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Ingy döt Net 2024-07-13 15:19:22 -07:00
parent 29a5eea0d4
commit 5c1bb7bfa9
2011 changed files with 35081 additions and 3229 deletions
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58
Task/P-Adic-numbers-basic/C++/p-adic-numbers-basic.cpp
View file

@ -37,21 +37,22 @@ private:
class P_adic {
public:
// Create a P-adic number, with p = 'prime', from the given rational 'numerator' / 'denominator'.
// Create a P_adic number, with p = 'prime', from the given rational 'numerator' / 'denominator'.
P_adic(const uint32_t& prime, int32_t numerator, int32_t denominator) : prime(prime) {
if ( denominator == 0 ) {
std::invalid_argument("Denominator cannot be zero");
throw std::invalid_argument("Denominator cannot be zero");
}
order = 0;
// Process rational zero
if ( numerator == 0 ) {
digits.assign(DIGITS_SIZE, 0);
order = ORDER_MAX;
return;
}
// Remove multiples of 'prime' and adjust the order of the P-adic number accordingly
// Remove multiples of 'prime' and adjust the order of the P_adic number accordingly
while ( modulo_prime(numerator) == 0 ) {
numerator /= static_cast<int32_t>(prime);
order += 1;
@ -62,7 +63,7 @@ public:
order -= 1;
}
// Standard calculation of P-adic digits
// Standard calculation of P_adic digits
const uint64_t inverse = modulo_inverse(denominator);
while ( digits.size() < DIGITS_SIZE ) {
const uint32_t digit = modulo_prime(numerator * inverse);
@ -85,17 +86,17 @@ public:
}
}
// Return the sum of this P-adic number with the given P-adic number.
// Return the sum of this P_adic number with the given P_adic number.
P_adic add(P_adic other) {
if ( prime != other.prime ) {
std::invalid_argument("Cannot add p-adic's with different primes");
throw std::invalid_argument("Cannot add p-adic's with different primes");
}
std::vector<uint32_t> this_digits = digits;
std::vector<uint32_t> other_digits = other.digits;
std::vector<uint32_t> result;
// Adjust the digits so that the P-adic points are aligned
// Adjust the digits so that the P_adic points are aligned
for ( int32_t i = 0; i < -order + other.order; ++i ) {
other_digits.insert(other_digits.begin(), 0);
}
@ -116,12 +117,12 @@ public:
return P_adic(prime, result, all_zero_digits(result) ? ORDER_MAX : std::min(order, other.order));
}
// Return the Rational representation of this P-adic number.
// Return the Rational representation of this P_adic number.
Rational convert_to_rational() {
std::vector<uint32_t> numbers = digits;
// Zero
if ( all_zero_digits(numbers) ) {
if ( numbers.empty() || all_zero_digits(numbers) ) {
return Rational(1, 0);
}
@ -171,37 +172,38 @@ public:
return Rational(numerator, denominator);
}
// Return a string representation of this p-adic.
// Return a string representation of this P_adic number.
std::string to_string() {
while ( digits.size() > PRECISION ) {
digits.pop_back();
}
pad_with_zeros(digits);
std::vector<uint32_t> numbers = digits;
pad_with_zeros(numbers);
std::string result = "";
for ( int64_t i = digits.size() - 1; i >= 0; --i ) {
for ( int64_t i = numbers.size() - 1; i >= 0; --i ) {
result += std::to_string(digits[i]);
}
if ( order >= 0 ) {
for ( int32_t i = 0; i < order; ++i ) {
result += "0";
result.erase(result.begin());
}
result += ".0";
} else {
result.insert(result.length() + order, ".");
while ( result[result.length() - 1] == '0' ) {
result = result.substr(0, result.length() - 1);
}
}
return " ..." + result;
return " ..." + result.substr(result.length() - PRECISION - 1);
}
private:
/**
* Create a P-adic, with p = 'prime', directly from a vector of digits.
* Create a P_adic, with p = 'prime', directly from a vector of digits.
*
* With 'order' = 0, the vector [1, 2, 3, 4, 5] creates the p-adic ...54321.0
* For example: with 'order' = 0, the vector [1, 2, 3, 4, 5] creates the p-adic ...54321.0,
* 'order' > 0 shifts the vector 'order' places to the left and
* 'order' < 0 shifts the vector 'order' places to the right.
*/
@ -209,10 +211,10 @@ private:
: prime(prime), digits(digits), order(order) {
}
// Transform the given vector of digits representing a p-adic number
// into a vector which represents the negation of the p-adic number.
void negate_digits(std::vector<uint32_t> numbers) {
numbers[0] = ( prime - numbers[0] ) % prime;
// Transform the given vector of digits representing a P_adic number
// into a vector which represents the negation of the P_adic number.
void negate_digits(std::vector<uint32_t>& numbers) {
numbers[0] = modulo_prime(prime - numbers[0]);
for ( uint64_t i = 1; i < numbers.size(); ++i ) {
numbers[i] = prime - 1 - numbers[i];
}
@ -221,7 +223,7 @@ private:
// Return the multiplicative inverse of the given number modulo 'prime'.
uint32_t modulo_inverse(const uint32_t& number) const {
uint32_t inverse = 1;
while ( ( inverse * number ) % prime != 1 ) {
while ( modulo_prime(inverse * number) != 1 ) {
inverse += 1;
}
return inverse;
@ -233,9 +235,9 @@ private:
return ( div >= 0 ) ? div : div + prime;
}
// The given vector is padded on the right by zeros up to a maximum length of 'PRECISION'.
void pad_with_zeros(std::vector<uint32_t> vector) {
while ( vector.size() < PRECISION ) {
// The given vector is padded on the right by zeros up to a maximum length of 'DIGITS_SIZE'.
void pad_with_zeros(std::vector<uint32_t>& vector) {
while ( vector.size() < DIGITS_SIZE ) {
vector.emplace_back(0);
}
}
@ -288,7 +290,7 @@ int main() {
std::cout << "4 / 97 => " << padic_two.to_string() << std::endl;
P_adic sum = padic_one.add(padic_two);
std::cout << "sum => " << sum.to_string() << std::endl;
std::cout << "sum => " << sum.to_string() << std::endl;
std::cout << "Rational = " << sum.convert_to_rational().to_string() << std::endl;
std::cout << std::endl;

35
Task/P-Adic-numbers-basic/Java/p-adic-numbers-basic.java
View file

@ -1,3 +1,8 @@
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.stream.Collectors;
public final class PAdicNumbersBasic {
public static void main(String[] args) {
@ -124,7 +129,7 @@ final class Padic {
List<Integer> numbers = new ArrayList<Integer>(digits);
// Zero
if ( allZeroDigits(numbers) ) {
if ( numbers.isEmpty() || allZeroDigits(numbers) ) {
return new Rational(0, 1);
}
@ -177,29 +182,28 @@ final class Padic {
/**
* Return a string representation of this p-adic.
*/
public String toString() {
while ( digits.size() > PRECISION ) {
digits.removeLast();
}
padWithZeros(digits);
StringBuilder builder = new StringBuilder();
for ( int i = digits.size() - 1; i >= 0; i-- ) {
builder.append(digits.get(i));
}
public String toString() {
List<Integer> numbers = new ArrayList<Integer>(digits);
padWithZeros(numbers);
Collections.reverse(numbers);
String numberString = numbers.stream().map(String::valueOf).collect(Collectors.joining());
StringBuilder builder = new StringBuilder(numberString);
if ( order >= 0 ) {
for ( int i = 0; i < order; i++ ) {
builder.append("0");
builder.deleteCharAt(0);
}
builder.append(".0");
} else {
builder.insert(builder.length() + order, ".");
while ( builder.toString().endsWith("0") ) {
builder.deleteCharAt(builder.length() - 1);
}
}
return " ..." + builder.toString();
return " ..." + builder.toString().substring(builder.length() - PRECISION - 1);
}
// PRIVATE //
@ -214,7 +218,6 @@ final class Padic {
private Padic(int aPrime, List<Integer> aDigits, int aOrder) {
prime = aPrime;
digits = new ArrayList<Integer>(aDigits);
padWithZeros(digits);
order = aOrder;
}
@ -235,7 +238,7 @@ final class Padic {
* into a list which represents the negation of the p-adic number.
*/
private void negateList(List<Integer> aDigits) {
aDigits.set(0, ( prime - aDigits.get(0) ) % prime);
aDigits.set(0, Math.floorMod(prime - aDigits.get(0), prime));
for ( int i = 1; i < aDigits.size(); i++ ) {
aDigits.set(i, prime - 1 - aDigits.get(i));
}
@ -266,7 +269,7 @@ final class Padic {
* The given list is padded on the right by zeros up to a maximum length of 'PRECISION'.
*/
private static void padWithZeros(List<Integer> aList) {
while ( aList.size() < PRECISION ) {
while ( aList.size() < DIGITS_SIZE ) {
aList.addLast(0);
}
}