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bshoring · 04-13-2016, 10:55 PM

(04-13-2016 12:54 AM)Gerson W. Barbosa Wrote:
(04-12-2016 04:16 AM)bshoring Wrote: Thanks. Works well on my actual HP-38C. Results as indicated.

Thanks for testing it on the real thing. Thanks also for the idea of using NPV to evaluate at least one of the polynomials. This has saved memory for a higher order arctangent polynomial.

At least one of the HP-12C results in my previous posting is wrong (copy & paste error) . This is the correct one:

0.9999 GTO 38 R/S --> 0.8102920566 ; acos(0.9999) ; [0.8102914375] {0.8102914371}

(04-12-2016 04:16 AM)bshoring Wrote: When I get time I'll set it up also on RPN-38 CX, to see how they compare.

Sin(x):

x (deg)......HP-38C.........RPN-38CX......HP-15C (1982)...HP-35 (1972)
------------------------------------------------------------------------
0.000000 0.000000000E+00 0.000000000E+00 0.000000000E+00 0.000000000E+00
0.000010 1.745329252E-07 1.745329252E-07 1.745329252E-07 1.745000000E-07
0.000110 1.919862177E-06 1.919862177E-06 1.919862177E-06 1.919800000E-06
0.022000 3.839724258E-04 3.839724260E-04 3.839724260E-04 3.839723931E-04
3.330000 5.808674960E-02 5.808674960E-02 5.808674960E-02 5.808674961E-02
14.44000 2.493660251E-01 2.493660251E-01 2.493660251E-01 2.493660250E-01
25.55000 4.312985869E-01 4.312985870E-01 4.312985870E-01 4.312985871E-01
36.66000 5.970652564E-01 5.970652564E-01 5.970652564E-01 5.970652561E-01
47.77000 7.404527823E-01 7.404527826E-01 7.404527827E-01 7.404527828E-01
58.88000 8.560867284E-01 8.560867282E-01 8.560867283E-01 8.560867285E-01
69.99000 9.396329131E-01 9.396329128E-01 9.396329127E-01 9.396329127E-01
81.11000 9.879868530E-01 9.879868529E-01 9.879868528E-01 9.879868527E-01
88.88000 9.998089502E-01 9.998089500E-01 9.998089500E-01 9.998089499E-01
89.99000 9.999999850E-01 9.999999848E-01 9.999999848E-01 9.999999848E-01
89.99900 1.000000000E+00 9.999999998E-01 9.999999998E-01 9.999999998E-01
90.00000 1.000000000E+00 1.000000000E+00 1.000000000E+00 1.000000000E+00

Tan(x):

x (deg)......HP-38C.........RPN-38CX......HP-15C (1982)...HP-35 (1972)
------------------------------------------------------------------------
0.000000 0.000000000E+00 0.000000000E+00 0.000000000E+00 0.000000000E+00
0.000010 1.745329252E-07 1.745329252E-07 1.745329252E-07 1.745000000E-07
0.000110 1.919862177E-06 1.919862177E-06 1.919862177E-06 1.919800000E-06
0.022000 3.839724258E-04 3.839724543E-04 3.839724543E-04 3.839724542E-04
3.330000 5.818499267E-02 5.818499267E-02 5.818499267E-02 5.818499266E-02
14.44000 2.575006491E-01 2.575006491E-01 2.575006491E-01 2.575006490E-01
25.55000 4.780471796E-01 4.780471798E-01 4.780471798E-01 4.780471798E-01
36.66000 7.442915883E-01 7.442915882E-01 7.442915883E-01 7.442915880E-01
47.77000 1.101686576E+00 1.101686577E+00 1.101686578E+00 1.101686578E+00
58.88000 1.656411391E+00 1.656411390E+00 1.656411391E+00 1.656411391E+00
69.99000 2.745986127E+00 2.745986118E+00 2.745986117E+00 2.745986119E+00
81.11000 6.393166511E+00 6.393166482E+00 6.393166451E+00 6.393166426E+00
88.88000 5.115045162E+01 5.115043063E+01 5.115042993E+01 5.115042860E+01
89.99900 5.773502604E+04 5.729581914E+04 5.729577951E+05 5.729655162E+04
89.99990 ....Error 0.... 5.729525534E+05 5.729577951E+05 5.730193057E+05
90.00000 ....Error 0.... ....Error 0.... 9.999999999E+99 9.999999999E+99

ArcTan(x):

...x........HP-38C.........RPN-38CX......HP-15C (1982)...HP-35 (1972)
-------------------------------------------------------------------------
0.00000 0.000000000E+00 0.000000000E+00 0.000000000E+00 0.000000000E+00
0.00011 6.302535741E-03 6.302535789E-03 6.302535721E-03 6.302535688E-03
0.15500 8.810733019E+00 8.810732984E+00 8.810732986E+00 8.810732984E+00
0.26795 1.500004317E+01 1.500004315E+01 1.500004317E+01 1.500004317E+01
0.41421 2.249982576E+01 2.249982574E+01 2.249982578E+01 2.249982579E+01
0.57735 2.999998843E+01 2.999998845E+01 2.999998843E+01 2.999998843E+01
0.77700 3.784720679E+01 3.784720676E+01 3.784720677E+01 3.784720676E+01
0.88800 4.160507644E+01 4.160507646E+01 4.160507646E+01 4.160507646E+01
1.00000 4.499999997E+01 4.500000000E+01 4.500000000E+01 4.500000000E+01
1.22200 5.070548705E+01 5.070548704E+01 5.070548702E+01 5.070548702E+01
1.48880 5.611145719E+01 5.611145720E+01 5.611145723E+01 5.611145722E+01
2.11100 6.465265739E+01 6.465265738E+01 6.465265735E+01 6.465265735E+01
4.88800 7.843782363E+01 7.843782359E+01 7.843782359E+01 7.843782360E+01
7.55500 8.246000676E+01 8.246000683E+01 8.246000683E+01 8.246000679E+01
99.9990 8.942705558E+01 8.942705557E+01 8.942705557E+01 8.942705555E+01
7777.77 8.999266614E+01 8.999263339E+01 8.999263339E+01 8.999263337E+01
1.0E+05 9.000000000E+01 8.999942704E+01 8.999942704E+01 8.999942704E+01

The arctangent polynomial constants have been changed slightly:

R4: 0.199991241
R5: 0.14251795
R6: -0.0616468

Also, steps 71 through 74 have been changed:

71- 9
72- .
73- 4
74- 1/x

Plot #1

Plot #2

Regards,

Gerson.

After updating my HP-38C with the new steps and constants in R4-6, I get
0.9999 GTO 38 R/S --> 0.8102920566 (.810291465 with my HP-35v.4)

TAN:
.00000 I get .01690354059 on HP-38C.
89.999 I get Error 0 (divide by 0) on HP-38C.

ArcTan:
.00000 I get Error 0 on HP-38C
99.999 I get 8.942705958E+01 on HP-38C

I didn't try every one, but of all the rest I tried, I got the same results as you.
Pretty good accuracy, I'd say. Going through this exercise gives me a great respect for the talented minds that created the first HP-35 !

Thanks,
Bob