From: asterix Date: Mon, 17 Mar 2008 10:19:59 +0000 (+0000) Subject: Add utility to compute ramp function. X-Git-Tag: 1.0.0~62 X-Git-Url: https://codewiz.org/gitweb?a=commitdiff_plain;h=c8f1a57907a25aeb9176ec2af0a41f4e9ba27fcb;p=bertos.git Add utility to compute ramp function. git-svn-id: https://src.develer.com/svnoss/bertos/trunk@1190 38d2e660-2303-0410-9eaa-f027e97ec537 --- diff --git a/drv/ramp.c b/drv/ramp.c new file mode 100644 index 00000000..9a2cc92e --- /dev/null +++ b/drv/ramp.c @@ -0,0 +1,206 @@ +/*! + * \file + * + * + * \brief Compute, save and load ramps for stepper motors (implementation) + * + * \version $Id$ + * + * \author Simone Zinanni + * \author Bernardo Innocenti + * \author Giovanni Bajo + * \author Daniele Basile + * + * + * The formula used by the ramp is the following: + * + * 
+ *            a * b
+ * f(t) = -------------
+ *         lerp(a,b,t)
+ *
+ * + * Where a and b are the maximum and minimum speed + * respectively (minimum and maximum wavelength respectively), and lerp + * is a linear interpolation with a factor: + * + * 
+ * lerp(a,b,t) =  a + t * (b - a)  =  (a * (1 - t)) + (b * t)
+ *
+ * + * t must be in the [0,1] interval. It is easy to see that the + * following holds true: + * + * 
+ * f(0) = b,   f(1) = a
+ *
+ * + * 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: + * + * 
+ *               a * b * MT
+ * g(t) = ----------------------------
+ *           (a * MT) + t * (b - a)
+ *
+ * + * It can be shown that this g(t) = f(t * MT). 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: + * + * 
+ * alpha = a * b * MT
+ * beta = a * MT
+ * gamma = b - a
+ *
+ *                alpha
+ * g(t) = ----------------------
+ *           beta + t * gamma
+ *
+ * + * and t 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: + * + * 
+ *                   a * b                         a
+ *  f(t) =  -------------------------  =  --------------------
+ *                 a                         a
+ *           b * ( - * (1 - t) + t )         - * (1 - t) + t
+ *                 b                         b
+ *
+ * + * t 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 + * t (and 1-t is just its twos-complement negation). + * a/b 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 + +#include // 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 + +