将C中的浮点数转换为IEEE标准

Question

I am trying to write a code in C that generates a random integer , performs simple calculation and then I am trying to print the values of the file in IEEE standard. But I am unable to do so , Please help.

I am unable to print it in Hexadecimal/Binary which is very important. If I type cast the values in fprintf , I am getting this Error expected expression before double .

int main (int argc, char *argv) {

     int limit = 20 ; double a[limit], b[limit];                //Inputs
     double result[limit]    ; int i , k ;            //Outputs
     printf("limit = %d", limit ); double q;


     for (i= 0 ; i< limit;i++)
         {
         a[i]= rand();
         b[i]= rand();
         printf ("A= %x B = %x\n",a[i],b[i]);

         }

     char op;

      printf("Enter the operand used : add,subtract,multiply,divide\n"); 
     scanf ("%c", &op); switch (op) {

     case '+': {
             for (k= 0 ; k< limit ; k++)
                 {

                 result [k]= a[k] + b[k];
            printf ("result= %f\n",result[k]);

                 }
             }
         break;

     case '*': {
             for (k= 0 ; k< limit ; k++)
                 {

                 result [k]= a[k] * b[k];

                 }
             }
         break;

     case '/': {
             for (k= 0 ; k< limit ; k++)
                 {

                 result [k]= a[k] / b[k];

                 }
             }
         break;

     case '-': {
             for (k= 0 ; k< limit ; k++)
                 {

                 result [k]= a[k] - b[k];

     }
             }
         break; }


     FILE *file; file = fopen("tb.txt","w"); for(k=0;k<limit;k++) {  
     fprintf (file,"%x\n
     %x\n%x\n\n",double(a[k]),double(b[k]),double(result[k]) );

     }


     fclose(file); /*done!*/
 }

Answer 1

If your C compiler supports IEEE-754 floating point format directly (because the CPU supports it) or fully emulates it, you may be able to print doubles simply as bytes. And that is the case for the x86/64 platform.

Here's an example:

#include <limits.h>
#include <stdio.h>
#include <string.h>
#include <math.h>
#include <float.h>

void PrintDoubleAsCBytes(double d, FILE* f)
{
  unsigned char a[sizeof(d)];
  unsigned i;
  memcpy(a, &d, sizeof(d));
  for (i = 0; i < sizeof(a); i++)
    fprintf(f, "%0*X ", (CHAR_BIT + 3) / 4, a[i]);
}

int main(void)
{
  PrintDoubleAsCBytes(0.0, stdout); puts("");
  PrintDoubleAsCBytes(0.5, stdout); puts("");
  PrintDoubleAsCBytes(1.0, stdout); puts("");
  PrintDoubleAsCBytes(2.0, stdout); puts("");
  PrintDoubleAsCBytes(-2.0, stdout); puts("");
  PrintDoubleAsCBytes(DBL_MIN, stdout); puts("");
  PrintDoubleAsCBytes(DBL_MAX, stdout); puts("");
  PrintDoubleAsCBytes(INFINITY, stdout); puts("");
#ifdef NAN
  PrintDoubleAsCBytes(NAN, stdout); puts("");
#endif
  return 0;
}

Output ( ideone ):

00 00 00 00 00 00 00 00 
00 00 00 00 00 00 E0 3F 
00 00 00 00 00 00 F0 3F 
00 00 00 00 00 00 00 40 
00 00 00 00 00 00 00 C0 
00 00 00 00 00 00 10 00 
FF FF FF FF FF FF EF 7F 
00 00 00 00 00 00 F0 7F 
00 00 00 00 00 00 F8 7F 

If IEEE-754 isn't supported directly, the problem becomes more complex. However, it can still be solved.

Here are a few related questions and answers that can help:

• How do I handle byte order differences when reading/writing floating-point types in C?
• Is there a tool to know whether a value has an exact binary representation as a floating point variable?
• C dynamically printf double, no loss of precision and no trailing zeroes

And, of course, all the IEEE-754 related info can be found in Wikipedia .

Answer 2

Try this in your fprint part:

fprintf (file,"%x\\n%x\\n%x\\n\\n",*((int*)(&a[k])),*((int*)(&b[k])),*((int*)(&result[k])));

That would translate the double as an integer so it's printed in IEEE standard.

But if you're running your program on a 32-bit machine on which int is 32-bit and double is 64-bit, I suppose you should use:

fprintf (file,"%x%x\\n%x%x\\n%x%x\\n\\n",*((int*)(&a[k])),*((int*)(&a[k])+1),*((int*)(&b[k])),*((int*)(&b[k])+1),*((int*)(&result[k])),*((int*)(&result[k])+1));

Answer 3

In C, there are two ways to get at the bytes in a float value: a pointer cast, or a union. I recommend a union.

I just tested this code with GCC and it worked:

#include <stdio.h>
typedef unsigned char BYTE;

int
main()
{
    float f = 3.14f;
    int i = sizeof(float) - 1;
    BYTE *p = (BYTE *)(&f);
    p[i] = p[i] | 0x80;  // set the sign bit
    printf("%f\n", f);  // prints -3.140000
}

We are taking the address of the variable f , then assigning it to a pointer to BYTE (unsigned char). We use a cast to force the pointer.

If you try to compile code with optimizations enabled and you do the pointer cast shown above, you might run into the compiler complaining about "type-punned pointer" issues. I'm not exactly sure when you can do this and when you can't. But you can always use the other way to get at the bits: put the float into a union with an array of bytes.

#include <stdio.h>

typedef unsigned char BYTE;

typedef union
{
    float f;
    BYTE b[sizeof(float)];
} UFLOAT;

int
main()
{
    UFLOAT u;
    int const i = sizeof(float) - 1;

    u.f = 3.14f;
    u.b[i] = u.b[i] | 0x80;  // set the sign bit
    printf("%f\n", u.f);  // prints -3.140000
}

What definitely will not work is to try to cast the float value directly to an unsigned integer or something like that. C doesn't know you just want to override the type, so C tries to convert the value, causing rounding.

float f = 3.14;
unsigned int i = (unsigned int)f;

if (i == 3)
    printf("yes\n"); // will print "yes"

PS Discussion of "type-punned" pointers here:

Dereferencing type-punned pointer will break strict-aliasing rules