1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
|
#!/usr/bin/env python3
from tabulate import tabulate
import matplotlib
import matplotlib.pyplot as plt
matplotlib.use("pgf")
matplotlib.rcParams.update({
"pgf.texsystem": "pdflatex",
'font.family': 'serif',
'text.usetex': True,
'pgf.rcfonts': False,
})
with open('input.txt') as f:
input_string = f.read().split('\n')
def twos_comp(num, length):
if num == 0:
return 0
return abs((num ^ ((1 << length) - 1)) + 1)
def arithmatic_shiftr(num, length, times):
for t in range(times):
num = (num >> 1) | ((1 << length - 1) & num)
return num
def arithmatic_shiftl(num, length):
if num & (1 << length - 1):
return (num << 1) | (1 << length - 1)
else:
return (num << 1) & ~(1 << length - 1)
def twoscomp_to_int(num, length):
if num & (1 << length - 1):
return (-1 * twos_comp(num, length))
return num & (1 << length) - 1
def debug(results):
headers = ['multiplicand bin', 'multiplier bin', 'multiplicand dec', 'multiplier dec', 'expected bin', 'expected dec', 'booth if correct', 'booth mod if correct']
table = []
for [multiplicand_bin, multiplier_bin, result_booth, result_booth_mod, length] in results:
multiplicand = twoscomp_to_int(multiplicand_bin, length)
multiplier = twoscomp_to_int(multiplier_bin, length)
expected = multiplicand * multiplier
expected_bin = (twos_comp(expected, length * 2), expected) [expected > 0]
success_b = [bin(result_booth), "PASS"] [result_booth == expected_bin]
success_bm = [bin(result_booth_mod), "PASS"] [result_booth_mod == expected_bin]
table.append([bin(multiplicand_bin), bin(multiplier_bin), multiplicand, multiplier, bin(expected_bin), expected, success_b, success_bm])
print("\nCHECKS: \n", tabulate(table, headers), "\n")
def booth(multiplier, multiplicand, length):
operations = 0
multiplicand_twos_comp = twos_comp(multiplicand, length)
result = multiplier << 1 # extended bit
for i in range(length):
op = result & 0b11
if op == 0b01:
operations += 1
result += multiplicand << (length + 1)
if op == 0b10:
operations += 1
result += multiplicand_twos_comp << (length + 1)
result &= (1 << (length * 2) + 1) - 1 # get rid of any overflows
result = arithmatic_shiftr(result, (length * 2) + 1, 1)
result = result >> 1
return (result, operations)
# TODO clean up
def booth_mod(multiplier, multiplicand, length):
operations = 0
multiplicand |= ((1 << length - 1) & multiplicand) << 1 # extend multiplicand sign to prevent overflow when mult/sub by 2
multiplicand_twos_comp = twos_comp(multiplicand, length + 1)
result = multiplier << 1 # extended bit
for i in range(int((length) / 2)):
op = result & 0b111
match op:
case 0b010 | 0b001: # add
print("add")
result += multiplicand << (length + 1)
operations += 1
case 0b011: # add * 2
print("add * 2")
result += arithmatic_shiftl(multiplicand, length + 1) << (length + 1)
operations += 1
case 0b100: # sub * 2
print("sub * 2")
result += arithmatic_shiftl(multiplicand_twos_comp, length + 1) << (length + 1)
operations += 1
case 0b101 | 0b110: # sub
print("sub ")
result += multiplicand_twos_comp << (length + 1)
operations += 1
result &= (1 << ((length * 2) + 2)) - 1 # get rid of any overflows
result = arithmatic_shiftr(result, (length * 2) + 2, 2)
# *barfs on your dog*
result = ((result | ((1 << ((length * 2) + 2)) >> 1)) & ((1 << ((length * 2) + 1)) - 1)) >> 1
return (result, operations)
if __name__ == "__main__":
result_headers = ['multiplicand', 'multiplier', 'result (bin)', 'result (hex)']
result_table = []
opcount_headers = ['multiplicand', 'multiplier', 'length', 'booth', 'modified booth']
opcount_table = []
lengths = [] # for matplotlib plot
ops_booth = []
ops_mod_booth = []
debug_results = []
for operation in input_string:
if operation == '' or operation[0] == '#':
continue
length = len(operation.split(" ")[0])
multiplicand = int(operation.split(" ")[0], 2)
multiplier = int(operation.split(" ")[1], 2)
# get result and operation count of both algorithims
result_booth = booth(multiplier, multiplicand, length)
result_mod_booth = booth_mod(multiplier, multiplicand, length)
# gather data for matplotlib
ops_booth.append(result_booth[1])
ops_mod_booth.append(result_mod_booth[1])
lengths.append(length)
#gather data for report results table
result_table.append([bin(multiplicand), bin(multiplier), bin(result_booth[0]), hex(result_booth[0])])
#gather data for test function to check if simulator is working
debug_results.append([multiplicand, multiplier, result_booth[0], result_mod_booth[0], length])
#gather data for operation count table
opcount_table.append([bin(multiplicand), bin(multiplier), length, result_booth[1], result_mod_booth[1]])
debug(debug_results)
print(tabulate(result_table, result_headers, tablefmt="latex"))
print(tabulate(opcount_table, opcount_headers))
# output
with open("report/result_table.tex", 'w') as f:
f.write(tabulate(result_table, result_headers, tablefmt="latex_booktabs"))
with open("report/speed_table.tex", "w") as f:
f.write(tabulate(opcount_table, opcount_headers, tablefmt="latex_booktabs"))
plt.title("Operations vs Operand Length")
plt.plot(lengths, ops_booth, '^--m', label='booths algorithim')
plt.plot(lengths, ops_mod_booth, 'v--c', label='modified booths algorithim')
plt.gca().set_xlabel("Length of Operands")
plt.gca().set_ylabel("Number of Additions and Subtractions")
plt.legend(loc='upper left')
plt.savefig('report/performance.pgf')
|
