Fwd: Your Try GMP! page

[tonybrown at cox.net]

Tony said:
> GMP also gives an answer of -87126356 for
> 
> -7295002640174 / 83729

I should have said, GMP also gives and answer of -87126356 for
7295002640174 / (-83729)

For some reason, GMP will not take the syntax
7295002640174 / -83729
But it will take the syntax
- 7295002640174 / 83729

Go figure

Thanks again,

Tony


> Date: Wed, 10 Jan 2007 21:43:08 -0800
> From:  <tonybrown at cox.net>
> To: gmp-discuss at swox.com
> Subject: Your Try GMP! page
> Cc: tonybrown at cox.net
> 
> I am attempting to write my own library, which processes large numbers for various purposes.  I am working on my division function.  I was using your Try GMP! page for testing (for which I thank you very much!) and discovered the following situation:
> 
> As a test case for my program, I wanted to perform the following division:
> 
> 7295002640174 / 83729
> 
> GMP, as well as my program, gives 
> 
> 87126355
> 
> as the answer. All well and dandy.
> 
> However, I also want my program to have sign correctness.
> 
> So, I tried my program as follows:
> 
> -7295002640174 / 83729
> 
> and got the answer:
> 
> -87126356
> 
> Notice the 6 on the end now.  So I tried GMP and it gave the same answer!
> 
> So, I reverted back to my basic number theory, any number should be expressible as 
> n = qk + r  where q=quotient and r=remainder.
> 
> When I divide with your GMP, you don't provide the remainder of the division.  However, taking simpler numbers, lets say we want to divide 7/4.   My take on this is as follows, using n=qk+r:
> 
> the sign of the quotient is the XOR of the signs of the dividend and divisor, so for example,
> 
> -7/4 :  quotient is -1 and if -7 = -1(k) + r , then k must be 4 and r must be -3
> 7/-4 :  quotient is -1 and if 7 = -1(k) + r , then k must be -4 and r must be 3
> -7/-4 :  quotient is 1 and if -7 = 1(k) + r , then k must be -4 and r must be -3
> 7/4 :  quotient is 1 and if 7 = 1(k) + r , then k must be 4 and r must be 3
> 
> GMP also gives an answer of -87126356 for
> 
> -7295002640174 / 83729
> 
> However, if both dividend and divisor are the same sign GMP always gives:
> 
> 87126355
> 
> Now, I had this same issue in my program and resolved it by running the algorithm as if both dividend and divisor were positive.  I calculated the signs independently.  I have not yet root caused the issue, but my current solution works, (even if not optimally!)
> 
> My program now gives the following results:
> 
> Operation: DIVISION
> Dividend:                                                        7295002640174
> Divisor:                                                                            83729
> Quotient:                                                                   87126355
> Remainder:                                                                    62379
> 
> Operation: DIVISION
> Dividend:                                                       -7295002640174
> Divisor:                                                                            83729
> Quotient:                                                                  -87126355
> Remainder:                                                                   -62379
> 
> Operation: DIVISION
> Dividend:                                                        7295002640174
> Divisor:                                                                           -83729
> Quotient:                                                                  -87126355
> Remainder:                                                                    62379
> 
> Operation: DIVISION
> Dividend:                                                       -7295002640174
> Divisor:                                                                           -83729
> Quotient:                                                                   87126355
> Remainder:                                                                   -62379
> 
> So, only the signs of the quotient and remainder are affected by the signs of the dividend and divisor, not the values.  Although the value of my remainder was never affected.
> 
> Please let me know what you think about this issue.  Again, thanks for helping me test my program as well as my understanding of basic numerical operations.
> 
> Tony 
>