Deconstructing and reconstructing a IEEE 754 float

floatreassemble.c

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


float simple(float n, int ii) {
	printf("simple original float: %f %x\n", n, *((unsigned int*)&n));
	float a = (float)(int)n;
	float b = n - a;
	float c = (float)ii + b;
	printf("simple generated float: %f %x\n", c, *((unsigned int*)&n));
	return c;
}

float handmade(float n, int ii) {
	int i;
	int ee;
	char s;
	int intbytes = (sizeof(int) * 8);
	
	// cast to access using bitwise operations
	unsigned int *c = (unsigned int *)&n;
	unsigned int e;
	
	printf("handmade original float: %f %x\n", n, *c);
	// first bit is sign of float
	s = *c & 0x80;
	
	// byte-align exponent and mantissa
	*c <<= 1;
	
	// extract and unbias exponent value
	e = *c >> (intbytes - 8);
	e -= 127;

	// align mantissa to byte int start
	*c <<= 8;
	
	// adjust mask to significand's exponent boundary and invert
	i = *c & ~(INT_MAX >> (e - 1));
	i >>= intbytes - e;	
	i |= 1 << e;
	
	// now align fractional part
	*c <<= e;
	
	// get the logarithm of the replacement int
	ee = (int)log2(ii);

	// shift to align the significand to its place in the float
	*c >>= ee;
	ii <<= intbytes - ee;
	*c |= ii;
	
	// add the bias
	ee += 127;

	// align float to exponent int
	*c >>= 8;
	ee <<= intbytes - 8;	
	*c |= ee;
	
	// shift to add the sign
	*c >>= 1;
	
	// todo: handle sign
	
	printf("handmade generated float: %f %x\n", *(float*)c, *c);
	return i;
}


int main() {
	float n = 21.9375;
	simple(n, 32);
	handmade(n, 32);
	return 0;
}