Anionic Functions for the HP-41

Overview
 

-The following routines are variants of the programs listed in "Anions for the HP41" paragraph 2°)
-The whole program is shorter but it sometimes uses more data registers.

-I've also added the "self-power function".
 
 

Program Listing
 
 

Data Registers:           •  R00 = n ( 2 , 4 , 8 , .... , 128 or 256 )        ( Registers R00 thru Rnn are to be initialized before executing these programs )

                                      •  R01   ......  •  Rnn = the n components of the anion

                                         Rn+1 ..........  R2n  - and even R2n+1 ...... R3n - are sometimes used for temporary data storage

  >>>  When the program stops:     R01   ......  Rnn = the n components of the result
 

Flags:  F05-F06  ( not always )
Subroutines:  /
 

-Lines 25-71-101 are three-byte GTOs
 
 

01 LBL "1/A"  02 LBL 18  03 XEQ 14  04 LASTX  05 RCL 01  06 X^2  07 +  08 CHS  09 RCL 00  10 X<>Y  11 1/X  12 XEQ 03  13 SIGN  14 ST* 01  15 RTN  16 LBL "ACOS"     17 XEQ 04  18 RCL 00  19 PI  20 2  21 /  22 ST- 01  23 SIGN  24 CHS  25 GTO 03  26 LBL "ASIN"  27 LBL 04  28 CF 05  29 GTO 04  30 LBL "ATAN"  31 SF 05  32 LBL 04  33 XEQ 06  34 XEQ 14  35 X#0?  36 GTO 04  37 SIGN  38 STO 02  39 LBL 04  40 0  41 STO 01  42 SIGN  43 X<>Y  44 XEQ 02  45 RCL 00  46 .1  47 %

48 ISG X  49 +  50 RCL 00  51 +  52 .1  53 %  54 1  55 +  56 STO O  57 REGMOVE       58 XEQ 09  59 FC? 05  60 XEQ 15  61 FS? 05  62 XEQ 16  63 RCL O  64 RCL 00  65 +  66 REGSWAP  67 XEQ 09  68 RCL 00  69 1  70 CHS  71 GTO 03  72 LBL "A^X"  73 LBL 12  74 STO M  75 XEQ 13  76 RCL 00  77 RCL M  78 XEQ 03  79 GTO 07  80 LBL "X^A"  81 LN  82 RCL 00  83 X<>Y  84 XEQ 03  85 GTO 07  86 LBL "A^A"  87 XEQ 06  88 XEQ 13  89 XEQ 09  90 LBL "E^A"  91 LBL 07  92 XEQ 14  93 R-D  94 RCL 01

95 E^X  96 P-R  97 STO 01  98 X<> Z  99 X=0? 100 SIGN 101 GTO 02 102 LBL "SIN" 103 LBL 19 104 CF 05 105 CF 06 106 GTO 04 107 LBL "COS"     108 LBL 20 109 SF 05 110 CF 06 111 GTO 04 112 LBL "SH" 113 LBL 11 114 CF 05 115 SF 06 116 GTO 04 117 LBL "CH" 118 LBL 00 119 SF 05 120 SF 06 121 LBL 04 122 XEQ 14 123 X<> 01 124 FC? 06 125 X<>Y 126 ENTER 127 E^X-1 128 LASTX 129 CHS 130 E^X-1 131 - 132 X<>Y 133 E^X 134 ENTER 135 1/X 136 + 137 2 138 ST/ Z 139 / 140 R^ 141 R-D

142 1 143 P-R 144 FS? 05 145 X<>Y 146 ST* T 147 RDN 148 * 149 FC? 05 150 FC? 06 151 X<>Y 152 FS? 05 153 FS? 06 154 FS? 30 155 CHS 156 X<>Y 157 X<> 01 158 X=0? 159 SIGN 160 GTO 02 161 LBL "ASH"      162 LBL 15 163 CF 05 164 GTO 04 165 LBL "ACH" 166 SF 05 167 LBL 04 168 XEQ 06 169 XEQ 09 170 1 171 FS? 05 172 CHS 173 ST+ 01 174 2 175 1/X 176 XEQ 12 177 RCL 00 178 ENTER 179 ST+ Y 180 LBL 08 181 RCL IND Y 182 ST+ IND Y 183 RDN 184 DSE Y 185 DSE X 186 GTO 08 187 LBL "LN" 188 LBL 13

189 XEQ 14 190 LASTX 191 RCL 01 192 X^2 193 + 194 SQRT 195 X=0? 196 GTO 04 197 LN 198 GTO 13 199 LBL 04 200 ACOS 201 TAN 202 CHS 203 LBL 13            204 X<> 01 205 R-P 206 RDN 207 D-R 208 X<>Y 209 X#0? 210 GTO 02 211 SIGN 212 STO 02 213 LBL 02 214 / 215 RCL 00 216  E-3 217 + 218 X<>Y 219 LBL 03 220 ST* IND Y 221 DSE Y 222 GTO 03 223 RTN 224 LBL "TAN" 225 XEQ 06 226 XEQ 19 227 X<> M 228 REGSWAP 229 XEQ 20 230 GTO 04 231 LBL "TH" 232 XEQ 06 233 XEQ 11 234 X<> M 235 REGSWAP

236 XEQ 00 237 LBL 04 238 XEQ 18 239 LBL 09 240 RCL 00 241  E-3 242 + 243 STO M 244 1 245 + 246 RCL 00 247 ST+ X 248 STO N 249 RCL IND Y     250 STO Y 251 RCL 01 252 * 253 LBL 01 254 RCL 01 255 RCL IND N 256 * 257 RCL IND M 258 R^ 259 ST* Y 260 RDN 261 + 262 X<> IND M 263 RCL IND N 264 * 265 - 266 DSE N 267 DSE M 268 GTO 01 269 STO 01 270 RTN 271 LBL 14 272 RCL 00 273  E-3 274 + 275 0 276 LBL 05 277 RCL IND Y 278 X^2 279 + 280 DSE Y 281 GTO 05 282 SQRT

283 ENTER 284 RTN 285 LBL 06 286 RCL 00 287 .1 288 % 289 ISG X 290 + 291 .1 292 % 293 1 294 + 295 STO M 296 REGMOVE      297 RTN 298 LBL "ATH" 299 LBL 16 300 XEQ 06 301 SIGN 302 ST- 01 303 RCL 00 304 X<>Y 305 ST+ Y 306 ST+ IND Y 307 RCL 00 308 X<>Y 309 CHS 310 XEQ 03 311 XEQ 13 312 X<> M 313 REGSWAP 314 XEQ 13 315 RCL 00 316 ENTER 317 ST+ Y 318 LBL 10 319 RCL IND X 320 RCL IND Z 321 - 322 2 323 / 324 STO IND Y 325 RDN 326 DSE Y 327 DSE X 328 GTO 10 329 END

 
      ( 620 bytes / SIZE n+1 or 2n+1 or 3n+1 )
 
 

STACK	INPUT	OUTPUT
X	/  or  x	/

   X-input x is required for "A^X" & "X^A" only.

Examples:      XEQ  DEG

1°)   Q = 6 + 7 i + 8 j + 9 k     Calculate  Q^Q

-Quaternion so:   4  STO 00

        6  STO 01  7  STO 02  8  STO 03  9  STO 04

        XEQ "A^A"  >>>>   0.710111872 + 0.426305198 i + 0.487205940 j + 0.548106683 k     in R01 thru R04
 

2°)   O = 0 + 0.1 e₁ + 0.2 e₂ + 0.3 e₃ + 0.3 e₄ + 0.4 e₅ + 0.5 e₆ + 0.6 e₇    Calculate Arc Sinh O

-Octonion so:    8  STO 00

     0  STO 01  0.1  STO 02  0.2  STO 03  0.3  STO 04  0.3  STO 05  0.4  STO 06  0.5  STO 07  0.6  STO 08  ( an octonion such that O^2 = -1 )

     XEQ "ASH"  >>>>   0 + 0.157079633 e₁ + 0.314159265 e₂ + 0.471238898 e₃ + 0.471238898 e₄       in R01-R02-R03-R04-R05
                                   + 0.628318531 e₅ + 0.785398164 e₆ + 0.942477796 e₇                                              R06-R07-R08
 

3°)    S = 1 + 0.95 e₁ + 0.9 e₂ + 0.85 e₃ + 0.8 e₄ + 0.75 e₅ + 0.7 e₆ + 0.65 e₇ + 0.6 e₈      Calculate  Tanh S
                  + 0.55 e₉ + 0.5 e₁₀ + 0.45 e₁₁ + 0.4 e₁₂ + 0.35 e₁₃ + 0.3 e₁₄ + 0.25 e₁₅

-Sedenion so:  16  STO 00

    1     STO 01         0.8    STO 05         0.6    STO 09       0.4    STO 13
  0.95  STO 02        0.75   STO 06        0.55   STO 10      0.35   STO 14
   0.9   STO 03         0.7    STO 07         0.5    STO 11       0.3    STO 15
  0.85  STO 04        0.65   STO 08        0.45   STO 12      0.25   STO 16

    XEQ "TH"   >>>>   0.909559410 - 0.093982576  e₁ - 0.089036125 e₂ - 0.084089673 e₃                  in  R01 thru R16
                                 - 0.079143222 e₄ - 0.074196771 e₅ - 0.069250319 e₆ - 0.064303868 e₇
                                 - 0.059357417 e₈ - 0.054410965 e₉ - 0.049464514 e₁₀ - 0.044518062 e₁₁
                                 - 0.039571611 e₁₂ - 0.034625160 e₁₃ - 0.029678708 e₁₄ - 0.024732257 e₁₅

    ... and so on ...
 

Notes:        The HP-41 must be in DEG mode

-The X-output is usually meaningless
-Lines 196 to 203 give Ln(0) = -9.999999999 E99  ( "almost" minus infinity )
-Thus, Arc Sinh & Arc Cosh work well when  a^2 +/- 1 = 0

-LBL 09 ( lines 239 to 270 ) calculates the product of 2 anions when the imaginary parts are proportional.

-Arc Sin , Arc Cos & Arc Tan use 3n+1 data registers
-Synthetic registers M & N are sometimes used and the alpha "register" is not cleared in this case.