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EE357-Nazarian-Fall09-Lab3-fp - 1 Introduction ....

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Fall 2009 1 EE 357 Lab 3 – FP Emulation 1 Introduction You will work in teams of one or two to write an assembly routine that will perform addition of 32 bit IEEE 754 single precision numbers. The assembly routine will be embedded in a C program. 2 What you will learn This lab is intended to teach you how to embed assembly code inside a C file. It will also demonstrate how using assembly provides access to features of a particular ISA that would otherwise not be possible in C. Finally, floating point representation and arithmetic will be reinforced. 3 Background Information and Notes IEEE 754 Floating Point 32 bit IEEE single precision floating point representation is shown below: 1 8 23 Sign Exponent (Excess 127) Fraction Figure 1 – IEEE 754 Single-Precision Format Many processors (especially low end embedded cores) do not include floating point HW, instead emulating the operations in SW if needed. You will write a program to take in two single precision floating point numbers and add them using only integer operations/instructions. To reduce complexity, we will make the assumption that no special values of FP numbers (i.e. 0, inf., NaN, etc.) will be input or be the result of an operation. To emulate FP addition of these numbers requires isolating the different fields into separate variables and manipulating them. To isolate each field can be accomplished with appropriate AND and shift instructions. To isolate the sign bit and move it to the LSB (which will yield a variable “signa” = 0 for pos. and 1 for neg.) can be achieved as follows. move.l a,d0 andi.l 0x80000000,d0 ; Set all bits but MSB to 0 move.l #31,d1 lsr.l d1,d0 ; Shift sign bit into LSB position move.l d0,signa
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EE 357 Lab 3 ‐ FP Emulation 2 Fall 2009 To implement FP addition, you should review the algorithm given in class and attempt to implement it in assembly. The code skeleton has allocated several temporary variables that we recommend you produce along the way. An explanation of these variables is provided below. You can add more variable declarations for other temporary values if you so desire. Temp. Variable Name Description signa, signb Sign of input a and b in LSB expa, expb 8 bit, Excess 127 exponents in LS 8 bits fraca, fracb Fractions fields with implied ‘1’ added. SEE EXPLANATION BELOW FOR FORMAT ageb 1 if entire value (exp + frac) of A >= B, 0 otherwise signg, expg, fracg, Sign, exponent, and fraction of larger/greater number fracl Fraction of smaller/lesser number exp_abs_diff Absolute value of difference between exponents (used for shift count of lesser fraction) opsub 1 for subtraction of fractions, 0 for addition fracsum Fraction result of addition/subtraction frac_norm, exp_norm Normalized fraction and exponent frac_round, exp_round Rounded fraction and exponent result Final output; reassembled from all fields Table 1 - Temporary Values and Descriptions Some more explanation of the representation of the fractions is required. After
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