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@ -386,89 +386,89 @@ void Planner::init() {
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// use Newton-Raphson for the calculation, and will strive to get way less cycles
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// use Newton-Raphson for the calculation, and will strive to get way less cycles
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// for the same result - Using C division, it takes 500cycles to complete .
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// for the same result - Using C division, it takes 500cycles to complete .
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A("clr %3") // idx = 0
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A("clr %3") // idx = 0
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A("mov %14,%6")
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A("mov %14,%6")
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A("mov %15,%7")
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A("mov %15,%7")
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A("mov %16,%8") // nr = interval
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A("mov %16,%8") // nr = interval
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A("tst %16") // nr & 0xFF0000 == 0 ?
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A("tst %16") // nr & 0xFF0000 == 0 ?
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A("brne 2f") // No, skip this
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A("brne 2f") // No, skip this
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A("mov %16,%15")
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A("mov %16,%15")
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A("mov %15,%14") // nr <<= 8, %14 not needed
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A("mov %15,%14") // nr <<= 8, %14 not needed
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A("subi %3,-8") // idx += 8
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A("subi %3,-8") // idx += 8
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A("tst %16") // nr & 0xFF0000 == 0 ?
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A("tst %16") // nr & 0xFF0000 == 0 ?
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A("brne 2f") // No, skip this
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A("brne 2f") // No, skip this
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A("mov %16,%15") // nr <<= 8, %14 not needed
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A("mov %16,%15") // nr <<= 8, %14 not needed
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A("clr %15") // We clear %14
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A("clr %15") // We clear %14
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A("subi %3,-8") // idx += 8
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A("subi %3,-8") // idx += 8
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// here %16 != 0 and %16:%15 contains at least 9 MSBits, or both %16:%15 are 0
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// here %16 != 0 and %16:%15 contains at least 9 MSBits, or both %16:%15 are 0
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L("2")
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L("2")
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A("cpi %16,0x10") // (nr & 0xF00000) == 0 ?
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A("cpi %16,0x10") // (nr & 0xF00000) == 0 ?
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A("brcc 3f") // No, skip this
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A("brcc 3f") // No, skip this
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A("swap %15") // Swap nibbles
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A("swap %15") // Swap nibbles
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A("swap %16") // Swap nibbles. Low nibble is 0
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A("swap %16") // Swap nibbles. Low nibble is 0
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A("mov %14, %15")
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A("mov %14, %15")
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A("andi %14,0x0F") // Isolate low nibble
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A("andi %14,0x0F") // Isolate low nibble
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A("andi %15,0xF0") // Keep proper nibble in %15
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A("andi %15,0xF0") // Keep proper nibble in %15
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A("or %16, %14") // %16:%15 <<= 4
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A("or %16, %14") // %16:%15 <<= 4
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A("subi %3,-4") // idx += 4
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A("subi %3,-4") // idx += 4
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L("3")
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L("3")
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A("cpi %16,0x40") // (nr & 0xC00000) == 0 ?
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A("cpi %16,0x40") // (nr & 0xC00000) == 0 ?
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A("brcc 4f") // No, skip this
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A("brcc 4f") // No, skip this
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A("add %15,%15")
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A("add %15,%15")
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A("adc %16,%16")
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A("adc %16,%16")
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A("add %15,%15")
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A("add %15,%15")
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A("adc %16,%16") // %16:%15 <<= 2
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A("adc %16,%16") // %16:%15 <<= 2
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A("subi %3,-2") // idx += 2
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A("subi %3,-2") // idx += 2
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L("4")
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L("4")
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A("cpi %16,0x80") // (nr & 0x800000) == 0 ?
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A("cpi %16,0x80") // (nr & 0x800000) == 0 ?
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A("brcc 5f") // No, skip this
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A("brcc 5f") // No, skip this
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A("add %15,%15")
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A("add %15,%15")
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A("adc %16,%16") // %16:%15 <<= 1
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A("adc %16,%16") // %16:%15 <<= 1
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A("inc %3") // idx += 1
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A("inc %3") // idx += 1
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// Now %16:%15 contains its MSBit set to 1, or %16:%15 is == 0. We are now absolutely sure
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// Now %16:%15 contains its MSBit set to 1, or %16:%15 is == 0. We are now absolutely sure
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// we have at least 9 MSBits available to enter the initial estimation table
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// we have at least 9 MSBits available to enter the initial estimation table
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L("5")
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L("5")
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A("add %15,%15")
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A("add %15,%15")
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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)
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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)
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A("add r30,%16") // Only use top 8 bits
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A("add r30,%16") // Only use top 8 bits
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A("adc r31,%13") // r31:r30 = inv_tab + (tidx)
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A("adc r31,%13") // r31:r30 = inv_tab + (tidx)
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A("lpm %14, Z") // %14 = inv_tab[tidx]
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A("lpm %14, Z") // %14 = inv_tab[tidx]
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A("ldi %15, 1") // %15 = 1 %15:%14 = inv_tab[tidx] + 256
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A("ldi %15, 1") // %15 = 1 %15:%14 = inv_tab[tidx] + 256
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// We must scale the approximation to the proper place
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// We must scale the approximation to the proper place
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A("clr %16") // %16 will always be 0 here
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A("clr %16") // %16 will always be 0 here
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A("subi %3,8") // idx == 8 ?
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A("subi %3,8") // idx == 8 ?
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A("breq 6f") // yes, no need to scale
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A("breq 6f") // yes, no need to scale
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A("brcs 7f") // If C=1, means idx < 8, result was negative!
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A("brcs 7f") // If C=1, means idx < 8, result was negative!
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// idx > 8, now %3 = idx - 8. We must perform a left shift. idx range:[1-8]
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// idx > 8, now %3 = idx - 8. We must perform a left shift. idx range:[1-8]
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A("sbrs %3,0") // shift by 1bit position?
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A("sbrs %3,0") // shift by 1bit position?
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A("rjmp 8f") // No
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A("rjmp 8f") // No
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A("add %14,%14")
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A("add %14,%14")
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A("adc %15,%15") // %15:16 <<= 1
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A("adc %15,%15") // %15:16 <<= 1
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L("8")
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L("8")
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A("sbrs %3,1") // shift by 2bit position?
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A("sbrs %3,1") // shift by 2bit position?
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A("rjmp 9f") // No
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A("rjmp 9f") // No
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A("add %14,%14")
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A("add %14,%14")
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A("adc %15,%15")
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A("adc %15,%15")
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A("add %14,%14")
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A("add %14,%14")
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A("adc %15,%15") // %15:16 <<= 1
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A("adc %15,%15") // %15:16 <<= 1
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L("9")
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L("9")
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A("sbrs %3,2") // shift by 4bits position?
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A("sbrs %3,2") // shift by 4bits position?
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A("rjmp 16f") // No
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A("rjmp 16f") // No
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A("swap %15") // Swap nibbles. lo nibble of %15 will always be 0
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A("swap %15") // Swap nibbles. lo nibble of %15 will always be 0
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A("swap %14") // Swap nibbles
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A("swap %14") // Swap nibbles
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A("mov %12,%14")
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A("mov %12,%14")
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A("andi %12,0x0F") // isolate low nibble
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A("andi %12,0x0F") // isolate low nibble
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A("andi %14,0xF0") // and clear it
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A("andi %14,0xF0") // and clear it
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A("or %15,%12") // %15:%16 <<= 4
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A("or %15,%12") // %15:%16 <<= 4
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L("16")
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L("16")
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A("sbrs %3,3") // shift by 8bits position?
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A("sbrs %3,3") // shift by 8bits position?
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A("rjmp 6f") // No, we are done
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A("rjmp 6f") // No, we are done
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A("mov %16,%15")
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A("mov %16,%15")
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A("mov %15,%14")
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A("mov %15,%14")
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A("clr %14")
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A("clr %14")
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@ -476,32 +476,32 @@ void Planner::init() {
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// idx < 8, now %3 = idx - 8. Get the count of bits
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// idx < 8, now %3 = idx - 8. Get the count of bits
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L("7")
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L("7")
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A("neg %3") // %3 = -idx = count of bits to move right. idx range:[1...8]
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A("neg %3") // %3 = -idx = count of bits to move right. idx range:[1...8]
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A("sbrs %3,0") // shift by 1 bit position ?
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A("sbrs %3,0") // shift by 1 bit position ?
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A("rjmp 10f") // No, skip it
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A("rjmp 10f") // No, skip it
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A("asr %15") // (bit7 is always 0 here)
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A("asr %15") // (bit7 is always 0 here)
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A("ror %14")
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A("ror %14")
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L("10")
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L("10")
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A("sbrs %3,1") // shift by 2 bit position ?
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A("sbrs %3,1") // shift by 2 bit position ?
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A("rjmp 11f") // No, skip it
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A("rjmp 11f") // No, skip it
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A("asr %15") // (bit7 is always 0 here)
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A("asr %15") // (bit7 is always 0 here)
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A("ror %14")
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A("ror %14")
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A("asr %15") // (bit7 is always 0 here)
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A("asr %15") // (bit7 is always 0 here)
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A("ror %14")
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A("ror %14")
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L("11")
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L("11")
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A("sbrs %3,2") // shift by 4 bit position ?
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A("sbrs %3,2") // shift by 4 bit position ?
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A("rjmp 12f") // No, skip it
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A("rjmp 12f") // No, skip it
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A("swap %15") // Swap nibbles
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A("swap %15") // Swap nibbles
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A("andi %14, 0xF0") // Lose the lowest nibble
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A("andi %14, 0xF0") // Lose the lowest nibble
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A("swap %14") // Swap nibbles. Upper nibble is 0
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A("swap %14") // Swap nibbles. Upper nibble is 0
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A("or %14,%15") // Pass nibble from upper byte
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A("or %14,%15") // Pass nibble from upper byte
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A("andi %15, 0x0F") // And get rid of that nibble
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A("andi %15, 0x0F") // And get rid of that nibble
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L("12")
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L("12")
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A("sbrs %3,3") // shift by 8 bit position ?
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A("sbrs %3,3") // shift by 8 bit position ?
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A("rjmp 6f") // No, skip it
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A("rjmp 6f") // No, skip it
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A("mov %14,%15")
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A("mov %14,%15")
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A("clr %15")
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A("clr %15")
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L("6") // %16:%15:%14 = initial estimation of 0x1000000 / d
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L("6") // %16:%15:%14 = initial estimation of 0x1000000 / d
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// Now, we must refine the estimation present on %16:%15:%14 using 1 iteration
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// Now, we must refine the estimation present on %16:%15:%14 using 1 iteration
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// of Newton-Raphson. As it has a quadratic convergence, 1 iteration is enough
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// of Newton-Raphson. As it has a quadratic convergence, 1 iteration is enough
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@ -517,33 +517,33 @@ void Planner::init() {
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A("clr %0")
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A("clr %0")
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A("clr %1")
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A("clr %1")
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A("clr %2")
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A("clr %2")
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A("ldi %3,2") // %3:%2:%1:%0 = 0x2000000
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A("ldi %3,2") // %3:%2:%1:%0 = 0x2000000
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A("mul %6,%14") // r1:r0 = LO(d) * LO(x)
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A("mul %6,%14") // r1:r0 = LO(d) * LO(x)
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A("sub %0,r0")
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A("sub %0,r0")
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A("sbc %1,r1")
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A("sbc %1,r1")
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A("sbc %2,%13")
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A("sbc %2,%13")
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A("sbc %3,%13") // %3:%2:%1:%0 -= LO(d) * LO(x)
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A("sbc %3,%13") // %3:%2:%1:%0 -= LO(d) * LO(x)
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A("mul %7,%14") // r1:r0 = MI(d) * LO(x)
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A("mul %7,%14") // r1:r0 = MI(d) * LO(x)
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A("sub %1,r0")
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A("sub %1,r0")
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A("sbc %2,r1" )
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A("sbc %2,r1" )
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A("sbc %3,%13") // %3:%2:%1:%0 -= MI(d) * LO(x) << 8
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A("sbc %3,%13") // %3:%2:%1:%0 -= MI(d) * LO(x) << 8
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A("mul %8,%14") // r1:r0 = HI(d) * LO(x)
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A("mul %8,%14") // r1:r0 = HI(d) * LO(x)
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A("sub %2,r0")
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A("sub %2,r0")
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A("sbc %3,r1") // %3:%2:%1:%0 -= MIL(d) * LO(x) << 16
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A("sbc %3,r1") // %3:%2:%1:%0 -= MIL(d) * LO(x) << 16
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A("mul %6,%15") // r1:r0 = LO(d) * MI(x)
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A("mul %6,%15") // r1:r0 = LO(d) * MI(x)
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A("sub %1,r0")
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A("sub %1,r0")
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A("sbc %2,r1")
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A("sbc %2,r1")
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A("sbc %3,%13") // %3:%2:%1:%0 -= LO(d) * MI(x) << 8
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A("sbc %3,%13") // %3:%2:%1:%0 -= LO(d) * MI(x) << 8
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A("mul %7,%15") // r1:r0 = MI(d) * MI(x)
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A("mul %7,%15") // r1:r0 = MI(d) * MI(x)
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A("sub %2,r0")
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A("sub %2,r0")
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A("sbc %3,r1") // %3:%2:%1:%0 -= MI(d) * MI(x) << 16
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A("sbc %3,r1") // %3:%2:%1:%0 -= MI(d) * MI(x) << 16
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A("mul %8,%15") // r1:r0 = HI(d) * MI(x)
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A("mul %8,%15") // r1:r0 = HI(d) * MI(x)
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A("sub %3,r0") // %3:%2:%1:%0 -= MIL(d) * MI(x) << 24
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A("sub %3,r0") // %3:%2:%1:%0 -= MIL(d) * MI(x) << 24
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A("mul %6,%16") // r1:r0 = LO(d) * HI(x)
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A("mul %6,%16") // r1:r0 = LO(d) * HI(x)
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A("sub %2,r0")
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A("sub %2,r0")
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A("sbc %3,r1") // %3:%2:%1:%0 -= LO(d) * HI(x) << 16
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A("sbc %3,r1") // %3:%2:%1:%0 -= LO(d) * HI(x) << 16
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A("mul %7,%16") // r1:r0 = MI(d) * HI(x)
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A("mul %7,%16") // r1:r0 = MI(d) * HI(x)
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A("sub %3,r0") // %3:%2:%1:%0 -= MI(d) * HI(x) << 24
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A("sub %3,r0") // %3:%2:%1:%0 -= MI(d) * HI(x) << 24
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// %3:%2:%1:%0 = (1<<25) - x*d [169]
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// %3:%2:%1:%0 = (1<<25) - x*d [169]
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// We need to multiply that result by x, and we are only interested in the top 24bits of that multiply
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// We need to multiply that result by x, and we are only interested in the top 24bits of that multiply
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@ -553,62 +553,62 @@ void Planner::init() {
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// %13 = 0
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// %13 = 0
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// result = %11:%10:%9:%5:%4
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// result = %11:%10:%9:%5:%4
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A("mul %14,%0") // r1:r0 = LO(x) * LO(acc)
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A("mul %14,%0") // r1:r0 = LO(x) * LO(acc)
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A("mov %4,r1")
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A("mov %4,r1")
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A("clr %5")
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A("clr %5")
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A("clr %9")
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A("clr %9")
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A("clr %10")
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A("clr %10")
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A("clr %11") // %11:%10:%9:%5:%4 = LO(x) * LO(acc) >> 8
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A("clr %11") // %11:%10:%9:%5:%4 = LO(x) * LO(acc) >> 8
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A("mul %15,%0") // r1:r0 = MI(x) * LO(acc)
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A("mul %15,%0") // r1:r0 = MI(x) * LO(acc)
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A("add %4,r0")
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A("add %4,r0")
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A("adc %5,r1")
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A("adc %5,r1")
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A("adc %9,%13")
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A("adc %9,%13")
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A("adc %10,%13")
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A("adc %10,%13")
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A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * LO(acc)
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A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * LO(acc)
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A("mul %16,%0") // r1:r0 = HI(x) * LO(acc)
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A("mul %16,%0") // r1:r0 = HI(x) * LO(acc)
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A("add %5,r0")
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A("add %5,r0")
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A("adc %9,r1")
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A("adc %9,r1")
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A("adc %10,%13")
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A("adc %10,%13")
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A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * LO(acc) << 8
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A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * LO(acc) << 8
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A("mul %14,%1") // r1:r0 = LO(x) * MIL(acc)
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A("mul %14,%1") // r1:r0 = LO(x) * MIL(acc)
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A("add %4,r0")
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A("add %4,r0")
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A("adc %5,r1")
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A("adc %5,r1")
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A("adc %9,%13")
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A("adc %9,%13")
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A("adc %10,%13")
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A("adc %10,%13")
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A("adc %11,%13") // %11:%10:%9:%5:%4 = LO(x) * MIL(acc)
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A("adc %11,%13") // %11:%10:%9:%5:%4 = LO(x) * MIL(acc)
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A("mul %15,%1") // r1:r0 = MI(x) * MIL(acc)
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A("mul %15,%1") // r1:r0 = MI(x) * MIL(acc)
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A("add %5,r0")
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A("add %5,r0")
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A("adc %9,r1")
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A("adc %9,r1")
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A("adc %10,%13")
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A("adc %10,%13")
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A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * MIL(acc) << 8
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A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * MIL(acc) << 8
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A("mul %16,%1") // r1:r0 = HI(x) * MIL(acc)
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A("mul %16,%1") // r1:r0 = HI(x) * MIL(acc)
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A("add %9,r0")
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A("add %9,r0")
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A("adc %10,r1")
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A("adc %10,r1")
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A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * MIL(acc) << 16
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A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * MIL(acc) << 16
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A("mul %14,%2") // r1:r0 = LO(x) * MIH(acc)
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A("mul %14,%2") // r1:r0 = LO(x) * MIH(acc)
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A("add %5,r0")
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A("add %5,r0")
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A("adc %9,r1")
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A("adc %9,r1")
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A("adc %10,%13")
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A("adc %10,%13")
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A("adc %11,%13") // %11:%10:%9:%5:%4 = LO(x) * MIH(acc) << 8
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A("adc %11,%13") // %11:%10:%9:%5:%4 = LO(x) * MIH(acc) << 8
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A("mul %15,%2") // r1:r0 = MI(x) * MIH(acc)
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A("mul %15,%2") // r1:r0 = MI(x) * MIH(acc)
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A("add %9,r0")
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A("add %9,r0")
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A("adc %10,r1")
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A("adc %10,r1")
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A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * MIH(acc) << 16
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A("adc %11,%13") // %11:%10:%9:%5:%4 += MI(x) * MIH(acc) << 16
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A("mul %16,%2") // r1:r0 = HI(x) * MIH(acc)
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A("mul %16,%2") // r1:r0 = HI(x) * MIH(acc)
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A("add %10,r0")
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A("add %10,r0")
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A("adc %11,r1") // %11:%10:%9:%5:%4 += MI(x) * MIH(acc) << 24
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A("adc %11,r1") // %11:%10:%9:%5:%4 += MI(x) * MIH(acc) << 24
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A("mul %14,%3") // r1:r0 = LO(x) * HI(acc)
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A("mul %14,%3") // r1:r0 = LO(x) * HI(acc)
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A("add %9,r0")
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A("add %9,r0")
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A("adc %10,r1")
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A("adc %10,r1")
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A("adc %11,%13") // %11:%10:%9:%5:%4 = LO(x) * HI(acc) << 16
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A("adc %11,%13") // %11:%10:%9:%5:%4 = LO(x) * HI(acc) << 16
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A("mul %15,%3") // r1:r0 = MI(x) * HI(acc)
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A("mul %15,%3") // r1:r0 = MI(x) * HI(acc)
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A("add %10,r0")
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A("add %10,r0")
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A("adc %11,r1") // %11:%10:%9:%5:%4 += MI(x) * HI(acc) << 24
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A("adc %11,r1") // %11:%10:%9:%5:%4 += MI(x) * HI(acc) << 24
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A("mul %16,%3") // r1:r0 = HI(x) * HI(acc)
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A("mul %16,%3") // r1:r0 = HI(x) * HI(acc)
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A("add %11,r0") // %11:%10:%9:%5:%4 += MI(x) * HI(acc) << 32
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A("add %11,r0") // %11:%10:%9:%5:%4 += MI(x) * HI(acc) << 32
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// At this point, %11:%10:%9 contains the new estimation of x.
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// At this point, %11:%10:%9 contains the new estimation of x.
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@ -619,47 +619,47 @@ void Planner::init() {
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A("ldi %3,1")
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A("ldi %3,1")
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A("clr %2")
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A("clr %2")
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A("clr %1")
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A("clr %1")
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A("clr %0") // %3:%2:%1:%0 = 0x1000000
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A("clr %0") // %3:%2:%1:%0 = 0x1000000
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A("mul %6,%9") // r1:r0 = LO(d) * LO(x)
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A("mul %6,%9") // r1:r0 = LO(d) * LO(x)
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A("sub %0,r0")
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A("sub %0,r0")
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A("sbc %1,r1")
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A("sbc %1,r1")
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A("sbc %2,%13")
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A("sbc %2,%13")
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A("sbc %3,%13") // %3:%2:%1:%0 -= LO(d) * LO(x)
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A("sbc %3,%13") // %3:%2:%1:%0 -= LO(d) * LO(x)
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A("mul %7,%9") // r1:r0 = MI(d) * LO(x)
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A("mul %7,%9") // r1:r0 = MI(d) * LO(x)
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A("sub %1,r0")
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A("sub %1,r0")
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A("sbc %2,r1")
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A("sbc %2,r1")
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A("sbc %3,%13") // %3:%2:%1:%0 -= MI(d) * LO(x) << 8
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A("sbc %3,%13") // %3:%2:%1:%0 -= MI(d) * LO(x) << 8
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A("mul %8,%9") // r1:r0 = HI(d) * LO(x)
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A("mul %8,%9") // r1:r0 = HI(d) * LO(x)
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A("sub %2,r0")
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A("sub %2,r0")
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A("sbc %3,r1") // %3:%2:%1:%0 -= MIL(d) * LO(x) << 16
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A("sbc %3,r1") // %3:%2:%1:%0 -= MIL(d) * LO(x) << 16
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A("mul %6,%10") // r1:r0 = LO(d) * MI(x)
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A("mul %6,%10") // r1:r0 = LO(d) * MI(x)
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A("sub %1,r0")
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A("sub %1,r0")
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A("sbc %2,r1")
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A("sbc %2,r1")
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A("sbc %3,%13") // %3:%2:%1:%0 -= LO(d) * MI(x) << 8
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A("sbc %3,%13") // %3:%2:%1:%0 -= LO(d) * MI(x) << 8
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A("mul %7,%10") // r1:r0 = MI(d) * MI(x)
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A("mul %7,%10") // r1:r0 = MI(d) * MI(x)
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A("sub %2,r0")
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A("sub %2,r0")
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A("sbc %3,r1") // %3:%2:%1:%0 -= MI(d) * MI(x) << 16
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A("sbc %3,r1") // %3:%2:%1:%0 -= MI(d) * MI(x) << 16
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A("mul %8,%10") // r1:r0 = HI(d) * MI(x)
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A("mul %8,%10") // r1:r0 = HI(d) * MI(x)
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A("sub %3,r0") // %3:%2:%1:%0 -= MIL(d) * MI(x) << 24
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A("sub %3,r0") // %3:%2:%1:%0 -= MIL(d) * MI(x) << 24
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A("mul %6,%11") // r1:r0 = LO(d) * HI(x)
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A("mul %6,%11") // r1:r0 = LO(d) * HI(x)
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A("sub %2,r0")
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A("sub %2,r0")
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A("sbc %3,r1") // %3:%2:%1:%0 -= LO(d) * HI(x) << 16
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A("sbc %3,r1") // %3:%2:%1:%0 -= LO(d) * HI(x) << 16
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A("mul %7,%11") // r1:r0 = MI(d) * HI(x)
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A("mul %7,%11") // r1:r0 = MI(d) * HI(x)
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A("sub %3,r0") // %3:%2:%1:%0 -= MI(d) * HI(x) << 24
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A("sub %3,r0") // %3:%2:%1:%0 -= MI(d) * HI(x) << 24
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// %3:%2:%1:%0 = r = (1<<24) - x*d
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// %3:%2:%1:%0 = r = (1<<24) - x*d
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// %8:%7:%6 = d = interval
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// %8:%7:%6 = d = interval
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// Perform the final correction
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// Perform the final correction
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A("sub %0,%6")
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A("sub %0,%6")
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A("sbc %1,%7")
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A("sbc %1,%7")
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A("sbc %2,%8") // r -= d
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A("sbc %2,%8") // r -= d
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A("brcs 14f") // if ( r >= d)
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A("brcs 14f") // if ( r >= d)
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// %11:%10:%9 = x
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// %11:%10:%9 = x
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A("ldi %3,1")
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A("ldi %3,1")
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A("add %9,%3")
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A("add %9,%3")
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A("adc %10,%13")
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A("adc %10,%13")
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A("adc %11,%13") // x++
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A("adc %11,%13") // x++
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L("14")
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L("14")
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// Estimation is done. %11:%10:%9 = x
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// Estimation is done. %11:%10:%9 = x
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