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x86 Disassembly/Floating Point Numbers

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x86 Disassembly

Floating Point Numbers

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This page will talk about how floating point numbers are used in assembly language constructs. This page will not talk about new constructs, it will not explain what the FPU instructions do, how floating point numbers are stored or manipulated, or the differences in floating-point data representations. However, this page will demonstrate briefly how floating-point numbers are used in code and data structures that we have already considered.

The x86 architecture does not have any registers specifically for floating point numbers, but it does have a special stack for them. The floating point stack is built directly into the processor, and has access speeds similar to those of ordinary registers. Notice that the FPU stack is not the same as the regular system stack.

Calling Conventions

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With the addition of the floating-point stack, there is an entirely new dimension for passing parameters and returning values. We will examine our calling conventions here, and see how they are affected by the presence of floating-point numbers. These are the functions that we will be assembling, using both GCC, and cl.exe: 

 __cdecl double MyFunction1(double x, double y, float z)
 {
 	return (x + 1.0) * (y + 2.0) * (z + 3.0);
 }
 
 __fastcall double MyFunction2(double x, double y, float z)
 {
 	return (x + 1.0) * (y + 2.0) * (z + 3.0);
 }
 
 __stdcall double MyFunction3(double x, double y, float z)
 {
 	return (x + 1.0) * (y + 2.0) * (z + 3.0);
 }


CDECL

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Here is the cl.exe assembly listing for MyFunction1: 

 PUBLIC	_MyFunction1
 PUBLIC	__real@3ff0000000000000
 PUBLIC	__real@4000000000000000
 PUBLIC	__real@4008000000000000
 EXTRN	__fltused:NEAR
 ;	COMDAT __real@3ff0000000000000
 CONST	SEGMENT
 __real@3ff0000000000000 DQ 03ff0000000000000r	; 1
 CONST	ENDS
 ;	COMDAT __real@4000000000000000
 CONST	SEGMENT
 __real@4000000000000000 DQ 04000000000000000r	; 2
 CONST	ENDS
 ;	COMDAT __real@4008000000000000
 CONST	SEGMENT
 __real@4008000000000000 DQ 04008000000000000r	; 3
 CONST	ENDS
 _TEXT	SEGMENT
 _x$ = 8							; size = 8
 _y$ = 16						; size = 8
 _z$ = 24						; size = 4
 _MyFunction1 PROC NEAR
 ; Line 2
 	push	ebp
 	mov	ebp, esp
 ; Line 3
 	fld	QWORD PTR _x$[ebp]
 	fadd	QWORD PTR __real@3ff0000000000000
 	fld	QWORD PTR _y$[ebp]
 	fadd	QWORD PTR __real@4000000000000000
 	fmulp	ST(1), ST(0)
 	fld	DWORD PTR _z$[ebp]
 	fadd	QWORD PTR __real@4008000000000000
 	fmulp	ST(1), ST(0)
 ; Line 4
 	pop	ebp
 	ret	0
 _MyFunction1 ENDP
 _TEXT	ENDS

Our first question is this: are the parameters passed on the stack, or on the floating-point register stack, or some place different entirely? Key to this question, and to this function is a knowledge of what fld and fstp do. fld (Floating-point Load) pushes a floating point value onto the FPU stack, while fstp (Floating-Point Store and Pop) moves a floating point value from ST0 to the specified location, and then pops the value from ST0 off the stack entirely. Remember that double values in cl.exe are treated as 8-byte storage locations (QWORD), while floats are only stored as 4-byte quantities (DWORD). It is also important to remember that floating point numbers are not stored in a human-readable form in memory, even if the reader has a solid knowledge of binary. Remember, these aren't integers. Unfortunately, the exact format of floating point numbers is well beyond the scope of this chapter.

x is offset +8, y is offset +16, and z is offset +24 from ebp. Therefore, z is pushed first, x is pushed last, and the parameters are passed right-to-left on the regular stack not the floating point stack. To understand how a value is returned however, we need to understand what fmulp does. fmulp is the "Floating-Point Multiply and Pop" instruction. It performs the instructions: 

ST1 := ST1 * ST0
FPU POP ST0

This multiplies ST(1) and ST(0) and stores the result in ST(1). Then, ST(0) is marked empty and stack pointer is incremented. Thus, contents of ST(1) are on the top of the stack. So the top 2 values are multiplied together, and the result is stored on the top of the stack. Therefore, in our instruction above, "fmulp ST(1), ST(0)", which is also the last instruction of the function, we can see that the last result is stored in ST0. Therefore, floating point parameters are passed on the regular stack, but floating point results are passed on the FPU stack.

One final note is that MyFunction2 cleans its own stack, as referenced by the ret 20 command at the end of the listing. Because none of the parameters were passed in registers, this function appears to be exactly what we would expect an STDCALL function would look like: parameters passed on the stack from right-to-left, and the function cleans its own stack. We will see below that this is actually a correct assumption.

For comparison, here is the GCC listing: 

 LC1:
 	.long	0
 	.long	1073741824
 	.align 8
 LC2:
 	.long	0
 	.long	1074266112
 .globl _MyFunction1
 	.def	_MyFunction1;	.scl	2;	.type	32;	.endef
 _MyFunction1:
 	pushl	%ebp
 	movl	%esp, %ebp
 	subl	$16, %esp
 	fldl	8(%ebp)
 	fstpl	-8(%ebp)
 	fldl	16(%ebp)
 	fstpl	-16(%ebp)
 	fldl	-8(%ebp)
 	fld1
 	faddp	%st, %st(1)
 	fldl	-16(%ebp)
 	fldl	LC1
 	faddp	%st, %st(1)
 	fmulp	%st, %st(1)
 	flds	24(%ebp)
 	fldl	LC2
 	faddp	%st, %st(1)
 	fmulp	%st, %st(1)
 	leave
 	ret
 	.align 8

This is a very difficult listing, so we will step through it (albeit quickly). 16 bytes of extra space is allocated on the stack. Then, using a combination of fldl and fstpl instructions, the first 2 parameters are moved from offsets +8 and +16, to offsets -8 and -16 from ebp. Seems like a waste of time, but remember, optimizations are off. fld1 loads the floating point value 1.0 onto the FPU stack. faddp then adds the top of the stack (1.0), to the value in ST1 ([ebp - 8], originally [ebp + 8]).

FASTCALL

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Here is the cl.exe listing for MyFunction2: 

 PUBLIC	@MyFunction2@20
 PUBLIC	__real@3ff0000000000000
 PUBLIC	__real@4000000000000000
 PUBLIC	__real@4008000000000000
 EXTRN	__fltused:NEAR
 ;	COMDAT __real@3ff0000000000000
 CONST	SEGMENT
 __real@3ff0000000000000 DQ 03ff0000000000000r	; 1
 CONST	ENDS
 ;	COMDAT __real@4000000000000000
 CONST	SEGMENT
 __real@4000000000000000 DQ 04000000000000000r	; 2
 CONST	ENDS
 ;	COMDAT __real@4008000000000000
 CONST	SEGMENT
 __real@4008000000000000 DQ 04008000000000000r	; 3
 CONST	ENDS
 _TEXT	SEGMENT
 _x$ = 8							; size = 8
 _y$ = 16						; size = 8
 _z$ = 24						; size = 4
 @MyFunction2@20 PROC NEAR
 ; Line 7
 	push	ebp
 	mov	ebp, esp
 ; Line 8
 	fld	QWORD PTR _x$[ebp]
 	fadd	QWORD PTR __real@3ff0000000000000
 	fld	QWORD PTR _y$[ebp]
 	fadd	QWORD PTR __real@4000000000000000
 	fmulp	ST(1), ST(0)
 	fld	DWORD PTR _z$[ebp]
 	fadd	QWORD PTR __real@4008000000000000
 	fmulp	ST(1), ST(0)
 ; Line 9
 	pop	ebp
 	ret	20					; 00000014H
 @MyFunction2@20 ENDP
 _TEXT	ENDS

We can see that this function is taking 20 bytes worth of parameters, because of the @20 decoration at the end of the function name. This makes sense, because the function is taking two double parameters (8 bytes each), and one float parameter (4 bytes each). This is a grand total of 20 bytes. We can notice at a first glance, without having to actually analyze or understand any of the code, that there is only one register being accessed here: ebp. This seems strange, considering that FASTCALL passes its regular 32-bit arguments in registers. However, that is not the case here: all the floating-point parameters (even z, which is a 32-bit float) are passed on the stack. We know this, because by looking at the code, there is no other place where the parameters could be coming from.

Notice also that fmulp is the last instruction performed again, as it was in the CDECL example. We can infer then, without investigating too deeply, that the result is passed at the top of the floating-point stack.

Notice also that x (offset [ebp + 8]), y (offset [ebp + 16]) and z (offset [ebp + 24]) are pushed in reverse order: z is first, x is last. This means that floating point parameters are passed in right-to-left order, on the stack. This is exactly the same as CDECL code, although only because we are using floating-point values.

Here is the GCC assembly listing for MyFunction2: 

 	.align 8
 LC5:
 	.long	0
 	.long	1073741824
 	.align 8
 LC6:
 	.long	0
 	.long	1074266112
 .globl @MyFunction2@20
 	.def	@MyFunction2@20;	.scl	2;	.type	32;	.endef
 @MyFunction2@20:
 	pushl	%ebp
 	movl	%esp, %ebp
 	subl	$16, %esp
 	fldl	8(%ebp)
 	fstpl	-8(%ebp)
 	fldl	16(%ebp)
 	fstpl	-16(%ebp)
 	fldl	-8(%ebp)
 	fld1
 	faddp	%st, %st(1)
 	fldl	-16(%ebp)
 	fldl	LC5
 	faddp	%st, %st(1)
 	fmulp	%st, %st(1)
 	flds	24(%ebp)
 	fldl	LC6
 	faddp	%st, %st(1)
 	fmulp	%st, %st(1)
 	leave
 	ret	$20

This is a tricky piece of code, but luckily we don't need to read it very close to find what we are looking for. First off, notice that no other registers are accessed besides ebp. Again, GCC passes all floating point values (even the 32-bit float, z) on the stack. Also, the floating point result value is passed on the top of the floating point stack.

We can see again that GCC is doing something strange at the beginning, taking the values on the stack from [ebp + 8] and [ebp + 16], and moving them to locations [ebp - 8] and [ebp - 16], respectively. Immediately after being moved, these values are loaded onto the floating point stack and arithmetic is performed. z isn't loaded till later, and isn't ever moved to [ebp - 24], despite the pattern.

LC5 and LC6 are constant values, that most likely represent floating point values (because the numbers themselves, 1073741824 and 1074266112 don't make any sense in the context of our example functions. Notice though that both LC5 and LC6 contain two .long data items, for a total of 8 bytes of storage? They are therefore most definitely double values.

STDCALL

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Here is the cl.exe listing for MyFunction3: 

 PUBLIC	_MyFunction3@20
 PUBLIC	__real@3ff0000000000000
 PUBLIC	__real@4000000000000000
 PUBLIC	__real@4008000000000000
 EXTRN	__fltused:NEAR
 ;	COMDAT __real@3ff0000000000000
 CONST	SEGMENT
 __real@3ff0000000000000 DQ 03ff0000000000000r	; 1
 CONST	ENDS
 ;	COMDAT __real@4000000000000000
 CONST	SEGMENT
 __real@4000000000000000 DQ 04000000000000000r	; 2
 CONST	ENDS
 ;	COMDAT __real@4008000000000000
 CONST	SEGMENT
 __real@4008000000000000 DQ 04008000000000000r	; 3
 CONST	ENDS
 _TEXT	SEGMENT
 _x$ = 8						; size = 8
 _y$ = 16						; size = 8
 _z$ = 24						; size = 4
 _MyFunction3@20 PROC NEAR
 ; Line 12
 	push	ebp
 	mov	ebp, esp
 ; Line 13
 	fld	QWORD PTR _x$[ebp]
 	fadd	QWORD PTR __real@3ff0000000000000
 	fld	QWORD PTR _y$[ebp]
 	fadd	QWORD PTR __real@4000000000000000
 	fmulp	ST(1), ST(0)
 	fld	DWORD PTR _z$[ebp]
 	fadd	QWORD PTR __real@4008000000000000
 	fmulp	ST(1), ST(0)
 ; Line 14
 	pop	ebp
 	ret	20					; 00000014H
 _MyFunction3@20 ENDP
 _TEXT	ENDS
 END

x is the highest on the stack, and z is the lowest, therefore these parameters are passed from right-to-left. We can tell this because x has the smallest offset (offset [ebp + 8]), while z has the largest offset (offset [ebp + 24]). We see also from the final fmulp instruction that the return value is passed on the FPU stack. This function also cleans the stack itself, as noticed by the call 'ret 20. It is cleaning exactly 20 bytes off the stack which is, incidentally, the total amount that we passed to begin with. We can also notice that the implementation of this function looks exactly like the FASTCALL version of this function. This is true because FASTCALL only passes DWORD-sized parameters in registers, and floating point numbers do not qualify. This means that our assumption above was correct.

Here is the GCC listing for MyFunction3: 

 	.align 8
 LC9:
 	.long	0
 	.long	1073741824
 	.align 8
 LC10:
 	.long	0
 	.long	1074266112
 .globl @MyFunction3@20
 	.def	@MyFunction3@20;	.scl	2;	.type	32;	.endef
 @MyFunction3@20:
 	pushl	%ebp
 	movl	%esp, %ebp
 	subl	$16, %esp
 	fldl	8(%ebp)
 	fstpl	-8(%ebp)
 	fldl	16(%ebp)
 	fstpl	-16(%ebp)
 	fldl	-8(%ebp)
 	fld1
 	faddp	%st, %st(1)
 	fldl	-16(%ebp)
 	fldl	LC9
 	faddp	%st, %st(1)
 	fmulp	%st, %st(1)
 	flds	24(%ebp)
 	fldl	LC10
 	faddp	%st, %st(1)
 	fmulp	%st, %st(1)
 	leave
 	ret	$20

Here we can also see, after all the opening nonsense, that [ebp - 8] (originally [ebp + 8]) is value x, and that [ebp - 24] (originally [ebp - 24]) is value z. These parameters are therefore passed right-to-left. Also, we can deduce from the final fmulp instruction that the result is passed in ST0. Again, the STDCALL function cleans its own stack, as we would expect.

Conclusions

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Floating point values are passed as parameters on the stack, and are passed on the FPU stack as results. Floating point values do not get put into the general-purpose integer registers (eax, ebx, etc...), so FASTCALL functions that only have floating point parameters collapse into STDCALL functions instead. double values are 8-bytes wide, and therefore will take up 8-bytes on the stack. float values however, are only 4-bytes wide.

Float to Int Conversions

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FPU Compares and Jumps

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