GF(2**8)的计算器

实现生成多项式为F(x) = x**8 + x**4 + x**3 + x**2 + 1的伽罗华域的加，减，乘，除，乘方运算。可以带括号。

将下面代码保存为pq.py,chmod +x pq.py，然后./pq.py即可进入计算器。按q退出。

解析算数表达式的程序有些问题，不支持乘方和其他运算混合。



#! /usr/bin/env python

# reference to http://www.cnblogs.com/flyingbread/archive/2007/02/03/638932.html

import re

def is_operator(ch):
    if ch == '+' or ch == '-' or ch == '*' or ch == '/' or ch == '**':
        return True
    else:
        return False

def is_parentheses_left(ch):
    if ch == '(':
        return True
    else:
        return False

def is_parentheses_right(ch):
    if ch == ')':
        return True
    else:
        return False

def opt_priority(ch):
    if ch == '+' or ch == '-':
        priority = 1
    elif ch == '*' or ch == '/':
        priority = 2
    elif ch == '**':
        priority = 3
    else:
        # maybe '('
        priority = 0
    return priority

# now we only support 2 operation number
def get_operation_number(ch):
    if ch == '+' or ch == '-' or ch == '*' or ch == '/' or ch == '**':
        return 2
    else:
        return 1

# primitive polynomial for GF(2**8)
# F(x) = x**8 + x**4 + x**3 + x**2 + 1
def do_add(a, b):
    return a ^ b

def do_sub(a, b):
    return a ^ b

gflog = [
    0x00, 0x00, 0x01, 0x19, 0x02, 0x32, 0x1a, 0xc6, 0x03, 0xdf, 0x33, 0xee, 0x1b, 0x68, 0xc7, 0x4b,
    0x04, 0x64, 0xe0, 0x0e, 0x34, 0x8d, 0xef, 0x81, 0x1c, 0xc1, 0x69, 0xf8, 0xc8, 0x08, 0x4c, 0x71,
    0x05, 0x8a, 0x65, 0x2f, 0xe1, 0x24, 0x0f, 0x21, 0x35, 0x93, 0x8e, 0xda, 0xf0, 0x12, 0x82, 0x45,
    0x1d, 0xb5, 0xc2, 0x7d, 0x6a, 0x27, 0xf9, 0xb9, 0xc9, 0x9a, 0x09, 0x78, 0x4d, 0xe4, 0x72, 0xa6,
    0x06, 0xbf, 0x8b, 0x62, 0x66, 0xdd, 0x30, 0xfd, 0xe2, 0x98, 0x25, 0xb3, 0x10, 0x91, 0x22, 0x88,
    0x36, 0xd0, 0x94, 0xce, 0x8f, 0x96, 0xdb, 0xbd, 0xf1, 0xd2, 0x13, 0x5c, 0x83, 0x38, 0x46, 0x40,
    0x1e, 0x42, 0xb6, 0xa3, 0xc3, 0x48, 0x7e, 0x6e, 0x6b, 0x3a, 0x28, 0x54, 0xfa, 0x85, 0xba, 0x3d,
    0xca, 0x5e, 0x9b, 0x9f, 0x0a, 0x15, 0x79, 0x2b, 0x4e, 0xd4, 0xe5, 0xac, 0x73, 0xf3, 0xa7, 0x57,
    0x07, 0x70, 0xc0, 0xf7, 0x8c, 0x80, 0x63, 0x0d, 0x67, 0x4a, 0xde, 0xed, 0x31, 0xc5, 0xfe, 0x18,
    0xe3, 0xa5, 0x99, 0x77, 0x26, 0xb8, 0xb4, 0x7c, 0x11, 0x44, 0x92, 0xd9, 0x23, 0x20, 0x89, 0x2e,
    0x37, 0x3f, 0xd1, 0x5b, 0x95, 0xbc, 0xcf, 0xcd, 0x90, 0x87, 0x97, 0xb2, 0xdc, 0xfc, 0xbe, 0x61,
    0xf2, 0x56, 0xd3, 0xab, 0x14, 0x2a, 0x5d, 0x9e, 0x84, 0x3c, 0x39, 0x53, 0x47, 0x6d, 0x41, 0xa2,
    0x1f, 0x2d, 0x43, 0xd8, 0xb7, 0x7b, 0xa4, 0x76, 0xc4, 0x17, 0x49, 0xec, 0x7f, 0x0c, 0x6f, 0xf6,
    0x6c, 0xa1, 0x3b, 0x52, 0x29, 0x9d, 0x55, 0xaa, 0xfb, 0x60, 0x86, 0xb1, 0xbb, 0xcc, 0x3e, 0x5a,
    0xcb, 0x59, 0x5f, 0xb0, 0x9c, 0xa9, 0xa0, 0x51, 0x0b, 0xf5, 0x16, 0xeb, 0x7a, 0x75, 0x2c, 0xd7,
    0x4f, 0xae, 0xd5, 0xe9, 0xe6, 0xe7, 0xad, 0xe8, 0x74, 0xd6, 0xf4, 0xea, 0xa8, 0x50, 0x58, 0xaf,
]

gfilog = [
    0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26,
    0x4c, 0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x03, 0x06, 0x0c, 0x18, 0x30, 0x60, 0xc0,
    0x9d, 0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23,
    0x46, 0x8c, 0x05, 0x0a, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1,
    0x5f, 0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0x0f, 0x1e, 0x3c, 0x78, 0xf0,
    0xfd, 0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2,
    0xd9, 0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0x0d, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce,
    0x81, 0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc,
    0x85, 0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54,
    0xa8, 0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73,
    0xe6, 0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff,
    0xe3, 0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41,
    0x82, 0x19, 0x32, 0x64, 0xc8, 0x8d, 0x07, 0x0e, 0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6,
    0x51, 0xa2, 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef, 0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x09,
    0x12, 0x24, 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5, 0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0x0b, 0x16,
    0x2c, 0x58, 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83, 0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e, 0x00,
]

def do_mul(a, b):
    if a == 0 or b == 0:
        return 0;
    else:
        tmp = gflog[a] + gflog[b]
        tmp = tmp % 255
        return gfilog[tmp]

def do_div(a, b):
    if a == 0:
        return 0
    elif b == 0:
        print 'can not div 0'
        return 0;
    else:
        tmp = gflog[a] - gflog[b]
        if tmp < 0:
            tmp = tmp + 255
        return gfilog[tmp]

def do_power(a, b):
    count = 0
    result = 1
    while (count < b):
        result = do_mul(result, a)
        count += 1
    return result

def calc_once(num, ch):
    if ch == '+':
        ret = do_add(num[1], num[0])
    elif ch == '-':
        ret = do_sub(num[1], num[0])
    elif ch == '*':
        ret = do_mul(num[1], num[0])
    elif ch == '/':
        ret = do_div(num[1], num[0])
    elif ch == '**':
        ret = do_power(num[1], num[0])
    else:
        print 'unknow operation'
        ret = 0
    return ret

# 1. get ch from left to right
# 2. if ch is a number, output it
# 3. if ch is a operator or parenthese:
#    a: if ch is '(', push to stack
#    b: if ch is ')', pop stack until meet '('
#    c: if ch is not parenthese, compare its priority with stack pop
#          if ch priority is higher than the stack pop, push ch to stack
#          else pop stack, push ch to stack
def midfix_to_posfix(midfix):
    stack = []
    posfix = []
    for ch in midfix:
        if is_parentheses_left(ch):
            stack.append(ch)
        elif is_parentheses_right(ch):
            while True:
                ch1 = stack.pop()
                if is_parentheses_left(ch1):
                    break
                else:
                    posfix.append(ch1)
        elif is_operator(ch):
            if len(stack) == 0:
                stack.append(ch)
            else:
                ch1 = stack[-1]
                if opt_priority(ch) > opt_priority(ch1):
                    stack.append(ch)
                else:
                    ch1 = stack.pop()
                    posfix.append(ch1)
                    stack.append(ch)
        else:
            if len(ch) > 2 and ch[0:2] == '0x':
                ch = int(ch, 16)
            else:
                ch = int(ch, 10)
            posfix.append(ch)
    while len(stack) != 0:
        posfix.append(stack.pop())
    return posfix

# get data from left to right
# if ch is a number, push to stack
# if ch is a operator, pop the number it needed, do calc, and push result to stack
# if data is paser comlete, pop the stack as result
def calc_posfix(posfix):
    stack = []
    for ch in posfix:
        if is_operator(ch):
            num = []
            num.append(stack.pop())
            if get_operation_number(ch) > 1:
                num.append(stack.pop())
            stack.append(calc_once(num, ch))
        else:
            stack.append(ch)
    return stack.pop()

def main_loop():
    # match all hex and dec number, and  +,-,*,/,**
    # note: hex must before dec number, and * must before **
    print "please do not use ** mix with other operation, it's not support!"
    regu_for_exp = re.compile('0x[0-9,a-f]+|[0-9]+|\*\*|\*|\+|\-|\/|\(|\)')
    while True:
        expression = raw_input('pq>:')
        if expression != 'quit' and expression != 'q' and expression != 'exit':
            midfix = regu_for_exp.findall(expression)
            posfix = midfix_to_posfix(midfix)
            result = calc_posfix(posfix)
            if result is not None:
                print "0x%02x" % result
            else:
                print result
        else:
            return
if __name__ == '__main__':
    main_loop()