1. Using the 80x87 Math Chip in Assembly
Bill Stockwell
11/21/2018

2. The Math Chip is builtin
Since the 486-DX, the IEEE math chip has been an integral part of the Intel processors. Before that, the math chip was a separate (and often expensive) add-on.
11/21/2018

3. Declaring Variables
Use DQ in Nasm to declare floating point constants and variables. For example:
x dq
DQ describles an 8-byte quantity which will be discussed next.
11/21/2018

4. The IEEE format (DQ) Floating point numbers are stored as
+/- 1.m x 2^p
where m is a 52 bit “mantissa” and p is an exponent that places the radix point.
What is stored in the 64 bits is then
s exp mantissa
With s = sign bit, exp = 11 bit exponent,
and mantissa the 52 bits with the numbers’ value.
11/21/2018

5. More on the IEEE format Again, +/- 1.m x 2^p is stored as
s exp mantissa (64 bits altogether)
s = 0 for positive, 1 for negative
exp = p , stored in 11 bits
m is the 52 bit mantissa. Note the exponent is stored so no sign is needed, the 1023 is added for that purpose.
11/21/2018

6. Actual Math Chip Architecture
There are 8 80-bit registers, organized as a stack.
These are referred to in Nasm code by
st0, st1, …, st7.
However, when you load a value onto the math chip stack, it is pushed onto the next available location, so often no direct reference to the registers is needed.
11/21/2018

7. Some instructions
All the math chip instructions begin with the letter ‘F’.
FLD – to push a value onto the math chip stack.
FST – opposite of FLD, it gets a value from the top of the math chip stack.
FADD – used to do floating point addition
11/21/2018

8. Some examples If x is defined as a DQ, we might have
fld qword [x]; push x onto math stack
fadd qword [x]; add x to TOS and push this. So now the stack has 2x on the top and x below that.
fmul qword [x]; This multiplies x by the TOS (2x) getting 2x^2 and pushes this.
11/21/2018

9. Some builtin constants
Various constants can be pushed as with
fldz ; push floating point zero
fld1 ; push 1.0
fldpi ; push PI ( to 20 places)
and there are others – these are the most useful.
11/21/2018