Post Reply 
A very long HP-17BII equation - Update
06-08-2022, 02:12 PM
Post: #3
RE: A very long HP-17BII equation - Update
(12-15-2014 05:48 PM)Gerson W. Barbosa pid='23033' dateline='1418665718' Wrote:  Formatting has been lost in the tables. I have yet to find out how to fix that.

Here's my attempt to fix this:

For example:

sin(0.0000010)   1.7455(0850398)E-8
tan(0.0000010)   1.745(50000000)E-8
asin(0.000001)   5.7295(8368089)E-5
acos(0.999999)   8.1028474(8648)E-2
atan(0.000001)   5.7295(8368089)E-5

This update fixes that:

sin(0.0000010)   1.74532925199E-8
tan(0.0000010)   1.74532925199E-8
asin(0.000001)   5.72957795131E-5
acos(0.999999)   8.1028475206(4)E-2
atan(0.000001)   5.72957795131E-5

Also, COS is now slightly more accurate for small arguments and the forensic result is better:

Keystrokes              Display                 corresponding 
                                                HP-42S results
                                               
9 DSP ALL X             X=9
SIN                     SIN=1.56434465039E-1    0.15643446504
STO X COS               COS=9.99996272738E-1    9.99996272743E-1
STO X TAN               TAN=1.74549998553E-2    1.74549998555E-2
STO X MORE ATAN         ATAN=9.99996272738E-1   9.99996272744E-1
MORE STO X MORE ACOS    ACOS=1.56434567554E-1   1.56434441642E-1
MORE STO X MORE ASIN    ASIN=9.00000594679      8.99999864267

(…)

Running times:

 SIN:  2.0 s
 COS:  1.8 s
 TAN:  2.8 s
 DEG:  2.3 s
 RAD:  2.8 s
ASIN:  5.3 s
ACOS:  8.2 s
ATAN: 11.0 s

Ranges:

SIN, COS, TAN: -999 999 999 999 to 999 999 999 999  (1) 
  ASIN & ACOS: -1 to 1
         ATAN: 1E-11 < |X| <=  9.99999999999E-499   (2) 

(1) For odd multiples of 90 degrees, TAN returns 249999999996, which should be regarded as infinity
(2) Exponents equal or greater than 18 will cause UNDERFLOW, but the results will be correct (either -90 or +90 degrees)

Some usage examples:

3    X                  X=3 
DEG                     DEG=171.887338539       ; 3 rad = 171.887338539°      
STO X TAN               TAN=-1.42546543094E-1   ; tan(3 rad) = -1.42546543094E-1
123456789 X COS         COS=-9.87688340595E-1   ; cos(123456789) = -9.87688340595E-1
777777777717 +/- X SIN  SIN=5.2335956243E-2     ; sin(-777777777717°) = 5.2335956243E-2
0.5 X MORE ACOS         60.0000000002           ; acos(0.5) = 60.0000000002°
MORE STO X MORE RAD     1.0471975512            ; acos(0.5) = 1.0471975512 rad 
shift MATH 3 LN         1.09861228867
2 +/- / EXP EXIT        5.77350269189E-1
MORE STO X MORE ATAN    ATAN=30.0000000001      ; atan(exp(-ln(3)/2)) = 30.0000000001°


We need both: select Courier as font and use e.g. Unicode U+2003 : EM SPACE instead of an ordinary space.
Find all posts by this user
Quote this message in a reply
Post Reply 


Messages In This Thread
RE: A very long HP-17BII equation - Update - Thomas Klemm - 06-08-2022 02:12 PM



User(s) browsing this thread: 1 Guest(s)