WP 34S Partition of Integers Programme & a Possible OS Bug

05082014, 10:53 AM
Post: #1




WP 34S Partition of Integers Programme & a Possible OS Bug
The programme PRT returns the number of integer partitions on stack level X for the input integer on stack level X; QRT similarly returns the number of partitions into distinct parts.
1 LBL 'PRT' 2 CF 01 3 SKIP 002 4 LBL 'QRT' 5 SF 01 6 DECM 7 DBLON 8 RAD 9 STO 00 10 # 024 11 1/X 12 FC? 01 13 +/ 14 + 15 STO 06 16 FS? 01 17 SKIP 011 18 √ 19 1 20 . 21 5 22 1/X 23 √ 24 STO 08 25 * 26 # π 27 * 28 STO 07 29 CLx 30 STO 01 31 1 32 STO 02 33 FIX 00 34 RCL 02 35 STO 03 36 CLx 37 STO 04 38 RCL 02 39 RCL 03 40 GCD 41 x≠1? 42 SKIP 033 43 RCL 02 44 x<>Y 45  46 x≠0? 47 SKIP 016 48 STO 05 49 CLx 50 LBL 00 51 RCL 03 52 RCL* 05 53 RCL/ 02 54 FP 55 RCL 05 56 RCL/ 02 57 # 1/2 58 STO Z 59  60 * 61 + 62 DSE 05 63 GTO 00 64 4 65 1/X 66 + 67 RCL 00 68 STO+ X 69 RCL* 03 70 RCL/ 02 71  72 # π 73 * 74 COS 75 STO+ 04 76 DSE 03 77 BACK 039 78 FS? 01 79 SKIP 030 80 RCL 07 81 RCL/ 02 82 e^x 83 ENTER 84 ENTER 85 1/X 86 STO Z 87 + 88 RCL* 08 89 RCL 06 90 STO/ Z 91 / 92 # π 93 * 94 RCL/ 02 95 x<>Y 96 RCL 06 97 √ 98 / 99  100 RCL 02 101 √ 102 * 103 # π 104 4 105 * 106 / 107 ENTER 108 INC 02 109 SKIP 035 110 RCL 06 111 # π 112 RCL/ 02 113 x^2 114 * 115 # 012 116 / 117 STO 03 118 CLx 119 1 120 ENTER 121 STO 05 122 ENTER 123 x<>Z 124 RCL* 03 125 RCL 05 126 STO/ Y 127 1 128 + 129 STO 05 130 / 131 STO+ Y 132 x<>Z 133 x≠? Y 134 BACK 011 135 # π 136 RCL/ 02 137 x^2 138 * 139 2 140 STO+ 02 141 6 142 * 143 / 144 STO Y 145 RCL* 04 146 RCL+ 01 147 STO 01 148 STO+ Y 149 ROUND 150 x<>Y 151 ROUND 152 x≠? Y 153 BACK 119 154 ALL 00 155 END I attempted to replace line 63 with "BACK 012" & delete line 50 but the programme then either misfunctioned or produced wrong answers  assistance on this point would be appreciated. All improvements welcome. 

05082014, 11:07 AM
Post: #2




RE: WP 34S Partition of Integers Programme & a Possible OS Bug
(05082014 10:53 AM)Gerald H Wrote: I attempted to replace line 63 with "BACK 012" & delete line 50 but the programme then either misfunctioned or produced wrong answers  assistance on this point would be appreciated. Try single stepping the program over the BACK instruction to see where it ends up  you can switch between program and run modes freely to help see what is going on. Better still, don't use BACK and SKIP  they save the instruction for the label, however they make programs far less maintainable and they don't provide a noticeable performance benefit and they make programs far less maintainable. The 34S isn't short of numeric labels. That rant all said, I'm pretty sure BACK does function correctly. At least it has done in the past  Pauli 

05082014, 11:22 AM
Post: #3




RE: WP 34S Partition of Integers Programme & a Possible OS Bug
Thank you.
I would not recommend the use of BACK & SKIP in a programming language but disagree concerning performance effects. My Pollard's Rho programme takes about half the time of that required in the version using labels & GTOs. Incidentally, all other SKIPs & BACKs the removed label fell in were adjusted to allow for the removal of one line. 

05082014, 11:47 AM
Post: #4




RE: WP 34S Partition of Integers Programme & a Possible OS Bug
(05082014 11:22 AM)Gerald H Wrote: I would not recommend the use of BACK & SKIP in a programming language but disagree concerning performance effects. My Pollard's Rho programme takes about half the time of that required in the version using labels & GTOs. Such a large performance change is quite a surprise, I've never noticed much of a difference. The Pollard Rho factorisation code looks to be stack and register manipulations predominately which might explain some of this  those are reasonably fast. The arithmetic register operations will likely be fairly slow. The *mod is specially coded and avoids the carry and overflow calculations which are surprisingly significant. The interpreter overhead is pretty large too. What does # n do in this program?  Pauli 

05082014, 04:24 PM
(This post was last modified: 05082014 04:26 PM by Gerald H.)
Post: #5




RE: WP 34S Partition of Integers Programme & a Possible OS Bug
It's not # n but # pi.


05082014, 09:52 PM
Post: #6




RE: WP 34S Partition of Integers Programme & a Possible OS Bug  
05182014, 04:33 PM
Post: #7




RE: WP 34S Partition of Integers Programme & a Possible OS Bug
I have now realized my error & withdraw the aspersions I cast on the OS. Here is the programme using only BACKs & SKIPs & no LBLs or GTOs:
1 LBL 'PRT' 2 CF 01 3 SKIP 002 4 LBL 'QRT' 5 SF 01 6 DECM 7 DBLON 8 RAD 9 STO 09 10 # 024 11 1/X 12 FC? 01 13 +/ 14 + 15 STO 06 16 FS? 01 17 SKIP 011 18 √ 19 1 20 . 21 5 22 1/X 23 √ 24 STO 08 25 * 26 # π 27 * 28 STO 07 29 CLx 30 STO 10 31 1 32 STO 02 33 FIX 00 34 RCL 02 35 STO 03 36 CLx 37 STO 04 38 RCL 02 39 RCL 03 40 GCD 41 x≠1? 42 SKIP 031 43 RCL 02 44 DEC X 45 x=0? 46 SKIP 015 47 STO 05 48 0 49 RCL 03 50 RCL* 05 51 RCL/ 02 52 FP 53 RCL 05 54 RCL/ 02 55 # 1/2 56 STO Z 57  58 * 59 + 60 DSE 05 61 BACK 012 62 4 63 1/X 64 + 65 RCL 09 66 STO+ X 67 RCL* 03 68 RCL/ 02 69  70 # π 71 * 72 COS 73 STO+ 04 74 DSE 03 75 BACK 037 76 FS? 01 77 SKIP 030 78 RCL 07 79 RCL/ 02 80 e^x 81 ENTER 82 ENTER 83 1/X 84 STO Z 85 + 86 RCL* 08 87 RCL 06 88 STO/ Z 89 / 90 # π 91 * 92 RCL/ 02 93 x<>Y 94 RCL 06 95 √ 96 / 97  98 RCL 02 99 √ 100 * 101 # π 102 4 103 * 104 / 105 ENTER 106 INC 02 107 SKIP 035 108 RCL 06 109 # π 110 RCL/ 02 111 x^2 112 * 113 # 012 114 / 115 STO 03 116 CLx 117 1 118 ENTER 119 STO 05 120 ENTER 121 x<>Z 122 RCL* 03 123 RCL 05 124 STO/ Y 125 1 126 + 127 STO 05 128 / 129 STO+ Y 130 x<>Z 131 x≠? Y 132 BACK 011 133 # π 134 RCL/ 02 135 x^2 136 * 137 2 138 STO+ 02 139 6 140 * 141 / 142 STO Y 143 RCL* 04 144 RCL+ 10 145 STO 10 146 STO+ Y 147 ROUND 148 x<>Y 149 ROUND 150 x≠? Y 151 BACK 117 152 ALL 00 153 END A very nice calculator for programming. Bravo! 

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