a.asm

#; Yang Zhou 260366321

.data
ZERO: 		.float 0.0
ONE: 		.float 1.0
TWO: 		.float 2.0
a:		.float 0.7
b:		.float 1.375
EPSILON:	.float 0.0001 			#; Value e in algorithm above.
INTERVAL: 	.float -5,5		#; Root is between these values.
POLYORDER:	.word  11        		#; Order of polynomial.
COEFFICIENTS:   					#; Integer coefficient of highest 
		.word 10,-2,2,-5,5,-5,5,0,1,-3,5,-5  		#; order comes first in list. 
			
.text
main:
	l.d	$f12, INTERVAL
	jal	findRoot
	li	$v0, 2
	mov.s	$f12, $f0
	syscall
	li	$v0, 10
	syscall


#; $f12 is a
#; $f13 is b
#; $f0 is the value of a root
findRoot:
	sw	$ra, ($sp)
	s.s	$f20, -4($sp)
	s.s	$f22, -8($sp)
	s.s	$f24, -12($sp)				
	addi	$sp, $sp, -16
	add.s	$f4, $f12, $f13			#; save registers onto stack
	l.s	$f6, TWO
	div.s	$f20, $f4, $f6
	mov.s	$f22, $f12
	mov.s	$f24, $f13				#; c = $f20, a = $f22, b = $f23
	mov.s	$f12, $f20
	sw	$ra, ($sp)
	addi	$sp, $sp, -4
	jal	evaluateP
	addi	$sp, $sp, 4
	lw	$ra, ($sp)
	l.s	$f4, ZERO
	c.eq.s	$f4, $f0
	mov.s	$f2, $f0
	mov.s	$f0, $f20
	bc1t	__return				#; p(c) == 0
	sub.s	$f4, $f22, $f24
	abs.s	$f4, $f4
	l.s	$f6, EPSILON
	c.lt.s	$f4, $f6
	bc1t	__return				#; if abs(a-b) < epsilon return c
	mov.s	$f12, $f22
	sw	$ra, ($sp)
	addi	$sp, $sp, -4
	jal	evaluateP
	addi	$sp, $sp, 4
	lw	$ra, ($sp)
	mul.s	$f6, $f2, $f0			#; p(a)*p(b)
	l.s	$f4, ZERO
	c.lt.s	$f4, $f6				#; test greater than zero
	movt.s	$f12, $f20
	movt.s	$f13, $f24
	movf.s	$f12, $f22
	movf.s	$f13, $f20				#; if true, a = c, b = b, if false, a = c, b = c
	addi	$sp, $sp, 12
	l.s	$f24, -8($sp)
	l.s	$f22, -4($sp)
	l.s	$f20, ($sp)					#; pop all the values off the stack since we no longer need them
	jal	findRoot					#; recursive call
	addi	$sp, $sp, 4				#; return, pop the function off the stack
	lw	$ra, ($sp)
	jr	$ra
	__return:						#; return c
	addi	$sp, $sp, 16
	l.s	$f24, -12($sp)
	l.s	$f22, -8($sp)
	l.s	$f20, -4($sp)
	lw	$ra, ($sp)
	jr	$ra



#; $f12 is x
#; $a0 is n
#; $f0 is x^n
power:
	sw	$ra, ($sp)
	addi	$sp, $sp, -4
	beq	$a0, $zero, __return1		#; if zero, return 1
	b	__else
	__return1:
	l.s	$f0, ONE
	addi	$sp, $sp, 4
	jr	$ra
	__else:
	mov.s	$f4, $f12
	addi	$a0, $a0, -1
	jal	power				
	mul.s	$f0, $f0, $f4			#; else return x * pow(x, n-1)
	addi	$sp, $sp, 4
	lw	$ra, ($sp)
	jr	$ra

#; $f12 is x
#; $f0 is the polynomial at x
evaluateP:
	lw	$a0, POLYORDER
	li	$t0, 0
	l.s	$f0, ZERO					#; $f0 starts at 0
	__start:
	bltz	$a0, __end
	sw	$a0, ($sp)
	addi	$sp, $sp, -4
	s.s	$f0, ($sp)
	addi	$sp, $sp, -4
	sw	$ra, ($sp)
	addi	$sp, $sp, -4			
	jal	power						#; calculate x to the current power
	addi	$sp, $sp, 4
	lw	$ra, ($sp)
	lwc1	$f4, COEFFICIENTS($t0)	
	cvt.s.w	$f4, $f4
	mul.s	$f4, $f4, $f0			#; load and multiply by the coefficient
	addi	$sp, $sp, 4
	l.s	$f0, ($sp)
	add.s	$f0, $f4, $f0			#; add it to f0
	addi	$t0, $t0, 4
	addi	$sp, $sp, 4
	lw	$a0, ($sp)
	addi	$a0, $a0, -1
	b	__start
	__end:
	jr	$ra