September Morn Update
This commit is contained in:
Ingy döt Net
parent
4e2d22a71d
commit
aac6731f2c
6856 changed files with 141342 additions and 21127 deletions
1
Task/Modular-exponentiation/00META.yaml
Normal file
1
Task/Modular-exponentiation/00META.yaml
Normal file
|
|
@ -0,0 +1 @@
|
|||
--- {}
|
||||
|
|
@ -0,0 +1,12 @@
|
|||
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));
|
||||
}
|
||||
}
|
||||
|
|
@ -3,4 +3,3 @@
|
|||
2351399303373464486466122544523690094744975233415544072992656881240319
|
||||
10 40 ^
|
||||
^mod .
|
||||
1527229998585248450016808958343740453059
|
||||
|
|
|
|||
|
|
@ -0,0 +1,258 @@
|
|||
'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
|
||||
|
|
@ -1,6 +1,18 @@
|
|||
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";
|
||||
|
|
|
|||
32
Task/Modular-exponentiation/Phix/modular-exponentiation.phix
Normal file
32
Task/Modular-exponentiation/Phix/modular-exponentiation.phix
Normal file
|
|
@ -0,0 +1,32 @@
|
|||
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)
|
||||
|
|
@ -1,6 +1,4 @@
|
|||
require 'openssl'
|
||||
|
||||
a = 2988348162058574136915891421498819466320163312926952423791023078876139
|
||||
b = 2351399303373464486466122544523690094744975233415544072992656881240319
|
||||
m = 10 ** 40
|
||||
puts a.to_bn.mod_exp(b, m)
|
||||
m = 10**40
|
||||
puts a.pow(b, m)
|
||||
|
|
|
|||
|
|
@ -1,18 +1,5 @@
|
|||
class Integer
|
||||
def rosetta_mod_exp(exp, mod)
|
||||
exp < 0 and raise ArgumentError, "negative exponent"
|
||||
prod = 1
|
||||
base = self % mod
|
||||
until exp.zero?
|
||||
exp.odd? and prod = (prod * base) % mod
|
||||
exp >>= 1
|
||||
base = (base * base) % mod
|
||||
end
|
||||
prod
|
||||
end
|
||||
end
|
||||
|
||||
require 'openssl'
|
||||
a = 2988348162058574136915891421498819466320163312926952423791023078876139
|
||||
b = 2351399303373464486466122544523690094744975233415544072992656881240319
|
||||
m = 10 ** 40
|
||||
puts a.rosetta_mod_exp(b, m)
|
||||
puts a.to_bn.mod_exp(b, m)
|
||||
|
|
|
|||
11
Task/Modular-exponentiation/Ruby/modular-exponentiation-3.rb
Normal file
11
Task/Modular-exponentiation/Ruby/modular-exponentiation-3.rb
Normal file
|
|
@ -0,0 +1,11 @@
|
|||
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
|
||||
|
|
@ -0,0 +1,48 @@
|
|||
/* 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;
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,20 @@
|
|||
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);
|
||||
}
|
||||
|
|
@ -0,0 +1,24 @@
|
|||
' 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
|
||||
Loading…
Add table
Add a link
Reference in a new issue