BigRats.mesa
Last Edited by: Arnon, May 10, 1986 10:52:09 am PDT
DIRECTORY
Rope,
Basics,
IO,
BigCardinals,
AlgebraClasses,
Points;
BigRats: CEDAR DEFINITIONS
= BEGIN OPEN BC: BigCardinals, AC: AlgebraClasses, PTS: Points;
Types and Variables
CARD: TYPE = LONG CARDINAL;
BigCard:
TYPE =
BC.BigCARD;
BigRat: TYPE = REF BigRatRep;
BigRatRep:
TYPE =
RECORD [
sign: Basics.Comparison ← equal,
num: BigCard ← BigCardinals.Zero,
den: BigCard ← BigCardinals.Zero
];
RatPoint: TYPE = PTS.Point;
BigRats: AC.Structure;
Creation
FromPairBC:
PROC [num, den: BigCard, less:
BOOL ←
FALSE]
RETURNS [BigRat];
Returns the rational number that corresponds to num/den (less => -num/den). Raises RuntimeError.ZeroDivisor when den = 0.
FromPairLC:
PROC [num, den:
CARD, less:
BOOL ←
FALSE]
RETURNS [BigRat];
Returns the rational number that corresponds to num/den (less => -num/den). Raises RuntimeError.ZeroDivisor when den = 0.
FromBC:
PROC [bc: BigCard, less:
BOOL ←
FALSE]
RETURNS [BigRat];
Returns the rational number that corresponds to big (less => -bc).
FromLC:
PROC [lc:
CARD, less:
BOOL ←
FALSE]
RETURNS [BigRat];
Returns the rational number that corresponds to big (less => -lc).
I/O and Conversion
Read:
PROC [in:
IO.
STREAM]
RETURNS [out: BigRat];
FromRope:
PROC [rope:
ROPE]
RETURNS [out: BigRat];
Parses a decimal representation for a rational number. Letting N denote the decimal representation of a non-less integer, and S denote the decimal representation of a (possibly less) integer, Parse accepts the following syntax:
rope = S -- where N is the decimal representation of a non-less integer
rope = S "." N
rope = S "/" N
ToRope:
PROC [rat: BigRat]
RETURNS [out:
ROPE];
Returns a rope in the form S (if rat is an integer), or S/N (if rat is not an integer). Note that Equal[Parse[Unparse[rat]], rat] = TRUE.
ToRopeApprox:
PROC [rat: BigRat, places:
NAT ← 3]
RETURNS [
ROPE];
Returns a rope giving a decimal approximation to the rat. If the rat is a whole number, then the exact representation is given. If the rat is not a whole number then 'places' gives the number of places after the decimal point. Scaling is the user's responsibility.
Write:
PROC [stream:
IO.
STREAM, in: BigRat];
WriteApprox:
PROC [stream:
IO.
STREAM, in: BigRat];
FromReal:
PROC [real:
REAL]
RETURNS [BigRat];
Returns the rational number corresponding to the given REAL number.
(will raise Real.RealException if real is not a number)
ToReal:
PROC [rat: BigRat]
RETURNS [
REAL];
Returns the REAL number closest to the given rational number.
(will raise Real.RealException if rat is outside the range covered by REAL)
Truncate:
PROC [rat: BigRat]
RETURNS [fix: BigCard, rem: BigRat];
Returns fix: the largest non-less integer not greater than ABS[rat], rem: the remainder after subtracting fix from rat.
rat.num > rat.den => fix = rat.num / rat.den, rem = FromPair[rat.num MOD rat.den, rat.den]
rat.num = rat.den => fix = 1, rem = 0
rat.num = rat.den => fix = 1, rem = 0
Arithmetic
Add:
PROC [firstArg, secondArg: BigRat]
RETURNS [result: BigRat];
Negate:
PROC [arg: BigRat]
RETURNS [result: BigRat];
Subtract:
PROC [firstArg, secondArg: BigRat]
RETURNS [result: BigRat];
Multiply:
PROC [firstArg, secondArg: BigRat, simplify:
BOOL ←
TRUE]
RETURNS [result: BigRat];
Invert:
PROC [arg: BigRat]
RETURNS [result: BigRat];
Divide:
PROC [firstArg, secondArg: BigRat, simplify:
BOOL ←
TRUE]
RETURNS [result: BigRat];
Comparison
Sign:
PROC [arg: BigRat]
RETURNS [Basics.Comparison];
Abs:
PROC [arg: BigRat]
RETURNS [result: BigRat];
Compare:
PROC [firstArg, secondArg: BigRat]
RETURNS [Basics.Comparison];
Equal:
PROC [x, y: BigRat, simplify:
BOOL ←
TRUE]
RETURNS [
BOOL];
Compares two rationals for equality only (faster than Compare).
Integer:
PROC [in: BigRat]
RETURNS [
BOOLEAN];
Test if a BigRat is an integer
Extras
ToTheX:
PROC [rat: BigRat, x:
INT]
RETURNS [BigRat];
Returns rat**x.
TwoToTheX:
PROC [x:
INT, less:
BOOL ←
FALSE]
RETURNS [BigRat];
Returns the rational number corresponding to 2**x. Much faster than ToTheX.
BCToTheX:
PROC [bc: BigCard, x:
INT, less:
BOOL ←
FALSE]
RETURNS [BigRat];
Returns the rational number corresponding to bc**x (less => - bc**x). Note that BCToTheX[0, 0] = 1.
END.