[Cyan]<CedarChest6.1>Combiner>RatNums.mesa!1

RatNums.mesa

Last Edited by: Arnon, June 10, 1985 4:19:22 pm PDT

DIRECTORY

Rope USING [ROPE],

IO USING [STREAM, PutRope],

BigCardinals;

RatNums: CEDAR DEFINITIONS

IMPORTS IO =

BEGIN OPEN BC: BigCardinals;

***** Data Structure *****

Sign: TYPE = { NEGATIVE, ZERO, POSITIVE };

RatNum: TYPE = RECORD [sign: Sign, numerator, denominator: BC.BigCARD ];

RatNum's equal to zero are expected to have sign ZER0 and zero numerator; their denominators are undefined.

***** Basic Arithmetic *****

RatNumAdd: PROC [in1, in2: RatNum] RETURNS [out: RatNum];

RatNumNegate: PROC [in: RatNum] RETURNS [out: RatNum];

RatNumABS: PROC [in: RatNum] RETURNS [out: RatNum];

RatNumSubtract: PROC [in1, in2: RatNum] RETURNS [RatNum];

RatNumMultiply: PROC [in1, in2: RatNum] RETURNS [out: RatNum];

RatNumInverse: PROC [in: RatNum] RETURNS [out: RatNum];

Inverse of a non-zero RatNum.

RatNumDivide: PROC [dividend, divisor: RatNum] RETURNS [RatNum];

***** Constructor Routines *****

RatNumFromBigCards: PROC [sign: INTEGER[-1..1], num, den: BC.BigCARD] RETURNS [out: RatNum];

RatNumFromSmallCards: PROC [sign: INTEGER[-1..1], num, den: CARDINAL] RETURNS [out: RatNum];

MakeRatNumZero: PROC RETURNS [out: RatNum];

Construct RatNum representation for zero

***** Conversion and I/O Routines *****

RatNumFromREALRope: PROC [in: Rope.ROPE] RETURNS [RatNum];

Intended to allow decimal notation input of RatNums.

RatNumToRatRope: PROC [in: RatNum, reuse: BOOLEAN ← FALSE, showDenomOne: BOOL ← FALSE] RETURNS [Rope.ROPE];

Used for displaying the values of RatNums. If in is positive, then the output Rope is unsigned. The default of reuse: FALSE preserves the input RatNum. If in is an integer, then if showDenomOne = FALSE the denominator of one is not printed, if TRUE then it is.

RatNumFromREAL: PROC [in: REAL] RETURNS [RatNum];

Convert a REAL to a RatNum. The REAL is viewed as a decimal fraction, whose numerator and denominator become the numerator and denominator of the resulting RatNum.

RatNumToREAL: PROC [in: RatNum, reuse: BOOLEAN ← FALSE] RETURNS [REAL];

Convert a RatNum to a real. For the time being, it is assumed that the RatNum is not so large in absolute value as to cause floating point overflow.

ReadRatNum: PROC [in: IO.STREAM] RETURNS [out: RatNum, ok: BOOL ← TRUE];

WriteRatNum: PROC [stream: IO.STREAM, in: RatNum] = INLINE {

IO.PutRope[ stream, RatNumToRatRope[in] ]

};

***** Comparison *****

RatNumRelation: TYPE = {ratLess, ratEqual, ratGreater};

RatNumCompare: PROC [in1, in2: RatNum] RETURNS [RatNumRelation];

RatNumRelationToRope: PROC [inRelation: RatNumRelation] RETURNS[Rope.ROPE];

RatNumGreater: PROC [in1, in2: RatNum] RETURNS [BOOLEAN];

RatNumEqual: PROC [in1, in2: RatNum] RETURNS [BOOLEAN];

RatNumLess: PROC [in1, in2: RatNum] RETURNS [BOOLEAN];

RatNumPositive: PROC [in: RatNum] RETURNS [BOOLEAN];

Test if a RatNum is zero

RatNumZero: PROC [in: RatNum] RETURNS [BOOLEAN];

Test if a RatNum is zero

RatNumNegative: PROC [in: RatNum] RETURNS [BOOLEAN];

Test if a RatNum is zero

RatNumInteger: PROC [in: RatNum] RETURNS [BOOLEAN];

Test if a RatNum is an integer

***** Miscellaneous BigCardinal routines *****

BigPowerOfTen: PROC [exponent: CARDINAL] RETURNS [power: BC.BigCARD];

BigToREAL: PROC [in: BC.BigCARD, reuse: BOOLEAN ← FALSE] RETURNS [out: REAL];

BigOne: PROC [in: BC.BigCARD] RETURNS [BOOLEAN];

Test if a BigCARD is the integer one.

END.