<content> rpn </content>

8b9ea747-437c-488d-b4c7-73ae55d59c02 221 Alvaro Diaz Falconi 4 5 false false 0 0 decimal

RPN Interpreter

For something between HP 33E & HP 41C

4 appVersion 1.0.8206.25180

App Programs:

https://www.hpmuseum.org/software/software.htm

https://www.hpmuseum.org/software/soft41.htm

rpn\0024\ - Unary A.11 CHS EXP LN RE IM 1/X ¬! SIGN ABS SQRT PI CHS exp ln Re Im RINV R#Not R#Fac sign abs sqrt PI 212 mat : A.12 SIN COS TAN ASIN ACOS ATAN sin cos tan asin acos atan 26 mat : A.13 SINH COSH TANH ASINH ACOSH ATANH sinh cosh tanh asinh acosh atanh 26 mat : A.14 FRAC INT FRAC trunc 22 mat : A.1 A.11 A.12 A.13 A.14 augment : - Binary A.2 + - * / Y^X & | < ≤ ≡ NTHROOT MOD R#a R#m R#t R#d R#p AND OR LT LE EQ nthroot mod 212 mat : A.3 R2P P2R xy2pol pol2xy 22 mat : A A.1 transpose 1 augment A.2 transpose 2 augment A.3 transpose 3 augment stack : - Progs: Shorthands M S T 02 matrix : A M k 1 A rows range s A k 2 el S1 el(S#,1) strrep S2 el(S#,2) strrep : s s Mt el(M#,t#) strrep K1 el(K#,1) strrep : A k 2 el s Ft el(F#,t#) strrep SMF mat(S#,M#,F#,1,3) strrep : 31 line for T T A stack : 21 line for T 31 line : - Progs T.1 X=0? if(S1≡0,0,K1:1) X≠0? if(S1≠0,0,K1:1) X<0? if(S1<0,0,K1:1) X>0? if(S1>0,0,K1:1) X≤0? if(S1≤0,0,K1:1) X≥0? if(S1≥0,0,K1:1) 62 mat : T.4 X=Y? if(S1≡S2,0,K1:1) X≠0? if(S1≠S2,0,K1:1) X<Y? if(S1<S2,0,K1:1) X>Y? if(S1>S2,0,K1:1) X≤Y? if(S1≤S2,0,K1:1) X≥Y? if(S1≥S2,0,K1:1) 62 mat : 12 mat T.5 X<>Y line(tmp#:S2,S2:S1,S1:tmp#,3,1) RUP S#:stack(el(S#,N#),submatrix(S#,1,N#-1,1,1)) RDN S#:stack(submatrix(S#,2,N#,1,1),S1) END break 42 mat : T.2 ↑ S#:stack(S1,S#) CLS S#:matrix(1,1) RET j#:PUSH(k#)+1 32 mat : T.3 MODE MODE(a#) CLX S#:submatrix(S#,2,N#,1,1) LST X S#:stack(el(K#,4),S#) 32 mat : 12 mat U.1 STO Mt:S1 STO+ Mt:Mt+S1 STO- Mt:Mt-S1 STO* Mt:Mt*S1 STO/ Mt:Mt/S1 52 mat : U.2 RCL S#:stack(Mt,S#) RCL+ S#:stack(Mt+S1,S#) RCL- S#:stack(Mt-S1,S#) RCL* S#:stack(Mt*S1,S#) RCL/ S#:stack(Mt/S1,S#) 52 mat : 12 mat U.4 PRG line(el(P#,t#):transpose(A#),break,2,1) XEQ SMF:XEQ(el(P#,t#),1) 22 mat : U.5 SF Ft:1 CF Ft:0 22 mat : U.6 FS? if(Ft≡1,0,K1:1) FC? if(Ft≡0,0,K1:1) 22 mat : 12 mat U.7 FS?C line(if(Ft≡1,0,K1:1),Ft:0,2,1) FC?S line(if(Ft≡0,0,K1:1),Ft:1,2,1) 22 mat : U.8 GTO j#:t#-1 GTO+ j#:j#+t#-1 GTO- j#:j#-t#+1 32 mat : U.9 GSB line(SMF:XEQ(B#,t#),k#:POP(j#,k#),2,1) GSB+ line(SMF:XEQ(B#,t#+j#),k#:POP(j#,k#),2,1) GSB- line(SMF:XEQ(B#,t#-j#),k#:POP(j#,k#),2,1) 32 mat : 12 mat A T.1 T.2 T.3 T.4 T.5 15 mat S U.1 U.2 U.4 U.5 U.6 U.7 U.8 U.9 18 mat S 13 mat eval 221 line :

ENTER 0 :

ENTER ENTER description :

A# Π# rpn a# t# val Clear x# CHS x# - : x# R#Fac x#! : x# RINV 1 x# / : x# y# R#d x# y# / : 14 mat x# y# R#a x# y# + : x# y# R#m x# y# - : x# y# R#t x# y# * : x# y# R#p x# y#^: 14 mat x# FRAC x# x# trunc - : x# PI π : 12 mat x# R#Not x# ¬ : x# y# AND x# y# & (: x# y# OR x# y# | (: 13 mat x# y# LT x# y# < (: x# y# LE x# y# ≤ (: x# y# EQ x# y# ≡ (: 13 mat m# n# σ# a# m# n# substr : s# L# s# IsString s# strlen 0 if 11 line : X# V W# 0 : k# 0 : 12 mat x# X# W# k# k# 1 + : el x# : for W# 31 line : 12 mat x# N2S# x# IsString x# x# num2str if : x# S2N# x# IsString x# str2num x# if : 12 mat n# a# FR# rpn\0024\ n# el a# 1 findrows : M# m# n# SV M# m# n# 11 submatrix : 12 mat j# k# POP k# j# k# stack : 11 line : k# PUSH push# k# 1 el : k# k# 2 k# length SV : push# 31 line : 12 mat x# MODE ToDo : B# j# XEQ S# M# F# K# P# 15 mat A# B# V : j# 1 + A# length SV DO# : S# M# F# 13 mat 21 line : A# DO# j# 1 : j# A# length ≤ j# j# 1 + : a# A# j# el : N# S# length : 12 mat a# IsString a# findstr 1 - ≠ a# a# strrep : while a# strlen 1 > (a# 11 substr ≡ (& a# a# 2 substr : if a# strlen 1 > (a# a# strlen 1 substr ≡ (& a# a# 1 a# strlen 1 - substr : if 31 line if a# RST ≡ Π# S# 11 matrix : M# RPN 1 matrix : F# M# : K# M# : P# M# : 15 mat : a# ≠ (a# ≠ (| (a# ENTER ≠ (| n# a# L# : (5 ≡ (α# 13 σ# : (SF ≡ (α# CF ≡ (| (& a# α# 42 σ# concat : if K# 1 el 0 ≡ f# 1 a# FR# : (0 ≠ K# 4 el S# 1 el : f# 3 el 1 ≡ S# 1 el f# 2 el (S# 1 el N2S#) concat S2N# : R# f# 2 el (S# 2 el N2S#, S# 1 el N2S#) concat S2N# : f# 3 el 2 ≡ S# R# S# 3 N# SV stack : S# R# 1 el R# 2 el S# 3 N# SV stack : if 21 line if 21 line f# 2 a# FR# : (0 ≠ val f# 2 el S2N# : n# a# L# : (4 > (f# 314 σ# FR# : (0 ≠ (& t# n# 1 - 2 σ# S2N# : val f# 2 el S2N# : 12 mat S# a# S2N# S# stack : if if if K# 1 el 0 : if 21 line if if 31 line for S# Re vectorize M# Re vectorize F# K# P# 15 mat 21 line : S# Π# 1 el : M# Π# 2 el : F# Π# 3 el : K# Π# 4 el : P# Π# 5 el : 15 mat As# A# N2S# ¦ ENTER strrep : Π# As# ENTER findstr 1 - ≡ A# V As# ENTER strsplit if DO# : (1 el transpose 171 line :

ToDo

MODE: PRG, DEG, FIX, SCI, ENG, STAT
R/S, ISG, ... etc.

\0020\\00A6\\0020\

MainToDo

STO, RCL, XEQ, GTO, etc. IND nn X, Y L ...

<content> RPN Examples </content>

Individual call

RPN 4 :

Mem, Prg & Flags length

RST RPN rpn 011 mat

RPN Stk Mem Flg Prg K 15 mat ≡

5 RPN rpn 5012 mat

3 RPN rpn 35013 mat

- RPN rpn 2012 mat

LN RPN rpn 0.6931 012 mat

STO 03 RPN rpn 0.6931 012 mat

RPN 2 el 3 el 0.6931

5 RPN rpn 5 0.6931 013 mat

1/X RPN rpn 0.2 0.6931 013 mat

Y^X RPN rpn 0.9293 012 mat

2 ln 5 nthroot 0.9293

6 RPN rpn 6 0.9293 013 mat

! RPN rpn 720 0.9293 013 mat

1/X RPN rpn 0.0014 0.9293 013 mat

CHS RPN rpn 0.0014 - 0.9293 013 mat

+ RPN rpn 0.9279 012 mat

RCL+03 RPN rpn 1.6211 0.9279 013 mat

3 RPN rpn 3 1.6211 0.9279 014 mat

RPN 3 el 2 el 0

2 RPN rpn 23 1.6211 0.9279 015 mat

SF 02 RPN rpn 23 1.6211 0.9279 015 mat

RPN 3 el 2 el 1

RDN RPN rpn 3 1.6211 0.9279 0215 mat

Grouped call

Three ways

RST RPN rpn 011 mat

1.

2 LN STO 03 5 NTHROOT 15 mat RPN rpn 0.9293 012 mat

6! 1/X CHS + RCL+03 32 SF 02 RDN 110 mat RPN rpn 3 1.6211 0.9279 0215 mat

2.

RST2LNSTO 035NTHROOT a 0 :

6!1/XCHS+RCL+0332SF 02RDN b 0 :

a description RPN rpn 0.9293 012 mat

b description RPN rpn 3 1.6211 0.9279 0215 mat

3.

RST ¦ 2 ¦ LN ¦ STO 03 ¦ 5 ¦ NTHROOT RPN rpn 0.9293 012 mat

6 ¦ ! ¦ 1/X ¦ CHS ¦ + ¦ RCL+03 ¦ 3 ¦ 2 ¦ SF 02 ¦ RDN RPN rpn 3 1.6211 0.9279 0215 mat

Functions check

CLS RPN rpn 011 mat

9 RPN rpn 9012 mat

↑ RPN rpn 99013 mat

2 RPN rpn 299014 mat

MOD RPN rpn 19013 mat

LST X RPN rpn 219014 mat

CLX RPN rpn 19013 mat

43 xy2pol 5 0.6435 21 sys

43 R2P 13 mat RPN rpn 5 0.6435 19015 mat

X<>Y 11 mat RPN rpn 0.6435 519015 mat

P2R RPN rpn 4319015 mat

RUP RPN rpn 0431915 mat

Programming

RPN 4 :

Simple program

RST A rpn 011 mat

RST PRG 02 X<Y? 500 STO 01 600 END 17 mat A rpn 011 mat

CLS 1120 XEQ 02 14 mat A rpn 2011013 mat

CLS 2010 XEQ 02 14 mat A rpn 1020013 mat

A 1020031 mat 000041 mat 000041 mat 000041 mat 0 RST PRG 02 X<Y? 500 STO 01 600 END 17 mat 0041 mat 15 mat

RSTPRG 01X<Y?500STO 01600END a 0 :

a description A rpn 011 mat

Programs must to be inside of
an only one rpn call, because
there are not PRG Mode.

CLS 1120 XEQ 01 14 mat A rpn 2011013 mat

CLS 2010 XEQ 01 14 mat A rpn 1020013 mat

A 1020031 mat 000041 mat 000041 mat 000041 mat RST PRG 01 X<Y? 500 STO 01 600 END 17 mat 00041 mat 15 mat

Calling another program

PRG 02 20 XEQ 01 STO 02 55 END 16 mat A rpn 1020013 mat

CLS 10 XEQ 02 13 mat A rpn 552010014 mat

CLS 30 XEQ 02 13 mat A rpn 552030014 mat

GTO

PRG 03 1 FC? 01 GTO 06 4 GTO 07 67 END 19 mat RPN rpn 0431915 mat

CLS CF 01 XEQ 03 13 mat RPN rpn 761014 mat

CLS SF 01 XEQ 03 13 mat RPN rpn 741014 mat

PRG 03 1 FC? 01 GTO+03 4 GTO+02 67 END 19 mat RPN rpn 741014 mat

CLS CF 01 XEQ 03 13 mat RPN rpn 761014 mat

CLS SF 01 XEQ 03 13 mat RPN rpn 741014 mat

GSB

PRG 04 20 X>Y? GSB 06 + END 55 RET 18 mat RPN rpn 741014 mat

CLS 10 XEQ 04 13 mat RPN rpn 7510013 mat

CLS 30 XEQ 04 13 mat RPN rpn 50012 mat

PRG 04 20 X>Y? GSB+03 + END 55 RET 18 mat RPN rpn 50012 mat

CLS 10 XEQ 04 13 mat RPN rpn 7510013 mat

CLS 30 XEQ 04 13 mat RPN rpn 50012 mat

RPN 50021 mat 00 0.6931 041 mat 110041 mat 000 0.6435 41 mat 00 PRG 03 1 FC? 01 GTO+03 4 GTO+02 67 END 19 mat PRG 04 20 X>Y? GSB+03 + END 55 RET 18 mat 41 mat 15 mat

<content> rpn Calculus 1V Example </content>

Calculus Example

x f x 3^5 x 2^* + 3 - x 2^1 + / :

x f

PRG 02XEQ 010.0000001STO+01X<>YXEQ 01-X<>YSTO-01/CHSEND df 0 :

PRG 01RCL 013Y^XRCL 012Y^X5*+3-RCL 012Y^X1+/END f 0 :

PRG 03RCL 01XEQ 01XEQ 02/RCL 01-CHSSTO 01-ABS0.0000000001X<Y?GTO+05CLXCLXRCL 01ENDCLXCLXGTO 01 nr 0 :

α 4 - :

4 - f 0.7647

Function

RST RPN rpn 011 mat

f description RPN rpn 011 mat

CLS α STO 01 XEQ 01 14 mat RPN rpn 0.7647 4 - 013 mat

Derivative

α f α diff 0.8304

df description RPN rpn 0.7647 4 - 013 mat

CLS α STO 01 XEQ 02 14 mat RPN rpn 0.8304 4 - 013 mat

Newton - Raphson

nr description RPN rpn 0.8304 4 - 013 mat

CLS α STO 01 XEQ 03 14 mat RPN rpn 4.8737 - 4 - 013 mat

Sanity check:

109 -^α β α α f α f α diff / - : (- abs < α β : while α 21 line 4.8737 -

RPN 1 el 1 el f 1.5501 1014 -^*

Alvaro