1.19. FLOATING-POINT UNIT
The FPU has a stack capable to holding 8 80-bit registers, and each register can hold a number in the IEEE
754111 format.
They areST(0)..ST(7). For brevity,IDAand OllyDbg showST(0)asST, which is represented in some
textbooks and manuals as “Stack Top”.
1.19.3 ARM, MIPS, x86/x64 SIMD
In ARM and MIPS the FPU is not a stack, but a set of registers, which can be accessed randomly, likeGPR.
The same ideology is used in the SIMD extensions of x86/x64 CPUs.
1.19.4 C/C++
The standard C/C++ languages offer at least two floating number types,float(single-precision^112 , 32 bits)
(^113) anddouble(double-precision (^114) , 64 bits).
In [Donald E. Knuth,The Art of Computer Programming, Volume 2, 3rd ed., (1997)246] we can find the
single-precisionmeans that the floating point value can be placed into a single [32-bit] machine word,
double-precisionmeans it can be stored in two words (64 bits).
GCC also supports thelong doubletype (extended precision^115 , 80 bit), which MSVC doesn’t.
Thefloattype requires the same number of bits as theinttype in 32-bit environments, but the number
representation is completely different.
1.19.5 Simple example
Let’s consider this simple example:
#include <stdio.h>
double f (double a, double b)
{
return a/3.14 + b*4.1;
};
int main()
{
printf ("%f\n", f(1.2, 3.4));
};
x86
MSVC
Compile it in MSVC 2010:
Listing 1.201: MSVC 2010:f()CONST SEGMENT
real@4010666666666666 DQ 04010666666666666r ; 4.1
CONST ENDS
CONST SEGMENT
real@40091eb851eb851f DQ 040091eb851eb851fr ; 3.14
CONST ENDS
_TEXT SEGMENT
(^111) wikipedia.org/wiki/IEEE_floating_point
(^112) wikipedia.org/wiki/Single-precision_floating-point_format
(^113) the single precision floating point number format is also addressed in theHandling float data type as a structure(1.24.6 on
page 373) section
(^114) wikipedia.org/wiki/Double-precision_floating-point_format
(^115) wikipedia.org/wiki/Extended_precision