fixed {
  if den == 0.0 { return 0.0 }
  return percent_clamp(num / den)
}

# linear interpolation a..b by a clamped t
function percent_lerp(a: fixed, b: fixed, t: fixed) -> fixed {
  let p = percent_clamp(t)
  return a + (b - a) * p
}

# value scaled by a clamped percent
function percent_apply(value: fixed, p: fixed) -> fixed { return value * percent_clamp(p) }