--- /dev/null
+/*!
+ * \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)
+ *
+ * \version $Id$
+ *
+ * \author Simone Zinanni <s.zinanni@develer.com>
+ * \author Bernardo Innocenti <bernie@develer.com>
+ * \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()
+
+/**
+ * Multiply \p a and \p b two integer at 32 bit and extract the high 16 bit word.
+ */
+#define FIX_MULT32(a,b) (((uint64_t)(a)*(uint32_t)(b)) >> 16)
+
+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
+
+
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