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Re: MachinePrecision vs. Arbitrary Precision
Posted:
Apr 29, 2011 6:34 AM


Bill Rowe <readnews@sbcglobal.net> writes:
> On 4/27/11 at 5:39 AM, worthless.trash.junk@gmail.com (Rafael Dunn) > wrote: > >>In:= >>N[Sin[Exp[100]]] >>N[Sin[Exp[100]], 1] >>N[Sin[Exp[100]], 11] > >>Out:= >>0.999105 >>0.1 >>0.14219812366 > >>I realize that N[exp] = N[exp, MachinePrecision]. This indicates >>when N[] is asked to calculate to MachinePrecision, > > More specifically, this asks hardware to do the required computation. > >>it produces an incorrect result in this example. > > That is due to the limitations of floating point arithmetic as > implemented in hardware. The actual result you get will vary > according to what hardware is being used.
To emphasize that this is the result from hardware here is a program in the C programming language:
#include <stdio.h> #include <math.h> int main(void) { printf("%g\n", sin(exp(100))); return 0; }
And here is its output:
0.999105
Scott  Scott Hemphill hemphill@alumni.caltech.edu "This isn't flying. This is falling, with style."  Buzz Lightyear



