module std::math;

fn int128 __divti3(int128 a, int128 b) @extern("__divti3") @weak @nostrip
{
	int128 sign_a = a >> 127; // -1 : 0
	int128 sign_b = b >> 127; // -1 : 0
	uint128 unsigned_a = (uint128)(a ^ sign_a) + (-sign_a);
	uint128 unsigned_b = (uint128)(b ^ sign_b) + (-sign_b);
	sign_a ^= sign_b; // quotient sign
	return __udivti3(unsigned_a, unsigned_b) @inline ^ sign_a + (-sign_a);
}

macro uint128 @__udivmodti4(uint128 a, uint128 b, bool $return_rem)
{
	Int128bits n = { .all = a };
	Int128bits d = { .all = b };
	Int128bits q @noinit;
	Int128bits r @noinit;
	uint sr;
	if (n.high == 0)
	{
		if (d.high == 0)
		{
			$if $return_rem:
				return n.low % d.low;
			$else
				return n.low / d.low;
			$endif
		}
		$if $return_rem:
			return n.low;
		$else
			return 0;
		$endif
	}
	if (d.low == 0)
	{
		if (d.high == 0)
		{
			$if $return_rem:
				return n.high % d.low;
			$else
				return n.high / d.low;
			$endif
		}
		if (n.low == 0)
		{
			$if $return_rem:
				r.high = n.high % d.high;
				r.low = 0;
				return r.all;
			$else
				return n.high / d.high;
			$endif
		}
		if (d.high & (d.high - 1) == 0) // d is pot
		{
			$if $return_rem:
				r.low = n.low;
				r.high = n.high & (d.high - 1);
				return r.all;
			$else
				return (uint128)(n.high >> $$ctz(d.high));
			$endif
		}
		sr = (uint)$$clz(d.high) - (uint)$$clz(n.high);
		// 0 <= sr <= n_udword_bits - 2 or sr large
		if (sr > 64 - 2)
		{
			$if $return_rem:
				return n.all;
			$else
				return 0;
			$endif
		}
		sr++;
		// 1 <= sr <= n_udword_bits - 1
		// q.all = n.all << (n_utword_bits - sr);
		q.low = 0;
		q.high = n.low << (64 - sr);
		r.high = n.high >> sr;
		r.low = (n.high << (64 - sr)) | (n.low >> sr);
	}
	else // d.s.low != 0
	{
		if (d.high == 0)
		{
			if (d.low & (d.low - 1) == 0) // if d is a power of 2
			{
				$if $return_rem:
					return (uint128)(n.low & (d.low - 1));
				$else
					if (d.low == 1) return n.all;
					sr = (uint)$$ctz(d.low);
					q.high = n.high >> sr;
					q.low = (n.high << (64 - sr)) | (n.low >> sr);
					return q.all;
			   $endif
			}
			sr = 1 + 64 + (uint)$$clz(d.low) - (uint)$$clz(n.high);
			// 2 <= sr <= n_utword_bits - 1
			// q.all = n.all << (n_utword_bits - sr);
			// r.all = n.all >> sr;
			switch
			{
				case sr == 64:
					q.low = 0;
					q.high = n.low;
					r.high = 0;
					r.low = n.high;
				case sr < 64:
					q.low = 0;
					q.high = n.low << (64 - sr);
					r.high = n.high >> sr;
					r.low = (n.high << (64 - sr)) | (n.low >> sr);
				default: // n_udword_bits + 1 <= sr <= n_utword_bits - 1
					q.low = n.low << (128 - sr);
					q.high = (n.high << (128 - sr)) | (n.low >> (sr - 64));
					r.high = 0;
					r.low = n.high >> (sr - 64);
			}
		}
		else
		{
			sr = (uint)$$clz(d.high) - (uint)$$clz(n.high);
			// 0 <= sr <= n_udword_bits - 1 or sr large
			if (sr > 64 - 1)
			{
				$if $return_rem:
					return n.all;
				$else
					return 0;
				$endif
			}

			sr++;
			// 1 <= sr <= n_udword_bits
			// q.all = n.all << (n_utword_bits - sr);
			// r.all = n.all >> sr;
			q.low = 0;
			if (sr == 64)
			{
				q.high = n.low;
				r.high = 0;
				r.low = n.high;
			}
			else
			{
				r.high = n.high >> sr;
				r.low = (n.high << (64 - sr)) | (n.low >> sr);
				q.high = n.low << (64 - sr);
			}
		}
	}
	// Not a special case
	// q and r are initialized with:
	// q.all = n.all << (128 - sr);
	// r.all = n.all >> sr;
	// 1 <= sr <= n_utword_bits - 1
	uint carry = 0;
	for (; sr > 0; sr--)
	{
		// r:q = ((r:q)  << 1) | carry
		r.high = (r.high << 1) | (r.low  >> (64 - 1));
		r.low  = (r.low  << 1) | (q.high >> (64 - 1));
		q.high = (q.high << 1) | (q.low  >> (64 - 1));
		q.low  = (q.low  << 1) | carry;
		// carry = 0;
		// if (r.all >= d.all)
		// {
		//     r.all -= d.all;
		//      carry = 1;
		// }
		int128 s = (int128)(d.all - r.all - 1) >> (128 - 1);
		carry = (uint)(s & 1);
		r.all -= d.all & s;
	}
	$if $return_rem:
		return r.all;
	$else
		return (q.all << 1) | carry;
	$endif
}

fn uint128 __umodti3(uint128 n, uint128 d) @extern("__umodti3") @weak @nostrip
{
	return @__udivmodti4(n, d, true);
}

fn uint128 __udivti3(uint128 n, uint128 d) @extern("__udivti3") @weak @nostrip
{
	return @__udivmodti4(n, d, false);
}

fn int128 __modti3(int128 a, int128 b) @extern("__modti3") @weak @nostrip
{
	int128 sign = b >> 127;
	uint128 unsigned_b = (uint128)(b ^ sign) + (-sign);
	sign = a >> 127;
	uint128 unsigned_a = (uint128)(a ^ sign) + (-sign);

	return __umodti3(unsigned_a, unsigned_b) ^ sign + (-sign);
}

union Int128bits @private
{
	struct
	{
		ulong low;
		ulong high;
	}
	uint128 all;
}

fn uint128 __lshrti3(uint128 a, uint b) @extern("__lshrti3") @weak @nostrip
{
	Int128bits result;
	result.all = a;
	if (b >= 64)
	{
		result.low = result.high >> (b - 64);
		result.high = 0;
	}
	else
	{
		if (b == 0) return a;
		result.low = (result.high << (64 - b)) | (result.low >> b);
		result.high  = result.high >> b;
	}
	return result.all;
}

fn int128 __ashrti3(int128 a, uint b) @extern("__ashrti3") @weak @nostrip
{
	Int128bits result;
	result.all = a;
	if (b >= 64)
	{
		result.low = result.high >> (b - 64);
		result.high = result.high >> 63;
	}
	else
	{
		if (b == 0) return a;
		result.low = result.high << (64 - b) | (result.low >> b);
		result.high  = result.high >> b;
	}
	return result.all;
}

fn int128 __ashlti3(int128 a, uint b) @extern("__ashlti3") @weak @nostrip
{
	Int128bits result;
	result.all = a;
	if (b >= 64)
	{
		result.low = 0;
		result.high = result.low << (b - 64);
	}
	else
	{
		if (b == 0) return a;
		result.high = (result.high << b) | (result.low >> (64 - b));
		result.low  = result.low << b;
	}
	return result.all;
}

// Returns: a * b

fn int128 __mulddi3(ulong a, ulong b) @private
{
	Int128bits r;
	const ulong LOWER_MASK = 0xffff_ffff;
	r.low = (a & LOWER_MASK) * (b & LOWER_MASK);
	ulong t = r.low >> 32;
	r.low &= LOWER_MASK;
	t += (a >> 32) * (b & LOWER_MASK);
	r.low += (t & LOWER_MASK) << 32;
	r.high = t >> 32;
	t = r.low >> 32;
	r.low &= LOWER_MASK;
	t += (b >> 32) * (a & LOWER_MASK);
	r.low += (t & LOWER_MASK) << 32;
	r.high += t >> 32;
	r.high += (a >> 32) * (b >> 32);
	return r.all;
}

fn int128 __multi3(int128 a, int128 b) @extern("__multi3") @weak @nostrip
{
	Int128bits x = { .all = a };
	Int128bits y = { .all = b };
	Int128bits r = { .all = __mulddi3(x.low, y.low) };
	r.high += x.high * y.low + x.low * y.high;
	return r.all;
}

fn float __floattisf(int128 a) @extern("__floattisf") @weak @nostrip => float_from_i128(float, a);
fn double __floattidf(int128 a) @extern("__floattidf") @weak @nostrip => float_from_i128(double, a);
fn float __floatuntisf(uint128 a) @extern("__floatuntisf") @weak @nostrip => float_from_u128(float, a);
fn double __floatuntidf(uint128 a) @extern("__floatuntidf") @weak @nostrip => float_from_u128(double, a);
fn uint128 __fixunsdfti(double a) @weak @extern("__fixunsdfti") @nostrip => fixuint(a);
fn uint128 __fixunssfti(float a) @weak @extern("__fixunssfti") @nostrip => fixuint(a);
fn int128 __fixdfti(double a) @weak @extern("__fixdfti") @nostrip => fixint(a);
fn int128 __fixsfti(float a) @weak @extern("__fixsfti") @nostrip => fixint(a);


macro float_from_i128($Type, a) @private
{
	var $Rep;
	$switch ($Type)
		$case double:
			$Rep = ulong;
			const MANT_DIG = DOUBLE_MANT_DIG;
			const SIGNIFICANT_BITS = 52;
			const EXP_BIAS = 1023;
			const MANTISSA_MASK = 0xFFFFF_FFFF_FFFFu64;
			const SIGN_BIT = 1u64 << 63;
		$case float:
			$Rep = uint;
			const MANT_DIG = FLOAT_MANT_DIG;
			const EXP_BIAS = 127;
			const SIGNIFICANT_BITS = 23;
			const MANTISSA_MASK = 0x7F_FFFFu32;
			const SIGN_BIT = 1u32 << 31;
		$case float16:
			$Rep = ushort;
			const MANT_DIG = HALF_MANT_DIG;
		$case float128:
			$Rep = uint128;
			const MANT_DIG = QUAD_MANT_DIG;
	$endswitch
	if (a == 0) return ($Type)0;
	// Grab and remove sign.
	int128 sign = a >> 127;
	a = (a ^ sign) - sign;
	int sd = 128 - (int)$$clz(a); // digits
	int e = sd - 1; // exponent
	if (sd > MANT_DIG)
	{
		switch (sd)
		{
			case MANT_DIG + 1:
				a <<= 1;
			case MANT_DIG + 2:
				break;
			default:
				a = (a >> (sd - (MANT_DIG + 2)))
					| (uint128)((a & ((uint128)(-1) >> ((128 + MANT_DIG + 2) - sd))) != 0);
		}
		a |= (uint128)((a & 4) != 0);
		a++;
		a >>= 2;
		if (a & (1i128 << MANT_DIG))
		{
			a >>= 1;
			e++;
		}
	}
	else
	{
		a <<= (MANT_DIG - sd);
	}
	return bitcast((($Rep)sign & SIGN_BIT) | ((($Rep)e + ($Rep)EXP_BIAS) << SIGNIFICANT_BITS) | (($Rep)a & ($Rep)MANTISSA_MASK), $Type);
}

macro float_from_u128($Type, a) @private
{
	var $Rep;
	$switch ($Type)
		$case double:
			$Rep = ulong;
			const MANT_DIG = DOUBLE_MANT_DIG;
			const SIGNIFICANT_BITS = 52;
			const EXP_BIAS = 1023;
			const MANTISSA_MASK = 0xFFFFF_FFFF_FFFFu64;
		$case float:
			$Rep = uint;
			const MANT_DIG = FLOAT_MANT_DIG;
			const EXP_BIAS = 127;
			const SIGNIFICANT_BITS = 23;
			const MANTISSA_MASK = 0x7F_FFFFu32;
		$case float16:
			$Rep = ushort;
			const MANT_DIG = HALF_MANT_DIG;
		$case float128:
			$Rep = uint128;
			const MANT_DIG = QUAD_MANT_DIG;
	$endswitch
	if (a == 0) return ($Type)0;
	int sd = 128 - (int)$$clz(a); // digits
	int e = sd - 1; // exponent
	if (sd > MANT_DIG)
	{
		switch (sd)
		{
			case MANT_DIG + 1:
				a <<= 1;
			case MANT_DIG + 2:
				break;
			default:
				a = (a >> (sd - (MANT_DIG + 2)))
					| (uint128)((a & ((uint128)(-1) >> ((128 + MANT_DIG + 2) - sd))) != 0);
		}
		a |= (uint128)((a & 4) != 0);
		a++;
		a >>= 2;
		if (a & (1i128 << MANT_DIG))
		{
			a >>= 1;
			e++;
		}
	}
	else
	{
		a <<= (MANT_DIG - sd);
	}
	return bitcast(((($Rep)e + ($Rep)EXP_BIAS) << SIGNIFICANT_BITS) | (($Rep)a & ($Rep)MANTISSA_MASK), $Type);
}


macro fixuint(a) @private
{
	var $Rep;
	$switch ($typeof(a))
		$case double:
			$Rep = ulong;
			const EXPONENT_BITS = 11;
			const SIGNIFICANT_BITS = 52;
		$case float:
			$Rep = uint;
			const EXPONENT_BITS = 8;
			const SIGNIFICANT_BITS = 23;
		$case float16:
			$Rep = ushort;
			const EXPONENT_BITS = 5;
			const SIGNIFICANT_BITS = 10;
		$case float128:
			$Rep = uint128;
			const EXPONENT_BITS = 15;
			const SIGNIFICANT_BITS = 112;
	$endswitch
	const $Rep MAX_EXPONENT = ($Rep)1 << EXPONENT_BITS - 1u;
	const $Rep EXPONENT_BIAS = MAX_EXPONENT >> 1u;
	const $Rep ONE_REP =EXPONENT_BIAS << SIGNIFICANT_BITS;
	const $Rep SIGN_BIT = ($Rep)1 << (EXPONENT_BITS + SIGNIFICANT_BITS);
	const $Rep ABS_MASK = SIGN_BIT - 1u;
	const $Rep IMPLICIT_BIT = ($Rep)1 << SIGNIFICANT_BITS;
	const $Rep SIGNIFICANT_MASK = IMPLICIT_BIT - 1u;
	const $Rep EXPONENT_MASK = ABS_MASK ^ SIGNIFICANT_MASK;
	const $Rep QUIET_BIT = IMPLICIT_BIT >> 1;
	const $Rep QNAN_REP = EXPONENT_MASK | QUIET_BIT;
	const $Rep INF_REP = EXPONENT_MASK;

	$Rep rep = bitcast(a, $Rep);
	$Rep abs = rep & ABS_MASK;
	int sign = rep & SIGN_BIT ? -1 : 1;
	int exponent = (int)((abs >> SIGNIFICANT_BITS) - EXPONENT_BIAS);
	$Rep significand = (abs & SIGNIFICANT_MASK) | IMPLICIT_BIT;
	if (sign == -1 || exponent < 0) return 0u128;
	if ((uint)exponent >= uint128.sizeof * 8) return ~0u128;
	if (exponent < SIGNIFICANT_BITS) return (uint128)significand >> (SIGNIFICANT_BITS - exponent);
	return (uint128)significand << (exponent - SIGNIFICANT_BITS);
}

macro fixint(a) @private
{
	var $Rep;
	$switch ($typeof(a))
		$case double:
			$Rep = ulong;
			const EXPONENT_BITS = 11;
			const SIGNIFICANT_BITS = 52;
		$case float:
			$Rep = uint;
			const EXPONENT_BITS = 8;
			const SIGNIFICANT_BITS = 23;
		$case float16:
			$Rep = ushort;
			const EXPONENT_BITS = 5;
			const SIGNIFICANT_BITS = 10;
		$case float128:
			$Rep = uint128;
			const EXPONENT_BITS = 15;
			const SIGNIFICANT_BITS = 112;
	$endswitch
	const $Rep MAX_EXPONENT = ($Rep)1 << EXPONENT_BITS - 1u;
	const $Rep EXPONENT_BIAS = MAX_EXPONENT >> 1u;
	const $Rep ONE_REP = EXPONENT_BIAS << SIGNIFICANT_BITS;
	const $Rep SIGN_BIT = ($Rep)1 << (EXPONENT_BITS + SIGNIFICANT_BITS);
	const $Rep ABS_MASK = SIGN_BIT - 1u;
	const $Rep IMPLICIT_BIT = ($Rep)1 << SIGNIFICANT_BITS;
	const $Rep SIGNIFICANT_MASK = IMPLICIT_BIT - 1u;
	const $Rep EXPONENT_MASK = ABS_MASK ^ SIGNIFICANT_MASK;
	const $Rep QUIET_BIT = IMPLICIT_BIT >> 1;
	const $Rep QNAN_REP = EXPONENT_MASK | QUIET_BIT;
	const $Rep INF_REP = EXPONENT_MASK;

	$Rep rep = bitcast(a, $Rep);
	$Rep abs = rep & ABS_MASK;
	int sign = rep & SIGN_BIT ? -1 : 1;
	int exponent = (int)((abs >> SIGNIFICANT_BITS) - EXPONENT_BIAS);
	$Rep significand = (abs & SIGNIFICANT_MASK) | IMPLICIT_BIT;
	if (exponent < 0) return 0;
	if ((uint)exponent >= uint128.sizeof * 8) return sign == 1 ? int128.max : int128.min;

	if (exponent < SIGNIFICANT_BITS) return sign * ((int128)significand >> (SIGNIFICANT_BITS - exponent));
	return sign * ((int128)significand << (exponent - SIGNIFICANT_BITS));
}