Documentation for RPNMS.EXE March 19, 1992
This document applies to version 3.0 of RPNMS
Copyright 1984-1992 by author Harry J Smith, Saratoga, CA
INTRODUCTION (Note: See RPNM.DOC first for general introduction)
To use the program type the name of the EXE file at the DOS prompt
line with a return and no parameters. The program will load and
respond with:
*** RPNMS *** Version 3.0, Mar 19, 1992
Copyright (c) 1984-1992 by author: Harry J. Smith,
19628 Via Monte Dr., Saratoga, CA 95070. All rights reserved.
Reverse Polish Notation Multiple-precision Scientific calculator
Has a stack of four 8992 decimal digit numbers (3694 bytes)
with a dynamic range of +/-9.9 ... 9 * 10 ** +/-39453
Press ESCAPE to interrupt a long calculation or a slow display
Bytes in mantissa = 12 ( > 24 decimal digits)
Max digits in display = 29552
Bytes to truncate in x for display = 2
Rounding is ON
Base = 10 base ten, Max digit = 9
**** PRESS ANY KEY TO CONTINUE HELP OR PRESS ESCAPE ****
n Enter a number, may not have a leading + or - sign
! X factorial
" Start/stop comment field or file name "CC...C"
* Multiply
** X = Y ** X Power (Integer part of X)
+ Add
- Subtract
/ Divide
1/X X = 1.0 / X
>DEG Convert X from radians to degrees
>RAD Convert X from degrees to radians
? Display this help menu
A Auto display on/off
ABS Absolute value of X
B Set base to X
BEL Bell prompt on/off
C Change sign of X
CO Cosine
CO- Arc-Cosine
CL Clear X
D Display X
**** PRESS ANY KEY TO CONTINUE HELP OR PRESS ESCAPE ****
DEG Set degree trig mode
DL Display learned line
E Enter X again
ECHO Echo input to output, toggle on/off
EP e to Power X
EX Execute learned line
EXX Execute X times
FRAC Fractional portion of X
I Interchange X and Y
INT Integer portion of X
L Last X
LGE Enter Log e = 0.434...
LN Natural Log (Base e = 2.718...)
LN2 Enter Ln 2 = 0.693...
LOG Common Log (Base 10)
LOP Reduce precision of x by one byte
LRN Learn
N= Don't display = sign
MMN Allow Max mantissa past accuracy of Pi etc.
OFF Exit back to system
ON Reinitialize
**** PRESS ANY KEY TO CONTINUE HELP OR PRESS ESCAPE ****
PI Enter Pi = 3.14...
PO Rectangular to Polar coordinate conversion
R Square Root
R1 Recall memory register 1
R2 Recall memory register 2
RAD Set radian trig mode (nominal)
RD Read and enter a number from file "CC...C"
RE Polar to Rectangular coordinate conversion
RN Generate a random number, 0.0 <= X < 1.0
RON Round results
ROF Do not round results
RRN Recall random number or seed
S Square
S1 Store X in memory register 1
S2 Store X in memory register 2
S<> Stop if X <> 0
S= Stop if X = 0
SD Set # of digits in display to X (1 - 29552)
SG Set digits per group for output display of X
SI Sine
SI- Arc-Sine
**** PRESS ANY KEY TO CONTINUE HELP OR PRESS ESCAPE ****
SM Set # of bytes in mantissa to X (2 - 3694)
SP Set spacing value, -1...3
SRN Set seed for random number to X
ST Set # of bytes to truncate for display to X (0 - 3694)
TA Tangent
TA- Arc-Tangent
U Rotate stack up (X -> Y -> Z -> T -> X)
V Rotate stack down (X <- Y <- Z <- T <- X)
WR Write register x into file "CC...C"
Y= Display = sign
YP Y to Power X
[N] Don't display number of bytes in mantissa
[Y] Display number of bytes in mantissa
**** PRESS ANY KEY TO ENTER CALCULATOR MODE ****
= 0.0
COMMAND:
Commands may be entered one at a time followed by a return or
several on a line separated by one or more spaces. A space is not
required between commands if there is no ambiguity of meaning.
Since this is an RPN calculator, 3 * (4 + 5) is entered as:
3 4 5 + * or 3 4 5+* or 4 5 + 3 * or 4 5+3*
Be careful not to enter more than 4 items on the stack at any one
time. The items on the stack are referred to as X, Y, Z, and T. X
is the item on the bottom of the stack, Y is just above X, then Z
above Y, and finally T is on the top. Operations that take two
arguments to generate one, will pop X and Y off of the bottom of
the stack, perform the operation, and push the result back onto
the bottom of the stack. Such an operation will always result
with Z and T being equal since when X is popped, T is duplicated
into Z. The stack is always full. A push operation loses T.
Operations that take only one argument will pop X, perform the
operation, and push the result.
When the program is loaded it determines how much internal memory
is available for X, Y, X, T and the other long registers needed.
It then makes these registers as long as possible to use up all
available memory. The size of the decimal digit numbers on your
system may be more or less than the indicated in the example
above.
This ends the introduction. I will now explain each command
taking them in ASCII sort order.
n Enter a number, may not have a leading + or - sign:
Here n refers to keying in a number like 0 or 12345.6789. The
number is merely pushed onto the stack. The way to enter a
negative number is to enter its absolute value and then change
its sign with the C command. Commas may be inserted in the number
between any two digits to aid in reading. For example
12,345.678,9^-1,2 is a legal input number.
! X factorial:
Replaces X with the factorial of X = 1 * 2 * 3 * ... * X. Only
the integer portion of X is used in the calculation.
" Start/stop comment field "CC...C":
Comments can be entered at any time and are quite useful on the
learned line, see LRN. The comment is started and ended with a "
mark. All spaces between the " marks become part of the comment.
Normally all commands are converted to upper case as they are
input. The characters of a comment are not converted to upper
case, they must be typed in upper case if upper case is desired.
* Multiply:
Pop X and Y, Push X times Y.
** X = Y ** X Power:
Pop X and Y, Push Y to the power of X. Only the integer portion
of the power X is used in the calculation. Use the YP command if
the fractional part of X is to be used.
+ Add:
Pop X and Y, Push sum of X and Y.
- Subtract:
Pop X and Y, Push Y minus X.
/ Divide:
Pop X and Y, Push Y divided by X.
1/X X = 1.0 / X:
Pop X, Push 1.0 divided by X.
>DEG Convert X from radians to degrees:
Multiplies X by 180 / Pi.
>RAD Convert X from degrees to radians:
Multiplies X by Pi / 180.
? Display this help menu:
Causes the help menu to be displayed. It is the same as the menu
displayed when you first enter the program, but the values
currently set by the SM, SD, ST, RON, ROF, and B commands are
displayed.
A Auto display on/off:
Normally, after each command line is executed, the contents of
the bottom of the stack, X, is converted to the selected base and
displayed. When computing with large numbers, the time spent in
this conversion can be more than the time spent in the
calculation. It is desirable then to be able to prevent this
automatic display. Each time the A command is given the selection
status of this option is reversed.
ABS Absolute value of X:
Forces the sign of X to be plus. The magnitude of X is unchanged.
B Set base to X:
Initially the base of both input and output display is set to
ten. It can be changed at any time to a number between 2 and 36
decimal. If the base is ten, the command 36 B would Pop X and
change the base to 36 base 10 and display:
Base = 36 base ten, Max digit = Z
Just as the digit F is worth fifteen when we are in base sixteen,
the digit Z is worth thirty-five when we are in base thirty-six.
Note that the value used to describe a base radix is always given
in the normal decimal base, i.e. base ten. When in a base greater
than ten, numbers may have to be entered with a leading 0 to
prevent being mistaken for a command. When in base sixteen, a ten
must be entered as 0A instead of A or the auto display status
will be changed.
A special case is made for getting back to base ten. If the X
register is zero when the B command is given, X is popped from
the stack and the base is set to ten.
BEL Bell prompt on/off:
This is good for timing long calculations.
C Change sign of X:
Same as multiplying X by minus one. The only way to enter a
negative number is to enter its absolute value and then change
its sign.
CO Cosine:
X is replaced with the cosine of X. All scientific functions are
computed using the full precision currently set by the SM
command. The RON and ROF commands can also affect the results of
these functions.
CO- Arc-Cosine:
X is replaced with the arc-cosine of X.
CL Clear X:
X is set to zero. Y, Z and T are not affected. CL + can be used
to perform a Pop operation.
D Display X:
This command is useful when the auto display is turned off. Also
useful in the learned line to display intermediate results.
DEG Set degree trig mode:
The trigonometric functions, CO, CO-, PO, RE, SI, SI-, TA, and,
TA-, normally assume the angle involved in either the input or
output is expressed in radians. If degrees are desired use the
DEG command. This mode stays selected until changed by the RAD
command.
DL Display learned line:
Displays the current contents of the learned line. While commands
may be given in either upper or lower case or even a mixture, the
non-comment portion of the learned line is always displayed in
upper case.
E Enter X again:
This duplicates X and Pushes it onto the stack. E E E will fill
the stack with X.
ECHO Echo input to output, toggle on/off:
RPNMS allows for commands to be input from a disk file instead of
the operator's keyboard. Also, the output can be directed to a
disk file instead of the operator's console. This is done by
entering at the DOS command line the following:
A>RPNMS in-file-name >out-file-name
Either or both fields may be present. When ECHO is off the input
commands are not sent to the output file. Normally ECHO should be
turned on with the first command of an input file.
EP e to Power X:
X is replaced with e ** X, where e is the base of the natural or
Napierian logarithms.
EX Execute learned line:
This will cause the learned line to be executed once if there is
no EX command in the learned line. Having LRN and/or EX in the
learned line can produce interesting results. A simple case is a
normal learned line with EX as its last command; this will cause
the learned line to be repeatedly executed until the ESCAPE key
is pressed.
EXX Execute X times:
This will Pop X and cause the learned line to be executed X
times. X must be in the range 0 <= X <= 65535.
FRAC Fractional portion of X:
X is replaced with only the fractional portion of X by truncating
the integer portion.
I Interchange X and Y:
Pop X, Pop Y, Push X, Push Y.
INT Integer portion of X:
X is replaced with only the integer portion of X by truncating
the fractional portion.
L Last X:
On all computational operations (!, *, **, +, -, /, 1/X, >DEG,
>RAD, B, CO, CO-, EP, FRAC, INT, LN, LOG, PO, RE, R, S, SD, SI,
SI-, SM, ST, TA, TA-, and YP) the value of X is saved in LASTX,
The L command retrieves LASTX and Pushes it onto the stack. This
is quite useful in undoing an operation performed by mistake. It
is one of the features that makes an RPN calculator desirable.
LGE Enter Log e = 0.434...:
Push the log base 10 of e onto the stack.
LN Natural Log (Base e = 2.718...):
X is replaced with the natural log of X.
LN2 Enter Ln 2 = 0.693...:
Push the natural log of 2 onto the stack.
LOG Common Log (Base 10):
X is replaced with the log base 10 of X.
LOP Reduce precision of X by one byte:
This command removes the least significant byte of X. If rounding
is turned on, the removed byte is used to round into the new
least significant byte. In RPNMS numbers are normalizes from both
sides. If a calculation results in a number with some trailing
zero bytes, these bytes are effectively removed by reducing the
count of the number of bytes in the mantissa. The LOP command can
result in a large number of bytes being removed if removing one
byte results in a large number of trailing zeros.
LRN Learn:
This command stores all of the commands following on the same
line as this one into the learned line. Execution of the current
line is stopped. This line as well as all command lines are
limited to 256 characters. Type the learned line:
LRN N= 1 2 LRN 1 C SP D "! = " 1 SP * D L 1 + EX
and then do two separate EX commands. You might want to key in a
control-P after the second EX command just before you hit return
to turn your printer on. This will print a table of factorials
from 2! to 10943! or so, if you wait long enough. Hit the ESCAPE
key twice to interrupt and abort the operation if you get tired
of waiting.
N= Don't display = sign:
Normally displayed results are preceded with an = sign. This is
handy so you can tell when a calculation is complete and the
display conversion is being done. Aborting a display conversion
with the ESCAPE key will not affect the value computed. If the =
sign is not desired, the N= command can be given.
MMN Allow Max mantissa past accuracy of Pi etc.:
When the program is first loaded values for Log e, Ln 2 and Pi
are read in from files LOGE.RPN, LN2.RPN and PI.RPN respectively.
If these files cannot be found on the default drive, drive b: is
also searched. The number of bytes in the mantissa of the
number with the shortest mantissa of these three numbers is used
to set the maximum mantissa allowed in the SM command. The number
of bytes in the mantissa of these numbers is currently 1018 and
these files are exactly 1024 bytes long. If it is desired to
allow calculations with mantissas with more precision than the
accuracy of the three constants, the MMN command can be given to
extend the maximum precision to the limits of available memory.
OFF Exit back to system:
The program exits back to the operating system.
ON Reinitialize:
This totally reinitializes the program, the same as reloading
from disk. Similar to the ? command except the parameters set by
the B, ROF, RON, SD, SM, SRN, and ST commands are reset to their
nominal values, and all registers are cleared.
PI Enter Pi = 3.14...:
Push the number pi onto the stack.
PO Rectangular to Polar coordinate conversion:
The X and Y registers are considered the rectangular coordinates
of the 2-dimensional point (x, y) and are replaced with the
corresponding polar coordinates of the same point. X becomes the
radius and Y becomes the angle.
R Square Root:
X is replaced with the square root of X.
R1 Recall memory register 1:
Besides the stack and last X there are two memory registers that
can hold any number that can be generated by this program. The R1
command will push the contents of the first of these registers
onto the stack.
R2 Recall memory register 2:
The R2 command will push the contents of the second memory
registers onto the stack.
RAD Set radian trig mode (nominal):
The trigonometric functions, CO, CO-, PO, RE, SI, SI-, TA, and,
TA-, normally assume the angle involved in either the input or
output is expressed in radians. If degrees are desired use the
DEG command. When radians are desired use the RAD command. This
mode stays selected until changed by the DEG command.
RD Read and enter a number from file "CC...C":
The RD command will use the last entered comment as a file name
and read this file as a RPNMS formatted number and push it onto
the stack. It is assumed that the file was created by the WR
command. See the WR command for the format of file names.
RE Polar to Rectangular coordinate conversion:
The X and Y registers are considered the polar coordinates of a
2-dimensional point, the radius is in X and the angle is in Y.
These are replaced with the corresponding rectangular coordinates
(x, y) of the same point.
RN Generate a random number, 0.0 <= X < 1.0:
The RN command generates a random number between zero and 1.0 and
pushes it onto the stack. This number will never have more than
80 significant bits. Theoretically the random number generator
will cycle after 2 ** 80 numbers, but the earth will not last
that long.
RON Round results:
This command sets rounding on. When rounding is on the results of
all arithmetic operations are rounded to the maximum number of
bytes in mantissa. Use the SM command to set the maximum number
of bytes in mantissa.
ROF Do not round results:
This command sets rounding off. When rounding is off the results
of all arithmetic operations are truncated to the maximum number
of bytes in mantissa. Use the SM command to set the maximum
number of bytes in mantissa.
RRN Recall random number or seed:
As random numbers are generated an 80 bit random integer is kept
and used as the basis for the next random number. The RRN command
pushes this value onto the stack. The value can be recorded at
the end of a session and reentered with the SRN command at the
beginning of a new session. This will prevent the same random
number from ever being reused. Care must be taken to ensure that
the number of bytes in mantissa is set to at least 10 and that
the units portion of X is being displayed when the seed is
recorded.
S Square:
X is replaced with the square of X.
S1 Store X in memory register 1:
Besides the stack and last X there are two memory registers that
can hold any number that can be generated by this program. The S1
command will set the contents of the first of these registers to
X. X remains unchanged.
S2 Store X in memory register 2:
The S2 command will set the contents of the second memory
registers to X. X remains unchanged.
S<> Stop if X <> 0:
This command is useful in the middle of a learned line that is
going to be executed repeatedly. It will cause the execution to
stop if X is not zero.
S= Stop if X = 0 :
This command is useful in the middle of a learned line that is
going to be executed repeatedly. It will cause the execution to
stop if X is zero.
SD Set # of digits in display to X (1 - 7360):
The SD command will set the maximum number of digits to display
to the current value of X, and then X is popped off the stack. If
this is set larger than the accuracy implied by the number of
bytes set by the SM command minus the number of bytes set by the
ST command, the smaller value will be used to determine the
number of digits to display.
SG Set digits per group for output display of X:
The SG command will set the number of digits per group to the
current value of X, and then X is popped off the stack. If this
is set to 3, numbers will be displayed with a comma after every
3rd digit like 1.234,567,89^34,457. If this is set to zero, 1 or
2, no commas will be displayed.
SI Sine:
X is replaced with the sine of X.
SI- Arc-Sine:
X is replaced with the arc-sine of X.
SM Set # of bytes in mantissa to X (2 - 920):
The SM command will set the maximum number of bytes in mantissa
portion of any floating point value used in or resulting from any
operation of the calculator. When this value is set to a smaller
value than was currently set, all floating point values in the
calculator are truncated to this number of bytes of precision in
their mantissa. X is popped off the stack.
SP Set spacing value, -1...3:
Pops X and uses it to set the spacing value. The spacing value is
initialized to two on start up which causes all output to be
double spaced, one will cause single spacing, 0 causes a single
blank character between outputs, and a -1 causes no space at all.
SRN Set seed for random number to X:
The SRN command stores the integer portion of the absolute value
of X into the seed of the random number generator. As random
numbers are generated an 80 bit random integer is kept and used
as the basis for the next random number. The value can be
recorded using the RRN command at the end of a session and
reentered with the SRN command at the beginning of a new session.
This will prevent the same random number from ever being reused.
X remains unchanged.
ST Set # of bytes to truncate for display to X (0 - 920):
The ST command will set the number of bytes to truncate for
display to the current value of X, and then X is popped off the
stack. If the number of digits to display, set by the SD command
is larger than the accuracy implied by the number of bytes set by
the SM command minus the number of bytes set by the ST command,
the smaller value will be used to determine the number of digits
to display.
TA Tangent:
X is replaced with the tangent of X.
TA- Arc-Tangent:
X is replaced with the arc-tangent of X.
U Rotate stack up (X -> Y -> Z -> T -> X):
This is the same as a Push X except that T is also placed on the
bottom of the stack and no stack items are lost.
V Rotate stack down (X <- Y <- Z <- T <- X):
This is the same as a Pop X except that X is also placed on the
top of the stack and no stack items are lost.
WR Write register X into file "CC...C":
The WR command will use the last entered comment as a file name
and write register X into this file as a RPNMS formatted number.
This number can be reread into X by the RD command. If the file
already exists it will be erased and recreated. For example, the
following are valid file names:
"file.ext" file.ext is on default drive, current user
"b:filename.ext" filename.ext is on b: drive, current user
"15/PI.RPN" PI.RPN is on default drive, user 15
"12/c:file.ext" file.ext is on c: drive, user 12
Y= Display = sign: (Note: Y stands for Yes not Y register)
Normally displayed results are preceded with an = sign. This is
handy so you can tell when a calculation is complete and the
display conversion is being done. Aborting a display conversion
with the ESCAPE key will not affect the value computed. If the =
sign is not desired, the N= command can be given. When the = sign
is again desired the Y= command is used.
YP Y to Power X:
Pop X and Y, Push Y to the power of X. Both the integer and
fractional portions of X and Y are used in the calculation. Use
the ** command if only the integer portion of the power X is to
be used.
[N] Don't display number of bytes in mantissa:
It is some times desirable and instructive to know how many bytes
are being used to represent a number in its internal binary
format. This option to display this is selected by the [Y]
command and deselected by the [N] command. For instance 1024 1/X
will display as = 9.76562,5^-4 [1] if the option is selected. The
number in brackets indicates that only one byte is being used to
store the mantissa of 0.0009765625. The number of bytes is always
displayed in decimal no matter what base is being used to display
the number itself.
[Y] Display number of bytes in mantissa:
Select the option to display the count of the number of bytes
being used to represent X in the internal binary format. See [N]
above.
Report any errors by writing me or call me at my home voice phone
(408) 741-0406 evenings or weekends.
Harry J. Smith
19628 Via Monte Dr.
Saratoga, CA 95070
times since October 20, 2004.