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diff --git a/src/algebra/fortmac.spad.pamphlet b/src/algebra/fortmac.spad.pamphlet deleted file mode 100644 index 5684244c..00000000 --- a/src/algebra/fortmac.spad.pamphlet +++ /dev/null @@ -1,458 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra fortmac.spad} -\author{Mike Dewar} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{domain MINT MachineInteger} -<<domain MINT MachineInteger>>= -)abbrev domain MINT MachineInteger -++ Author: Mike Dewar -++ Date Created: December 1993 -++ Date Last Updated: -++ Basic Operations: -++ Related Domains: -++ Also See: FortranExpression, FortranMachineTypeCategory, MachineFloat, -++ MachineComplex -++ AMS Classifications: -++ Keywords: -++ Examples: -++ References: -++ Description: A domain which models the integer representation -++ used by machines in the AXIOM-NAG link. -MachineInteger(): Exports == Implementation where - - S ==> String - - Exports ==> Join(FortranMachineTypeCategory,IntegerNumberSystem) with - maxint : PositiveInteger -> PositiveInteger - ++ maxint(u) sets the maximum integer in the model to u - maxint : () -> PositiveInteger - ++ maxint() returns the maximum integer in the model - coerce : Expression Integer -> Expression $ - ++ coerce(x) returns x with coefficients in the domain - - Implementation ==> Integer add - - MAXINT : PositiveInteger := 2**32 - - maxint():PositiveInteger == MAXINT - - maxint(new:PositiveInteger):PositiveInteger == - old := MAXINT - MAXINT := new - old - - coerce(u:Expression Integer):Expression($) == - map(coerce,u)$ExpressionFunctions2(Integer,$) - - coerce(u:Integer):$ == - import S - abs(u) > MAXINT => - message: S := concat [string u," > MAXINT(",string MAXINT,")"] - error message - per u - - retract(u:$):Integer == rep u - - retractIfCan(u:$):Union(Integer,"failed") == rep u - -@ -\section{domain MFLOAT MachineFloat} -<<domain MFLOAT MachineFloat>>= -)abbrev domain MFLOAT MachineFloat -++ Author: Mike Dewar -++ Date Created: December 1993 -++ Date Last Updated: -++ Basic Operations: -++ Related Domains: -++ Also See: FortranExpression, FortranMachineTypeCategory, MachineInteger, -++ MachineComplex -++ AMS Classifications: -++ Keywords: -++ Examples: -++ References: -++ Description: A domain which models the floating point representation -++ used by machines in the AXIOM-NAG link. -MachineFloat(): Exports == Implementation where - - PI ==> PositiveInteger - NNI ==> NonNegativeInteger - F ==> Float - I ==> Integer - S ==> String - FI ==> Fraction Integer - SUP ==> SparseUnivariatePolynomial - SF ==> DoubleFloat - - Exports ==> Join(FloatingPointSystem,FortranMachineTypeCategory,Field, - RetractableTo(Float),RetractableTo(Fraction(Integer)),CharacteristicZero) with - precision : PI -> PI - ++ precision(p) sets the number of digits in the model to p - precision : () -> PI - ++ precision() returns the number of digits in the model - base : PI -> PI - ++ base(b) sets the base of the model to b - maximumExponent : I -> I - ++ maximumExponent(e) sets the maximum exponent in the model to e - maximumExponent : () -> I - ++ maximumExponent() returns the maximum exponent in the model - minimumExponent : I -> I - ++ minimumExponent(e) sets the minimum exponent in the model to e - minimumExponent : () -> I - ++ minimumExponent() returns the minimum exponent in the model - coerce : $ -> F - ++ coerce(u) transforms a MachineFloat to a standard Float - coerce : MachineInteger -> $ - ++ coerce(u) transforms a MachineInteger into a MachineFloat - mantissa : $ -> I - ++ mantissa(u) returns the mantissa of u - exponent : $ -> I - ++ exponent(u) returns the exponent of u - changeBase : (I,I,PI) -> $ - ++ changeBase(exp,man,base) \undocumented{} - - Implementation ==> add - - import F - import FI - - Rep := Record(mantissa:I,exponent:I) - - -- Parameters of the Floating Point Representation - P : PI := 16 -- Precision - B : PI := 2 -- Base - EMIN : I := -1021 -- Minimum Exponent - EMAX : I := 1024 -- Maximum Exponent - - -- Useful constants - POWER : PI := 53 -- The maximum power of B which will yield P - -- decimal digits. - MMAX : PI := B**POWER - - - -- locals - locRound:(FI)->I - checkExponent:($)->$ - normalise:($)->$ - newPower:(PI,PI)->Void - - retractIfCan(u:$):Union(FI,"failed") == - mantissa(u)*(B/1)**(exponent(u)) - - wholePart(u:$):Integer == - man:I:=mantissa u - exp:I:=exponent u - f:= - positive? exp => man*B**(exp pretend PI) - zero? exp => man - wholePart(man/B**((-exp) pretend PI)) - normalise(u:$):$ == - -- We want the largest possible mantissa, to ensure a canonical - -- representation. - exp : I := exponent u - man : I := mantissa u - BB : I := B pretend I - sgn : I := sign man ; man := abs man - zero? man => [0,0]$Rep - if man < MMAX then - while man < MMAX repeat - exp := exp - 1 - man := man * BB - if man > MMAX then - q1:FI:= man/1 - BBF:FI:=BB/1 - while wholePart(q1) > MMAX repeat - q1:= q1 / BBF - exp:=exp + 1 - man := locRound(q1) - positive?(sgn) => checkExponent [man,exp]$Rep - checkExponent [-man,exp]$Rep - - mantissa(u:$):I == elt(u,mantissa)$Rep - exponent(u:$):I == elt(u,exponent)$Rep - - newPower(base:PI,prec:PI):Void == - power : PI := 1 - target : PI := 10**prec - current : PI := base - while (current := current*base) < target repeat power := power+1 - POWER := power - MMAX := B**POWER - - changeBase(exp:I,man:I,base:PI):$ == - newExp : I := 0 - f : FI := man*(base pretend I)::FI**exp - sign : I := sign f - f : FI := abs f - newMan : I := wholePart f - zero? f => [0,0]$Rep - BB : FI := (B pretend I)::FI - if newMan < MMAX then - while newMan < MMAX repeat - newExp := newExp - 1 - f := f*BB - newMan := wholePart f - if newMan > MMAX then - while newMan > MMAX repeat - newExp := newExp + 1 - f := f/BB - newMan := wholePart f - [sign*newMan,newExp]$Rep - - checkExponent(u:$):$ == - exponent(u) < EMIN or exponent(u) > EMAX => - message :S := concat(["Exponent out of range: ", - string EMIN, "..", string EMAX])$S - error message - u - - coerce(u:$):OutputForm == - coerce(u::F) - - coerce(u:MachineInteger):$ == - checkExponent changeBase(0,retract(u)@Integer,10) - - coerce(u:$):F == - oldDigits : PI := digits(P)$F - r : F := float(mantissa u,exponent u,B)$Float - digits(oldDigits)$F - r - - coerce(u:F):$ == - checkExponent changeBase(exponent(u)$F,mantissa(u)$F,base()$F) - - coerce(u:I):$ == - checkExponent changeBase(0,u,10) - - coerce(u:FI):$ == (numer u)::$/(denom u)::$ - - retract(u:$):FI == - value : Union(FI,"failed") := retractIfCan(u) - value case "failed" => error "Cannot retract to a Fraction Integer" - value::FI - - retract(u:$):F == u::F - - retractIfCan(u:$):Union(F,"failed") == u::F::Union(F,"failed") - - retractIfCan(u:$):Union(I,"failed") == - value:FI := mantissa(u)*(B pretend I)::FI**exponent(u) - zero? fractionPart(value) => wholePart(value)::Union(I,"failed") - "failed"::Union(I,"failed") - - retract(u:$):I == - result : Union(I,"failed") := retractIfCan u - result = "failed" => error "Not an Integer" - result::I - - precision(p: PI):PI == - old : PI := P - newPower(B,p) - P := p - old - - precision():PI == P - - base(b:PI):PI == - old : PI := b - newPower(b,P) - B := b - old - - base():PI == B - - maximumExponent(u:I):I == - old : I := EMAX - EMAX := u - old - - maximumExponent():I == EMAX - - minimumExponent(u:I):I == - old : I := EMIN - EMIN := u - old - - minimumExponent():I == EMIN - - 0 == [0,0]$Rep - 1 == changeBase(0,1,10) - - zero?(u:$):Boolean == u=[0,0]$Rep - - - - f1:$ - f2:$ - - - locRound(x:FI):I == - abs(fractionPart(x)) >= 1/2 => wholePart(x)+sign(x) - wholePart(x) - - recip f1 == - zero? f1 => "failed" - normalise [ locRound(B**(2*POWER)/mantissa f1),-(exponent f1 + 2*POWER)] - - f1 * f2 == - normalise [mantissa(f1)*mantissa(f2),exponent(f1)+exponent(f2)]$Rep - - f1 **(p:FI) == - ((f1::F)**p)::% - ---inline - f1 / f2 == - zero? f2 => error "division by zero" - zero? f1 => 0 - f1=f2 => 1 - normalise [locRound(mantissa(f1)*B**(2*POWER)/mantissa(f2)), - exponent(f1)-(exponent f2 + 2*POWER)] - - inv(f1) == 1/f1 - - f1 exquo f2 == f1/f2 - - divide(f1,f2) == [ f1/f2,0] - - f1 quo f2 == f1/f2 - f1 rem f2 == 0 - u:I * f1 == - normalise [u*mantissa(f1),exponent(f1)]$Rep - - f1 = f2 == mantissa(f1)=mantissa(f2) and exponent(f1)=exponent(f2) - - f1 + f2 == - m1 : I := mantissa f1 - m2 : I := mantissa f2 - e1 : I := exponent f1 - e2 : I := exponent f2 - e1 > e2 => ---insignificance - e1 > e2 + POWER + 2 => - zero? f1 => f2 - f1 - normalise [m1*(B pretend I)**((e1-e2) pretend NNI)+m2,e2]$Rep - e2 > e1 + POWER +2 => - zero? f2 => f1 - f2 - normalise [m2*(B pretend I)**((e2-e1) pretend NNI)+m1,e1]$Rep - - - f1 == [- mantissa f1,exponent f1]$Rep - - f1 - f2 == f1 + (-f2) - - f1 < f2 == - m1 : I := mantissa f1 - m2 : I := mantissa f2 - e1 : I := exponent f1 - e2 : I := exponent f2 - sign(m1) = sign(m2) => - e1 < e2 => true - e1 = e2 and m1 < m2 => true - false - sign(m1) = 1 => false - sign(m1) = 0 and sign(m2) = -1 => false - true - - characteristic:NNI == 0 - -@ -\section{domain MCMPLX MachineComplex} -<<domain MCMPLX MachineComplex>>= -)abbrev domain MCMPLX MachineComplex -++ Date Created: December 1993 -++ Date Last Updated: -++ Basic Operations: -++ Related Domains: -++ Also See: FortranExpression, FortranMachineTypeCategory, MachineInteger, -++ MachineFloat -++ AMS Classifications: -++ Keywords: -++ Examples: -++ References: -++ Description: A domain which models the complex number representation -++ used by machines in the AXIOM-NAG link. -MachineComplex():Exports == Implementation where - - Exports ==> Join (FortranMachineTypeCategory, - ComplexCategory(MachineFloat)) with - coerce : Complex Float -> $ - ++ coerce(u) transforms u into a MachineComplex - coerce : Complex Integer -> $ - ++ coerce(u) transforms u into a MachineComplex - coerce : Complex MachineFloat -> $ - ++ coerce(u) transforms u into a MachineComplex - coerce : Complex MachineInteger -> $ - ++ coerce(u) transforms u into a MachineComplex - coerce : $ -> Complex Float - ++ coerce(u) transforms u into a COmplex Float - - Implementation ==> Complex MachineFloat add - - coerce(u:Complex Float):$ == - complex(real(u)::MachineFloat,imag(u)::MachineFloat) - - coerce(u:Complex Integer):$ == - complex(real(u)::MachineFloat,imag(u)::MachineFloat) - - coerce(u:Complex MachineInteger):$ == - complex(real(u)::MachineFloat,imag(u)::MachineFloat) - - coerce(u:Complex MachineFloat):$ == - complex(real(u),imag(u)) - - coerce(u:$):Complex Float == - complex(real(u)::Float,imag(u)::Float) - -@ -\section{License} -<<license>>= ---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. ---All rights reserved. --- ---Redistribution and use in source and binary forms, with or without ---modification, are permitted provided that the following conditions are ---met: --- --- - Redistributions of source code must retain the above copyright --- notice, this list of conditions and the following disclaimer. --- --- - Redistributions in binary form must reproduce the above copyright --- notice, this list of conditions and the following disclaimer in --- the documentation and/or other materials provided with the --- distribution. --- --- - Neither the name of The Numerical ALgorithms Group Ltd. nor the --- names of its contributors may be used to endorse or promote products --- derived from this software without specific prior written permission. --- ---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS ---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A ---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER ---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, ---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, ---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR ---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF ---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING ---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -@ -<<*>>= -<<license>> - -<<domain MINT MachineInteger>> -<<domain MFLOAT MachineFloat>> -<<domain MCMPLX MachineComplex>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} |