frechett@spot.Colorado.EDU (-=Runaway Daemon=-) (03/03/91)
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