Modular exponentiation

Modular exponentiation
You are encouraged to solve this task according to the task description, using any language you may know.

Find the last   40   decimal digits of   $a^{b}$,   where

•   $a=2988348162058574136915891421498819466320163312926952423791023078876139$
•   $b=2351399303373464486466122544523690094744975233415544072992656881240319$

A computer is too slow to find the entire value of   $a^{b}$.

Instead, the program must use a fast algorithm for modular exponentiation:   $a^{b}\mod m$.

The algorithm must work for any integers   $a,b,m$,     where   $b\geq 0$   and   $m>0$.

11l

Translation of: D

F pow_mod(BigInt =base, BigInt =exponent, BigInt modulus)
   BigInt result = 1

   L exponent != 0
      I exponent % 2 != 0
         result = (result * base) % modulus
      exponent I/= 2
      base = (base * base) % modulus

   R result

print(pow_mod(BigInt(‘2988348162058574136915891421498819466320163312926952423791023078876139’),
              BigInt(‘2351399303373464486466122544523690094744975233415544072992656881240319’),
              BigInt(10) ^ 40))

Output:

1527229998585248450016808958343740453059

Ada

Using the big integer implementation from a cryptographic library [1].

with Ada.Text_IO, Ada.Command_Line, Crypto.Types.Big_Numbers;

procedure Mod_Exp is

   A: String :=
     "2988348162058574136915891421498819466320163312926952423791023078876139";
   B: String :=
     "2351399303373464486466122544523690094744975233415544072992656881240319";

   D: constant Positive := Positive'Max(Positive'Max(A'Length, B'Length), 40);
     -- the number of decimals to store A, B, and result
   Bits: constant Positive := (34*D)/10;
     -- (slightly more than) the number of bits to store A, B, and result
   package LN is new Crypto.Types.Big_Numbers (Bits + (32 - Bits mod 32));
     -- the actual number of bits has to be a multiple of 32
   use type LN.Big_Unsigned;

   function "+"(S: String) return LN.Big_Unsigned
     renames LN.Utils.To_Big_Unsigned;

   M: LN.Big_Unsigned := (+"10") ** (+"40");

begin
   Ada.Text_IO.Put("A**B (mod 10**40) = ");
   Ada.Text_IO.Put_Line(LN.Utils.To_String(LN.Mod_Utils.Pow((+A), (+B), M)));
end Mod_Exp;

Output:

A**B (mod 10**40) = 1527229998585248450016808958343740453059

ALGOL 68

The code below uses Algol 68 Genie which provides arbitrary precision arithmetic for LONG LONG modes.

BEGIN
   PR precision=1000 PR
   MODE LLI = LONG LONG INT;	CO For brevity CO
   PROC mod power = (LLI base, exponent, modulus) LLI :
   BEGIN
      LLI result := 1, b := base, e := exponent;
      IF exponent < 0
      THEN
	 put (stand error, (("Negative exponent", exponent, newline)))
      ELSE
	 WHILE e > 0 
	 DO
	    (ODD e | result := (result * b) MOD modulus);
	    e OVERAB 2; b := (b * b) MOD modulus
	 OD
      FI;
      result
   END;
   LLI a = 2988348162058574136915891421498819466320163312926952423791023078876139;
   LLI b = 2351399303373464486466122544523690094744975233415544072992656881240319;
   LLI m = 10000000000000000000000000000000000000000;
   printf (($"Last 40 digits = ", 40dl$, mod power (a, b, m)))
END

Output:

Last 40 digits = 1527229998585248450016808958343740453059

Arturo

a: 2988348162058574136915891421498819466320163312926952423791023078876139
b: 2351399303373464486466122544523690094744975233415544072992656881240319

loop [40 80 180 888] 'm ->
    print ["(a ^ b) % 10 ^" m "=" powmod a b 10^m]

Output:

(a ^ b) % 10 ^ 40 = 1527229998585248450016808958343740453059 
(a ^ b) % 10 ^ 80 = 53259517041910225328867076245698908287781527229998585248450016808958343740453059 
(a ^ b) % 10 ^ 180 = 31857295076204937005344367438778481743660325586328069392203762862423884839076695547212682454523811053259517041910225328867076245698908287781527229998585248450016808958343740453059 
(a ^ b) % 10 ^ 888 = 261284964380836515397030706363442226571397237057488951313684545241085642329943676248755716124260447188788530017182951051652748425560733974835944416069466176713156182727448301838517000343485327001656948285381173038339073779331230132340669899896448938858785362771190460312412579875349871655999446205426049662261450633448468931573506876255644749155348923523680730999869785472779116009356696816952771965930728940530517799329942590114178284009260298426735086579254282591289756840358811822151307479352856856983393715348870715239020037962938019847992960978849852850613063177471175191444262586321233906926671000476591123695550566585083205841790404069511972417770392822283604206143472509425391114072344402850867571806031857295076204937005344367438778481743660325586328069392203762862423884839076695547212682454523811053259517041910225328867076245698908287781527229998585248450016808958343740453059

AutoHotkey

Library: MPL

#NoEnv
#SingleInstance, Force
SetBatchLines, -1
#Include mpl.ahk

  MP_SET(base, "2988348162058574136915891421498819466320163312926952423791023078876139")
, MP_SET(exponent, "2351399303373464486466122544523690094744975233415544072992656881240319")
, MP_SET(modulus, "10000000000000000000000000000000000000000")

, NumGet(exponent,0,"Int") = -1 ? return : ""
, MP_SET(result, "1")
, MP_SET(TWO, "2")
while !MP_IS0(exponent)
	MP_DIV(q, r, exponent, TWO)
	, (MP_DEC(r) = 1
		? (MP_MUL(temp, result, base)
		, MP_DIV(q, result, temp, modulus))
		: "")
	, MP_DIV(q, r, exponent, TWO)
	, MP_CPY(exponent, q)
	, MP_CPY(base1, base)
	, MP_MUL(base2, base1, base)
	, MP_DIV(q, base, base2, modulus)

msgbox % MP_DEC(result)
Return

Output:

1527229998585248450016808958343740453059

BBC BASIC

Works with: BBC BASIC for Windows

Uses the Huge Integer Math & Encryption library.

      INSTALL @lib$+"HIMELIB"
      PROC_himeinit("")
      
      PROC_hiputdec(1, "2988348162058574136915891421498819466320163312926952423791023078876139")
      PROC_hiputdec(2, "2351399303373464486466122544523690094744975233415544072992656881240319")
      PROC_hiputdec(3, "10000000000000000000000000000000000000000")
      h1% = 1 : h2% = 2 : h3% = 3 : h4% = 4
      SYS `hi_PowMod`, ^h1%, ^h2%, ^h3%, ^h4%
      PRINT FN_higetdec(4)

Output:

1527229998585248450016808958343740453059

Bracmat

Translation of: Icon_and_Unicon

  ( ( mod-power
    =   base exponent modulus result
      .   !arg:(?base,?exponent,?modulus)
        & !exponent:~<0
        & 1:?result
        &   whl
          ' ( !exponent:>0
            &     ( (   mod$(!exponent.2):1
                      & mod$(!result*!base.!modulus):?result
                      & -1
                    | 0
                    )
                  + !exponent
                  )
                * 1/2
              : ?exponent
            & mod$(!base^2.!modulus):?base
            )
        & !result
    )
  & ( a
    = 2988348162058574136915891421498819466320163312926952423791023078876139
    )
  & ( b
    = 2351399303373464486466122544523690094744975233415544072992656881240319
    )
  & out$("last 40 digits = " mod-power$(!a,!b,10^40))
  )

Output:

last 40 digits =  1527229998585248450016808958343740453059

C

Given numbers are too big for even 64 bit integers, so might as well take the lazy route and use GMP:

Library: GMP

#include <gmp.h>

int main()
{
	mpz_t a, b, m, r;

	mpz_init_set_str(a,	"2988348162058574136915891421498819466320"
				"163312926952423791023078876139", 0);
	mpz_init_set_str(b,	"2351399303373464486466122544523690094744"
				"975233415544072992656881240319", 0);
	mpz_init(m);
	mpz_ui_pow_ui(m, 10, 40);

	mpz_init(r);
	mpz_powm(r, a, b, m);

	gmp_printf("%Zd\n", r); /* ...16808958343740453059 */

	mpz_clear(a);
	mpz_clear(b);
	mpz_clear(m);
	mpz_clear(r);

	return 0;
}

Output:

1527229998585248450016808958343740453059

C#

We can use the built-in function from BigInteger.

using System;
using System.Numerics;

class Program
{
    static void Main() {
        var a = BigInteger.Parse("2988348162058574136915891421498819466320163312926952423791023078876139");
        var b = BigInteger.Parse("2351399303373464486466122544523690094744975233415544072992656881240319");
        var m = BigInteger.Pow(10, 40);
        Console.WriteLine(BigInteger.ModPow(a, b, m));
    }
}

Output:

1527229998585248450016808958343740453059

C++

Library: Boost

#include <iostream>
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/integer.hpp>

int main() {
    using boost::multiprecision::cpp_int;
    using boost::multiprecision::pow;
    using boost::multiprecision::powm;
    cpp_int a("2988348162058574136915891421498819466320163312926952423791023078876139");
    cpp_int b("2351399303373464486466122544523690094744975233415544072992656881240319");
    std::cout << powm(a, b, pow(cpp_int(10), 40)) << '\n';
    return 0;
}

Output:

1527229998585248450016808958343740453059

Clojure

(defn powerMod "modular exponentiation" [b e m]
  (defn m* [p q] (mod (* p q) m))
  (loop [b b, e e, x 1]
    (if (zero? e) x
      (if (even? e) (recur (m* b b) (/ e 2) x)
        (recur (m* b b) (quot e 2) (m* b x))))))

(defn modpow
  " b^e mod m (using Java which solves some cases the pure clojure method has to be modified to tackle--i.e. with large b & e and 
    calculation simplications when gcd(b, m) == 1 and gcd(e, m) == 1) "
  [b e m]
  (.modPow (biginteger b) (biginteger e) (biginteger m)))

Common Lisp

(defun rosetta-mod-expt (base power divisor)
  "Return BASE raised to the POWER, modulo DIVISOR.
  This function is faster than (MOD (EXPT BASE POWER) DIVISOR), but
  only works when POWER is a non-negative integer."
  (setq base (mod base divisor))
  ;; Multiply product with base until power is zero.
  (do ((product 1))
      ((zerop power) product)
    ;; Square base, and divide power by 2, until power becomes odd.
    (do () ((oddp power))
      (setq base (mod (* base base) divisor)
	    power (ash power -1)))
    (setq product (mod (* product base) divisor)
	  power (1- power))))
 
(let ((a 2988348162058574136915891421498819466320163312926952423791023078876139)
      (b 2351399303373464486466122544523690094744975233415544072992656881240319))
  (format t "~A~%" (rosetta-mod-expt a b (expt 10 40))))

Works with: CLISP

;; CLISP provides EXT:MOD-EXPT
(let ((a 2988348162058574136915891421498819466320163312926952423791023078876139)
      (b 2351399303373464486466122544523690094744975233415544072992656881240319))
  (format t "~A~%" (mod-expt a b (expt 10 40))))

Implementation with LOOP

(defun mod-expt (a n m)
   (loop with c = 1 while (plusp n) do
      (if (oddp n) (setf c (mod (* a c) m)))
      (setf n (ash n -1))
      (setf a (mod (* a a) m))
      finally (return c)))

Crystal

require "big"

module Integer 
  module Powmod

    # Compute self**e mod m
    def powmod(e, m)
      r, b = 1, self.to_big_i
      while e > 0
        r = (b * r) % m if e.odd?
        b = (b * b) % m
        e >>= 1
      end
      r
    end
  end
end

struct Int; include Integer::Powmod end

a = "2988348162058574136915891421498819466320163312926952423791023078876139".to_big_i
b = "2351399303373464486466122544523690094744975233415544072992656881240319".to_big_i
m = 10.to_big_i ** 40

puts a.powmod(b, m)

Output:

1527229998585248450016808958343740453059

D

Translation of: Icon_and_Unicon

Compile this module with -version=modular_exponentiation to see the output.

module modular_exponentiation;

private import std.bigint;

BigInt powMod(BigInt base, BigInt exponent, in BigInt modulus)
pure nothrow /*@safe*/ in {
   assert(exponent >= 0);
} body {
    BigInt result = 1;

    while (exponent) {
        if (exponent & 1)
            result = (result * base) % modulus;
        exponent /= 2;
        base = base ^^ 2 % modulus;
    }

    return result;
}

version (modular_exponentiation)
    void main() {
        import std.stdio;

        powMod(BigInt("29883481620585741369158914214988194" ~
                      "66320163312926952423791023078876139"),
               BigInt("235139930337346448646612254452369009" ~
                      "4744975233415544072992656881240319"),
               BigInt(10) ^^ 40).writeln;
    }

Output:

1527229998585248450016808958343740453059

Dc

2988348162058574136915891421498819466320163312926952423791023078876139 2351399303373464486466122544523690094744975233415544072992656881240319 10 40^|p

Delphi

Library: System.SysUtils

Library: Velthuis.BigIntegers

Translation of: C#

Thanks for Rudy Velthuis, BigIntegers library [2].

program Modular_exponentiation;

{$APPTYPE CONSOLE}

uses
  System.SysUtils,
  Velthuis.BigIntegers;

var
  a, b, m: BigInteger;

begin
  a := BigInteger.Parse('2988348162058574136915891421498819466320163312926952423791023078876139');
  b := BigInteger.Parse('2351399303373464486466122544523690094744975233415544072992656881240319');
  m := BigInteger.Pow(10, 40);
  Writeln(BigInteger.ModPow(a, b, m).ToString);
  readln;
end.

Output:

1527229998585248450016808958343740453059

EchoLisp

(lib 'bigint)

(define a 2988348162058574136915891421498819466320163312926952423791023078876139)
(define b 2351399303373464486466122544523690094744975233415544072992656881240319)
(define m 1e40)

(powmod a b m)
    → 1527229998585248450016808958343740453059

;; powmod is a native function
;; it could be defined as follows :

(define (xpowmod base exp mod)
    (define result 1)
    (while ( !zero? exp)
        (when (odd? exp) (set! result (% (* result base) mod)))
    (/= exp 2)
    (set! base (% (* base base) mod)))
result)

(xpowmod a b m)
    → 1527229998585248450016808958343740453059

Emacs Lisp

Library: Calc

(let ((a "2988348162058574136915891421498819466320163312926952423791023078876139")
      (b "2351399303373464486466122544523690094744975233415544072992656881240319"))
  ;; "$ ^ $$ mod (10 ^ 40)" performs modular exponentiation.
  ;; "unpack(-5, x)_1" unpacks the integer from the modulo form.
  (message "%s" (calc-eval "unpack(-5, $ ^ $$ mod (10 ^ 40))_1" nil a b)))

Erlang

%%% For details of the algorithms used see
%%% https://en.wikipedia.org/wiki/Modular_exponentiation

-module modexp_rosetta.
-export [mod_exp/3,binary_exp/2,test/0].

mod_exp(Base,Exp,Mod) when
      is_integer(Base),    
      is_integer(Exp),
      is_integer(Mod),
      Base > 0,
      Exp > 0,
      Mod > 0 ->
    binary_exp_mod(Base,Exp,Mod).

binary_exp(Base,Exponent) ->
    binary_exp(Base,Exponent,1).
binary_exp(_,0,Result) ->
    Result;
binary_exp(Base,Exponent,Acc) ->
    binary_exp(Base*Base,Exponent bsr 1,Acc * exp_factor(Base,Exponent)).


binary_exp_mod(Base,Exponent,Mod) ->
    binary_exp_mod(Base rem Mod,Exponent,Mod,1).
binary_exp_mod(_,0,_,Result) ->
   Result;
binary_exp_mod(Base,Exponent,Mod,Acc) ->
    binary_exp_mod((Base*Base) rem Mod,
		   Exponent bsr 1,Mod,(Acc * exp_factor(Base,Exponent))rem Mod).

exp_factor(_,0) ->
    1;
exp_factor(Base,1) ->
    Base;
exp_factor(Base,Exponent) ->
    exp_factor(Base,Exponent band 1).

test() ->
    445 = mod_exp(4,13,497),
    %% Rosetta code example:
    mod_exp(2988348162058574136915891421498819466320163312926952423791023078876139,
	    2351399303373464486466122544523690094744975233415544072992656881240319,
	    binary_exp(10,40)).

34> modexp_rosetta:test().
modexp_rosetta:test().
1527229998585248450016808958343740453059
35> 

F#

let expMod a b n =
    let rec loop a b c =
        if b = 0I then c else
            loop (a*a%n) (b>>>1) (if b&&&1I = 0I then c else c*a%n)
    loop a b 1I

[<EntryPoint>]
let main argv =
    let a = 2988348162058574136915891421498819466320163312926952423791023078876139I
    let b = 2351399303373464486466122544523690094744975233415544072992656881240319I
    printfn "%A" (expMod a b (10I**40))    // -> 1527229998585248450016808958343740453059
    0

Factor

! Built-in
2988348162058574136915891421498819466320163312926952423791023078876139
2351399303373464486466122544523690094744975233415544072992656881240319
10 40 ^
^mod .

Output:

1527229998585248450016808958343740453059

FreeBASIC

 
'From first principles (No external library)
Function _divide(n1 As String,n2 As String,decimal_places As Integer=10,dpflag As String="s") As String
    Dim As String number=n1,divisor=n2
    dpflag=Lcase(dpflag)
    'For MOD
    Dim As Integer modstop
    If dpflag="mod" Then 
        If Len(n1)<Len(n2) Then Return n1
        If Len(n1)=Len(n2) Then
            If n1<n2 Then Return n1
        End If
        modstop=Len(n1)-Len(n2)+1
    End If
    If dpflag<>"mod" Then
        If dpflag<>"s"  Then dpflag="raw" 
    End If
    Dim runcount As Integer
    '_______  LOOK UP TABLES ______________
    Dim Qmod(0 To 19) As Ubyte
    Dim bool(0 To 19) As Ubyte
    For z As Integer=0 To 19
        Qmod(z)=(z Mod 10+48)
        bool(z)=(-(10>z))
    Next z
    Dim answer As String   'THE ANSWER STRING  
    
    '_______ SET THE DECIMAL WHERE IT SHOULD BE AT _______
    Dim As String part1,part2
    #macro set(decimal)
    #macro insert(s,char,position)
    If position > 0 And position <=Len(s) Then
        part1=Mid(s,1,position-1)
        part2=Mid(s,position)
        s=part1+char+part2
    End If
    #endmacro
    insert(answer,".",decpos)
    answer=thepoint+zeros+answer
    If dpflag="raw" Then
        answer=Mid(answer,1,decimal_places)
    End If
    #endmacro
    '______________________________________________
    '__________ SPLIT A STRING ABOUT A CHARACTRR __________
    Dim As String var1,var2
    Dim pst As Integer
    #macro split(stri,char,var1,var2)
    pst=Instr(stri,char)
    var1="":var2=""
    If pst<>0 Then
        var1=Rtrim(Mid(stri,1,pst),".")
        var2=Ltrim(Mid(stri,pst),".")
    Else
        var1=stri
    End If
    #endmacro
    
    #macro Removepoint(s)
    split(s,".",var1,var2)
    #endmacro
    '__________ GET THE SIGN AND CLEAR THE -ve __________________
    Dim sign As String
    If Left(number,1)="-" Xor Left (divisor,1)="-" Then sign="-"
    If Left(number,1)="-" Then  number=Ltrim(number,"-")
    If Left (divisor,1)="-" Then divisor=Ltrim(divisor,"-")
    
    'DETERMINE THE DECIMAL POSITION BEFORE THE DIVISION
    Dim As Integer lennint,lenddec,lend,lenn,difflen
    split(number,".",var1,var2)
    lennint=Len(var1)
    split(divisor,".",var1,var2)
    lenddec=Len(var2)
    
    If Instr(number,".") Then 
        Removepoint(number)
        number=var1+var2
    End If
    If Instr(divisor,".") Then 
        Removepoint(divisor)
        divisor=var1+var2
    End If
    Dim As Integer numzeros
    numzeros=Len(number)
    number=Ltrim(number,"0"):divisor=Ltrim (divisor,"0")
    numzeros=numzeros-Len(number)
    lend=Len(divisor):lenn=Len(number)
    If lend>lenn Then difflen=lend-lenn
    Dim decpos As Integer=lenddec+lennint-lend+2-numzeros 'THE POSITION INDICATOR
    Dim _sgn As Byte=-Sgn(decpos)
    If _sgn=0 Then _sgn=1
    Dim As String thepoint=String(_sgn,".") 'DECIMAL AT START (IF)
    Dim As String zeros=String(-decpos+1,"0")'ZEROS AT START (IF) e.g. .0009
    If dpflag<>"mod" Then
        If Len(zeros) =0 Then dpflag="s"
    End If
    Dim As Integer runlength
    If Len(zeros) Then 
        runlength=decimal_places
        answer=String(Len(zeros)+runlength+10,"0")
        If dpflag="raw" Then 
            runlength=1
            answer=String(Len(zeros)+runlength+10,"0")
            If decimal_places>Len(zeros) Then
                runlength=runlength+(decimal_places-Len(zeros))
                answer=String(Len(zeros)+runlength+10,"0")
            End If
        End If
        
    Else
        decimal_places=decimal_places+decpos
        runlength=decimal_places
        answer=String(Len(zeros)+runlength+10,"0")
    End If
    '___________DECIMAL POSITION DETERMINED  _____________
    
    'SET UP THE VARIABLES AND START UP CONDITIONS
    number=number+String(difflen+decimal_places,"0")
    Dim count As Integer
    Dim temp As String
    Dim copytemp As String
    Dim topstring As String
    Dim copytopstring As String
    Dim As Integer lenf,lens
    Dim As Ubyte takeaway,subtractcarry
    Dim As Integer n3,diff
    If Ltrim(divisor,"0")="" Then Return "Error :division by zero"   
    lens=Len(divisor)
    topstring=Left(number,lend)
    copytopstring=topstring
    Do
        count=0
        Do
            count=count+1
            copytemp=temp
            
            Do
                '___________________ QUICK SUBTRACTION loop _________________              
                
                lenf=Len(topstring)
                If  lens<lenf=0 Then 'not
                    If Lens>lenf Then
                        temp= "done"
                        Exit Do
                    End If
                    If divisor>topstring Then 
                        temp= "done"
                        Exit Do
                    End If
                End If
                
                diff=lenf-lens
                temp=topstring
                subtractcarry=0
                
                For n3=lenf-1 To diff Step -1
                    takeaway= topstring[n3]-divisor[n3-diff]+10-subtractcarry
                    temp[n3]=Qmod(takeaway)
                    subtractcarry=bool(takeaway)
                Next n3 
                If subtractcarry=0 Then Exit Do
                If n3=-1 Then Exit Do
                For n3=n3 To 0 Step -1 
                    takeaway= topstring[n3]-38-subtractcarry
                    temp[n3]=Qmod(takeaway)
                    subtractcarry=bool(takeaway)
                    If subtractcarry=0 Then Exit Do
                Next n3
                Exit Do
                
            Loop 'single run
            temp=Ltrim(temp,"0")
            If temp="" Then temp= "0"
            topstring=temp
        Loop Until temp="done"
        ' INDIVIDUAL CHARACTERS CARVED OFF ________________       
        runcount=runcount+1
        If count=1 Then
            topstring=copytopstring+Mid(number,lend+runcount,1)
        Else
            topstring=copytemp+Mid(number,lend+runcount,1)
        End If
        copytopstring=topstring
        topstring=Ltrim(topstring,"0")
        If dpflag="mod" Then
            If runcount=modstop Then 
                If topstring="" Then Return "0"
                Return Mid(topstring,1,Len(topstring)-1)
            End If
        End If
        answer[runcount-1]=count+47
        If topstring="" And runcount>Len(n1)+1 Then
            Exit Do
        End If
    Loop Until runcount=runlength+1
    
    ' END OF RUN TO REQUIRED DECIMAL PLACES
    set(decimal) 'PUT IN THE DECIMAL POINT
    'THERE IS ALWAYS A DECIMAL POINT SOMEWHERE IN THE ANSWER
    'NOW GET RID OF IT IF IT IS REDUNDANT
    answer=Rtrim(answer,"0")
    answer=Rtrim(answer,".")
    answer=Ltrim(answer,"0")
    If answer="" Then Return "0"
    Return sign+answer
End Function

Dim Shared As Integer _Mod(0 To 99),_Div(0 To 99)
For z As Integer=0 To 99:_Mod(z)=(z Mod 10+48):_Div(z)=z\10:Next
    
    Function Qmult(a As String,b As String) As String
        Var flag=0,la = Len(a),lb = Len(b)
        If Len(b)>Len(a) Then flag=1:Swap a,b:Swap la,lb
        Dim As Ubyte n,carry,ai
        Var c =String(la+lb,"0")
        For i As Integer =la-1 To 0 Step -1
            carry=0:ai=a[i]-48
            For j As Integer =lb-1 To 0 Step -1
                n = ai * (b[j]-48) + (c[i+j+1]-48) + carry
                carry =_Div(n):c[i+j+1]=_Mod(n)
            Next j
            c[i]+=carry
        Next i
        If flag Then Swap a,b
        Return Ltrim(c,"0")
    End Function
    '=======================================================================
    #define mod_(a,b) _divide((a),(b),,"mod")
    #define div_(a,b) iif(len((a))<len((b)),"0",_divide((a),(b),-2))
    
    Function Modular_Exponentiation(base_num As String, exponent As String, modulus As String) As String
        Dim b1 As String = base_num
        Dim e1 As String = exponent
        Dim As String result="1"
        b1 = mod_(b1,modulus)
        Do While e1 <> "0"
            Var L=Len(e1)-1
            If e1[L] And 1 Then
                result=mod_(Qmult(result,b1),modulus)
            End If
            b1=mod_(qmult(b1,b1),modulus)
            e1=div_(e1,"2")
        Loop
        Return result
    End Function
    
  
   
    
    var base_num="2988348162058574136915891421498819466320163312926952423791023078876139"
    var exponent="2351399303373464486466122544523690094744975233415544072992656881240319"
    var modulus="10000000000000000000000000000000000000000"
    dim as double t=timer
    var ans=Modular_Exponentiation(base_num,exponent,modulus)
    print "Result:"
    Print ans
    print "time taken  ";(timer-t)*1000;" milliseconds"
    Print "Done"
    Sleep

Result:
1527229998585248450016808958343740453059
time taken   93.09767815284431 milliseconds
Done

Frink

a = 2988348162058574136915891421498819466320163312926952423791023078876139
b = 2351399303373464486466122544523690094744975233415544072992656881240319
println[modPow[a,b,10^40]]

Output:

1527229998585248450016808958343740453059

GAP

# Built-in
a := 2988348162058574136915891421498819466320163312926952423791023078876139;
b := 2351399303373464486466122544523690094744975233415544072992656881240319;
PowerModInt(a, b, 10^40);
1527229998585248450016808958343740453059

# Implementation
PowerModAlt := function(a, n, m)
    local r;
    r := 1;
    while n > 0 do
        if IsOddInt(n) then
            r := RemInt(r*a, m);
        fi;
        n := QuoInt(n, 2);
        a := RemInt(a*a, m);
    od;
    return r;
end;

PowerModAlt(a, b, 10^40);

gnuplot

_powm(b, e, m, r) = (e == 0 ? r : (e % 2 == 1 ? _powm(b * b % m, e / 2, m, r * b % m) : _powm(b * b % m, e / 2, m, r)))
powm(b, e, m) = _powm(b, e, m, 1)
# Usage
print powm(2, 3453, 131)
# Where b is the base, e is the exponent, m is the modulus, i.e.: b^e mod m

Go

package main

import (
    "fmt"
    "math/big"
)

func main() {
    a, _ := new(big.Int).SetString(
        "2988348162058574136915891421498819466320163312926952423791023078876139", 10)
    b, _ := new(big.Int).SetString(
        "2351399303373464486466122544523690094744975233415544072992656881240319", 10)
    m := big.NewInt(10)
    r := big.NewInt(40)
    m.Exp(m, r, nil)

    r.Exp(a, b, m)
    fmt.Println(r)
}

Output:

1527229998585248450016808958343740453059

Groovy

println 2988348162058574136915891421498819466320163312926952423791023078876139.modPow(
            2351399303373464486466122544523690094744975233415544072992656881240319,
            10000000000000000000000000000000000000000)

Ouput:

1527229998585248450016808958343740453059

Haskell

modPow :: Integer -> Integer -> Integer -> Integer -> Integer
modPow b e 1 r = 0
modPow b 0 m r = r
modPow b e m r
  | e `mod` 2 == 1 = modPow b' e' m (r * b `mod` m)
  | otherwise = modPow b' e' m r
  where
    b' = b * b `mod` m
    e' = e `div` 2

main = do
  print (modPow 2988348162058574136915891421498819466320163312926952423791023078876139
    2351399303373464486466122544523690094744975233415544072992656881240319
    (10 ^ 40)
    1)

Output:

1527229998585248450016808958343740453059

or in terms of until:

powerMod :: Integer -> Integer -> Integer -> Integer
powerMod b e m = x
  where
    (_, _, x) =
      until
        (\(_, e, _) -> e <= 0)
        (\(b, e, x) ->
            ( mod (b * b) m
            , div e 2
            , if 0 /= mod e 2
                then mod (b * x) m
                else x))
        (b, e, 1)

main :: IO ()
main =
  print $
  powerMod
    2988348162058574136915891421498819466320163312926952423791023078876139
    2351399303373464486466122544523690094744975233415544072992656881240319
    (10 ^ 40)

Output:

1527229998585248450016808958343740453059

Icon and Unicon

This uses the exponentiation procedure from RSA Code an example of the right to left binary method.

procedure main()
    a := 2988348162058574136915891421498819466320163312926952423791023078876139
    b := 2351399303373464486466122544523690094744975233415544072992656881240319 
    write("last 40 digits = ",mod_power(a,b,(10^40))   
end

procedure mod_power(base, exponent, modulus)   # fast modular exponentation 
   if exponent < 0 then runerr(205,m)          # added for this task
   result := 1
   while exponent > 0 do {
      if exponent % 2 = 1 then 
         result := (result * base) % modulus
      exponent /:= 2   
      base := base ^ 2 % modulus
      }  
   return result
end

Output:

last 40 digits = 1527229998585248450016808958343740453059

J

Solution:

   m&|@^

Example:

   a =: 2988348162058574136915891421498819466320163312926952423791023078876139x
   b =: 2351399303373464486466122544523690094744975233415544072992656881240319x
   m =: 10^40x

   a m&|@^ b
1527229998585248450016808958343740453059

Discussion: The phrase a m&|@^ b is the natural expression of a^b mod m in J, and is recognized by the interpreter as an opportunity for optimization, by avoiding the exponentiation.

Java

java.math.BigInteger.modPow solves this task. Inside OpenJDK, BigInteger.java implements BigInteger.modPow with a fast algorithm from Colin Plumb's bnlib. This "window algorithm" caches odd powers of the base, to decrease the number of squares and multiplications. It also exploits both the Chinese remainder theorem and the Montgomery reduction.

import java.math.BigInteger;

public class PowMod {
    public static void main(String[] args){
        BigInteger a = new BigInteger(
      "2988348162058574136915891421498819466320163312926952423791023078876139");
        BigInteger b = new BigInteger(
      "2351399303373464486466122544523690094744975233415544072992656881240319");
        BigInteger m = new BigInteger("10000000000000000000000000000000000000000");
        
        System.out.println(a.modPow(b, m));
    }
}

Output:

1527229998585248450016808958343740453059

Julia

Works with: Julia version 1.0

We can use the built-in powermod function with the built-in BigInt type (based on GMP):

a = 2988348162058574136915891421498819466320163312926952423791023078876139
b = 2351399303373464486466122544523690094744975233415544072992656881240319
m = big(10) ^ 40
@show powermod(a, b, m)

Output:

powermod(a, b, m) = 1527229998585248450016808958343740453059

Kotlin

// version 1.0.6

import java.math.BigInteger

fun main(args: Array<String>) {
    val a = BigInteger("2988348162058574136915891421498819466320163312926952423791023078876139")
    val b = BigInteger("2351399303373464486466122544523690094744975233415544072992656881240319")
    val m = BigInteger.TEN.pow(40)
    println(a.modPow(b, m))
}

Output:

1527229998585248450016808958343740453059

Lambdatalk

Following scheme

We will call the lib_BN library for big numbers: 

{require lib_BN}

In this library {BN.compare a b} returns 1 if a > b, 0 if a = b and -1 if a < b. 
For a better readability we define three small functions

{def BN.= {lambda {:a :b} {= {BN.compare :a :b} 0}}} 
-> BN.=
{def BN.even? {lambda {:n} {= {BN.compare {BN.% :n 2} 0} 0}}} 
-> BN.even?
{def BN.square {lambda {:n} {BN.* :n :n}}} 
-> BN.square

{def mod-exp
 {lambda {:a :n :mod}
  {if {BN.= :n 0}
   then 1
   else {if {BN.even? :n}
   then {BN.% {BN.square {mod-exp :a {BN./ :n 2} :mod}} :mod}
   else {BN.% {BN.* :a   {mod-exp :a {BN.- :n 1} :mod}} :mod}}}}}
-> mod-exp

{mod-exp 
  2988348162058574136915891421498819466320163312926952423791023078876139 
  2351399303373464486466122544523690094744975233415544072992656881240319 
  {BN.pow 10 40}}
-> 1527229998585248450016808958343740453059   // 3300ms

Maple

a := 2988348162058574136915891421498819466320163312926952423791023078876139:
b := 2351399303373464486466122544523690094744975233415544072992656881240319:
a &^ b mod 10^40;

Output:

1527229998585248450016808958343740453059

Mathematica/Wolfram Language

a = 2988348162058574136915891421498819466320163312926952423791023078876139;
b = 2351399303373464486466122544523690094744975233415544072992656881240319;
m = 10^40;
PowerMod[a, b, m]
-> 1527229998585248450016808958343740453059

Maxima

a: 2988348162058574136915891421498819466320163312926952423791023078876139$
b: 2351399303373464486466122544523690094744975233415544072992656881240319$
power_mod(a, b, 10^40);
/* 1527229998585248450016808958343740453059 */

Nim

Library: bigints

import bigints

proc powmod(b, e, m: BigInt): BigInt =
  assert e >= 0
  var e = e
  var b = b
  result = initBigInt(1)
  while e > 0:
    if e mod 2 == 1:
      result = (result * b) mod m
    e = e div 2
    b = (b.pow 2) mod m

var
  a = initBigInt("2988348162058574136915891421498819466320163312926952423791023078876139")
  b = initBigInt("2351399303373464486466122544523690094744975233415544072992656881240319")

echo powmod(a, b, 10.pow 40)

Output:

1527229998585248450016808958343740453059

OCaml

Using the zarith library:

let a = Z.of_string "2988348162058574136915891421498819466320163312926952423791023078876139" in
let b = Z.of_string "2351399303373464486466122544523690094744975233415544072992656881240319" in
let m = Z.pow (Z.of_int 10) 40 in
Z.powm a b m
|> Z.to_string
|> print_endline

Output:

1527229998585248450016808958343740453059

Oforth

Usage : a b mod powmod

: powmod(base, exponent, modulus)
   1 exponent dup ifZero: [ return ]
    while ( dup 0 > ) [ 
      dup isEven ifFalse: [ swap base * modulus mod swap ] 
      2 / base sq modulus mod ->base
      ] drop ;

Output:

>2988348162058574136915891421498819466320163312926952423791023078876139
ok
>2351399303373464486466122544523690094744975233415544072992656881240319
ok
>10 40 pow
ok
>powmod println
1527229998585248450016808958343740453059
ok

ooRexx

/* Modular exponentiation */

numeric digits 100
say powerMod(,
 2988348162058574136915891421498819466320163312926952423791023078876139,,
 2351399303373464486466122544523690094744975233415544072992656881240319,,
 1e40)
exit

powerMod: procedure

use strict arg base, exponent, modulus

exponent=exponent~d2x~x2b~strip('L','0')
result=1
base = base // modulus
do exponentPos=exponent~length to 1 by -1
  if (exponent~subChar(exponentPos) == '1')
    then result = (result * base) // modulus
  base = (base * base) // modulus
end
return result

Output:

1527229998585248450016808958343740453059

PARI/GP

a=2988348162058574136915891421498819466320163312926952423791023078876139;
b=2351399303373464486466122544523690094744975233415544072992656881240319;
lift(Mod(a,10^40)^b)

Pascal

Works with: Free_Pascal

Library: GMP

A port of the C example using gmp.

Program ModularExponentiation(output);

uses
  gmp;
  
var
  a, b, m, r: mpz_t;
  fmt: pchar;

begin
  mpz_init_set_str(a, '2988348162058574136915891421498819466320163312926952423791023078876139', 10);
  mpz_init_set_str(b, '2351399303373464486466122544523690094744975233415544072992656881240319', 10);
  mpz_init(m);
  mpz_ui_pow_ui(m, 10, 40);

  mpz_init(r);
  mpz_powm(r, a, b, m);

  fmt := '%Zd' + chr(13) + chr(10);
  mp_printf(fmt, @r); (* ...16808958343740453059 *)
  
  mpz_clear(a);
  mpz_clear(b);
  mpz_clear(m);
  mpz_clear(r);
end.

Output:

% ./ModularExponentiation
1527229998585248450016808958343740453059

Perl

Calculating the result both with an explicit algorithm (borrowed from Raku example) and with a built-in available when the use bigint pragma is invoked. Note that bmodpow modifies the base value (here $a) while expmod does not.

use bigint;

sub expmod {
    my($a, $b, $n) = @_;
    my $c = 1;
    do {
        ($c *= $a) %= $n if $b % 2;
        ($a *= $a) %= $n;
    } while ($b = int $b/2);
    $c;
}

my $a = 2988348162058574136915891421498819466320163312926952423791023078876139;
my $b = 2351399303373464486466122544523690094744975233415544072992656881240319;
my $m = 10 ** 40;

print expmod($a, $b, $m), "\n";
print $a->bmodpow($b, $m), "\n";

Output:

1527229998585248450016808958343740453059
1527229998585248450016808958343740453059

Phix

Library: Phix/mpfr

Already builtin as mpz_powm, but here is an explicit version

with javascript_semantics 
include mpfr.e
procedure mpz_mod_exp(mpz base, exponent, modulus, result)
    if mpz_cmp_si(exponent,1)=0 then
        mpz_set(result,base)
    else
        mpz _exp = mpz_init_set(exponent) -- (use a copy)
        bool odd = mpz_odd(_exp)
        if odd then
            mpz_sub_ui(_exp,_exp,1)
        end if
        mpz_fdiv_q_2exp(_exp,_exp,1)
        mpz_mod_exp(base,_exp,modulus,result)
        _exp = mpz_free(_exp)
        mpz_mul(result,result,result)
        if odd then
            mpz_mul(result,result,base)
        end if
    end if
    mpz_mod(result,result,modulus)
end procedure
 
mpz base     = mpz_init("2988348162058574136915891421498819466320163312926952423791023078876139"),
    exponent = mpz_init("2351399303373464486466122544523690094744975233415544072992656881240319"),
    modulus  = mpz_init("1"&repeat('0',40)),
    result   = mpz_init()
 
mpz_mod_exp(base,exponent,modulus,result)
?mpz_get_str(result)
 
-- check against the builtin:
mpz_powm(result,base,exponent,modulus)
?mpz_get_str(result)

Output:

"1527229998585248450016808958343740453059"
"1527229998585248450016808958343740453059"

PHP

<?php
$a = '2988348162058574136915891421498819466320163312926952423791023078876139';
$b = '2351399303373464486466122544523690094744975233415544072992656881240319';
$m = '1' . str_repeat('0', 40);
echo bcpowmod($a, $b, $m), "\n";

Output:

1527229998585248450016808958343740453059

PicoLisp

The following function is taken from "lib/rsa.l":

(de **Mod (X Y N)
   (let M 1
      (loop
         (when (bit? 1 Y)
            (setq M (% (* M X) N)) )
         (T (=0 (setq Y (>> 1 Y)))
            M )
         (setq X (% (* X X) N)) ) ) )

Test:

: (**Mod
   2988348162058574136915891421498819466320163312926952423791023078876139
   2351399303373464486466122544523690094744975233415544072992656881240319
   10000000000000000000000000000000000000000 )
-> 1527229998585248450016808958343740453059

Prolog

Works with: SWI Prolog

SWI Prolog has a built-in function named powm for this purpose.

main:-
    A = 2988348162058574136915891421498819466320163312926952423791023078876139,
    B = 2351399303373464486466122544523690094744975233415544072992656881240319,
    M is 10 ** 40,
    P is powm(A, B, M),
    writeln(P).

Output:

1527229998585248450016808958343740453059

Python

a = 2988348162058574136915891421498819466320163312926952423791023078876139
b = 2351399303373464486466122544523690094744975233415544072992656881240319
m = 10 ** 40
print(pow(a, b, m))

Output:

1527229998585248450016808958343740453059

def power_mod(b, e, m):
    " Without using builtin function "
    x = 1
    while e > 0:
        b, e, x = (
            b * b % m,
            e // 2,
            b * x % m if e % 2 else x
        )

    return x


a = 2988348162058574136915891421498819466320163312926952423791023078876139
b = 2351399303373464486466122544523690094744975233415544072992656881240319
m = 10 ** 40
print(power_mod(a, b, m))

Output:

1527229998585248450016808958343740453059

Quackery

  [ temp put 1 unrot
    [ dup while
      dup 1 & if
        [ unrot tuck *
          temp share mod
          swap rot ]
      1 >> 
      swap dup *
      temp share mod
      swap again ]
    2drop temp release ] is **mod ( n n n --> n )
 
 2988348162058574136915891421498819466320163312926952423791023078876139
 2351399303373464486466122544523690094744975233415544072992656881240319
 10 40 ** **mod echo

Output:

1527229998585248450016808958343740453059

Racket

#lang racket
(require math)
(define a 2988348162058574136915891421498819466320163312926952423791023078876139)
(define b 2351399303373464486466122544523690094744975233415544072992656881240319)
(define m (expt 10 40))
(modular-expt a b m)

Output:

1527229998585248450016808958343740453059

Raku

(formerly Perl 6) This is specced as a built-in, but here's an explicit version:

sub expmod(Int $a is copy, Int $b is copy, $n) {
    my $c = 1;
    repeat while $b div= 2 {
        ($c *= $a) %= $n if $b % 2;
        ($a *= $a) %= $n;
    }
    $c;
}

say expmod
    2988348162058574136915891421498819466320163312926952423791023078876139,
    2351399303373464486466122544523690094744975233415544072992656881240319,
    10**40;

Output:

1527229998585248450016808958343740453059

REXX

version 1

This REXX program attempts to handle   any   a,   b,   or   m,   but there are limits for any computer language.

For some REXXes, it's around eight million digits for any arithmetic expression or value, which puts limitations on
the values of   a²   or   10^m.

This REXX program code has code to   automatically   adjust the number of decimal digits to accommodate huge
numbers which are computed when raising large numbers to some arbitrary power.

/*REXX program  displays the  modular exponentiation  of:         a**b  mod  m          */
parse arg a b m                                       /*obtain optional args from the CL*/
if a=='' | a==","  then a= 2988348162058574136915891421498819466320163312926952423791023078876139
if b=='' | b==","  then b= 2351399303373464486466122544523690094744975233415544072992656881240319
if m ='' | m =","  then m= 40                         /*Not specified? Then use default.*/
say 'a=' a               "     ("length(a)  'digits)' /*display the value of A (&length)*/
say 'b=' b               "     ("length(b)  'digits)' /*   "     "    "    " B     "    */
       do j=1  for words(m);           y= word(m, j)  /*use one of the MM powers (list).*/
       say copies('═', linesize() - 1)                /*show a nice separator fence line*/
       say 'a**b (mod 10**'y")="  powerMod(a,b,10**y) /*display the answer ───► console.*/
       end   /*j*/
exit 0                                                /*stick a fork in it, we're done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
powerMod: procedure;  parse arg x,p,mm                /*fast modular exponentiation code*/
          parse value max(x*x, p, mm)'E0'  with "E" e /*obtain the biggest of the three.*/
          numeric digits max(40, e+e)                 /*ensure big enough to handle  A².*/
          $= 1                                        /*use this for the first value.   */
                  do  until p==0                      /*perform until P is equal to zero*/
                  if p // 2  then $= $ * x  //  mm    /*is P odd?  (is ÷ remainder ≡ 1?)*/
                  p= p % 2;       x= x * x  //  mm    /*halve  P;   calculate  x² mod n */
                  end   /*until*/;         return $   /* [↑]  keep mod'ing until P=zero.*/

This REXX program makes use of   LINESIZE   REXX program (or BIF) which is used to determine the screen width (or linesize) of the terminal (console).
The BIF is used to determine the width of a line separator   (which are used to separate different outputs).
The   LINESIZE.REX   REXX program is included here   ──►   LINESIZE.REX.

output   when using the inputs of:     ,   ,   40   80   180   888

a= 2988348162058574136915891421498819466320163312926952423791023078876139      (70 digits)
b= 2351399303373464486466122544523690094744975233415544072992656881240319      (70 digits)
═══════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════
a**b (mod 10**40)= 1527229998585248450016808958343740453059
═══════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════
a**b (mod 10**80)= 53259517041910225328867076245698908287781527229998585248450016808958343740453059
═══════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════
a**b (mod 10**180)= 31857295076204937005344367438778481743660325586328069392203762862423884839076695547212682454523811053259517041910225328867076245698908287781527229998585248450016808958343740453059
═══════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════════
a**b (mod 10**888)= 261284964380836515397030706363442226571397237057488951313684545241085642329943676248755716124260447188788530017182951051652748425560733974835944416069466176713156182727448301838517000343485327001656948285381173038339073779331230132340669899896448938858785362771190460312412579875349871655999446205426049662261450633448468931573506876255644749155348923523680730999869785472779116009356696816952771965930728940530517799329942590114178284009260298426735086579254282591289756840358811
822151307479352856856983393715348870715239020037962938019847992960978849852850613063177471175191444262586321233906926671000476591123695550566585083205841790404069511972417770392822283604206143472509425391114072344402850867571806031857295076204937005344367438778481743660325586328069392203762862423884839076695547212682454523811053259517041910225328867076245698908287781527229998585248450016808958343740453059

version 2

This REXX version handles only up to 100 decimal digits.

/* REXX  Modular exponentiation */ 

numeric digits 100
say powerMod(, 
 2988348162058574136915891421498819466320163312926952423791023078876139,, 
 2351399303373464486466122544523690094744975233415544072992656881240319,, 
 1e40)
exit 

powerMod: procedure

parse arg base, exponent, modulus 

exponent = strip(x2b(d2x(exponent)), 'L', '0')
result = 1
base = base // modulus
do exponentPos=length(exponent) to 1 by -1  
  if substr(exponent, exponentPos, 1) = '1'    
    then result = (result * base) // modulus  
  base = (base * base) // modulus
end
return result

Output:

1527229998585248450016808958343740453059

Ruby

Built in since version 2.5.

a = 2988348162058574136915891421498819466320163312926952423791023078876139
b = 2351399303373464486466122544523690094744975233415544072992656881240319
m = 10**40
puts a.pow(b, m)

Using OpenSSL standard library

Library: OpenSSL

require 'openssl'
a = 2988348162058574136915891421498819466320163312926952423791023078876139
b = 2351399303373464486466122544523690094744975233415544072992656881240319
m = 10 ** 40
puts a.to_bn.mod_exp(b, m)

Written in Ruby

def mod_exp(n, e, mod)
    fail ArgumentError, 'negative exponent' if e < 0
    prod = 1
    base = n % mod
    until e.zero?
      prod = (prod * base) % mod if e.odd?
      e >>= 1
      base = (base * base) % mod
    end
    prod
  end

Rust

/* Add this line to the [dependencies] section of your Cargo.toml file:
num = "0.2.0"
*/


use num::bigint::BigInt;
use num::bigint::ToBigInt;


// The modular_exponentiation() function takes three identical types
// (which get cast to BigInt), and returns a BigInt:
fn modular_exponentiation<T: ToBigInt>(n: &T, e: &T, m: &T) -> BigInt {
    // Convert n, e, and m to BigInt:
    let n = n.to_bigint().unwrap();
    let e = e.to_bigint().unwrap();
    let m = m.to_bigint().unwrap();

    // Sanity check:  Verify that the exponent is not negative:
    assert!(e >= Zero::zero());

    use num::traits::{Zero, One};

    // As most modular exponentiations do, return 1 if the exponent is 0:
    if e == Zero::zero() {
        return One::one()
    }

    // Now do the modular exponentiation algorithm:
    let mut result: BigInt = One::one();
    let mut base = n % &m;
    let mut exp = e;

    // Loop until we can return out result:
    loop {
        if &exp % 2 == One::one() {
            result *= &base;
            result %= &m;
        }

        if exp == One::one() {
            return result
        }

        exp /= 2;
        base *= base.clone();
        base %= &m;
    }
}

Test code:

fn main() {
    let (a, b, num_digits) = (
  "2988348162058574136915891421498819466320163312926952423791023078876139",
  "2351399303373464486466122544523690094744975233415544072992656881240319",
  "40",
                    );

    // Covert a, b, and num_digits to numbers:
    let a = BigInt::parse_bytes(a.as_bytes(), 10).unwrap();
    let b = BigInt::parse_bytes(b.as_bytes(), 10).unwrap();
    let num_digits = num_digits.parse().unwrap();

    // Calculate m from num_digits:
    let m = num::pow::pow(10.to_bigint().unwrap(), num_digits);

    // Get the result and print it:
    let result = modular_exponentiation(&a, &b, &m);
    println!("The last {} digits of\n{}\nto the power of\n{}\nare:\n{}",
             num_digits, a, b, result);
}

Output:

The last 40 digits of
2988348162058574136915891421498819466320163312926952423791023078876139
to the power of
2351399303373464486466122544523690094744975233415544072992656881240319
are:
1527229998585248450016808958343740453059

Scala

import scala.math.BigInt

val a = BigInt(
  "2988348162058574136915891421498819466320163312926952423791023078876139")
val b = BigInt(
  "2351399303373464486466122544523690094744975233415544072992656881240319")

println(a.modPow(b, BigInt(10).pow(40)))

Scheme

(define (square n)
  (* n n))

(define (mod-exp a n mod)
  (cond ((= n 0) 1)
        ((even? n) 
         (remainder (square (mod-exp a (/ n 2) mod)) 
                    mod))
        (else (remainder (* a (mod-exp a (- n 1) mod)) 
                         mod))))

(define result
  (mod-exp 2988348162058574136915891421498819466320163312926952423791023078876139 
           2351399303373464486466122544523690094744975233415544072992656881240319 
           (expt 10 40)))

Output:

> result
1527229998585248450016808958343740453059

Seed7

The library bigint.s7i defines the function modPow, which does modular exponentiation.

$ include "seed7_05.s7i";
  include "bigint.s7i";

const proc: main is func
  begin
    writeln(modPow(2988348162058574136915891421498819466320163312926952423791023078876139_,
                   2351399303373464486466122544523690094744975233415544072992656881240319_,
                   10_ ** 40));
  end func;

Output:

1527229998585248450016808958343740453059

The library bigint.s7i defines modPow with:

const func bigInteger: modPow (in var bigInteger: base,
    in var bigInteger: exponent, in bigInteger: modulus) is func
  result
    var bigInteger: power is 1_;
  begin
    if exponent < 0_ or modulus < 0_ then
      raise RANGE_ERROR;
    else
      while exponent > 0_ do
        if odd(exponent) then
          power := (power * base) mod modulus;
        end if;
        exponent >>:= 1;
        base := base ** 2 mod modulus;
      end while;
    end if;
  end func;

Original source: [3]

Sidef

Built-in:

say expmod(
    2988348162058574136915891421498819466320163312926952423791023078876139,
    2351399303373464486466122544523690094744975233415544072992656881240319,
    10**40)

User-defined:

func expmod(a, b, n) {
    var c = 1
    do {
        (c *= a) %= n if b.is_odd
        (a *= a) %= n
    } while (b //= 2)
    c
}

Output:

1527229998585248450016808958343740453059

Swift

Library: AttaSwift BigInt

AttaSwift's BigInt has a built-in modPow method, but here we define a generic modPow.

import BigInt

func modPow<T: BinaryInteger>(n: T, e: T, m: T) -> T {
  guard e != 0 else {
    return 1
  }

  var res = T(1)
  var base = n % m
  var exp = e

  while true {
    if exp & 1 == 1 {
      res *= base
      res %= m
    }

    if exp == 1 {
      return res
    }

    exp /= 2
    base *= base
    base %= m
  }
}

let a = BigInt("2988348162058574136915891421498819466320163312926952423791023078876139")
let b = BigInt("2351399303373464486466122544523690094744975233415544072992656881240319")

print(modPow(n: a, e: b, m: BigInt(10).power(40)))

Output:

1527229998585248450016808958343740453059

Tcl

While Tcl does have arbitrary-precision arithmetic (from 8.5 onwards), it doesn't expose a modular exponentiation function. Thus we implement one ourselves.

Recursive

package require Tcl 8.5

# Algorithm from http://introcs.cs.princeton.edu/java/78crypto/ModExp.java.html
# but Tcl has arbitrary-width integers and an exponentiation operator, which
# helps simplify the code.
proc tcl::mathfunc::modexp {a b n} {
    if {$b == 0} {return 1}
    set c [expr {modexp($a, $b / 2, $n)**2 % $n}]
    if {$b & 1} {
	set c [expr {($c * $a) % $n}]
    }
    return $c
}

Demonstrating:

set a 2988348162058574136915891421498819466320163312926952423791023078876139
set b 2351399303373464486466122544523690094744975233415544072992656881240319
set n [expr {10**40}]
puts [expr {modexp($a,$b,$n)}]

Output:

 1527229998585248450016808958343740453059

Iterative

package require Tcl 8.5
proc modexp {a b n} {
    for {set c 1} {$b} {set a [expr {$a*$a % $n}]} {
	if {$b & 1} {
	    set c [expr {$c*$a % $n}]
	}
	set b [expr {$b >> 1}]
    }
    return $c 
}

Demonstrating:

set a 2988348162058574136915891421498819466320163312926952423791023078876139
set b 2351399303373464486466122544523690094744975233415544072992656881240319
set n [expr {10**40}]
puts [modexp $a $b $n]

Output:

 1527229998585248450016808958343740453059

TXR

From your system prompt:

$ txr -p '(exptmod 2988348162058574136915891421498819466320163312926952423791023078876139
                   2351399303373464486466122544523690094744975233415544072992656881240319
                   (expt 10 40)))'
1527229998585248450016808958343740453059

Visual Basic .NET

Works with: Visual Basic .NET version 2011

' Modular exponentiation - VB.Net - 21/01/2019
    Imports System.Numerics

    Private Sub Main()
        Dim a, b, m, x As BigInteger
        a = BigInteger.Parse("2988348162058574136915891421498819466320163312926952423791023078876139")
        b = BigInteger.Parse("2351399303373464486466122544523690094744975233415544072992656881240319")
        m = BigInteger.Pow(10, 40)   '=10^40
        x = ModPowBig(a, b, m)
        Debug.Print("x=" & x.ToString)
    End Sub 'Main

    Function ModPowBig(ByVal base As BigInteger, ByVal exponent As BigInteger, ByVal modulus As BigInteger) As BigInteger
        Dim result As BigInteger
        result = 1
        Do While exponent > 0
            If (exponent Mod 2) = 1 Then
                result = (result * base) Mod modulus
            End If
            exponent = exponent / 2
            base = (base * base) Mod modulus
        Loop
        Return result
    End Function 'ModPowBig

Output:

x=1527229998585248450016808958343740453059

Wren

Library: Wren-big

import "/big" for BigInt

var a = BigInt.new("2988348162058574136915891421498819466320163312926952423791023078876139")
var b = BigInt.new("2351399303373464486466122544523690094744975233415544072992656881240319")
var m = BigInt.ten.pow(40)
System.print(a.modPow(b, m))

Output:

1527229998585248450016808958343740453059

zkl

Using the GMP big num library:

var BN=Import("zklBigNum");
a:=BN("2988348162058574136915891421498819466320163312926952423791023078876139");
b:=BN("2351399303373464486466122544523690094744975233415544072992656881240319");
m:=BN(10).pow(40);
a.powm(b,m).println();
a.powm(b,m) : "%,d".fmt(_).println();

Output:

1527229998585248450016808958343740453059
1,527,229,998,585,248,450,016,808,958,343,740,453,059