History and changes

For more details, view the commit log in the git repository https://github.com/fredrik-johansson/arb

Old releases of the code can be accessed from https://github.com/fredrik-johansson/arb/releases

2017-02-27 - version 2.10.0

  • General
    • Changed a large number of methods from inline functions to normal functions, substantially reducing the size of the built library.
    • Fixed a few minor memory leaks (missing clear() calls).
  • Basic arithmetic
    • Added arb_is_int_2exp_si and acb_is_int_2exp_si.
    • Added arf_sosq for computing x^2+y^2 of floating-point numbers.
    • Improved error bounds for complex square roots in the left half plane.
    • Improved error bounds for complex reciprocal (acb_inv) and division.
    • Added the internal helper mag_get_d_log2_approx as a public method.
  • Elliptic functions and integrals
    • New module acb_elliptic.h for elliptic functions and integrals.
    • Added complete elliptic integral of the third kind.
    • Added Legendre incomplete elliptic integrals (first, second, third kinds).
    • Added Carlson symmetric incomplete elliptic integrals (RF, RC, RG, RJ, RD).
    • Added Weierstrass elliptic zeta and sigma functions.
    • Added inverse Weierstrass elliptic p-function.
    • Added utility functions for computing the Weierstrass invariants and lattice roots.
    • Improved computation of derivatives of Jacobi theta functions by using modular transformations, and added a main evaluation function (acb_modular_theta_jet).
    • Improved detection of pure real or pure imaginary parts in various cases of evaluating theta and modular functions.
  • Other special functions
    • New, far more efficient implementation of the dilogarithm function (acb_polylog with s = 2).
    • Fixed an issue in the Hurwitz zeta function leading to unreasonable slowdown for certain complex input.
    • Added add acb_poly_exp_pi_i_series.
    • Added arb_poly_log1p_series, acb_poly_log1p_series.

2016-12-02 - version 2.9.0

  • License
    • Changed license from GPL to LGPL.
  • Build system and compatibility
    • Fixed FLINT includes to use flint/foo.h instead of foo.h, simplifying compilation on many systems.
    • Added another alias for the dynamic library to fix make check on certain systems (contributed by Andreas Enge).
    • Travis CI support (contributed by Isuru Fernando).
    • Added support for ARB_TEST_MULTIPLIER environment variable to control the number of test iterations.
    • Support building with CMake (contributed by Isuru Fernando).
    • Support building with MSVC on Windows (contributed by Isuru Fernando).
    • Fixed unsafe use of FLINT_ABS for slong -> ulong conversion in arf.h, which caused failures on MIPS and ARM systems.
  • Basic arithmetic and methods
    • Fixed mag_addmul(x,x,x) with x having a mantissa of all ones. This could produce a non-normalized mag_t value, potentially leading to incorrect results in arb and acb level arithmetic. This bug was caught by new test code, and fortunately would have been hard to trigger accidentally.
    • Added fasth paths for error bound calculations in arb_sqrt and arb_div, speeding up these operations significantly at low precision
    • Added support for round-to-nearest in all arf methods.
    • Added fprint methods (contributed by Alex Griffing).
    • Added acb_printn and acb_fprintn methods to match arb_printn.
    • Added arb_equal_si and acb_equal_si.
    • Added arb_can_round_mpfr.
    • Added arb_get_ubound_arf, arb_get_lbound_arf (contributed by Tommy Hofmann).
    • Added sign function (arb_sgn).
    • Added complex sign functions (acb_sgn, acb_csgn).
    • Rewrote arb_contains_fmpq to make the test exact.
    • Optimized mag_get_fmpq.
    • Optimized arf_get_fmpz and added more robust test code.
    • Rewrote arb_get_unique_fmpz and arb_get_interval_fmpz_2exp, reducing overhead, making them more robust with huge exponents, and documenting their behavior more carefully.
    • Optimized arb_union.
    • Optimized arf_is_int, arf_is_int_2exp_si and changed these from inline to normal functions.
    • Added mag_const_pi, mag_sub, mag_expinv.
    • Optimized binary-to-decimal conversion for huge exponents by using exponential function instead of binary powering.
    • Added arb_intersection (contributed by Alex Griffing).
    • Added arb_min, arb_max (contributed by Alex Griffing).
    • Fixed a bug in arb_log and in test code on 64-bit Windows due to unsafe use of MPFR which only uses 32-bit exponents on Win64.
    • Improved some test functions to reduce the chance of reporting spurious failures.
    • Added squaring functions (arb_sqr, acb_sqr) (contributed by Ricky Farr).
    • Added arf_frexp.
    • Added arf_cmp_si, arf_cmp_ui, arf_cmp_d.
    • Added methods to count allocated bytes (arb_allocated_bytes, _arb_vec_allocated_bytes, etc.).
    • Added methods to predict memory usage for large vectors (_arb/_acb_vec_estimate_allocated_bytes).
    • Changed clear() methods from inline to normal functions, giving 8% faster compilation and 25% smaller libarb.so.
    • Added acb_unit_root and _acb_vec_unit_roots (contributed by Pascal Molin).
  • Polynomials
    • Added sinh and cosh functions of power series (arb/acb_poly_sinh/cosh_series and sinh_cosh_series).
    • Use basecase series inversion algorithm to improve speed and error bounds in arb/acb_poly_inv_series.
    • Added functions for fast polynomial Taylor shift (arb_poly_taylor_shift, acb_poly_taylor_shift and variants).
    • Fast handling of special cases in polynomial composition.
    • Added acb_poly scalar mul and div convenience methods (contributed by Alex Griffing).
    • Added set_trunc, set_trunc_round convenience methods.
    • Added add_series, sub_series methods for truncating addition.
    • Added polynomial is_zero, is_one, is_x, valuation convenience methods.
    • Added hack to arb_poly_mullow and acb_poly_mullow to avoid overhead when doing an in-place multiplication with length at most 2.
    • Added binomial and Borel transform methods for acb_poly.
  • Matrices
    • Added Cholesky decomposition plus solving and inverse for positive definite matrices (arb_mat_cho, arb_mat_spd_solve, arb_mat_spd_inv and related methods) (contributed by Alex Griffing).
    • Added LDL decomposition and inverse and solving based on LDL decomposition for real matrices (arb_mat_ldl, arb_mat_solve_ldl_precomp, arb_mat_inv_ldl_precomp) (contributed by Alex Griffing).
    • Improved the entrywise error bounds in matrix exponential computation to preserve sparsity and give exact entries where possible in many cases (contributed by Alex Griffing).
    • Added public functions for computing the truncated matrix exponential Taylor series (arb_mat_exp_taylor_sum, acb_mat_exp_taylor_sum).
    • Added functions related to sparsity structure (arb_mat_entrywise_is_zero, arb_mat_count_is_zero, etc.) (contributed by Alex Griffing).
    • Entrywise multiplication (arb_mat_mul_entrywise, acb_mat_mul_entrywise) (contributed by Alex Griffing).
    • Added is_empty and is_square convenience methods (contributed by Alex Griffing).
    • Added the bool_mat helper module for matrices over the boolean semiring (contributed by Alex Griffing).
    • Added Frobenius norm computation (contributed by Alex Griffing).
  • Miscellaneous special functions
    • Added evaluation of Bernoulli polynomials (arb_bernoulli_poly_ui, acb_bernoulli_poly_ui).
    • Added convenience function for evaluation of huge Bernoulli numbers (arb_bernoulli_fmpz).
    • Added Euler numbers (arb_euler_number_ui, arb_euler_number_fmpz).
    • Added fast approximate partition function (arb_partitions_fmpz/ui).
    • Optimized partition function for n < 1000 by using recurrence for the low 64 bits.
    • Improved the worst-case error bound in arb_atan.
    • Added arb_log_base_ui.
    • Added complex sinc function (acb_sinc).
    • Special handling of z = 1 when computing polylogarithms.
    • Fixed agm(-1,-1) to output 0 instead of indeterminate.
    • Made working precision in arb_gamma and acb_gamma more sensitive to the input accuracy.
  • Hypergeometric functions
    • Compute erf and erfc without cancellation problems for large or complex z.
    • Avoid re-computing the square root of pi in several places.
    • Added generalized hypergeometric function (acb_hypgeom_pfq).
    • Implement binary splitting and rectangular splitting for evaluation of hypergeometric series with a power series parameter, greatly speeding up Y_n, K_n and other functions at high precision, as well as speeding up high-order parameter derivatives.
    • Use binary splitting more aggressively in acb_hypgeom_pfq_sum to reduce error bound inflation.
    • Asymptotic expansions of hypergeometric functions: more accurate parameter selection, and better handling of terminating cases.
    • Tweaked algorithm selection and working precision in acb_hypgeom_m.
    • Avoid dividing by the denominator of the next term in acb_hypgeom_sum, which would lead to a division by zero when evaluating hypergeometric polynomials.
    • Fixed a bug in hypergeometric series evaluation resulting in near-integers not being skipped in some cases, leading to unnecessary loss of precision.
    • Added series expansions of Airy functions (acb_hypgeom_airy_series, acb_hypgeom_airy_jet).
    • Fixed a case where Airy functions accidentally chose the worst algorithm instead of the best one.
    • Added functions for computing erf, erfc, erfi of power series in the acb_hypgeom module.
    • Added series expansion of the logarithmic integral (acb_hypgeom_li_series).
    • Added Fresnel integrals (acb_hypgeom_fresnel, acb_hypgeom_fresnel_series).
    • Added the lower incomplete gamma function (acb_hypgeom_gamma_lower) (contributed by Alex Griffing).
    • Added series expansion of the lower incomplete gamma function (acb_hypgeom_gamma_lower_series) (contributed by Alex Griffing).
    • Added support for computing the regularized incomplete gamma functions.
    • Use slightly sharper error bound for analytic continuation of 2F1.
    • Added support for computing finite limits of 2F1 with inexact parameters differing by integers.
    • Added the incomplete beta function (acb_hypgeom_beta_lower, acb_hypgeom_beta_lower_series)
    • Improved acb_hypgeom_u to use a division-avoiding algorithm for small polynomial cases.
    • Added arb_hypgeom module, wrapping the complex hypergeometric functions for more convenient use with the arb_t type.
  • Dirichlet L-functions and Riemann zeta function
    • New module dirichlet for working algebraically with Dirichlet groups and characters (contributed by Pascal Molin).
    • New module acb_dirichlet for numerical evaluation of Dirichlet characters and L-functions (contributed by Pascal Molin).
    • Efficient representation and manipulation of Dirichlet characters using the Conrey representation (contributed by Pascal Molin).
    • New module dlog for word-size discrete logarithm evaluation, used to support algorithms on Dirichlet characters (contributed by Pascal Molin).
    • Methods for properties, evaluation, iteration, pairing, lift, lowering etc. of Dirichlet characters (contributed by Pascal Molin).
    • Added acb_dirichlet_roots methods for fast evaluation of many roots of unity (contributed by Pascal Molin).
    • Added acb_dirichlet_hurwitz_precomp methods for fast multi-evaluation of the Hurwitz zeta function for many parameter values.
    • Added methods for computing Gauss, Jacobi and theta sums over Dirichlet characters (contributed by Pascal Molin).
    • Added methods (acb_dirichlet_l, acb_dirichlet_l_jet, acb_dirichlet_l_series) for evaluation of Dirichlet L-functions and their derivatives.
    • Implemented multiple algorithms for evaluation of Dirichlet L-functions depending on the argument (Hurwitz zeta function decomposition, Euler product, functional equation).
    • Added methods (acb_dirichlet_hardy_z, acb_dirichlet_hardy_z_series, etc.) for computing the Hardy Z-function corresponding to a Dirichlet L-function.
    • Added fast bound for Hurwitz zeta function (mag_hurwitz_zeta_uiui).
    • Improved parameter selection in Hurwitz zeta function to target relative instead of absolute error for large positive s.
    • Improved parameter selection in Hurwitz zeta function to avoid computing unnecessary Bernoulli numbers for large imaginary s.
    • Added Dirichlet eta function (acb_dirichlet_eta).
    • Implemented the Riemann-Siegel formula for faster evaluation of the Riemann zeta function at large height.
    • Added smooth-index algorithm for the main sum when evaluating the Riemann zeta function, avoiding the high memory usage of the full sieving algorithm when the number of terms gets huge.
    • Improved tuning for using the Euler product when computing the Riemann zeta function.
  • Example programs
    • Added logistic map example program.
    • Added lvalue example program.
    • Improved poly_roots in several ways: identify roots that are exactly real, automatically perform squarefree factorization, use power hack, and allow specifying a product of polynomials as input on the command line.
  • Housekeeping
    • New section in the documentation giving an introduction to ball arithmetic and using the library.
    • Tidied, documented and added test code for the fmpz_extras module.
    • Added proper documentation and test code for many helper methods.
    • Removed the obsolete fmprb module entirely.
    • Documented more algorithms and formulas.
    • Clarified integer overflow issues and use of ARF_PREC_EXACT in the documentation.
    • Added .gitignore file.
    • Miscellaneous improvements to the documentation.

2015-12-31 - version 2.8.1

  • Fixed 32-bit test failure for the Laguerre function.
  • Made the Laguerre function indeterminate at negative integer orders, to be consistent with the test code.

2015-12-29 - version 2.8.0

  • Compatibility and build system
    • Windows64 support (contributed by Bill Hart).
    • Fixed a bug that broke basic arithmetic on targets where FLINT uses fallback code instead of assembly code, such as PPC64 (contributed by Jeroen Demeyer).
    • Fixed configure to use EXTRA_SHARED_FLAGS/LDFLAGS, and other build system fixes (contributed by Tommy Hofmann, Bill Hart).
    • Added soname versioning (contributed by Julien Puydt).
    • Fixed test code on MinGW (contributed by Hrvoje Abraham).
    • Miscellaneous fixes to simplify interfacing Arb from Julia.
  • Arithmetic and elementary functions
    • Fixed arf_get_d to handle underflow/overflow correctly and to support round-to-nearest.
    • Added more complex inverse hyperbolic functions (acb_asin, acb_acos, acb_asinh, acb_acosh, acb_atanh).
    • Added arb_contains_int and acb_contains_int for testing whether an interval contains any integer.
    • Added acb_quadratic_roots_fmpz.
    • Improved arb_sinh to use a more accurate formula for x < 0.
    • Added sinc function (arb_sinc) (contributed by Alex Griffing).
    • Fixed bug in arb_exp affecting convergence for huge input.
    • Faster implementation of arb_div_2expm1_ui.
    • Added mag_root, mag_geom_series.
    • Improved and added test code for arb_add_error functions.
    • Changed arb_pow and acb_pow to make pow(0,positive) = 0 instead of nan.
    • Improved acb_sqrt to return finite output for finite input straddling the branch cut.
    • Improved arb_set_interval_arf so that [inf,inf] = inf instead of an infinite interval.
    • Added computation of Bell numbers (arb_bell_fmpz).
    • Added arb_power_sum_vec for computing power sums using Bernoulli numbers.
    • Added computation of the Fujiwara root bound for acb_poly.
    • Added code to identify all the real roots of a real polynomial (acb_poly_validate_real_roots).
    • Added several convenient assignment functions, including arb_set_d, acb_set_d, acb_set_d_d, acb_set_fmpz_fmpz (contributed by Ricky Farr).
    • Added many accessor functions (_arb/acb_vec_entry_ptr, arb_get_mid/rad_arb, acb_real/imag_ptr, arb_mid/rad_ptr, acb_get_real/imag).
    • Added missing functions acb_add_si, acb_sub_si.
    • Renamed arb_root to arb_root_ui (keeping alias) and added acb_root_ui.
  • Special functions
    • Implemented the Gauss hypergeometric function 2F1 and its regularized version.
    • Fixed two bugs in acb_hypgeom_pfq_series_direct discovered while implementing 2F1. In rare cases, these could lead to incorrect values for functions depending on parameter derivatives of hypergeometric series.
      • The first bug involved incorrect handling of negative integer parameters. The bug only affected 2F1 and higher functions; it did not affect correctness of any previously implemented functions that relied on acb_hypgeom_pfq_series_direct (such as Bessel Y and K functions of integer order).
      • The second bug involved a too small bound being computed for the sum of a geometric series. The geometric series bound is nearly tight for 2F1, and the incorrect version caused immediate test failures for that function. Theoretically, this bug affected correctness of some previously-implemented functions that relied on acb_hypgeom_pfq_series_direct (such as Bessel Y and K functions of integer order), but since the geometric bound is not as tight in those cases, those functions were still reliable in practice (no failing test case has been found).
    • Implemented Airy functions and their derivatives (acb_hypgeom_airy).
    • Implemented the confluent hypergeometric function 0F1 (acb_hypgeom_0f1).
    • Implemented associated Legendre functions P and Q.
    • Implemented Chebyshev, Jacobi, Gegenbauer, Laguerre, Hermite functions.
    • Implemented spherical harmonics.
    • Added function for computing Bessel J and Y functions simultaneously.
    • Added rising factorials for non-integer n (arb_rising, acb_rising).
    • Made rising factorials use gamma function for large integer n.
    • Faster algorithm for theta constants and Dedekind eta function at very high precision.
    • Fixed erf to give finite values instead of +/-inf for big imaginary input.
    • Improved acb_zeta (and arb_zeta) to automatically use fast code for integer zeta values.
    • Added double factorial (arb_doublefac_ui).
    • Added code for generating Hilbert class polynomials (acb_modular_hilbert_class_poly).
  • Matrices
    • Added faster matrix squaring (arb/acb_mat_sqr) (contributed by Alex Griffing).
    • Added matrix trace (arb/acb_mat_trace) (contributed by Alex Griffing).
    • Added arb/acb_mat_set_round_fmpz_mat, acb_mat_set(_round)_arb_mat (contributed by Tommy Hofmann).
    • Added arb/acb_mat_transpose (contributed by Tommy Hofmann).
    • Added comparison methods arb/acb_mat_eq/ne (contributed by Tommy Hofmann).
  • Other
    • Added complex_plot example program.
    • Added Airy functions to real_roots example program.
    • Other minor patches were contributed by Alexander Kobel, Marc Mezzarobba, Julien Puydt.
    • Removed obsolete file config.h.

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.
    • Fixed 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.
    • Added 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.
    • Added 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 (first commit).