众所周知,计算机中int用32位表示,可表示范围0 - 2^32,约42亿, long用64位表示,可表示范围为0-2^64 约184亿亿。如果运算是超出这个范围,就会溢出,即无法获取正确的计算结果。这时候就需要一种特殊的计算程序。本文通过Python语言,实现了一个简单的大数计算程序:通过输入两个任意长度的由数字组成的字符串,进行+ - * /计算,计算结果也是一个字符串。
1.代码
实现原理很简单,就是把我们平时笔算的过程写成了程序。由于输入是字符串,计算过程完全是笔算的逻辑,所以可支持任意长度的数据进行运算。2.代码
代码如下:
bigdata_calc.py
#! /usr/bin/python # -*- coding: utf-8 -*- import sys def get_10(c): return ord(c)-ord(‘0‘) def add_one_bit(n1,n2,n3=0): a = get_10(n1) b = get_10(n2) sum = a+b+n3 yu = sum%10 shang = (sum-yu)/10 return str(yu),shang def add(n1,n2): l1=len(n1) l2=len(n2) s1 = n1 s2 = n2 if l1>l2: s1 = n2 s2 = n1 l1 = len(s1) l2 = len(s2) sum = [] shang = 0 for i in range(l1): c,shang = add_one_bit(s1[l1-1-i],s2[l2-1-i],shang) sum.append(c) for i in range(l1,l2): c,shang = add_one_bit(‘0‘,s2[l2-1-i],shang) sum.append(c) if shang > 0: sum.append(str(shang)) for i in range(len(sum)/2): tmp = sum[i] sum[i]=sum[len(sum)-1-i] sum[len(sum)-1-i] = tmp return sum def mul(n1,n2): l = len(n1) sum=[] for i in range(l): v = get_10(n1[i]) if v>0: sum_tmp = n2 for j in range(l-1-i): sum_tmp += "0" add_v = sum_tmp for j in range(1,v): sum_tmp = add(sum_tmp,add_v) if i==0: sum = sum_tmp else: sum = add(sum,sum_tmp) return sum def sub_one_bit(n1,n2,n3): a = get_10(n1) b = get_10(n2) sub = a-b-n3 jie=0 while sub<0: jie += 1 sub += 10 return str(sub),jie def large(n1,n2): if len(n1)>len(n2): return True elif len(n1)<len(n2): return False else: for i in range(len(n1)): if ord(n1[i])>=ord(n2[i]): return True return False def sub(n1,n2): s1 = n1 s2 = n2 flag=False if not large(n1,n2): s1 = n2 s2 = n1 flag = True l1 = len(s1) l2 = len(s2) sub = [] jie = 0 for i in range(l2): c,jie = sub_one_bit(s1[l1-1-i],s2[l2-1-i],jie) sub.append(c) has_jie = 0 if jie>0: c,jie = sub_one_bit(n1[l2-1-l1],str(jie),0) sub.append(c) has_jie=1 while has_jie<l1-l2: sub.append(s1[l1-l2-1-has_jie]) has_jie += 1 if flag: sub.append(‘-‘) for i in range(len(sub)/2): tmp = sub[i] sub[i]=sub[len(sub)-1-i] sub[len(sub)-1-i] = tmp return sub def div(n1,n2): return "Todo..." def calc(n1,op,n2): if op == ‘+‘: return add(n1,n2) elif op == ‘-‘: return sub(n1,n2) elif op == ‘*‘: return mul(n1,n2) elif op == ‘/‘: return div(n1,n2) else: return "unsupported operation" if __name__ == ‘__main__‘: if len(sys.argv)<4: print "Usage: bigdata_calc.py num1 {+,-,*,/} num2" else: res = calc(sys.argv[1],sys.argv[2],sys.argv[3]) print "%50s\n%s\n%50s\n=\n%50s" %(sys.argv[1],sys.argv[2],sys.argv[3],"".join(res))
说明:仅为个人娱乐性编写, 程序目前仅支持正数据的加 、减 、乘运算,除法还未实现。
虽然个人进行了测试,但难免还有bug,请指正。
3.测试
测试一:
123
*
456
=
56088
测试二:
123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789
*
123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789
=
15241578780673678546105778311537878076969977842402077607834177373266277138698376
90413047663907941887364731910821521934278311957735101981191892004648682028105472
0515622620750190521
结果如下: