public static UFix16 Lerp(UFix16 left, UFix16 right, ushort fraction)
{
var tempOut = left._value * ((1 << 16) - fraction);
tempOut += (long)right._value * fraction;
tempOut >>= 16;
var result = (uint)tempOut;
return(*(UFix16 *)&result);
}
public static UFix16 Lerp(UFix16 left, UFix16 right, uint fraction)
{
var tempOut = (long)left._value * (0 - fraction);
tempOut += (long)right._value * fraction;
tempOut >>= 32;
var result = tempOut;
return(*(UFix16 *)&result);
}
private static UFix16 Divide(UFix16 left, UFix16 right, out bool overflow)
{
overflow = false;
if (right == Zero)
{
throw new DivideByZeroException();
}
uint a = *(uint *)&left, b = *(uint *)&right;
//var result = ((ulong)a <<16) / ((ulong)b<<16);
//result >>=16;
ulong remainder = a;
ulong divider = b;
ulong quotient = 0u;
var bitPos = 17;
while ((divider & 0xF) is 0 && bitPos >= 4)
{
divider >>= 4;
bitPos -= 4;
}
while (remainder is not 0 && bitPos >= 0)
{
// Shift remainder as much as we can without overflowing
var shift = (int)Clz((uint)remainder);
if (shift > bitPos)
{
shift = bitPos;
}
remainder <<= shift;
bitPos -= shift;
var div = remainder / divider;
remainder %= divider;
quotient += div << bitPos;
var mask = 0x1FFFFFFFFu >> bitPos--;
if ((div & ~mask) is not 0)
{
overflow = true;
}
remainder <<= 1;
}
quotient++;
var result = quotient >> 1;
return(overflow ? MaxValue : *(UFix16 *)&result);
}
private static UFix16 Subtract(UFix16 left, UFix16 right, out bool overflow)
{
overflow = false;
var l = *(uint *)&left;
var r = *(uint *)&right;
var result = l - r;
if (r > l)
{
overflow = true;
}
return(overflow ? MinValue : Raw(result));
}
private static UFix16 Add(UFix16 left, UFix16 right, out bool overflow)
{
overflow = false;
var l = *(uint *)&left;
var r = *(uint *)&right;
var result = l + r;
if (result < l || result < r)
{
overflow = true;
}
return(overflow ? MaxValue : Raw(result));
}
private static UFix16 Multiply(UFix16 left, UFix16 right, out bool overflow)
{
overflow = false;
var product = (ulong)*(uint *)&left * *(uint *)&right;
// The upper 16 bits should all be the same (the sign).
var upper = product >> 48;
if (upper is not 0)
{
overflow = true;
}
var result = (int)(product >> 16);
var temp = *(UFix16 *)&result;
result += (int)(product & 0x8000) >> 15;
return(overflow ? MaxValue : *(UFix16 *)&result);
}
public static UFix16 Sqrt(UFix16 value)
{
var num = *(uint *)&value;
var result = 0u;
var bit = 0u;
byte n;
// Many numbers will be less than 15, so
// this gives a good balance between time spent
// in if vs. time spent in the while loop
// when searching for the starting value.
bit = (num & 0xFFF00000) != 0 ?
1u << 30 :
1u << 18;
while (bit > num)
{
bit >>= 2;
}
// The main part is executed twice, in order to avoid
// using 64 bit values in computations.
for (n = 0; n < 2; n++)
{
// First we get the top 24 bits of the answer.
while (bit != 0)
{
if (num >= result + bit)
{
num -= result + bit;
result = (result >> 1) + bit;
}
else
{
result >>= 1;
}
bit >>= 2;
}
if (n == 0)
{
// Then process it again to get the lowest 8 bits.
if (num > 65535)
{
// The remainder 'num' is too large to be shifted left
// by 16, so we have to add 1 to result manually and
// adjust 'num' accordingly.
// num = a - (result + 0.5)^2
// = num + result^2 - (result + 0.5)^2
// = num - result - 0.5
num -= result;
num = (num << 16) - 0x8000;
result = (result << 16) + 0x8000;
}
else
{
num <<= 16;
result <<= 16;
}
bit = 1 << 14;
}
}
// Finally, if next bit would have been 1, round the result upwards.
if (num > result)
{
result++;
}
return(new UFix16()
{
_value = result
});
}
public static UFix16 Divide(UFix16 left, UFix16 right) => Divide(left, right, out _);
public static UFix16 Multiply(UFix16 left, UFix16 right) => Multiply(left, right, out _);
public static UFix16 Subtract(UFix16 left, UFix16 right) => Subtract(left, right, out _);
public static UFix16 Add(UFix16 left, UFix16 right) => Add(left, right, out _);
public static UFix16 CheckedDivide(UFix16 left, UFix16 right)
{
var value = Divide(left, right, out var overflow);
return(overflow ? throw new OverflowException() : value);
}