the picalc__example.s) template:

.text #.align 2 .globl main main: la $t0, toss move $t1, $0 # init $t1 = 0

li $a0, 44 #43 = random float, 44 = random double jal srand L1: bge $t1, 4, exit # check loop condition lw $t2, 0($t0) # load # of tosses ############ begin your code ################################ # current code will just print out 3 random numbers generated L2: jal rand_range # use rand_range function to get random number # $f0 has the random number # j L2 ############ end your code ################################### mov.s $f12, $f0 # move result to print argument li $v0, 2 # 2 = print float, 3 = print double syscall # system call for print result addi $a0, $0, 0xA # ascii code for LF addi $v0, $0, 0xB # syscall 11 syscall addi $t1, $t1, 1 # increment $t1 add $t0, $t0, 4 # adjust index j L1 # iterate outer loop exit: li $v0, 10 # system call for exit syscall # we are out of here

# random float range rand_range: addi $sp, $sp, -12 sw $t0, 0($sp) sw $t1, 4($sp) sw $ra, 8($sp) jal rand # $v0 has random number mtc1 $v0, $f20 # move the int to $fp reg, mtc1.d for double cvt.s.w $f20, $f20 # convert int to float, cvt.d.w for double # la $t0, rmax # lw $t1, 0($t0) # mtc1 $t1, $f21 # cvt.s.w $f21, $f21 # f21 = rmax l.s $f21, rmaxf div.s $f22,$f20,$f21 # random = rand()/rmax l.s $f23, LB # f23 = lb l.s $f24, diff # f24 = diff mul.s $f25,$f22,$f24 # f25 = f22*f24 add.s $f0, $f23, $f25 lw $t0, 0($sp) lw $t1, 4($sp) lw $ra, 8($sp) addi $sp, $sp, 12 jr $ra

# For seeding the random number generator srand: addi $sp, $sp, -4 sw $t0, 0($sp) la $t0, rseed # Store the given seed sw $a0, 0($t0) lw $t0, 0($sp) addi $sp, $sp, 4 jr $ra # random number generator # seed = seed * 1103515245 +12345; rand: addi $sp, $sp, -20 sw $t0, 0($sp) sw $t1, 4($sp) sw $t2, 8($sp) sw $t5, 12($sp) sw $ra, 16($sp) la $t5,rseed # Get the current seed lw $t0,0($t5) li $t1,1103515245 # seed * 1103515245 mul $t2,$t0,$t1 add $v0,$t2,12345 # (seed * 1103515245) + 12345 li $t0,0x7FFFFFFF # ((seed * 1103515245) + 12345)&0x7FFFFFFF and $v0,$v0,$t0 sw $v0,0($t5) # Save the seed lw $t0, 0($sp) lw $t1, 4($sp) lw $t2, 8($sp) lw $t5, 12($sp) lw $ra, 16($sp) addi $sp, $sp, 20 jr $ra

.data .align 0 pi: .float 0.0 toss: .word 100, 1000, 10000 rseed: .word 1 rmax: .word 2147483647 rmaxf: .float 2147483647.0 LB: .float -1.0 UB: .float 1.0 diff: .float 2.0

the picalc__example.s) template:

.text #.align 2 .globl main main: la $t0, toss move $t1, $0 # init $t1 = 0

li $a0, 44 #43 = random float, 44 = random double jal srand L1: bge $t1, 4, exit # check loop condition lw $t2, 0($t0) # load # of tosses ############ begin your code ################################ # current code will just print out 3 random numbers generated L2: jal rand_range # use rand_range function to get random number # $f0 has the random number # j L2 ############ end your code ################################### mov.s $f12, $f0 # move result to print argument li $v0, 2 # 2 = print float, 3 = print double syscall # system call for print result addi $a0, $0, 0xA # ascii code for LF addi $v0, $0, 0xB # syscall 11 syscall addi $t1, $t1, 1 # increment $t1 add $t0, $t0, 4 # adjust index j L1 # iterate outer loop exit: li $v0, 10 # system call for exit syscall # we are out of here

# random float range rand_range: addi $sp, $sp, -12 sw $t0, 0($sp) sw $t1, 4($sp) sw $ra, 8($sp) jal rand # $v0 has random number mtc1 $v0, $f20 # move the int to $fp reg, mtc1.d for double cvt.s.w $f20, $f20 # convert int to float, cvt.d.w for double # la $t0, rmax # lw $t1, 0($t0) # mtc1 $t1, $f21 # cvt.s.w $f21, $f21 # f21 = rmax l.s $f21, rmaxf div.s $f22,$f20,$f21 # random = rand()/rmax l.s $f23, LB # f23 = lb l.s $f24, diff # f24 = diff mul.s $f25,$f22,$f24 # f25 = f22*f24 add.s $f0, $f23, $f25 lw $t0, 0($sp) lw $t1, 4($sp) lw $ra, 8($sp) addi $sp, $sp, 12 jr $ra

# For seeding the random number generator srand: addi $sp, $sp, -4 sw $t0, 0($sp) la $t0, rseed # Store the given seed sw $a0, 0($t0) lw $t0, 0($sp) addi $sp, $sp, 4 jr $ra # random number generator # seed = seed * 1103515245 +12345; rand: addi $sp, $sp, -20 sw $t0, 0($sp) sw $t1, 4($sp) sw $t2, 8($sp) sw $t5, 12($sp) sw $ra, 16($sp) la $t5,rseed # Get the current seed lw $t0,0($t5) li $t1,1103515245 # seed * 1103515245 mul $t2,$t0,$t1 add $v0,$t2,12345 # (seed * 1103515245) + 12345 li $t0,0x7FFFFFFF # ((seed * 1103515245) + 12345)&0x7FFFFFFF and $v0,$v0,$t0 sw $v0,0($t5) # Save the seed lw $t0, 0($sp) lw $t1, 4($sp) lw $t2, 8($sp) lw $t5, 12($sp) lw $ra, 16($sp) addi $sp, $sp, 20 jr $ra

.data .align 0 pi: .float 0.0 toss: .word 100, 1000, 10000 rseed: .word 1 rmax: .word 2147483647 rmaxf: .float 2147483647.0 LB: .float -1.0 UB: .float 1.0 diff: .float 2.0

2. [50pts] Suppose we toss darts randomly at a square dartboard, whose bullseye is at the origin, and whose sides are 2 feet in length. Suppose also that there's a circle inscribed in the square dartboard. The radius of the circle is 1 foot, and its area is square feet. If the points that are hit by the darts are uniformly distributed (and we always hit the square), then the number of darts that hit inside the circle should approximately satisfy the equation (number in circle total )/ (number of toss) = /4 since the ratio of the area of the circle to the area of the square is /4 We can use this formula to estimate the value of with a random number generator: float pi-estimate = 0.0; int for number-in-circle = 0; (toss = 0; toss