diff --git a/.travis.yml b/.travis.yml
index 4ca3b13ab8b9270d154315ab95d361c4cf6def37..568f9c6cd2098770160dc6971fd734c632291a5c 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -118,7 +118,7 @@ script:
# Add a Sled Z Probe, use UBL Cartesian moves, use Japanese language
#
- opt_set LANGUAGE kana_utf8
- - opt_enable Z_PROBE_SLED SKEW_CORRECTION SKEW_CORRECTION_FOR_Z SKEW_CORRECTION_GCODE
+ - opt_enable Z_PROBE_SLED SKEW_CORRECTION SKEW_CORRECTION_FOR_Z SKEW_CORRECTION_GCODE BEZIER_JERK_CONTROL
- opt_disable SEGMENT_LEVELED_MOVES
- opt_enable_adv BABYSTEP_ZPROBE_OFFSET DOUBLECLICK_FOR_Z_BABYSTEPPING
- build_marlin
diff --git a/Marlin/Configuration.h b/Marlin/Configuration.h
index 1a416dd6f2f1182d65cfb2a815359a9d38b81f7e..7d0efcc303ceb82b1ea0a75ba786385d9e2f8137 100644
--- a/Marlin/Configuration.h
+++ b/Marlin/Configuration.h
@@ -594,6 +594,17 @@
#define DEFAULT_ZJERK 0.3
#define DEFAULT_EJERK 5.0
+/**
+ * Realtime Jerk Control
+ *
+ * This option eliminates vibration during printing by fitting a Bézier
+ * curve to move acceleration, producing much smoother direction changes.
+ * Because this is computationally-intensive, a 32-bit MCU is required.
+ *
+ * See https://github.com/synthetos/TinyG/wiki/Jerk-Controlled-Motion-Explained
+ */
+//#define BEZIER_JERK_CONTROL
+
//===========================================================================
//============================= Z Probe Options =============================
//===========================================================================
diff --git a/Marlin/macros.h b/Marlin/macros.h
index a5f92a2d9f5c5ca57edb2454def64b4f3bb50a1f..74dd68ec6b900c597625ccd61f0e40326fd8c29f 100644
--- a/Marlin/macros.h
+++ b/Marlin/macros.h
@@ -117,6 +117,9 @@
#define STRINGIFY_(M) #M
#define STRINGIFY(M) STRINGIFY_(M)
+#define A(CODE) " " CODE "\n\t"
+#define L(CODE) CODE ":\n\t"
+
// Macros for bit masks
#undef _BV
#define _BV(b) (1<<(b))
diff --git a/Marlin/planner.cpp b/Marlin/planner.cpp
index 7a05ccc4938d33ae675a84a4749ae253daed702b..21f7cdd47585f1509a2c0e01293439d02c22da23 100644
--- a/Marlin/planner.cpp
+++ b/Marlin/planner.cpp
@@ -204,6 +204,514 @@ void Planner::init() {
clear_block_buffer();
}
+#if ENABLED(BEZIER_JERK_CONTROL)
+
+ // This routine, for AVR, returns 0x1000000 / d, but trying to get the inverse as
+ // fast as possible. A fast converging iterative Newton-Raphson method is able to
+ // reach full precision in just 1 iteration, and takes 211 cycles (worst case, mean
+ // case is less, up to 30 cycles for small divisors), instead of the 500 cycles a
+ // normal division would take.
+ //
+ // Inspired by the following page,
+ // https://stackoverflow.com/questions/27801397/newton-raphson-division-with-big-integers
+ //
+ // Suppose we want to calculate
+ // floor(2 ^ k / B) where B is a positive integer
+ // Then
+ // B must be <= 2^k, otherwise, the quotient is 0.
+ //
+ // The Newton - Raphson iteration for x = B / 2 ^ k yields:
+ // q[n + 1] = q[n] * (2 - q[n] * B / 2 ^ k)
+ //
+ // We can rearrange it as:
+ // q[n + 1] = q[n] * (2 ^ (k + 1) - q[n] * B) >> k
+ //
+ // Each iteration of this kind requires only integer multiplications
+ // and bit shifts.
+ // Does it converge to floor(2 ^ k / B) ?: Not necessarily, but, in
+ // the worst case, it eventually alternates between floor(2 ^ k / B)
+ // and ceiling(2 ^ k / B)).
+ // So we can use some not-so-clever test to see if we are in this
+ // case, and extract floor(2 ^ k / B).
+ // Lastly, a simple but important optimization for this approach is to
+ // truncate multiplications (i.e.calculate only the higher bits of the
+ // product) in the early iterations of the Newton - Raphson method.The
+ // reason to do so, is that the results of the early iterations are far
+ // from the quotient, and it doesn't matter to perform them inaccurately.
+ // Finally, we should pick a good starting value for x. Knowing how many
+ // digits the divisor has, we can estimate it:
+ //
+ // 2^k / x = 2 ^ log2(2^k / x)
+ // 2^k / x = 2 ^(log2(2^k)-log2(x))
+ // 2^k / x = 2 ^(k*log2(2)-log2(x))
+ // 2^k / x = 2 ^ (k-log2(x))
+ // 2^k / x >= 2 ^ (k-floor(log2(x)))
+ // floor(log2(x)) simply is the index of the most significant bit set.
+ //
+ // If we could improve this estimation even further, then the number of
+ // iterations can be dropped quite a bit, thus saving valuable execution time.
+ // The paper "Software Integer Division" by Thomas L.Rodeheffer, Microsoft
+ // Research, Silicon Valley,August 26, 2008, that is available at
+ // https://www.microsoft.com/en-us/research/wp-content/uploads/2008/08/tr-2008-141.pdf
+ // suggests , for its integer division algorithm, that using a table to supply the
+ // first 8 bits of precision, and due to the quadratic convergence nature of the
+ // Newton-Raphon iteration, then just 2 iterations should be enough to get
+ // maximum precision of the division.
+ // If we precompute values of inverses for small denominator values, then
+ // just one Newton-Raphson iteration is enough to reach full precision
+ // We will use the top 9 bits of the denominator as index.
+ //
+ // The AVR assembly function is implementing the following C code, included
+ // here as reference:
+ //
+ // uint32_t get_period_inverse(uint32_t d) {
+ // static const uint8_t inv_tab[256] = {
+ // 255,253,252,250,248,246,244,242,240,238,236,234,233,231,229,227,
+ // 225,224,222,220,218,217,215,213,212,210,208,207,205,203,202,200,
+ // 199,197,195,194,192,191,189,188,186,185,183,182,180,179,178,176,
+ // 175,173,172,170,169,168,166,165,164,162,161,160,158,157,156,154,
+ // 153,152,151,149,148,147,146,144,143,142,141,139,138,137,136,135,
+ // 134,132,131,130,129,128,127,126,125,123,122,121,120,119,118,117,
+ // 116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,
+ // 100,99,98,97,96,95,94,93,92,91,90,89,88,88,87,86,
+ // 85,84,83,82,81,80,80,79,78,77,76,75,74,74,73,72,
+ // 71,70,70,69,68,67,66,66,65,64,63,62,62,61,60,59,
+ // 59,58,57,56,56,55,54,53,53,52,51,50,50,49,48,48,
+ // 47,46,46,45,44,43,43,42,41,41,40,39,39,38,37,37,
+ // 36,35,35,34,33,33,32,32,31,30,30,29,28,28,27,27,
+ // 26,25,25,24,24,23,22,22,21,21,20,19,19,18,18,17,
+ // 17,16,15,15,14,14,13,13,12,12,11,10,10,9,9,8,
+ // 8,7,7,6,6,5,5,4,4,3,3,2,2,1,0,0
+ // };
+ //
+ // // For small denominators, it is cheaper to directly store the result,
+ // // because those denominators would require 2 Newton-Raphson iterations
+ // // to converge to the required result precision. For bigger ones, just
+ // // ONE Newton-Raphson iteration is enough to get maximum precision!
+ // static const uint32_t small_inv_tab[111] PROGMEM = {
+ // 16777216,16777216,8388608,5592405,4194304,3355443,2796202,2396745,2097152,1864135,1677721,1525201,1398101,1290555,1198372,1118481,
+ // 1048576,986895,932067,883011,838860,798915,762600,729444,699050,671088,645277,621378,599186,578524,559240,541200,
+ // 524288,508400,493447,479349,466033,453438,441505,430185,419430,409200,399457,390167,381300,372827,364722,356962,
+ // 349525,342392,335544,328965,322638,316551,310689,305040,299593,294337,289262,284359,279620,275036,270600,266305,
+ // 262144,258111,254200,250406,246723,243148,239674,236298,233016,229824,226719,223696,220752,217885,215092,212369,
+ // 209715,207126,204600,202135,199728,197379,195083,192841,190650,188508,186413,184365,182361,180400,178481,176602,
+ // 174762,172960,171196,169466,167772,166111,164482,162885,161319,159783,158275,156796,155344,153919,152520
+ // };
+ //
+ // // For small divisors, it is best to directly retrieve the results
+ // if (d <= 110)
+ // return pgm_read_dword(&small_inv_tab[d]);
+ //
+ // // Compute initial estimation of 0x1000000/x -
+ // // Get most significant bit set on divider
+ // uint8_t idx = 0;
+ // uint32_t nr = d;
+ // if (!(nr & 0xFF0000)) {
+ // nr <<= 8;
+ // idx += 8;
+ // if (!(nr & 0xFF0000)) {
+ // nr <<= 8;
+ // idx += 8;
+ // }
+ // }
+ // if (!(nr & 0xF00000)) {
+ // nr <<= 4;
+ // idx += 4;
+ // }
+ // if (!(nr & 0xC00000)) {
+ // nr <<= 2;
+ // idx += 2;
+ // }
+ // if (!(nr & 0x800000)) {
+ // nr <<= 1;
+ // idx += 1;
+ // }
+ //
+ // // Isolate top 9 bits of the denominator, to be used as index into the initial estimation table
+ // uint32_t tidx = nr >> 15; // top 9 bits. bit8 is always set
+ // uint32_t ie = inv_tab[tidx & 0xFF] + 256; // Get the table value. bit9 is always set
+ // uint32_t x = idx <= 8 ? (ie >> (8 - idx)) : (ie << (idx - 8)); // Position the estimation at the proper place
+ //
+ // // Now, refine estimation by newton-raphson. 1 iteration is enough
+ // x = uint32_t((x * uint64_t((1 << 25) - x * d)) >> 24);
+ //
+ // // Estimate remainder
+ // uint32_t r = (1 << 24) - x * d;
+ //
+ // // Check if we must adjust result
+ // if (r >= d) x++;
+ //
+ // // x holds the proper estimation
+ // return uint32_t(x);
+ // }
+ //
+ static uint32_t get_period_inverse(uint32_t d) {
+
+ static const uint8_t inv_tab[256] PROGMEM = {
+ 255,253,252,250,248,246,244,242,240,238,236,234,233,231,229,227,
+ 225,224,222,220,218,217,215,213,212,210,208,207,205,203,202,200,
+ 199,197,195,194,192,191,189,188,186,185,183,182,180,179,178,176,
+ 175,173,172,170,169,168,166,165,164,162,161,160,158,157,156,154,
+ 153,152,151,149,148,147,146,144,143,142,141,139,138,137,136,135,
+ 134,132,131,130,129,128,127,126,125,123,122,121,120,119,118,117,
+ 116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,
+ 100,99,98,97,96,95,94,93,92,91,90,89,88,88,87,86,
+ 85,84,83,82,81,80,80,79,78,77,76,75,74,74,73,72,
+ 71,70,70,69,68,67,66,66,65,64,63,62,62,61,60,59,
+ 59,58,57,56,56,55,54,53,53,52,51,50,50,49,48,48,
+ 47,46,46,45,44,43,43,42,41,41,40,39,39,38,37,37,
+ 36,35,35,34,33,33,32,32,31,30,30,29,28,28,27,27,
+ 26,25,25,24,24,23,22,22,21,21,20,19,19,18,18,17,
+ 17,16,15,15,14,14,13,13,12,12,11,10,10,9,9,8,
+ 8,7,7,6,6,5,5,4,4,3,3,2,2,1,0,0
+ };
+
+ // For small denominators, it is cheaper to directly store the result.
+ // For bigger ones, just ONE Newton-Raphson iteration is enough to get
+ // maximum precision we need
+ static const uint32_t small_inv_tab[111] PROGMEM = {
+ 16777216,16777216,8388608,5592405,4194304,3355443,2796202,2396745,2097152,1864135,1677721,1525201,1398101,1290555,1198372,1118481,
+ 1048576,986895,932067,883011,838860,798915,762600,729444,699050,671088,645277,621378,599186,578524,559240,541200,
+ 524288,508400,493447,479349,466033,453438,441505,430185,419430,409200,399457,390167,381300,372827,364722,356962,
+ 349525,342392,335544,328965,322638,316551,310689,305040,299593,294337,289262,284359,279620,275036,270600,266305,
+ 262144,258111,254200,250406,246723,243148,239674,236298,233016,229824,226719,223696,220752,217885,215092,212369,
+ 209715,207126,204600,202135,199728,197379,195083,192841,190650,188508,186413,184365,182361,180400,178481,176602,
+ 174762,172960,171196,169466,167772,166111,164482,162885,161319,159783,158275,156796,155344,153919,152520
+ };
+
+ // For small divisors, it is best to directly retrieve the results
+ if (d <= 110)
+ return pgm_read_dword(&small_inv_tab[d]);
+
+ register uint8_t r8 = d & 0xFF;
+ register uint8_t r9 = (d >> 8) & 0xFF;
+ register uint8_t r10 = (d >> 16) & 0xFF;
+ register uint8_t r2,r3,r4,r5,r6,r7,r11,r12,r13,r14,r15,r16,r17,r18;
+ register const uint8_t* ptab = inv_tab;
+
+ __asm__ __volatile__(
+ // %8:%7:%6 = interval
+ // r31:r30: MUST be those registers, and they must point to the inv_tab
+
+ A("clr %13") // %13 = 0
+
+ // Now we must compute
+ // result = 0xFFFFFF / d
+ // %8:%7:%6 = interval
+ // %16:%15:%14 = nr
+ // %13 = 0
+
+ // A plain division of 24x24 bits should take 388 cycles to complete. We will
+ // use Newton-Raphson for the calculation, and will strive to get way less cycles
+ // for the same result - Using C division, it takes 500cycles to complete .
+
+ A("clr %3") // idx = 0
+ A("mov %14,%6")
+ A("mov %15,%7")
+ A("mov %16,%8") // nr = interval
+ A("tst %16") // nr & 0xFF0000 == 0 ?
+ A("brne 2f") // No, skip this
+ A("mov %16,%15")
+ A("mov %15,%14") // nr <<= 8, %14 not needed
+ A("subi %3,-8") // idx += 8
+ A("tst %16") // nr & 0xFF0000 == 0 ?
+ A("brne 2f") // No, skip this
+ A("mov %16,%15") // nr <<= 8, %14 not needed
+ A("clr %15") // We clear %14
+ A("subi %3,-8") // idx += 8
+
+ // here %16 != 0 and %16:%15 contains at least 9 MSBits, or both %16:%15 are 0
+ L("2")
+ A("cpi %16,0x10") // (nr & 0xF00000) == 0 ?
+ A("brcc 3f") // No, skip this
+ A("swap %15") // Swap nibbles
+ A("swap %16") // Swap nibbles. Low nibble is 0
+ A("mov %14, %15")
+ A("andi %14,0x0F") // Isolate low nibble
+ A("andi %15,0xF0") // Keep proper nibble in %15
+ A("or %16, %14") // %16:%15 <<= 4
+ A("subi %3,-4") // idx += 4
+
+ L("3")
+ A("cpi %16,0x40") // (nr & 0xC00000) == 0 ?
+ A("brcc 4f") // No, skip this
+ A("add %15,%15")
+ A("adc %16,%16")
+ A("add %15,%15")
+ A("adc %16,%16") // %16:%15 <<= 2
+ A("subi %3,-2") // idx += 2
+
+ L("4")
+ A("cpi %16,0x80") // (nr & 0x800000) == 0 ?
+ A("brcc 5f") // No, skip this
+ A("add %15,%15")
+ A("adc %16,%16") // %16:%15 <<= 1
+ A("inc %3") // idx += 1
+
+ // Now %16:%15 contains its MSBit set to 1, or %16:%15 is == 0. We are now absolutely sure
+ // we have at least 9 MSBits available to enter the initial estimation table
+ L("5")
+ A("add %15,%15")
+ A("adc %16,%16") // %16:%15 = tidx = (nr <<= 1), we lose the top MSBit (always set to 1, %16 is the index into the inverse table)
+ A("add r30,%16") // Only use top 8 bits
+ A("adc r31,%13") // r31:r30 = inv_tab + (tidx)
+ A("lpm %14, Z") // %14 = inv_tab[tidx]
+ A("ldi %15, 1") // %15 = 1 %15:%14 = inv_tab[tidx] + 256
+
+ // We must scale the approximation to the proper place
+ A("clr %16") // %16 will always be 0 here
+ A("subi %3,8") // idx == 8 ?
+ A("breq 6f") // yes, no need to scale
+ A("brcs 7f") // If C=1, means idx < 8, result was negative!
+
+ // idx > 8, now %3 = idx - 8. We must perform a left shift. idx range:[1-8]
+ A("sbrs %3,0") // shift by 1bit position?
+ A("rjmp 8f") // No
+ A("add %14,%14")
+ A("adc %15,%15") // %15:16 <<= 1
+ L("8")
+ A("sbrs %3,1") // shift by 2bit position?
+ A("rjmp 9f") // No
+ A("add %14,%14")
+ A("adc %15,%15")
+ A("add %14,%14")
+ A("adc %15,%15") // %15:16 <<= 1
+ L("9")
+ A("sbrs %3,2") // shift by 4bits position?
+ A("rjmp 16f") // No
+ A("swap %15") // Swap nibbles. lo nibble of %15 will always be 0
+ A("swap %14") // Swap nibbles
+ A("mov %12,%14")
+ A("andi %12,0x0F") // isolate low nibble
+ A("andi %14,0xF0") // and clear it
+ A("or %15,%12") // %15:%16 <<= 4
+ L("16")
+ A("sbrs %3,3") // shift by 8bits position?
+ A("rjmp 6f") // No, we are done
+ A("mov %16,%15")
+ A("mov %15,%14")
+ A("clr %14")
+ A("jmp 6f")
+
+ // idx < 8, now %3 = idx - 8. Get the count of bits
+ L("7")
+ A("neg %3") // %3 = -idx = count of bits to move right. idx range:[1...8]
+ A("sbrs %3,0") // shift by 1 bit position ?
+ A("rjmp 10f") // No, skip it
+ A("asr %15") // (bit7 is always 0 here)
+ A("ror %14")
+ L("10")
+ A("sbrs %3,1") // shift by 2 bit position ?
+ A("rjmp 11f") // No, skip it
+ A("asr %15") // (bit7 is always 0 here)
+ A("ror %14")
+ A("asr %15") // (bit7 is always 0 here)
+ A("ror %14")
+ L("11")
+ A("sbrs %3,2") // shift by 4 bit position ?
+ A("rjmp 12f") // No, skip it
+ A("swap %15") // Swap nibbles
+ A("andi %14, 0xF0") // Lose the lowest nibble
+ A("swap %14") // Swap nibbles. Upper nibble is 0
+ A("or %14,%15") // Pass nibble from upper byte
+ A("andi %15, 0x0F") // And get rid of that nibble
+ L("12")
+ A("sbrs %3,3") // shift by 8 bit position ?
+ A("rjmp 6f") // No, skip it
+ A("mov %14,%15")
+ A("clr %15")
+ L("6") // %16:%15:%14 = initial estimation of 0x1000000 / d)
+
+ // Now, we must refine the estimation present on %16:%15:%14 using 1 iteration
+ // of Newton-Raphson. As it has a quadratic convergence, 1 iteration is enough
+ // to get more than 18bits of precision (the initial table lookup gives 9 bits of
+ // precision to start from). 18bits of precision is all what is needed here for result
+
+ // %8:%7:%6 = d = interval
+ // %16:%15:%14 = x = initial estimation of 0x1000000 / d
+ // %13 = 0
+ // %3:%2:%1:%0 = working accumulator
+
+ // Compute 1<<25 - x*d. Result should never exceed 25 bits and should always be positive
+ A("clr %0")
+ A("clr %1")
+ A("clr %2")
+ A("ldi %3,2") // %3:%2:%1:%0 = 0x2000000
+ A("mul %6,%14") // r1:r0 = LO(d) * LO(x)
+ A("sub %0,r0")
+ A("sbc %1,r1")
+ A("sbc %2,%13")
+ A("sbc %3,%13") // %3:%2:%1:%0 -= LO(d) * LO(x)
+ A("mul %7,%14") // r1:r0 = MI(d) * LO(x)
+ A("sub %1,r0")
+ A("sbc %2,r1")
+ A("sbc %3,%13") // %3:%2:%1:%0 -= MI(d) * LO(x) << 8
+ A("mul %8,%14") // r1:r0 = HI(d) * LO(x)
+ A("sub %2,r0")
+ A("sbc %3,r1") // %3:%2:%1:%0 -= MIL(d) * LO(x) << 16
+ A("mul %6,%15") // r1:r0 = LO(d) * MI(x)
+ A("sub %1,r0")
+ A("sbc %2,r1")
+ A("sbc %3,%13") // %3:%2:%1:%0 -= LO(d) * MI(x) << 8
+ A("mul %7,%15") // r1:r0 = MI(d) * MI(x)
+ A("sub %2,r0")
+ A("sbc %3,r1") // %3:%2:%1:%0 -= MI(d) * MI(x) << 16
+ A("mul %8,%15") // r1:r0 = HI(d) * MI(x)
+ A("sub %3,r0") // %3:%2:%1:%0 -= MIL(d) * MI(x) << 24
+ A("mul %6,%16") // r1:r0 = LO(d) * HI(x)
+ A("sub %2,r0")
+ A("sbc %3,r1") // %3:%2:%1:%0 -= LO(d) * HI(x) << 16
+ A("mul %7,%16") // r1:r0 = MI(d) * HI(x)
+ A("sub %3,r0") // %3:%2:%1:%0 -= MI(d) * HI(x) << 24
+ // %3:%2:%1:%0 = (1<<25) - x*d [169]
+
+ // We need to multiply that result by x, and we are only interested in the top 24bits of that multiply
+
+ // %16:%15:%14 = x = initial estimation of 0x1000000 / d
+ // %3:%2:%1:%0 = (1<<25) - x*d = acc
+ // %13 = 0
+
+ // result = %11:%10:%9:%5:%4
+ A("mul %14,%0") // r1:r0 = LO(x) * LO(acc)
+ A("mov %4,r1")
+ A("clr %5")
+ A("clr %9")
+ A("clr %10")
+ A("clr %11") // %11:%10:%9:%5:%4 = LO(x) * LO(acc) >> 8
+ A("mul %15,%0") // r1:r0 = MI(x) * LO(acc)
+ A("add %4,r0")
+ A("adc %5,r1")
+ A("adc %9,%13")
+ A("adc %10,%13")
+ A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * LO(acc)
+ A("mul %16,%0") // r1:r0 = HI(x) * LO(acc)
+ A("add %5,r0")
+ A("adc %9,r1")
+ A("adc %10,%13")
+ A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * LO(acc) << 8
+
+ A("mul %14,%1") // r1:r0 = LO(x) * MIL(acc)
+ A("add %4,r0")
+ A("adc %5,r1")
+ A("adc %9,%13")
+ A("adc %10,%13")
+ A("adc %11,%13") // %11:%10:%9:%5:%4 = LO(x) * MIL(acc)
+ A("mul %15,%1") // r1:r0 = MI(x) * MIL(acc)
+ A("add %5,r0")
+ A("adc %9,r1")
+ A("adc %10,%13")
+ A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * MIL(acc) << 8
+ A("mul %16,%1") // r1:r0 = HI(x) * MIL(acc)
+ A("add %9,r0")
+ A("adc %10,r1")
+ A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * MIL(acc) << 16
+
+ A("mul %14,%2") // r1:r0 = LO(x) * MIH(acc)
+ A("add %5,r0")
+ A("adc %9,r1")
+ A("adc %10,%13")
+ A("adc %11,%13") // %11:%10:%9:%5:%4 = LO(x) * MIH(acc) << 8
+ A("mul %15,%2") // r1:r0 = MI(x) * MIH(acc)
+ A("add %9,r0")
+ A("adc %10,r1")
+ A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * MIH(acc) << 16
+ A("mul %16,%2") // r1:r0 = HI(x) * MIH(acc)
+ A("add %10,r0")
+ A("adc %11,r1") // %11:%10:%9:%5:%4 += MI(x) * MIH(acc) << 24
+
+ A("mul %14,%3") // r1:r0 = LO(x) * HI(acc)
+ A("add %9,r0")
+ A("adc %10,r1")
+ A("adc %11,%13") // %11:%10:%9:%5:%4 = LO(x) * HI(acc) << 16
+ A("mul %15,%3") // r1:r0 = MI(x) * HI(acc)
+ A("add %10,r0")
+ A("adc %11,r1") // %11:%10:%9:%5:%4 += MI(x) * HI(acc) << 24
+ A("mul %16,%3") // r1:r0 = HI(x) * HI(acc)
+ A("add %11,r0") // %11:%10:%9:%5:%4 += MI(x) * HI(acc) << 32
+
+ // At this point, %11:%10:%9 contains the new estimation of x.
+
+ // Finally, we must correct the result. Estimate remainder as
+ // (1<<24) - x*d
+ // %11:%10:%9 = x
+ // %8:%7:%6 = d = interval" "\n\t"
+ A("ldi %3,1")
+ A("clr %2")
+ A("clr %1")
+ A("clr %0") // %3:%2:%1:%0 = 0x1000000
+ A("mul %6,%9") // r1:r0 = LO(d) * LO(x)
+ A("sub %0,r0")
+ A("sbc %1,r1")
+ A("sbc %2,%13")
+ A("sbc %3,%13") // %3:%2:%1:%0 -= LO(d) * LO(x)
+ A("mul %7,%9") // r1:r0 = MI(d) * LO(x)
+ A("sub %1,r0")
+ A("sbc %2,r1")
+ A("sbc %3,%13") // %3:%2:%1:%0 -= MI(d) * LO(x) << 8
+ A("mul %8,%9") // r1:r0 = HI(d) * LO(x)
+ A("sub %2,r0")
+ A("sbc %3,r1") // %3:%2:%1:%0 -= MIL(d) * LO(x) << 16
+ A("mul %6,%10") // r1:r0 = LO(d) * MI(x)
+ A("sub %1,r0")
+ A("sbc %2,r1")
+ A("sbc %3,%13") // %3:%2:%1:%0 -= LO(d) * MI(x) << 8
+ A("mul %7,%10") // r1:r0 = MI(d) * MI(x)
+ A("sub %2,r0")
+ A("sbc %3,r1") // %3:%2:%1:%0 -= MI(d) * MI(x) << 16
+ A("mul %8,%10") // r1:r0 = HI(d) * MI(x)
+ A("sub %3,r0") // %3:%2:%1:%0 -= MIL(d) * MI(x) << 24
+ A("mul %6,%11") // r1:r0 = LO(d) * HI(x)
+ A("sub %2,r0")
+ A("sbc %3,r1") // %3:%2:%1:%0 -= LO(d) * HI(x) << 16
+ A("mul %7,%11") // r1:r0 = MI(d) * HI(x)
+ A("sub %3,r0") // %3:%2:%1:%0 -= MI(d) * HI(x) << 24
+ // %3:%2:%1:%0 = r = (1<<24) - x*d
+ // %8:%7:%6 = d = interval
+
+ // Perform the final correction
+ A("sub %0,%6")
+ A("sbc %1,%7")
+ A("sbc %2,%8") // r -= d
+ A("brcs 14f") // if ( r >= d)
+
+ // %11:%10:%9 = x
+ A("ldi %3,1")
+ A("add %9,%3")
+ A("adc %10,%13")
+ A("adc %11,%13") // x++
+ L("14")
+
+ // Estimation is done. %11:%10:%9 = x
+ A("clr __zero_reg__") // Make C runtime happy
+ // [211 cycles total]
+ : "=r" (r2),
+ "=r" (r3),
+ "=r" (r4),
+ "=d" (r5),
+ "=r" (r6),
+ "=r" (r7),
+ "+r" (r8),
+ "+r" (r9),
+ "+r" (r10),
+ "=d" (r11),
+ "=r" (r12),
+ "=r" (r13),
+ "=d" (r14),
+ "=d" (r15),
+ "=d" (r16),
+ "=d" (r17),
+ "=d" (r18),
+ "+z" (ptab)
+ :
+ : "r0", "r1", "cc"
+ );
+
+ // Return the result
+ return r11 | (uint16_t(r12) << 8) | (uint32_t(r13) << 16);
+ }
+
+#endif // BEZIER_JERK_CONTROL
+
#define MINIMAL_STEP_RATE 120
/**
@@ -218,6 +726,10 @@ void Planner::calculate_trapezoid_for_block(block_t* const block, const float &e
NOLESS(initial_rate, MINIMAL_STEP_RATE);
NOLESS(final_rate, MINIMAL_STEP_RATE);
+ #if ENABLED(BEZIER_JERK_CONTROL)
+ uint32_t cruise_rate = initial_rate;
+ #endif
+
const int32_t accel = block->acceleration_steps_per_s2;
// Steps required for acceleration, deceleration to/from nominal rate
@@ -235,16 +747,43 @@ void Planner::calculate_trapezoid_for_block(block_t* const block, const float &e
NOLESS(accelerate_steps, 0); // Check limits due to numerical round-off
accelerate_steps = min((uint32_t)accelerate_steps, block->step_event_count);//(We can cast here to unsigned, because the above line ensures that we are above zero)
plateau_steps = 0;
+
+ #if ENABLED(BEZIER_JERK_CONTROL)
+ // We won't reach the cruising rate. Let's calculate the speed we will reach
+ cruise_rate = final_speed(initial_rate, accel, accelerate_steps);
+ #endif
}
+ #if ENABLED(BEZIER_JERK_CONTROL)
+ else // We have some plateau time, so the cruise rate will be the nominal rate
+ cruise_rate = block->nominal_rate;
+ #endif
// block->accelerate_until = accelerate_steps;
// block->decelerate_after = accelerate_steps+plateau_steps;
+ #if ENABLED(BEZIER_JERK_CONTROL)
+ // Jerk controlled speed requires to express speed versus time, NOT steps
+ uint32_t acceleration_time = ((float)(cruise_rate - initial_rate) / accel) * (HAL_STEPPER_TIMER_RATE),
+ deceleration_time = ((float)(cruise_rate - final_rate) / accel) * (HAL_STEPPER_TIMER_RATE);
+
+ // And to offload calculations from the ISR, we also calculate the inverse of those times here
+ uint32_t acceleration_time_inverse = get_period_inverse(acceleration_time);
+ uint32_t deceleration_time_inverse = get_period_inverse(deceleration_time);
+
+ #endif
+
CRITICAL_SECTION_START; // Fill variables used by the stepper in a critical section
if (!TEST(block->flag, BLOCK_BIT_BUSY)) { // Don't update variables if block is busy.
block->accelerate_until = accelerate_steps;
block->decelerate_after = accelerate_steps + plateau_steps;
block->initial_rate = initial_rate;
+ #if ENABLED(BEZIER_JERK_CONTROL)
+ block->acceleration_time = acceleration_time;
+ block->deceleration_time = deceleration_time;
+ block->acceleration_time_inverse = acceleration_time_inverse;
+ block->deceleration_time_inverse = deceleration_time_inverse;
+ block->cruise_rate = cruise_rate;
+ #endif
block->final_rate = final_rate;
}
CRITICAL_SECTION_END;
@@ -1286,10 +1825,12 @@ void Planner::_buffer_steps(const int32_t (&target)[XYZE]
}
block->acceleration_steps_per_s2 = accel;
block->acceleration = accel / steps_per_mm;
- block->acceleration_rate = (long)(accel * 16777216.0 / ((F_CPU) * 0.125)); // * 8.388608
+ #if DISABLED(BEZIER_JERK_CONTROL)
+ block->acceleration_rate = (long)(accel * (4096.0 * 4096.0 / (HAL_STEPPER_TIMER_RATE))); // * 8.388608
+ #endif
#if ENABLED(LIN_ADVANCE)
if (block->use_advance_lead) {
- block->advance_speed = ((F_CPU) * 0.125) / (extruder_advance_K * block->e_D_ratio * block->acceleration * axis_steps_per_mm[E_AXIS]);
+ block->advance_speed = (HAL_STEPPER_TIMER_RATE) / (extruder_advance_K * block->e_D_ratio * block->acceleration * axis_steps_per_mm[E_AXIS]);
#if ENABLED(LA_DEBUG)
if (extruder_advance_K * block->e_D_ratio * block->acceleration * 2 < block->nominal_speed * block->e_D_ratio)
SERIAL_ECHOLNPGM("More than 2 steps per eISR loop executed.");
diff --git a/Marlin/planner.h b/Marlin/planner.h
index e051c4a0dcef101f3b129bdf79507d3f614c6bcf..79e2c2ee33e7079e7572499b24b83c23803e9edb 100644
--- a/Marlin/planner.h
+++ b/Marlin/planner.h
@@ -90,9 +90,24 @@ typedef struct {
uint32_t mix_event_count[MIXING_STEPPERS]; // Scaled step_event_count for the mixing steppers
#endif
+ // Settings for the trapezoid generator
int32_t accelerate_until, // The index of the step event on which to stop acceleration
- decelerate_after, // The index of the step event on which to start decelerating
- acceleration_rate; // The acceleration rate used for acceleration calculation
+ decelerate_after; // The index of the step event on which to start decelerating
+
+ uint32_t nominal_rate, // The nominal step rate for this block in step_events/sec
+ initial_rate, // The jerk-adjusted step rate at start of block
+ final_rate, // The minimal rate at exit
+ acceleration_steps_per_s2; // acceleration steps/sec^2
+
+ #if ENABLED(BEZIER_JERK_CONTROL)
+ uint32_t cruise_rate; // The actual cruise rate to use, between end of the acceleration phase and start of deceleration phase
+ uint32_t acceleration_time, // Acceleration time and deceleration time in STEP timer counts
+ deceleration_time;
+ uint32_t acceleration_time_inverse, // Inverse of acceleration and deceleration periods, expressed as integer. Scale depends on CPU being used
+ deceleration_time_inverse;
+ #else
+ int32_t acceleration_rate; // The acceleration rate used for acceleration calculation
+ #endif
uint8_t direction_bits; // The direction bit set for this block (refers to *_DIRECTION_BIT in config.h)
@@ -112,12 +127,6 @@ typedef struct {
millimeters, // The total travel of this block in mm
acceleration; // acceleration mm/sec^2
- // Settings for the trapezoid generator
- uint32_t nominal_rate, // The nominal step rate for this block in step_events/sec
- initial_rate, // The jerk-adjusted step rate at start of block
- final_rate, // The minimal rate at exit
- acceleration_steps_per_s2; // acceleration steps/sec^2
-
#if FAN_COUNT > 0
uint16_t fan_speed[FAN_COUNT];
#endif
@@ -661,6 +670,15 @@ class Planner {
return SQRT(sq(target_velocity) - 2 * accel * distance);
}
+ #if ENABLED(BEZIER_JERK_CONTROL)
+ /**
+ * Calculate the speed reached given initial speed, acceleration and distance
+ */
+ static float final_speed(const float &initial_velocity, const float &accel, const float &distance) {
+ return SQRT(sq(initial_velocity) + 2 * accel * distance);
+ }
+ #endif
+
static void calculate_trapezoid_for_block(block_t* const block, const float &entry_factor, const float &exit_factor);
static void reverse_pass_kernel(block_t* const current, const block_t * const next);
diff --git a/Marlin/stepper.cpp b/Marlin/stepper.cpp
index 06dc29dc181f6eac49110b08045409d3defe4786..1f03e3ccb3e590abcd54ee52a704b2fe18a1e32b 100644
--- a/Marlin/stepper.cpp
+++ b/Marlin/stepper.cpp
@@ -41,8 +41,16 @@
* along with Grbl. If not, see <http://www.gnu.org/licenses/>.
*/
-/* The timer calculations of this module informed by the 'RepRap cartesian firmware' by Zack Smith
- and Philipp Tiefenbacher. */
+/**
+ * Timer calculations informed by the 'RepRap cartesian firmware' by Zack Smith
+ * and Philipp Tiefenbacher.
+ */
+
+/**
+ * Jerk controlled movements planner added Apr 2018 by Eduardo José Tagle.
+ * Equations based on Synthethos TinyG2 sources, but the fixed-point
+ * implementation is new, as we are running the ISR with a variable period.
+ */
#include "Marlin.h"
#include "stepper.h"
@@ -98,6 +106,16 @@ int32_t Stepper::counter_X = 0,
volatile uint32_t Stepper::step_events_completed = 0; // The number of step events executed in the current block
+#if ENABLED(BEZIER_JERK_CONTROL)
+ int32_t __attribute__((used)) Stepper::bezier_A __asm__("bezier_A"); // A coefficient in Bézier speed curve with alias for assembler
+ int32_t __attribute__((used)) Stepper::bezier_B __asm__("bezier_B"); // B coefficient in Bézier speed curve with alias for assembler
+ int32_t __attribute__((used)) Stepper::bezier_C __asm__("bezier_C"); // C coefficient in Bézier speed curve with alias for assembler
+ uint32_t __attribute__((used)) Stepper::bezier_F __asm__("bezier_F"); // F coefficient in Bézier speed curve with alias for assembler
+ uint32_t __attribute__((used)) Stepper::bezier_AV __asm__("bezier_AV"); // AV coefficient in Bézier speed curve with alias for assembler
+ bool __attribute__((used)) Stepper::A_negative __asm__("A_negative"); // If A coefficient was negative
+ bool Stepper::bezier_2nd_half; // =false If Bézier curve has been initialized or not
+#endif
+
#if ENABLED(LIN_ADVANCE)
uint32_t Stepper::LA_decelerate_after;
@@ -134,8 +152,10 @@ volatile signed char Stepper::count_direction[NUM_AXIS] = { 1, 1, 1, 1 };
uint8_t Stepper::step_loops, Stepper::step_loops_nominal;
-uint16_t Stepper::OCR1A_nominal,
- Stepper::acc_step_rate; // needed for deceleration start point
+uint16_t Stepper::OCR1A_nominal;
+#if DISABLED(BEZIER_JERK_CONTROL)
+ uint16_t Stepper::acc_step_rate; // needed for deceleration start point
+#endif
volatile int32_t Stepper::endstops_trigsteps[XYZ];
@@ -232,41 +252,41 @@ volatile int32_t Stepper::endstops_trigsteps[XYZ];
//
#define MultiU24X32toH16(intRes, longIn1, longIn2) \
asm volatile ( \
- "clr r26 \n\t" \
- "mul %A1, %B2 \n\t" \
- "mov r27, r1 \n\t" \
- "mul %B1, %C2 \n\t" \
- "movw %A0, r0 \n\t" \
- "mul %C1, %C2 \n\t" \
- "add %B0, r0 \n\t" \
- "mul %C1, %B2 \n\t" \
- "add %A0, r0 \n\t" \
- "adc %B0, r1 \n\t" \
- "mul %A1, %C2 \n\t" \
- "add r27, r0 \n\t" \
- "adc %A0, r1 \n\t" \
- "adc %B0, r26 \n\t" \
- "mul %B1, %B2 \n\t" \
- "add r27, r0 \n\t" \
- "adc %A0, r1 \n\t" \
- "adc %B0, r26 \n\t" \
- "mul %C1, %A2 \n\t" \
- "add r27, r0 \n\t" \
- "adc %A0, r1 \n\t" \
- "adc %B0, r26 \n\t" \
- "mul %B1, %A2 \n\t" \
- "add r27, r1 \n\t" \
- "adc %A0, r26 \n\t" \
- "adc %B0, r26 \n\t" \
- "lsr r27 \n\t" \
- "adc %A0, r26 \n\t" \
- "adc %B0, r26 \n\t" \
- "mul %D2, %A1 \n\t" \
- "add %A0, r0 \n\t" \
- "adc %B0, r1 \n\t" \
- "mul %D2, %B1 \n\t" \
- "add %B0, r0 \n\t" \
- "clr r1 \n\t" \
+ A("clr r26") \
+ A("mul %A1, %B2") \
+ A("mov r27, r1") \
+ A("mul %B1, %C2") \
+ A("movw %A0, r0") \
+ A("mul %C1, %C2") \
+ A("add %B0, r0") \
+ A("mul %C1, %B2") \
+ A("add %A0, r0") \
+ A("adc %B0, r1") \
+ A("mul %A1, %C2") \
+ A("add r27, r0") \
+ A("adc %A0, r1") \
+ A("adc %B0, r26") \
+ A("mul %B1, %B2") \
+ A("add r27, r0") \
+ A("adc %A0, r1") \
+ A("adc %B0, r26") \
+ A("mul %C1, %A2") \
+ A("add r27, r0") \
+ A("adc %A0, r1") \
+ A("adc %B0, r26") \
+ A("mul %B1, %A2") \
+ A("add r27, r1") \
+ A("adc %A0, r26") \
+ A("adc %B0, r26") \
+ A("lsr r27") \
+ A("adc %A0, r26") \
+ A("adc %B0, r26") \
+ A("mul %D2, %A1") \
+ A("add %A0, r0") \
+ A("adc %B0, r1") \
+ A("mul %D2, %B1") \
+ A("add %B0, r0") \
+ A("clr r1") \
: \
"=&r" (intRes) \
: \
@@ -345,6 +365,732 @@ void Stepper::set_directions() {
extern volatile uint8_t e_hit;
#endif
+#if ENABLED(BEZIER_JERK_CONTROL)
+ /**
+ * We are using a quintic (fifth-degree) Bézier polynomial for the velocity curve.
+ * This gives us a "linear pop" velocity curve; with pop being the sixth derivative of position:
+ * velocity - 1st, acceleration - 2nd, jerk - 3rd, snap - 4th, crackle - 5th, pop - 6th
+ *
+ * The Bézier curve takes the form:
+ *
+ * V(t) = P_0 * B_0(t) + P_1 * B_1(t) + P_2 * B_2(t) + P_3 * B_3(t) + P_4 * B_4(t) + P_5 * B_5(t)
+ *
+ * Where 0 <= t <= 1, and V(t) is the velocity. P_0 through P_5 are the control points, and B_0(t)
+ * through B_5(t) are the Bernstein basis as follows:
+ *
+ * B_0(t) = (1-t)^5 = -t^5 + 5t^4 - 10t^3 + 10t^2 - 5t + 1
+ * B_1(t) = 5(1-t)^4 * t = 5t^5 - 20t^4 + 30t^3 - 20t^2 + 5t
+ * B_2(t) = 10(1-t)^3 * t^2 = -10t^5 + 30t^4 - 30t^3 + 10t^2
+ * B_3(t) = 10(1-t)^2 * t^3 = 10t^5 - 20t^4 + 10t^3
+ * B_4(t) = 5(1-t) * t^4 = -5t^5 + 5t^4
+ * B_5(t) = t^5 = t^5
+ * ^ ^ ^ ^ ^ ^
+ * | | | | | |
+ * A B C D E F
+ *
+ * Unfortunately, we cannot use forward-differencing to calculate each position through
+ * the curve, as Marlin uses variable timer periods. So, we require a formula of the form:
+ *
+ * V_f(t) = A*t^5 + B*t^4 + C*t^3 + D*t^2 + E*t + F
+ *
+ * Looking at the above B_0(t) through B_5(t) expanded forms, if we take the coefficients of t^5
+ * through t of the Bézier form of V(t), we can determine that:
+ *
+ * A = -P_0 + 5*P_1 - 10*P_2 + 10*P_3 - 5*P_4 + P_5
+ * B = 5*P_0 - 20*P_1 + 30*P_2 - 20*P_3 + 5*P_4
+ * C = -10*P_0 + 30*P_1 - 30*P_2 + 10*P_3
+ * D = 10*P_0 - 20*P_1 + 10*P_2
+ * E = - 5*P_0 + 5*P_1
+ * F = P_0
+ *
+ * Now, since we will (currently) *always* want the initial acceleration and jerk values to be 0,
+ * We set P_i = P_0 = P_1 = P_2 (initial velocity), and P_t = P_3 = P_4 = P_5 (target velocity),
+ * which, after simplification, resolves to:
+ *
+ * A = - 6*P_i + 6*P_t = 6*(P_t - P_i)
+ * B = 15*P_i - 15*P_t = 15*(P_i - P_t)
+ * C = -10*P_i + 10*P_t = 10*(P_t - P_i)
+ * D = 0
+ * E = 0
+ * F = P_i
+ *
+ * As the t is evaluated in non uniform steps here, there is no other way rather than evaluating
+ * the Bézier curve at each point:
+ *
+ * V_f(t) = A*t^5 + B*t^4 + C*t^3 + F [0 <= t <= 1]
+ *
+ * Floating point arithmetic execution time cost is prohibitive, so we will transform the math to
+ * use fixed point values to be able to evaluate it in realtime. Assuming a maximum of 250000 steps
+ * per second (driver pulses should at least be 2uS hi/2uS lo), and allocating 2 bits to avoid
+ * overflows on the evaluation of the Bézier curve, means we can use
+ *
+ * t: unsigned Q0.32 (0 <= t < 1) |range 0 to 0xFFFFFFFF unsigned
+ * A: signed Q24.7 , |range = +/- 250000 * 6 * 128 = +/- 192000000 = 0x0B71B000 | 28 bits + sign
+ * B: signed Q24.7 , |range = +/- 250000 *15 * 128 = +/- 480000000 = 0x1C9C3800 | 29 bits + sign
+ * C: signed Q24.7 , |range = +/- 250000 *10 * 128 = +/- 320000000 = 0x1312D000 | 29 bits + sign
+ * F: signed Q24.7 , |range = +/- 250000 * 128 = 32000000 = 0x01E84800 | 25 bits + sign
+ *
+ * The trapezoid generator state contains the following information, that we will use to create and evaluate
+ * the Bézier curve:
+ *
+ * blk->step_event_count [TS] = The total count of steps for this movement. (=distance)
+ * blk->initial_rate [VI] = The initial steps per second (=velocity)
+ * blk->final_rate [VF] = The ending steps per second (=velocity)
+ * and the count of events completed (step_events_completed) [CS] (=distance until now)
+ *
+ * Note the abbreviations we use in the following formulae are between []s
+ *
+ * For Any 32bit CPU:
+ *
+ * At the start of each trapezoid, we calculate the coefficients A,B,C,F and Advance [AV], as follows:
+ *
+ * A = 6*128*(VF - VI) = 768*(VF - VI)
+ * B = 15*128*(VI - VF) = 1920*(VI - VF)
+ * C = 10*128*(VF - VI) = 1280*(VF - VI)
+ * F = 128*VI = 128*VI
+ * AV = (1<<32)/TS ~= 0xFFFFFFFF / TS (To use ARM UDIV, that is 32 bits) (this is computed at the planner, to offload expensive calculations from the ISR)
+ *
+ * And for each point, we will evaluate the curve with the following sequence:
+ *
+ * void lsrs(uint32_t& d, uint32_t s, int cnt) {
+ * d = s >> cnt;
+ * }
+ * void lsls(uint32_t& d, uint32_t s, int cnt) {
+ * d = s << cnt;
+ * }
+ * void lsrs(int32_t& d, uint32_t s, int cnt) {
+ * d = uint32_t(s) >> cnt;
+ * }
+ * void lsls(int32_t& d, uint32_t s, int cnt) {
+ * d = uint32_t(s) << cnt;
+ * }
+ * void umull(uint32_t& rlo, uint32_t& rhi, uint32_t op1, uint32_t op2) {
+ * uint64_t res = uint64_t(op1) * op2;
+ * rlo = uint32_t(res & 0xFFFFFFFF);
+ * rhi = uint32_t((res >> 32) & 0xFFFFFFFF);
+ * }
+ * void smlal(int32_t& rlo, int32_t& rhi, int32_t op1, int32_t op2) {
+ * int64_t mul = int64_t(op1) * op2;
+ * int64_t s = int64_t(uint32_t(rlo) | ((uint64_t(uint32_t(rhi)) << 32U)));
+ * mul += s;
+ * rlo = int32_t(mul & 0xFFFFFFFF);
+ * rhi = int32_t((mul >> 32) & 0xFFFFFFFF);
+ * }
+ * int32_t _eval_bezier_curve_arm(uint32_t curr_step) {
+ * register uint32_t flo = 0;
+ * register uint32_t fhi = bezier_AV * curr_step;
+ * register uint32_t t = fhi;
+ * register int32_t alo = bezier_F;
+ * register int32_t ahi = 0;
+ * register int32_t A = bezier_A;
+ * register int32_t B = bezier_B;
+ * register int32_t C = bezier_C;
+ *
+ * lsrs(ahi, alo, 1); // a = F << 31
+ * lsls(alo, alo, 31); //
+ * umull(flo, fhi, fhi, t); // f *= t
+ * umull(flo, fhi, fhi, t); // f>>=32; f*=t
+ * lsrs(flo, fhi, 1); //
+ * smlal(alo, ahi, flo, C); // a+=(f>>33)*C
+ * umull(flo, fhi, fhi, t); // f>>=32; f*=t
+ * lsrs(flo, fhi, 1); //
+ * smlal(alo, ahi, flo, B); // a+=(f>>33)*B
+ * umull(flo, fhi, fhi, t); // f>>=32; f*=t
+ * lsrs(flo, fhi, 1); // f>>=33;
+ * smlal(alo, ahi, flo, A); // a+=(f>>33)*A;
+ * lsrs(alo, ahi, 6); // a>>=38
+ *
+ * return alo;
+ * }
+ *
+ * This will be rewritten in ARM assembly to get peak performance and will take 43 cycles to execute
+ *
+ * For AVR, we scale precision of coefficients to make it possible to evaluate the Bézier curve in
+ * realtime: Let's reduce precision as much as possible. After some experimentation we found that:
+ *
+ * Assume t and AV with 24 bits is enough
+ * A = 6*(VF - VI)
+ * B = 15*(VI - VF)
+ * C = 10*(VF - VI)
+ * F = VI
+ * AV = (1<<24)/TS (this is computed at the planner, to offload expensive calculations from the ISR)
+ *
+ * Instead of storing sign for each coefficient, we will store its absolute value,
+ * and flag the sign of the A coefficient, so we can save to store the sign bit.
+ * It always holds that sign(A) = - sign(B) = sign(C)
+ *
+ * So, the resulting range of the coefficients are:
+ *
+ * t: unsigned (0 <= t < 1) |range 0 to 0xFFFFFF unsigned
+ * A: signed Q24 , range = 250000 * 6 = 1500000 = 0x16E360 | 21 bits
+ * B: signed Q24 , range = 250000 *15 = 3750000 = 0x393870 | 22 bits
+ * C: signed Q24 , range = 250000 *10 = 2500000 = 0x1312D0 | 21 bits
+ * F: signed Q24 , range = 250000 = 250000 = 0x0ED090 | 20 bits
+ *
+ * And for each curve, we estimate its coefficients with:
+ *
+ * void _calc_bezier_curve_coeffs(int32_t v0, int32_t v1, uint32_t av) {
+ * // Calculate the Bézier coefficients
+ * if (v1 < v0) {
+ * A_negative = true;
+ * bezier_A = 6 * (v0 - v1);
+ * bezier_B = 15 * (v0 - v1);
+ * bezier_C = 10 * (v0 - v1);
+ * }
+ * else {
+ * A_negative = false;
+ * bezier_A = 6 * (v1 - v0);
+ * bezier_B = 15 * (v1 - v0);
+ * bezier_C = 10 * (v1 - v0);
+ * }
+ * bezier_F = v0;
+ * }
+ *
+ * And for each point, we will evaluate the curve with the following sequence:
+ *
+ * // unsigned multiplication of 24 bits x 24bits, return upper 16 bits
+ * void umul24x24to16hi(uint16_t& r, uint24_t op1, uint24_t op2) {
+ * r = (uint64_t(op1) * op2) >> 8;
+ * }
+ * // unsigned multiplication of 16 bits x 16bits, return upper 16 bits
+ * void umul16x16to16hi(uint16_t& r, uint16_t op1, uint16_t op2) {
+ * r = (uint32_t(op1) * op2) >> 16;
+ * }
+ * // unsigned multiplication of 16 bits x 24bits, return upper 24 bits
+ * void umul16x24to24hi(uint24_t& r, uint16_t op1, uint24_t op2) {
+ * r = uint24_t((uint64_t(op1) * op2) >> 16);
+ * }
+ *
+ * int32_t _eval_bezier_curve(uint32_t curr_step) {
+ * // To save computing, the first step is always the initial speed
+ * if (!curr_step)
+ * return bezier_F;
+ *
+ * uint16_t t;
+ * umul24x24to16hi(t, bezier_AV, curr_step); // t: Range 0 - 1^16 = 16 bits
+ * uint16_t f = t;
+ * umul16x16to16hi(f, f, t); // Range 16 bits (unsigned)
+ * umul16x16to16hi(f, f, t); // Range 16 bits : f = t^3 (unsigned)
+ * uint24_t acc = bezier_F; // Range 20 bits (unsigned)
+ * if (A_negative) {
+ * uint24_t v;
+ * umul16x24to24hi(v, f, bezier_C); // Range 21bits
+ * acc -= v;
+ * umul16x16to16hi(f, f, t); // Range 16 bits : f = t^4 (unsigned)
+ * umul16x24to24hi(v, f, bezier_B); // Range 22bits
+ * acc += v;
+ * umul16x16to16hi(f, f, t); // Range 16 bits : f = t^5 (unsigned)
+ * umul16x24to24hi(v, f, bezier_A); // Range 21bits + 15 = 36bits (plus sign)
+ * acc -= v;
+ * }
+ * else {
+ * uint24_t v;
+ * umul16x24to24hi(v, f, bezier_C); // Range 21bits
+ * acc += v;
+ * umul16x16to16hi(f, f, t); // Range 16 bits : f = t^4 (unsigned)
+ * umul16x24to24hi(v, f, bezier_B); // Range 22bits
+ * acc -= v;
+ * umul16x16to16hi(f, f, t); // Range 16 bits : f = t^5 (unsigned)
+ * umul16x24to24hi(v, f, bezier_A); // Range 21bits + 15 = 36bits (plus sign)
+ * acc += v;
+ * }
+ * return acc;
+ * }
+ * Those functions will be translated into assembler to get peak performance. coefficient calculations takes 70 cycles,
+ * Bezier point evaluation takes 150 cycles
+ *
+ */
+
+ // For AVR we use assembly to maximize speed
+ void Stepper::_calc_bezier_curve_coeffs(const int32_t v0, const int32_t v1, const uint32_t av) {
+
+ // Store advance
+ bezier_AV = av;
+
+ // Calculate the rest of the coefficients
+ register uint8_t r2 = v0 & 0xFF;
+ register uint8_t r3 = (v0 >> 8) & 0xFF;
+ register uint8_t r12 = (v0 >> 16) & 0xFF;
+ register uint8_t r5 = v1 & 0xFF;
+ register uint8_t r6 = (v1 >> 8) & 0xFF;
+ register uint8_t r7 = (v1 >> 16) & 0xFF;
+ register uint8_t r4,r8,r9,r10,r11;
+
+ __asm__ __volatile__(
+ /* Calculate the Bézier coefficients */
+ /* %10:%1:%0 = v0*/
+ /* %5:%4:%3 = v1*/
+ /* %7:%6:%10 = temporary*/
+ /* %9 = val (must be high register!)*/
+ /* %10 (must be high register!)*/
+
+ /* Store initial velocity*/
+ A("sts bezier_F, %0")
+ A("sts bezier_F+1, %1")
+ A("sts bezier_F+2, %10") /* bezier_F = %10:%1:%0 = v0 */
+
+ /* Get delta speed */
+ A("ldi %2,-1") /* %2 = 0xFF, means A_negative = true */
+ A("clr %8") /* %8 = 0 */
+ A("sub %0,%3")
+ A("sbc %1,%4")
+ A("sbc %10,%5") /* v0 -= v1, C=1 if result is negative */
+ A("brcc 1f") /* branch if result is positive (C=0), that means v0 >= v1 */
+
+ /* Result was negative, get the absolute value*/
+ A("com %10")
+ A("com %1")
+ A("neg %0")
+ A("sbc %1,%2")
+ A("sbc %10,%2") /* %10:%1:%0 +1 -> %10:%1:%0 = -(v0 - v1) = (v1 - v0) */
+ A("clr %2") /* %2 = 0, means A_negative = false */
+
+ /* Store negative flag*/
+ L("1")
+ A("sts A_negative, %2") /* Store negative flag */
+
+ /* Compute coefficients A,B and C [20 cycles worst case]*/
+ A("ldi %9,6") /* %9 = 6 */
+ A("mul %0,%9") /* r1:r0 = 6*LO(v0-v1) */
+ A("sts bezier_A, r0")
+ A("mov %6,r1")
+ A("clr %7") /* %7:%6:r0 = 6*LO(v0-v1) */
+ A("mul %1,%9") /* r1:r0 = 6*MI(v0-v1) */
+ A("add %6,r0")
+ A("adc %7,r1") /* %7:%6:?? += 6*MI(v0-v1) << 8 */
+ A("mul %10,%9") /* r1:r0 = 6*HI(v0-v1) */
+ A("add %7,r0") /* %7:%6:?? += 6*HI(v0-v1) << 16 */
+ A("sts bezier_A+1, %6")
+ A("sts bezier_A+2, %7") /* bezier_A = %7:%6:?? = 6*(v0-v1) [35 cycles worst] */
+
+ A("ldi %9,15") /* %9 = 15 */
+ A("mul %0,%9") /* r1:r0 = 5*LO(v0-v1) */
+ A("sts bezier_B, r0")
+ A("mov %6,r1")
+ A("clr %7") /* %7:%6:?? = 5*LO(v0-v1) */
+ A("mul %1,%9") /* r1:r0 = 5*MI(v0-v1) */
+ A("add %6,r0")
+ A("adc %7,r1") /* %7:%6:?? += 5*MI(v0-v1) << 8 */
+ A("mul %10,%9") /* r1:r0 = 5*HI(v0-v1) */
+ A("add %7,r0") /* %7:%6:?? += 5*HI(v0-v1) << 16 */
+ A("sts bezier_B+1, %6")
+ A("sts bezier_B+2, %7") /* bezier_B = %7:%6:?? = 5*(v0-v1) [50 cycles worst] */
+
+ A("ldi %9,10") /* %9 = 10 */
+ A("mul %0,%9") /* r1:r0 = 10*LO(v0-v1) */
+ A("sts bezier_C, r0")
+ A("mov %6,r1")
+ A("clr %7") /* %7:%6:?? = 10*LO(v0-v1) */
+ A("mul %1,%9") /* r1:r0 = 10*MI(v0-v1) */
+ A("add %6,r0")
+ A("adc %7,r1") /* %7:%6:?? += 10*MI(v0-v1) << 8 */
+ A("mul %10,%9") /* r1:r0 = 10*HI(v0-v1) */
+ A("add %7,r0") /* %7:%6:?? += 10*HI(v0-v1) << 16 */
+ A("sts bezier_C+1, %6")
+ " sts bezier_C+2, %7" /* bezier_C = %7:%6:?? = 10*(v0-v1) [65 cycles worst] */
+ : "+r" (r2),
+ "+d" (r3),
+ "=r" (r4),
+ "+r" (r5),
+ "+r" (r6),
+ "+r" (r7),
+ "=r" (r8),
+ "=r" (r9),
+ "=r" (r10),
+ "=d" (r11),
+ "+r" (r12)
+ :
+ : "r0", "r1", "cc", "memory"
+ );
+ }
+
+ FORCE_INLINE int32_t Stepper::_eval_bezier_curve(const uint32_t curr_step) {
+
+ // If dealing with the first step, save expensive computing and return the initial speed
+ if (!curr_step)
+ return bezier_F;
+
+ register uint8_t r0 = 0; /* Zero register */
+ register uint8_t r2 = (curr_step) & 0xFF;
+ register uint8_t r3 = (curr_step >> 8) & 0xFF;
+ register uint8_t r4 = (curr_step >> 16) & 0xFF;
+ register uint8_t r1,r5,r6,r7,r8,r9,r10,r11; /* Temporary registers */
+
+ __asm__ __volatile(
+ /* umul24x24to16hi(t, bezier_AV, curr_step); t: Range 0 - 1^16 = 16 bits*/
+ A("lds %9,bezier_AV") /* %9 = LO(AV)*/
+ A("mul %9,%2") /* r1:r0 = LO(bezier_AV)*LO(curr_step)*/
+ A("mov %7,r1") /* %7 = LO(bezier_AV)*LO(curr_step) >> 8*/
+ A("clr %8") /* %8:%7 = LO(bezier_AV)*LO(curr_step) >> 8*/
+ A("lds %10,bezier_AV+1") /* %10 = MI(AV)*/
+ A("mul %10,%2") /* r1:r0 = MI(bezier_AV)*LO(curr_step)*/
+ A("add %7,r0")
+ A("adc %8,r1") /* %8:%7 += MI(bezier_AV)*LO(curr_step)*/
+ A("lds r1,bezier_AV+2") /* r11 = HI(AV)*/
+ A("mul r1,%2") /* r1:r0 = HI(bezier_AV)*LO(curr_step)*/
+ A("add %8,r0") /* %8:%7 += HI(bezier_AV)*LO(curr_step) << 8*/
+ A("mul %9,%3") /* r1:r0 = LO(bezier_AV)*MI(curr_step)*/
+ A("add %7,r0")
+ A("adc %8,r1") /* %8:%7 += LO(bezier_AV)*MI(curr_step)*/
+ A("mul %10,%3") /* r1:r0 = MI(bezier_AV)*MI(curr_step)*/
+ A("add %8,r0") /* %8:%7 += LO(bezier_AV)*MI(curr_step) << 8*/
+ A("mul %9,%4") /* r1:r0 = LO(bezier_AV)*HI(curr_step)*/
+ A("add %8,r0") /* %8:%7 += LO(bezier_AV)*HI(curr_step) << 8*/
+ /* %8:%7 = t*/
+
+ /* uint16_t f = t;*/
+ A("mov %5,%7") /* %6:%5 = f*/
+ A("mov %6,%8")
+ /* %6:%5 = f*/
+
+ /* umul16x16to16hi(f, f, t); / Range 16 bits (unsigned) [17] */
+ A("mul %5,%7") /* r1:r0 = LO(f) * LO(t)*/
+ A("mov %9,r1") /* store MIL(LO(f) * LO(t)) in %9, we need it for rounding*/
+ A("clr %10") /* %10 = 0*/
+ A("clr %11") /* %11 = 0*/
+ A("mul %5,%8") /* r1:r0 = LO(f) * HI(t)*/
+ A("add %9,r0") /* %9 += LO(LO(f) * HI(t))*/
+ A("adc %10,r1") /* %10 = HI(LO(f) * HI(t))*/
+ A("adc %11,%0") /* %11 += carry*/
+ A("mul %6,%7") /* r1:r0 = HI(f) * LO(t)*/
+ A("add %9,r0") /* %9 += LO(HI(f) * LO(t))*/
+ A("adc %10,r1") /* %10 += HI(HI(f) * LO(t)) */
+ A("adc %11,%0") /* %11 += carry*/
+ A("mul %6,%8") /* r1:r0 = HI(f) * HI(t)*/
+ A("add %10,r0") /* %10 += LO(HI(f) * HI(t))*/
+ A("adc %11,r1") /* %11 += HI(HI(f) * HI(t))*/
+ A("mov %5,%10") /* %6:%5 = */
+ A("mov %6,%11") /* f = %10:%11*/
+
+ /* umul16x16to16hi(f, f, t); / Range 16 bits : f = t^3 (unsigned) [17]*/
+ A("mul %5,%7") /* r1:r0 = LO(f) * LO(t)*/
+ A("mov %1,r1") /* store MIL(LO(f) * LO(t)) in %1, we need it for rounding*/
+ A("clr %10") /* %10 = 0*/
+ A("clr %11") /* %11 = 0*/
+ A("mul %5,%8") /* r1:r0 = LO(f) * HI(t)*/
+ A("add %1,r0") /* %1 += LO(LO(f) * HI(t))*/
+ A("adc %10,r1") /* %10 = HI(LO(f) * HI(t))*/
+ A("adc %11,%0") /* %11 += carry*/
+ A("mul %6,%7") /* r1:r0 = HI(f) * LO(t)*/
+ A("add %1,r0") /* %1 += LO(HI(f) * LO(t))*/
+ A("adc %10,r1") /* %10 += HI(HI(f) * LO(t))*/
+ A("adc %11,%0") /* %11 += carry*/
+ A("mul %6,%8") /* r1:r0 = HI(f) * HI(t)*/
+ A("add %10,r0") /* %10 += LO(HI(f) * HI(t))*/
+ A("adc %11,r1") /* %11 += HI(HI(f) * HI(t))*/
+ A("mov %5,%10") /* %6:%5 =*/
+ A("mov %6,%11") /* f = %10:%11*/
+ /* [15 +17*2] = [49]*/
+
+ /* %4:%3:%2 will be acc from now on*/
+
+ /* uint24_t acc = bezier_F; / Range 20 bits (unsigned)*/
+ A("clr %9") /* "decimal place we get for free"*/
+ A("lds %2,bezier_F")
+ A("lds %3,bezier_F+1")
+ A("lds %4,bezier_F+2") /* %4:%3:%2 = acc*/
+
+ /* if (A_negative) {*/
+ A("lds r0,A_negative")
+ A("or r0,%0") /* Is flag signalling negative? */
+ A("brne 3f") /* If yes, Skip next instruction if A was negative*/
+ A("rjmp 1f") /* Otherwise, jump */
+
+ /* uint24_t v; */
+ /* umul16x24to24hi(v, f, bezier_C); / Range 21bits [29] */
+ /* acc -= v; */
+ L("3")
+ A("lds %10, bezier_C") /* %10 = LO(bezier_C)*/
+ A("mul %10,%5") /* r1:r0 = LO(bezier_C) * LO(f)*/
+ A("sub %9,r1")
+ A("sbc %2,%0")
+ A("sbc %3,%0")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= HI(LO(bezier_C) * LO(f))*/
+ A("lds %11, bezier_C+1") /* %11 = MI(bezier_C)*/
+ A("mul %11,%5") /* r1:r0 = MI(bezier_C) * LO(f)*/
+ A("sub %9,r0")
+ A("sbc %2,r1")
+ A("sbc %3,%0")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= MI(bezier_C) * LO(f)*/
+ A("lds %1, bezier_C+2") /* %1 = HI(bezier_C)*/
+ A("mul %1,%5") /* r1:r0 = MI(bezier_C) * LO(f)*/
+ A("sub %2,r0")
+ A("sbc %3,r1")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= HI(bezier_C) * LO(f) << 8*/
+ A("mul %10,%6") /* r1:r0 = LO(bezier_C) * MI(f)*/
+ A("sub %9,r0")
+ A("sbc %2,r1")
+ A("sbc %3,%0")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= LO(bezier_C) * MI(f)*/
+ A("mul %11,%6") /* r1:r0 = MI(bezier_C) * MI(f)*/
+ A("sub %2,r0")
+ A("sbc %3,r1")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= MI(bezier_C) * MI(f) << 8*/
+ A("mul %1,%6") /* r1:r0 = HI(bezier_C) * LO(f)*/
+ A("sub %3,r0")
+ A("sbc %4,r1") /* %4:%3:%2:%9 -= HI(bezier_C) * LO(f) << 16*/
+
+ /* umul16x16to16hi(f, f, t); / Range 16 bits : f = t^3 (unsigned) [17]*/
+ A("mul %5,%7") /* r1:r0 = LO(f) * LO(t)*/
+ A("mov %1,r1") /* store MIL(LO(f) * LO(t)) in %1, we need it for rounding*/
+ A("clr %10") /* %10 = 0*/
+ A("clr %11") /* %11 = 0*/
+ A("mul %5,%8") /* r1:r0 = LO(f) * HI(t)*/
+ A("add %1,r0") /* %1 += LO(LO(f) * HI(t))*/
+ A("adc %10,r1") /* %10 = HI(LO(f) * HI(t))*/
+ A("adc %11,%0") /* %11 += carry*/
+ A("mul %6,%7") /* r1:r0 = HI(f) * LO(t)*/
+ A("add %1,r0") /* %1 += LO(HI(f) * LO(t))*/
+ A("adc %10,r1") /* %10 += HI(HI(f) * LO(t))*/
+ A("adc %11,%0") /* %11 += carry*/
+ A("mul %6,%8") /* r1:r0 = HI(f) * HI(t)*/
+ A("add %10,r0") /* %10 += LO(HI(f) * HI(t))*/
+ A("adc %11,r1") /* %11 += HI(HI(f) * HI(t))*/
+ A("mov %5,%10") /* %6:%5 =*/
+ A("mov %6,%11") /* f = %10:%11*/
+
+ /* umul16x24to24hi(v, f, bezier_B); / Range 22bits [29]*/
+ /* acc += v; */
+ A("lds %10, bezier_B") /* %10 = LO(bezier_B)*/
+ A("mul %10,%5") /* r1:r0 = LO(bezier_B) * LO(f)*/
+ A("add %9,r1")
+ A("adc %2,%0")
+ A("adc %3,%0")
+ A("adc %4,%0") /* %4:%3:%2:%9 += HI(LO(bezier_B) * LO(f))*/
+ A("lds %11, bezier_B+1") /* %11 = MI(bezier_B)*/
+ A("mul %11,%5") /* r1:r0 = MI(bezier_B) * LO(f)*/
+ A("add %9,r0")
+ A("adc %2,r1")
+ A("adc %3,%0")
+ A("adc %4,%0") /* %4:%3:%2:%9 += MI(bezier_B) * LO(f)*/
+ A("lds %1, bezier_B+2") /* %1 = HI(bezier_B)*/
+ A("mul %1,%5") /* r1:r0 = MI(bezier_B) * LO(f)*/
+ A("add %2,r0")
+ A("adc %3,r1")
+ A("adc %4,%0") /* %4:%3:%2:%9 += HI(bezier_B) * LO(f) << 8*/
+ A("mul %10,%6") /* r1:r0 = LO(bezier_B) * MI(f)*/
+ A("add %9,r0")
+ A("adc %2,r1")
+ A("adc %3,%0")
+ A("adc %4,%0") /* %4:%3:%2:%9 += LO(bezier_B) * MI(f)*/
+ A("mul %11,%6") /* r1:r0 = MI(bezier_B) * MI(f)*/
+ A("add %2,r0")
+ A("adc %3,r1")
+ A("adc %4,%0") /* %4:%3:%2:%9 += MI(bezier_B) * MI(f) << 8*/
+ A("mul %1,%6") /* r1:r0 = HI(bezier_B) * LO(f)*/
+ A("add %3,r0")
+ A("adc %4,r1") /* %4:%3:%2:%9 += HI(bezier_B) * LO(f) << 16*/
+
+ /* umul16x16to16hi(f, f, t); / Range 16 bits : f = t^5 (unsigned) [17]*/
+ A("mul %5,%7") /* r1:r0 = LO(f) * LO(t)*/
+ A("mov %1,r1") /* store MIL(LO(f) * LO(t)) in %1, we need it for rounding*/
+ A("clr %10") /* %10 = 0*/
+ A("clr %11") /* %11 = 0*/
+ A("mul %5,%8") /* r1:r0 = LO(f) * HI(t)*/
+ A("add %1,r0") /* %1 += LO(LO(f) * HI(t))*/
+ A("adc %10,r1") /* %10 = HI(LO(f) * HI(t))*/
+ A("adc %11,%0") /* %11 += carry*/
+ A("mul %6,%7") /* r1:r0 = HI(f) * LO(t)*/
+ A("add %1,r0") /* %1 += LO(HI(f) * LO(t))*/
+ A("adc %10,r1") /* %10 += HI(HI(f) * LO(t))*/
+ A("adc %11,%0") /* %11 += carry*/
+ A("mul %6,%8") /* r1:r0 = HI(f) * HI(t)*/
+ A("add %10,r0") /* %10 += LO(HI(f) * HI(t))*/
+ A("adc %11,r1") /* %11 += HI(HI(f) * HI(t))*/
+ A("mov %5,%10") /* %6:%5 =*/
+ A("mov %6,%11") /* f = %10:%11*/
+
+ /* umul16x24to24hi(v, f, bezier_A); / Range 21bits [29]*/
+ /* acc -= v; */
+ A("lds %10, bezier_A") /* %10 = LO(bezier_A)*/
+ A("mul %10,%5") /* r1:r0 = LO(bezier_A) * LO(f)*/
+ A("sub %9,r1")
+ A("sbc %2,%0")
+ A("sbc %3,%0")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= HI(LO(bezier_A) * LO(f))*/
+ A("lds %11, bezier_A+1") /* %11 = MI(bezier_A)*/
+ A("mul %11,%5") /* r1:r0 = MI(bezier_A) * LO(f)*/
+ A("sub %9,r0")
+ A("sbc %2,r1")
+ A("sbc %3,%0")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= MI(bezier_A) * LO(f)*/
+ A("lds %1, bezier_A+2") /* %1 = HI(bezier_A)*/
+ A("mul %1,%5") /* r1:r0 = MI(bezier_A) * LO(f)*/
+ A("sub %2,r0")
+ A("sbc %3,r1")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= HI(bezier_A) * LO(f) << 8*/
+ A("mul %10,%6") /* r1:r0 = LO(bezier_A) * MI(f)*/
+ A("sub %9,r0")
+ A("sbc %2,r1")
+ A("sbc %3,%0")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= LO(bezier_A) * MI(f)*/
+ A("mul %11,%6") /* r1:r0 = MI(bezier_A) * MI(f)*/
+ A("sub %2,r0")
+ A("sbc %3,r1")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= MI(bezier_A) * MI(f) << 8*/
+ A("mul %1,%6") /* r1:r0 = HI(bezier_A) * LO(f)*/
+ A("sub %3,r0")
+ A("sbc %4,r1") /* %4:%3:%2:%9 -= HI(bezier_A) * LO(f) << 16*/
+ A("jmp 2f") /* Done!*/
+
+ L("1")
+
+ /* uint24_t v; */
+ /* umul16x24to24hi(v, f, bezier_C); / Range 21bits [29]*/
+ /* acc += v; */
+ A("lds %10, bezier_C") /* %10 = LO(bezier_C)*/
+ A("mul %10,%5") /* r1:r0 = LO(bezier_C) * LO(f)*/
+ A("add %9,r1")
+ A("adc %2,%0")
+ A("adc %3,%0")
+ A("adc %4,%0") /* %4:%3:%2:%9 += HI(LO(bezier_C) * LO(f))*/
+ A("lds %11, bezier_C+1") /* %11 = MI(bezier_C)*/
+ A("mul %11,%5") /* r1:r0 = MI(bezier_C) * LO(f)*/
+ A("add %9,r0")
+ A("adc %2,r1")
+ A("adc %3,%0")
+ A("adc %4,%0") /* %4:%3:%2:%9 += MI(bezier_C) * LO(f)*/
+ A("lds %1, bezier_C+2") /* %1 = HI(bezier_C)*/
+ A("mul %1,%5") /* r1:r0 = MI(bezier_C) * LO(f)*/
+ A("add %2,r0")
+ A("adc %3,r1")
+ A("adc %4,%0") /* %4:%3:%2:%9 += HI(bezier_C) * LO(f) << 8*/
+ A("mul %10,%6") /* r1:r0 = LO(bezier_C) * MI(f)*/
+ A("add %9,r0")
+ A("adc %2,r1")
+ A("adc %3,%0")
+ A("adc %4,%0") /* %4:%3:%2:%9 += LO(bezier_C) * MI(f)*/
+ A("mul %11,%6") /* r1:r0 = MI(bezier_C) * MI(f)*/
+ A("add %2,r0")
+ A("adc %3,r1")
+ A("adc %4,%0") /* %4:%3:%2:%9 += MI(bezier_C) * MI(f) << 8*/
+ A("mul %1,%6") /* r1:r0 = HI(bezier_C) * LO(f)*/
+ A("add %3,r0")
+ A("adc %4,r1") /* %4:%3:%2:%9 += HI(bezier_C) * LO(f) << 16*/
+
+ /* umul16x16to16hi(f, f, t); / Range 16 bits : f = t^3 (unsigned) [17]*/
+ A("mul %5,%7") /* r1:r0 = LO(f) * LO(t)*/
+ A("mov %1,r1") /* store MIL(LO(f) * LO(t)) in %1, we need it for rounding*/
+ A("clr %10") /* %10 = 0*/
+ A("clr %11") /* %11 = 0*/
+ A("mul %5,%8") /* r1:r0 = LO(f) * HI(t)*/
+ A("add %1,r0") /* %1 += LO(LO(f) * HI(t))*/
+ A("adc %10,r1") /* %10 = HI(LO(f) * HI(t))*/
+ A("adc %11,%0") /* %11 += carry*/
+ A("mul %6,%7") /* r1:r0 = HI(f) * LO(t)*/
+ A("add %1,r0") /* %1 += LO(HI(f) * LO(t))*/
+ A("adc %10,r1") /* %10 += HI(HI(f) * LO(t))*/
+ A("adc %11,%0") /* %11 += carry*/
+ A("mul %6,%8") /* r1:r0 = HI(f) * HI(t)*/
+ A("add %10,r0") /* %10 += LO(HI(f) * HI(t))*/
+ A("adc %11,r1") /* %11 += HI(HI(f) * HI(t))*/
+ A("mov %5,%10") /* %6:%5 =*/
+ A("mov %6,%11") /* f = %10:%11*/
+
+ /* umul16x24to24hi(v, f, bezier_B); / Range 22bits [29]*/
+ /* acc -= v;*/
+ A("lds %10, bezier_B") /* %10 = LO(bezier_B)*/
+ A("mul %10,%5") /* r1:r0 = LO(bezier_B) * LO(f)*/
+ A("sub %9,r1")
+ A("sbc %2,%0")
+ A("sbc %3,%0")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= HI(LO(bezier_B) * LO(f))*/
+ A("lds %11, bezier_B+1") /* %11 = MI(bezier_B)*/
+ A("mul %11,%5") /* r1:r0 = MI(bezier_B) * LO(f)*/
+ A("sub %9,r0")
+ A("sbc %2,r1")
+ A("sbc %3,%0")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= MI(bezier_B) * LO(f)*/
+ A("lds %1, bezier_B+2") /* %1 = HI(bezier_B)*/
+ A("mul %1,%5") /* r1:r0 = MI(bezier_B) * LO(f)*/
+ A("sub %2,r0")
+ A("sbc %3,r1")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= HI(bezier_B) * LO(f) << 8*/
+ A("mul %10,%6") /* r1:r0 = LO(bezier_B) * MI(f)*/
+ A("sub %9,r0")
+ A("sbc %2,r1")
+ A("sbc %3,%0")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= LO(bezier_B) * MI(f)*/
+ A("mul %11,%6") /* r1:r0 = MI(bezier_B) * MI(f)*/
+ A("sub %2,r0")
+ A("sbc %3,r1")
+ A("sbc %4,%0") /* %4:%3:%2:%9 -= MI(bezier_B) * MI(f) << 8*/
+ A("mul %1,%6") /* r1:r0 = HI(bezier_B) * LO(f)*/
+ A("sub %3,r0")
+ A("sbc %4,r1") /* %4:%3:%2:%9 -= HI(bezier_B) * LO(f) << 16*/
+
+ /* umul16x16to16hi(f, f, t); / Range 16 bits : f = t^5 (unsigned) [17]*/
+ A("mul %5,%7") /* r1:r0 = LO(f) * LO(t)*/
+ A("mov %1,r1") /* store MIL(LO(f) * LO(t)) in %1, we need it for rounding*/
+ A("clr %10") /* %10 = 0*/
+ A("clr %11") /* %11 = 0*/
+ A("mul %5,%8") /* r1:r0 = LO(f) * HI(t)*/
+ A("add %1,r0") /* %1 += LO(LO(f) * HI(t))*/
+ A("adc %10,r1") /* %10 = HI(LO(f) * HI(t))*/
+ A("adc %11,%0") /* %11 += carry*/
+ A("mul %6,%7") /* r1:r0 = HI(f) * LO(t)*/
+ A("add %1,r0") /* %1 += LO(HI(f) * LO(t))*/
+ A("adc %10,r1") /* %10 += HI(HI(f) * LO(t))*/
+ A("adc %11,%0") /* %11 += carry*/
+ A("mul %6,%8") /* r1:r0 = HI(f) * HI(t)*/
+ A("add %10,r0") /* %10 += LO(HI(f) * HI(t))*/
+ A("adc %11,r1") /* %11 += HI(HI(f) * HI(t))*/
+ A("mov %5,%10") /* %6:%5 =*/
+ A("mov %6,%11") /* f = %10:%11*/
+
+ /* umul16x24to24hi(v, f, bezier_A); / Range 21bits [29]*/
+ /* acc += v; */
+ A("lds %10, bezier_A") /* %10 = LO(bezier_A)*/
+ A("mul %10,%5") /* r1:r0 = LO(bezier_A) * LO(f)*/
+ A("add %9,r1")
+ A("adc %2,%0")
+ A("adc %3,%0")
+ A("adc %4,%0") /* %4:%3:%2:%9 += HI(LO(bezier_A) * LO(f))*/
+ A("lds %11, bezier_A+1") /* %11 = MI(bezier_A)*/
+ A("mul %11,%5") /* r1:r0 = MI(bezier_A) * LO(f)*/
+ A("add %9,r0")
+ A("adc %2,r1")
+ A("adc %3,%0")
+ A("adc %4,%0") /* %4:%3:%2:%9 += MI(bezier_A) * LO(f)*/
+ A("lds %1, bezier_A+2") /* %1 = HI(bezier_A)*/
+ A("mul %1,%5") /* r1:r0 = MI(bezier_A) * LO(f)*/
+ A("add %2,r0")
+ A("adc %3,r1")
+ A("adc %4,%0") /* %4:%3:%2:%9 += HI(bezier_A) * LO(f) << 8*/
+ A("mul %10,%6") /* r1:r0 = LO(bezier_A) * MI(f)*/
+ A("add %9,r0")
+ A("adc %2,r1")
+ A("adc %3,%0")
+ A("adc %4,%0") /* %4:%3:%2:%9 += LO(bezier_A) * MI(f)*/
+ A("mul %11,%6") /* r1:r0 = MI(bezier_A) * MI(f)*/
+ A("add %2,r0")
+ A("adc %3,r1")
+ A("adc %4,%0") /* %4:%3:%2:%9 += MI(bezier_A) * MI(f) << 8*/
+ A("mul %1,%6") /* r1:r0 = HI(bezier_A) * LO(f)*/
+ A("add %3,r0")
+ A("adc %4,r1") /* %4:%3:%2:%9 += HI(bezier_A) * LO(f) << 16*/
+ L("2")
+ " clr __zero_reg__" /* C runtime expects r1 = __zero_reg__ = 0 */
+ : "+r"(r0),
+ "+r"(r1),
+ "+r"(r2),
+ "+r"(r3),
+ "+r"(r4),
+ "+r"(r5),
+ "+r"(r6),
+ "+r"(r7),
+ "+r"(r8),
+ "+r"(r9),
+ "+r"(r10),
+ "+r"(r11)
+ :
+ :"cc","r0","r1"
+ );
+ return (r2 | (uint16_t(r3) << 8)) | (uint32_t(r4) << 16);
+ }
+
+#endif // BEZIER_JERK_CONTROL
+
/**
* Stepper Driver Interrupt
*
@@ -463,7 +1209,54 @@ void Stepper::isr() {
if (!(current_block = planner.get_current_block())) return;
}
- trapezoid_generator_reset();
+ // Initialize the trapezoid generator from the current block.
+ static int8_t last_extruder = -1;
+
+ #if ENABLED(LIN_ADVANCE)
+ #if E_STEPPERS > 1
+ if (current_block->active_extruder != last_extruder) {
+ current_adv_steps = 0; // If the now active extruder wasn't in use during the last move, its pressure is most likely gone.
+ LA_active_extruder = current_block->active_extruder;
+ }
+ #endif
+
+ if ((use_advance_lead = current_block->use_advance_lead)) {
+ LA_decelerate_after = current_block->decelerate_after;
+ final_adv_steps = current_block->final_adv_steps;
+ max_adv_steps = current_block->max_adv_steps;
+ }
+ #endif
+
+ if (current_block->direction_bits != last_direction_bits || current_block->active_extruder != last_extruder) {
+ last_direction_bits = current_block->direction_bits;
+ last_extruder = current_block->active_extruder;
+ set_directions();
+ }
+
+ // No acceleration / deceleration time elapsed so far
+ acceleration_time = deceleration_time = 0;
+
+ // No step events completed so far
+ step_events_completed = 0;
+
+ // step_rate to timer interval
+ OCR1A_nominal = calc_timer_interval(current_block->nominal_rate);
+
+ // make a note of the number of step loops required at nominal speed
+ step_loops_nominal = step_loops;
+
+ #if DISABLED(BEZIER_JERK_CONTROL)
+ // Set as deceleration point the initial rate of the block
+ acc_step_rate = current_block->initial_rate;
+ #endif
+
+ #if ENABLED(BEZIER_JERK_CONTROL)
+ // Initialize the Bézier speed curve
+ _calc_bezier_curve_coeffs(current_block->initial_rate, current_block->cruise_rate, current_block->acceleration_time_inverse);
+
+ // We have not started the 2nd half of the trapezoid
+ bezier_2nd_half = false;
+ #endif
// Initialize Bresenham counters to 1/2 the ceiling
counter_X = counter_Y = counter_Z = counter_E = -(current_block->step_event_count >> 1);
@@ -705,11 +1498,19 @@ void Stepper::isr() {
// Calculate new timer value
if (step_events_completed <= (uint32_t)current_block->accelerate_until) {
- MultiU24X32toH16(acc_step_rate, acceleration_time, current_block->acceleration_rate);
- acc_step_rate += current_block->initial_rate;
+ #if ENABLED(BEZIER_JERK_CONTROL)
+ // Get the next speed to use (Jerk limited!)
+ uint16_t acc_step_rate =
+ acceleration_time < current_block->acceleration_time
+ ? _eval_bezier_curve(acceleration_time)
+ : current_block->cruise_rate;
+ #else
+ MultiU24X32toH16(acc_step_rate, acceleration_time, current_block->acceleration_rate);
+ acc_step_rate += current_block->initial_rate;
- // upper limit
- NOMORE(acc_step_rate, current_block->nominal_rate);
+ // upper limit
+ NOMORE(acc_step_rate, current_block->nominal_rate);
+ #endif
// step_rate to timer interval
const uint16_t interval = calc_timer_interval(acc_step_rate);
@@ -734,14 +1535,32 @@ void Stepper::isr() {
}
else if (step_events_completed > (uint32_t)current_block->decelerate_after) {
uint16_t step_rate;
- MultiU24X32toH16(step_rate, deceleration_time, current_block->acceleration_rate);
- if (step_rate < acc_step_rate) { // Still decelerating?
- step_rate = acc_step_rate - step_rate;
- NOLESS(step_rate, current_block->final_rate);
- }
- else
- step_rate = current_block->final_rate;
+ #if ENABLED(BEZIER_JERK_CONTROL)
+ // If this is the 1st time we process the 2nd half of the trapezoid...
+ if (!bezier_2nd_half) {
+
+ // Initialize the Bézier speed curve
+ _calc_bezier_curve_coeffs(current_block->cruise_rate, current_block->final_rate, current_block->deceleration_time_inverse);
+ bezier_2nd_half = true;
+ }
+
+ // Calculate the next speed to use
+ step_rate = deceleration_time < current_block->deceleration_time
+ ? _eval_bezier_curve(deceleration_time)
+ : current_block->final_rate;
+ #else
+
+ // Using the old trapezoidal control
+ MultiU24X32toH16(step_rate, deceleration_time, current_block->acceleration_rate);
+
+ if (step_rate < acc_step_rate) { // Still decelerating?
+ step_rate = acc_step_rate - step_rate;
+ NOLESS(step_rate, current_block->final_rate);
+ }
+ else
+ step_rate = current_block->final_rate;
+ #endif
// step_rate to timer interval
const uint16_t interval = calc_timer_interval(step_rate);
@@ -1104,6 +1923,7 @@ void Stepper::init() {
// Init Stepper ISR to 122 Hz for quick starting
OCR1A = 0x4000;
TCNT1 = 0;
+
ENABLE_STEPPER_DRIVER_INTERRUPT();
endstops.enable(true); // Start with endstops active. After homing they can be disabled
diff --git a/Marlin/stepper.h b/Marlin/stepper.h
index 597600e805fbf0e8b24f163f351bf05ba3be81ac..087b8593e4960ad61fde1b1f63462091d352bf93 100644
--- a/Marlin/stepper.h
+++ b/Marlin/stepper.h
@@ -55,6 +55,7 @@ extern Stepper stepper;
#define ENABLE_STEPPER_DRIVER_INTERRUPT() SBI(TIMSK1, OCIE1A)
#define DISABLE_STEPPER_DRIVER_INTERRUPT() CBI(TIMSK1, OCIE1A)
#define STEPPER_ISR_ENABLED() TEST(TIMSK1, OCIE1A)
+#define HAL_STEPPER_TIMER_RATE ((F_CPU) * 0.125)
// intRes = intIn1 * intIn2 >> 16
// uses:
@@ -62,16 +63,16 @@ extern Stepper stepper;
// r27 to store the byte 1 of the 24 bit result
#define MultiU16X8toH16(intRes, charIn1, intIn2) \
asm volatile ( \
- "clr r26 \n\t" \
- "mul %A1, %B2 \n\t" \
- "movw %A0, r0 \n\t" \
- "mul %A1, %A2 \n\t" \
- "add %A0, r1 \n\t" \
- "adc %B0, r26 \n\t" \
- "lsr r0 \n\t" \
- "adc %A0, r26 \n\t" \
- "adc %B0, r26 \n\t" \
- "clr r1 \n\t" \
+ A("clr r26") \
+ A("mul %A1, %B2") \
+ A("movw %A0, r0") \
+ A("mul %A1, %A2") \
+ A("add %A0, r1") \
+ A("adc %B0, r26") \
+ A("lsr r0") \
+ A("adc %A0, r26") \
+ A("adc %B0, r26") \
+ A("clr r1") \
: \
"=&r" (intRes) \
: \
@@ -122,6 +123,16 @@ class Stepper {
static int32_t counter_X, counter_Y, counter_Z, counter_E;
static volatile uint32_t step_events_completed; // The number of step events executed in the current block
+ #if ENABLED(BEZIER_JERK_CONTROL)
+ static int32_t bezier_A, // A coefficient in Bézier speed curve
+ bezier_B, // B coefficient in Bézier speed curve
+ bezier_C; // C coefficient in Bézier speed curve
+ static uint32_t bezier_F, // F coefficient in Bézier speed curve
+ bezier_AV; // AV coefficient in Bézier speed curve
+ static bool A_negative, // If A coefficient was negative
+ bezier_2nd_half; // If Bézier curve has been initialized or not
+ #endif
+
#if ENABLED(LIN_ADVANCE)
static uint32_t LA_decelerate_after; // Copy from current executed block. Needed because current_block is set to NULL "too early".
@@ -145,8 +156,10 @@ class Stepper {
static int32_t acceleration_time, deceleration_time;
static uint8_t step_loops, step_loops_nominal;
- static uint16_t OCR1A_nominal,
- acc_step_rate; // needed for deceleration start point
+ static uint16_t OCR1A_nominal;
+ #if DISABLED(BEZIER_JERK_CONTROL)
+ static uint16_t acc_step_rate; // needed for deceleration start point
+ #endif
static volatile int32_t endstops_trigsteps[XYZ];
static volatile int32_t endstops_stepsTotal, endstops_stepsDone;
@@ -330,8 +343,8 @@ class Stepper {
private:
- FORCE_INLINE static unsigned short calc_timer_interval(unsigned short step_rate) {
- unsigned short timer;
+ FORCE_INLINE static uint16_t calc_timer_interval(uint16_t step_rate) {
+ uint16_t timer;
NOMORE(step_rate, MAX_STEP_FREQUENCY);
@@ -370,43 +383,10 @@ class Stepper {
return timer;
}
- // Initialize the trapezoid generator from the current block.
- // Called whenever a new block begins.
- FORCE_INLINE static void trapezoid_generator_reset() {
-
- static int8_t last_extruder = -1;
-
- #if ENABLED(LIN_ADVANCE)
- #if E_STEPPERS > 1
- if (current_block->active_extruder != last_extruder) {
- current_adv_steps = 0; // If the now active extruder wasn't in use during the last move, its pressure is most likely gone.
- LA_active_extruder = current_block->active_extruder;
- }
- #endif
-
- if ((use_advance_lead = current_block->use_advance_lead)) {
- LA_decelerate_after = current_block->decelerate_after;
- final_adv_steps = current_block->final_adv_steps;
- max_adv_steps = current_block->max_adv_steps;
- }
- #endif
-
- if (current_block->direction_bits != last_direction_bits || current_block->active_extruder != last_extruder) {
- last_direction_bits = current_block->direction_bits;
- last_extruder = current_block->active_extruder;
- set_directions();
- }
-
- deceleration_time = 0;
- // step_rate to timer interval
- OCR1A_nominal = calc_timer_interval(current_block->nominal_rate);
- // make a note of the number of step loops required at nominal speed
- step_loops_nominal = step_loops;
- acc_step_rate = current_block->initial_rate;
- acceleration_time = calc_timer_interval(acc_step_rate);
- _NEXT_ISR(acceleration_time);
-
- }
+ #if ENABLED(BEZIER_JERK_CONTROL)
+ static void _calc_bezier_curve_coeffs(const int32_t v0, const int32_t v1, const uint32_t av);
+ static int32_t _eval_bezier_curve(const uint32_t curr_step);
+ #endif
#if HAS_DIGIPOTSS || HAS_MOTOR_CURRENT_PWM
static void digipot_init();