Fixed and Arbitrary Precision Numerical Fields - Sage

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Sage Reference Manual: Fixed and Arbitrary Precision Numerical Fields, Release 6.2sage: time_alloc_list(2)[2.2, 2.1]24 Chapter 1. Double Precision Real Numbers
CHAPTERTWOARBITRARY PRECISION REALNUMBERSArbitrary Precision Real NumbersAUTHORS:• Kyle Schalm (2005-09)• William Stein: bug fixes, examples, maintenance• Didier Deshommes (2006-03-19): examples• David Harvey (2006-09-20): compatibility with Element._parent• William Stein (2006-10): default printing truncates to avoid base-2 rounding confusing (fix suggested by BillHart)• Didier Deshommes: special constructor for QD numbers• Paul Zimmermann (2008-01): added new functions from mpfr-2.3.0, replaced some, e.g., sech = 1/cosh, by theiroriginal mpfr version.• Carl Witty (2008-02): define floating-point rank and associated functions; add some documentation• Robert Bradshaw (2009-09): decimal literals, optimizations• Jeroen Demeyer (2012-05-27): set the MPFR exponent range to the maximal possible value (trac ticket #13033)• Travis Scrimshaw (2012-11-02): Added doctests for full coverageThis is a binding for the MPFR arbitrary-precision floating point library.We define a class RealField, where each instance of RealField specifies a field of floating-point numbers witha specified precision and rounding mode. Individual floating-point numbers are of RealNumber.In Sage (as in MPFR), floating-point numbers of precision p are of the form sm2 e−p , where s ∈ {−1, 1}, 2 p−1 ≤m < 2 p , and −2 B + 1 ≤ e ≤ 2 B − 1 where B = 30 on 32-bit systems and B = 62 on 64-bit systems; additionally,there are the special values +0, -0, +infinity, -infinity and NaN (which stands for Not-a-Number).Operations in this module which are direct wrappers of MPFR functions are “correctly rounded”; we briefly describewhat this means. Assume that you could perform the operation exactly, on real numbers, to get a result r. If this resultcan be represented as a floating-point number, then we return that number.Otherwise, the result r is between two floating-point numbers. For the directed rounding modes (round to plus infinity,round to minus infinity, round to zero), we return the floating-point number in the indicated direction from r. Forround to nearest, we return the floating-point number which is nearest to r.25
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CHAPTERFOURFIELD OF ARBITRARY PRECI
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CHAPTERFIVEFILE:SAGE/RINGS/REAL_INT
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CHAPTERSIXTHESE CLASSES ARE VERY LA
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CHAPTERSEVENDOUBLE PRECISION COMPLE
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CHAPTERNINEARBITRARY PRECISION COMP
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CHAPTERTENARBITRARY PRECISION COMPL
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CHAPTERELEVENFIELD OF ARBITRARY PRE
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CHAPTERTWELVEARBITRARY PRECISION CO
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CHAPTERTHIRTEENINDICES AND TABLES
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PYTHON MODULE INDEXrsage.rings.comp
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INDEXAabs() (sage.rings.complex_dou
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Fixed and Arbitrary Precision Numerical Fields - Sage

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