Fixed point math

[savage]

When I used trunc it gave me slight incorrect values converting back, but maybe that's ok for you.

[Legolas]

Comparing C and Pascal results, all seems ok. I have preferred to use trunc because AFAIK it should be faster than round, at least on delphi/win32. On fpc/arm it should be faster too, I suppose :think:

[pziko]

I think Round will be much faster (twice?) than Trunc because Trunc has to reset the FPU. Try each a couple of million times in a loop and see.

[Mirage]

Round() much faster.
I also thought that Trunc() faster then Round() and now have to change a lot of code.

[michalis]

Calling Trunc is doing exactly what the C code does. In C, typecasting float to integer causes automatic truncing (rounding to nearest integer towards zero, this is exactly what the Trunc in Pascal does).

BTW, what speed differences do you guys get with Delphi/win32 between Round and Trunc ?

I tested with FPC 2.0.4, Linux, i386, and got

Test Single:
Trunc time:       4.35
Round time:       3.37
Test Double:
Trunc time:       4.58
Round time:       3.37
Test Extended:
Trunc time:       5.82
Round time:       5.08

which means that Round is indeed faster, but not terribly (and it matters only if you really do an awful lot of these calls, so it does not necessarily matter).

[Legolas]

I think Round will be much faster (twice?) than Trunc because Trunc has to reset the FPU. Try each a couple of million times in a loop and see.

Uhm... I'm working on ARM cpu, where the FPU is not present. I'm wondering about the speed in this case :think:

[Sly]

These might do a fair chunk of what you need. I've been playing around recently with fixed point math in C using templated classes. It is easier when the precision is the same for both fixed point numbers, but there are calculations for when both fixed point numbers have different precisions and you want the result in a third precision.

Edit: The FixedToInt function went missing, and the IntToFixed function had a typo.

type
  Fixed = Integer;

const
  Prec = 12;

function IntToFixed(Value: Integer): Fixed;
begin
  IntToFixed := Value shl Prec;
end;

function FixedToInt(Value: Fixed): Integer;
begin
  FixedToInt := Value shr Prec;
end;

function FloatToFixed(Value: Single): Fixed;
begin
  FloatToFixed := Round(Value * (1 shl Prec));
end;

function FixedToFloat(Value: Fixed): Single;
begin
  { Multiply by 1.0 to convert to floating point before the divide }
  FixedToFloat := (Value * 1.0) / ((1 shl Prec) * 1.0);
end;

function FixedAdd(A, B: Fixed): Fixed;
begin
  FixedAdd := A + B;
end;

function FixedSub(A, B: Fixed): Fixed;
begin
  FixedSub := A - B;
end;

function FixedMul(A, B: Fixed): Fixed;
begin
  FixedMul := (A * B) shr Prec;
end;

function FixedDiv(A, B: Fixed): Fixed;
begin
  FixedDiv := (A shl Prec) / B;
end;

[Mirage]

Uhm... I'm working on ARM cpu, where the FPU is not present. I'm wondering about the speed in this case :think:

In that case Trunc() may be faster. It needs testing.

[Legolas]

Sly: thanks a lot! That's gold for me

[Sly]

I hope they help. They were coded in my head as I haven't actually done fixed-point in Pascal before (only done it in C). So I hope they work.