diff --git a/Marlin/src/inc/SanityCheck.h b/Marlin/src/inc/SanityCheck.h index 8d25c9b53f..210246a9cc 100644 --- a/Marlin/src/inc/SanityCheck.h +++ b/Marlin/src/inc/SanityCheck.h @@ -99,8 +99,6 @@ #error "Z_ENDSTOP_SERVO_NR is now Z_PROBE_SERVO_NR. Please update your configuration." #elif defined(DEFAULT_XYJERK) #error "DEFAULT_XYJERK is deprecated. Use DEFAULT_XJERK and DEFAULT_YJERK instead." -#elif ENABLED(BEZIER_JERK_CONTROL) && !defined(CPU_32_BIT) - #error "BEZIER_JERK_CONTROL is computationally intensive and requires a 32-bit board." #elif defined(XY_TRAVEL_SPEED) #error "XY_TRAVEL_SPEED is deprecated. Use XY_PROBE_SPEED instead." #elif defined(PROBE_SERVO_DEACTIVATION_DELAY) diff --git a/Marlin/src/module/planner.cpp b/Marlin/src/module/planner.cpp index cd95bb04f9..bb0cb8eb2e 100644 --- a/Marlin/src/module/planner.cpp +++ b/Marlin/src/module/planner.cpp @@ -56,6 +56,10 @@ * * IntersectionDistance[s1_, s2_, a_, d_] := (2 a d - s1^2 + s2^2)/(4 a) * + * -- + * + * The fast inverse function needed for Bézier interpolation for AVR + * was designed, written and tested by Eduardo José Tagle on April/2018 */ #include "planner.h" @@ -215,6 +219,523 @@ void Planner::init() { #endif } +#if ENABLED(BEZIER_JERK_CONTROL) + + #ifdef __AVR__ + // 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 */ + + " clr %13" "\n\t" /* %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 .*/ + + " clr %3" "\n\t" /* idx = 0 */ + " mov %14,%6" "\n\t" + " mov %15,%7" "\n\t" + " mov %16,%8" "\n\t" /* nr = interval */ + " tst %16" "\n\t" /* nr & 0xFF0000 == 0 ? */ + " brne 2f" "\n\t" /* No, skip this */ + " mov %16,%15" "\n\t" + " mov %15,%14" "\n\t" /* nr <<= 8, %14 not needed */ + " subi %3,-8" "\n\t" /* idx += 8 */ + " tst %16" "\n\t" /* nr & 0xFF0000 == 0 ? */ + " brne 2f" "\n\t" /* No, skip this */ + " mov %16,%15" "\n\t" /* nr <<= 8, %14 not needed */ + " clr %15" "\n\t" /* We clear %14 */ + " subi %3,-8" "\n\t" /* idx += 8 */ + + /* here %16 != 0 and %16:%15 contains at least 9 MSBits, or both %16:%15 are 0 */ + "2:" "\n\t" + " cpi %16,0x10" "\n\t" /* (nr & 0xf00000) == 0 ? */ + " brcc 3f" "\n\t" /* No, skip this */ + " swap %15" "\n\t" /* Swap nibbles */ + " swap %16" "\n\t" /* Swap nibbles. Low nibble is 0 */ + " mov %14, %15" "\n\t" + " andi %14,0x0f" "\n\t" /* Isolate low nibble */ + " andi %15,0xf0" "\n\t" /* Keep proper nibble in %15 */ + " or %16, %14" "\n\t" /* %16:%15 <<= 4 */ + " subi %3,-4" "\n\t" /* idx += 4 */ + + "3:" "\n\t" + " cpi %16,0x40" "\n\t" /* (nr & 0xc00000) == 0 ? */ + " brcc 4f" "\n\t" /* No, skip this*/ + " add %15,%15" "\n\t" + " adc %16,%16" "\n\t" + " add %15,%15" "\n\t" + " adc %16,%16" "\n\t" /* %16:%15 <<= 2 */ + " subi %3,-2" "\n\t" /* idx += 2 */ + + "4:" "\n\t" + " cpi %16,0x80" "\n\t" /* (nr & 0x800000) == 0 ? */ + " brcc 5f" "\n\t" /* No, skip this */ + " add %15,%15" "\n\t" + " adc %16,%16" "\n\t" /* %16:%15 <<= 1 */ + " inc %3" "\n\t" /* 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*/ + "5:" "\n\t" + " add %15,%15" "\n\t" + " adc %16,%16" "\n\t" /* %16:%15 = tidx = (nr <<= 1), we lose the top MSBit (always set to 1, %16 is the index into the inverse table)*/ + " add r30,%16" "\n\t" /* Only use top 8 bits */ + " adc r31,%13" "\n\t" /* r31:r30 = inv_tab + (tidx) */ + " lpm %14, Z" "\n\t" /* %14 = inv_tab[tidx] */ + " ldi %15, 1" "\n\t" /* %15 = 1 %15:%14 = inv_tab[tidx] + 256 */ + + /* We must scale the approximation to the proper place*/ + " clr %16" "\n\t" /* %16 will always be 0 here */ + " subi %3,8" "\n\t" /* idx == 8 ? */ + " breq 6f" "\n\t" /* yes, no need to scale*/ + " brcs 7f" "\n\t" /* 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]*/ + " sbrs %3,0" "\n\t" /* shift by 1bit position?*/ + " rjmp 8f" "\n\t" /* No*/ + " add %14,%14" "\n\t" + " adc %15,%15" "\n\t" /* %15:16 <<= 1*/ + "8:" "\n\t" + " sbrs %3,1" "\n\t" /* shift by 2bit position?*/ + " rjmp 9f" "\n\t" /* No*/ + " add %14,%14" "\n\t" + " adc %15,%15" "\n\t" + " add %14,%14" "\n\t" + " adc %15,%15" "\n\t" /* %15:16 <<= 1*/ + "9:" "\n\t" + " sbrs %3,2" "\n\t" /* shift by 4bits position?*/ + " rjmp 16f" "\n\t" /* No*/ + " swap %15" "\n\t" /* Swap nibbles. lo nibble of %15 will always be 0*/ + " swap %14" "\n\t" /* Swap nibbles*/ + " mov %12,%14" "\n\t" + " andi %12,0x0f" "\n\t" /* isolate low nibble*/ + " andi %14,0xf0" "\n\t" /* and clear it*/ + " or %15,%12" "\n\t" /* %15:%16 <<= 4*/ + "16:" "\n\t" + " sbrs %3,3" "\n\t" /* shift by 8bits position?*/ + " rjmp 6f" "\n\t" /* No, we are done */ + " mov %16,%15" "\n\t" + " mov %15,%14" "\n\t" + " clr %14" "\n\t" + " jmp 6f" "\n\t" + + /* idx < 8, now %3 = idx - 8. Get the count of bits */ + "7:" "\n\t" + " neg %3" "\n\t" /* %3 = -idx = count of bits to move right. idx range:[1...8]*/ + " sbrs %3,0" "\n\t" /* shift by 1 bit position ?*/ + " rjmp 10f" "\n\t" /* No, skip it*/ + " asr %15" "\n\t" /* (bit7 is always 0 here)*/ + " ror %14" "\n\t" + "10:" "\n\t" + " sbrs %3,1" "\n\t" /* shift by 2 bit position ?*/ + " rjmp 11f" "\n\t" /* No, skip it*/ + " asr %15" "\n\t" /* (bit7 is always 0 here)*/ + " ror %14" "\n\t" + " asr %15" "\n\t" /* (bit7 is always 0 here)*/ + " ror %14" "\n\t" + "11:" "\n\t" + " sbrs %3,2" "\n\t" /* shift by 4 bit position ?*/ + " rjmp 12f" "\n\t" /* No, skip it*/ + " swap %15" "\n\t" /* Swap nibbles*/ + " andi %14, 0xf0" "\n\t" /* Lose the lowest nibble*/ + " swap %14" "\n\t" /* Swap nibbles. Upper nibble is 0*/ + " or %14,%15" "\n\t" /* Pass nibble from upper byte*/ + " andi %15, 0x0f" "\n\t" /* And get rid of that nibble*/ + "12:" "\n\t" + " sbrs %3,3" "\n\t" /* shift by 8 bit position ?*/ + " rjmp 6f" "\n\t" /* No, skip it*/ + " mov %14,%15" "\n\t" + " clr %15" "\n\t" + "6:" "\n\t" /* %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*/ + " clr %0" "\n\t" + " clr %1" "\n\t" + " clr %2" "\n\t" + " ldi %3,2" "\n\t" /* %3:%2:%1:%0 = 0x2000000*/ + " mul %6,%14" "\n\t" /* r1:r0 = LO(d) * LO(x)*/ + " sub %0,r0" "\n\t" + " sbc %1,r1" "\n\t" + " sbc %2,%13" "\n\t" + " sbc %3,%13" "\n\t" /* %3:%2:%1:%0 -= LO(d) * LO(x)*/ + " mul %7,%14" "\n\t" /* r1:r0 = MI(d) * LO(x)*/ + " sub %1,r0" "\n\t" + " sbc %2,r1" "\n\t" + " sbc %3,%13" "\n\t" /* %3:%2:%1:%0 -= MI(d) * LO(x) << 8*/ + " mul %8,%14" "\n\t" /* r1:r0 = HI(d) * LO(x)*/ + " sub %2,r0" "\n\t" + " sbc %3,r1" "\n\t" /* %3:%2:%1:%0 -= MIL(d) * LO(x) << 16*/ + " mul %6,%15" "\n\t" /* r1:r0 = LO(d) * MI(x)*/ + " sub %1,r0" "\n\t" + " sbc %2,r1" "\n\t" + " sbc %3,%13" "\n\t" /* %3:%2:%1:%0 -= LO(d) * MI(x) << 8*/ + " mul %7,%15" "\n\t" /* r1:r0 = MI(d) * MI(x)*/ + " sub %2,r0" "\n\t" + " sbc %3,r1" "\n\t" /* %3:%2:%1:%0 -= MI(d) * MI(x) << 16*/ + " mul %8,%15" "\n\t" /* r1:r0 = HI(d) * MI(x)*/ + " sub %3,r0" "\n\t" /* %3:%2:%1:%0 -= MIL(d) * MI(x) << 24*/ + " mul %6,%16" "\n\t" /* r1:r0 = LO(d) * HI(x)*/ + " sub %2,r0" "\n\t" + " sbc %3,r1" "\n\t" /* %3:%2:%1:%0 -= LO(d) * HI(x) << 16*/ + " mul %7,%16" "\n\t" /* r1:r0 = MI(d) * HI(x)*/ + " sub %3,r0" "\n\t" /* %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*/ + " mul %14,%0" "\n\t" /* r1:r0 = LO(x) * LO(acc)*/ + " mov %4,r1" "\n\t" + " clr %5" "\n\t" + " clr %9" "\n\t" + " clr %10" "\n\t" + " clr %11" "\n\t" /* %11:%10:%9:%5:%4 = LO(x) * LO(acc) >> 8*/ + " mul %15,%0" "\n\t" /* r1:r0 = MI(x) * LO(acc)*/ + " add %4,r0" "\n\t" + " adc %5,r1" "\n\t" + " adc %9,%13" "\n\t" + " adc %10,%13" "\n\t" + " adc %11,%13" "\n\t" /* %11:%10:%9:%5:%4 += MI(x) * LO(acc) */ + " mul %16,%0" "\n\t" /* r1:r0 = HI(x) * LO(acc)*/ + " add %5,r0" "\n\t" + " adc %9,r1" "\n\t" + " adc %10,%13" "\n\t" + " adc %11,%13" "\n\t" /* %11:%10:%9:%5:%4 += MI(x) * LO(acc) << 8*/ + + " mul %14,%1" "\n\t" /* r1:r0 = LO(x) * MIL(acc)*/ + " add %4,r0" "\n\t" + " adc %5,r1" "\n\t" + " adc %9,%13" "\n\t" + " adc %10,%13" "\n\t" + " adc %11,%13" "\n\t" /* %11:%10:%9:%5:%4 = LO(x) * MIL(acc)*/ + " mul %15,%1" "\n\t" /* r1:r0 = MI(x) * MIL(acc)*/ + " add %5,r0" "\n\t" + " adc %9,r1" "\n\t" + " adc %10,%13" "\n\t" + " adc %11,%13" "\n\t" /* %11:%10:%9:%5:%4 += MI(x) * MIL(acc) << 8*/ + " mul %16,%1" "\n\t" /* r1:r0 = HI(x) * MIL(acc)*/ + " add %9,r0" "\n\t" + " adc %10,r1" "\n\t" + " adc %11,%13" "\n\t" /* %11:%10:%9:%5:%4 += MI(x) * MIL(acc) << 16*/ + + " mul %14,%2" "\n\t" /* r1:r0 = LO(x) * MIH(acc)*/ + " add %5,r0" "\n\t" + " adc %9,r1" "\n\t" + " adc %10,%13" "\n\t" + " adc %11,%13" "\n\t" /* %11:%10:%9:%5:%4 = LO(x) * MIH(acc) << 8*/ + " mul %15,%2" "\n\t" /* r1:r0 = MI(x) * MIH(acc)*/ + " add %9,r0" "\n\t" + " adc %10,r1" "\n\t" + " adc %11,%13" "\n\t" /* %11:%10:%9:%5:%4 += MI(x) * MIH(acc) << 16*/ + " mul %16,%2" "\n\t" /* r1:r0 = HI(x) * MIH(acc)*/ + " add %10,r0" "\n\t" + " adc %11,r1" "\n\t" /* %11:%10:%9:%5:%4 += MI(x) * MIH(acc) << 24*/ + + " mul %14,%3" "\n\t" /* r1:r0 = LO(x) * HI(acc)*/ + " add %9,r0" "\n\t" + " adc %10,r1" "\n\t" + " adc %11,%13" "\n\t" /* %11:%10:%9:%5:%4 = LO(x) * HI(acc) << 16*/ + " mul %15,%3" "\n\t" /* r1:r0 = MI(x) * HI(acc)*/ + " add %10,r0" "\n\t" + " adc %11,r1" "\n\t" /* %11:%10:%9:%5:%4 += MI(x) * HI(acc) << 24*/ + " mul %16,%3" "\n\t" /* r1:r0 = HI(x) * HI(acc)*/ + " add %11,r0" "\n\t" /* %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" /* */ + " ldi %3,1" "\n\t" + " clr %2" "\n\t" + " clr %1" "\n\t" + " clr %0" "\n\t" /* %3:%2:%1:%0 = 0x1000000*/ + " mul %6,%9" "\n\t" /* r1:r0 = LO(d) * LO(x)*/ + " sub %0,r0" "\n\t" + " sbc %1,r1" "\n\t" + " sbc %2,%13" "\n\t" + " sbc %3,%13" "\n\t" /* %3:%2:%1:%0 -= LO(d) * LO(x)*/ + " mul %7,%9" "\n\t" /* r1:r0 = MI(d) * LO(x)*/ + " sub %1,r0" "\n\t" + " sbc %2,r1" "\n\t" + " sbc %3,%13" "\n\t" /* %3:%2:%1:%0 -= MI(d) * LO(x) << 8*/ + " mul %8,%9" "\n\t" /* r1:r0 = HI(d) * LO(x)*/ + " sub %2,r0" "\n\t" + " sbc %3,r1" "\n\t" /* %3:%2:%1:%0 -= MIL(d) * LO(x) << 16*/ + " mul %6,%10" "\n\t" /* r1:r0 = LO(d) * MI(x)*/ + " sub %1,r0" "\n\t" + " sbc %2,r1" "\n\t" + " sbc %3,%13" "\n\t" /* %3:%2:%1:%0 -= LO(d) * MI(x) << 8*/ + " mul %7,%10" "\n\t" /* r1:r0 = MI(d) * MI(x)*/ + " sub %2,r0" "\n\t" + " sbc %3,r1" "\n\t" /* %3:%2:%1:%0 -= MI(d) * MI(x) << 16*/ + " mul %8,%10" "\n\t" /* r1:r0 = HI(d) * MI(x)*/ + " sub %3,r0" "\n\t" /* %3:%2:%1:%0 -= MIL(d) * MI(x) << 24*/ + " mul %6,%11" "\n\t" /* r1:r0 = LO(d) * HI(x)*/ + " sub %2,r0" "\n\t" + " sbc %3,r1" "\n\t" /* %3:%2:%1:%0 -= LO(d) * HI(x) << 16*/ + " mul %7,%11" "\n\t" /* r1:r0 = MI(d) * HI(x)*/ + " sub %3,r0" "\n\t" /* %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*/ + " sub %0,%6" "\n\t" + " sbc %1,%7" "\n\t" + " sbc %2,%8" "\n\t" /* r -= d*/ + " brcs 14f" "\n\t" /* if ( r >= d) */ + + /* %11:%10:%9 = x */ + " ldi %3,1" "\n\t" + " add %9,%3" "\n\t" + " adc %10,%13" "\n\t" + " adc %11,%13" "\n\t" /* x++*/ + "14:" "\n\t" + + /* Estimation is done. %11:%10:%9 = x */ + " clr __zero_reg__" "\n\t" /* 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); + } + #else + // All the other 32 CPUs can easily perform the inverse using hardware division, + // so we don´t need to reduce precision or to use assembly language at all. + + // This routine, for all the other archs, returns 0x100000000 / d ~= 0xFFFFFFFF / d + static FORCE_INLINE uint32_t get_period_inverse(uint32_t d) { + return 0xFFFFFFFF / d; + } + #endif +#endif + #define MINIMAL_STEP_RATE 120 /** @@ -266,8 +787,13 @@ void Planner::calculate_trapezoid_for_block(block_t* const block, const float &e #if ENABLED(BEZIER_JERK_CONTROL) // Jerk controlled speed requires to express speed versus time, NOT steps - int32_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; + 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 @@ -278,6 +804,8 @@ void Planner::calculate_trapezoid_for_block(block_t* const block, const float &e #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; diff --git a/Marlin/src/module/planner.h b/Marlin/src/module/planner.h index 0c752c1f87..17c133a1d0 100644 --- a/Marlin/src/module/planner.h +++ b/Marlin/src/module/planner.h @@ -96,8 +96,10 @@ typedef struct { #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 - int32_t acceleration_time, // Acceleration time and deceleration time in STEP timer counts - deceleration_time; + 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 diff --git a/Marlin/src/module/stepper.cpp b/Marlin/src/module/stepper.cpp index 2b0974efa5..7be9c9ead2 100644 --- a/Marlin/src/module/stepper.cpp +++ b/Marlin/src/module/stepper.cpp @@ -117,11 +117,14 @@ long 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 Stepper::bezier_A, // A coefficient in Bézier speed curve - Stepper::bezier_B, // B coefficient in Bézier speed curve - Stepper::bezier_C, // C coefficient in Bézier speed curve - Stepper::bezier_F; // F coefficient in Bézier speed curve - uint32_t Stepper::bezier_AV; // AV coefficient in Bézier speed curve + 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 + #ifdef __AVR__ + bool __attribute__((used)) Stepper::A_negative __asm__("A_negative"); // If A coefficient was negative + #endif bool Stepper::bezier_2nd_half; // =false If Bézier curve has been initialized or not #endif @@ -391,130 +394,735 @@ void Stepper::set_directions() { * * Note the abbreviations we use in the following formulae are between []s * - * At the start of each trapezoid, we calculate the coefficients A,B,C,F and Advance [AV], as follows: + * For Any 32bit CPU: * - * 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) + * At the start of each trapezoid, we calculate the coefficients A,B,C,F and Advance [AV], as follows: * - * And for each point, we will evaluate the curve with the following sequence: + * 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) * - * uint32_t t = bezier_AV * curr_step; // t: Range 0 - 1^32 = 32 bits - * uint64_t f = t; - * f *= t; // Range 32*2 = 64 bits (unsigned) - * f >>= 32; // Range 32 bits (unsigned) - * f *= t; // Range 32*2 = 64 bits (unsigned) - * f >>= 32; // Range 32 bits : f = t^3 (unsigned) - * int64_t acc = (int64_t) bezier_F << 31; // Range 63 bits (signed) - * acc += ((uint32_t) f >> 1) * (int64_t) bezier_C; // Range 29bits + 31 = 60bits (plus sign) - * f *= t; // Range 32*2 = 64 bits - * f >>= 32; // Range 32 bits : f = t^3 (unsigned) - * acc += ((uint32_t) f >> 1) * (int64_t) bezier_B; // Range 29bits + 31 = 60bits (plus sign) - * f *= t; // Range 32*2 = 64 bits - * f >>= 32; // Range 32 bits : f = t^3 (unsigned) - * acc += ((uint32_t) f >> 1) * (int64_t) bezier_A; // Range 28bits + 31 = 59bits (plus sign) - * acc >>= (31 + 7); // Range 24bits (plus sign) + * And for each point, we will evaluate the curve with the following sequence: * - * This can be translated to the following ARM assembly 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; * - * At start: - * fhi = AV, flo = CS, alo = F + * 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 * - * muls fhi,flo | f = AV * CS 1 cycles - * mov t,fhi | t = AV * CS 1 cycles - * lsrs ahi,alo,#1 | a = F << 31 1 cycles - * lsls alo,alo,#31 | 1 cycles - * umull flo,fhi,fhi,t | f *= t 5 cycles [fhi:flo=64bits - * umull flo,fhi,fhi,t | f>>=32; f*=t 5 cycles [fhi:flo=64bits - * lsrs flo,fhi,#1 | 1 cycles [31bits - * smlal alo,ahi,flo,C | a+=(f>>33)*C; 5 cycles - * umull flo,fhi,fhi,t | f>>=32; f*=t 5 cycles [fhi:flo=64bits - * lsrs flo,fhi,#1 | 1 cycles [31bits - * smlal alo,ahi,flo,B | a+=(f>>33)*B; 5 cycles - * umull flo,fhi,fhi,t | f>>=32; f*=t 5 cycles [fhi:flo=64bits - * lsrs flo,fhi,#1 | f>>=33; 1 cycles [31bits - * smlal alo,ahi,flo,A | a+=(f>>33)*A; 5 cycles - * lsrs alo,ahi,#6 | a>>=38 1 cycles - * 43 cycles total */ - FORCE_INLINE void Stepper::_calc_bezier_curve_coeffs(const int32_t v0, const int32_t v1, const uint32_t interval) { - // Calculate the Bézier coefficients - bezier_A = 768 * (v1 - v0); - bezier_B = 1920 * (v0 - v1); - bezier_C = 1280 * (v1 - v0); - bezier_F = 128 * v0; - bezier_AV = 0xFFFFFFFF / interval; - } + #ifdef __AVR__ - FORCE_INLINE int32_t Stepper::_eval_bezier_curve(const uint32_t curr_step) { - #if defined(__ARM__) || defined(__thumb__) + // 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) { - // For ARM CORTEX M3/M4 CPUs, we have the optimized assembler version, that takes 43 cycles to execute - 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; + // Store advance + bezier_AV = av; - __asm__ __volatile__( - ".syntax unified" "\n\t" // is to prevent CM0,CM1 non-unified syntax - " lsrs %[ahi],%[alo],#1" "\n\t" // a = F << 31 1 cycles - " lsls %[alo],%[alo],#31" "\n\t" // 1 cycles - " umull %[flo],%[fhi],%[fhi],%[t]" "\n\t" // f *= t 5 cycles [fhi:flo=64bits] - " umull %[flo],%[fhi],%[fhi],%[t]" "\n\t" // f>>=32; f*=t 5 cycles [fhi:flo=64bits] - " lsrs %[flo],%[fhi],#1" "\n\t" // 1 cycles [31bits] - " smlal %[alo],%[ahi],%[flo],%[C]" "\n\t" // a+=(f>>33)*C; 5 cycles - " umull %[flo],%[fhi],%[fhi],%[t]" "\n\t" // f>>=32; f*=t 5 cycles [fhi:flo=64bits] - " lsrs %[flo],%[fhi],#1" "\n\t" // 1 cycles [31bits] - " smlal %[alo],%[ahi],%[flo],%[B]" "\n\t" // a+=(f>>33)*B; 5 cycles - " umull %[flo],%[fhi],%[fhi],%[t]" "\n\t" // f>>=32; f*=t 5 cycles [fhi:flo=64bits] - " lsrs %[flo],%[fhi],#1" "\n\t" // f>>=33; 1 cycles [31bits] - " smlal %[alo],%[ahi],%[flo],%[A]" "\n\t" // a+=(f>>33)*A; 5 cycles - " lsrs %[alo],%[ahi],#6" "\n\t" // a>>=38 1 cycles - : [alo]"+r"( alo ) , - [flo]"+r"( flo ) , - [fhi]"+r"( fhi ) , - [ahi]"+r"( ahi ) , - [A]"+r"( A ) , // <== Note: Even if A, B, C, and t registers are INPUT ONLY - [B]"+r"( B ) , // GCC does bad optimizations on the code if we list them as - [C]"+r"( C ) , // such, breaking this function. So, to avoid that problem, - [t]"+r"( t ) // we list all registers as input-outputs. + // 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*/ + " sts bezier_F, %0" "\n\t" + " sts bezier_F+1, %1" "\n\t" + " sts bezier_F+2, %10" "\n\t" /* bezier_F = %10:%1:%0 = v0 */ + + /* Get delta speed */ + " ldi %2,-1" "\n\t" /* %2 = 0xff, means A_negative = true */ + " clr %8" "\n\t" /* %8 = 0 */ + " sub %0,%3" "\n\t" + " sbc %1,%4" "\n\t" + " sbc %10,%5" "\n\t" /* v0 -= v1, C=1 if result is negative */ + " brcc 1f" "\n\t" /* branch if result is positive (C=0), that means v0 >= v1 */ + + /* Result was negative, get the absolute value*/ + " com %10" "\n\t" + " com %1" "\n\t" + " neg %0" "\n\t" + " sbc %1,%2" "\n\t" + " sbc %10,%2" "\n\t" /* %10:%1:%0 +1 -> %10:%1:%0 = -(v0 - v1) = (v1 - v0) */ + " clr %2" "\n\t" /* %2 = 0, means A_negative = false */ + + /* Store negative flag*/ + "1:" "\n\t" + " sts A_negative, %2" "\n\t" /* Store negative flag */ + + /* Compute coefficients A,B and C [20 cycles worst case]*/ + " ldi %9,6" "\n\t" /* %9 = 6 */ + " mul %0,%9" "\n\t" /* r1:r0 = 6*LO(v0-v1) */ + " sts bezier_A, r0" "\n\t" + " mov %6,r1" "\n\t" + " clr %7" "\n\t" /* %7:%6:r0 = 6*LO(v0-v1) */ + " mul %1,%9" "\n\t" /* r1:r0 = 6*MI(v0-v1) */ + " add %6,r0" "\n\t" + " adc %7,r1" "\n\t" /* %7:%6:?? += 6*MI(v0-v1) << 8 */ + " mul %10,%9" "\n\t" /* r1:r0 = 6*HI(v0-v1) */ + " add %7,r0" "\n\t" /* %7:%6:?? += 6*HI(v0-v1) << 16 */ + " sts bezier_A+1, %6" "\n\t" + " sts bezier_A+2, %7" "\n\t" /* bezier_A = %7:%6:?? = 6*(v0-v1) [35 cycles worst] */ + + " ldi %9,15" "\n\t" /* %9 = 15 */ + " mul %0,%9" "\n\t" /* r1:r0 = 5*LO(v0-v1) */ + " sts bezier_B, r0" "\n\t" + " mov %6,r1" "\n\t" + " clr %7" "\n\t" /* %7:%6:?? = 5*LO(v0-v1) */ + " mul %1,%9" "\n\t" /* r1:r0 = 5*MI(v0-v1) */ + " add %6,r0" "\n\t" + " adc %7,r1" "\n\t" /* %7:%6:?? += 5*MI(v0-v1) << 8 */ + " mul %10,%9" "\n\t" /* r1:r0 = 5*HI(v0-v1) */ + " add %7,r0" "\n\t" /* %7:%6:?? += 5*HI(v0-v1) << 16 */ + " sts bezier_B+1, %6" "\n\t" + " sts bezier_B+2, %7" "\n\t" /* bezier_B = %7:%6:?? = 5*(v0-v1) [50 cycles worst] */ + + " ldi %9,10" "\n\t" /* %9 = 10 */ + " mul %0,%9" "\n\t" /* r1:r0 = 10*LO(v0-v1) */ + " sts bezier_C, r0" "\n\t" + " mov %6,r1" "\n\t" + " clr %7" "\n\t" /* %7:%6:?? = 10*LO(v0-v1) */ + " mul %1,%9" "\n\t" /* r1:r0 = 10*MI(v0-v1) */ + " add %6,r0" "\n\t" + " adc %7,r1" "\n\t" /* %7:%6:?? += 10*MI(v0-v1) << 8 */ + " mul %10,%9" "\n\t" /* r1:r0 = 10*HI(v0-v1) */ + " add %7,r0" "\n\t" /* %7:%6:?? += 10*HI(v0-v1) << 16 */ + " sts bezier_C+1, %6" "\n\t" + " 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) : - : "cc" + : "r0", "r1", "cc", "memory" ); - return alo; + } - #else + FORCE_INLINE int32_t Stepper::_eval_bezier_curve(const uint32_t curr_step) { - // For non ARM targets, we provide a fallback implementation. Really doubt it - // will be useful, unless the processor is extremely fast. + // If dealing with the first step, save expensive computing and return the initial speed + if (!curr_step) + return bezier_F; - uint32_t t = bezier_AV * curr_step; // t: Range 0 - 1^32 = 32 bits - uint64_t f = t; - f *= t; // Range 32*2 = 64 bits (unsigned) - f >>= 32; // Range 32 bits (unsigned) - f *= t; // Range 32*2 = 64 bits (unsigned) - f >>= 32; // Range 32 bits : f = t^3 (unsigned) - int64_t acc = (int64_t) bezier_F << 31; // Range 63 bits (signed) - acc += ((uint32_t) f >> 1) * (int64_t) bezier_C; // Range 29bits + 31 = 60bits (plus sign) - f *= t; // Range 32*2 = 64 bits - f >>= 32; // Range 32 bits : f = t^3 (unsigned) - acc += ((uint32_t) f >> 1) * (int64_t) bezier_B; // Range 29bits + 31 = 60bits (plus sign) - f *= t; // Range 32*2 = 64 bits - f >>= 32; // Range 32 bits : f = t^3 (unsigned) - acc += ((uint32_t) f >> 1) * (int64_t) bezier_A; // Range 28bits + 31 = 59bits (plus sign) - acc >>= (31 + 7); // Range 24bits (plus sign) - return (int32_t) acc; + 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 */ - #endif - } + __asm__ __volatile( + /* umul24x24to16hi(t, bezier_AV, curr_step); t: Range 0 - 1^16 = 16 bits*/ + " lds %9,bezier_AV" "\n\t" /* %9 = LO(AV)*/ + " mul %9,%2" "\n\t" /* r1:r0 = LO(bezier_AV)*LO(curr_step)*/ + " mov %7,r1" "\n\t" /* %7 = LO(bezier_AV)*LO(curr_step) >> 8*/ + " clr %8" "\n\t" /* %8:%7 = LO(bezier_AV)*LO(curr_step) >> 8*/ + " lds %10,bezier_AV+1" "\n\t" /* %10 = MI(AV)*/ + " mul %10,%2" "\n\t" /* r1:r0 = MI(bezier_AV)*LO(curr_step)*/ + " add %7,r0" "\n\t" + " adc %8,r1" "\n\t" /* %8:%7 += MI(bezier_AV)*LO(curr_step)*/ + " lds r1,bezier_AV+2" "\n\t" /* r11 = HI(AV)*/ + " mul r1,%2" "\n\t" /* r1:r0 = HI(bezier_AV)*LO(curr_step)*/ + " add %8,r0" "\n\t" /* %8:%7 += HI(bezier_AV)*LO(curr_step) << 8*/ + " mul %9,%3" "\n\t" /* r1:r0 = LO(bezier_AV)*MI(curr_step)*/ + " add %7,r0" "\n\t" + " adc %8,r1" "\n\t" /* %8:%7 += LO(bezier_AV)*MI(curr_step)*/ + " mul %10,%3" "\n\t" /* r1:r0 = MI(bezier_AV)*MI(curr_step)*/ + " add %8,r0" "\n\t" /* %8:%7 += LO(bezier_AV)*MI(curr_step) << 8*/ + " mul %9,%4" "\n\t" /* r1:r0 = LO(bezier_AV)*HI(curr_step)*/ + " add %8,r0" "\n\t" /* %8:%7 += LO(bezier_AV)*HI(curr_step) << 8*/ + /* %8:%7 = t*/ + /* uint16_t f = t;*/ + " mov %5,%7" "\n\t" /* %6:%5 = f*/ + " mov %6,%8" "\n\t" + /* %6:%5 = f*/ + + /* umul16x16to16hi(f, f, t); / Range 16 bits (unsigned) [17] */ + " mul %5,%7" "\n\t" /* r1:r0 = LO(f) * LO(t)*/ + " mov %9,r1" "\n\t" /* store MIL(LO(f) * LO(t)) in %9, we need it for rounding*/ + " clr %10" "\n\t" /* %10 = 0*/ + " clr %11" "\n\t" /* %11 = 0*/ + " mul %5,%8" "\n\t" /* r1:r0 = LO(f) * HI(t)*/ + " add %9,r0" "\n\t" /* %9 += LO(LO(f) * HI(t))*/ + " adc %10,r1" "\n\t" /* %10 = HI(LO(f) * HI(t))*/ + " adc %11,%0" "\n\t" /* %11 += carry*/ + " mul %6,%7" "\n\t" /* r1:r0 = HI(f) * LO(t)*/ + " add %9,r0" "\n\t" /* %9 += LO(HI(f) * LO(t))*/ + " adc %10,r1" "\n\t" /* %10 += HI(HI(f) * LO(t)) */ + " adc %11,%0" "\n\t" /* %11 += carry*/ + " mul %6,%8" "\n\t" /* r1:r0 = HI(f) * HI(t)*/ + " add %10,r0" "\n\t" /* %10 += LO(HI(f) * HI(t))*/ + " adc %11,r1" "\n\t" /* %11 += HI(HI(f) * HI(t))*/ + " mov %5,%10" "\n\t" /* %6:%5 = */ + " mov %6,%11" "\n\t" /* f = %10:%11*/ + + /* umul16x16to16hi(f, f, t); / Range 16 bits : f = t^3 (unsigned) [17]*/ + " mul %5,%7" "\n\t" /* r1:r0 = LO(f) * LO(t)*/ + " mov %1,r1" "\n\t" /* store MIL(LO(f) * LO(t)) in %1, we need it for rounding*/ + " clr %10" "\n\t" /* %10 = 0*/ + " clr %11" "\n\t" /* %11 = 0*/ + " mul %5,%8" "\n\t" /* r1:r0 = LO(f) * HI(t)*/ + " add %1,r0" "\n\t" /* %1 += LO(LO(f) * HI(t))*/ + " adc %10,r1" "\n\t" /* %10 = HI(LO(f) * HI(t))*/ + " adc %11,%0" "\n\t" /* %11 += carry*/ + " mul %6,%7" "\n\t" /* r1:r0 = HI(f) * LO(t)*/ + " add %1,r0" "\n\t" /* %1 += LO(HI(f) * LO(t))*/ + " adc %10,r1" "\n\t" /* %10 += HI(HI(f) * LO(t))*/ + " adc %11,%0" "\n\t" /* %11 += carry*/ + " mul %6,%8" "\n\t" /* r1:r0 = HI(f) * HI(t)*/ + " add %10,r0" "\n\t" /* %10 += LO(HI(f) * HI(t))*/ + " adc %11,r1" "\n\t" /* %11 += HI(HI(f) * HI(t))*/ + " mov %5,%10" "\n\t" /* %6:%5 =*/ + " mov %6,%11" "\n\t" /* 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)*/ + " clr %9" "\n\t" /* "decimal place we get for free"*/ + " lds %2,bezier_F" "\n\t" + " lds %3,bezier_F+1" "\n\t" + " lds %4,bezier_F+2" "\n\t" /* %4:%3:%2 = acc*/ + + /* if (A_negative) {*/ + " lds r0,A_negative" "\n\t" + " or r0,%0" "\n\t" /* Is flag signalling negative? */ + " brne 3f" "\n\t" /* If yes, Skip next instruction if A was negative*/ + " rjmp 1f" "\n\t" /* Otherwise, jump */ + + /* uint24_t v; */ + /* umul16x24to24hi(v, f, bezier_C); / Range 21bits [29] */ + /* acc -= v; */ + "3:" "\n\t" + " lds %10, bezier_C" "\n\t" /* %10 = LO(bezier_C)*/ + " mul %10,%5" "\n\t" /* r1:r0 = LO(bezier_C) * LO(f)*/ + " sub %9,r1" "\n\t" + " sbc %2,%0" "\n\t" + " sbc %3,%0" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= HI(LO(bezier_C) * LO(f))*/ + " lds %11, bezier_C+1" "\n\t" /* %11 = MI(bezier_C)*/ + " mul %11,%5" "\n\t" /* r1:r0 = MI(bezier_C) * LO(f)*/ + " sub %9,r0" "\n\t" + " sbc %2,r1" "\n\t" + " sbc %3,%0" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= MI(bezier_C) * LO(f)*/ + " lds %1, bezier_C+2" "\n\t" /* %1 = HI(bezier_C)*/ + " mul %1,%5" "\n\t" /* r1:r0 = MI(bezier_C) * LO(f)*/ + " sub %2,r0" "\n\t" + " sbc %3,r1" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= HI(bezier_C) * LO(f) << 8*/ + " mul %10,%6" "\n\t" /* r1:r0 = LO(bezier_C) * MI(f)*/ + " sub %9,r0" "\n\t" + " sbc %2,r1" "\n\t" + " sbc %3,%0" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= LO(bezier_C) * MI(f)*/ + " mul %11,%6" "\n\t" /* r1:r0 = MI(bezier_C) * MI(f)*/ + " sub %2,r0" "\n\t" + " sbc %3,r1" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= MI(bezier_C) * MI(f) << 8*/ + " mul %1,%6" "\n\t" /* r1:r0 = HI(bezier_C) * LO(f)*/ + " sub %3,r0" "\n\t" + " sbc %4,r1" "\n\t" /* %4:%3:%2:%9 -= HI(bezier_C) * LO(f) << 16*/ + + /* umul16x16to16hi(f, f, t); / Range 16 bits : f = t^3 (unsigned) [17]*/ + " mul %5,%7" "\n\t" /* r1:r0 = LO(f) * LO(t)*/ + " mov %1,r1" "\n\t" /* store MIL(LO(f) * LO(t)) in %1, we need it for rounding*/ + " clr %10" "\n\t" /* %10 = 0*/ + " clr %11" "\n\t" /* %11 = 0*/ + " mul %5,%8" "\n\t" /* r1:r0 = LO(f) * HI(t)*/ + " add %1,r0" "\n\t" /* %1 += LO(LO(f) * HI(t))*/ + " adc %10,r1" "\n\t" /* %10 = HI(LO(f) * HI(t))*/ + " adc %11,%0" "\n\t" /* %11 += carry*/ + " mul %6,%7" "\n\t" /* r1:r0 = HI(f) * LO(t)*/ + " add %1,r0" "\n\t" /* %1 += LO(HI(f) * LO(t))*/ + " adc %10,r1" "\n\t" /* %10 += HI(HI(f) * LO(t))*/ + " adc %11,%0" "\n\t" /* %11 += carry*/ + " mul %6,%8" "\n\t" /* r1:r0 = HI(f) * HI(t)*/ + " add %10,r0" "\n\t" /* %10 += LO(HI(f) * HI(t))*/ + " adc %11,r1" "\n\t" /* %11 += HI(HI(f) * HI(t))*/ + " mov %5,%10" "\n\t" /* %6:%5 =*/ + " mov %6,%11" "\n\t" /* f = %10:%11*/ + + /* umul16x24to24hi(v, f, bezier_B); / Range 22bits [29]*/ + /* acc += v; */ + " lds %10, bezier_B" "\n\t" /* %10 = LO(bezier_B)*/ + " mul %10,%5" "\n\t" /* r1:r0 = LO(bezier_B) * LO(f)*/ + " add %9,r1" "\n\t" + " adc %2,%0" "\n\t" + " adc %3,%0" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += HI(LO(bezier_B) * LO(f))*/ + " lds %11, bezier_B+1" "\n\t" /* %11 = MI(bezier_B)*/ + " mul %11,%5" "\n\t" /* r1:r0 = MI(bezier_B) * LO(f)*/ + " add %9,r0" "\n\t" + " adc %2,r1" "\n\t" + " adc %3,%0" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += MI(bezier_B) * LO(f)*/ + " lds %1, bezier_B+2" "\n\t" /* %1 = HI(bezier_B)*/ + " mul %1,%5" "\n\t" /* r1:r0 = MI(bezier_B) * LO(f)*/ + " add %2,r0" "\n\t" + " adc %3,r1" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += HI(bezier_B) * LO(f) << 8*/ + " mul %10,%6" "\n\t" /* r1:r0 = LO(bezier_B) * MI(f)*/ + " add %9,r0" "\n\t" + " adc %2,r1" "\n\t" + " adc %3,%0" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += LO(bezier_B) * MI(f)*/ + " mul %11,%6" "\n\t" /* r1:r0 = MI(bezier_B) * MI(f)*/ + " add %2,r0" "\n\t" + " adc %3,r1" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += MI(bezier_B) * MI(f) << 8*/ + " mul %1,%6" "\n\t" /* r1:r0 = HI(bezier_B) * LO(f)*/ + " add %3,r0" "\n\t" + " adc %4,r1" "\n\t" /* %4:%3:%2:%9 += HI(bezier_B) * LO(f) << 16*/ + + /* umul16x16to16hi(f, f, t); / Range 16 bits : f = t^5 (unsigned) [17]*/ + " mul %5,%7" "\n\t" /* r1:r0 = LO(f) * LO(t)*/ + " mov %1,r1" "\n\t" /* store MIL(LO(f) * LO(t)) in %1, we need it for rounding*/ + " clr %10" "\n\t" /* %10 = 0*/ + " clr %11" "\n\t" /* %11 = 0*/ + " mul %5,%8" "\n\t" /* r1:r0 = LO(f) * HI(t)*/ + " add %1,r0" "\n\t" /* %1 += LO(LO(f) * HI(t))*/ + " adc %10,r1" "\n\t" /* %10 = HI(LO(f) * HI(t))*/ + " adc %11,%0" "\n\t" /* %11 += carry*/ + " mul %6,%7" "\n\t" /* r1:r0 = HI(f) * LO(t)*/ + " add %1,r0" "\n\t" /* %1 += LO(HI(f) * LO(t))*/ + " adc %10,r1" "\n\t" /* %10 += HI(HI(f) * LO(t))*/ + " adc %11,%0" "\n\t" /* %11 += carry*/ + " mul %6,%8" "\n\t" /* r1:r0 = HI(f) * HI(t)*/ + " add %10,r0" "\n\t" /* %10 += LO(HI(f) * HI(t))*/ + " adc %11,r1" "\n\t" /* %11 += HI(HI(f) * HI(t))*/ + " mov %5,%10" "\n\t" /* %6:%5 =*/ + " mov %6,%11" "\n\t" /* f = %10:%11*/ + + /* umul16x24to24hi(v, f, bezier_A); / Range 21bits [29]*/ + /* acc -= v; */ + " lds %10, bezier_A" "\n\t" /* %10 = LO(bezier_A)*/ + " mul %10,%5" "\n\t" /* r1:r0 = LO(bezier_A) * LO(f)*/ + " sub %9,r1" "\n\t" + " sbc %2,%0" "\n\t" + " sbc %3,%0" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= HI(LO(bezier_A) * LO(f))*/ + " lds %11, bezier_A+1" "\n\t" /* %11 = MI(bezier_A)*/ + " mul %11,%5" "\n\t" /* r1:r0 = MI(bezier_A) * LO(f)*/ + " sub %9,r0" "\n\t" + " sbc %2,r1" "\n\t" + " sbc %3,%0" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= MI(bezier_A) * LO(f)*/ + " lds %1, bezier_A+2" "\n\t" /* %1 = HI(bezier_A)*/ + " mul %1,%5" "\n\t" /* r1:r0 = MI(bezier_A) * LO(f)*/ + " sub %2,r0" "\n\t" + " sbc %3,r1" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= HI(bezier_A) * LO(f) << 8*/ + " mul %10,%6" "\n\t" /* r1:r0 = LO(bezier_A) * MI(f)*/ + " sub %9,r0" "\n\t" + " sbc %2,r1" "\n\t" + " sbc %3,%0" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= LO(bezier_A) * MI(f)*/ + " mul %11,%6" "\n\t" /* r1:r0 = MI(bezier_A) * MI(f)*/ + " sub %2,r0" "\n\t" + " sbc %3,r1" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= MI(bezier_A) * MI(f) << 8*/ + " mul %1,%6" "\n\t" /* r1:r0 = HI(bezier_A) * LO(f)*/ + " sub %3,r0" "\n\t" + " sbc %4,r1" "\n\t" /* %4:%3:%2:%9 -= HI(bezier_A) * LO(f) << 16*/ + " jmp 2f" "\n\t" /* Done!*/ + + "1:" "\n\t" + + /* uint24_t v; */ + /* umul16x24to24hi(v, f, bezier_C); / Range 21bits [29]*/ + /* acc += v; */ + " lds %10, bezier_C" "\n\t" /* %10 = LO(bezier_C)*/ + " mul %10,%5" "\n\t" /* r1:r0 = LO(bezier_C) * LO(f)*/ + " add %9,r1" "\n\t" + " adc %2,%0" "\n\t" + " adc %3,%0" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += HI(LO(bezier_C) * LO(f))*/ + " lds %11, bezier_C+1" "\n\t" /* %11 = MI(bezier_C)*/ + " mul %11,%5" "\n\t" /* r1:r0 = MI(bezier_C) * LO(f)*/ + " add %9,r0" "\n\t" + " adc %2,r1" "\n\t" + " adc %3,%0" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += MI(bezier_C) * LO(f)*/ + " lds %1, bezier_C+2" "\n\t" /* %1 = HI(bezier_C)*/ + " mul %1,%5" "\n\t" /* r1:r0 = MI(bezier_C) * LO(f)*/ + " add %2,r0" "\n\t" + " adc %3,r1" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += HI(bezier_C) * LO(f) << 8*/ + " mul %10,%6" "\n\t" /* r1:r0 = LO(bezier_C) * MI(f)*/ + " add %9,r0" "\n\t" + " adc %2,r1" "\n\t" + " adc %3,%0" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += LO(bezier_C) * MI(f)*/ + " mul %11,%6" "\n\t" /* r1:r0 = MI(bezier_C) * MI(f)*/ + " add %2,r0" "\n\t" + " adc %3,r1" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += MI(bezier_C) * MI(f) << 8*/ + " mul %1,%6" "\n\t" /* r1:r0 = HI(bezier_C) * LO(f)*/ + " add %3,r0" "\n\t" + " adc %4,r1" "\n\t" /* %4:%3:%2:%9 += HI(bezier_C) * LO(f) << 16*/ + + /* umul16x16to16hi(f, f, t); / Range 16 bits : f = t^3 (unsigned) [17]*/ + " mul %5,%7" "\n\t" /* r1:r0 = LO(f) * LO(t)*/ + " mov %1,r1" "\n\t" /* store MIL(LO(f) * LO(t)) in %1, we need it for rounding*/ + " clr %10" "\n\t" /* %10 = 0*/ + " clr %11" "\n\t" /* %11 = 0*/ + " mul %5,%8" "\n\t" /* r1:r0 = LO(f) * HI(t)*/ + " add %1,r0" "\n\t" /* %1 += LO(LO(f) * HI(t))*/ + " adc %10,r1" "\n\t" /* %10 = HI(LO(f) * HI(t))*/ + " adc %11,%0" "\n\t" /* %11 += carry*/ + " mul %6,%7" "\n\t" /* r1:r0 = HI(f) * LO(t)*/ + " add %1,r0" "\n\t" /* %1 += LO(HI(f) * LO(t))*/ + " adc %10,r1" "\n\t" /* %10 += HI(HI(f) * LO(t))*/ + " adc %11,%0" "\n\t" /* %11 += carry*/ + " mul %6,%8" "\n\t" /* r1:r0 = HI(f) * HI(t)*/ + " add %10,r0" "\n\t" /* %10 += LO(HI(f) * HI(t))*/ + " adc %11,r1" "\n\t" /* %11 += HI(HI(f) * HI(t))*/ + " mov %5,%10" "\n\t" /* %6:%5 =*/ + " mov %6,%11" "\n\t" /* f = %10:%11*/ + + /* umul16x24to24hi(v, f, bezier_B); / Range 22bits [29]*/ + /* acc -= v;*/ + " lds %10, bezier_B" "\n\t" /* %10 = LO(bezier_B)*/ + " mul %10,%5" "\n\t" /* r1:r0 = LO(bezier_B) * LO(f)*/ + " sub %9,r1" "\n\t" + " sbc %2,%0" "\n\t" + " sbc %3,%0" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= HI(LO(bezier_B) * LO(f))*/ + " lds %11, bezier_B+1" "\n\t" /* %11 = MI(bezier_B)*/ + " mul %11,%5" "\n\t" /* r1:r0 = MI(bezier_B) * LO(f)*/ + " sub %9,r0" "\n\t" + " sbc %2,r1" "\n\t" + " sbc %3,%0" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= MI(bezier_B) * LO(f)*/ + " lds %1, bezier_B+2" "\n\t" /* %1 = HI(bezier_B)*/ + " mul %1,%5" "\n\t" /* r1:r0 = MI(bezier_B) * LO(f)*/ + " sub %2,r0" "\n\t" + " sbc %3,r1" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= HI(bezier_B) * LO(f) << 8*/ + " mul %10,%6" "\n\t" /* r1:r0 = LO(bezier_B) * MI(f)*/ + " sub %9,r0" "\n\t" + " sbc %2,r1" "\n\t" + " sbc %3,%0" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= LO(bezier_B) * MI(f)*/ + " mul %11,%6" "\n\t" /* r1:r0 = MI(bezier_B) * MI(f)*/ + " sub %2,r0" "\n\t" + " sbc %3,r1" "\n\t" + " sbc %4,%0" "\n\t" /* %4:%3:%2:%9 -= MI(bezier_B) * MI(f) << 8*/ + " mul %1,%6" "\n\t" /* r1:r0 = HI(bezier_B) * LO(f)*/ + " sub %3,r0" "\n\t" + " sbc %4,r1" "\n\t" /* %4:%3:%2:%9 -= HI(bezier_B) * LO(f) << 16*/ + + /* umul16x16to16hi(f, f, t); / Range 16 bits : f = t^5 (unsigned) [17]*/ + " mul %5,%7" "\n\t" /* r1:r0 = LO(f) * LO(t)*/ + " mov %1,r1" "\n\t" /* store MIL(LO(f) * LO(t)) in %1, we need it for rounding*/ + " clr %10" "\n\t" /* %10 = 0*/ + " clr %11" "\n\t" /* %11 = 0*/ + " mul %5,%8" "\n\t" /* r1:r0 = LO(f) * HI(t)*/ + " add %1,r0" "\n\t" /* %1 += LO(LO(f) * HI(t))*/ + " adc %10,r1" "\n\t" /* %10 = HI(LO(f) * HI(t))*/ + " adc %11,%0" "\n\t" /* %11 += carry*/ + " mul %6,%7" "\n\t" /* r1:r0 = HI(f) * LO(t)*/ + " add %1,r0" "\n\t" /* %1 += LO(HI(f) * LO(t))*/ + " adc %10,r1" "\n\t" /* %10 += HI(HI(f) * LO(t))*/ + " adc %11,%0" "\n\t" /* %11 += carry*/ + " mul %6,%8" "\n\t" /* r1:r0 = HI(f) * HI(t)*/ + " add %10,r0" "\n\t" /* %10 += LO(HI(f) * HI(t))*/ + " adc %11,r1" "\n\t" /* %11 += HI(HI(f) * HI(t))*/ + " mov %5,%10" "\n\t" /* %6:%5 =*/ + " mov %6,%11" "\n\t" /* f = %10:%11*/ + + /* umul16x24to24hi(v, f, bezier_A); / Range 21bits [29]*/ + /* acc += v; */ + " lds %10, bezier_A" "\n\t" /* %10 = LO(bezier_A)*/ + " mul %10,%5" "\n\t" /* r1:r0 = LO(bezier_A) * LO(f)*/ + " add %9,r1" "\n\t" + " adc %2,%0" "\n\t" + " adc %3,%0" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += HI(LO(bezier_A) * LO(f))*/ + " lds %11, bezier_A+1" "\n\t" /* %11 = MI(bezier_A)*/ + " mul %11,%5" "\n\t" /* r1:r0 = MI(bezier_A) * LO(f)*/ + " add %9,r0" "\n\t" + " adc %2,r1" "\n\t" + " adc %3,%0" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += MI(bezier_A) * LO(f)*/ + " lds %1, bezier_A+2" "\n\t" /* %1 = HI(bezier_A)*/ + " mul %1,%5" "\n\t" /* r1:r0 = MI(bezier_A) * LO(f)*/ + " add %2,r0" "\n\t" + " adc %3,r1" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += HI(bezier_A) * LO(f) << 8*/ + " mul %10,%6" "\n\t" /* r1:r0 = LO(bezier_A) * MI(f)*/ + " add %9,r0" "\n\t" + " adc %2,r1" "\n\t" + " adc %3,%0" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += LO(bezier_A) * MI(f)*/ + " mul %11,%6" "\n\t" /* r1:r0 = MI(bezier_A) * MI(f)*/ + " add %2,r0" "\n\t" + " adc %3,r1" "\n\t" + " adc %4,%0" "\n\t" /* %4:%3:%2:%9 += MI(bezier_A) * MI(f) << 8*/ + " mul %1,%6" "\n\t" /* r1:r0 = HI(bezier_A) * LO(f)*/ + " add %3,r0" "\n\t" + " adc %4,r1" "\n\t" /* %4:%3:%2:%9 += HI(bezier_A) * LO(f) << 16*/ + "2:" "\n\t" + " 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); + } + + #else + + // For all the other 32bit CPUs + FORCE_INLINE void Stepper::_calc_bezier_curve_coeffs(const int32_t v0, const int32_t v1, const uint32_t av) { + // Calculate the Bézier coefficients + bezier_A = 768 * (v1 - v0); + bezier_B = 1920 * (v0 - v1); + bezier_C = 1280 * (v1 - v0); + bezier_F = 128 * v0; + bezier_AV = av; + } + + FORCE_INLINE int32_t Stepper::_eval_bezier_curve(const uint32_t curr_step) { + #if defined(__ARM__) || defined(__thumb__) + + // For ARM Cortex M3/M4 CPUs, we have the optimized assembler version, that takes 43 cycles to execute + 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; + + __asm__ __volatile__( + ".syntax unified" "\n\t" // is to prevent CM0,CM1 non-unified syntax + " lsrs %[ahi],%[alo],#1" "\n\t" // a = F << 31 1 cycles + " lsls %[alo],%[alo],#31" "\n\t" // 1 cycles + " umull %[flo],%[fhi],%[fhi],%[t]" "\n\t" // f *= t 5 cycles [fhi:flo=64bits] + " umull %[flo],%[fhi],%[fhi],%[t]" "\n\t" // f>>=32; f*=t 5 cycles [fhi:flo=64bits] + " lsrs %[flo],%[fhi],#1" "\n\t" // 1 cycles [31bits] + " smlal %[alo],%[ahi],%[flo],%[C]" "\n\t" // a+=(f>>33)*C; 5 cycles + " umull %[flo],%[fhi],%[fhi],%[t]" "\n\t" // f>>=32; f*=t 5 cycles [fhi:flo=64bits] + " lsrs %[flo],%[fhi],#1" "\n\t" // 1 cycles [31bits] + " smlal %[alo],%[ahi],%[flo],%[B]" "\n\t" // a+=(f>>33)*B; 5 cycles + " umull %[flo],%[fhi],%[fhi],%[t]" "\n\t" // f>>=32; f*=t 5 cycles [fhi:flo=64bits] + " lsrs %[flo],%[fhi],#1" "\n\t" // f>>=33; 1 cycles [31bits] + " smlal %[alo],%[ahi],%[flo],%[A]" "\n\t" // a+=(f>>33)*A; 5 cycles + " lsrs %[alo],%[ahi],#6" "\n\t" // a>>=38 1 cycles + : [alo]"+r"( alo ) , + [flo]"+r"( flo ) , + [fhi]"+r"( fhi ) , + [ahi]"+r"( ahi ) , + [A]"+r"( A ) , // <== Note: Even if A, B, C, and t registers are INPUT ONLY + [B]"+r"( B ) , // GCC does bad optimizations on the code if we list them as + [C]"+r"( C ) , // such, breaking this function. So, to avoid that problem, + [t]"+r"( t ) // we list all registers as input-outputs. + : + : "cc" + ); + return alo; + + #else + + // For non ARM targets, we provide a fallback implementation. Really doubt it + // will be useful, unless the processor is fast and 32bit + + uint32_t t = bezier_AV * curr_step; // t: Range 0 - 1^32 = 32 bits + uint64_t f = t; + f *= t; // Range 32*2 = 64 bits (unsigned) + f >>= 32; // Range 32 bits (unsigned) + f *= t; // Range 32*2 = 64 bits (unsigned) + f >>= 32; // Range 32 bits : f = t^3 (unsigned) + int64_t acc = (int64_t) bezier_F << 31; // Range 63 bits (signed) + acc += ((uint32_t) f >> 1) * (int64_t) bezier_C; // Range 29bits + 31 = 60bits (plus sign) + f *= t; // Range 32*2 = 64 bits + f >>= 32; // Range 32 bits : f = t^3 (unsigned) + acc += ((uint32_t) f >> 1) * (int64_t) bezier_B; // Range 29bits + 31 = 60bits (plus sign) + f *= t; // Range 32*2 = 64 bits + f >>= 32; // Range 32 bits : f = t^3 (unsigned) + acc += ((uint32_t) f >> 1) * (int64_t) bezier_A; // Range 28bits + 31 = 59bits (plus sign) + acc >>= (31 + 7); // Range 24bits (plus sign) + return (int32_t) acc; + + #endif + } + #endif #endif // BEZIER_JERK_CONTROL /** @@ -660,7 +1268,7 @@ void Stepper::isr() { #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); + _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; @@ -953,7 +1561,7 @@ void Stepper::isr() { 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); + _calc_bezier_curve_coeffs(current_block->cruise_rate, current_block->final_rate, current_block->deceleration_time_inverse); bezier_2nd_half = true; } diff --git a/Marlin/src/module/stepper.h b/Marlin/src/module/stepper.h index d7fca16f2b..88bbab8743 100644 --- a/Marlin/src/module/stepper.h +++ b/Marlin/src/module/stepper.h @@ -98,12 +98,15 @@ class Stepper { 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 - bezier_F; // F coefficient in Bézier speed curve - static uint32_t bezier_AV; // AV coefficient in Bézier speed curve - static bool bezier_2nd_half; // If Bézier curve has been initialized or not + 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 + static uint32_t bezier_AV; // AV coefficient in Bézier speed curve + #ifdef __AVR__ + static bool A_negative; // If A coefficient was negative + #endif + static bool bezier_2nd_half; // If Bézier curve has been initialized or not #endif #if ENABLED(LIN_ADVANCE) @@ -361,7 +364,7 @@ class Stepper { } #if ENABLED(BEZIER_JERK_CONTROL) - static void _calc_bezier_curve_coeffs(const int32_t v0, const int32_t v1, const uint32_t steps); + 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