Delphi SetRoundMode: gets sets part of the 8087 control word (related: GetRoundMode and TFPURoundingMode)

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:

• Delphi 2007:
  • [Wayback] Math.TFPURoundingMode Enumeration
  • [Wayback] Math.GetRoundMode Function
  • [Wayback] Math.SetRoundMode Function
• Delphi 2009:
  • [Wayback] Math.TFPUPrecisionMode Enumeration
  • [Wayback] Math.GetPrecisionMode Function
  • [Wayback] Math.SetPrecisionMode Function
  • [Wayback] Math.TFPURoundingMode Enumeration
  • [Wayback] Math.GetRoundMode Function
  • [Wayback] Math.SetRoundMode Function
• Delphi 2010:
  • [Wayback] Math.TFPUException – RAD Studio VCL Reference
  • [Wayback] Math.TFPUExceptionMask – RAD Studio VCL Reference
  • [Wayback] Math.TFPUPrecisionMode – RAD Studio VCL Reference
  • [Wayback] Math.TFPURoundingMode – RAD Studio VCL Reference
  • [Wayback] Math.ClearExceptions – RAD Studio VCL Reference
  • [Wayback] Math.GetExceptionMask – RAD Studio VCL Reference
  • [Wayback] Math.SetExceptionMask – RAD Studio VCL Reference
  • [Wayback] Math.GetPrecisionMode – RAD Studio VCL Reference
  • [Wayback] Math.SetPrecisionMode – RAD Studio VCL Reference
  • [Wayback] Math.GetRoundMode – RAD Studio VCL Reference
  • [Wayback] Math.SetRoundMode – RAD Studio VCL Reference
• Delphi XE:
  • [Wayback] Math.TFPUException – XE API Documentation
  • [Wayback] Math.TFPUExceptionMask – XE API Documentation
  • [Wayback] Math.TFPUPrecisionMode – XE API Documentation
  • [Wayback] Math.TFPURoundingMode – XE API Documentation
  • [Wayback] Math.ClearExceptions – XE API Documentation
  • [Wayback] Math.GetExceptionMask – XE API Documentation
  • [Wayback] Math.SetExceptionMask – XE API Documentation
  • [Wayback] Math.GetPrecisionMode – XE API Documentation
  • [Wayback] Math.SetPrecisionMode – XE API Documentation
  • [Wayback] Math.GetRoundMode – XE API Documentation
  • [Wayback] Math.SetRoundMode – XE API Documentation
• Delphi XE2: the System namespace got prepended, x64 support added and a rudimentary page [Wayback] Floating-Point Rounding Issues – RAD Studio XE2 added
  • [Wayback] Floating point precision control (Delphi for x64) – RAD Studio XE2: $EXCESSPRECISION
  • [Wayback] System.GetMXCSR – XE2 API Documentation
  • [Wayback] System.SetMXCSR – XE2 API Documentation
  • [Wayback] System.ResetMXCSR – XE2 API Documentation
  • [Wayback] System.Math.TFPUException – XE2 API Documentation
  • [Wayback] System.Math.TFPUExceptionMask – XE2 API Documentation
  • [Wayback] System.Math.TFPUPrecisionMode – XE2 API Documentation
  • [Wayback] System.Math.TFPURoundingMode – XE2 API Documentation
  • [Wayback] System.Math.TSSEException – XE2 API Documentation
  • [Wayback] System.Math.TSSEExceptionMask – XE2 API Documentation
  • There is no TSSEPrecisionMode
  • [Wayback] System.Math.TSSERoundingMode – XE2 API Documentation
  • [Wayback] System.Math.ClearExceptions – XE2 API Documentation
  • [Wayback] System.Math.GetExceptionMask – XE2 API Documentation
  • [Wayback] System.Math.SetExceptionMask – XE2 API Documentation
  • [Wayback] System.Math.ClearFPUExceptions – XE2 API Documentation
  • [Wayback] System.Math.GetFPUExceptionMask – XE2 API Documentation
  • [Wayback] System.Math.SetFPUExceptionMask – XE2 API Documentation
  • [Wayback] System.Math.ClearSSEExceptions – XE2 API Documentation
  • [Wayback] System.Math.GetSSEExceptionMask – XE2 API Documentation
  • [Wayback] System.Math.SetSSEExceptionMask – XE2 API Documentation
  • There is no SetSSEPrecisionMode
  • There is no GetSSEPrecisionMode
  • [Wayback] System.Math.GetSSERoundMode – XE2 API Documentation
  • [Wayback] System.Math.SetSSERoundMode – XE2 API Documentation
  • [Wayback] System.Math.GetPrecisionMode – XE2 API Documentation
  • [Wayback] System.Math.SetPrecisionMode – XE2 API Documentation
  • [Wayback] System.Math.GetRoundMode – XE2 API Documentation
  • [Wayback] System.Math.SetRoundMode – XE2 API Documentation

–jeroen