From 2c5806a66b32ba28b3f62da3df0d0ae0394f8933 Mon Sep 17 00:00:00 2001 From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Date: Wed, 1 Sep 2021 17:00:24 +0000 Subject: [PATCH] Documentation for f7d656cb17c8b355fa6a51e45a070cd6995ed110 --- d5/d88/md__d_i_r_e_c_t_o_r_y.html | 3 +- d6/db8/inv__sqrt_8cpp.html | 349 +++++++++++ d6/db8/inv__sqrt_8cpp.js | 7 + ...8dca7b867074164d5f45b0f3851269d_cgraph.map | 6 + ...8dca7b867074164d5f45b0f3851269d_cgraph.md5 | 1 + ...8dca7b867074164d5f45b0f3851269d_cgraph.svg | 67 +++ ...66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map | 8 + ...66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5 | 1 + ...66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg | 109 ++++ d7/d53/inv__sqrt_8cpp__incl.map | 7 + d7/d53/inv__sqrt_8cpp__incl.md5 | 1 + d7/d53/inv__sqrt_8cpp__incl.svg | 82 +++ dir_296d53ceaeaa7e099814a6def439fe8a.html | 3 + dir_296d53ceaeaa7e099814a6def439fe8a.js | 1 + files.html | 53 +- globals_f.html | 3 + globals_func_f.html | 3 + globals_func_m.html | 1 + 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d6/db8/inv__sqrt_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map create mode 100644 d6/db8/inv__sqrt_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5 create mode 100644 d6/db8/inv__sqrt_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg create mode 100644 d7/d53/inv__sqrt_8cpp__incl.map create mode 100644 d7/d53/inv__sqrt_8cpp__incl.md5 create mode 100644 d7/d53/inv__sqrt_8cpp__incl.svg diff --git a/d5/d88/md__d_i_r_e_c_t_o_r_y.html b/d5/d88/md__d_i_r_e_c_t_o_r_y.html index 53fe21e29..ac7d6084c 100644 --- a/d5/d88/md__d_i_r_e_c_t_o_r_y.html +++ b/d5/d88/md__d_i_r_e_c_t_o_r_y.html @@ -297,6 +297,7 @@ Math
  • Gcd Of N Numbers
  • Gcd Recursive Euclidean
  • Integral Approximation
    • +
  • Inv Sqrt
  • Large Factorial
  • Large Number
  • Largest Power
    • @@ -469,7 +470,7 @@ Strings
  • Brute Force String Searching
  • Horspool
  • Knuth Morris Pratt
    • -
  • Manacher's Algorithm
    • +
  • Manacher Algorithm
  • Rabin Karp
    • diff --git a/d6/db8/inv__sqrt_8cpp.html b/d6/db8/inv__sqrt_8cpp.html new file mode 100644 index 000000000..ced09b9e3 --- /dev/null +++ b/d6/db8/inv__sqrt_8cpp.html @@ -0,0 +1,349 @@ + + + + + + + +Algorithms_in_C++: math/inv_sqrt.cpp File Reference + + + + + + + + + + + + + + + +
    +
    + + + + + + +
    +
    Algorithms_in_C++ +  1.0.0 +
    +
    Set of algorithms implemented in C++.
    +
    +
    + + + + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    inv_sqrt.cpp File Reference
    +
    +
    + +

    Implementation of the inverse square root Root. +More...

    +
    #include <cassert>
    +#include <cmath>
    +#include <iostream>
    +#include <limits>
    +
    +Include dependency graph for inv_sqrt.cpp:
    +
    +
    +
    +
    +
    + + + + + + + + + + + + + + + +

    +Functions

    template<typename T = double, char iterations = 2>
    T Fast_InvSqrt (T x)
     for numeric_limits More...
     
    template<typename T = double>
    T Standard_InvSqrt (T number)
     This is the function that calculates the fast inverse square root. The following code is the fast inverse square root with standard lib (cmath) More information can be found at LinkedIn More...
     
    static void test ()
     Self-test implementations. More...
     
    int main ()
     Main function. More...
     
    +

    Detailed Description

    +

    Implementation of the inverse square root Root.

    +

    Two implementation to calculate inverse inverse root, from Quake III Arena (C++ version) and with a standard library (cmath). This algorithm is used to calculate shadows in Quake III Arena.

    +

    Function Documentation

    + +

    ◆ Fast_InvSqrt()

    + +
    +
    +
    +template<typename T = double, char iterations = 2>
    + + + + + +
    + + + + + + + + +
    T Fast_InvSqrt (T x)
    +     		+inline
    +
    + +

    for numeric_limits

    +

    for assert for std::sqrt for IO operations

    +

    This is the function that calculates the fast inverse square root. The following code is the fast inverse square root implementation from Quake III Arena (Adapted for C++). More information can be found at Wikipedia

    Template Parameters
    + + + +
    Tfloating type
    iterationsinverse square root, the greater the number of iterations, the more exact the result will be (1 or 2).
    +
    +
    +
    Parameters
    + + +
    xvalue to calculate
    +
    +
    +
    Returns
    the inverse square root
    +
    28  {
    +
    29  using Tint = typename std::conditional<sizeof(T) == 8, std::int64_t,
    +
    30  std::int32_t>::type;
    +
    31  T y = x;
    +
    32  T x2 = y * 0.5;
    +
    33 
    +
    34  Tint i =
    +
    35  *reinterpret_cast<Tint *>(&y); // Store floating-point bits in integer
    +
    36 
    +
    37  i = (sizeof(T) == 8 ? 0x5fe6eb50c7b537a9 : 0x5f3759df) -
    +
    38  (i >> 1); // Initial guess for Newton's method
    +
    39 
    +
    40  y = *reinterpret_cast<T *>(&i); // Convert new bits into float
    +
    41 
    +
    42  y = y * (1.5 - (x2 * y * y)); // 1st iteration Newton's method
    +
    43  if (iterations == 2) {
    +
    44  y = y * (1.5 - (x2 * y * y)); // 2nd iteration, the more exact result
    +
    45  }
    +
    46  return y;
    +
    47 }
    + + +
    +
    +
    + +

    ◆ main()

    + +
    +
    + + + + + + + + +
    int main (void )
    +
    + +

    Main function.

    +
    Returns
    0 on exit
    +
    87  {
    +
    88  test(); // run self-test implementations
    +
    89  std::cout << "The Fast inverse square root of 36 is: "
    +
    90  << Fast_InvSqrt<float, 1>(36.0f) << std::endl;
    +
    91  std::cout << "The Fast inverse square root of 36 is: "
    +
    92  << Fast_InvSqrt<double, 2>(36.0f) << " (2 iterations)"
    +
    93  << std::endl;
    +
    94  std::cout << "The Fast inverse square root of 100 is: "
    +
    95  << Fast_InvSqrt(100.0f)
    +
    96  << " (With default template type and iterations: double, 2)"
    +
    97  << std::endl;
    +
    98  std::cout << "The Standard inverse square root of 36 is: "
    +
    99  << Standard_InvSqrt<float>(36.0f) << std::endl;
    +
    100  std::cout << "The Standard inverse square root of 100 is: "
    +
    101  << Standard_InvSqrt(100.0f)
    +
    102  << " (With default template type: double)" << std::endl;
    +
    103 }
    + +
    std::endl
    T endl(T... args)
    +
    Standard_InvSqrt
    T Standard_InvSqrt(T number)
    This is the function that calculates the fast inverse square root. The following code is the fast inv...
    Definition: inv_sqrt.cpp:59
    +
    test
    static void test()
    Self-test implementations.
    Definition: inv_sqrt.cpp:68
    +
    Fast_InvSqrt
    T Fast_InvSqrt(T x)
    for numeric_limits
    Definition: inv_sqrt.cpp:28
    +
    +Here is the call graph for this function:
    +
    +
    +
    +
    + +
    +
    + +

    ◆ Standard_InvSqrt()

    + +
    +
    +
    +template<typename T = double>
    + + + + + + + + +
    T Standard_InvSqrt (T number)
    +
    + +

    This is the function that calculates the fast inverse square root. The following code is the fast inverse square root with standard lib (cmath) More information can be found at LinkedIn

    +
    Template Parameters
    + + +
    Tfloating type
    +
    +
    +
    Parameters
    + + +
    numbervalue to calculate
    +
    +
    +
    Returns
    the inverse square root
    +
    59  {
    +
    60  T squareRoot = sqrt(number);
    +
    61  return 1.0f / squareRoot;
    +
    62 }
    +
    std::sqrt
    T sqrt(T... args)
    +
    +
    +
    + +

    ◆ test()

    + +
    +
    + + + + + +
    + + + + + + + +
    static void test ()
    +     		+static
    +
    + +

    Self-test implementations.

    +
    Returns
    void
    +
    68  {
    +
    69  const float epsilon = 1e-3f;
    +
    70 
    +
    71  /* Tests with multiple values */
    +
    72  assert(std::fabs(Standard_InvSqrt<float>(100.0f) - 0.0998449f) < epsilon);
    +
    73  assert(std::fabs(Standard_InvSqrt<double>(36.0f) - 0.166667f) < epsilon);
    +
    74  assert(std::fabs(Standard_InvSqrt(12.0f) - 0.288423f) < epsilon);
    +
    75  assert(std::fabs(Standard_InvSqrt<double>(5.0f) - 0.447141f) < epsilon);
    +
    76 
    +
    77  assert(std::fabs(Fast_InvSqrt<float, 1>(100.0f) - 0.0998449f) < epsilon);
    +
    78  assert(std::fabs(Fast_InvSqrt<double, 1>(36.0f) - 0.166667f) < epsilon);
    +
    79  assert(std::fabs(Fast_InvSqrt(12.0f) - 0.288423) < epsilon);
    +
    80  assert(std::fabs(Fast_InvSqrt<double>(5.0f) - 0.447141) < epsilon);
    +
    81 }
    +
    std::fabs
    T fabs(T... args)
    +
    +Here is the call graph for this function:
    +
    +
    +
    +
    + +
    +
    +
    +
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      +file  inv_sqrt.cpp + Implementation of the inverse square root Root.
    +  file  large_factorial.cpp  Compute factorial of any arbitratily large number/.
      diff --git a/dir_296d53ceaeaa7e099814a6def439fe8a.js b/dir_296d53ceaeaa7e099814a6def439fe8a.js index 8e2bddffe..4d0eac4c2 100644 --- a/dir_296d53ceaeaa7e099814a6def439fe8a.js +++ b/dir_296d53ceaeaa7e099814a6def439fe8a.js @@ -21,6 +21,7 @@ var dir_296d53ceaeaa7e099814a6def439fe8a = [ "gcd_of_n_numbers.cpp", "d1/d11/gcd__of__n__numbers_8cpp.html", "d1/d11/gcd__of__n__numbers_8cpp" ], [ "gcd_recursive_euclidean.cpp", "d4/d45/gcd__recursive__euclidean_8cpp.html", "d4/d45/gcd__recursive__euclidean_8cpp" ], [ "integral_approximation.cpp", "d1/de9/integral__approximation_8cpp.html", "d1/de9/integral__approximation_8cpp" ], + [ "inv_sqrt.cpp", "d6/db8/inv__sqrt_8cpp.html", "d6/db8/inv__sqrt_8cpp" ], [ "large_factorial.cpp", "d6/d9d/large__factorial_8cpp.html", "d6/d9d/large__factorial_8cpp" ], [ "large_number.h", "d4/d86/large__number_8h.html", [ [ "large_number", "db/d82/classlarge__number.html", "db/d82/classlarge__number" ] diff --git a/files.html b/files.html index e77eb0d05..4c3df5194 100644 --- a/files.html +++ b/files.html @@ -213,32 +213,33 @@ solve-a-rat-in-a-maze-c-java-pytho/"  gcd_of_n_numbers.cppThis program aims at calculating the GCD of n numbers by division method  gcd_recursive_euclidean.cppCompute the greatest common denominator of two integers using recursive form of Euclidean algorithm  integral_approximation.cppCompute integral approximation of the function using Riemann sum - large_factorial.cppCompute factorial of any arbitratily large number/ - large_number.hLibrary to perform arithmatic operations on arbitrarily large numbers - largest_power.cppAlgorithm to find largest x such that p^x divides n! (factorial) using Legendre's Formula - lcm_sum.cppAn algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\) - least_common_multiple.cpp - magic_number.cppA simple program to check if the given number is a magic number or not. A number is said to be a magic number, if the sum of its digits are calculated till a single digit recursively by adding the sum of the digits after every addition. If the single digit comes out to be 1,then the number is a magic number - miller_rabin.cpp - modular_division.cppAn algorithm to divide two numbers under modulo p Modular Division - modular_exponentiation.cppC++ Program for Modular Exponentiation Iteratively - modular_inverse_fermat_little_theorem.cppC++ Program to find the modular inverse using Fermat's Little Theorem - n_bonacci.cppImplementation of the N-bonacci series - n_choose_r.cppCombinations n choose r function implementation - ncr_modulo_p.cppThis program aims at calculating nCr modulo p - number_of_positive_divisors.cppC++ Program to calculate the number of positive divisors - power_for_huge_numbers.cppCompute powers of large numbers - power_of_two.cppImplementation to check whether a number is a power of 2 or not - prime_factorization.cppPrime factorization of positive integers - prime_numbers.cppGet list of prime numbers - primes_up_to_billion.cppCompute prime numbers upto 1 billion - realtime_stats.cppCompute statistics for data entered in rreal-time - sieve_of_eratosthenes.cppGet list of prime numbers using Sieve of Eratosthenes - sqrt_double.cppCalculate the square root of any positive real number in \(O(\log N)\) time, with precision fixed using bisection method of root-finding - string_fibonacci.cppThis Programme returns the Nth fibonacci as a string - sum_of_binomial_coefficient.cppAlgorithm to find sum of binomial coefficients of a given positive integer - sum_of_digits.cppA C++ Program to find the Sum of Digits of input integer - vector_cross_product.cppCalculates the Cross Product and the magnitude of two mathematical 3D vectors + inv_sqrt.cppImplementation of the inverse square root Root + large_factorial.cppCompute factorial of any arbitratily large number/ + large_number.hLibrary to perform arithmatic operations on arbitrarily large numbers + largest_power.cppAlgorithm to find largest x such that p^x divides n! (factorial) using Legendre's Formula + lcm_sum.cppAn algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) + \mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\) + least_common_multiple.cpp + magic_number.cppA simple program to check if the given number is a magic number or not. A number is said to be a magic number, if the sum of its digits are calculated till a single digit recursively by adding the sum of the digits after every addition. If the single digit comes out to be 1,then the number is a magic number + miller_rabin.cpp + modular_division.cppAn algorithm to divide two numbers under modulo p Modular Division + modular_exponentiation.cppC++ Program for Modular Exponentiation Iteratively + modular_inverse_fermat_little_theorem.cppC++ Program to find the modular inverse using Fermat's Little Theorem + n_bonacci.cppImplementation of the N-bonacci series + n_choose_r.cppCombinations n choose r function implementation + ncr_modulo_p.cppThis program aims at calculating nCr modulo p + number_of_positive_divisors.cppC++ Program to calculate the number of positive divisors + power_for_huge_numbers.cppCompute powers of large numbers + power_of_two.cppImplementation to check whether a number is a power of 2 or not + prime_factorization.cppPrime factorization of positive integers + prime_numbers.cppGet list of prime numbers + primes_up_to_billion.cppCompute prime numbers upto 1 billion + realtime_stats.cppCompute statistics for data entered in rreal-time + sieve_of_eratosthenes.cppGet list of prime numbers using Sieve of Eratosthenes + sqrt_double.cppCalculate the square root of any positive real number in \(O(\log N)\) time, with precision fixed using bisection method of root-finding + string_fibonacci.cppThis Programme returns the Nth fibonacci as a string + sum_of_binomial_coefficient.cppAlgorithm to find sum of binomial coefficients of a given positive integer + sum_of_digits.cppA C++ Program to find the Sum of Digits of input integer + vector_cross_product.cppCalculates the Cross Product and the magnitude of two mathematical 3D vectors  ► numerical_methods  bisection_method.cppSolve the equation \(f(x)=0\) using bisection method  brent_method_extrema.cppFind real extrema of a univariate real function in a given interval using Brent's method diff --git a/globals_f.html b/globals_f.html index 2f190e074..fbf07b03f 100644 --- a/globals_f.html +++ b/globals_f.html @@ -102,6 +102,9 @@ $(document).ready(function(){initNavTree('globals_f.html',''); initResizable();
  • factors : prime_factorization.cpp
    • +
  • Fast_InvSqrt() +: inv_sqrt.cpp +
  • fast_power_linear() : fast_power.cpp
    • diff --git a/globals_func_f.html b/globals_func_f.html index 42db7c519..2df5ccdfc 100644 --- a/globals_func_f.html +++ b/globals_func_f.html @@ -99,6 +99,9 @@ $(document).ready(function(){initNavTree('globals_func_f.html',''); initResizabl
  • factorial() : factorial.cpp
    • +
  • Fast_InvSqrt() +: inv_sqrt.cpp +
  • fast_power_linear() : fast_power.cpp
    • diff --git a/globals_func_m.html b/globals_func_m.html index 001dc0b0a..3cbd934f2 100644 --- a/globals_func_m.html +++ b/globals_func_m.html @@ -185,6 +185,7 @@ $(document).ready(function(){initNavTree('globals_func_m.html',''); initResizabl , gcd_of_n_numbers.cpp , gcd_recursive_euclidean.cpp , integral_approximation.cpp +, inv_sqrt.cpp , large_factorial.cpp , largest_power.cpp , lcm_sum.cpp diff --git a/globals_func_s.html b/globals_func_s.html index 4981e10ce..fc16957b7 100644 --- a/globals_func_s.html +++ b/globals_func_s.html @@ -126,12 +126,12 @@ $(document).ready(function(){initNavTree('globals_func_s.html',''); initResizabl
  • show_pascal() : pascal_triangle.cpp
    • -
  • sieve() -: sieve_of_eratosthenes.cpp -
  • Sieve() : primes_up_to_billion.cpp
    • +
  • sieve() +: sieve_of_eratosthenes.cpp +
  • SieveOfEratosthenes() : prime_factorization.cpp
    • @@ -141,6 +141,9 @@ $(document).ready(function(){initNavTree('globals_func_s.html',''); initResizabl
  • Sqrt() : sqrt_double.cpp
    • +
  • Standard_InvSqrt() +: inv_sqrt.cpp +
  • struzik_search() : exponential_search.cpp
    • diff --git a/globals_func_t.html b/globals_func_t.html index eb182c825..383f600f3 100644 --- a/globals_func_t.html +++ b/globals_func_t.html @@ -137,6 +137,7 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl , fibonacci.cpp , fibonacci_matrix_exponentiation.cpp , fibonacci_sum.cpp +, inv_sqrt.cpp , largest_power.cpp , lcm_sum.cpp , modular_division.cpp diff --git a/globals_m.html b/globals_m.html index 227da562b..2569118ce 100644 --- a/globals_m.html +++ b/globals_m.html @@ -185,6 +185,7 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable(); , gcd_of_n_numbers.cpp , gcd_recursive_euclidean.cpp , integral_approximation.cpp +, inv_sqrt.cpp , large_factorial.cpp , largest_power.cpp , lcm_sum.cpp diff --git a/globals_p.html b/globals_p.html index 2e3578112..180dccaed 100644 --- a/globals_p.html +++ b/globals_p.html @@ -130,12 +130,12 @@ $(document).ready(function(){initNavTree('globals_p.html',''); initResizable();
  • predict_OLS_regressor() : ordinary_least_squares_regressor.cpp
    • -
  • PRIME -: rabin_karp.cpp -
  • prime : primes_up_to_billion.cpp
    • +
  • PRIME +: rabin_karp.cpp +
  • prime_factorization() : prime_factorization.cpp
    • diff --git a/globals_s.html b/globals_s.html index 3ec5d0aab..5c8422e8d 100644 --- a/globals_s.html +++ b/globals_s.html @@ -126,12 +126,12 @@ $(document).ready(function(){initNavTree('globals_s.html',''); initResizable();
  • show_pascal() : pascal_triangle.cpp
    • -
  • sieve() -: sieve_of_eratosthenes.cpp -
  • Sieve() : primes_up_to_billion.cpp
    • +
  • sieve() +: sieve_of_eratosthenes.cpp +
  • SieveOfEratosthenes() : prime_factorization.cpp
    • @@ -147,6 +147,9 @@ $(document).ready(function(){initNavTree('globals_s.html',''); initResizable();
  • stack_idx : paranthesis_matching.cpp
    • +
  • Standard_InvSqrt() +: inv_sqrt.cpp +
  • struzik_search() : exponential_search.cpp
    • diff --git a/globals_t.html b/globals_t.html index 78d6df92a..3c941e4b7 100644 --- a/globals_t.html +++ b/globals_t.html @@ -137,6 +137,7 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable(); , fibonacci.cpp , fibonacci_matrix_exponentiation.cpp , fibonacci_sum.cpp +, inv_sqrt.cpp , largest_power.cpp , lcm_sum.cpp , modular_division.cpp diff --git a/namespacemembers.html b/namespacemembers.html index 0138c4e4e..0a8511eb4 100644 --- a/namespacemembers.html +++ b/namespacemembers.html @@ -366,12 +366,12 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza
  • quadraticProbe() : quadratic_probing
    • -
  • quicksort() -: sorting -
  • quickSort() : sorting
    • +
  • quicksort() +: sorting +
    • diff --git a/namespacemembers_func.html b/namespacemembers_func.html index 0c64c200b..a7f1fc616 100644 --- a/namespacemembers_func.html +++ b/namespacemembers_func.html @@ -354,12 +354,12 @@ $(document).ready(function(){initNavTree('namespacemembers_func.html',''); initR
  • quadraticProbe() : quadratic_probing
    • -
  • quicksort() -: sorting -
  • quickSort() : sorting
    • +
  • quicksort() +: sorting +
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