CSE 2021 Computer Organization. Hugh Chesser, CSEB 1012U W4-W

Transcription

1 CE 01 Computer Organization Hugh Chesser, CEB 101U

2 Agenda for Today 1. Floating Point Addition, Multiplication. FP Instructions. Quiz 1 Patterson: ections.

3 Floating Point: ingle Precision 1. In MIP, decimal numbers are represented with the IEEE binary representation that uses the normalized standard scientific binary notation defined as ( 1) (1 + fraction) exponent bias. A number in normalized scientific notation has a mantissa that has no leading 0 s and must be of the form (1 + fraction). For example, the binary representations.0, 0.,.0, and 1.0 are all equivalent but only 1.0 is the normalized scientific binary notation.. MIP allows for two floating point representations: ingle precision and double precision.. ingle precision has a bias of 1 while double precision has a bias of 10.. In single precision, the floating point representation is bit long and has the following form two exponent fraction (8 bits) ( bits) where represents the sign bit, which is 1 for negative numbers and 0 for positive numbers. Activity : Represent 0. ten in single precision of IEEE binary representation.

4 Floating Point: Double Precision 1. In double precision, the value of bias in is 10. ( 1) (1 + fraction) exponent bias. In single precision, the floating point representation is bit long and has the following form two exponent (11 bits) fraction (Total of bits) fraction (continued) Activity : Represent 0. ten in double precision of IEEE binary representation. Activity : how that the largest magnitude that can be represented using single precision is ±.8 ten 10 8, while the smallest fraction that can be represented is ±.9 ten 10 8.

5 Floating Point Registers Name floating point registers each is bits long Memory w/ 0 words Example $f0,$f1,$f,$f,$f,,$f1 Memory[0], Memory[], Memory[999] Comments MIP floating point registers are used in pairs for double precision numbers Memory is accessed one floating point (single or double precision) at a time The following is the established register usage convention for the floating point registers: $f0,$f1,$f,$f: $f,$f,, $f11: $f1,$f1,$f1,$f1: $f1,$f1,$f18,$f19: $f0,$f1,, $f1: Function-returned values Temporary values Arguments passed into a function More Temporary values aved values A handy online calculator/converter for IEEE FP format is at:

6 Floating Point Instructions Category Instruction Example Meaning Comments FP add single add.s $f,$f,$f $f $f+$f ingle Prec. FP subtract single sub.s $f,$f,$f $f $f-$f ingle Prec. FP multiply single mul.s $f,$f,$f $f $f $f ingle Prec. Arithmetic FP divide single FP add double div.s $f,$f,$f add.d $f,$f,$f $f $f/$f $f $f+$f ingle Prec. FP subtract double sub.d $f,$f,$f $f $f-$f FP multiply double mul.d $f,$f,$f $f $f $f FP divide double div.d $f,$f,$f $f $f/$f Data Transfer load word FP ingle store word FP ingle lwc1 $f,100($s) swc1 $f,100($s) $f Mem[$s+100] Mem[$s+100] $f ingle Prec. ingle Prec. FP compare single (eq, ne, lt, le, gt, ge) c.lt.s $f,$f if($f<$f)cond = 1, else cond = 0 ingle Prec. Conditional branch FP compare double (eq, ne, lt, le, gt, ge) Branch on FP true Branch on FP false c.lt.d $f,$f bc1t bc1f if($f<$f)cond = 1, else cond = 0 if cond==1 go to PC+100+ if cond==0 go to PC+100+ ingle/ ingle/

7 Example # calculate area of a circle.data Ans:.asciiz "The area of the circle is: " Ans_add:.word Ans # Pointer to tring (Ans) Pi:.double Rad:.double Rad_add:.word Rad # Pointer to float (Rad).text main: lw $a0, Ans_add($0) # load address of Ans into $a0 addi $v0, $0, # ys Call (Print tring) syscall # # load float (Pseudoinstruction) la $s0, Pi # load address of Pi into $s0 ldc1 $f, 0($s0) # $f = Pi # # load float (MIP Instruction) lw $s0, Rad_add($0) # load address of Rad into $s0 ldc1 $f, 0($s0) # $f = Rad mul.d $f1, $f, $f mul.d $f1, $f1, $f addi $v0, $0, # ys Call (Print Double) syscall exit: jr $ra