CODEWITHSUNDEEP
cfloating-point
Ankur Agarwal
Ankur Agarwal

Reputation: 24788

Can C not print/represent denormalized floating point numbers?

 $ gcc --version
Configured with: --prefix=/Library/Developer/CommandLineTools/usr --with-gxx-include-dir=/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/include/c++/4.2.1
Apple clang version 12.0.5 (clang-1205.0.22.9)
Target: x86_64-apple-darwin20.3.0
Thread model: posix
InstalledDir: /Library/Developer/CommandLineTools/usr/bin
$ uname -a
Darwin MacBook-Air.local 20.3.0 Darwin Kernel Version 20.3.0: Thu Jan 21 00:07:06 PST 2021; root:xnu-7195.81.3~1/RELEASE_X86_64 x86_64

Code:

#include <stdio.h>

int main(void) {


    int i = 2;
    printf("int \"2\" as %%.128f:                  %.128f\n", i);

    printf("int \"2\" as %%.128lf:                 %.128lf\n", i);

    printf("int \"2\" as %%.128LF:                 %.128Lf\n", i);

    return 0;

}

Compile:

$ gcc floatingpointtypes.c

Execute:

$ ./a.out
int "2" as %.128f:                  0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
int "2" as %.128lf:                 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
int "2" as %.128LF:                 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

When binary of integer 2 is interpreted as IEEE-754 single precision (32 bit) or double precision (64 bit) floating point number format then it is a denormalized float (exponent bits are all 0s) and the resultant value in decimal is 2e-148.

Question:

Why does my code print 0s? Is it because C can't interpret denormalized floating point numbers to their correct value ?

Upvotes: 1

Views: 474

Answers (2)

Chris Dodd
Chris Dodd

Reputation: 126546

If you want to convert the 'bits' of an int to a floating point type, the easiest way to do that is with a union:

#include <stdio.h>
#include <stdint.h>

union u32 {
    int32_t     i;
    float       f;
};

union u64 {
    int64_t     i;
    double      d;
};

int main() {
    union u32 a;
    union u64 b;

    a.i = 2;
    b.i = 2;

    printf("%g\n", a.f);
    printf("%g\n", b.d);
    return 0;
}

resulting output:

2.8026e-45
9.88131e-324

What is likely happening with your code is that you're using a system which passes arguments in different registers depending on the type (integer registers for int values and floating point registers for fp types). So the call puts 2 into an integer register, but the value getting printed by %f is whatever value happens to be in the first floating point register used for arguments -- probably 0 as no fp code has run before the call.

Upvotes: 6

TheNumberOne
TheNumberOne

Reputation: 444

In addition to undefined behavior, you overestimated the size of the float because the %f specifier expects double-precision floating-point numbers. The exact value of the number printed is 2^-1073. The first non-zero happens 324 decimal digits after the decimal place, but you were only printing the first 128 digits. Try:

#include <stdio.h>

int main(void)
{
    long long i = 2;
    printf("long long \"2\" as %%.1073f:                  %.1073f\n", *(double *) &i);
    return 0;
}

Output:

long long "2" as %.1073:                  0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000988131291682493088353137585736442744730119605228649528851171365001351014540417503730599672723271984759593129390891435461853313420711879592797549592021563756252601426380622809055691634335697964207377437272113997461446100012774818307129968774624946794546339230280063430770796148252477131182342053317113373536374079120621249863890543182984910658610913088802254960259419999083863978818160833126649049514295738029453560318710477223100269607052986944038758053621421498340666445368950667144166486387218476578691673612021202301233961950615668455463665849580996504946155275185449574931216955640746893939906729403594535543517025132110239826300978220290207572547633450191167477946719798732961988232841140527418055848553508913045817507736501283943653106689453125

Upvotes: 2

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