I didn't find any detailed information about the "Q23 fixed point representation" that your machine uses, so I made up my own definition, wrote some conversion routines and tested them for some few values:
#include <limits.h>
#include <stdio.h>
#include <stdlib.h>
/**
* q23 is a fixed-point two's-complement type:
* - 1 bit sign,
* - 8 bit integer part,
* - 23 bit fraction part.
*
* long is assumed to be 32 bit two's complement without padding bits.
*/
typedef long q23;
static q23
cvt_float_to_q23(float f) {
return f * (1 << 23);
}
static float
cvt_q23_to_float(q23 x) {
return ((float) x) / (1 << 23);
}
/*
* Here starts the testing code.
*/
static unsigned errors = 0;
static void
assert_q23_is(q23 fixed, float f) {
if (cvt_q23_to_float(fixed) != f) {
fprintf(stderr, "E: cvt_q23_to_float(%08lx) expected %.10f, got %.10f\n",
fixed, f, cvt_q23_to_float(fixed));
errors++;
}
}
static void
assert_float_is(float f, q23 fixed) {
if (cvt_float_to_q23(f) != fixed) {
fprintf(stderr, "E: cvt_float_to_q23(%f) expected %08lx, got %08lx\n",
f, fixed, cvt_float_to_q23(f));
errors++;
}
}
static void
assert_equals(q23 fixed, float f) {
assert_q23_is(fixed, f);
assert_float_is(f, fixed);
}
int
main() {
/* Some values have equivalent representation. */
assert_equals(LONG_MIN, -256.0f);
assert_equals(LONG_MIN / 2, -128.0f);
assert_equals(0, 0.0f);
assert_equals(LONG_MAX / 2 + 1, 128.0f);
/* There will be a fixpoint ... */
assert_float_is(1.0 / 3, 0x002aaaaa);
assert_q23_is(0x002aaaaa, 0.3333332539f);
/* float only has 24 bits of precision */
assert_equals(0x2aaaaac0, 256.0 / 3);
if (errors == 0) {
printf("ok\n");
return EXIT_SUCCESS;
}
return EXIT_FAILURE;
}
Some remarks:
- If you need saturated rounding you have to implement that yourself by checking the argument to
cvt_float_to_q23
.
- There will be rounding errors everywhere, and they are inevitable. Be sure to handle them appropriately.