a ߙfb\@sdZddlZddlZddlmZdddZdddZddZ d d Z d d Z d Z d ddZ d!ddZd"ddZddZddZddZddZeeZeeZeeZejeddZejeddZdS)#acTime 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 Furthermore, some helper routines to turn strings and other types of objects into two values, and vice versa. NcCst||\}}|dur>t||\}}|||7}t||\}}|dur||}t||\}} t|| \} } | |7} | | 8} | | |} t|| \}}t|} t|| \}}|||7}t|}| |7} t|| \}}|||7}| |fS)a,Return the sum of ``val1`` and ``val2`` as two float64s. The returned floats are an integer part and the fractional remainder, with the latter guaranteed to be within -0.5 and 0.5 (inclusive on either side, as the integer is rounded to even). The arithmetic is all done with exact floating point operations so no precision is lost to rounding error. It is assumed the sum is less than about 1e16, otherwise the remainder will be greater than 1.0. Parameters ---------- val1, val2 : array of float Values to be summed. factor : float, optional If given, multiply the sum by it. divisor : float, optional If given, divide the sum by it. Returns ------- day, frac : float64 Integer and fractional part of val1 + val2. N)two_sum two_productnpround)val1val2factordivisorZsum12Zerr12ZcarryZq1Zp1Zp2Zd1Zd2Zq2dayZextraZfracZexcessr 1lib/python3.9/site-packages/astropy/time/utils.pyday_fracs*      r cCs|dur0t|\}}t|\}}||||fSz|jtj}Wn"tyd|tjdfYS0|dkrzt|jdS|dkrt|jd|dStj|j}t|jd|dSdS)aLike ``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. Ng?)r)r ) quantity_day_fracZunittour ExceptionZto_valuer value)rrZres11Zres12Zres21Zres22rr r r r rKs    rcCs4||}||}||}||}||}|||fS)a 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 r )abxZebZear r r rvs rc Csh||}t|\}}t|\}}||}||}||} || 8}||} || 8}||} | |}||fS)a 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 )split) rrrahalZbhZblZy1yZy2Zy3Zy4r r r rs  rcCs(d|}||}||}||}||fS)z 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 gAr )rcZabigrrr r r rs r"cCsl|dur|jd}n,t|j|j}|j|dd}|j|dd}t||\}}|jtdd|jtddfS)NrF)copy)ZdtypetyperZ result_typeastyper float)rrZ best_typeifr r r longdouble_to_twovalsr$cCsXt0}t|_t|}t|}||}Wdn1s>0Yt|t|fSN)decimal localcontext_enough_decimal_placesprecDecimalrr!)rrctxdr"r#r r r decimal_to_twoval1s   &r-cCst|dSNascii)r-decoderrr r r bytes_to_twoval1sr2cCs|tj|tjSr%)r rZ longdoubler1r r r twoval_to_longdoublesr3cCsFt*}t|_t|t|WdS1s80YdSr%)r&r'r(r)r*)rrr+r r r twoval_to_decimal1s r4cCs>|dkrt|Stt|||d}|ddkr:|d7}|S)Nr0.)strformatr4strip)rrfmtresultr r r twoval_to_string1s  r=cCst|||dSr.)r=encode)rrr;r r r twoval_to_bytes1sr?r;)Zexcluded)NN)N)N)N)N)__doc__r&ZnumpyrZ astropy.unitsZunitsrr rrrrr(r$r-r2r3r4r=r?Z vectorizeZdecimal_to_twovalZbytes_to_twovalZtwoval_to_decimalZtwoval_to_stringZtwoval_to_bytesr r r r s*   9 +