Trigonometric Functions for the HP-38C/HP-12C

[Gerson W. Barbosa]

(03-26-2016 08:21 PM)bshoring Wrote:  The Trig functions are working like a charm.

Even better now!

Thanks for the fun, even though today is still Easter Sunday Eve. Well, no programming tomorrow then :-)

Gerson.

Fast and Accurate Trigonometric Functions on the RPN-38 CX Simulator

Code:


01 - 3            3
02 - 71           ÷
03 - 21 11        STO n
04 - 31           ENTER
05 - 61           ×
06 - 31           ENTER
07 - 31           ENTER
08 - 31           ENTER
09 - 22 61 8      RCL × 8
10 - 22 51 7      RCL + 7
11 - 61           ×
12 - 22 41 6      RCL − 6
13 - 61           ×
14 - 22 51 0      RCL + 0
15 - 22 11        RCL n
16 - 61           ×
17 - 31           ENTER
18 - 31           ENTER
19 - 61           ×
20 - 4            4
21 - 61           ×
22 - 32           CHS
23 - 3            3
24 - 51           +
25 - 61           ×
26 - 31           ENTER
27 - 31           ENTER
28 - 31           ENTER
29 - 61           ×
30 - 32           CHS
31 - 1            1
32 - 51           +
33 - 24 21        √x
34 - 25 7 00      GTO 00
35 - 25 6         x=0
36 - 25 7 00      GTO 00
37 - 31           ENTER
38 - 61           ×
39 - 24 71        1/x
40 - 1            1
41 - 41           −
42 - 24 71        1/x
43 - 25 7 49      GTO 49
44 - 31           ENTER
45 - 61           ×
46 - 24 71        1/x
47 - 1            1
48 - 41           −
49 - 24 21        √x
50 - 25 6         x=0
51 - 25 7 00      GTO 00
52 - 1            1
53 - 33           x≷y
54 - 25 5         x≤y
55 - 25 7 58      GTO 58
56 - 24 71        1/x
57 - 9            9
58 - 0            0
59 - 21 15        STO FV
60 - 25 33        R↓
61 - 24 71        1/x
62 - 21 11        STO n
63 - 31           ENTER
64 - 61           ×
65 - 51           +
66 - 24 21        √x
67 - 22 11        RCL n
68 - 41           −
69 - 21 11        STO n
70 - 31           ENTER
71 - 61           ×
72 - 31           ENTER
73 - 31           ENTER
74 - 31           ENTER
75 - 22 61 5      RCL × 5
76 - 22 41 4      RCL − 4
77 - 61           ×
78 - 22 51 3      RCL + 3
79 - 61           ×
80 - 22 41 2      RCL − 2
81 - 61           ×
82 - 22 51 1      RCL + 1
83 - 61           ×
84 - 3            3
85 - 24 71        1/x
86 - 41           −
87 - 61           ×
88 - 1            1
89 - 51           +
90 - 22 11        RCL n
91 - 61           ×
92 - 2            2
93 - 61           ×
94 - 22 71 0      RCL ÷ 0
95 - 22 15        RCL FV
96 - 25 6         x=0
97 - 33           x≷y
98 - 33           x≷y
99 - 41           −

------------------------------------------

1.745329252E-02 STO 0
0.199999779 STO 1
0.142841665 STO 2
1.107161127E-01 STO 3
0.086263068 STO 4
0.05051923 STO 5
8.860961462E-07 STO 6
1.349582775E-11 STO 7
9.73259E-17 STO 8

------------------------------------------
Alternatively, but no significant difference:

1745329251 ENTER 99433 + g EEX 10 / STO 0

8860961462 ENTER .4934 + g EEX 16 / STO 6
------------------------------------------

Usage:


Trigonometric functions:


Enter angles in degrees, -90 =< x <= 90 (*):


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

GTO 35 R/S => arcsin(x)
GTO 44 R/S => arccos(x)
GTO 50 R/S => arctan(x)

------------------------------------------

0.0001 R/S --> 1.000000000 ; cos(0.0001)
x<>y --> 1.745329252E-06 ; sin(0.0001)
/ --> 1.745329252E-06 ; tan(0.0001)

0.9999 GTO 35 R/S --> 89.18960866 ; asin(0.9999)
0.9999 GTO 44 R/S --> 0.8102914371 ; acos(0.9999)
0.9999 GTO 50 R/S --> 44.99713507 ; atan(0.9999)


Other examples:

sin(0.01) = 0.9999999848
sin(0.01) = 1.745329243E-04
tan(0.01) = 1.745329270E-04

sin(30) = 0.8660254038
cos(30) = 0.5000000000
tan(30) = 0.5773502692

sin(60) = 0.500000000(1)
cos(60) = 0.866025403(7)
tan(60) = 1.73205080(8)

sin(89.99) = 0.9999999848
cos(89.99) = 1.7453(37879)E-4
tan(89.99) = 5729.5(49544)

sin(89.9999) = 1.000000000
cos(89.9999) = 1.7462(35540)E-6
tan(89.9999) = 572(660.4329)

asin(0) = 0.000000000
acos(0) = Error 0
atan(0) = 0.000000000

asin(1e-10) = 90.00000000

atan(0.4142135624) = 22.50000000

atan(1) = 45.00000000

acos(0.8660254038) = 30.00000000

atan(50) = 88.85423716

------------------------------------------

Forensic result:

9 R/S x<>y R/S R/S / GTO 50 R/S GTO 44 R/S GTO 35 R/S --> 9.000000272

------------------------------------------


P.S.:

(03-26-2016 08:21 PM)bshoring Wrote:  The emulator for the HP-38C allows RCL arithmetic so in some cases I've been able to combine steps, so I can put GOTO instructions at the beginning so now I can use:
COS(x): [R/S]
SIN(x): [R/S] [x<>y]
TAN(x): [R/S] [/]
ASIN(x): [g] [GTO] 02 [R/S]
ACOS(x): [g] [GTO] 03 [R/S]
ATAN(x): [g] [GTO] 04 [R/S]

If you replace register n with register 9 then you can save at least three steps, but I think this won't be enough. Anyway, the new labels (35, 44, and 50) are somewhat easier to remember.