Square root of bignum using GMP

Question

I need to get the square root of a 210 digit number accurately, I thought GMP was the right tool for the job, what am I doing wrong?

#include <stdlib.h>
#include <stdio.h>
#include "gmp.h"

int
main (int argc, char *argv[])
{
  mpz_t sq_me, sq_out, test;
  mpz_init(sq_me);
  mpz_init(sq_out);
  mpz_init(test);
  mpz_set_str (sq_me, argv[1], 10);

  mpz_sqrt(sq_out, sq_me);
  mpz_mul(test,sq_out,sq_out);

  gmp_printf ("%Zd\n\n", sq_out);
  gmp_printf ("%Zd\n\n", test);

  return 0;
}

Input:

24524664490027821197651766357308801846702678767833275974341445171506160083003858 72169522083993320715491036268271916798640797767232430056005920356312465612184658 17904100131859299619933817012149335034875870551067

Output:

49522383313031109809242226159886283348695660460381271324714928680654813093947239 9634016783775955618921028

24524664490027821197651766357308801846702678767833275974341445171506160083003858 72169522083993320715491034366358025027526868495267716284867043049443779615862887 47102011391915422793532619329760963626718900576784

Answer 1

You're getting the result as an integer and then squaring that. The input number must not be a perfect square, so it is truncating the decimals and decreasing the precision of the number. Look into the 'mpf' category of functions for floats rather than 'mpz' for integers.

Answer 2

Here's the code you need for floating point square root, you can see that the initial input and final output are identical.

#include <stdlib.h>
#include <stdio.h>
#include "gmp.h"

int main (int argc, char *argv[]) {
    mpf_t sq_me, sq_out, test;
    mpf_set_default_prec (10000);
    mpf_init(sq_me);
    mpf_init(sq_out);
    mpf_init(test);
    mpf_set_str (sq_me, argv[1], 10);

    mpf_sqrt(sq_out, sq_me);
    mpf_mul(test,sq_out,sq_out);

    gmp_printf ("Input:       %Ff\n\n", sq_me);
    gmp_printf ("Square root: %.200Ff\n\n", sq_out);
    gmp_printf ("Re-squared:  %Ff\n\n", test);

    return 0;
}

Here's the output with your parameter:

Input:       2452466449002782119765176635730880184670267876783327597434144
51715061600830038587216952208399332071549103626827191679864079776723243005
60059203563124656121846581790410013185929961993381701214933503487587055106
7.000000

Square root: 4952238331303110980924222615988628334869566046038127132471492
86806548130939472399634016783775955618921028.19202568258368255653837168412
92356432661548614332014106174638951390596672950394981098992388116308833260
04535647648563996144250924277757344248059826024201642748515325655438898558
17807282091590722890002

Re-squared:  2452466449002782119765176635730880184670267876783327597434144
51715061600830038587216952208399332071549103626827191679864079776723243005
60059203563124656121846581790410013185929961993381701214933503487587055106
7.000000

Answer 3

I am using a libgmp-3.dll

In vb.net I wrote this function for a high precision square root. I haven't tested it thoroughly but it gets me the Square Root of 3 to any precision I need

 Public Shared Function SquareRoot(ByVal Value As BigInt, ByVal Precision As Integer) As String
    Dim Ten As New BigInt(10)
    Dim DecLen As Integer = Value.Sqrt.ToString.Length
    Dim RootDigits As String = (Value * Ten.Power(Precision * 2)).Sqrt

    'Add trailing zeros
    RootDigits = RootDigits.PadRight((DecLen + Precision), "0")
    Return RootDigits.Substring(0, DecLen) & "." & RootDigits.Substring(DecLen)
End Function