)abbrev domain MINT MachineInteger
++ Author: Mike Dewar
++ Date Created:  December 1993
++ 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 from S
      abs(u) > MAXINT =>
        message : S := concat [convert(u)@S,"  > MAXINT(",convert(MAXINT)@S,")"]
        error message
      u pretend %

    retract(u : %) : Integer == u pretend Integer

    retractIfCan(u:%):Union(Integer,"failed") == u pretend Integer

)abbrev domain MFLOAT MachineFloat
++ Author: Mike Dewar
++ Date Created:  December 1993
++ 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
    base   : () -> PI
      ++ base() returns the base of the model
    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 from F
    import from 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
      void()

    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: ",
                              convert(EMIN)@S, "..", convert(EMAX)@S])$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

    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

)abbrev domain MCMPLX MachineComplex
++ Date Created:  December 1993
++ 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)

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