(35S) Accurate Trig Functions Corrected
06-29-2015, 03:33 PM (This post was last modified: 06-15-2017 01:26 PM by Gene.)
Post: #1
 Gerald H Senior Member Posts: 1,458 Joined: May 2014
(35S) Accurate Trig Functions Corrected
All of the copies of Hosoda's improved trig functions I have found err in missing out lines H005 & H006 - I have at last decided to supply the lack.

Code:
 SIN H001 LBL H H002 XEQ J015 H003 χ<>y H004 XEQ I006 H005 FS? 3 H006 +/- H007 XEQ J004 H008 RTN COS I001 LBL I I002 XEQ J015 I003 XEQ I006 I004 XEQ J004 I005 RTN TAN TO COS I006 i1 I007 × I008 + I009 LASTχ I010 χ<>y I011 ÷ I012 ABS I013 FS? 3 I014 +/- I015 FS? 4 I016 +/- I017 RTN TAN J001 LBL J J002 XEQ J015 J003 ÷ RESTORE REGS J004 3 J005 STO I J006 CLχ J007 RCL(I) J008 DSE I J009 GTO J007 J010 R↑ J011 χ<>(I) J012 ABS J013 χ<>(I) J014 RTN SAVE REGS J015 RPN J016 STO J J017 CLχ J018 4 J019 STO I J020 STO(I) J021 DSE I J022 R↑ J023 STO(I) J024 DSE I J025 GTO J022  J026 RCL J J027 STO(I) RANGE REDUCTION J028 CF 1 J029 SF 2 J030 CF 3 J031 CF 4 J032 χ<0? J033 SF 1 J034 ABS J035 ENTER J036 ENTER J037 π J038 STO I J039 RMDR J040 χ<>y J041 LASTχ J042 INT÷ J043 STO J J044 2 J045 RMDR J046 χ≠0? J047 SF 4 J048 R↓ J049 0.25 J050 RCL× I J051 χ<y? J052 CF 2 J053 CLχ J054 0.5 J055 RCL× I J056 x≤y? J057 SF 3 J058 CLχ J059 0.75 J060 RCL× I J061 χ<>y J062 χ<y? J063 GTO J068 J064 SF 2 J065 RCL- I J066 ISG J J067 2007 09/06 J068 FS? 2 J069 GTO J078 J070 ENTER J071 + J072 RCL- I J073 0.5 J074 × J075 LASTχ J076 STO+ J J077 CLχ J078 2.06761537357E-13 J079 RCL× J J080 + TAN APPROXIMATION J081 STO J J082 χ² J083 ENTER J084 ENTER J085 ENTER J086 7.7158e-2 J087 × J088 11 J089 - J090 ÷ J091 9 J092 + J093 ÷ J094 7 J095 - J096 ÷ J097 5 J098 + J099 ÷ J100 3 J101 - J102 ÷ J103 1 J104 + J105 RCL J J106 χ<>y J107 FS? 2 J108 GTO J111 J109 +/- J110 χ<>y J111 FS? 1 J112 +/- J113 RTN
07-24-2015, 02:46 AM (This post was last modified: 07-24-2015 11:26 AM by Marcio.)
Post: #2
 Marcio Senior Member Posts: 438 Joined: Feb 2015
RE: HP 35S: Accurate Trig Functions Corrected
Dear Gerald,

Have you ever used Hosoda's to solve an equation inside a program?

I do hope I am missing something because it seems to me that the 35s's solver enters an infinite loop when I try to solve equations as simple as $$y=sin(p)$$.

This is the program I am using, assuming $$y=1$$:

F001 LBL F
F002 RCL P
F003 XEQ H001;
F004 1
F005 -
F006 RTN

FN = F

Solve for P.

The 35s, 50g and Prime will get at least 4 digits correct for this specific example, the final digits will vary based on the start guess provided.

$$p=89.9999....$$

Thanks.

Marcio
07-24-2015, 05:34 AM
Post: #3
 Gerald H Senior Member Posts: 1,458 Joined: May 2014
RE: HP 35S: Accurate Trig Functions Corrected
This is a question about the Solver, Marcio, so please start a new thread, best place is general forum.
07-24-2015, 05:35 AM
Post: #4
 Gerald H Senior Member Posts: 1,458 Joined: May 2014
RE: HP 35S: Accurate Trig Functions Corrected
Here's a link to Hosoda's original article:

http://www.finetune.co.jp/~lyuka/technot...hp35s.html
07-24-2015, 10:07 AM (This post was last modified: 07-24-2015 11:26 AM by Marcio.)
Post: #5
 Marcio Senior Member Posts: 438 Joined: Feb 2015
RE: HP 35S: Accurate Trig Functions Corrected
(07-24-2015 05:34 AM)Gerald H Wrote:  This is a question about the Solver, Marcio, so please start a new thread, best place is general forum.

I suspect Hosoda's gets affected by bug 20:
Code:
 BUG 20: Solve infinite loops for some program based functions. Assign FN=D and SOLVE the following for X.  The solve doesn't finish. This seems to be related to using a loop in the function being solved. D001 LBL D D002 10 D003 STO N D004 DSE N D005 GTO D004 D006 RCL X D007 COS D008 RTN

but I have not had the time to check if the workaround will actually work in this case. I will open a new thread as soon as I am back from work.

Thanks.
08-02-2015, 05:04 PM (This post was last modified: 08-02-2015 05:05 PM by lyuka.)
Post: #6
 lyuka Junior Member Posts: 48 Joined: May 2014
RE: HP 35S: Accurate Trig Functions Corrected
(06-29-2015 03:33 PM)Gerald H Wrote:  All of the copies of Hosoda's improved trig functions I have found err in missing out lines H005 & H006 - I have at last decided to supply the lack.

Code:
 H005 FS? 3 H006 +/-

Thanks Gerald. I corrected the missing two lines of the code on my websites now.
08-02-2015, 05:58 PM
Post: #7
 Gerald H Senior Member Posts: 1,458 Joined: May 2014
RE: HP 35S: Accurate Trig Functions Corrected
Pleased to see the corrected programme.

Nice work.
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