Thread: IEEE floating point armithmetic

Alright, so I'm trying to make an program that does calculates the sum of two numbers through two methods. One is basic integer arithmetic (simple), and the other is through IEEE floating point arithmetic (not so simple). I'm using basic bit manipulation C commands (shift, bit macros, ect. . .) The int main() code was prewritten for me; I was just tasked with writing the functions. I know the first three function properly because I've tested them with a working compute function. Unfortunately, when I plug in my compute function it compiles, but doesn't work the way it's supposed to at all. Here's my code (the functions are declared in the header, but everything else is in the .c file):

Code:

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include "floatcomp.h"
#define BIT31 ((uint) 0x80000000)
#define BIT30 ((uint) 0x7f800000)
#define BIT22 ((uint) 0x007fffff)
#define BIT0 ((uint) 0x00000000)
#define BIT1 ((uint) 0x00800000)
#define BITALL ((uint) 0xffffffff)

int showmode = 0;

int main(int argc, char *argv[])
{
    float f1, f2, r1, r2;
    char op;
    int stop = 0, nitem;

    if ((argc == 2) && (argv[1][0]=='v'))
      showmode = 1;

    while ((nitem = scanf("%f %c %f", &f1, &op, &f2)) == 3) {
      switch (op) {
      case '+': r1 = f1 + f2; break;
      case '-': r1 = f1 - f2; break;
      case '*': r1 = f1 * f2; break;
      case '/': r1 = f1 / f2; break;
      default: 
        stop = 1;
        break;
      }
  
      if (stop) break;

      if (showmode) {
        printf("\n");
        printf("---- standard computation ---------\n\n");
      }
      printf("%13.6f %c %13.6f = %13.6f\n", f1, op, f2, r1);

      uint xf1 = *(uint *)&f1;
      uint xf2 = *(uint *)&f2;

      if (showmode) {
        printf("\n");
        printf("---- integer based computation ----\n\n");
        printf("  f1: 0x%08x\n", xf1);
        printf("  f2: 0x%08x\n", xf2);
        printf("\n");
      }

      r2 = compute(xf1, xf2, op);

      if (showmode) {
        printf("\n");
      }

      printf("%13.6f %c %13.6f = %13.6f\n\n", f1, op, f2, r2);
    }

    if (nitem != EOF)
    printf("input expression format error\n");
}

uint unpack(uint n, int *s, int *e, int *f) // extracts the sign bit, exponent string, and the mantissa from the //number
{
    *s= (BIT31 & n) >> 31;
    *e= (BIT30 & n) >> 23;
    *f= (BIT22 & n);

        if(*e!=0)
    *f = *f | BIT1;     

    *e = *e - 127;
}

uint  pack(int s, int e, int f) // opposite of unpack, puts the disassembled binary back together
{
    s = s << 31;
    e = (e + 127) << 23;
    f = (f & BIT22);

    int n = s | e | f;

    return (n);    
}

int   first_nzb(int f) //finds left-most non-zero bit and returns location in the bit
{
    int i;
    for(i=31;i>=0;i--)
    {
        if((1<<i) & f)
            return (i);
        if(i==0)
            return(-1);
    }
}

void  normalize(int k, int *e, int *f) //puts the fraction where it's supposed to be and determines if the exponent //needs to be accordingly increased or decreased.
{
    int shift = k - 23;
    if (shift > 0)
        *f = *f >> shift;
    else
        *f = *f << (-shift);
    
    *e = *e + shift;
}

float compute(uint n1, uint n2, char op)
{
    int shift;
    int s1, e1, f1, s2, e2, f2; 
    int k, n3, f3, s3, e3;
    unpack(n1, &s1, &e1, &f1); //extract appropriate parts from the bit numbers
    unpack(n2, &s2, &e2, &f2);
    if (op == '-')
    {
        if(n2<0) //if it's a negative number, take two's compliment by toggling numbers and adding one
        n2 = ~n2 + 1;
        if(f1>f2) //if the number being subtracted from is greater, sign is positive
        {
            s3=s1;
        }
        if(f1<f2) //if the number being subtracted is larger, sign is negative
        {
            s3=s2;
        }
    }

    if(e1 > e2)
    { 
                //if exponent of n1 is larger, use it's exponent and shift fraction 2 the difference between the //exponents
        e3 = e1;
        f2 = f2 << (e1 - e2); 
    }
    else if(e2 > e1)//if exponent of n1 is larger, use it's exponent
    { 
                //same as last function, just opposite
        e3 = e2;
        f1 = f1 << (e2 - e1); 
    }
    else if(e1 == e2)
    {
        if((f1+f2) > 0)
        {
            e3 = e2 + 1; // if the exponents are equal, but the fraction is greater than 0, shift 1
            shift = 1;
        }
        else
        e3 = e2;
    }

    if(op == '+')
    {
        s3=s1; //if adding, just pick first sign, because they're both the same
    }
    f3 = f1 + f2; // add fractions, then call predefined functions to prepare for addition
    if(shift==1) f3 = f3 >> 1;
    normalize(first_nzb(f3),&e3, &f3);
    f3 = f3 & BIT22;
    uint x = pack(s3,e3,f3);
    float *fp;
    fp = &x;
    return *fp;
}

I'll admit, I'm a little bit in over my head with this. I usually program in C++, and this is my first experience with bit manipulation commands. I'm sure I'm making some blatant logic error, but I just don't understand the syntax well enough to see what it is. Anyways, the numbers I get are drastically off. Well, the second one at least, obviously the addition done by integer arithmetic (the first number it returns) is correct. This is a lab assignment, and the TA said we could ask outside sources for advice, but, obviously, don't just give me the entire code, or it would defeat the purpose.

Thanks,
Aaron

Oh, forgot to say that I'm compiling in the linux terminal. I only get one warning, and I've been told by my TA it's a necessary one. It's about an incompatible pointer type when the *fp is assigned.

If you're only getting one warning, you need to compile with these flags: "-Wall -pedantic".

Also, you could replace

Code:

#define BITALL ((uint) 0xffffffff)

/* to */

#define BITALL (0xffffffffu)

and then make the same change to the rest of them

I'm new to linux and I'm unsure as to how to compile with flags.

Also, I changed the bit declarations, no change.

Yeah, I need to make allowances for those cases, but I'm just focusing on getting it to function basically first. I made some tweaks that give me the proper numbers, unfortunately, it only works for a few calculations in a row, then it starts doing wonky things to the sum, like divide by 2. . .

Since you've given no indication of noticing, please note that I've pointed out a couple of errors in your code in my post above.