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im fairly new to Multiple Precision Arithmetic, and after a few days of trying to figure this out im at a loss. im trying to take the inverse of a number to a high number of deciaml places and have been attempting to work out how to do this using GMP or the mpz/mpf package. however i am a little lost with understanding the example from this link:

http://sepwww.stanford.edu/sep/claudio/Research/Prst_ExpRefl/ShtPSPI/intel/mkl/10.0.3.020/examples/gmp/source/mpz_invert_example.c

/* to compute the inverse of op1 modulo op2 and put result in rop    */
/*                 p*x = s*n + 1    ( rop = p, op1 = x, op2 = n )    */
/*                                                                   */
    n = mpz_invert ( rop, op1, op2 );

I have duplicated this example in my ide complied and run and im getting the correct output:

/* rop =  2288                                                       */
/* n = 1

However i dont understand what 2288 is? i.e. compute the inverse of op1 modulo op2 and put result in rop

could anyone explain how this number is obtained?

or a simple example to say taking:

1875 ^ -6

or w.r.t the following link: How does one calculate 2 ^ -18 using GMP?

taking:

1 / (1875 ^ 6)

Any help would be much appreciated!

Community
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Why_Is_This_Hard
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2 Answers2

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mpz_invert is used to calculate a very specific value which is the modular multiplicative inverse of a mod b.

Basically rop is an integer such that op1*rop ≡ 1 (mod op2) which implies that (op1*rop - 1) mod op2 = 0.

Indeed that's the case, with

op1 = 12682271391376756984
op2 = 3527
rop = 2288

op1 * rop = 29017036943470019979392
(op1 * rop - 1) mod op2 = 29017036943470019979391 % 3527 = 0
Jack
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  • Thanks Jack for the answer. however i dont understand what the example is trying to achieve? are we trying to find the inverse of 12682271391376756984 or the modular inverse? i.e. what about finding the inverse of 12682271391376756984 and representing that as a float? – Why_Is_This_Hard Jul 02 '16 at 03:10
  • so i guess the question then becomes how do i take the inverse of 12682271391376756984 and represent it as a float that has accuracy over 16d.p. ? – Why_Is_This_Hard Jul 02 '16 at 03:39
  • You are getting the modular inverse. Arbitrary precision arithmetics and floats (which are limited precision) don't work well together as far as I can see... – Paul Stelian Jul 02 '16 at 09:27
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Ok so after some consultation on the mathematics q&a it seems that calculating the Modular multiplicative inverse is going to be of no use to me.

The problem then is, how do i calculate the inverse of a large integer to >16 d.p. in C ? w.r.t the above example, how do i calculate 1/12682271391376756984 for a value of:

4.263162382267667173889615631246062574813592315276851 × 10^-16

that can be represented in an extended format float?

Why_Is_This_Hard
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