How does Delphi round Currency during multiplication

Question

rate : Currency;
mod1 : Currency;
mod2 : Currency;
mod_rate : Currency;

rate := 29.90;
mod1 := 0.95;
mod2 := 1.39;

mod_rate := rate * mod1 * mod2;

If you perform this calculation on a calculator you get a value of 39.45295. Since Delphi's Currency datatype is only precise to 4 decimals it internally rounds the value. My testing indicates that it uses Banker's rounding so that mod_rate should contain a value of 39.4530, however in this particular case it truncates to 39.4529.

I have 40,000 of these calculations and all are correct except the above. Here is an example that rounds up:

rate := 32.25;
mod1 := 0.90;
mod2 := 1.15;

This equals 33.37875 on a calculator and according to Banker's rounding would go to 33.3788, which is what Delphi does.

Could someone shed some light as to what Delphi is doing here?

Answer 1

Currency calculations takes place in the fpu with extended precision, even though the currency itself is a 64 bit integer value.

The problem you have is with floating point binary representation, rather than rounding errors. You can see the floating point representation of 39.45295 here: What is the exact value of a floating-point variable?

39.45295 = + 39.45294 99999 99999 99845 67899 95771 03240 88111 51981 35375 97656 25

The extended precision value is below 39.45295, hence the rounding downwards.

Use a decimal arithmetic library instead to avoid these kind of errors.

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To see that the floating point arithmetic is performed in the fpu for currency calculations, here is a disassembly:

mod_rate := rate * mod1 * mod2;
0041D566 DF2D20584200     fild qword ptr [$00425820]
0041D56C DF2D28584200     fild qword ptr [$00425828]
0041D572 DEC9             fmulp st(1)
0041D574 DF2D30584200     fild qword ptr [$00425830]
0041D57A DEC9             fmulp st(1)
0041D57C D835C4D54100     fdiv dword ptr [$0041d5c4]
0041D582 DF3D38584200     fistp qword ptr [$00425838]
0041D588 9B               wait 

fmulp and fdiv are done with extended precision. If integer operations had been used, the instructions would have been fimul and fidiv.