First of all, we can remove Currency
from the question, because the two functions that you use don't have Currency
overloads. The value is converted to an IEEE754 floating point value and then follows the same path as your Double
code.
Let's look at RoundTo
first of all. It is quick to check, using the debugger, or an additional Writeln
that RoundTo(d,0) = 534
. Why is that?
Well, the documentation for RoundTo
says:
Rounds a floating-point value to a specified digit or power of ten using "Banker's rounding".
Indeed in the implementation of RoundTo
we see that the rounding mode is temporarily switched to TRoundingMode.rmNearest
before being restored to its original value. The rounding mode only applies when the value is exactly half way between two integers. Which is precisely the case we have here.
So Banker's rounding applies. Which means that when the value is exactly half way between two integers, the rounding algorithm chooses the adjacent even integer.
So it makes sense that RoundTo(534.5,0) = 534
, and equally you can check that RoundTo(535.5,0) = 536
.
Understanding FormatFloat
is quite a different matter. Quite frankly its behaviour is somewhat opaque. It performs an ad hoc rounding in code that differs for different platforms. For instance it is assembler on 32 bit Windows, but Pascal on 64 bit Windows. The overall approach appears to be to take the mantissa of the floating point value, convert it to an integer, convert that to text digits, and then perform the rounding based on those text digits. No respect is paid to the current rounding mode when the rounding is performed, and the algorithm appears to implement the round half away from zero policy. However, even that is not implemented robustly for all possible floating point values. It works correctly for your value, but for values with more digits in the mantissa the algorithm breaks down.
In fact it is fairly well known that the Delphi RTL routines for converting between floating point values and text are fundamentally broken by design. There are no routines in the Delphi RTL that can correctly convert from text to float, or from float to text. In fact, I have recently implemented my own conversion routines, that do this correctly, based on existing open source code used by other language runtimes. One of these days I will get around to publishing this code for use by others.
I'm not sure what your exact needs are, but if you are wishing to exert some control over rounding, then you can do so if you take charge of the rounding. Whilst RoundTo
always uses Banker's rounding, you can instead use Round
which uses the current rounding mode. This will allow you to perform the round using the rounding algorithm of your choice (by calling SetRoundMode
), and then you can convert the rounded value to text. That's the key. Keep the value in an arithmetic type, perform the rounding, and only convert to text at the very last moment, after the correct rounding has been applied.
FormatFloat
number is evaluated in assembly code. A bit difficult to debug. Since the last Delphi version gives the same result in 64-bit mode, I tracked it down to functionSysUtils.ExtToDecimal
. It boils down to that if the last digit is 5 or more, its rounded up. – Rincon