working with negative numbers in python

Question

I am a student in a concepts of programming class. The lab is run by a TA and today in lab he gave us a real simple little program to build. It was one where it would multiply by addition. Anyway, he had us use absolute to avoid breaking the prog with negatives. I whipped it up real quick and then argued with him for 10 minutes that it was bad math. It was, 4 * -5 does not equal 20, it equals -20. He said that he really dosen't care about that and that it would be too hard to make the prog handle the negatives anyway. So my question is how do I go about this.

here is the prog I turned in:

#get user input of numbers as variables

numa, numb = input("please give 2 numbers to multiply seperated with a comma:")

#standing variables
total = 0
count = 0

#output the total
while (count< abs(numb)):
    total = total + numa
    count = count + 1

#testing statements
if (numa, numb <= 0):
    print abs(total)
else:
    print total

I want to do it without absolutes, but every time I input negative numbers I get a big fat goosegg. I know there is some simple way to do it, I just can't find it.

Solution 1

Perhaps you would accomplish this with something to the effect of

text = raw_input("please give 2 numbers to multiply separated with a comma:")
split_text = text.split(',')
a = int(split_text[0])
b = int(split_text[1])
# The last three lines could be written: a, b = map(int, text.split(','))
# but you may find the code I used a bit easier to understand for now.

if b > 0:
    num_times = b
else:
    num_times = -b

total = 0
# While loops with counters basically should not be used, so I replaced the loop 
# with a for loop. Using a while loop at all is rare.
for i in xrange(num_times):
    total += a 
    # We do this a times, giving us total == a * abs(b)

if b < 0:
    # If b is negative, adjust the total to reflect this.
    total = -total

print total

or maybe

a * b

Solution 2

Too hard? Your TA is... well, the phrase would probably get me banned. Anyways, check to see if numb is negative. If it is then multiply numa by -1 and do numb = abs(numb). Then do the loop.

Solution 3

The abs() in the while condition is needed, since, well, it controls the number of iterations (how would you define a negative number of iterations?). You can correct it by inverting the sign of the result if numb is negative.

So this is the modified version of your code. Note I replaced the while loop with a cleaner for loop.

#get user input of numbers as variables
numa, numb = input("please give 2 numbers to multiply seperated with a comma:")

#standing variables
total = 0

#output the total
for count in range(abs(numb)):
    total += numa

if numb < 0:
    total = -total

print total

Solution 4

Try this on your TA:

# Simulate multiplying two N-bit two's-complement numbers
# into a 2N-bit accumulator
# Use shift-add so that it's O(base_2_log(N)) not O(N)

for numa, numb in ((3, 5), (-3, 5), (3, -5), (-3, -5), (-127, -127)):
    print numa, numb,
    accum = 0
    negate = False
    if numa < 0:
        negate = True
        numa = -numa
    while numa:
        if numa & 1:
            accum += numb
        numa >>= 1
        numb <<= 1
    if negate:
        accum = -accum
    print accum

output:

3 5 15
-3 5 -15
3 -5 -15
-3 -5 15
-127 -127 16129

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