History and changes
For more details, view the commit log
in the git repository https://github.com/fredrik-johansson/arb
- 2015-07-14 - version 2.7.0
- hypergeometric functions
- implemented Bessel I and Y functions (acb_hypgeom_bessel_i, acb_hypgeom_bessel_y)
- fixed bug in Bessel K function giving the wrong branch for negative real arguments
- added code for evaluating complex hypergeometric series binary splitting
- added code for evaluating complex hypergeometric series using fast multipoint evaluation
- gamma related functions
- implemented the Barnes G-function and its continuous logarithm (acb_barnes_g, acb_log_barnes_g)
- implemented the generalized polygamma function (acb_polygamma)
- implemented the reflection formula for the logarithmic gamma function (acb_lgamma, acb_poly_lgamma_series)
- implemented the digamma function of power series (arb_poly_digamma_series, acb_poly_digamma_series)
- improved acb_poly_zeta_series to produce exact zero imaginary parts in most cases when the result should be real-valued
- made the real logarithmic gamma function (arb_lgamma, arb_poly_lgamma_series) abort more quickly for negative input
- elementary functions
- added arb_exp_expinv and acb_exp_expinv functions for simultaneously computing exp(x), exp(-x)
- improved acb_tan, acb_tan_pi, acb_cot and acb_cot_pi for input with large imaginary parts
- added complex hyperbolic functions (acb_sinh, acb_cosh, acb_sinh_cosh, acb_tanh, acb_coth)
- added acb_log_sin_pi for computing the logarithmic sine function without branch cuts away from the real line
- added arb_poly_cot_pi_series, acb_poly_cot_pi_series
- added arf_root and improved speed of arb_root
- tuned algorithm selection in arb_pow_fmpq
- other
- added documentation for arb and acb vector functions
- 2015-04-19 - version 2.6.0
- special functions
- added the Bessel K function
- added the confluent hypergeometric functions M and U
- added exponential, trigonometric and logarithmic integrals ei, si, shi, ci, chi, li
- added the complete elliptic integral of the second kind E
- added support for computing hypergeometric functions with power series as parameters
- fixed special cases in Bessel J function returning useless output
- fix precision of zeta function accidentally being capped at 7000 digits (bug in 2.5)
- special-cased real input in the gamma functions for complex types
- fixed exp of huge numbers outputting unnecessarily useless intervals
- fixed broken code in erf that sometimes gave useless output
- made selection of number of terms in hypergeometric series more robust
- polynomials and power series
- added sin_pi, cos_pi and sin_cos_pi for real and complex power series
- speeded up series reciprocal and division for length = 2
- added add_si methods for polynomials
- made inv_series and div_series with zero input produce indeterminates instead of aborting
- added arb_poly_majorant, acb_poly_majorant
- basic functions
- added comparison methods arb_eq, arb_ne, arb_lt, arb_le, arb_gt, arb_ge, acb_eq, acb_ne
- added acb_rel_accuracy_bits and improved the real version
- fixed precision of constants like pi behaving more nondeterministically than necessary
- fixed arf_get_mag_lower(nan) to output 0 instead of inf
- other
- removed call to fmpq_dedekind_sum which only exists in the git version of flint
- fixed a test code bug that could cause crashes on some systems
- added fix for static build on OS X (thanks Marcello Seri)
- miscellaneous corrections to the documentation
- 2015-01-28 - version 2.5.0
- string conversion
- added arb_set_str
- added arb_get_str and arb_printn for pretty-printed rigorous decimal output
- added helper functions for binary to decimal conversion
- core arithmetic
- improved speed of division when using GMP instead of MPIR
- improved complex division with a small denominator
- removed a little bit of overhead for complex squaring
- special functions
- faster code for atan at very high precision, used instead of mpfr_atan
- optimized elementary functions slightly for small input
- added modified error functions erfc and erfi
- added the generalized exponential integral
- added the upper incomplete gamma function
- implemented the complete elliptic integral of the first kind
- implemented the arithmetic-geometric mean of complex numbers
- optimized arb_digamma for small integers
- made mag_log_ui, mag_binpow_uiui and mag_polylog_tail proper functions
- added pow, agm, erf, elliptic_k, elliptic_p as functions of complex power series
- added incomplete gamma function of complex power series
- improved code for bounding complex rising factorials (the old code could
potentially have given wrong results in degenerate cases)
- added arb_sqrt1pm1, arb_atanh, arb_asinh, arb_atanh
- added arb_log1p, acb_log1p, acb_atan
- added arb_hurwitz_zeta
- improved parameter selection in the Hurwitz zeta function to try to
avoid stalling when given enormous input
- optimized sqrt and rsqrt of power series when given a binomial as input
- made arb_bernoulli_ui(2^64-2) not crash
- fixed rgamma of negative integers returning indeterminate
- polynomials and matrices
- added characteristic polynomial computation for real and complex matrices
- added polynomial set_round methods
- added is_real methods for more types
- added more get_unique_fmpz methods
- added code for generating Swinnerton-Dyer polynomials
- improved error bounding in det() and exp() of complex matrices to
recognize when the result is real-valued
- changed polynomial divrem to return success/fail instead of aborting on divide by zero
- miscellaneous
- added logo to documentation
- made inlined functions build as part of the library
- silenced a clang warning
- made _acb_vec_sort_pretty a library function
- 2014-11-15 - version 2.4.0
- arithmetic and core functions
- made evaluation of sin, cos and exp at medium precision faster using the sqrt trick
- optimized arb_sinh and arb_sinh_cosh
- optimized complex division with a small denominator
- optimized cubing of complex numbers
- added floor and ceil functions for the arf and arb types
- added acb_poly powering functions
- added acb_exp_pi_i
- added functions for evaluation of Chebyshev polynomials
- fixed arb_div to output nan for input containing nan
- added a module acb_hypgeom for hypergeometric functions
- evaluation of the generalized hypergeometric function in convergent cases
- evaluation of confluent hypergeometric functions using asymptotic expansions
- the Bessel function of the first kind for complex input
- the error function for complex input
- added a module acb_modular for modular forms and elliptic functions
- support for working with modular transformations
- mapping a point to the fundamental domain
- evaluation of Jacobi theta functions and their series expansions
- the Dedekind eta function
- the j-invariant and the modular lambda and delta function
- Eisenstein series
- the Weierstrass elliptic function and its series expansion
- miscellaneous
- fixed mag_print printing a too large exponent
- fixed printd methods to use a fallback instead of aborting when printing numbers too large for MPFR
- added version number string (arb_version)
- various additions to the documentation
- 2014-09-25 - version 2.3.0
- removed most of the legacy (Arb 1.x) modules
- updated build scripts, hopefully fixing various issues
- new implementations of arb_sin, arb_cos, arb_sin_cos, arb_atan, arb_log, arb_exp, arb_expm1, much faster up to a few thousand bits
- ported the bit-burst code for high-precision exponentials to the arb type
- speeded up arb_log_ui_from_prev
- added mag_exp, mag_expm1, mag_exp_tail, mag_pow_fmpz
- improved various mag functions
- added arb_get/set_interval_mpfr, arb_get_interval_arf, and improved arb_set_interval_arf
- improved arf_get_fmpz
- prettier printing of complex numbers with negative imaginary part
- changed some frequently-used functions from inline to non-inline to reduce code size
- 2014-08-01 - version 2.2.0
- added functions for computing polylogarithms and order expansions
of polylogarithms, with support for real and complex s, z
- added a missing cast affecting C++ compatibility
- generalized powsum functions to allow a geometric factor
- improved powsum functions slightly when the exponent is an integer
- faster arb_log_ui_from_prev
- added mag_sqrt and mag_rsqrt functions
- fixed various minor bugs and added missing tests and documentation entries
- 2014-06-20 - version 2.1.0
- ported most of the remaining functions to the new arb/acb types,
including:
- elementary functions (log, atan, etc.)
- hypergeometric series summation
- the gamma function
- the Riemann zeta function and related functions
- Bernoulli numbers
- the partition function
- the calculus modules (rigorous real root isolation, rigorous numerical integration of complex-valued functions)
- example programs
- added several missing utility functions to the arf and mag modules
- 2014-05-27 - version 2.0.0
- new modules mag, arf, arb, arb_poly, arb_mat, acb, acb_poly,
acb_mat for higher-performance ball arithmetic
- poly_roots2 and hilbert_matrix2 example programs
- vector dot product and norm functions (contributed by Abhinav Baid)
- 2014-05-03 - version 1.1.0
- faster and more accurate error bounds for polynomial multiplication
(error bounds are now always as good as with classical multiplication,
and multiplying high-degree polynomials with approximately equal
coefficients now has proper quasilinear complexity)
- faster and much less memory-hungry exponentials at very high precision
- improved the partition function to support n bigger than a single word,
and enabled the possibility to use two threads for the computation
- fixed a bug in floating-point arithmetic that caused a too small bound
for the rounding error to be reported when the result of an inexact
operation was rounded up to a power of two (this bug did
not affect the correctness of ball arithmetic, because operations on
ball midpoints always round down)
- minor optimizations to floating-point arithmetic
- improved argument reduction of the digamma function and short series
expansions of the rising factorial
- removed the holonomic module for now, as it did not really do anything
very useful
- 2013-12-21 - version 1.0.0
- new example programs directory
- poly_roots example program
- real_roots example program
- pi_digits example program
- hilbert_matrix example program
- keiper_li example program
- new fmprb_calc module for calculus with real functions
- bisection-based root isolation
- asymptotically fast Newton root refinement
- new fmpcb_calc module for calculus with complex functions
- numerical integration using Taylor series
- scalar functions
- simplified fmprb_const_euler using published error bound
- added fmprb_inv
- fmprb_trim, fmpcb_trim
- added fmpcb_rsqrt (complex reciprocal square root)
- fixed bug in fmprb_sqrtpos with nonfinite input
- slightly improved fmprb powering code
- added various functions for bounding fmprs by powers of two
- added fmpr_is_int
- polynomials and power series
- implemented scaling to speed up blockwise multiplication
- slightly faster basecase power series exponentials
- improved sin/cos/tan/exp for short power series
- added complex sqrt_series, rsqrt_series
- implemented the Riemann-Siegel Z and theta functions for real power series
- added fmprb_poly_pow_series, fmprb_poly_pow_ui and related methods
- fmprb/fmpcb_poly_contains_fmpz_poly
- faster composition by monomials
- implemented Borel transform and binomial transform for real power series
- matrices
- implemented matrix exponentials
- multithreaded fmprb_mat_mul
- added matrix infinity norm functions
- added some more matrix-scalar functions
- added matrix contains and overlaps methods
- zeta function evaluation
- multithreaded power sum evaluation
- faster parameter selection when computing many derivatives
- implemented binary splitting to speed up computing many derivatives
- miscellaneous
- corrections for C++ compatibility (contributed by Jonathan Bober)
- several minor bugfixes and test code enhancements
- 2013-08-07 - version 0.7
- floating-point and ball functions
- documented, added test code, and fixed bugs for various operations involving a ball containing an infinity or NaN
- added reciprocal square root functions (fmpr_rsqrt, fmprb_rsqrt) based on mpfr_rec_sqrt
- faster high-precision division by not computing an explicit remainder
- slightly faster computation of pi by using new reciprocal square root and division code
- added an fmpr function for approximate division to speed up certain radius operations
- added fmpr_set_d for conversion from double
- allow use of doubles to optionally compute the partition function faster but without an error bound
- bypass mpfr overflow when computing the exponential function to extremely high precision (approximately 1 billion digits)
- made fmprb_exp faster for large numbers at extremely high precision by skipping the log(2) removal
- made fmpcb_lgamma faster at high precision by speeding up the argument reduction branch computation
- added fmprb_asin, fmprb_acos
- added various other utility functions to the fmprb module
- added a function for computing the Glaisher constant
- optimized evaluation of the Riemann zeta function at high precision
- polynomials and power series
- made squaring of polynomials faster than generic multiplication
- implemented power series reversion (various algorithms) for the fmprb_poly type
- added many fmprb_poly utility functions (shifting, truncating, setting/getting coefficients, etc.)
- improved power series division when either operand is short
- improved power series logarithm when the input is short
- improved power series exponential to use the basecase algorithm for short input regardless of the output size
- added power series square root and reciprocal square root
- added atan, tan, sin, cos, sin_cos, asin, acos fmprb_poly power series functions
- added Newton iteration macros to simplify various functions
- added gamma functions of real and complex power series ([fmprb/fmpcb]_poly_[gamma/rgamma/lgamma]_series)
- added wrappers for computing the Hurwitz zeta function of a power series ([fmprb/fmpcb]_poly_zeta_series)
- implemented sieving and other optimizations to improve performance for evaluating the zeta function of a short power series
- improved power series composition when the inner series is linear
- added many fmpcb_poly versions of nearly all fmprb_poly functions
- improved speed and stability of series composition/reversion by balancing the power table exponents
- other
- added support for freeing all cached data by calling flint_cleanup()
- introduced fmprb_ptr, fmprb_srcptr, fmpcb_ptr, fmpcb_srcptr typedefs for cleaner function signatures
- various bug fixes and general cleanup
- 2013-05-31 - version 0.6
- made fast polynomial multiplication over the reals numerically stable by using a blockwise algorithm
- disabled default use of the Gauss formula for multiplication of complex polynomials, to improve numerical stability
- added division and remainder for complex polynomials
- added fast multipoint evaluation and interpolation for complex polynomials
- added missing fmprb_poly_sub and fmpcb_poly_sub functions
- faster exponentials (fmprb_exp and dependent functions) at low precision, using precomputation
- rewrote fmpr_add and fmpr_sub using mpn level code, improving efficiency at low precision
- ported the partition function implementation from flint (using ball arithmetic
in all steps of the calculation to guarantee correctness)
- ported algorithm for computing the cosine minimal polynomial from flint (using
ball arithmetic to guarantee correctness)
- support using gmp instead of mpir
- only use thread-local storage when enabled in flint
- slightly faster error bounding for the zeta function
- added some other helper functions
- 2013-03-28 - version 0.5
- arithmetic and elementary functions
- added fmpr_get_fmpz, fmpr_get_si
- fixed accuracy problem with fmprb_div_2expm1
- special-cased squaring of complex numbers
- added various fmpcb convenience functions (addmul_ui, etc)
- optimized fmpr_cmp_2exp_si and fmpr_cmpabs_2exp_si, and added test code for comparison functions
- added fmprb_atan2, also fixing a bug in fmpcb_arg
- added fmprb_sin_pi, cos_pi, sin_cos_pi etc.
- added fmprb_sin_pi_fmpq (etc.) using algebraic methods for fast evaluation of roots of unity
- faster fmprb_poly_evaluate and evaluate_fmpcb using rectangular splitting
- added fmprb_poly_evaluate2, evaluate2_fmpcb for simultaneously evaluating the derivative
- added fmprb_poly root polishing code using near-optimal Newton steps (experimental)
- added fmpr_root, fmprb_root (currently based on MPFR)
- added fmpr_min, fmpr_max
- added fmprb_set_interval_fmpr, fmprb_union
- added fmpr_bits, fmprb_bits, fmpcb_bits for obtaining the mantissa width
- added fmprb_hypot
- added complex square roots
- improved fmprb_log to slightly improve speed, and properly support huge arguments
- fixed exp, cosh, sinh to work with huge arguments
- added fmprb_expm1
- fixed sin, cos, atan to work with huge arguments
- improved fmprb_pow and fmpcb_pow, including automatic detection of small integer and half-integer exponents
- added many more elementary functions: fmprb_tan/cot/tanh/coth, fmpcb_tan/cot, and pi versions
- added fmprb const_e, const_log2, const_log10, const_catalan
- fixed ball containment/overlap checking to work operate efficiently and correctly with huge exponents
- strengthened test code for many core operations
- special functions
- reorganized zeta function related code
- faster evaluation of the Riemann zeta function via sieving
- documented and improved efficiency of the zeta constant binary splitting code
- calculate error bound in Borwein’s algorithm with fmprs instead of using doubles
- optimized divisions in zeta evaluation via the Euler product
- use functional equation for Riemann zeta function of a negative argument
- compute single Bernoulli numbers using ball arithmetic instead of relying on the floating-point code in flint
- initial code for evaluating the gamma function using its Taylor series
- much faster rising factorials at high precision, using difference polynomials
- much faster gamma function at high precision
- added complex gamma function, log gamma function, and other versions
- added fmprb_agm (real arithmetic-geometric mean)
- added fmprb_gamma_fmpq, supporting rapid computation of gamma(p/q) for q = 1,2,3,4,6
- added real and complex digamma function
- fixed unnecessary recomputation of Bernoulli numbers
- optimized computation of Euler’s constant, and added proper error bounds
- avoid reliance on doubles in the hypergeometric series tail bound
- cleaned up factorials and binomials, computing factorials via gamma
- other
- added an fmpz_extras module to collect various internal fmpz helper functions
- fixed detection of flint header files
- fixed various other small bugs
- 2013-01-26 - version 0.4
- much faster fmpr_mul, fmprb_mul and set_round, resulting in general speed improvements
- code for computing the complex Hurwitz zeta function with derivatives
- fixed and documented error bounds for hypergeometric series
- better algorithm for series evaluation of the gamma function at a rational point
- much faster generation of Bernoulli numbers
- complex log, exp, pow, trigonometric functions (currently based on MPFR)
- complex nth roots via Newton iteration
- added code for arithmetic on fmpcb_polys
- code for computing Khinchin’s constant
- code for rising factorials of polynomials or power series
- faster sin_cos
- better div_2expm1
- many other new helper functions
- improved thread safety
- more test code for core operations
- 2012-11-07 - version 0.3
- converted documentation to sphinx
- new module fmpcb for ball interval arithmetic over the complex numbers
- conversions, utility functions and arithmetic operations
- new module fmpcb_mat for matrices over the complex numbers
- conversions, utility functions and arithmetic operations
- multiplication, LU decomposition, solving, inverse and determinant
- new module fmpcb_poly for polynomials over the complex numbers
- root isolation for complex polynomials
- new module fmpz_holonomic for functions/sequences
defined by linear differential/difference equations
with polynomial coefficients
- functions for creating various special sequences and functions
- some closure properties for sequences
- Taylor series expansion for differential equations
- computing the nth entry of a sequence using binary splitting
- computing the nth entry mod p using fast multipoint evaluation
- generic binary splitting code with automatic error bounding is now
used for evaluating hypergeometric series
- matrix powering
- various other helper functions
- 2012-09-29 - version 0.2
- code for computing the gamma function (Karatsuba, Stirling’s series)
- rising factorials
- fast exp_series using Newton iteration
- improved multiplication of small polynomials by using classical multiplication
- implemented error propagation for square roots
- polynomial division (Newton-based)
- polynomial evaluation (Horner) and composition (divide-and-conquer)
- product trees, fast multipoint evaluation and interpolation (various algorithms)
- power series composition (Horner, Brent-Kung)
- added the fmprb_mat module for matrices of balls of real numbers
- matrix multiplication
- interval-aware LU decomposition, solving, inverse and determinant
- many helper functions and small bugfixes
- 2012-09-14 - version 0.1
- 2012-08-05 - began simplified rewrite
- 2012-04-05 - experimental ball and polynomial code