I thought I had written about this a long time ago, as Math.SetRoundMode (and now System.Math.SetRoundMode) has been introduced since at least Delphi 2007. There are also related GetRoundMode and TFPURoundingMode.
Delphi 2009 also introduced TFPUPrecisionMode, GetPrecisionMode and SetPrecisionMode.
Delphi 2010 also introduced TFPUException, TFPUExceptionMask, TFPUPrecisionMode, TFPURoundingMode, ClearExceptions, GetExceptionMask, and SetExceptionMask.
Delphi XE2 introduced namespaces, so prepended the unit Math with the namespace System. to become unit System.Math. It also introduced $EXCESSPRECISION (for x64), GetMXCSR, SetMXCSR, ResetMXCSR, ClearFPUExceptions, TSSEException, TSSEExceptionMask, GetSSEExceptionMask, SetSSEExceptionMask, ClearSSEExceptions, TSSERoundingMode, GetSSERoundMode, SetSSERoundMode.
The documentation basically only had formatting changes. This is the most important part of SetRoundMode:
function SetRoundMode(const RoundMode: TFPURoundingMode): TFPURoundingMode;
…
Call SetRoundingMode to specify how the FPU handles rounding issues. The rounding mode can be any of the following values:
|
Value
|
Meaning
|
|
rmNearest
|
Rounds to the closest value.
|
|
rmDown
|
Rounds toward negative infinity.
|
|
rmUp
|
Rounds toward positive infinity.
|
|
rmTruncate
|
Truncates the value, rounding positive numbers down and negative numbers up.
|
This is the most important bit of SetPrecisionMode:
function SetPrecisionMode(const Precision: TFPUPrecisionMode): TFPUPrecisionMode;
…
Call SetPrecisionMode to specify the level of precision that the FPU (floating-point unit) uses for floating-point calculations. The precision control mode can be any of the following values:
|
Value
|
Meaning
|
|
pmSingle
|
single precision
|
|
pmReserved
|
not used
|
|
pmDouble
|
double precision
|
|
pmExtended
|
extended precision
|
SetPrecisionMode returns the previous precision control mode.
Both are functions, so so they return the previous value which you can use to set it back later: this is important as it is a process wide. SetPrecisionMode documents this, but SetRoundMode does not!
Global side effects and avoiding them
Since SetRoundMode and SetPrecisionMode set the 8087 CW (and on XE2 and up SetMXCSR), it means all usual Set8087CW caveats apply: changing the global 8087 CW setting impacts all running code, which means that threads, DLLs (especially ones written in other languages), etc might malfunction. You can find some of the caveat effects on my bog by searching for [Wayback] Set8087CW site:wiert.me – Google Search.
If you want to avoid global side effects, you might try the solution in [Wayback] c# – What is the equivalent of Math.Round() with MidpointRounding.AwayFromZero in Delphi? – Stack Overflow by [Wayback] Andreas Rejbrand.
On MXCSR
[Wayback/Archive.is] SSE Instruction Set (not sure why Embarcadero used this as reference material from their docwiki, but hey, Intel documentation is likely outdated):
SSE — MXCSR
The MXCSR register is a 32-bit register containing flags for control and status information regarding SSE instructions. As of SSE3, only bits 0-15 have been defined.
| Pnemonic |
Bit Location |
Description |
| FZ |
bit 15 |
Flush To Zero |
| R+ |
bit 14 |
Round Positive |
| R- |
bit 13 |
Round Negative |
| RZ |
bits 13 and 14 |
Round To Zero |
| RN |
bits 13 and 14 are 0 |
Round To Nearest |
| PM |
bit 12 |
Precision Mask |
| UM |
bit 11 |
Underflow Mask |
| OM |
bit 10 |
Overflow Mask |
| ZM |
bit 9 |
Divide By Zero Mask |
| DM |
bit 8 |
Denormal Mask |
| IM |
bit 7 |
Invalid Operation Mask |
| DAZ |
bit 6 |
Denormals Are Zero |
| PE |
bit 5 |
Precision Flag |
| UE |
bit 4 |
Underflow Flag |
| OE |
bit 3 |
Overflow Flag |
| ZE |
bit 2 |
Divide By Zero Flag |
| DE |
bit 1 |
Denormal Flag |
| IE |
bit 0 |
Invalid Operation Flag |
FZ mode causes all underflowing operations to simply go to zero. This saves some processing time, but loses precision.
The R+, R-, RN, and RZ rounding modes determine how the lowest bit is generated. Normally, RN is used.
PM, UM, MM, ZM, DM, and IM are masks that tell the processor to ignore the exceptions that happen, if they do. This keeps the program from having to deal with problems, but might cause invalid results.
DAZ tells the CPU to force all Denormals to zero. A Denormal is a number that is so small that FPU can’t renormalize it due to limited exponent ranges. They’re just like normal numbers, but they take considerably longer to process. Note that not all processors support DAZ.
PE, UE, ME, ZE, DE, and IE are the exception flags that are set if they happen, and aren’t unmasked. Programs can check these to see if something interesting happened. These bits are “sticky”, which means that once they’re set, they stay set forever until the program clears them. This means that the indicated exception could have happened several operations ago, but nobody bothered to clear it.
DAZ wasn’t available in the first version of SSE. Since setting a reserved bit in MXCSR causes a general protection fault, we need to be able to check the availability of this feature without causing problems. To do this, one needs to set up a 512-byte area of memory to save the SSE state to, using fxsave, and then one needs to inspect bytes 28 through 31 for the MXCSR_MASK value. If bit 6 is set, DAZ is supported, otherwise, it isn’t.
Architectures Software Developer’s Manual: Intel® 64 and IA-32 includes supporting processors programming environment and architecture.
[Wayback] Intel® 64 and IA-32 Architectures Developer’s Manual: Vol. 1
[Wayback]
https://web.archive.org/web/20130603170547/http://www.intel.com/content/dam/www/public/us/en/documents/manuals/64-ia-32-architectures-software-developer-vol-1-manual.pdf
Documentation links
Some of the documentation links (that regrettably do not explain what happens behind the scenes with the 8087 CW) are these:
–jeroen
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