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*To*: Alex Shinn <alexshinn@x>*Subject*: Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0*From*: Mark H Weaver <mhw@x>*Date*: Sun, 23 Dec 2012 17:51:43 -0500*Cc*: John Cowan <cowan@x>, scheme-reports <scheme-reports@x>*In-reply-to*: <CAMMPzYMU5-h+aLd45Hu2vY-oDeRs4DiHTV9fBfo9RtiTB9ds2w@mail.gmail.com> (Alex Shinn's message of "Sat, 22 Dec 2012 15:17:14 +0900")*References*: <87bodu4r0r.fsf@tines.lan> <20121216041031.GE10312@mercury.ccil.org> <87pq25yh5s.fsf@tines.lan> <20121219221955.GH4477@mercury.ccil.org> <87d2y5y6fb.fsf@tines.lan> <20121221055315.GB28661@mercury.ccil.org> <87y5grsrvm.fsf@tines.lan> <CAMMPzYMQVzkQFLsgcYAWZaFO__Y13T_kOXD+CrLqVXPQOcjXGw@mail.gmail.com> <20121221171601.GC23915@mercury.ccil.org> <CAMMPzYO5m64sWGQT2b7SSPbm=zRbVT4oEx8E-DoLLATNZxtj_w@mail.gmail.com> <20121222024255.GH8521@mercury.ccil.org> <CAMMPzYOtVMoyiE=ToLHvmNf=Lbq_FOE9v9CcrZoBrcdB_mnoVQ@mail.gmail.com> <87licqr5jz.fsf@tines.lan> <CAMMPzYMU5-h+aLd45Hu2vY-oDeRs4DiHTV9fBfo9RtiTB9ds2w@mail.gmail.com>

Alex Shinn <alexshinn@x> writes: > On Sat, Dec 22, 2012 at 2:58 PM, Mark H Weaver <mhw@x> wrote: > > Alex Shinn <alexshinn@x> writes: > > Exact arithmetic can run out of memory. > > So can your proposed inexacts. In order to avoid underflow and > overflow, the number of representable values cannot be finite, > because > there can be no maximum or minimum representable magnitude. > Therefore > the amount of memory needed to represent your numbers is > unbounded. No > matter how clever your compression method is, that fact is > unavoidable. > > It's not a compression technique, and the amount of > memory is in practice bounded by the limitations of > computation. What external representation will you use for these numbers? For example, even if you can efficiently handle something like this: (do ((i 10000000 (- i 1)) (x 1e300 (expt x x))) ((zero? i) (/ x))) What will you do if someone applies 'number->string' to the result? Mark _______________________________________________ Scheme-reports mailing list Scheme-reports@x http://lists.scheme-reports.org/cgi-bin/mailman/listinfo/scheme-reports

**Follow-Ups**:**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*Alex Shinn <alexshinn@x>

**References**:**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*Mark H Weaver <mhw@x>

**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*John Cowan <cowan@x>

**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*Mark H Weaver <mhw@x>

**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*John Cowan <cowan@x>

**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*Mark H Weaver <mhw@x>

**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*John Cowan <cowan@x>

**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*Mark H Weaver <mhw@x>

**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*Alex Shinn <alexshinn@x>

**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*John Cowan <cowan@x>

**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*Alex Shinn <alexshinn@x>

**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*John Cowan <cowan@x>

**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*Alex Shinn <alexshinn@x>

**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*Mark H Weaver <mhw@x>

**Re: [Scheme-reports] Strong win later reversed: Real numbers have imaginary part #e0***From:*Alex Shinn <alexshinn@x>

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