cp_library/math/conv/fwht_fn.py

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• Last update: 2025-03-30 20:17:47+09:00

Required by

• cp_library/math/conv/fwht_inv_fn.py
• cp_library/math/conv/ixor_conv_fn.py
• cp_library/math/conv/mod/fwht_inv_fn.py
• cp_library/math/conv/mod/ixor_conv_fn.py
• cp_library/math/conv/mod/xor_conv_fn.py
• cp_library/math/conv/xor_conv_fn.py

Verified with

• test/library-checker/convolution/bitwise_xor_convolution.test.py

Code

import cp_library.__header__
import cp_library.math.__header__
import cp_library.math.conv.__header__

def fwht(A: list, N: int):
    Z = len(A)
    for i in range(N):
        m = b = 1<<i
        while m < Z:
            a0, a1 = A[m^b], A[m]
            A[m^b], A[m] = a0+a1, a0-a1
            m = m+1|b
    return A

'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
             https://kobejean.github.io/cp-library               
'''

'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
    x₀ ────────●─●────────●───●────────●───────●────────► X₀
                ╳          ╲ ╱          ╲     ╱          
    x₄ ────────●─●────────●─╳─●────────●─╲───╱─●────────► X₁
                           ╳ ╳          ╲ ╲ ╱ ╱          
    x₂ ────────●─●────────●─╳─●────────●─╲─╳─╱─●────────► X₂
                ╳          ╱ ╲          ╲ ╳ ╳ ╱          
    x₆ ────────●─●────────●───●────────●─╳─╳─╳─●────────► X₃
                                        ╳ ╳ ╳ ╳         
    x₁ ────────●─●────────●───●────────●─╳─╳─╳─●────────► X₄
                ╳          ╲ ╱          ╱ ╳ ╳ ╲          
    x₅ ────────●─●────────●─╳─●────────●─╱─╳─╲─●────────► X₅
                           ╳ ╳          ╱ ╱ ╲ ╲          
    x₃ ────────●─●────────●─╳─●────────●─╱───╲─●────────► X₆
                ╳          ╱ ╲          ╱     ╲          
    x₇ ────────●─●────────●───●────────●───────●────────► X₇
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
                      Math - Convolution                     
'''

def fwht(A: list, N: int):
    Z = len(A)
    for i in range(N):
        m = b = 1<<i
        while m < Z:
            a0, a1 = A[m^b], A[m]
            A[m^b], A[m] = a0+a1, a0-a1
            m = m+1|b
    return A

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