Template

Tides(3) for the HP-41

Overview

1°) 4 M-Code Routines
2°) Los Angeles
3°) Miami
4°) Seattle
5°) Washington

-The 4 M-Code routines listed in §1 employ a polynomial approximation to calculate Cos x

>>> The formula is:    Cos x ~ 1 - 1.5127 E-4 x² + 3.445 E-9 x⁴ where x is between -90° & +90°

-The maximum error is about 0.00074
-So, it may be used to calculate the water-levels with a very small error.

-This method is already employed in one version of "WL37" but this program is very long and uses a lot of registers.
-So, if you want to calculate the water-levels for just one port, you can rewrite one of the programs listed in "Tides(2) for the HP41"
  which will run significantly faster than the focal version.

1°) 4 M-Code Routines

08C "L"
013 "S"
003 "C"
288 SF 7
0B3 JNC+22d
0AF "/"
013 "S"
003 "C"
248 SF 9
02B JNC+05
0AA "*"
013 "S"
003 "C"
244 CF 9
0F8 C=X
10E A=C ALL
0B8 C=Y
0E8 X=C
0AE A<>C ALL
0A8 Y=C
108 SF 8
033 JNC+06
093 "S"
003 "C"
284 CF 7
244 CF 9
104 CF 8
2A0 SETDEC
0F8 C=X
128 L=C
05E C= | C |
10E A=C ALL
04E C
35C
050 =
210
226
226 180
268 Q=C
1FA C=C+C M
044 C
070 =
171
064 AmodC
10E A=C ALL
278 C=Q
2BE C=-C
01D C=
061 A+C
05E C= | C |
070 N=C ALL
10E A=C ALL
04E C
2BE
35C =
250
226 -90
268 Q=C
01D C=
060 A+C
2FE ?C<0
047 JC+08
278 C=Q
025 C=
060 AB+C
070 N=C ALL
278 C=Q
2BE C=-C
268 Q=C
0B0 C=N ALL
10E A=C ALL
135 C=
060 A*C
070 N=C ALL
04E C
35C
0D0
110
110
150 =
21C
250
250
050 3.445 E-9
13D C=
060 AB*C
04E C
35C
2BE
050
150 =
050
090
1D0
21C
250
250
190 -1.5127 E-4
025 C=
060 AB+C
0B0 C=N ALL
13D C=
060 AB*C
001 C=
060 AB+1
10E A=C ALL
278 C=Q
11E A=C MS
0AE A<>C ALL
0E8 X=C
10C FS? 8
067 JC+12d
28C FS? 7
3A0 ?NC RTN
078 C=Z
028 T=C
0B8 C=Y
068 Z=C
0F8 C=X
0A8 Y=C
138 C=L
0E8 X=C
3E0 RTN
10E A=C ALL
0B8 C=Y
24C FS? 9
05F JC+11d
135 C=
060 A*C
0E8 X=C
078 C=Z
0A8 Y=C
046 C
270 =
038 T
068 Z=C
3E0 RTN
261 C=
060 A/C
3B3 JNC-10d

( 140 lines )

"CS" calculates Cos x with the polynomial approximation:    1 - 1.5127 E-4 x² + 3.445 E-9 x⁴ ( -90° <= x <= +90° )

"CSL" is "CS" LASTX
"CS*" calculates X Cos Y
"CS/" returns ( Cos Y ) / X

Warning: These routines do not check for alpha data

-Here are a few examples:

2°) Los Angeles CA 9410660

Data Registers:    R00 to R07: temp
Flags: /
Subroutine: "J2" ( or "J0" or "J1" cf "Julian & Gregorian Calendars for the HP41" )

01 LBL "WLLA"
02 HR
03 24
04 /
05 X<>Y
06 XEQ "J2"
07 +
08 STO 00
09 .985647
10 *
11 STO 01
12 96
13 +
14 66
15 CS*
16 RCL 00
17 360
18 *
19 STO 02
20 46
21 +
22 3
23 CS*
24 -
25 RCL 02
26 RCL 01
27 -
28 STO 03
29 35
30 -
31 STO 07
32 RCL 00
33 .052954
34 *
35 235
36 +
37 STO 04
38 -
39 89
40 CS/
41 RCL 07
42 CS
43 -
44 107
45 *
46 +
47 RCL 02
48 RCL 03
49 +

50 53
51 +
52 12
53 CS*
54 -
55 RCL 01
56 ST+ 01
57 RCL 02
58 +
59 STO 03
60 17.7
61 -
62 STO 07
63 CSL
64 RCL 04
65 ST+ 07
66 -
67 50
68 CS/
69 -
70 RCL 07
71 7.4
72 CS/
73 +
74 343
75 *
76 -
77 RCL 02
78 ST+ 02
79 RCL 03
80 +
81 9
82 +
83 3
84 CS*
85 +
86 RCL 00
87 13.064993
88 *
89 STO 05
90 RCL 03
91 +
92 81
93 -
94 CSL
95 RCL 04
96 +
97 5
98 CS/

99 +
100 20
101 *
102 +
103 RCL 03
104 RCL 05
105 -
106 19
107 +
108 CSL
109 RCL 04
110 +
111 5
112 CS/
113 +
114 12
115 *
116 +
117 RCL 00
118 26.352793
119 *
120 STO 06
121 RCL 03
122 X<>Y
123 ST- 03
124 +
125 17
126 +
127 CSL
128 RCL 04
129 +
130 STO 07
131 .64
132 CS*
133 +
134 RCL 07
135 RCL 04
136 +
137 7
138 CS/
139 +
140 11
141 *
142 -
143 RCL 03
144 65.8
145 -
146 CSL
147 RCL 04

148 -
149 STO 07
150 5.3
151 CS/
152 +
153 RCL 07
154 RCL 04
155 -
156 166
157 CS/
158 -
159 218
160 *
161 +
162 RCL 03
163 RCL 05
164 +
165 32
166 +
167 4
168 CS*
169 -
170 RCL 03
171 RCL 05
172 -
173 STO 00
174 7
175 -
176 CSL
177 RCL 04
178 -
179 5.3
180 CS/
181 +
182 39
183 *
184 -
185 RCL 00
186 RCL 05
187 -
188 44
189 +
190 4
191 CS*
192 +
193 RCL 02
194 38.9
195 +
196 203

197 CS*
198 -
199 RCL 02
200 RCL 05
201 -
202 65
203 +
204 3
205 CS*
206 -
207 RCL 01
208 ST- 06
209 RCL 02
210 +
211 STO 00
212 64
213 +
214 STO 07
215 CSL
216 RCL 04
217 ST+ 07
218 -
219 77
220 CS/
221 -
222 RCL 07
223 .3
224 CS*
225 +
226 RCL 07
227 RCL 04
228 +
229 31
230 CS/
231 +
232 60
233 *
234 +
235 RCL 00
236 RCL 05
237 -
238 63
239 -
240 2
241 CS*
242 +
243 RCL 03
244 RCL 06
245 -

246 STO 03
247 RCL 05
248 +
249 29
250 +
251 CSL
252 RCL 04
253 -
254 5.3
255 CS/
256 +
257 8
258 *
259 -
260 RCL 02
261 RCL 06
262 -
263 STO 03
264 9
265 -
266 CSL
267 RCL 04
268 -
269 27
270 CS/
271 -
272 515
273 *
274 +
275 RCL 03
276 1.5
277 *
278 35
279 +
280 3
281 CS*
282 +
283 RCL 03
284 RCL 05
285 +
286 49
287 -
288 8
289 CS*
290 +
291 RCL 03
292 RCL 05
293 -

294 STO 00
295 64
296 +
297 CSL
298 RCL 04
299 -
300 27
301 CS/
302 -
303 121
304 *
305 -
306 RCL 00
307 RCL 05
308 -
309 35
310 -
311 15
312 CS*
313 -
314 RCL 03
315 RCL 06
316 -
317 STO 03
318 5
319 +
320 17
321 CS*
322 -
323 RCL 03
324 RCL 05
325 +
326 90
327 -
328 CSL
329 RCL 04
330 -
331 27
332 CS/
333 -
334 23
335 *
336 +
337 861
338 +
339 E3
340 /
341 END

( 508 bytes / SIZE 008 )


STACK	INPUTS	OUTPUTS
Y	YYYY.MNDD	/
X	HH.MNSS (UT)	water level (m)

Example: Water level in Los Angeles on 2015/07/16 at 21h41m UT ( YMD format )

2015.0716 ENTER^ ---Execution time = 27s---
21.41 XEQ "WLLA" >>>> h = 0.708 m

Note:

-We have saved 12 seconds

3°) Miami Beach FL 8723170

Data Registers: R00 to R07: temp
Flags: /
Subroutine: "J2" ( or "J0" or "J1" cf "Julian & Gregorian Calendars for the HP41" )

01 LBL "WLM"
02 HR
03 24
04 /
05 X<>Y
06 XEQ "J2"
07 +
08 STO 00
09 .985647
10 *
11 STO 01
12 81
13 +
14 88
15 CS*
16 RCL 00
17 360
18 *
19 STO 02
20 RCL 01
21 -
22 STO 03
23 78
24 -
25 13
26 CS*
27 -
28 RCL 02
29 RCL 03

30 +
31 41
32 -
33 4
34 CS*
35 +
36 RCL 01
37 ST+ 01
38 RCL 02
39 ST+ 02
40 +
41 STO 03
42 55
43 -
44 STO 07
45 CS
46 RCL 00
47 .052954
48 *
49 235
50 +
51 STO 04
52 RCL 07
53 +
54 7.4
55 CS/
56 +
57 42
58 *

59 -
60 RCL 03
61 RCL 00
62 26.352793
63 *
64 STO 06
65 -
66 STO 03
67 38
68 +
69 CSL
70 RCL 04
71 -
72 5.3
73 CS/
74 +
75 34
76 *
77 -
78 RCL 03
79 RCL 00
80 13.064993
81 *
82 STO 05
83 -
84 STO 00
85 78
86 +
87 CSL

88 RCL 04
89 -
90 5
91 CS/
92 +
93 6
94 *
95 +
96 RCL 01
97 49
98 -
99 62
100 CS*
101 -
102 RCL 02
103 44
104 -
105 75
106 CS*
107 +
108 RCL 01
109 ST- 06
110 RCL 02
111 +
112 STO 00
113 36
114 -
115 CSL
116 RCL 04

117 +
118 .3
119 CS*
120 +
121 20
122 *
123 -
124 RCL 00
125 RCL 05
126 -
127 48
128 +
129 CSL
130 RCL 04
131 +
132 .4
133 CS*
134 +
135 ST+ X
136 +
137 RCL 02
138 RCL 06
139 -
140 STO 03
141 64
142 -
143 CSL
144 RCL 04
145 -

146 27
147 CS/
148 -
149 373
150 *
151 -
152 RCL 03
153 RCL 05
154 +
155 62
156 +
157 10
158 CS*
159 +
160 RCL 03
161 RCL 05
162 -
163 STO 00
164 7
165 +
166 CSL
167 RCL 04
168 -
169 27
170 CS/
171 -
172 85
173 *
174 +

175 RCL 00
176 RCL 05
177 -
178 78
179 +
180 11
181 CS*
182 -
183 RCL 03
184 RCL 06
185 -
186 STO 03
187 84
188 -
189 11
190 CS*
191 +
192 RCL 03
193 RCL 05
194 +
195 38
196 +
197 16
198 CS*
199 +
200 428
201 +
202 E3
203 /
204 END

( 314 bytes / SIZE 008 )


STACK	INPUTS	OUTPUTS
Y	YYYY.MNDD	/
X	HH.MNSS (UT)	water level (m)

Example: Let's find the water level in Miami on 2015/08/08 at 7h41m UT

2015.0808 ENTER^
7.41 XEQ "WLS" >>>> h = 0.772 m ---Execution time = 16s---

Note:

-We have saved 8 seconds

4°) Seattle WA 9447130

Data Registers: R00 to R07: temp
Flags: /
Subroutine: "J2" ( or "J0" or "J1" cf "Julian & Gregorian Calendars for the HP41" )

01 LBL "WLS"
02 HR
03 24
04 /
05 X<>Y
06 XEQ "J2"
07 +
08 STO 00
09 .985647
10 *
11 STO 01
12 13
13 -
14 77
15 CS*
16 RCL 00
17 360
18 *
19 STO 02
20 44
21 -
22 16
23 CS*
24 -
25 RCL 02
26 RCL 01
27 -
28 STO 03
29 73
30 +
31 STO 07
32 RCL 00
33 .052954
34 *
35 235
36 +
37 STO 04
38 -
39 89
40 CS/
41 RCL 07
42 CS
43 -
44 258
45 *
46 -
47 RCL 02
48 RCL 03
49 +
50 34
51 -
52 16
53 CS*
54 +
55 RCL 01
56 ST+ 01
57 RCL 02
58 +
59 STO 03
60 87
61 -
62 STO 07
63 CLS
64 RCL 04
65 ST+ 07
66 -
67 50
68 CS/
69 -
70 RCL 07
71 7.4
72 CS/

73 +
74 834
75 *
76 -
77 RCL 02
78 ST+ 02
79 RCL 03
80 +
81 41
82 -
83 2
84 CS*
85 -
86 RCL 00
87 13.064993
88 *
89 STO 05
90 RCL 03
91 +
92 3
93 +
94 STO 06
95 CLS
96 RCL 04
97 ST+ 06
98 -
99 34
100 CS/
101 -
102 RCL 06
103 5
104 CS/
105 +
106 40
107 *
108 -
109 RCL 03
110 RCL 05
111 -
112 78
113 -
114 CLS
115 RCL 04
116 +
117 5
118 CS/
119 +
120 27
121 *
122 +
123 RCL 03
124 RCL 00
125 13.176396
126 *
127 STO 06
128 ST+ 06
129 -
130 72
131 -
132 5
133 CS*
134 -
135 RCL 06
136 77
137 -
138 CLS
139 RCL 04
140 +
141 2.4
142 CS/
143 +
144 22

145 *
146 +
147 RCL 03
148 3
149 *
150 RCL 06
151 -
152 68
153 +
154 STO 07
155 CLS
156 RCL 04
157 ST+ 07
158 -
159 18
160 CS/
161 -
162 RCL 07
163 7.4
164 CS/
165 +
166 34
167 *
168 +
169 RCL 03
170 RCL 06
171 ST- 03
172 +
173 75
174 -
175 CLS
176 RCL 04
177 +
178 STO 07
179 .64
180 CS*
181 +
182 RCL 04
183 RCL 07
184 +
185 7.5
186 CS/
187 +
188 32
189 *
190 -
191 RCL 03
192 51.9
193 +
194 CLS
195 RCL 04
196 -
197 STO 07
198 5.3
199 CS/
200 +
201 RCL 07
202 RCL 04
203 -
204 166
205 CS/
206 -
207 461
208 *
209 -
210 RCL 03
211 RCL 05
212 +
213 65
214 -
215 CLS
216 RCL 04

217 -
218 5.4
219 CS/
220 +
221 10
222 *
223 -
224 RCL 03
225 RCL 05
226 -
227 STO 00
228 72
229 -
230 CLS
231 RCL 04
232 -
233 5.3
234 CS/
235 +
236 75
237 *
238 -
239 RCL 00
240 RCL 05
241 -
242 22
243 -
244 CLS
245 RCL 04
246 -
247 5.3
248 CS/
249 +
250 8
251 *
252 +
253 RCL 01
254 31
255 -
256 33
257 CS*
258 +
259 RCL 02
260 37
261 -
262 268
263 CS*
264 +
265 RCL 02
266 RCL 05
267 -
268 3
269 +
270 20
271 CS*
272 +
273 RCL 01
274 ST- 06
275 RCL 02
276 +
277 STO 00
278 18
279 -
280 STO 07
281 CLS
282 RCL 04
283 ST+ 07
284 -
285 77
286 CS/
287 -
288 RCL 07

289 .3
290 CS*
291 +
292 RCL 07
293 RCL 04
294 +
295 31
296 CS/
297 +
298 79
299 *
300 -
301 RCL 00
302 RCL 05
303 -
304 15
305 +
306 CLS
307 RCL 04
308 +
309 .44
310 CS*
311 +
312 11
313 *
314 +
315 RCL 03
316 RCL 06
317 -
318 STO 03
319 RCL 05
320 +
321 35
322 -
323 CLS
324 RCL 04
325 -
326 5.3
327 CS/
328 +
329 15
330 *
331 -
332 RCL 02
333 RCL 03
334 +
335 36
336 +
337 STO 07
338 CLS
339 RCL 04
340 ST+ 07
341 -
342 16
343 CS/
344 +
345 RCL 07
346 50
347 CS/
348 -
349 34
350 *
351 -
352 RCL 02
353 RCL 06
354 -
355 STO 03
356 54.1
357 -
358 CLS
359 RCL 04
360 -

361 27
362 CS/
363 -
364 1072
365 *
366 -
367 RCL 02
368 RCL 06
369 +
370 59
371 -
372 8
373 CS*
374 +
375 RCL 03
376 3
377 *
378 STO 00
379 84
380 -
381 CLS
382 RCL 04
383 -
384 9
385 CS/
386 -
387 9
388 *
389 -
390 RCL 00
391 2
392 /
393 42
394 +
395 5
396 CS*
397 +
398 RCL 03
399 RCL 05
400 +
401 29
402 +
403 CLS
404 RCL 04
405 -
406 27
407 CS/
408 -
409 45
410 *
411 +
412 RCL 03
413 RCL 05
414 -
415 STO 00
416 27
417 +
418 CLS
419 RCL 04
420 -
421 27
422 CS/
423 -
424 216
425 *
426 +
427 RCL 00
428 RCL 05
429 -
430 69
431 -
432 24

433 CS*
434 +
435 RCL 03
436 RCL 06
437 -
438 STO 03
439 36
440 +
441 CLS
442 RCL 04
443 -
444 27
445 CS/
446 -
447 34
448 *
449 +
450 RCL 03
451 RCL 05
452 +
453 46
454 +
455 CLS
456 RCL 04
457 -
458 27
459 CS/
460 -
461 45
462 *
463 +
464 RCL 02
465 RCL 03
466 +
467 STO 03
468 73
469 +
470 CLS
471 RCL 04
472 -
473 13
474 CS/
475 -
476 21
477 *
478 +
479 RCL 03
480 ST+ 06
481 RCL 05
482 -
483 29
484 -
485 9
486 CS*
487 +
488 RCL 06
489 87
490 +
491 CLS
492 RCL 04
493 -
494 28
495 CS/
496 -
497 12
498 *
499 -
500 2024
501 +
502 E3
503 /
504 END

( 741 bytes / SIZE 008 )


STACK	INPUTS	OUTPUTS
Y	YYYY.MNDD	/
X	HH.MNSS (UT)	water level (m)

Example: Let's find the water level in Seattle on 2015/07/16 at 12h34m56s UT

2015.0716 ENTER^
12.3456 XEQ "WLS" >>>> h = 3.070 m ---Execution time = 38s---

Note:

-We have saved about 22 seconds.

5°) Washington D.C. 8594900

Data Registers: R00 to R07: temp
Flags: /
Subroutine: "J2" ( or "J0" or "J1" cf "Julian & Gregorian Calendars for the HP41" )

01 LBL "WLW"
02 HR
03 24
04 /
05 X<>Y
06 XEQ "J2"
07 +
08 STO 00
09 .985647
10 *
11 STO 01
12 169
13 +
14 77
15 CS*
16 RCL 00
17 360
18 *
19 STO 02
20 36
21 +
22 12
23 CS*
24 -
25 RCL 02
26 RCL 01
27 -
28 STO 03
29 14
30 -
31 STO 07
32 RCL 00
33 .052954
34 *
35 235
36 +
37 STO 04
38 -
39 89
40 CS/
41 RCL 07
42 CS
43 -
44 13
45 *
46 -
47 RCL 02
48 RCL 03
49 +
50 79
51 +
52 5

53 CS*
54 -
55 RCL 01
56 ST+ 01
57 RCL 02
58 +
59 STO 03
60 13
61 +
62 CSL
63 RCL 04
64 +
65 7.4
66 CS/
67 +
68 46
69 *
70 +
71 RCL 02
72 ST+ 02
73 RCL 03
74 +
75 90
76 +
77 4
78 CS*
79 +
80 RCL 00
81 13.064993
82 *
83 STO 05
84 RCL 03
85 +
86 26
87 -
88 3
89 CS*
90 -
91 RCL 03
92 RCL 05
93 -
94 52
95 +
96 2
97 CS*
98 -
99 RCL 00
100 26.352793
101 *
102 STO 06
103 RCL 03
104 3

105 *
106 X<>Y
107 -
108 71
109 +
110 CSL
111 RCL 04
112 +
113 7.4
114 CS/
115 +
116 12
117 *
118 -
119 RCL 03
120 RCL 06
121 ST- 03
122 +
123 16
124 +
125 CSL
126 RCL 04
127 +
128 .64
129 CS*
130 +
131 3
132 *
133 +
134 RCL 03
135 76
136 -
137 CSL
138 RCL 04
139 -
140 5.3
141 CS/
142 +
143 35
144 *
145 -
146 RCL 03
147 RCL 05
148 -
149 STO 00
150 12
151 +
152 CSL
153 RCL 04
154 -
155 5.3
156 CS/

157 +
158 7
159 *
160 +
161 RCL 00
162 RCL 05
163 -
164 CS
165 -
166 RCL 01
167 20
168 -
169 38
170 CS*
171 -
172 RCL 02
173 64
174 -
175 52
176 CS*
177 +
178 RCL 02
179 RCL 05
180 -
181 6
182 +
183 13
184 CS*
185 +
186 RCL 01
187 ST- 06
188 RCL 02
189 +
190 STO 00
191 42
192 -
193 STO 07
194 CSL
195 RCL 04
196 +
197 .3
198 CS*
199 +
200 18
201 *
202 -
203 RCL 00
204 RCL 05
205 -
206 38
207 +
208 CSL

209 RCL 04
210 +
211 .44
212 CS*
213 +
214 7
215 *
216 +
217 RCL 03
218 RCL 06
219 -
220 STO 03
221 RCL 05
222 +
223 CS
224 +
225 RCL 02
226 RCL 03
227 +
228 4
229 -
230 11
231 CS*
232 +
233 RCL 02
234 RCL 06
235 -
236 STO 03
237 63.9
238 -
239 CSL
240 RCL 04
241 -
242 27
243 CS/
244 -
245 407
246 *
247 -
248 RCL 03
249 3
250 *
251 STO 00
252 38
253 +
254 CSL
255 RCL 04
256 -
257 9
258 CS/
259 -
260 12

261 *
262 -
263 RCL 03
264 RCL 05
265 +
266 62
267 +
268 CSL
269 RCL 04
270 -
271 27
272 CS/
273 -
274 27
275 *
276 +
277 RCL 03
278 RCL 05
279 -
280 STO 00
281 12
282 +
283 CSL
284 RCL 04
285 -
286 27
287 CS/
288 -
289 75
290 *
291 +
292 RCL 00
293 RCL 05
294 -
295 84
296 -
297 7
298 CS*
299 +
300 RCL 03
301 RCL 06
302 -
303 STO 03
304 25
305 -
306 8
307 CS*
308 -
309 RCL 03
310 RCL 05
311 +
312 40

313 +
314 17
315 CS*
316 +
317 RCL 02
318 RCL 03
319 +
320 STO 03
321 48
322 -
323 CSL
324 RCL 04
325 -
326 13
327 CS/
328 -
329 42
330 *
331 +
332 RCL 03
333 RCL 05
334 -
335 27
336 +
337 CSL
338 RCL 04
339 -
340 13
341 CS/
342 -
343 16
344 *
345 -
346 RCL 03
347 ST+ X
348 80
349 +
350 4
351 CS*
352 +
353 RCL 03
354 RCL 06
355 +
356 53
357 -
358 11
359 CS*
360 -
361 472
362 +
363 E3
364 /
365 END

( 531 bytes / SIZE 008 )


STACK	INPUTS	OUTPUTS
Y	YYYY.MNDD	/
X	HH.MNSS (UT)	water level (m)

Example: Water level in Washington on 2015/06/22 at 17h06 UT

2015.0622 ENTER^
17.06 XEQ "WLW" >>>> h = 0.899 m ---Execution time = 28s---

Notes:

-In this example, we have saved 13 seconds.

-All the other programs listed in "Tides(2) for the HP41" paragraph 2°) may be transformed in the same way.
-Use Sin x = Cos ( x - 90° ) or Sin x = - Cos ( x + 90° ) ....
-It doesn't change a lot the number of bytes.

hp41programs

Tides(3) for the HP-41