This program calculates and prints roots of numbers between 1 and 100 to 400 places. The program was originally written by Sven-Arne Wallin, after I had send him an article from the HP Journal [May 1977, pages 22-24] which described the method used in (HP-) calculators to find square roots. [Two extensions, which allow finding of roots of numbers with more than 10 digits and finding more than 400 digits, were written by me and an also included program for re-displaying the calculated root was originally written by Palmer O. Hanson, the editor of TI\PPC Notes]
The version presented here has been changed considerably with respect to Sven's original version. Modifications include:
To obtain the high precision this program delivers, use is made of the following method: :lq.
The above process is a only a rough outline of the method used. A much better description can be found in the above mentioned article in the HP Journal. :note.Another way of expressing the above method can be found in the "Some last notes" section at the end of this chapter. :elq .pa
000 92 RTN 060 06 06 120 13 13 180 93 . 001 09 9 061 01 1 121 02 2 181 07 7 002 00 0 062 93 . 122 42 STO 182 02 2 003 42 STO 063 97 DSZ 123 07 07 183 54 ) 004 03 03 064 07 07 124 05 5 184 61 GTO 005 42 STO 065 00 00 125 00 0 185 02 02 006 05 05 066 40 40 126 42 STO 186 39 39 007 05 5 067 69 OP 127 06 06 187 00 0 008 00 0 068 29 29 128 43 RCL 188 00 0 009 42 STO 069 02 2 129 08 08 189 00 0 010 04 04 070 44 SUM 130 48 EXC 190 00 0 011 42 STO 071 89 89 131 03 03 191 00 0 012 06 06 072 61 GTO 132 29 CP 192 00 0 013 43 RCL 073 00 00 133 22 INV 193 00 0 014 08 08 074 01 01 134 74 SM* 194 00 0 015 42 STO 075 97 DSZ 135 06 06 195 00 0 016 07 07 076 00 00 136 69 OP 196 00 0 017 94 +/- 077 00 00 137 36 36 197 00 0 018 44 SUM 078 96 96 138 32 X:T 198 00 0 019 03 03 079 24 CE 139 74 SM* 199 00 0 020 44 SUM 080 01 1 140 06 06 200 76 LBL 021 04 04 081 00 0 141 53 ( 201 11 A 022 73 RC* 082 48 EXC 142 73 RC* 202 50 IxI 023 03 03 083 00 00 143 06 06 203 32 X:T 024 69 OP 084 48 EXC 144 55 ö 204 69 OP 025 23 23 085 09 09 145 43 RCL 205 00 00 026 32 X:T 086 99 PRT 146 01 01 206 69 OP 027 73 RC* 087 68 NOP 147 54 ) 207 05 05 028 04 04 088 69 OP 148 53 ( 208 09 9 029 69 OP 089 28 28 149 59 INT 209 69 OP 030 24 24 090 97 DSZ 150 65 x 210 17 17 031 67 X=T 091 02 02 151 32 X:T 211 47 CMS 032 00 00 092 00 00 152 43 RCL 212 32 X:T 033 22 22 093 96 96 153 01 01 213 42 STO 034 22 INV 094 00 0 154 54 ) 214 49 49 035 77 XòT 095 81 RST 155 97 DSZ 215 99 PRT 036 00 00 096 43 RCL 156 03 03 216 92 RTN 037 75 75 097 07 07 157 01 01 217 42 STO 038 29 CP 098 42 STO 158 33 33 218 02 02 039 00 0 099 03 03 159 09 9 219 01 1 040 69 OP 100 01 1 160 00 0 220 00 0 041 35 35 101 00 0 161 97 DSZ 221 42 STO 042 69 OP 102 49 PRD 162 07 07 222 00 00 043 36 36 103 09 09 163 01 01 223 22 INV 044 22 INV 104 69 OP 164 26 26 224 28 LOG 045 74 SM* 105 35 35 165 09 9 225 42 STO 046 06 06 106 64 PD* 166 94 +/- 226 01 01 047 73 RC* 107 05 05 167 61 GTO 227 01 1 048 05 05 108 97 DSZ 168 00 00 228 42 STO 049 22 INV 109 03 03 169 70 70 229 08 08 050 74 SM* 110 01 01 170 76 LBL 230 42 STO 051 06 06 111 04 04 171 13 C 231 89 89 052 73 RC* 112 33 Xý 172 42 STO 232 69 OP 053 06 06 113 69 OP 173 02 02 233 05 05 054 77 XòT 114 36 36 174 53 ( 234 60 DEG 055 00 00 115 64 PD* 175 43 RCL 235 04 4 056 62 62 116 06 06 176 01 01 236 05 5 057 43 RCL 117 97 DSZ 177 85 + 237 30 TAN 058 01 01 118 07 07 178 01 1 238 33 Xý 059 74 SM* 119 01 01 179 01 1 239 86 STF <\pre>The Long Number Version
User Instructions
- Enter the program listed on the next page.
- Enter the number of digits in the number, divided by 10 and rounded to the next greater integer and press A. The number of digits must be greater than 10 and less than or equal to 400.
- Enter the number in groups of ten digits and press R/S. The number has to be entered from the left to the right (pad the last group with zeroes) and all parts must have the same exponent, except for trailing zeroes.
An example:
To find the root of 1.2345\67891\01112\13141\51617, you perform the following steps:
- Enter 3 and press A.
- Enter 1.234567891 and press R/S.
- Enter 0.111213141 and press R/S.
- Enter 5.161700000 and press R/S.
- When a flashing 1 appears press 7 EE to start the calculations in Fast Mode.
- If a printer is being used then each group of ten digits is printed as it is completed. The calculator stops with a zero in the display when the calculations are complete.
The program will find the first 10N digits of the root of the number you have entered, where N\=\INT((#\of\digits\+\10)\/\10)
- For operation without a printer, you can change the command at program step\087 from NOP to R/S. The program will stop to permit read-out of each group of ten digits as it is completed. Press R/S to proceed to the next group.
- Once the program has ended, you can enter the Standard Version, use a -1 in the display to read the card, to find more digits of the number you entered. To do so, you must use the C-option of that program. Once again you must make sure that the total number of groups of ten digits does not exceed 40. [For the above example you cannot enter more than 37]
Listing of the Long Number Version
000 92 RTN 060 06 06 120 33 Xý 180 41 41 001 09 9 061 01 1 121 69 OP 181 09 9 002 00 0 062 93 . 122 36 36 182 94 +/- 003 42 STO 063 97 DSZ 123 64 PD* 183 69 OP 004 03 03 064 07 07 124 06 06 184 22 22 005 42 STO 065 00 00 125 97 DSZ 185 61 GTO 006 05 05 066 40 40 126 07 07 186 00 00 007 05 5 067 69 OP 127 01 01 187 70 70 008 00 0 068 29 29 128 21 21 188 76 LBL 009 42 STO 069 02 2 129 02 2 189 11 A 010 04 04 070 44 SUM 130 42 STO 190 32 X:T 011 42 STO 071 89 89 131 07 07 191 69 OP 012 06 06 072 61 GTO 132 53 ( 192 00 00 013 43 RCL 073 00 00 133 05 5 193 69 OP 014 08 08 074 01 01 134 00 0 194 05 05 015 42 STO 075 97 DSZ 135 85 + 195 09 9 016 07 07 076 00 00 136 43 RCL 196 69 OP 017 94 +/- 077 00 00 137 02 02 197 17 17 018 44 SUM 078 96 96 138 42 STO 198 47 CMS 019 03 03 079 24 CE 139 03 03 199 04 4 020 44 SUM 080 01 1 140 54 ) 200 09 9 021 04 04 081 00 0 141 42 STO 201 42 STO 022 73 RC* 082 48 EXC 142 06 06 202 00 00 023 03 03 083 00 00 143 43 RCL 203 32 X:T 024 69 OP 084 48 EXC 144 08 08 204 42 STO 025 23 23 085 09 09 145 44 SUM 205 02 02 026 32 X:T 086 99 PRT 146 03 03 206 42 STO 027 73 RC* 087 68 NOP 147 29 CP 207 03 03 028 04 04 088 69 OP 148 00 0 208 92 RTN 029 69 OP 089 28 28 149 22 INV 209 50 IxI 030 24 24 090 97 DSZ 150 74 SM* 210 72 ST* 031 67 X=T 091 02 02 151 06 06 211 00 00 032 00 00 092 00 00 152 69 OP 212 69 OP 033 22 22 093 96 96 153 36 36 213 20 20 034 22 INV 094 00 0 154 32 X:T 214 99 PRT 035 77 XòT 095 81 RST 155 74 SM* 215 97 DSZ 036 00 00 096 69 OP 156 06 06 216 03 03 037 75 75 097 32 32 157 53 ( 217 02 02 038 29 CP 098 43 RCL 158 73 RC* 218 08 08 039 00 0 099 07 07 159 06 06 219 01 1 040 69 OP 100 42 STO 160 55 ö 220 00 0 041 35 35 101 03 03 161 43 RCL 221 42 STO 042 69 OP 102 43 RCL 162 01 01 222 00 00 043 36 36 103 02 02 163 54 ) 223 22 INV 044 22 INV 104 44 SUM 164 53 ( 224 28 LOG 045 74 SM* 105 06 06 165 59 INT 225 42 STO 046 06 06 106 44 SUM 166 65 x 226 01 01 047 73 RC* 107 07 07 167 32 X:T 227 01 1 048 05 05 108 01 1 168 43 RCL 228 42 STO 049 22 INV 109 00 0 169 01 01 229 08 08 050 74 SM* 110 49 PRD 170 54 ) 230 42 STO 051 06 06 111 09 09 171 97 DSZ 231 89 89 052 73 RC* 112 69 OP 172 03 03 232 69 OP 053 06 06 113 35 35 173 01 01 233 05 05 054 77 XòT 114 64 PD* 174 49 49 234 60 DEG 055 00 00 115 05 05 175 09 9 235 04 4 056 62 62 116 97 DSZ 176 00 0 236 05 5 057 43 RCL 117 03 03 177 97 DSZ 237 30 TAN 058 01 01 118 01 01 178 07 07 238 33 Xý 059 74 SM* 119 12 12 179 01 01 239 86 STF <\pre>The Very Extended Precision Extension I
User Instructions
:note.Using the Very Extended Precision Extension I without a printer yields very inconvenient operation, so if you don't have one it might be better to use the second version of this extension, even though it is a little less accurate.
- Enter the program listed on the next page. The program should be recorded in a 9\OP\17 partitioning!
- Enter the number of additional groups of ten digits and press E'. The number of additional groups should not exceed the total number of groups you have generated with the A and C options of the Standard Version! It is important to realise that you do not have to generate the maximum possible number of digits with the Standard Version.
- When a flashing 1.\E10 appears press 7 EE to start the calculations in Fast Mode.
- The program will stop with every group of ten digits in the display and if a printer is connected, it will print the group. The calculator will stop with a zero in the display when the calculations are complete. :note.If you have a printer, you may replace the R/S at step 084 with NOP, to avoid having to press R/S every time.
- To generate more additional groups of ten digits after the calculator has stopped, you can enter the number of additional groups and press E. You must make sure that the total number of of groups entered using modes E' and E is not larger than twice the total number of digits generated by the Standard Version.
- Again the calculator will stop with a flashing 1.\E10 in the display, and again you press 7 EE to start calculations in Fast Mode. Additional groups of ten digits will be displayed and printed as they are completed.
Listing of the Very Extended Precision Extension I
000 92 RTN 060 06 06 120 53 ( 180 00 0 001 09 9 061 01 1 121 73 RC* 181 00 0 002 00 0 062 93 . 122 06 06 182 00 0 003 42 STO 063 97 DSZ 123 55 ö 183 00 0 004 03 03 064 07 07 124 43 RCL 184 00 0 005 42 STO 065 00 00 125 01 01 185 00 0 006 05 05 066 40 40 126 54 ) 186 00 0 007 05 5 067 69 OP 127 53 ( 187 00 0 008 00 0 068 29 29 128 59 INT 188 00 0 009 42 STO 069 61 GTO 129 65 x 189 00 0 010 04 04 070 00 00 130 32 X:T 190 00 0 011 42 STO 071 01 01 131 43 RCL 191 00 0 012 06 06 072 97 DSZ 132 01 01 192 00 0 013 43 RCL 073 00 00 133 54 ) 193 00 0 014 08 08 074 00 00 134 97 DSZ 194 00 0 015 42 STO 075 91 91 135 07 07 195 00 0 016 07 07 076 24 CE 136 01 01 196 00 0 017 94 +/- 077 01 1 137 12 12 197 00 0 018 44 SUM 078 00 0 138 61 GTO 198 00 0 019 03 03 079 48 EXC 139 00 00 199 00 0 020 44 SUM 080 00 00 140 01 01 200 00 0 021 04 04 081 48 EXC 141 00 0 201 00 0 022 73 RC* 082 09 09 142 00 0 202 00 0 023 03 03 083 99 PRT 143 00 0 203 00 0 024 69 OP 084 68 NOP 144 00 0 204 00 0 025 23 23 085 97 DSZ 145 00 0 205 00 0 026 32 X:T 086 02 02 146 00 0 206 00 0 027 73 RC* 087 00 00 147 00 0 207 00 0 028 04 04 088 91 91 148 00 0 208 00 0 029 69 OP 089 00 0 149 00 0 209 00 0 030 24 24 090 81 RST 150 00 0 210 00 0 031 67 X=T 091 01 1 151 00 0 211 00 0 032 00 00 092 00 0 152 00 0 212 00 0 033 22 22 093 49 PRD 153 00 0 213 00 0 034 22 INV 094 09 09 154 00 0 214 00 0 035 77 XòT 095 69 OP 155 00 0 215 00 0 036 00 00 096 36 36 156 00 0 216 00 0 037 72 72 097 64 PD* 157 00 0 217 00 0 038 29 CP 098 06 06 158 00 0 218 00 0 039 00 0 099 97 DSZ 159 00 0 219 00 0 040 69 OP 100 07 07 160 00 0 220 00 0 041 35 35 101 00 00 161 00 0 221 76 LBL 042 69 OP 102 95 95 162 00 0 222 10 E' 043 36 36 103 05 5 163 00 0 223 69 OP 044 22 INV 104 00 0 164 00 0 224 38 38 045 74 SM* 105 42 STO 165 00 0 225 76 LBL 046 06 06 106 06 06 166 00 0 226 15 E 047 73 RC* 107 43 RCL 167 00 0 227 42 STO 048 05 05 108 08 08 168 00 0 228 02 02 049 22 INV 109 48 EXC 169 00 0 229 53 ( 050 74 SM* 110 07 07 170 00 0 230 43 RCL 051 06 06 111 29 CP 171 00 0 231 01 01 052 73 RC* 112 22 INV 172 00 0 232 85 + 053 06 06 113 74 SM* 173 00 0 233 01 1 054 77 XòT 114 06 06 174 00 0 234 01 1 055 00 00 115 69 OP 175 00 0 235 93 . 056 62 62 116 36 36 176 00 0 236 02 2 057 43 RCL 117 32 X:T 177 00 0 237 02 2 058 01 01 118 74 SM* 178 00 0 238 54 ) 059 74 SM* 119 06 06 179 00 0 239 86 STF <\pre>The Very Extended Precision Extension II
User Instructions
:note.This second version of the Very Extended Precision Extension is a little less accurate than the first version. In the case of &SQR.3, the result is good to only 796 places, as opposed to 799 digits for the first version.
- Enter the program listed on the next page. The program should be recorded in a 9\OP\17 partitioning!
- Enter the number of additional groups of ten digits and press E'. The number of additional groups should not exceed the total number of groups you have generated with the A and C options of the Standard Version! It is important to realise that you do not have to generate the maximum possible number of digits with the Standard Version.
- When a flashing\1 appears press 7 EE to start the calculations in Fast Mode.
- The program will stop with every group of ten digits in the display and if a printer is connected, it will print the group. The calculator will stop with a zero in the display when the calculations are complete. :note.To get an uninterrupted printout, you may replace the R/S at step 165 with a NOP, even in case you don't have a printer, as the result can always be recalled by using the builtin reprint root routine.
- To generate more additional groups of ten digits after the calculator has stopped, you can enter the number of additional groups and press E. You must make sure that the total number of of groups entered using modes E' and E is not larger than twice the total number of digits generated by the Standard Version.
- Again the calculator will stop with a flashing\1 in the display, and again you press 7 EE to start calculations in Fast Mode. Additional groups of ten digits will be displayed and printed as they are completed.
- To redisplay or reprint the solution, you can press B, repeatedly followed by R/S. The read-out is complete when a flashing zero appears.
Listing of the Very Extended Precision Extension II
000 92 RTN 060 43 RCL 120 00 00 180 42 STO 001 01 1 061 08 08 121 00 00 181 02 02 002 00 0 062 42 STO 122 01 01 182 54 ) 003 49 PRD 063 07 07 123 43 RCL 183 42 STO 004 09 09 064 94 +/- 124 08 08 184 03 03 005 69 OP 065 44 SUM 125 42 STO 185 43 RCL 006 36 36 066 03 03 126 03 03 186 08 08 007 64 PD* 067 44 SUM 127 94 +/- 187 22 INV 008 06 06 068 04 04 128 44 SUM 188 44 SUM 009 97 DSZ 069 73 RC* 129 05 05 189 02 02 010 07 07 070 03 03 130 44 SUM 190 73 RC* 011 00 00 071 69 OP 131 06 06 191 03 03 012 05 05 072 23 23 132 43 RCL 192 69 OP 013 05 5 073 32 X:T 133 09 09 193 23 23 014 00 0 074 73 RC* 134 63 EX* 194 99 PRT 015 42 STO 075 04 04 135 05 05 195 91 R/S 016 06 06 076 69 OP 136 69 OP 196 97 DSZ 017 43 RCL 077 24 24 137 25 25 197 02 02 018 08 08 078 67 X=T 138 97 DSZ 198 01 01 019 48 EXC 079 00 00 139 03 03 199 90 90 020 07 07 080 69 69 140 01 01 200 00 0 021 29 CP 081 22 INV 141 34 34 201 69 OP 022 22 INV 082 77 XòT 142 00 0 202 68 68 023 74 SM* 083 01 01 143 63 EX* 203 92 RTN 024 06 06 084 19 19 144 06 06 204 00 0 025 69 OP 085 29 CP 145 69 OP 205 00 0 026 36 36 086 00 0 146 26 26 206 00 0 027 32 X:T 087 69 OP 147 97 DSZ 207 00 0 028 74 SM* 088 35 35 148 07 07 208 00 0 029 06 06 089 69 OP 149 01 01 209 00 0 030 53 ( 090 36 36 150 43 43 210 00 0 031 73 RC* 091 22 INV 151 69 OP 211 00 0 032 06 06 092 74 SM* 152 38 38 212 00 0 033 55 ö 093 06 06 153 43 RCL 213 00 0 034 43 RCL 094 73 RC* 154 08 08 214 00 0 035 01 01 095 05 05 155 42 STO 215 00 0 036 54 ) 096 22 INV 156 07 07 216 00 0 037 53 ( 097 74 SM* 157 01 1 217 00 0 038 59 INT 098 06 06 158 00 0 218 00 0 039 65 x 099 73 RC* 159 48 EXC 219 00 0 040 32 X:T 100 06 06 160 00 00 220 00 0 041 43 RCL 101 77 XòT 161 48 EXC 221 76 LBL 042 01 01 102 01 01 162 09 09 222 10 E' 043 54 ) 103 09 09 163 24 CE 223 69 OP 044 97 DSZ 104 43 RCL 164 99 PRT 224 38 38 045 07 07 105 01 01 165 91 R/S 225 32 X:T 046 00 00 106 74 SM* 166 97 DSZ 226 43 RCL 047 22 22 107 06 06 167 02 02 227 08 08 048 09 9 108 01 1 168 00 00 228 82 HIR 049 00 0 109 93 . 169 01 01 229 08 08 050 42 STO 110 97 DSZ 170 00 0 230 32 X:T 051 03 03 111 07 07 171 81 RST 231 76 LBL 052 42 STO 112 00 00 172 76 LBL 232 15 E 053 05 05 113 87 87 173 12 B 233 42 STO 054 05 5 114 69 OP 174 53 ( 234 02 02 055 00 0 115 29 29 175 09 9 235 04 4 056 42 STO 116 61 GTO 176 00 0 236 05 5 057 04 04 117 00 00 177 75 - 237 30 TAN 058 42 STO 118 48 48 178 82 HIR 238 33 Xý 059 06 06 119 97 DSZ 179 18 18 239 86 STF <\pre>The Reprint Root Routine
Using the Standard and Long Number Versions without a printer yields very inconvenient operation. To overcome this problem you can use the following short program to re-display or reprint the result. The program can be used at any moment, without disturbing any registers, so you may use it after having generated for example 200 digits, and continue afterwards with more digits!
User Instructions
- Enter the program below. It should be recorded in a 9\OP\17 partitioning.
- Press B, repeatedly followed by R/S to display and print the result again. The read-out is complete when a flashing zero appears.
When you have used this program after the Standard Version and you want to continue with that program, you must re-enter the card containing that program with a -1 in the display.
Listing of the Reprint Root Routine
000 76 LBL 011 42 STO 022 43 RCL 033 91 R/S 001 12 B 012 03 03 023 01 01 034 69 OP 002 53 ( 013 00 0 024 48 EXC 035 23 23 003 09 9 014 42 STO 025 04 04 036 97 DSZ 004 00 0 015 04 04 026 75 - 037 02 02 005 75 - 016 53 ( 027 22 INV 038 00 00 006 43 RCL 017 73 RC* 028 59 INT 039 16 16 007 07 07 018 03 03 029 49 PRD 040 00 0 008 42 STO 019 55 ö 030 04 04 041 69 OP 009 02 02 020 02 2 031 54 ) 042 68 68 010 54 ) 021 85 + 032 99 PRT 043 92 RTN <\pre> .sp 5 .ce This page intentionally left blank. .paThe TI-58 Versions
The user instructions for all of the TI-58 versions of the program are equal to those of the corresponding TI-59 versions. The difference is the fact that the TI-58 programs can only calculate roots up to 100 places. :note.Even though it is very well possible to use all versions on a TI-58, it requires a lot of determination to key in every program. I personally wouldn't do it!
The modifications needed to create the TI-58 versions are described below.
The Standard Version
To modify the Standard Version for use on a TI-58, you must make the following changes:
To modify the Long Number Version for use on a TI-58, you must make the following changes:
To modify the Very Extended Precision Extension I for use on a TI-58, you must make the following changes:
To modify the Very Extended Precision Extension II for use on a TI-58, you must make the following changes:
To modify the Reprint Root Routine for use on a TI-58, you must make the following change:
000 04 4 050 FB 06 100 B9 94 150 00 0 001 00 0 051 69 XòT 101 37 Xý 151 65 DSZ 002 32 STO 052 D0 58 102 23 OP 152 FC 07 003 F8 03 053 33 RCL 103 9A 36 153 F6 01 004 32 STO 054 F6 01 104 F4 PD* 154 85 15 005 FA 05 055 B4 SM* 105 FB 06 155 09 9 006 02 2 056 FB 06 106 65 DSZ 156 1A +/- 007 05 5 057 01 1 107 FC 07 157 27 GTO 008 32 STO 058 19 . 108 F6 01 158 D7 65 009 F9 04 059 65 DSZ 109 F7 02 159 29 LBL 010 32 STO 060 FC 07 110 02 2 160 14 C 011 FB 06 061 9B 37 111 32 STO 161 32 STO 012 33 RCL 062 23 OP 112 FC 07 162 F7 02 013 FD 08 063 93 29 113 02 2 163 27 GTO 014 32 STO 064 02 2 114 05 5 164 EC 86 015 FC 07 065 34 SUM 115 32 STO 165 29 LBL 016 1A +/- 066 9D 39 116 FB 06 166 10 A 017 34 SUM 067 26 RST 117 33 RCL 167 6B CMS 018 F8 03 068 65 DSZ 118 FD 08 168 59 PRT 019 34 SUM 069 F5 00 119 73 EXC 169 32 STO 020 F9 04 070 EC 86 120 F8 03 170 8E 24 021 B3 RC* 071 01 1 121 41 CP 171 A9 RTN 022 F8 03 072 00 0 122 29 LBL 172 32 STO 023 23 OP 073 73 EXC 123 B4 SM* 173 F7 02 024 8D 23 074 F5 00 124 FB 06 174 01 1 025 24 X:T 075 73 EXC 125 23 OP 175 00 0 026 B3 RC* 076 FE 09 126 9A 36 176 32 STO 027 F9 04 077 59 PRT 127 24 X:T 177 F5 00 028 23 OP 078 63 NOP 128 B4 SM* 178 31 INV 029 8E 24 079 23 OP 129 FB 06 179 75 LOG 030 64 X=T 080 92 28 130 2A ( 180 32 STO 031 8B 21 081 65 DSZ 131 B3 RC* 181 F6 01 032 31 INV 082 F7 02 132 FB 06 182 01 1 033 69 XòT 083 EC 86 133 3D / 183 32 STO 034 DA 68 084 00 0 134 33 RCL 184 FD 08 035 41 CP 085 A9 RTN 135 F6 01 185 32 STO 036 00 0 086 33 RCL 136 2B ) 186 9D 39 037 23 OP 087 FC 07 137 2A ( 187 26 RST 038 99 35 088 32 STO 138 76 INT 039 23 OP 089 F8 03 139 3C x 040 9A 36 090 01 1 140 24 X:T 041 31 INV 091 00 0 141 33 RCL 042 B4 SM* 092 74 PRD 142 F6 01 043 FB 06 093 FE 09 143 2B ) 044 B3 RC* 094 23 OP 144 1A +/- 045 FA 05 095 99 35 145 65 DSZ 046 31 INV 096 F4 PD* 146 F8 03 047 B4 SM* 097 FA 05 147 F6 01 048 FB 06 098 65 DSZ 148 8D 23 049 B3 RC* 099 F8 03 149 04 4 <\pre>The Very Extended Precision Extension
User Instructions
:note.Using the Very Extended Precision Extension without a printer yields very inconvenient operation. To solve this problem, you can make more or less the same changes as in the TI-59 version.
- Enter the program listed on the next page.
- Enter the number of additional groups of ten digits and press E'. The number of additional groups should not exceed the total number of groups you have generated with the A and C options of the Standard Version! It is important to realise that you do not have to generate the maximum possible number of digits with the Standard Version.
- The program will stop with every group of ten digits in the display and if a printer is connected, it will print the group. The calculator will stop with a zero in the display when the calculations are complete. :note.If you have a printer, you may replace the R/S at step 075 with NOP, to avoid having to press R/S every time.
- To generate more additional groups of ten digits after the calculator has stopped, you can enter the number of additional groups and press E. You must make sure that the total number of of groups entered using modes E' and E is not larger than twice the total number of digits generated by the Standard Version.
Listing of the Very Extended Precision Extension
000 04 4 040 9A 36 080 A9 RTN 120 33 RCL 001 00 0 041 31 INV 081 01 1 121 F6 01 002 32 STO 042 B4 SM* 082 00 0 122 2B ) 003 F8 03 043 FB 06 083 74 PRD 123 1A +/- 004 32 STO 044 B3 RC* 084 FE 09 124 65 DSZ 005 FA 05 045 FA 05 085 23 OP 125 FC 07 006 02 2 046 31 INV 086 9A 36 126 F6 01 007 05 5 047 B4 SM* 087 F4 PD* 127 F7 02 008 32 STO 048 FB 06 088 FB 06 128 26 RST 009 F9 04 049 B3 RC* 089 65 DSZ 129 29 LBL 010 32 STO 050 FB 06 090 FC 07 130 58 E' 011 FB 06 051 69 XòT 091 EB 85 131 23 OP 012 33 RCL 052 D0 58 092 02 2 132 9C 38 013 FD 08 053 33 RCL 093 05 5 133 29 LBL 014 32 STO 054 F6 01 094 32 STO 134 18 E 015 FC 07 055 B4 SM* 095 FB 06 135 32 STO 016 1A +/- 056 FB 06 096 33 RCL 136 F7 02 017 34 SUM 057 01 1 097 FD 08 137 27 GTO 018 F8 03 058 19 . 098 73 EXC 138 E7 81 019 34 SUM 059 65 DSZ 099 FC 07 020 F9 04 060 FC 07 100 41 CP 021 B3 RC* 061 9B 37 101 29 LBL 022 F8 03 062 23 OP 102 B4 SM* 023 23 OP 063 93 29 103 FB 06 024 8D 23 064 26 RST 104 23 OP 025 24 X:T 065 65 DSZ 105 9A 36 026 B3 RC* 066 F5 00 106 24 X:T 027 F9 04 067 E7 81 107 B4 SM* 028 23 OP 068 01 1 108 FB 06 029 8E 24 069 00 0 109 2A ( 030 64 X=T 070 73 EXC 110 B3 RC* 031 8B 21 071 F5 00 111 FB 06 032 31 INV 072 73 EXC 112 3D / 033 69 XòT 073 FE 09 113 33 RCL 034 D7 65 074 59 PRT 114 F6 01 035 41 CP 075 25 R/S 115 2B ) 036 00 0 076 65 DSZ 116 2A ( 037 23 OP 077 F7 02 117 76 INT 038 99 35 078 E7 81 118 3C x 039 23 OP 079 00 0 119 24 X:T <\pre>The Reprint Root Routine
Using the Standard Version without a printer yields very inconvenient operation. To overcome this problem you can use the following short program to re-display or reprint the result.
User Instructions
- Enter the program below.
- Press B, repeatedly followed by R/S to display and print the result again. The read-out is complete when a zero appears.
Listing of the Reprint Root Routine
000 29 LBL 011 32 STO 022 33 RCL 033 25 R/S 001 12 B 012 F8 03 023 F6 01 034 23 OP 002 2A ( 013 00 0 024 73 EXC 035 8D 23 003 04 4 014 32 STO 025 F9 04 036 65 DSZ 004 00 0 015 F9 04 026 3B - 037 F7 02 005 3B - 016 2A ( 027 31 INV 038 86 16 006 33 RCL 017 B3 RC* 028 76 INT 039 00 0 007 FC 07 018 F8 03 029 74 PRD 040 A9 RTN 008 32 STO 019 3D / 030 F9 04 009 F7 02 020 02 2 031 2B ) 010 2B ) 021 3A + 032 59 PRT <\pre>Some last notes about the programs
Let's find &SQR.3,\[1.73205\08075\68877\29352\...] .sk \\\\\\\\\\\\\\\\3.00\00\00\00\00 \\\\\\\\?\x\?\\\\\\|\\|\\|\\|\\|\\\\\Find the largest ?, so that \\\\\\\\\\\\\\\\\\\|\\|\\|\\|\\|\\\\\? &ML ? is as close to 3 as 1\\\\\\\1\x\1\=\1.\|\\|\\|\\|\\|\\\\\possible. Subract. \\\\\\\\\\\\\\\\2.00\\|\\|\\|\\|\\\\\Add 1 and 1 \\\\\\\2?\x\?\\\\\\\\\|\\|\\|\\|\\\\\Find the largest ?, so that \\\\\\\\\\\\\\\\\\\\\\|\\|\\|\\|\\\\\2? &ML ? is as close to 200 as 7\\\\\\27\x\7\=\1.89\\|\\|\\|\\|\\\\\possible. Subtract. \\\\\\\\\\\\\\\\\\11\00\\|\\|\\|\\\\\Add 27 and 7 \\\\\\34?\x\?\\\\\\\\\\\\|\\|\\|\\\\\Find the largest ?, so that \\\\\\\\\\\\\\\\\\\\\\\\\|\\|\\|\\\\\34? &ML ? is as close to 1100 3\\\\\343\x\3\=\\\10\29\\|\\|\\|\\\\\as possible. Subtract. \\\\\\\\\\\\\\\\\\\\\71\00\\|\\|\\\\\Add 343 and 3 \\\\\346?\x\?\\\\\\\\\\\\\\\|\\|\\\\\Etc \\\\\\\\\\\\\\\\\\\\\\\\\\\\|\\| 2\\\\3462\x\2\=\\\\\\69\24\\|\\| \\\\\\\\\\\\\\\\\\\\\\1\76\00\\|\\\\\Add 3462 and 2 \\\\3464?\x\?\\\\\\\\\\\\\\\\\\|\\\\\Etc \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\| 0\\\34640\x\0\=\\\\\\\0\00\00\\| \\\\\\\\\\\\\\\\\\\\\\1\76\00\00\\\\\Add 34640 and 0 \\\34640?\x\?\\\\\\\\\\\\\\\\\\\\\\\\Etc .sk 5\\346405\x\5\=\\\\\\\1\73\20\25 \\\\\\\\\\\\\\\\\\\\\\\\\2\79\75\\\\\Add 346405 and 5 .fo on
You see that the ?'s placed after each other are &SQR.3, at this point we have 1.73205. You can continue the process as long as you like.
The above "figure" has another advantage over the mathematical description of the method:
If you take a closer look at it, you will notice that the first factor only changes in the last digits. Also having noticed that fact, it seemed very natural to me to try to divide 27975 by 346410. Doing so I got 0.0807\56906\55581. It can be seen that the first 6 digits after the decimal point of this quotient are the next 6 digits of &SQR.3, that is we can find &SQR.3 to at least 11 valid digits by first finding 6 digits by the above method and then dividing the rest by two times the first 6 digits! It was the above "figure" that led to the Very Extended Precision Extension of the program!