线性同余生成器的浮点异常（核心转储）

Posted 2023-02-22

【中文标题】线性同余生成器的浮点异常（核心转储）

【英文标题】：Floating point exception (core dumped) for Linear Congruential Generator

【发布时间】：2020-04-30 03:11:52

【问题描述】：

我正在完成基于线性同余生成器 (LCG) 的密码程序的头文件。它接收两个 unsigned long 值（m 和 c）并使用这些值生成 LCG 结构。在我的 getA() 中，我试图让它将 temp 变量添加到 uPrimes 数组中（以防它不能减少到 1，因此在计算 p 时可以包含它）但我一直收到错误：“浮点异常（核心转储）”。如果我不尝试这样做，它将运行到完成，但不会按需要执行。在最新的迭代中，我尝试将 uPrimes 数组的第一个值分配为 1，一旦 while 循环完成，它会将 temp 的值分配给第一个值，结果相同。任何帮助将不胜感激！ （对于不匹配的变量声明，我提前道歉，我正在随意摆弄数据类型以尝试解决问题）

/* Header guard prevents errors if header is included twice */
#ifndef LCG_H
#define LCG_H
#include <stdlib.h>

struct LinearCongruentialGenerator

  unsigned long m; /* modulus */
  unsigned long c; /* increment */
  unsigned long a; /* multiplier */
  unsigned long x; /* value in sequence */
;

/***************************************************************/
/* Initialize an LCG with modulus m and increment c.           */
/* Calculate multiplier a such that:                           */
/*        a = 1+2p, if 4 is a factor of m, otherwise, a = 1+p. */
/*        p = (product of m’s unique prime factors).           */
/*        a < m                                                */
/* Seed value x is same as increment c.                        */
/* If values are invalid for LCG, set all fields to zero.      */
/***************************************************************/
struct LinearCongruentialGenerator makeLCG(unsigned long m, unsigned long c);

/* Update lcg and return next value in the sequence. */
unsigned long getNextRandomValue(struct LinearCongruentialGenerator* lcg);

unsigned long getA(unsigned long m);

int checkInput(unsigned long m, unsigned long c);

struct LinearCongruentialGenerator makeLCG(unsigned long m, unsigned long c)

  struct LinearCongruentialGenerator lcg;
  if(checkInput(m,c) && (getA(m)<m && getA(m)>0))
    
    lcg.m = m;
    lcg.c = c;
    lcg.a = getA(m);
    lcg.x = c;
   else
  
    lcg.m = 0; lcg.c = 0;
    lcg.a = 0; lcg.x = 0;
  
  return lcg;


unsigned long getNextRandomValue(struct LinearCongruentialGenerator* lcg)

  lcg->x = ((lcg->a*lcg->x)+lcg->c)%lcg->m;
  return lcg->x;


unsigned long getA(unsigned long m)

  unsigned long primes[15] = 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47;
  int uPrimes[63];
  unsigned long temp = m; int y = 0; int p = 1;
  int prev; int z; unsigned long a; int q = 1;
  uPrimes[0] = 1;
  while(y < 16)
  
    if(temp % primes[y] == 0)
    
      if(primes[y] != prev)
      
        uPrimes[q] = primes[y];
        prev = primes[y];
        q++; y++;
        printf("Unique Prime for %lu is: %d\n", m, uPrimes[q-1]);
       else temp = temp/primes[y];
     else y++;
  
  uPrimes[0] = temp;
  for(z = 0; z < q; z++)
  
    p = p * uPrimes[z];
    printf("P for %lu is %d\n", m, p);
  
  if(m % 4 == 0)a = 1+(2*p);
  else a = 1+p;
  if(a < m && a > 0)return a;
  else return 0;


int checkInput(unsigned long m, unsigned long c)

  int x = 2;
  if(c > m || c <= 0)return 0;
  else 
  
    while(x < c)
    
      if(m % x == 0 && c % x == 0)
      return 0;
      else x++;
    
    return 1;
  

#endif

这是给我的测试文件，用于验证我的头文件是否按需要工作：

#include <stdio.h>
#include "lcg.h"

/* Print LCG values along with a message */
void printLCG(struct LinearCongruentialGenerator* lcg, char* msg)

  printf("%s (m=%lu,a=%lu,c=%lu,x=%lu)\n", msg, lcg->m, lcg->a, lcg->c, lcg->x);


/* Print message and n values generated by the LCG */
void testValues(struct LinearCongruentialGenerator* lcg, char* msg, int n)

  int i;
  printf("%s\n", msg);

  for(i = 0; i < n; ++i)
  
    unsigned long x = getNextRandomValue(lcg);
    printf("%lu\n", x);
  


/* Create and test a few LCGs */
int main()

  struct LinearCongruentialGenerator lcg1 = makeLCG(126,25);
  struct LinearCongruentialGenerator lcg2 = makeLCG(38875,1234);
  struct LinearCongruentialGenerator lcg3 = makeLCG(4611686018427387904,961168601842738797);

  /* Some error cases */
  struct LinearCongruentialGenerator lcg4 = makeLCG(4,3);
  struct LinearCongruentialGenerator lcg5 = makeLCG(0,5);
  struct LinearCongruentialGenerator lcg6 = makeLCG(5,0);


  printLCG(&lcg1, "initialized lcg1");
  printLCG(&lcg2, "initialized lcg2");
  printLCG(&lcg3, "initialized lcg3");

  printLCG(&lcg4, "initialized error test lcg4");
  printLCG(&lcg5, "initialized error test lcg5");
  printLCG(&lcg6, "initialized error test lcg6");

  testValues(&lcg1, "test lcg1", 10);
  testValues(&lcg2, "test lcg2", 10);
  testValues(&lcg3, "test lcg3", 10);

  printLCG(&lcg1, "lcg1 after first test");
  printLCG(&lcg2, "lcg2 after first test");
  printLCG(&lcg3, "lcg3 after first test");

  testValues(&lcg1, "test lcg1 again", 20);

  printLCG(&lcg1, "lcg1 after second test");

  return 0;

【问题讨论】：

在调试器中运行并在发生异常时检查变量。很有可能您会看到一个看起来错误的值，然后您可以从那里进行调试。

我不会撒谎，我在最后一个问题上被告知了这一点，我不知道为什么我不记得了。我想挫败感刚刚战胜了我，但谢谢你，我现在试试。

【参考方案1】：

至少这个问题，primes[15]不存在。 15primes[0] ... primes[15-1] 确实存在。

代码可能随后尝试%0 导致“浮点异常（核心转储）”。由于各种原因，整数 div 被 0 或余数报告为 FP 错误。

 unsigned long primes[15] =  ... 

 while(y < 16) 
   if(temp % primes[y] == 0)

建议while(y < 15)

【参考方案2】：

清理后（删除clang -Weverything 发出的所有警告），修复@chux 发现的off-by-one，并添加更多跟踪我得到了这个

#include <stdlib.h>
#include <stdio.h>

struct LinearCongruentialGenerator 
  unsigned long m;              /* modulus */
  unsigned long c;              /* increment */
  unsigned long a;              /* multiplier */
  unsigned long x;              /* value in sequence */
;

/***************************************************************/
/* Initialize an LCG with modulus m and increment c.           */
/* Calculate multiplier a such that:                           */
/*        a = 1+2p, if 4 is a factor of m, otherwise, a = 1+p. */
/*        p = (product of m’s unique prime factors).           */
/*        a < m                                                */
/* Seed value x is same as increment c.                        */
/* If values are invalid for LCG, set all fields to zero.      */
/***************************************************************/
struct LinearCongruentialGenerator makeLCG(unsigned long m, unsigned long c);

/* Update lcg and return next value in the sequence. */
unsigned long getNextRandomValue(struct LinearCongruentialGenerator *lcg);

unsigned long getA(unsigned long m);

int checkInput(unsigned long m, unsigned long c);

void printLCG(struct LinearCongruentialGenerator *lcg, char *msg);

void testValues(struct LinearCongruentialGenerator *lcg, char *msg, int n);

struct LinearCongruentialGenerator makeLCG(unsigned long m, unsigned long c)

  struct LinearCongruentialGenerator lcg;
  if (checkInput(m, c) && (getA(m) < m && getA(m) > 0)) 
    lcg.m = m;
    lcg.c = c;
    lcg.a = getA(m);
    lcg.x = c;
   else 
    lcg.m = 0;
    lcg.c = 0;
    lcg.a = 0;
    lcg.x = 0;
  
  return lcg;


unsigned long getNextRandomValue(struct LinearCongruentialGenerator *lcg)

  lcg->x = lcg->a * lcg->x;
  lcg->x = lcg->x + lcg->c;
  lcg->x = lcg->x % lcg->m;
  return lcg->x;


unsigned long getA(unsigned long m)

  unsigned long primes[15] =
       2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 ;
  unsigned long uPrimes[63];
  unsigned long temp = m;
  unsigned long y = 0;
  unsigned long p = 1;
  unsigned long prev = 0;
  unsigned long z;
  unsigned long a;
  unsigned long q = 1;
  uPrimes[0] = 1;
  while (y < 15) 
    if (temp % primes[y] == 0) 
      if (primes[y] != prev) 
        uPrimes[q] = primes[y];
        prev = primes[y];
        q++;
        y++;
        printf("Unique Prime for %lu is: %lu\n", m, uPrimes[q - 1]);
       else
        temp = temp / primes[y];
     else
      y++;
  
  uPrimes[0] = temp;
  printf("q = %lu\n", q);
  for (z = 0; z < q; z++) 
    p = p * uPrimes[z];
    printf("P for %lu is %lu\n", m, p);
  
  if (m % 4 == 0) 
    a = 1 + (2 * p);
   else 
    a = 1 + p;
  
  printf("getA(m): m = %lu, a = %lu\n", m, a);
  if (a < m && a > 0) 
    return a;
   else 
    return 0;
  


int checkInput(unsigned long m, unsigned long c)

  unsigned long x = 2;
  printf("checkInput(m = %lu, c = %lu)\n", m, c);
  if (c > m || c <= 0) 
    return 0;
   else 
    while (x < c) 
      if (m % x == 0 && c % x == 0) 
        return 0;
       else
        x++;
    
    return 1;
  


/* Print LCG values along with a message */
void printLCG(struct LinearCongruentialGenerator *lcg, char *msg)

  printf("%s (m=%lu,a=%lu,c=%lu,x=%lu)\n", msg, lcg->m, lcg->a, lcg->c, lcg->x);


/* Print message and n values generated by the LCG */
void testValues(struct LinearCongruentialGenerator *lcg, char *msg, int n)

  int i;
  printf("%s\n", msg);

  for (i = 0; i < n; ++i) 
    unsigned long x = getNextRandomValue(lcg);
    printf("%lu\n", x);
  


/* Create and test a few LCGs */
int main(void)

  puts("makeLCG(126,25)");
  struct LinearCongruentialGenerator lcg1 = makeLCG(126, 25);
  puts("makeLCG(38875,1234)");
  struct LinearCongruentialGenerator lcg2 = makeLCG(38875, 1234);
  //puts("makeLCG(4611686018427387904,961168601842738797)");
  //struct LinearCongruentialGenerator lcg3 = makeLCG(4611686018427387904,961168601842738797);

  /* Some error cases */
  struct LinearCongruentialGenerator lcg4 = makeLCG(4, 3);
  struct LinearCongruentialGenerator lcg5 = makeLCG(0, 5);
  struct LinearCongruentialGenerator lcg6 = makeLCG(5, 0);


  printLCG(&lcg1, "initialized lcg1");
  printLCG(&lcg2, "initialized lcg2");
  //printLCG(&lcg3, "initialized lcg3");

  printLCG(&lcg4, "initialized error test lcg4");
  printLCG(&lcg5, "initialized error test lcg5");
  printLCG(&lcg6, "initialized error test lcg6");

  testValues(&lcg1, "test lcg1", 10);
  testValues(&lcg2, "test lcg2", 10);
  //testValues(&lcg3, "test lcg3", 10);

  printLCG(&lcg1, "lcg1 after first test");
  printLCG(&lcg2, "lcg2 after first test");
  //printLCG(&lcg3, "lcg3 after first test");

  testValues(&lcg1, "test lcg1 again", 20);

  printLCG(&lcg1, "lcg1 after second test");

  return 0;

使用clang -g3 -O3 -Weverything -std=c11 lcg.c -o lcg 编译并在调试器 (gdb) 中运行它会得到（这里！）：

makeLCG(126,25)
checkInput(m = 126, c = 25)
Unique Prime for 126 is: 2
Unique Prime for 126 is: 3
Unique Prime for 126 is: 7
q = 4
P for 126 is 126
P for 126 is 252
P for 126 is 756
P for 126 is 5292
getA(m): m = 126, a = 5293
Unique Prime for 126 is: 2
Unique Prime for 126 is: 3
Unique Prime for 126 is: 7
q = 4
P for 126 is 126
P for 126 is 252
P for 126 is 756
P for 126 is 5292
getA(m): m = 126, a = 5293
makeLCG(38875,1234)
checkInput(m = 38875, c = 1234)
Unique Prime for 38875 is: 5
q = 2
P for 38875 is 38875
P for 38875 is 194375
getA(m): m = 38875, a = 194376
Unique Prime for 38875 is: 5
q = 2
P for 38875 is 38875
P for 38875 is 194375
getA(m): m = 38875, a = 194376
checkInput(m = 4, c = 3)
Unique Prime for 4 is: 2
q = 2
P for 4 is 4
P for 4 is 8
getA(m): m = 4, a = 17
Unique Prime for 4 is: 2
q = 2
P for 4 is 4
P for 4 is 8
getA(m): m = 4, a = 17
checkInput(m = 0, c = 5)
checkInput(m = 5, c = 0)
initialized lcg1 (m=0,a=0,c=0,x=0)
initialized lcg2 (m=0,a=0,c=0,x=0)
initialized error test lcg4 (m=0,a=0,c=0,x=0)
initialized error test lcg5 (m=0,a=0,c=0,x=0)
initialized error test lcg6 (m=0,a=0,c=0,x=0)
test lcg1

Program received signal SIGFPE, Arithmetic exception.
0x0000000000400b1b in getNextRandomValue (lcg=<optimized out>) at lcg.c:54
54    lcg->x = lcg->x % lcg->m;

除以零是因为getA(m) 总是返回零，因为a 中的计算值总是大于m 并且来自getA() 的零导致makeLCG() 调用第二个分支来设置所有值struct 归零。

【讨论】：

非常感谢！我能够理解你指出的大部分内容，但你强调了一些我仍然错过的东西。