Invalid floating point operation calling Trunc()

Question

I'm getting a (repeatable) floating point exception when i try to Trunc() a Real value.

e.g.:

Trunc(1470724508.0318);

In reality the actual code is more complex:

 ns: Real;
 v: Int64;

 ns := ((HighPerformanceTickCount*1.0)/g_HighResolutionTimerFrequency) * 1000000000;
 v := Trunc(ns);

But in the end it still boils down to:

Trunc(ARealValue);

Now, i cannot repeat it anywhere else - just at this one spot. Where it fails every time.

It's not voodoo

Fortunately computers are not magic. The Intel CPU performs very specific observable actions. So i should be able to figure out why the floating point operation fails.

Going into the CPU window

v := Trunc(ns)

fld qword ptr [ebp-$10]

This loads the 8-byte floating point value at ebp-$10 into floating point register ST0.

The bytes at memory address [ebp-$10] are:

0018E9D0: 6702098C 41D5EA5E    (as DWords)
0018E9D0: 41D5EA5E6702098C     (as QWords)
0018E9D0:   1470724508.0318    (as Doubles)

The call succeeds, and the floating point register the contains the appropriate value:

Next is the actual call to the RTL Trunc function:

call @TRUNC

Next is the guts of Delphi RTL's Trunc function:

@TRUNC:

sub esp,$0c
wait
fstcw word ptr [esp]       //Store Floating-Point Control Word on the stack
wait
fldcw word ptr [cwChop]    //Load Floating-Point Control Word
fistp qword ptr [esp+$04]  //Converts value in ST0 to signed integer
                           //stores the result in the destination operand
                             //and pops the stack (increments the stack pointer)
wait
fldcw word ptr [esp]       //Load Floating-Point Control Word
pop ecx
pop eax
pop edx
ret

Or i suppose i could have just pasted it from the rtl, rather than transcribing it from the CPU window:

const cwChop : Word = $1F32;

procedure       _TRUNC;
asm
        { ->    FST(0)   Extended argument       }
        { <-    EDX:EAX  Result                  }

        SUB     ESP,12
        FSTCW   [ESP]              //Store foating-control word in ESP
        FWAIT
        FLDCW   cwChop             //Load new control word $1F32
        FISTP   qword ptr [ESP+4]  //Convert ST0 to int, store in ESP+4, and pop the stack
        FWAIT
        FLDCW   [ESP]              //restore the FPCW
        POP     ECX
        POP     EAX
        POP     EDX
end;

The exception happens during the actual fistp operation.

fistp qword ptr [esp+$04]

At the moment of this call, the ST0 register will contains the same floating point value:

Note: The careful observer will note the value in the above screenshot doesn't match the first screenshot. That's because i took it on a different run. I'd rather not have to carefully redo all the constants in the question just to make them consistent - but trust me: it's the same when i reach the fistp instruction as it was after the fld instruction.

Leading up to it:

• sub esp,$0c: I watch it push the the stack down by 12 bytes
• fstcw word ptr [esp]: i watch it push $027F into the the current stack pointer
• fldcw word ptr [cwChop]: i watch the floating point control flags change
• fistp qword ptr [esp+$04]: and it's about to write the Int64 into the room it made on the stack

and then it crashes.

What can actually be going on here?

It happens with other values as well, it's not like there's something wrong with this particular floating point value. But i even tried to setup the test-case elsewhere.

Knowing that the 8-byte hex value of the float is: $41D5EA5E6702098C, i tried to contrive the setup:

var
    ns: Real;
    nsOverlay: Int64 absolute ns;
    v: Int64;
begin
   nsOverlay := $41d62866a2f270dc;
   v := Trunc(ns);
end;

Which gives:

nsOverlay := $41d62866a2f270dc;

mov [ebp-$08],$a2f270dc
mov [ebp-$04],$41d62866

v := Trunc(ns)

fld qword ptr [ebp-$08]
call @TRUNC

And at the point of the call to @trunc, the floating point register ST0 contains a value:

But the call does not fail. It only fails, every time in this one section of my code.

What could be possibly happening that is causing the CPU to throw an invalid floating point exception?

What is the value of cwChop before it loads the control word?

The value of cwChop looks to be correct before the load control word, $1F32. But after the load, the actual control word is wrong:

Bonus Chatter

The actual function that is failing is something to convert high-performance tick counts into nanoseconds:

function PerformanceTicksToNs(const HighPerformanceTickCount: Int64): Int64; 
//Convert high-performance ticks into nanoseconds
var
    ns: Real;
    v: Int64;
begin
    Result := 0;

    if HighPerformanceTickCount = 0 then
        Exit;

    if g_HighResolutionTimerFrequency = 0 then
        Exit;

    ns := ((HighPerformanceTickCount*1.0)/g_HighResolutionTimerFrequency) * 1000000000;

    v := Trunc(ns);
    Result := v;
end;

I created all the intermeidate temporary variables to try to track down where the failure is.

I even tried to use that as a template to try to reproduce it:

var
    i1, i2: Int64;
    ns: Real;
    v: Int64;
    vOver: Int64 absolute ns;
begin
    i1 := 5060170;
    i2 := 3429541;
    ns := ((i1*1.0)/i2) * 1000000000;
    //vOver := $41d62866a2f270dc;
    v := Trunc(ns);

But it works fine. There's something about when it's called during a DUnit unit test.

Floating Point control word flags

Delphi's standard control word: $1332:

$1332 = 0001 00 11 00 110010
                           0 ;Don't allow invalid numbers
                          1  ;Allow denormals (very small numbers)
                         0   ;Don't allow divide by zero
                        0    ;Don't allow overflow
                       1     ;Allow underflow
                      1      ;Allow inexact precision
                    0        ;reserved exception mask
                   0         ;reserved  
                11           ;Precision Control - 11B (Double Extended Precision - 64 bits)
             00              ;Rounding control - 
           0                 ;Infinity control - 0 (not used)

The Windows API required value: $027F

$027F = 0000 00 10 01 111111
                           1 ;Allow invalid numbers
                          1  ;Allow denormals (very small numbers)
                         1   ;Allow divide by zero
                        1    ;Allow overflow
                       1     ;Allow underflow
                      1      ;Allow inexact precision
                    1        ;reserved exception mask
                   0         ;reserved  
                10           ;Precision Control - 10B (double precision)
             00              ;Rounding control
           0                 ;Infinity control - 0 (not used)

The crChop control word: $1F32

$1F32 = 0001 11 11 00 110010
                           0 ;Don't allow invalid numbers
                          1  ;Allow denormals (very small numbers)
                         0   ;Don't allow divide by zero
                        0    ;Don't allow overflow
                       1     ;Allow underflow
                      1      ;Allow inexact precision
                    0        ;reserved exception mask
                   0         ;unused
                11           ;Precision Control - 11B (Double Extended Precision - 64 bits)
             11              ;Rounding Control
           1                 ;Infinity control - 1 (not used)
        000                ;unused 

The CTRL flags after loading $1F32: $1F72

$1F72 = 0001 11 11 01 110010
                           0 ;Don't allow invalid numbers
                          1  ;Allow denormals (very small numbers)
                         0   ;Don't allow divide by zero
                        0    ;Don't allow overflow
                       1     ;Allow underflow
                      1      ;Allow inexact precision
                    1        ;reserved exception mask
                   0         ;unused
                11           ;Precision Control - 11B (Double Extended Precision - 64 bits)
             11              ;Rounding control 
           1                 ;Infinity control - 1 (not used)
        00011                ;unused 

All the CPU is doing is turning on a reserved, unused, mask bit.

RaiseLastFloatingPointError()

If you're going to develop programs for Windows, you really need to accept the fact that floating point exceptions should be masked by the CPU, meaning you have to watch for them yourself. Like Win32Check or RaiseLastWin32Error, we'd like a RaiseLastFPError. The best i can come up with is:

procedure RaiseLastFPError();
var
    statWord: Word;
const
    ERROR_InvalidOperation = $01;
//  ERROR_Denormalized = $02;
    ERROR_ZeroDivide = $04;
    ERROR_Overflow = $08;
//  ERROR_Underflow = $10;
//  ERROR_InexactResult = $20;
begin
    {
        Excellent reference of all the floating point instructions.
        (Intel's architecture manuals have no organization whatsoever)
        http://www.plantation-productions.com/Webster/www.artofasm.com/Linux/HTML/RealArithmetica2.html

        Bits 0:5 are exception flags (Mask = $2F)
            0: Invalid Operation
            1: Denormalized - CPU handles correctly without a problem. Do not throw
            2: Zero Divide
            3: Overflow
            4: Underflow - CPU handles as you'd expect. Do not throw.
            5: Precision - Extraordinarily common. CPU does what you'd want. Do not throw
    }
    asm
        fwait                   //Wait for pending operations
        FSTSW statWord    //Store floating point flags in AX.
                                //Waits for pending operations. (Use FNSTSW AX to not wait.)
        fclex                   //clear all exception bits the stack fault bit,
                                //and the busy flag in the FPU status register
    end;

    if (statWord and $0D) <> 0 then
    begin
        //if (statWord and ERROR_InexactResult) <> 0 then raise EInexactResult.Create(SInexactResult)
        //else if (statWord and ERROR_Underflow) <> 0 then raise EUnderflow.Create(SUnderflow)}
        if (statWord and ERROR_Overflow) <> 0 then raise EOverflow.Create(SOverflow)
        else if (statWord and ERROR_ZeroDivide) <> 0 then raise EZeroDivide.Create(SZeroDivide)
        //else if (statWord and ERROR_Denormalized) <> 0 then raise EUnderflow.Create(SUnderflow)
        else if (statWord and ERROR_InvalidOperation) <> 0 then raise EInvalidOp.Create(SInvalidOp);
    end;
end;

A reproducible case!

I found a case, when Delphi's default floating point control word, that was the cause of an invalid floating point exception (although I never saw it before now because it was masked). Now that i'm seeing it, why is it happening! And it's reproducible:

procedure TForm1.Button1Click(Sender: TObject);
var
    d: Real;
    dover: Int64 absolute d;
begin
    d := 1.35715152325557E020;
//  dOver := $441d6db44ff62b68; //1.35715152325557E020
    d := Round(d); //<--floating point exception
    Self.Caption := FloatToStr(d);
end;

You can see that the ST0 register contains a valid floating point value. The floating point control word is $1372. There floating point exception flag are all clear:

And then, as soon as it executes, it's an invalid operation:

• IE (Invalid operation) flag is set
• ES (Exception) flag is set

I was tempted to ask this as another question, but it would be the exact same question - except this time calling Round().

Answer 1

Your latest update essentially asks a different question. It asks about the exception raised by this code:

procedure foo;
var
  d: Real;
  i: Int64;
begin
  d := 1.35715152325557E020;
  i := Round(d);
end;

This code fails because the job of Round() is to round d to the nearest Int64 value. But your value of d is greater than the largest possible value that can be stored in an Int64 and hence the floating point unit traps.