/*!
* \file
* <!--
* Copyright 2004, 2008 Develer S.r.l. (http://www.develer.com/)
* All Rights Reserved.
* -->
*
* \brief Compute, save and load ramps for stepper motors (implementation)
*
*
* \author Simone Zinanni <s.zinanni@develer.com>
* \author Bernie Innocenti <bernie@codewiz.org>
* \author Giovanni Bajo <rasky@develer.com>
* \author Daniele Basile <asterix@develer.com>
*
*
* The formula used by the ramp is the following:
*
* <pre>
* a * b
* f(t) = -------------
* lerp(a,b,t)
* </pre>
*
* Where <code>a</code> and <code>b</code> are the maximum and minimum speed
* respectively (minimum and maximum wavelength respectively), and <code>lerp</code>
* is a linear interpolation with a factor:
*
* <pre>
* lerp(a,b,t) = a + t * (b - a) = (a * (1 - t)) + (b * t)
* </pre>
*
* <code>t</code> must be in the [0,1] interval. It is easy to see that the
* following holds true:
*
* <pre>
* f(0) = b, f(1) = a
* </pre>
*
* And that the function is monotonic. So, the function effectively interpolates
* between the maximum and minimum speed through its domain ([0,1] -> [b,a]).
*
* The curve drawn by this function is similar to 1 / (sqrt(n)), so it is slower
* than a linear acceleration (which would be 1/n).
*
* The floating point version uses a slightly modified function which accepts
* the parameter in the domain [0, MT] (where MT is maxTime, the length of the
* ramp, which is a setup parameter for the ramp). This is done to reduce the
* number of operations per step. The formula looks like this:
*
* <pre>
* a * b * MT
* g(t) = ----------------------------
* (a * MT) + t * (b - a)
* </pre>
*
* It can be shown that this <code>g(t) = f(t * MT)</code>. The denominator
* is a linear interpolation in the range [b*MT, a*MT], as t moves in the
* interval [0, MT]. So the interpolation interval of the function is again
* [b, a]. The implementation caches the value of the numerator and parts
* of the denominator, so that the formula becomes:
*
* <pre>
* alpha = a * b * MT
* beta = a * MT
* gamma = b - a
*
* alpha
* g(t) = ----------------------
* beta + t * gamma
* </pre>
*
* and <code>t</code> is exactly the parameter that ramp_evaluate() gets,
* that is the current time (in range [0, MT]). The operations performed
* for each step are just an addition, a multiplication and a division.
*
* The fixed point version of the formula instead transforms the original
* function as follows:
*
* <pre>
* a * b a
* f(t) = ------------------------- = --------------------
* a a
* b * ( - * (1 - t) + t ) - * (1 - t) + t
* b b
* </pre>
*
* <code>t</code> must be computed by dividing the current time (24 bit integer)
* by the maximum time (24 bit integer). This is done by precomputing the
* reciprocal of the maximum time as a 0.32 fixed point number, and multiplying
* it to the current time. Multiplication is performed 8-bits a time by
* FIX_MULT32(), so that we end up with a 0.16 fixed point number for
* <code>t</code> (and <code>1-t</code> is just its twos-complement negation).
* <code>a/b</code> is in the range [0,1] (because a is always less than b,
* being the minimum wavelength), so it is precomputed as a 0.16 fixed point.
* The final step is then computing the denominator and executing the division
* (32 cycles using the 1-step division instruction in the DSP).
*
* The assembly implementation is needed for efficiency, but a C version of it
* can be easily written, in case it is needed in the future.
*
*/
#include "ramp.h"
#include <cfg/debug.h>
#include <string.h> // memcpy()
void ramp_compute(struct Ramp *ramp, uint32_t clocksRamp, uint16_t clocksMinWL, uint16_t clocksMaxWL)
{
ASSERT(clocksMaxWL >= clocksMinWL);
// Save values in ramp struct
ramp->clocksRamp = clocksRamp;
ramp->clocksMinWL = clocksMinWL;
ramp->clocksMaxWL = clocksMaxWL;
#if RAMP_USE_FLOATING_POINT
ramp->precalc.gamma = ramp->clocksMaxWL - ramp->clocksMinWL;
ramp->precalc.beta = (float)ramp->clocksMinWL * (float)ramp->clocksRamp;
ramp->precalc.alpha = ramp->precalc.beta * (float)ramp->clocksMaxWL;
#else
ramp->precalc.max_div_min = ((uint32_t)clocksMinWL << 16) / (uint32_t)clocksMaxWL;
/* Calcola 1/total_time in fixed point .32. Assumiamo che la rampa possa al
* massimo avere 25 bit (cioé valore in tick fino a 2^25, che con il
* prescaler=3 sono circa 7 secondi). Inoltre, togliamo qualche bit di precisione
* da destra (secondo quanto specificato in RAMP_CLOCK_SHIFT_PRECISION).
*/
ASSERT(ramp->clocksRamp < (1UL << (24 + RAMP_CLOCK_SHIFT_PRECISION)));
ramp->precalc.inv_total_time = 0xFFFFFFFFUL / (ramp->clocksRamp >> RAMP_CLOCK_SHIFT_PRECISION);
ASSERT(ramp->precalc.inv_total_time < 0x1000000UL);
#endif
}
void ramp_setup(struct Ramp* ramp, uint32_t length, uint32_t minFreq, uint32_t maxFreq)
{
uint32_t minWL, maxWL;
minWL = TIME2CLOCKS(FREQ2MICROS(maxFreq));
maxWL = TIME2CLOCKS(FREQ2MICROS(minFreq));
ASSERT2(minWL < 65536UL, "Maximum frequency too high");
ASSERT2(maxWL < 65536UL, "Minimum frequency too high");
ASSERT(maxFreq > minFreq);
ramp_compute(
ramp,
TIME2CLOCKS(length),
TIME2CLOCKS(FREQ2MICROS(maxFreq)),
TIME2CLOCKS(FREQ2MICROS(minFreq))
);
}
void ramp_default(struct Ramp *ramp)
{
ramp_setup(ramp, RAMP_DEF_TIME, RAMP_DEF_MINFREQ, RAMP_DEF_MAXFREQ);
}
#if RAMP_USE_FLOATING_POINT
float ramp_evaluate(const struct Ramp* ramp, float curClock)
{
return ramp->precalc.alpha / (curClock * ramp->precalc.gamma + ramp->precalc.beta);
}
#else
INLINE uint32_t fix_mult32(uint32_t m1, uint32_t m2)
{
uint32_t accum = 0;
accum += m1 * ((m2 >> 0) & 0xFF);
accum >>= 8;
accum += m1 * ((m2 >> 8) & 0xFF);
accum >>= 8;
accum += m1 * ((m2 >> 16) & 0xFF);
return accum;
}
// a*b >> 16
INLINE uint16_t fix_mult16(uint16_t a, uint32_t b)
{
return (b*(uint32_t)a) >> 16;
}
uint16_t FAST_FUNC ramp_evaluate(const struct Ramp* ramp, uint32_t curClock)
{
uint16_t t = FIX_MULT32(curClock >> RAMP_CLOCK_SHIFT_PRECISION, ramp->precalc.inv_total_time);
uint16_t denom = fix_mult16((uint16_t)~t + 1, ramp->precalc.max_div_min) + t;
uint16_t cur_delta = ((uint32_t)ramp->clocksMinWL << 16) / denom;
return cur_delta;
}
#endif