base58 for private key

I would like to generate a WIF private key from a random 256 bit private key.
I use the private key given in "mastering Bitcoin" :
http://chimera.labs.oreilly.com/books/1234000001802/ch04.html#_implementing_keys_and_addresses_in_python
Example 4-4.

Code:

print "Private Key (hex) is: ", private_key
print "Private Key (decimal) is: ", decoded_private_key
# Convert private key to WIF format
wif_encoded_private_key = bitcoin.encode_privkey(decoded_private_key, 'wif')
print "Private Key (WIF) is: ", wif_encoded_private_key

the output is:

Code:

Private Key (hex) is:       3aba4162c7251c891207b747840551a71939b0de081f85c4e44cf7c13e41daa6
Private Key (decimal) is:  26563230048437957592232553826663696440606756685920117476832299673293013768870
Private Key (WIF) is:       5JG9hT3beGTJuUAmCQEmNaxAuMacCTfXuw1R3FCXig23RQHMr4K

Here is my code (with GMP: GNU Multiple Precision Arithmetic Library):

Code:

#include <iostream>
#include <string>
#include <algorithm>
#include <gmpxx.h>
using namespace std;

mpz_class base58ToBigNum (const string);
string bigNum2base58 (mpz_class);
int main (void)
{	
    mpz_class bigNumber = 0;
	
    string privKeyHexa("3aba4162c7251c891207b747840551a71939b0de081f85c4e44cf7c13e41daa6");
	
    cout << endl << "privKeyHexa:" << privKeyHexa << endl;
    bigNumber = hexaToBigNum(privKeyHexa);
    cout << endl << "bigNumber: " << bigNumber << endl;

    string strBase58WIF = bigNum2base58(bigNumber);
    cout << "strBase58WIF : " << strBase58WIF << endl << endl;
    
    return 0;
}


// ex: A259BD07F
// = 10 * 16^8 + 2 * 16^7 + 5 * 16^6 + 9 * 16^5 + 11 * 16^4 + 13 * 16^3 + 0 * 16^2 + 7 * 16^1 + 15 * 16^0
// = 43580641407
mpz_class hexaToBigNum (const string myString)
{
    string hexa_digits = "0123456789ABCDEF";
	
    int index;
    mpz_class m = 0;
       
    for( size_t i = 0; i < myString.size(); i++ ) {
        m *= 16;
        index = hexa_digits.find(toupper(myString[i]));
        m += index;
    }
    
    return m;
}


string bigNum2base58 (mpz_class bigNumber)
{
    string b58_digits = "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz";
	
    string base58string;
    string mycharString;

    mpz_class divisor(58), quotient, remainder;
    mpz_class x = bigNumber;
    
    while (x > 0) {
    	mpz_fdiv_qr(quotient.get_mpz_t(), remainder.get_mpz_t(), x.get_mpz_t(), divisor.get_mpz_t());
    	mycharString = string(1, b58_digits[mpz_get_ui(remainder.get_mpz_t())]);
    	base58string.insert(0, mycharString);
    	x = quotient;
    }
    
    return base58string;
}

The while loop in pseudocode is simply:

Code:

   while(x > 0) 
       {
           (x, remainder) = divide(x, 58)
           output_string.append(b58_digits[remainder])
       }

and my output is

Code:

privKeyHexa:  3aba4162c7251c891207b747840551a71939b0de081f85c4e44cf7c13e41daa6
bigNumber:    26563230048437957592232553826663696440606756685920117476832299673293013768870
base58 :      4xFNZQXb9uCKNsupB4AsWmiyd1N7Rk1ibQ42GbytvTed

The base58 string (WIF) should start with 5.
Questions:
according to: mastering Bitcoin Table 4-1.
I have to add a version prefix of 0x80, but where ?
I have the same bigNumber than Example 4-4.
if I add 0x80 to privKeyHexa : 803aba4162c7251c89....
I have a different big number and a wrong result: f6Lnp6NkNmwag....
So where do I add this prefix ?
And do I have to do a checksum somewhere ?