Easter Sunday Trigs ( rpn38-CX)

[Gerson W. Barbosa]

(04-02-2016 11:12 PM)bshoring Wrote:  Gerson,
For what it's worth, I was able to eliminate one program step on the latest and greatest trig program.

I replaced the 2nd & 3rd steps:
02 - 31 ENTER
03 - 61 ×

with a single "RCL X 8" as that squares the value in X register. Having previously removed the line that swapped X<>Y at step 30, the program is now 97 steps.

Regards,
Bob

Great! Also, the same can be done twice around 60 steps further in the program. Since I prefer sine in X, I can spare yet another step:

Code:



Trigonometric Functions

R.0: 5.817764173314432e-03
R.1: 0.199999779
R.2: 0.142841665
R.3: 1.107161127e-01
R.4: 0.086263068
R.5: 0.05051923
R.6: 3.2818376136867e-08
R.7: 5.553916059e-14
R.8: 4.4756602e-20
R.9: 2.0935e-26


Angles in DEGREES

-90 =< x <= 90

R/S               --> sin(x)
R/S x<>y      --> cos(x)
R/S x<>y /    --> tan(x)

GTO 30 R/S --> asin(x)       0 =< x <= 1
GTO 41 R/S --> acos(x)      0 =< x <= 1
GTO 49 R/S --> atan(x)   1e-50 < x < 1e42

by Gerson W. Barbosa - Apr/2016


01 - 21 8         STO 8
02 - 22 61 8      RCL × 8
03 - 31           ENTER
04 - 31           ENTER
05 - 31           ENTER
06 - 86 61 9      RCL × .9
07 - 86 41 8      RCL − .8
08 - 61           ×
09 - 86 51 7      RCL + .7
10 - 61           ×
11 - 86 41 6      RCL − .6
12 - 61           ×
13 - 86 51 0      RCL + .0
14 - 22 61 8      RCL × 8
15 - 21 8         STO 8
16 - 21 51 8      STO + 8
17 - 3            3
18 - 22 8         RCL 8
19 - 22 61 8      RCL × 8
20 - 41           −
21 - 61           ×
22 - 21 8         STO 8
23 - 22 61 8      RCL × 8
24 - 32           CHS
25 - 1            1
26 - 51           +
27 - 24 21        √x
28 - 22 8         RCL 8
29 - 25 7 00      GTO 00
30 - 25 6         x=0
31 - 25 7 00      GTO 00
32 - 31           ENTER
33 - 61           ×
34 - 24 71        1/x
35 - 1            1
36 - 41           −
37 - 25 6         x=0
38 - 22 73 9      RCL .9
39 - 24 71        1/x
40 - 25 7 48      GTO 48
41 - 25 6         x=0
42 - 25 7 38      GTO 38
43 - 31           ENTER
44 - 61           ×
45 - 24 71        1/x
46 - 1            1
47 - 41           −
48 - 24 21        √x
49 - 25 6         x=0
50 - 25 7 00      GTO 00
51 - 1            1
52 - 33           x≷y
53 - 25 5         x≤y
54 - 25 7 57      GTO 57
55 - 24 71        1/x
56 - 9            9
57 - 0            0
58 - 21 9         STO 9
59 - 25 33        R↓
60 - 24 71        1/x
61 - 21 8         STO 8
62 - 22 61 8      RCL × 8
63 - 51           +
64 - 24 21        √x
65 - 22 41 8      RCL − 8
66 - 21 8         STO 8
67 - 22 61 8      RCL × 8
68 - 31           ENTER
69 - 31           ENTER
70 - 31           ENTER
71 - 86 61 5      RCL × .5
72 - 86 41 4      RCL − .4
73 - 61           ×
74 - 86 51 3      RCL + .3
75 - 61           ×
76 - 86 41 2      RCL − .2
77 - 61           ×
78 - 86 51 1      RCL + .1
79 - 61           ×
80 - 3            3
81 - 24 71        1/x
82 - 41           −
83 - 61           ×
84 - 1            1
85 - 51           +
86 - 22 61 8      RCL × 8
87 - 8            8
88 - 25 12        12÷
89 - 61           ×
90 - 86 71 0      RCL ÷ .0
91 - 22 9         RCL 9
92 - 25 6         x=0
93 - 33           x≷y
94 - 33           x≷y
95 - 41           −
96 - 25 7 00      GTO 00

By storing the constant 1/3 in register 7 and replacing the steps 80 through 82 with a single RCL- 7 instruction, per Willy's idea above, two other steps can be saved, thus leaving us six steps more to play with.

Regards,

Gerson.