HP4950G Square root many (50 or more) digits

04242021, 11:08 PM
Post: #1




HP4950G Square root many (50 or more) digits
HP4950G Square root many digits
Of course there are plenty ways of calculating the square root. Here is a sequence of commands included in one single program that can be used as a userassigned key. ROOT2 \<< "\[] 1 Arg \[] Put below 101 if you want 100 digits " DROP 51 \> digit \<< 105 CF DUP "\v/" SWAP + SWAP DUP \v/ SWAP DUP \>STR SWAP FP \> nb f \<< IF f 0 \=/ THEN nb "." POS 1  \> pos \<< nb "." "" SREPL DROP DUP SIZE \> nb1 sz1 \<< pos 2 / FP 0 == IF THEN sz1 2 / FP 0 \=/ IF THEN nb1 0 + 'nb1' STO END ELSE sz1 2 / FP 0 == IF THEN nb1 0 + 'nb1' STO END END nb1 \>> \>> ELSE nb "." "" SREPL DROP END \>> DUP SIZE 2 / FP 0 == "" 0 IFTE SWAP + DUP SIZE 2 / \> n sz \<< { } 0 sz 1  FOR i n i 2 * 1 + DUP 1 + SUB OBJ\> + NEXT 'n' STO 0 0 0 0 1 \> a b m s k \<< WHILE k digit < REPEAT a b  100 * 'a' STO k sz \<= IF THEN n k GET 'a' STO+ END 1 'k' STO+ 9 's' STO WHILE 20 m * s + s * a > REPEAT 1 's' STO+ END 20 m * s + s * 'b' STO 10 m * s + 'm' STO END m \>STR \> st \<< st 2 50 FOR i st i digit 1  SUB OBJ\> 0 == IF THEN 1 i 1  SUB digit 1  'i' STO END NEXT OBJ\> DUP2 == IF THEN SWAP DROP END \>> \>> \>> \>> \>> 52.3 ASN (Or 52.1 ASN or 52.2 ASN.) We assign (ASN command) this program to the square root key 52. Example 1 Introduce for instance 9 and LS User Then sqrtkey (under the EVALkey). You get in level stack 2 sqrt(9) 3 in level stack 1 Example 2 Introduce now 9 and LS User Then sqrtkey (under the EVALkey). You get in level stack 3 sqrt(900) 30 in level stack 2 (normally an approximation). 3, which represents the first "50 digits, less the redundant zeroes". Example 3 Insure yourself that you are in exact mode. Type 1234567891234 Then press ENTER Then press a second time ENTER Ptess * in order to multiply both identical numbers in the stack. You should get 1524157878065965654042756 Now LS User Then sqrtkey (under the EVALkey). You get in level stack 3 "Sqrt(1524157878065965654042756)" In stack level 2 the approximative result 1.23456789124E12 And 1234567891234 in level 1 (the zeroes after the second digit 4 on the right are left out). Example 4 Insure yourself that you are in exact mode. Type as argument 1524157878065965654042757 (757 at the end, and not 756). Now LS User Then sqrtkey (under the EVALkey). You get in level stack 3 "Sqrt(1524157878065965654042756)" In stack level 2 the approximative result 1.23456789124E12 And 1234567891234 in level 1 (the zeroes after the second digit 4 on the right are left out). Example 4 Insure yourself that you are in exact mode. Type as argument 1524157878065965654042757 (757 at the end, and not 756). Now LS User Then sqrtkey (under the EVALkey). You get in level stack 3 "Sqrt(1524157878065965654042757)" In stack level 2 the approximative result 1.23456789124E12 And 12345678912340000000000004050000032806863265750682 in level 1. Note that, this time, the zeroes after the second digit 4 on the right do appear as, after them, do appear also different ≠0digits. Example 5 12.178 LSUser SQRTKey Gives "sqrt(12.178) " in stack level 3 3.48969912743 in stack level 2 and, in stack level 1, 34896991274320484031821999216879351359311052016725 Example 6 Sqrt 1.2178 Gives, in stack level 3,"sqrt(1.2178)" 1.10353975914 in stack level 2 and, in stack level 1, 11035397591387453041375873710499307803985079728862. Seems to work fine. Best is to use the phone EMU48 application if you don't want to way too much for the answers. Note that you can modify the number of digits to be calculated and shown. Regards, Gil Campart 

04272021, 05:30 PM
Post: #2




RE: HP4950G Square root many (50 or more) digits
Version 2
You can keep the version 1. For 50 digits, this new version instead going to a loop = "511" and k<51, has its loop that goes, more logically, directly up to the required digit 50 (not 511) and k<= 50 (not k<51). The new code and in bold the changes \<< "\[] 1 Arg \[] Put below 100 if you want 100 digits " DROP 50 \> digit \<< 105 CF DUP "\v/" SWAP + SWAP DUP \v/ SWAP DUP \>STR SWAP FP \> nb f \<< IF f 0 \=/ THEN nb "." POS 1  \> pos \<< nb "." "" SREPL DROP DUP SIZE \> nb1 sz1 \<< pos 2 / FP 0 == IF THEN sz1 2 / FP 0 \=/ IF THEN nb1 0 + 'nb1' STO END ELSE sz1 2 / FP 0 == IF THEN nb1 0 + 'nb1' STO END END nb1 \>> \>> ELSE nb "." "" SREPL DROP END \>> DUP SIZE 2 / FP 0 == "" 0 IFTE SWAP + DUP SIZE 2 / \> n sz \<< { } 0 sz 1  FOR i n i 2 * 1 + DUP 1 + SUB OBJ\> + NEXT 'n' STO 0 0 0 0 1 \> a b m s k \<< WHILE k digit \<= REPEAT a b  100 * 'a' STO k sz \<= IF THEN n k GET 'a' STO+ END 1 'k' STO+ 9 's' STO WHILE 20 m * s + s * a > REPEAT 1 's' STO+ END 20 m * s + s * 'b' STO 10 m * s + 'm' STO END m \>STR \> st \<< st 2 50 FOR i st i digit SUB OBJ\> 0 == IF THEN 1 i 1  SUB digit 'i' STO END NEXT OBJ\> DUP2 == IF THEN SWAP DROP END \>> \>> \>> \>> \>> Then for assigning to sqrtkey write : 52.3 ASN ENTER. Regards, Gil 

05042021, 02:24 PM
Post: #3




RE: HP4950G Square root many (50 or more) digits
RE: HP4950G
Square root many (50 or more) digits Version 3 Corrected / trapped some small errors. Allows now to enter as argument 1) A positive/negative number like: 4 (you will get a complex as an answer) 4.6 2.56E28 715.57E19 2) Or a string — for more or full precision when working with exponents (or with "," + many digits) — like: "4. 11111111234567888889067" "4.62345778933456789" "2.564546677890677E28" "715.575675677889E19" 3 or 4 results 3 results:  how many last digits of 50 (or of 100, depending on your settings) were calculated being = 0 and were cut in the final result; (note that if no digit was cut in the result, then that first line information will not appear);  the initial argument in a string with the sqrt sign;  the exact or approximate result as calculated by the sqrt key function of the calculator. 4 results: When the exact value is not possible with the normal sqrt function of the calculator, a last (fourth) line is added with all the significative digits ≠ 0 (in principle, 50 digits, but remember that when last digits calculated are = 0, the latter are not shown). Here is the full, changed code: \<< "\[] 1 Arg \[] Put below 100 if you want 100 digits " DROP 50 \> digit \<< DUP TYPE 2 \=/ IF THEN \>STR END DUPDUP SIZE SWAP OBJ\> \> x0 s0 x1 \<< 3 SF 105 CF "\v/" x0 + x1 \v/ x0 "" "" SREPL DROP 'x0' STO x0 DUP "E" POS DUP 0 == IF THEN DROP 1 s0 ELSE 1 SWAP 1  END SUB "." "" SREPL DROP DUP SIZE 's0' STO 'x0' STO x1 MANT x1 XPON \> man xpo \<< s0 2 / FP 0 \=/ IF THEN 0 x0 xpo 2 / FP 0 \=/ { SWAP } IFT + ELSE xpo 2 / FP 0 == IF THEN 0 x0 + 0 + ELSE x0 END END DUPDUP 'x0' STO SIZE 2 / \> n sz \<< { } 0 sz 1  FOR i n i 2 * 1 + DUP 1 + SUB OBJ\> + NEXT 'n' STO 0 0 0 0 1 \> a b m s k \<< WHILE k digit \<= REPEAT a b  100 * 'a' STO k sz \<= IF THEN n k GET 'a' STO+ END 1 'k' STO+ 9 's' STO WHILE 20 m * s + s * a > REPEAT 1 's' STO+ END 20 m * s + s * 'b' STO 10 m * s + 'm' STO END m \>STR \> st \<< st 2 digit FOR i st i digit SUB OBJ\> 0 == IF THEN digit i  1 + " last # of \v/ =0" + 4 ROLLD 1 i 1  SUB digit 'i' STO END NEXT OBJ\> DUP2 \> r1 r2 \<< r1 DUP TYPE 1 == IF THEN IM END MANT \>STR "." "" SREPL DROP DUP "E" POS DUP 0 > IF THEN 1  1 SWAP SUB OBJ\> ELSE DROP OBJ\> END r2 == IF THEN DROP END \>> \>> \>> \>> \>> \>> \>> \>> 523 ASN Regards, Gil 

05042021, 08:19 PM
Post: #4




RE: HP4950G Square root many (50 or more) digits
Just corrected the code
for cases of the type sqrt (2E2). Besides you can now choose how many digits you want to be calculated by using as input: {X xx},  where X is the number of which you want the square root  and where cx is number of digits to be calculated. By default, the number xx is 50. In that case, you can directly enter as argument: X or "XX" (double quotation mark). The full, new code is: \<< "Version 4 Give 1 Arg \[] 2.5 or 2.5E6 or 2.5 or 2.5E6 or \[] or" "1234567891234567" "with quotation mark! \[] or {X xx} with X: like above & xx: # digits " 3 DROPN DUP TYPE 5 == IF THEN OBJ\> DROP ELSE 50 "Put above 100 if you want 100 digits" DROP END \> digit \<< DUP TYPE 2 \=/ IF THEN \>STR END DUPDUP SIZE SWAP OBJ\> \> x0 s0 x1 \<< 3 SF 105 CF "\v/" x0 + x1 \v/ x0 "" "" SREPL DROP 'x0' STO x0 DUP "E" POS DUP 0 == IF THEN DROP 1 s0 ELSE 1 SWAP 1  END SUB "." "" SREPL DROP OBJ\> \>STR DUP SIZE 's0' STO 'x0' STO x1 MANT x1 XPON \> man xpo \<< s0 2 / FP 0 \=/ IF THEN 0 x0 xpo 2 / FP 0 \=/ { SWAP } IFT + ELSE xpo 2 / FP 0 == IF THEN 0 x0 + 0 + ELSE x0 END END DUPDUP 'x0' STO SIZE 2 / \> n sz \<< { } 0 sz 1  FOR i n i 2 * 1 + DUP 1 + SUB OBJ\> + NEXT 'n' STO 0 0 0 0 1 \> a b m s k \<< WHILE k digit \<= REPEAT a b  100 * 'a' STO k sz \<= IF THEN n k GET 'a' STO+ END 1 'k' STO+ 9 's' STO WHILE 20 m * s + s * a > REPEAT 1 's' STO+ END 20 m * s + s * 'b' STO 10 m * s + 'm' STO END m \>STR \> st \<< st 2 digit FOR i st i digit SUB OBJ\> 0 == IF THEN digit i  1 + " last # of \v/ =0" + 4 ROLLD 1 i 1  SUB digit 'i' STO END NEXT OBJ\> DUP2 \> r1 r2 \<< r1 DUP TYPE 1 == IF THEN IM END MANT \>STR "." "" SREPL DROP DUP "E" POS DUP 0 > IF THEN 1  1 SWAP SUB OBJ\> ELSE DROP OBJ\> END r2 == IF THEN DROP END \>> \>> \>> \>> \>> \>> \>> \>> 

« Next Oldest  Next Newest »

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