public static PackedVelocity ToReachHeight(int height, int gravity256)
{
// v^2 = u^2 + 2as
// v = 0 at top of jump
// 0 = u^2 + 2as
// u = sqrt(-2as)
// For fixed-point gravity and velocity (this is the old version):
//
// u*256 = sqrt(-2 (a*256)/256 s) * 256
// u*256 = sqrt(-2 (a*256) s) * 16
// Using fixed-point sqrt:
//
// u*256 = sqrt(-2 (a*256)/256 s) * 256
// u*256 = sqrt(-2 (a*256) s) * 16
// u*256 = FPSR(-2 (a*256) s)/65536 * 16
// u*256 = FPSR(-2 (a*256) s)/65536 * 16
// u*256 = FPSR(-2 (a*256) s) / 4096
// u*256 = FPSR(-2 (a*256) s) >> 12
int velocity256 = Fixed65536.Sqrt(-2 * gravity256 * height).value65536 >> 12;
// NOTE: TEMP: Validate that my maths is more-or-less correct (matches old code) -AR
Debug.Assert(System.Math.Abs(velocity256 - (int)System.Math.Round(System.Math.Sqrt(-2.0 * gravity256 * height) * 16)) < 10);
return(new PackedVelocity(velocity256));
}
// Based on https://github.com/chmike/fpsqrt
public static Fixed65536 Sqrt(Fixed65536 v)
{
if (v.value65536 < 0)
{
throw new InvalidOperationException();
}
uint r = (uint)v.value65536;
uint b = 0x40000000;
uint q = 0;
while (b > 0x40)
{
uint t = q + b;
if (r >= t)
{
r -= t;
q = t + b; // equivalent to q += 2*b
}
r <<= 1;
b >>= 1;
}
q >>= 8;
return(new Fixed65536((int)q));
}
/// <summary>Round up for positive values</summary>
public Fixed65536 PositiveRoundUp(Fixed65536 toNearest)
{
int tn = toNearest.value65536;
return(new Fixed65536(((value65536 + tn - 1) / tn) * tn));
}