The X-Philes (2nd Revision)/The X-Philes Number 1 (1995).iso/xphiles/hp48_1/err.cal

Text File | 1995-03-23 | 8KB | 502 lines

Article 4720 of comp.sys.handhelds:
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From: [e-mail] (-=Runaway Daemon=-)
Newsgroups: comp.sys.handhelds
Subject: Operations with imprecise numbers.
Keywords: errors
Message-ID: <[e-mail]>
Date: 3 Mar 91 09:01:11 GMT
Sender: [e-mail] (news)
Organization: University of Colorado, Boulder
Lines: 487

I just picked up these routines from the hpbbs.  Unfortunately, I downloaded
them straight from the bbs into the calc so I don't have the message header to
go with it, but I  see it down in the code.. (John A. Kyle)  This is a set of
routines to deal with numbers like 2+-.5 or 3.056 +- .67 when doing the
operations + - * / and ^.  Those operations are treated as absolute errors so
that 2.0 +- .5 + 3.0 +-.5 will result in 6.0 +- 0.0.
Then there is an operation for dealing with stuff in a random fashion, with 90%
assurance.  For an example, I could choose the EQ 'X + Y' and enter the numbers
X = 2.0 dX = .5  Y= 3.0 dY= .5 and yeilds "To correct SIG.FIG's 5.0+-0.7"
and the real result 5.0+-0.707106781187.

For anyone with a physics class that requires any sort of error analysis of the
data, this set of programs is a MUST.  The routines are completely idiot proof
as they will tell you what to do if you don't have the right data.  Just
download this directory and when it it, hit CST and then INTRO.  That will get
you started.. I have found no problems in it yet.

        ian

--
-=Runaway Daemon
----- X1DX --------------------------------------------
%%HP: T(3)A(D)F(.);
DIR
  WORK
    DIR
      WIPE
        \<< 'WIPE'
DUP RCL CLVAR SWAP
STO
        \>>
    END
  X\177dX
    \<<
"Press left-shifted
menu key for HELP"
CLLCD 1 DISP 1
FREEZE { { "INTRO"
{
      \<< IN
      \>> } } { " + "
{
      \<< ADD
      \>>
      \<< IN.A
      \>> } } { " - "
{
      \<< SUBT
      \>>
      \<< IN.S
      \>> } } { " * "
{
      \<< MUL
      \>>
      \<< IN.M
      \>> } } { " / "
{
      \<< DIV
      \>>
      \<< IN.D
      \>> } } { " ^ "
{
      \<< PWR
      \>>
      \<< IN.P
      \>> } } { "\|^\|v"
{
      \<< SWP2
      \>>
      \<< IN.SW
      \>> } } {
"f(x)" {
      \<< RANDM
      \>>
      \<< IN.R
      \>> } } { "\-> %"
{
      \<< P.UNC
      \>>
      \<< IN.%
      \>> } } {
"SIGFIG" {
      \<< SIGFIG
      \>>
      \<< IN.SI
      \>> } } } MENU
    \>>
  IN
    \<<
"
  UNCERTAINTY
     CALCULATION
            PROGRAM

      for the HP 48SX
[\|v]"
CLLCD 1 DISP 0 WAIT
"Written for the public
domain by

 John A. Kyle

       UBC 1991
[\|v]              v 1.1"
CLLCD 1 DISP 0 WAIT
" Absolute     Random
  error       error
functions    function
---------    --------
+ - * / ^      f(x)

[\|v]"
CLLCD 1 DISP 0 WAIT
"The absolute functions
calculate total error
whereas the random
function calculates a
less pessimistic error
with a 90% confidence
[\|v]          level"
CLLCD 1 DISP 0 WAIT
"utilizing:

 Z=f(x,..)
                   1/2
dZ=[(\.df/\.dx)^2*dx^2+..]

[\|v]"
CLLCD 1 DISP 0 WAIT
"NOTE:

   Use 0 for dX when
 X has no uncertainty
 associated with it,
 etc."
CLLCD 1 DISP 0 WAIT
6 DROPN
    \>>
  IN.A
    \<<
"Enter like so..

(X\177dX) + (Y\177dY)
                4:   X
        \->       3:  dX
                2:   Y
                1:  dY"
CLLCD 1 DISP 7
FREEZE
    \>>
  IN.S
    \<<
"Enter like so..

(X\177dX) - (Y\177dY)
                4:   X
        \->       3:  dX
                2:   Y
                1:  dY"
CLLCD 1 DISP 7
FREEZE
    \>>
  IN.M
    \<<
"Enter like so..

(X\177dX) * (Y\177dY)
                4:   X
        \->       3:  dX
                2:   Y
                1:  dY"
CLLCD 1 DISP 7
FREEZE
    \>>
  IN.D
    \<<
"Enter like so..

(X\177dX) / (Y\177dY)
                4:   X
        \->       3:  dX
                2:   Y
                1:  dY"
CLLCD 1 DISP 7
FREEZE
    \>>
  IN.P
    \<<
"Enter like so..

         x
   (Y\177dY)
                3:   Y
       \->        2:  dY
                1:   x"
CLLCD 1 DISP 7
FREEZE
    \>>
  IN.R
    \<<
"
 Use EQUATION WRITER
to enter symbolic
expression..

then press f(x) key
and follow prompts."
CLLCD 1 DISP 7
FREEZE
    \>>
  IN.SW
    \<<
"Rotates levels 1&2
with 3&4..

4:   X          4:   Y
3:  dX   \->      3:  dY
2:   Y          2:   X
1:  dY          1:  dX"
CLLCD 1 DISP 7
FREEZE
    \>>
  IN.%
    \<<
"
  Utility to convert
  from absolute to
  % uncertainty

ie. X\177dX  \->  X\177dX%"
CLLCD 1 DISP 7
FREEZE
    \>>
  IN.SI
    \<<
"
   Utility to display
 X\177dX with the correct
 significant figures
 as determined by the
 uncertainty.

"
CLLCD 1 DISP 7
FREEZE
    \>>
  PRESERVE
    \<< RCLF \-> f
      \<< EVAL f STOF
      \>>
    \>>
  CST { { "INTRO" {
    \<< IN
    \>> } } { " + " {
    \<< ADD
    \>>
    \<< IN.A
    \>> } } { " - " {
    \<< SUBT
    \>>
    \<< IN.S
    \>> } } { " * " {
    \<< MUL
    \>>
    \<< IN.M
    \>> } } { " / " {
    \<< DIV
    \>>
    \<< IN.D
    \>> } } { " ^ " {
    \<< PWR
    \>>
    \<< IN.P
    \>> } } { "\|^\|v" {
    \<< SWP2
    \>>
    \<< IN.SW
    \>> } } { "f(x)"
{
    \<< RANDM
    \>>
    \<< IN.R
    \>> } } { "\-> %" {
    \<< P.UNC
    \>>
    \<< IN.%
    \>> } } {
"SIGFIG" {
    \<< SIGFIG
    \>>
    \<< IN.SI
    \>> } } }
  SUBT
    \<<
      IFERR \-> x dx
y dy
        \<< x y - 'Z'
\->TAG dx dy + 'dZ'
\->TAG SIGFIG
        \>>
      THEN IN.S
      END
    \>>
  MUL
    \<<
      IFERR \-> x dx
y dy
        \<< x y * 'Z'
\->TAG dx y * x dy *
+ 'dZ' \->TAG SIGFIG
        \>>
      THEN IN.M
      END
    \>>
  DIV
    \<<
      IFERR \-> x dx
y dy
        \<< x y / 'Z'
\->TAG dx y * x dy *
+ y 2 ^ / 'dZ' \->TAG
SIGFIG
        \>>
      THEN IN.D
      END
    \>>
  PWR
    \<<
      IFERR \-> y dy
x
        \<< y x ^ "Z"
\->TAG dy x * y x 1 -
^ * "dZ" \->TAG
SIGFIG
        \>>
      THEN IN.P
      END
    \>>
  P.UNC
    \<<
      IFERR DUP2
DTAG SWAP DTAG \-> dz
z
        \<< "  " 2
FIX z \->STR " \177 "
" % " dz z / 100 *
ABS \->STR STD + + +
+ CLLCD 2 DISP
"Percent Uncertainty"
1 DISP 1 FREEZE
        \>>
      THEN
"
 Requires entry
like so..

 Z\177dZ
       \->    2:       Z
            1:      dZ"
CLLCD 1 DISP 7
FREEZE
      END
    \>>
  SIGFIG
    \<<
      IFERR DUP2
DTAG SWAP DTAG \-> dx
x
        \<<
          IF x TYPE
0 == x 0 \=/ AND dx
TYPE 0 == dx 0 \=/
AND AND
          THEN "( "
x XPON DUP dx XPON
- FIX x DUP SIGN
SWAP MANT * SWAP
ALOG dx SWAP / "\177"
SWAP " )E" + + + +
STD x XPON +
" To correct SIG.FIG's
"
SWAP + CLLCD 1 DISP
1 FREEZE
          END
        \>>
      THEN
"
 Requires entry
like so..

  Z\177dZ
         \->    2:     Z
              1:    dZ"
CLLCD 1 DISP 7
FREEZE
      END
    \>>
  RANDM
    \<<
      IFERR DUP
        \<< -2 SF -3
CF
          IF TYPE 9
==
          THEN DUP
{ } 0 { } \-> equ
dequ finlst ans
varlst
            \<<
"stop"
              WHILE
dequ "stop" SAME
NOT
              REPEAT
CASE dequ TYPE 9 ==
  THEN dequ OBJ\->
DROP2
  END dequ TYPE 6
==
  THEN varlst 1 3
CF
    IF varlst SIZE
    THEN
      DO GETI
        IF dequ
SAME
        THEN 3 SF
        END
      UNTIL -64 FS?
      END
    END
    IF 3 FC?
    THEN dequ
'varlst' STO+
    END DROP2
  END
END 'dequ' STO
              END 3
CF varlst 1
              DO
GETI \-> i
\<<
" Enter values for.."
": " i ":
:d" i ":"
+ + + + { { 1 0 } V
} + INPUT OBJ\-> equ
i \.d * SQ 'ans' STO+
DTAG i SWAP
'finlst' STO+
'finlst' STO+
\>>
              UNTIL
-64 FS?
              END
DROP2 equ finlst |
"Z" \->TAG ans finlst
| \v/ "dZ" \->TAG
SIGFIG
            \>>
          ELSE IN.R
          END
        \>> PRESERVE
      THEN IN.R
      END
    \>>
  SWP2
    \<<
      IFERR 4 ROLL
4 ROLL
      THEN DROP
IN.SW
      END
    \>>
  ADD
    \<<
      IFERR \-> x dx
y dy
        \<< x y + 'Z'
\->TAG dx dy + 'dZ'
\->TAG SIGFIG
        \>>
      THEN IN.A
      END
    \>>
END