HPA111@DE0HRZ1A.BITNET ("Michael Drechsler +49 343062", 0201) (05/09/88)
Hello, at the end of Wirth's book PIM2 ed.3 (german version) is a listing of the def mod MathLib0, but no description. This module contains the two procedures "real" and "entier". I have some ideas what this procs do, but I'm not sure. Is the PROCEDURE real(x:INTEGER): REAL; only another form of FLOAT(CARDINAL(x)) or is the PROCEDURE entier(x:REAL): INTEGER; just another form of INTEGER(TRUNC(x)) ? Thanks for your help, Mike
harv@harris.cis.ksu.EDU (Harvard Townsend) (05/09/88)
>>Is the >> PROCEDURE real(x:INTEGER): REAL; >>only another form of FLOAT(CARDINAL(x)) Correct. That's all our implementation does: "RETURN (FLOAT(x));" >>or is the >> PROCEDURE entier(x:REAL): INTEGER; >>just another form of INTEGER(TRUNC(x)) ? This one is a little different. I understand it to be the "nearest integer to REAL x". So I guess it is a TRUNC with rounding. Any REAL number with a fractional part >= .5 is rounded up to the next highest integer. Anything < .5 is equivalent to TRUNC(x). ______________________________________ Harvard Townsend, Systems Manager Dept. of Computing & Information Sciences Kansas State University, Manhattan, KS 66506 (913)532-6350 CSNET: harv@cis.ksu.edu -or- harv@kansas-state.csnet BITNET: harv@ksuvax1.bitnet -or- harv%ksuvax1.bitnet@cunyvm.cuny.edu UUCP: {ihnp4,cbatt,dcdwest}!ncr-sd!ncrwic!ksuvax1!harv -or- ihnp4!wnuxa!ksuvax1!harv -or- ...!psuvax1!ksuvax1.bitnet!harv
alan@pdn.UUCP (Alan Lovejoy) (05/10/88)
In article <INFO-M2%88050910174344@DB0TUI11> Info-Modula2 Distribution List <INFO-M2%UCF1VM.bitnet@jade.berkeley.edu> writes: >Is the > PROCEDURE real(x:INTEGER): REAL; >only another form of FLOAT(CARDINAL(x)) Real is a function defined on INTEGERs instead of CARDINALs. Note that if x < 0, then CARDINAL(x) is gibberish. >or is the > PROCEDURE entier(x:REAL): INTEGER; >just another form of INTEGER(TRUNC(x)) ? Entier is a function whose domain is the INTEGERs, not the natural numbers (CARDINALs). It is known in American math jargon as "floor". It returns the greatest number not less than its input, where greater and lesser are defined arithmetically, not in terms of absolute magnitude. The distinction is important for INTEGERs, but not for CARDINALs. -- Alan Lovejoy; alan@pdn; 813-530-8241; Paradyne Corporation: Largo, Florida. Disclaimer: Do not confuse my views with the official views of Paradyne Corporation (regardless of how confusing those views may be). Motto: Never put off to run-time what you can do at compile-time!
alan@pdn.UUCP (Alan Lovejoy) (05/10/88)
In article <8805091402.AA23129@harris.cis.ksu.edu> Info-Modula2 Distribution List <INFO-M2%UCF1VM.bitnet@jade.berkeley.edu> writes: >Correct. That's all our implementation does: "RETURN (FLOAT(x));" But he wrote "FLOAT(CARDINAL(x))", which is not necessarily equivalent! >>> PROCEDURE entier(x:REAL): INTEGER; >>>just another form of INTEGER(TRUNC(x)) ? > >This one is a little different. I understand it to be the "nearest integer >to REAL x". So I guess it is a TRUNC with rounding. Any REAL number with >a fractional part >= .5 is rounded up to the next highest integer. >Anything < .5 is equivalent to TRUNC(x). In PIM2/3rd Ed., pg. 162, Wirth states: TRUNC(x) real number x truncated to its integral part (of type CARDINAL). Wirth does not define "entier". But when I researched it back in 1984, If found it to be a europeanism for "floor", which does no rounding. Now if I could just remember where I found that piece of information... -- Alan Lovejoy; alan@pdn; 813-530-8241; Paradyne Corporation: Largo, Florida. Disclaimer: Do not confuse my views with the official views of Paradyne Corporation (regardless of how confusing those views may be). Motto: Never put off to run-time what you can do at compile-time!
nagler%olsen@unizh.UUCP (Robert Nagler) (05/10/88)
Modula-2 doesn't allow conversion of reals to integers, i.e. you can't
convert a negative integer to a real or vice-versa. Apparently, Dr. Wirth
found this to be a needed feature, so he included it in a library. Doing
type coercions to CARDINAL while yield incorrect results (unless there
are other bugs in the language implementation).
Enclosed (below) you will find implementations of these two routines
which are a "best guess" at how these procedures might be implemented
in a portable library. Most compiler companies supply libraries which
play around with assembly language or floating point chips, therefore
it is often fruitless to look at them for algorithms.
NOTE: Modula-2 has problems with twos complement integers (MININT),
therefore the implementations provided will fail if they are passed MININT.
One can handle the problem, but I felt it would detract from the presentation
of the algorithm if I included the special case code.
Rob
PS. If you are wondering about the FLOAT usage (i.e. FLOAT is passed
an integer), Modula-2 states that cardinals and integers are assignment
compatible which means you can pass positive INTEGERs to procedures
that accept CARDINALs.
---------------------------------------------------------
PROCEDURE real( (* Convert an integer to a real *)
x : INTEGER (* should be in the range: [ -MAX( x ) .. MAX( x ) ] *)
) : REAL;
VAR
result : REAL;
BEGIN (* real *)
IF x >= 0 THEN
RETURN FLOAT( x );
END;
result := FLOAT( -x ); (* breaks here if MININT (except on Univacs) *)
RETURN -result;
END real;
PROCEDURE entier( (* Truncate a real towards negative infinity *)
x : REAL (* same restrictions as "real" *)
) : INTEGER;
VAR
result : INTEGER;
BEGIN (* entier *)
IF x > 0.0 THEN
RETURN TRUNC( x );
END;
x := -x;
result := TRUNC( x );
(* If the number is not exact, must adjust towards negative infinity *)
IF FLOAT( result ) # x THEN
INC( result );
END;
RETURN -result;
END entier;