This macro is pretty expensive (700 bytes, well, stuff is now
calculated at runtime), so there's no chance to use it in multiple
places and we likely also need this in dda_lookahead.c to achieve
full 4 axis compatibility there.
For now this is for the initial rampup calculation, only, notably
for moving the Z axis (which else gets far to few rampup steps on
a typical mendel-like printer).
The used macro was verified with this test code (in mendel.c):
[...]
int main (void) {
init();
uint32_t speed, spm;
char string[128];
for (spm = 2000; spm < 4099000; spm <<= 1) {
for (speed = 11; speed < 65536; speed *= 8) {
sersendf_P(PSTR("spm = %lu speed %lu ==> macro %lu "),
spm, speed, ACCELERATE_RAMP_LEN_SPM(speed, spm));
delay_ms(10);
sprintf(string, "double %f\n",
(double)speed * (double)speed / ((double)7200000 * (double)ACCELERATION / (double)spm));
serial_writestr((uint8_t *)string);
delay_ms(10);
}
}
[...]
Note: to link the test code, this linker flag is required to add
the full printf library (which does print doubles):
LDFLAGS += -Wl,-u,vfprintf -lprintf_flt -lm
His implementation was done on every step and as it turns out,
the very same maths works just fine in the clock interrupt.
Reason for the clock interrupt is: it allows about 3 times
higher step rates.
This strategy is not only substantially faster, but also
a bit smaller.
One funny anecdote: the acceleration initialisation value, C0,
was taken from elsewhere in the code as-is. Still it had to be
adjusted by a factor of sqrt(2) to now(!) match the physics
formulas and to get ramps reasonably matching the prediction
(and my pocket calculator). Apparently the code before
accumulated enough rounding errors to compensate for the
wrong formula.
This 1/sqrt(x) implementation is a 12 bits fixed point implementation
and a bit faster than a 32 bits divide (it takes about 11% less time
to complete) and could be even faster if one requires only 8 bits.
Also, precision starts getting poor for big values of n which are
likely to be required by small acceleration values.
This means, modify existing code to let the lookahead algorithms
do their work. It also means to remove some unused code in
dda_lookahead.c and reordering some code to make it work with
LOOKAHEAD undefined.
This is a version of muldiv() with qn and rn precalculated,
so it can be avoided to re-calclulate it on every instance.
Yet another 116 bytes, unfortunately.
This gets rid of overflows at micrometer to step conversion as
much as possible within 31 bits. It also opens the door to get
STEPS_PER_M configurable at runtime.
This also costs 290 bytes, unfortunately.
We have multiplies followed by divides all over the place and
most of them are difficult to handle regarding overflows. This
new algorithm handles this fine in all cases, as long as all
three operators and the overall result fits into 32 bits.
Markus Hitter
Roland Brochard