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Each of the following programs takes up only one label and will always give at least 11 correct digits for arguments in degrees ( 999,999,999,909 <= x <= 999,999,999,999 ).
Gerson.
L0001 LBL L
L0002 x<>y
L0003 STO A
L0004 x<>y
L0005 +/
L0006 90
L0007 +
L0008 360
L0009 RMDR
L0010 STO B
L0011 90
L0012 INT/
L0013 STO C
L0014 ENTER
L0015 ENTER
L0016 2
L0017 INT/
L0018 
L0019 180
L0020 *
L0021 RCL B
L0022 1
L0023 RCL C
L0024 ENTER
L0025 x!
L0026 +
L0027 y^x
L0028 *
L0029 STO B
L0030 x^2
L0031 ENTER
L0032 ENTER
L0033 ENTER
L0034 2.0934E26
L0035 *
L0036 4.47566E20
L0037 
L0038 *
L0039 5.55391606E14
L0040 +
L0041 *
L0042 3.28183761372E08
L0043 
L0044 *
L0045 5.81776417331E03
L0046 +
L0047 RCL* B
L0048 ENTER
L0049 x^2
L0050 4
L0051 *
L0052 +/
L0053 3
L0054 +
L0055 *
L0056 RCL A
L0057 x<>y
L0058 RTN
LN=330
CK=AE03
M0001 LBL M
M0002 DEG
M0003 x<>y
M0004 STO D
M0005 x<>y
M0006 SIN
M0007 LASTx
M0008 XEQ L
M0009 /
M0010 RCL D
M0011 x<>y
M0012 RTN
LN=36
CK=3737
89.9999999 XEQ L > 1.74532925199E9
89.9999999 COS > 1.74532000000E9
actual > 1.74532925199433E9
89.9999999 XEQ M > 572,957,795.132
89.9999999 TAN > 572,960,832.397
actual > 572,957,795.1308232
5555 XEQ L > 9.06307787035E1
5555 COS > 9.06307787037E1
actual > 9.06307787036650E1
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Thanks Gerson for sharing yet another version of your minimax polynomial approximations of some of the trigonometric functions.
For fussbudgets like me, this will be very useful, and I will enter them in my HP35S (the porting should be easy) when I get it.
I am actually more troubled by the persistence of the cosine bug than the inconvenient entry of hex numbers everyone seems so fussed about. The persistence of the digit loss for arguments approaching 90 degrees has accuracy implications for the sine of very small angles, the tangent function, complex number math, and of course rectangularpolar conversions.
FWIW, can someone with a 35S compute the cosine for 89.99, 89.999, 89.9999, and 89.99999, etc., degrees and let us all know?
Les
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Quote:
FWIW, can someone with a 35S compute the cosine for 89.99, 89.999, 89.9999, and 89.99999, etc., degrees
cos(89.99) = 1.74532924306 E4
cos(89.999) = 1.74532925091 E5
cos(89.9999) = 1.74532925 E6
cos(89.99999) = 1.7453292 E7
cos(89.999999) = 1.745329 E8
cos(89.9999999) = 1.74532 E9
cos(89.99999999) = 1.74532925199 E10
cos(89.999999999) = 1.74532925199 E11
cos(89.9999999999) = 1.74532925199 E12
cos(89.99999999999) = 1.74532925199 E12
cos(89.999999999999) = 1.74532925199 E12
.
.
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Edited: 23 July 2007, 11:14 p.m.
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Thanks!
Yep, the cosine bug has survived unchanged.
I am actually intrigued that when one gets to 89.99999999, full 12digit accuracy in the result returns. Weird! I am sure someone once explained the cause of this bug.
Les
Edited: 24 July 2007, 5:35 a.m.
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Hi Les (and all).
The 35s review at the hpcc.org site stated that the COS bug was still there. This was available the day the 35s was announced.
Datafile 35s review
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Quote:
I will enter them in my HP35S (the porting should be easy) when I get it.
Hello Les,
I think it will run with no modification on the HP35s. But it will require three keystrokes to access the function, by what I've read: [XEQ] [L] [ENTER], for instance, instead of the more convenient [XEQ] [COS] on the HP33s.
Best regards,
Gerson.
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Gerson,
Your routines are very fast. Say what you like about the now obsolete 33S, but it does run keystroke programs with lightning quickness. I understand that in many cases the 35S may actually be slower!
I also like how you preserve the contents of the Y register for subsequent calculations. Unfortunately the routines don't keep the entire stack in its original state, but this is a nice touch. One problem about RPN programs is they make a mess of the stack sometimes, unlike the internal routines. RPL programs tend not to do this, unless you want them too.
Les
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Hello Les,
Quote:
Your routines are very fast. Say what you like about the now obsolete 33S, but it does run keystroke programs with lightning quickness. I understand that in many cases the 35S may actually be slower!
Too bad they don't run fast enough on the 35s: about 1.5 seconds. They appear to run 10 times faster on the 33s (no timing so far).
Also, [XEG] [COS] [ENTER] is very inconvenient. And having to press [>] to see the exponent is pretty cumbersome. Didn't they realize the exponent is much more important than the least significant digits? I prefer ALL mode, not that I don't care about all those digits, but because I don't like integers being displayed will all those zeros. I am very inclined to getting rid of this 35s and getting another obsolete 33s...
Regards,
Gerson.
