Calculate 200^300 with SOLVE

02282016, 12:01 PM
(This post was last modified: 02282016 12:19 PM by tomisan.)
Post: #1




Calculate 200^300 with SOLVE
I use this short program on my 42S to get an approximate answer for exponentiation of large arguments, e.g. 200^300 = 2.037x10^690
00 {15Byte Prgm} 01 LBL "~Y↑X" 02 X<>Y 03 LOG 04 x 05 IP 06 LASTX 07 FP 08 10↑X 09 END 200 <ENTER> 300 <XEQ> ~Y↑X gives X:2.03703597073 Y:690 Playing with my newly acquired 17BII I came up with the following SOLVE equation (works also on the 17BII+): ~Y'X: 0xL(E:IP(L(M1:LOG(Y)xX)))+ 0xL(M:ALOG(FP(G(M1))))+ IF(S(MANT):MANTG(M):EXPG(E))=0 SOLVE is fun to use and amazingly powerful. 

02282016, 05:25 PM
(This post was last modified: 02292016 04:42 PM by Gerson W. Barbosa.)
Post: #2




RE: Calculate 200^300 with SOLVE
(02282016 12:01 PM)tomisan Wrote: I use this short program on my 42S to get an approximate answer for exponentiation of large arguments, e.g. 200^300 = 2.037x10^690 Quite acceptable result for this exponent when compared to the HP42S fullaccuracy answer: \[\frac{200^{300}}{2 ^{300}}=\left ( \frac{200}{2} \right )^{300}=100^{300}= \left ( 10^{2} \right )^{300}=10^{600}\] \[200^{300}=2^{300}\cdot 10^{600}=2.03703597633\cdot 10^{90}\cdot 10^{600}=2.03703597633\cdot 10^{690}\] The following allows for large exponents on the wp34S (DBLOFF, SSIZE4) while keeping full accuracy. Somewhat limited, however. Code:
200 ENTER 300 A > 2.037035976334486 x<>y > 690 450 ENTER 550 A > 1.848768685494735 x<>y > 1459 550 ENTER 650 A > +∞ Error (02282016 12:01 PM)tomisan Wrote: Playing with my newly acquired 17BII I came up with the following SOLVE equation (works also on the 17BII+): Indeed! As long as the equations remain short, of course :) Gerson. Edited to replace a dot with an = above. 

02282016, 06:59 PM
Post: #3




RE: Calculate 200^300 with SOLVE
This works on the 95LX:
LogPower=L(x,LOG(Base)*Power)+0*L(MANT,RND( ALOG(FP(G(x))),IP(LOG(L(XPON,IP(G(x)))))15))*MANT*XPON 

03012016, 02:57 AM
(This post was last modified: 03012016 03:03 AM by Tugdual.)
Post: #4




RE: Calculate 200^300 with SOLVE
And the 50g returns the exact result with all digits. There are plenty of zeros at the end and i was wondering if this was correct.
Note: probably yes since 200^300 = 2^300 * 100^300 The 50g is a wild animal... 

03012016, 06:18 AM
Post: #5




RE: Calculate 200^300 with SOLVE
The TI89 tops out at around 614 digits for an exact results answer so 200^300 returns 2.03704E690 on my emulator.


03012016, 02:25 PM
(This post was last modified: 03012016 02:33 PM by Gerson W. Barbosa.)
Post: #6




RE: Calculate 200^300 with SOLVE
(03012016 06:18 AM)Steve Simpkin Wrote: The TI89 tops out at around 614 digits for an exact results answer so 200^300 returns 2.03704E690 on my emulator. On the HP 50g, exact mode on: 203703597633448608626844568840937816105146839366593625063614044935438129976333670618339737600000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 Code:
The maximum number of digits is limited by available memory, I think. P.S.: This confirms Tugdual's post above, which I hadn't read yet. The HP49G was the first HP calculator to be able to solve this, by the way. 

03012016, 08:49 PM
Post: #7




RE: Calculate 200^300 with SOLVE
And the Prime? Anybody?


03012016, 09:18 PM
(This post was last modified: 03012016 09:19 PM by Arno K.)
Post: #8




RE: Calculate 200^300 with SOLVE  
03012016, 09:24 PM
Post: #9




RE: Calculate 200^300 with SOLVE  
03022016, 02:22 AM
Post: #10




RE: Calculate 200^300 with SOLVE
(03012016 02:25 PM)Gerson W. Barbosa Wrote:(03012016 06:18 AM)Steve Simpkin Wrote: The TI89 tops out at around 614 digits for an exact results answer so 200^300 returns 2.03704E690 on my emulator. I just typed 200 300 ^ on my 50g and got the same answer in under a second. Is there a reason that you used a loop with multiplication instead? John 

03022016, 03:29 AM
(This post was last modified: 03022016 11:12 AM by Gerson W. Barbosa.)
Post: #11




RE: Calculate 200^300 with SOLVE
(03022016 02:22 AM)John Keith Wrote:(03012016 02:25 PM)Gerson W. Barbosa Wrote: On the HP 50g, exact mode on: Yes, in 0.4193 s here. Then I was using the emulator in Debug4. I'd have to check the flags settings, but I'm sure it was in Exact Mode. Anyway, when I did 200 300 ^ I got an answer in scientific notation, not an overflow by what I can remember. I'll check it again later, as I'm away from the desktop computer now. Gerson. P.S.: I'd gotten 9.99999999999E499. I only didn't get an overflow error because of flag 21 setting. Upon checking the CAS MODES screen I noticed Numeric had been checked. D'oh, just unchecking it might've been easier! 

03022016, 06:09 PM
Post: #12




RE: Calculate 200^300 with SOLVE
(03022016 03:29 AM)Gerson W. Barbosa Wrote: P.S.: I'd gotten 9.99999999999E499. I only didn't get an overflow error because of flag 21 setting. Upon checking the CAS MODES screen I noticed Numeric had been checked. D'oh, just unchecking it might've been easier! The different behaviors based on flag and CAS configurations is both a blessing and a curse. It's nice to be able to set or clear a flag to make wholesale changes in how things are processed, but the sheer quantity of them makes troubleshooting and comparing experiences with other users prone to puzzling inconsistencies sometimes. Perhaps I'll set a signature for my account here that says something along the lines of "...this is how it works on my particular calculator with my particular configuration. Your experiences may vary drastically from the above. " Like you, I also tend to use the emulator with Debug4x when trying things out before loading up my 50g. I'm reluctant to say how often I've been caught by the fact that ZINTs get converted automatically to REALs if the emulated calculator is in approximate mode when the UserRPL program is transferred to it by Debug4x. Subsequent mode changes don't matter at that point. The program object was compiled by the calculator with REALs, so the damage has already been done. Knowing about the issue and actually remembering to make the mode change before pressing "F9" are two different things, though. 

03032016, 09:19 PM
Post: #13




RE: Calculate 200^300 with SOLVE
(03022016 06:09 PM)DavidM Wrote: I'm reluctant to say how often I've been caught by the fact that ZINTs get converted automatically to REALs if the emulated calculator is in approximate mode ... Thanks for reporting these little annoyances, I'm always looking in the forum for issues like this one to make sure newRPL does not repeat errors from the past. In this regards, newRPL compiler does not depend on any flags. If you write a number, the number is compiled "as written" by the user, even if it has more digits than the current system precision. I'm also for flagfree calculations (or as free as possible), ideally a command (or operator) output should be fully determined by its input, no flags should be involved. Back to the original topic, the exponents limits in newRPL are 30000 to +30000 so 200^300 is not an issue. 200^300 at any given precision gives the 2.03703...E690 with as many digits as you have requested. Setting the system precision to 91 digits is enough to get the exact result, with 90 you lose one digit. A trailing dot indicates when a result is approximated or exact, which in this case it comes handy to know if you are overflowing the current precision without having to actually look at all the digits. 

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