Custom floating point

//Do note that much greater precision can be achieved if a long double is used instead.
//A long double version of log(), floor(), and pow() would need to be used, though.

#include<stdio.h>
#include <math.h>
#define abs(a) ((a)<0?-(a):(a))

void store_float(FILE* f, double value, int bytes){
    bytes--;
    int power = floor(bytes*8-log(value)/log(2));
    if( power < -64 || power >= 64 || isinf(value) || isnan(value) )
        power = 63;
    int is_negative = value >= 0 ? 0 : 1;
    value = abs( value );
    value *= pow( 2, power );
    value = floor( value );
    power = (power + 64) & 0xFF;
    power |= is_negative << 7;
    fputc( power, f );
    while( value > 0 && bytes > 0 ){
        fputc( value-floor(value/256)*256, f );
        value = floor( value/256 );
        bytes--;
    }
}

double read_float( FILE *f, int bytes ){
    bytes--;
    int power = fgetc( f );
    int is_negative = power & 0x80;
    power &= 0x7F;
    power -= 64;
    double value = 0;
    double multiplier = 1;
    while( bytes-- > 0 ){
        value += (double)fgetc( f ) * multiplier;
        multiplier *= 256;
    }
    if( is_negative )
        value *= -1;
    value /= pow( 2, power );
    if( power == 63 )
        value = pow(2, 1024);
    return value;
}

int main(){
    FILE *f = fopen( "test.bin", "w" );

    store_float( f, 1080.746356, 8 );
    store_float( f, 1080.746356, 4 );
    store_float( f, 1080.746356, 2 );
    store_float( f, 1234567890123456789.123456789, 8 );
    store_float( f, 1234567890123456789.123456789, 4 );
    store_float( f, 1234567890123456789.123456789, 2 );
    store_float( f, pow(2,1024), 2 );

    fclose(f);


    f = fopen( "test.bin", "r" );

    printf("%f\n", read_float( f, 8 ));
    printf("%f\n", read_float( f, 4 ));
    printf("%f\n", read_float( f, 2 ));
    printf("%f\n", read_float( f, 8 ));
    printf("%f\n", read_float( f, 4 ));
    printf("%f\n", read_float( f, 2 ));
    printf("%f\n", read_float( f, 2 ));

    fclose(f);

}


/* Output:

1080.746356
1080.746338
1080.000000
1234567890123456800.000000
1234567802111655900.000000
1233986297899515900.000000
1.#INF00



Contents of test.bin (hex dump, separated by stored value):
6D 90 65 FA 25 E2 17 87
4D E2 17 87
3D 87
3B 08 4C EF A3 87 10 89
1B 87 10 89
0B 89
7F 00
*/