mirror of
https://github.com/vale981/arb
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283 lines
13 KiB
ReStructuredText
283 lines
13 KiB
ReStructuredText
.. _history:
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History and changes
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===============================================================================
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For more details, view the commit log
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in the git repository https://github.com/fredrik-johansson/arb
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* 2014-05-03 - version 1.1.0
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* faster and more accurate error bounds for polynomial multiplication
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(error bounds are now always as good as with classical multiplication,
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and multiplying high-degree polynomials with approximately equal
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coefficients now has proper quasilinear complexity)
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* faster and much less memory-hungry exponentials at very high precision
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* improved the partition function to support n bigger than a single word,
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and enabled the possibility to use two threads for the computation
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* fixed a bug in floating-point arithmetic that caused a too small bound
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for the rounding error to be reported when the result of an inexact
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operation was rounded up to a power of two (this bug did
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not affect the correctness of ball arithmetic, because operations on
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ball midpoints always round down)
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* minor optimizations to floating-point arithmetic
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* improved argument reduction of the digamma function and short series
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expansions of the rising factorial
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* removed the holonomic module for now, as it did not really do anything
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very useful
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* 2013-12-21 - version 1.0.0
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* new example programs directory
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* poly_roots example program
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* real_roots example program
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* pi_digits example program
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* hilbert_matrix example program
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* keiper_li example program
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* new fmprb_calc module for calculus with real functions
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* bisection-based root isolation
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* asymptotically fast Newton root refinement
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* new fmpcb_calc module for calculus with complex functions
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* numerical integration using Taylor series
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* scalar functions
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* simplified fmprb_const_euler using published error bound
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* added fmprb_inv
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* fmprb_trim, fmpcb_trim
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* added fmpcb_rsqrt (complex reciprocal square root)
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* fixed bug in fmprb_sqrtpos with nonfinite input
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* slightly improved fmprb powering code
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* added various functions for bounding fmprs by powers of two
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* added fmpr_is_int
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* polynomials and power series
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* implemented scaling to speed up blockwise multiplication
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* slightly faster basecase power series exponentials
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* improved sin/cos/tan/exp for short power series
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* added complex sqrt_series, rsqrt_series
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* implemented the Riemann-Siegel Z and theta functions for real power series
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* added fmprb_poly_pow_series, fmprb_poly_pow_ui and related methods
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* fmprb/fmpcb_poly_contains_fmpz_poly
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* faster composition by monomials
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* implemented Borel transform and binomial transform for real power series
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* matrices
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* implemented matrix exponentials
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* multithreaded fmprb_mat_mul
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* added matrix infinity norm functions
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* added some more matrix-scalar functions
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* added matrix contains and overlaps methods
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* zeta function evaluation
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* multithreaded power sum evaluation
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* faster parameter selection when computing many derivatives
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* implemented binary splitting to speed up computing many derivatives
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* miscellaneous
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* corrections for C++ compatibility (contributed by Jonathan Bober)
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* several minor bugfixes and test code enhancements
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* 2013-08-07 - version 0.7
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* floating-point and ball functions
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* documented, added test code, and fixed bugs for various operations involving a ball containing an infinity or NaN
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* added reciprocal square root functions (fmpr_rsqrt, fmprb_rsqrt) based on mpfr_rec_sqrt
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* faster high-precision division by not computing an explicit remainder
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* slightly faster computation of pi by using new reciprocal square root and division code
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* added an fmpr function for approximate division to speed up certain radius operations
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* added fmpr_set_d for conversion from double
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* allow use of doubles to optionally compute the partition function faster but without an error bound
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* bypass mpfr overflow when computing the exponential function to extremely high precision (approximately 1 billion digits)
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* made fmprb_exp faster for large numbers at extremely high precision by skipping the log(2) removal
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* made fmpcb_lgamma faster at high precision by speeding up the argument reduction branch computation
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* added fmprb_asin, fmprb_acos
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* added various other utility functions to the fmprb module
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* added a function for computing the Glaisher constant
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* optimized evaluation of the Riemann zeta function at high precision
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* polynomials and power series
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* made squaring of polynomials faster than generic multiplication
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* implemented power series reversion (various algorithms) for the fmprb_poly type
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* added many fmprb_poly utility functions (shifting, truncating, setting/getting coefficients, etc.)
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* improved power series division when either operand is short
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* improved power series logarithm when the input is short
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* improved power series exponential to use the basecase algorithm for short input regardless of the output size
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* added power series square root and reciprocal square root
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* added atan, tan, sin, cos, sin_cos, asin, acos fmprb_poly power series functions
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* added Newton iteration macros to simplify various functions
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* added gamma functions of real and complex power series ([fmprb/fmpcb]_poly_[gamma/rgamma/lgamma]_series)
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* added wrappers for computing the Hurwitz zeta function of a power series ([fmprb/fmpcb]_poly_zeta_series)
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* implemented sieving and other optimizations to improve performance for evaluating the zeta function of a short power series
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* improved power series composition when the inner series is linear
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* added many fmpcb_poly versions of nearly all fmprb_poly functions
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* improved speed and stability of series composition/reversion by balancing the power table exponents
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* other
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* added support for freeing all cached data by calling flint_cleanup()
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* introduced fmprb_ptr, fmprb_srcptr, fmpcb_ptr, fmpcb_srcptr typedefs for cleaner function signatures
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* various bug fixes and general cleanup
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* 2013-05-31 - version 0.6
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* made fast polynomial multiplication over the reals numerically stable by using a blockwise algorithm
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* disabled default use of the Gauss formula for multiplication of complex polynomials, to improve numerical stability
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* added division and remainder for complex polynomials
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* added fast multipoint evaluation and interpolation for complex polynomials
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* added missing fmprb_poly_sub and fmpcb_poly_sub functions
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* faster exponentials (fmprb_exp and dependent functions) at low precision, using precomputation
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* rewrote fmpr_add and fmpr_sub using mpn level code, improving efficiency at low precision
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* ported the partition function implementation from flint (using ball arithmetic
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in all steps of the calculation to guarantee correctness)
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* ported algorithm for computing the cosine minimal polynomial from flint (using
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ball arithmetic to guarantee correctness)
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* support using gmp instead of mpir
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* only use thread-local storage when enabled in flint
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* slightly faster error bounding for the zeta function
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* added some other helper functions
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* 2013-03-28 - version 0.5
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* arithmetic and elementary functions
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* added fmpr_get_fmpz, fmpr_get_si
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* fixed accuracy problem with fmprb_div_2expm1
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* special-cased squaring of complex numbers
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* added various fmpcb convenience functions (addmul_ui, etc)
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* optimized fmpr_cmp_2exp_si and fmpr_cmpabs_2exp_si, and added test code for comparison functions
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* added fmprb_atan2, also fixing a bug in fmpcb_arg
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* added fmprb_sin_pi, cos_pi, sin_cos_pi etc.
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* added fmprb_sin_pi_fmpq (etc.) using algebraic methods for fast evaluation of roots of unity
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* faster fmprb_poly_evaluate and evaluate_fmpcb using rectangular splitting
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* added fmprb_poly_evaluate2, evaluate2_fmpcb for simultaneously evaluating the derivative
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* added fmprb_poly root polishing code using near-optimal Newton steps (experimental)
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* added fmpr_root, fmprb_root (currently based on MPFR)
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* added fmpr_min, fmpr_max
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* added fmprb_set_interval_fmpr, fmprb_union
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* added fmpr_bits, fmprb_bits, fmpcb_bits for obtaining the mantissa width
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* added fmprb_hypot
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* added complex square roots
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* improved fmprb_log to slightly improve speed, and properly support huge arguments
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* fixed exp, cosh, sinh to work with huge arguments
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* added fmprb_expm1
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* fixed sin, cos, atan to work with huge arguments
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* improved fmprb_pow and fmpcb_pow, including automatic detection of small integer and half-integer exponents
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* added many more elementary functions: fmprb_tan/cot/tanh/coth, fmpcb_tan/cot, and pi versions
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* added fmprb const_e, const_log2, const_log10, const_catalan
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* fixed ball containment/overlap checking to work operate efficiently and correctly with huge exponents
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* strengthened test code for many core operations
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* special functions
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* reorganized zeta function related code
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* faster evaluation of the Riemann zeta function via sieving
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* documented and improved efficiency of the zeta constant binary splitting code
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* calculate error bound in Borwein's algorithm with fmprs instead of using doubles
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* optimized divisions in zeta evaluation via the Euler product
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* use functional equation for Riemann zeta function of a negative argument
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* compute single Bernoulli numbers using ball arithmetic instead of relying on the floating-point code in flint
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* initial code for evaluating the gamma function using its Taylor series
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* much faster rising factorials at high precision, using difference polynomials
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* much faster gamma function at high precision
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* added complex gamma function, log gamma function, and other versions
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* added fmprb_agm (real arithmetic-geometric mean)
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* added fmprb_gamma_fmpq, supporting rapid computation of gamma(p/q) for q = 1,2,3,4,6
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* added real and complex digamma function
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* fixed unnecessary recomputation of Bernoulli numbers
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* optimized computation of Euler's constant, and added proper error bounds
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* avoid reliance on doubles in the hypergeometric series tail bound
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* cleaned up factorials and binomials, computing factorials via gamma
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* other
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* added an fmpz_extras module to collect various internal fmpz helper functions
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* fixed detection of flint header files
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* fixed various other small bugs
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* 2013-01-26 - version 0.4
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* much faster fmpr_mul, fmprb_mul and set_round, resulting in general speed improvements
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* code for computing the complex Hurwitz zeta function with derivatives
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* fixed and documented error bounds for hypergeometric series
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* better algorithm for series evaluation of the gamma function at a rational point
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* much faster generation of Bernoulli numbers
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* complex log, exp, pow, trigonometric functions (currently based on MPFR)
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* complex nth roots via Newton iteration
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* added code for arithmetic on fmpcb_polys
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* code for computing Khinchin's constant
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* code for rising factorials of polynomials or power series
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* faster sin_cos
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* better div_2expm1
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* many other new helper functions
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* improved thread safety
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* more test code for core operations
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* 2012-11-07 - version 0.3
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* converted documentation to sphinx
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* new module fmpcb for ball interval arithmetic over the complex numbers
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* conversions, utility functions and arithmetic operations
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* new module fmpcb_mat for matrices over the complex numbers
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* conversions, utility functions and arithmetic operations
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* multiplication, LU decomposition, solving, inverse and determinant
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* new module fmpcb_poly for polynomials over the complex numbers
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* root isolation for complex polynomials
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* new module fmpz_holonomic for functions/sequences
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defined by linear differential/difference equations
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with polynomial coefficients
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* functions for creating various special sequences and functions
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* some closure properties for sequences
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* Taylor series expansion for differential equations
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* computing the nth entry of a sequence using binary splitting
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* computing the nth entry mod p using fast multipoint evaluation
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* generic binary splitting code with automatic error bounding is now
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used for evaluating hypergeometric series
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* matrix powering
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* various other helper functions
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* 2012-09-29 - version 0.2
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* code for computing the gamma function (Karatsuba, Stirling's series)
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* rising factorials
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* fast exp_series using Newton iteration
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* improved multiplication of small polynomials by using classical multiplication
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* implemented error propagation for square roots
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* polynomial division (Newton-based)
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* polynomial evaluation (Horner) and composition (divide-and-conquer)
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* product trees, fast multipoint evaluation and interpolation (various algorithms)
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* power series composition (Horner, Brent-Kung)
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* added the fmprb_mat module for matrices of balls of real numbers
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* matrix multiplication
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* interval-aware LU decomposition, solving, inverse and determinant
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* many helper functions and small bugfixes
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* 2012-09-14 - version 0.1
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* 2012-08-05 - began simplified rewrite
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* 2012-04-05 - experimental ball and polynomial code
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