σ šίΘ[c@`s~dZddlmZmZmZmZddlZddlm Z ddd„Z dd„Z d „Zd „Zd „ZdS( uτTime utilities. In particular, routines to do basic arithmetic on numbers represented by two doubles, using the procedure of Shewchuk, 1997, Discrete & Computational Geometry 18(3):305-363 -- http://www.cs.berkeley.edu/~jrs/papers/robustr.pdf i(tabsolute_importtdivisiontprint_functiontunicode_literalsNi(tunitsgπ?cC`s&t||ƒ\}}tj|dkƒret||ƒ\}}|||7}t||ƒ\}}ntj|dkƒrι||}t||ƒ\}} t|| ƒ\} } | |7} | | 8} | | |} t|| ƒ\}}ntj|ƒ} t|| ƒ\}}|||7}| |fS(uD Return the sum of ``val1`` and ``val2`` as two float64s, an integer part and the fractional remainder. If ``factor`` is not 1.0 then multiply the sum by ``factor``. If ``divisor`` is not 1.0 then divide the sum by ``divisor``. The arithmetic is all done with exact floating point operations so no precision is lost to rounding error. This routine assumes the sum is less than about 1e16, otherwise the ``frac`` part will be greater than 1.0. Returns ------- day, frac : float64 Integer and fractional part of val1 + val2. gπ?(ttwo_sumtnptanyt two_producttround(tval1tval2tfactortdivisortsum12terr12tcarrytq1tp1tp2td1td2tq2tdaytextratfrac((s1lib/python2.7/site-packages/astropy/time/utils.pytday_fracs"   cC`sΣ|dk rBt|ƒ\}}t|ƒ\}}||||fSy|jjtjƒ}Wn$tk r|jtjƒdfSX|dkr€t|j dd|ƒStjj|jƒ}t|j dd|ƒSdS(u‚Like ``day_frac``, but for quantities with units of time. The quantities are separately converted to days. Here, we need to take care with the conversion since while the routines here can do accurate multiplication, the conversion factor itself may not be accurate. For instance, if the quantity is in seconds, the conversion factor is 1./86400., which is not exactly representable as a float. To work around this, for conversion factors less than unity, rather than multiply by that possibly inaccurate factor, the value is divided by the conversion factor of a day to that unit (i.e., by 86400. for seconds). For conversion factors larger than 1, such as 365.25 for years, we do just multiply. With this scheme, one has precise conversion factors for all regular time units that astropy defines. Note, however, that it does not necessarily work for all custom time units, and cannot work when conversion to time is via an equivalency. For those cases, one remains limited by the fact that Quantity calculations are done in double precision, not in quadruple precision as for time. ggπ?R R N( tNonetquantity_day_fractunitttotuRt Exceptiontto_valueRtvalue(R R tres11tres12tres21tres22R R ((s1lib/python2.7/site-packages/astropy/time/utils.pyR:s   cC`s@||}||}||}||}||}|||fS(uΡ Add ``a`` and ``b`` exactly, returning the result as two float64s. The first is the approximate sum (with some floating point error) and the second is the error of the float64 sum. Using the procedure of Shewchuk, 1997, Discrete & Computational Geometry 18(3):305-363 http://www.cs.berkeley.edu/~jrs/papers/robustr.pdf Returns ------- sum, err : float64 Approximate sum of a + b and the exact floating point error ((tatbtxtebtea((s1lib/python2.7/site-packages/astropy/time/utils.pyRbs      c C`sˆ||}t|ƒ\}}t|ƒ\}}||}||}||} || 8}||} || 8}||} | |}||fS(uί Multiple ``a`` and ``b`` exactly, returning the result as two float64s. The first is the approximate product (with some floating point error) and the second is the error of the float64 product. Uses the procedure of Shewchuk, 1997, Discrete & Computational Geometry 18(3):305-363 http://www.cs.berkeley.edu/~jrs/papers/robustr.pdf Returns ------- prod, err : float64 Approximate product a * b and the exact floating point error (tsplit( R'R(R)tahtaltbhtblty1tyty2ty3ty4((s1lib/python2.7/site-packages/astropy/time/utils.pyRys         cC`s2d|}||}||}||}||fS(uΔ Split float64 in two aligned parts. Uses the procedure of Shewchuk, 1997, Discrete & Computational Geometry 18(3):305-363 http://www.cs.berkeley.edu/~jrs/papers/robustr.pdf g A((R'tctabigR-R.((s1lib/python2.7/site-packages/astropy/time/utils.pyR,–s    (t__doc__t __future__RRRRtnumpyRtRRRRRRRR,(((s1lib/python2.7/site-packages/astropy/time/utils.pyts" * (