OpenMath Content Dictionary: bigfloat1

Canonical URL:
http://www.openmath.org/cd/bigfloat1.ocd
CD File:
bigfloat1.ocd
CD as XML Encoded OpenMath:
bigfloat1.omcd
Defines:
bigfloat, bigfloatprec
Date:
2001-03-12
Version:
2
Review Date:
2003-04-01
Status:
official
Uses CD:
relation1, arith1, rounding1, transc1

This CD provides a common representation of "bigfloats" in a mantissa/ radix/exponent format. There is a further version, which provides an opportunity to state a precision (only required in a different radix). No operations are defined here -- see arith and alg.

Written by James Davenport on 1999-07-13.
bigfloatprec added 1999-07-21.

bigfloat

The bigfloat constructor takes three arguments, a mantissa, a base and the exponent.

Commented Mathematical property (CMP):
bigfloat(m,r,e)=m*r^e
Formal Mathematical property (FMP):
<OMOBJ>
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMA>
      <OMS cd="bigfloat1" name="bigfloat"/>
      <OMV name="m"/>
      <OMV name="r"/>
      <OMV name="e"/>
    </OMA>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMV name="m"/>
      <OMA>
        <OMS cd="arith1" name="power"/>
        <OMV name="r"/>
        <OMV name="e"/>
      </OMA>
    </OMA>
  </OMA>
</OMOBJ>

eq (bigfloat ( m, r, e) , times ( m, power ( r, e) ) )

Signatures:
sts


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bigfloatprec

The bigfloat "with precision specified in (another) radix" constructor. Takes 3 arguments, the first argument is a floating point number constructed with the bigfloat constructor, the second is the new radix, whilst the third specifies how many digits are significant.

Commented Mathematical property (CMP):
bigfloatprec(f,r,p)=f However, if converted to radix r, only p digits in that radix are significant. This usually means that it originated in radix r, and has since (e.g. for display purposes) been converted into its current radix. For exposition, f = m*r^e.
Formal Mathematical property (FMP):
<OMOBJ>
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMA>
      <OMS cd="bigfloat1" name="bigfloatprec"/>
      <OMA>
        <OMS cd="bigfloat1" name="bigfloat"/>
        <OMV name="m"/>
        <OMV name="r"/>
        <OMV name="e"/>
      </OMA>
      <OMV name="r"/>
      <OMA>
        <OMS cd="rounding1" name="ceiling"/>
        <OMA>
          <OMS cd="transc1" name="log"/>
          <OMV name="r"/>
          <OMV name="m"/>
        </OMA>
      </OMA>
    </OMA>
    <OMA>
      <OMS cd="bigfloat1" name="bigfloat"/>
      <OMV name="m"/>
      <OMV name="r"/>
      <OMV name="e"/>
    </OMA>
  </OMA>
</OMOBJ>

eq (bigfloatprec (bigfloat ( m, r, e) , r, ceiling (log ( r, m) ) ) , bigfloat ( m, r, e) )

Signatures:
sts


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