Revision history for Math-AnyNum

0.38    2021-02-21

        - Changed the result of `RATIONAL % INTEGER` to match the output of `ratmod`.

0.37    2021-01-19

        - Added the `faulhaber_polynomial(n,x)` function (also aliased as `faulhaber`).
        - Fixed some memory leaks in some special cases, such as `index(o, s)`, where `o` is a Math::AnyNum object.

0.36    2020-11-22

        - Make a copy of Math::{GMPz,GMPq,MPC,MPFR} objects when passed to Math::AnyNum->new().

0.35    2020-09-13

        [ADDITIONS]

        - is_rough(n,k)         true if all prime factors p|n are p >= k
        - smooth_part(n,k)      the largest k-smooth divisor of n
        - rough_part(n,k)       the largest k-rough divisor of n
        - make_coprime(n,k)     make n coprime to k by removing factors from n
        - dirichlet_sum(n,...)  the Dirichlet hyperbola method
        - ratmod(r,m)           modular rational operation, returning an integer

        [IMPROVEMENTS]

        - Optimizations in `sum(...)` for integer arguments.
        - Optimizations in `faulhaber_sum(n,k)` for k = 2 and k >= n.
        - Extended `powmod(b, n, m)` to support rational bases `b`.
        - Internal code simplifications.

0.34    2020-01-23

        - Increased the default value of `r` in `is_prime` from 20 to 23.
        - Documented the Baillie-PSW test used by `is_prime` with GMP >= 6.2.0.
        - LCM of an empty list, now returns 1. (previously returned 0)

0.33    2019-08-18

        [ADDITIONS]

        - Added the `digits2num(\@digits, $base)` function.
        - Extended the method `length()` to accept an optional argument specifying the base.

        [IMPROVEMENTS]

        - Faster (subquadratic-time) algorithms in `digits(n,b)` and `sumdigits(n,b)` for bases b > 62.
        - Minor optimizations in the `ilog(n,k)`, `ilog2(n)` and `ilog10(n)` functions.

0.32    2019-06-07

        - Minor documentation improvements.
        - Minor optimizations in the computation of the Lucas sequences.
        - NaN is now returned for negative `n` in Lucas sequences.

0.31    2019-01-07

        [ADDITIONS]

        - Added the `min(@list)` and `max(@list)` functions.
        - Added the `base(n,b)` function, which returns a string-representation of `n` in base `b`.

        [IMPROVEMENTS]

        - Minor optimization in `kronecker(n,k)` when `n` is a native integer or when both `n` and `k` are native integers.

        [FIXES]

        - Fixed `fibmod(0, m)` and `lucasmod(0, m)`.
        - Fixed `is_prime(n)` for negative `n` to always return 0.

0.30    2018-12-13

        - Fixed an `:overload` issue for integers in the range [2^32, 2^64] on 32-bit systems with 64-bit Perl.

0.29    2018-11-11

        [ADDITIONS]

        - is_smooth_over_prod(n,k)      return 1 if n is smooth over the primes p|k

        [IMPROVEMENTS]

        - Much faster algorithm in `is_smooth(n, k)`.
        - Cached the values of the `bernoulli(n)` function for `n <= 500`.
        - Also cached the Bernoulli numbers that are internally used in `bernoulli_polynomial(n, x)` and `faulhaber_sum(n, k)`.

0.28    2018-09-29

        [ADDITIONS]

        - lucasU(p, q, n)               Lucas U sequence
        - lucasV(p, q, n)               Lucas V sequence
        - lucasUmod(p, q, n, m)         Lucas U sequence mod m
        - lucasVmod(p, q, n, m)         Lucas V sequence mod m
        - bit_scan0(n, k)               index of the first 0-bit of n with index >= k
        - bit_scan1(n, k)               index of the first 1-bit of n with index >= k
        - hamdist(n, k)                 Hamming distance (number of bit-positions where the bits differ)
        - gcdext(n, k)                  return (u,v,d) where `u*n + v*k = d`
        - is_congruent(n, k, m)`        true if `n` is congruent to `k` mod `m`

        [IMPROVEMENTS]

        - More efficient algorithms in `fibmod(n, m)` and `lucasmod(n, m)`.
        - Optimized the `div(Scalar, AnyNum)` case. It no longer converts the Scalar to a temporary object.
        - Extended the `catalan()` function to accept an optional argument, computing the entries of Catalan's triangle `C(n,k)`.

0.27    2018-07-04

        [ADDITIONS]

        - Added the `laguerreL(n,x)` function for computing the Laguerre polynomials: `L_n(x)`.
        - Added the `legendreP(n,x)` function for computing the Legendre polynomials: `P_n(x)`.
        - Added the `chebyshevT(n,x)` and `chebyshevU(n,x)` functions for computing the Chebyshev polynomials of 1st and 2nd kind.
        - Added the `hermiteH(n,x)` and `hermiteHe(n,x)` functions for computing the physicists' and probabilists' Hermite polynomials: `H_n(x)` and `He_n(x)`.
        - Added the `secant_number(n)` and `tangent_number(n)` functions for computing the secant/zig numbers (A000364) and the tangent/zag numbers (A000182).
        - Added the `fibmod(n,m)` and `lucasmod(n,m)` functions for efficiently computing the n-th Fibonacci and n-th Lucas number modulo m.

        [IMPROVEMENTS]

        - Optimized the case `sub(Scalar, AnyNum)` by using the `*_ui_sub()` functions from Math::{GMPz,MPFR,MPC}.
        - Use `mpz_powm_ui()` in `powmod(n, k, m)` when `k` fits inside an unsigned native integer, as it is considerably faster than `mpz_powm()` for small `k`.

0.26    2018-05-30

        [CHANGES]

        - Boolification of `NaN` is now false (before `NaN` evaluated to a true value in boolean context, which was not very convenient).

        [BUG-FIXES]

        - Fixed `superfactorial(n)` and `hyperfactorial(n)` for n={0, 1}.

0.25    2018-05-25

        [ADDITIONS]

        - sum(a,b,c,...)              sum of a list of numbers.
        - prod(a,b,c,...)             product of a list of numbers (using binary splitting).
        - as_rat(n,b)                 rational string-representation of n in base b
        - bell(n)                     n-th Bell number (OEIS: A000110)
        - catalan(n)                  n-th Catalan number (OEIS: A000108)
        - euler(n)                    n-th Euler number (OEIS: A122045).
        - euler_polynomial(n, x)      Euler polynomial (also available as `euler(n, x)`)
        - bernoulli_polynomial(n, x)  Bernoulli polynomial (also available as `bernoulli(n, x)`).
        - geometric_sum(n,r)          geometric sum: r^0 + r^1 + ... + r^n
        - superfactorial(n)           product of first n factorials
        - lnsuperfactorial(n)         natural logarithm of superfactorial(n)
        - hyperfactorial(n)           product of k^k for k=1..n
        - lnhyperfactorial(n)         natural logarithm of hyperfactorial(n)
        - bsearch(n,\&f)              binary search from 0 to n (exact match)
        - bsearch(a,b,\&f)            binary search from a to b (exact match)
        - bsearch_le(n,\&f)           binary search from 0 to n (less than or equal to)
        - bsearch_le(a,b,\&f)         binary search from a to b (less than or equal to)
        - bsearch_ge(n,\&f)           binary search from 0 to n (greater than or equal to)
        - bsearch_ge(a,b,\&f)         binary search from a to b (greater than or equal to)

        [IMPROVEMENTS]

        - Extended the `gcd()` and `lcm()` functions to accept an arbitrary number of arguments.
        - Extended the optimizations in `digits(n, b)` and `sumdigits(n, b)` for all values of b <= 62.
        - Extended the allowed value of `b` in `base(n, b)`, `as_int(n, b)`, `as_frac(n, b)` and `new(n, b`) to be between 2 and 62.
        - Extended the `float(x)` function to convert `x` to any floating-point number, either real or complex (in this order).
        - Documentation improvements: added a brief description for each function at the top of the POD file.

        [INCOMPATIBLE CHANGES]

        - Renamed the Euler-Mascheroni constant from `euler` to `EulerGamma`.
        - Renamed the Catalan constant from `catalan` to `CatalanG`.

        [OTHER]

        - Increased the minimum required version of Perl from 5.14 to 5.16 (for `__SUB__`).
        - Merged all the `AnyNum/*.pm` files into the main `AnyNum.pm` file.

0.24    2018-05-06

        [ADDITIONS]

        - Added the `sumdigits(n, b)` function, to sum the digits of `n` in base `b`.
        - Added the `approx_cmp(x, y, [k])` function, to compare two numbers by first rounding them to k-th decimal places.
        - Extended the `fibonacci()` function to accept an optional argument specifying the order of the Fibonacci numbers (2 = Fibonacci, 3 = Tribonacci, 4 = Tetranacci, ...).

        [IMPROVEMENTS]

        - Minor optimization in `ipow(n,k)` when `k` is an object and `n` is a native unsigned integer.

0.23    2018-04-09

        [ADDITIONS]

        - getbit(n, k), setbit(n, k), flipbit(n, k) and clearbit(n, k).

        [OTHER]

        - Stricter validation for native integers.

0.22    2018-02-17

        [ADDITIONS]

            - is_smooth(n, k)           :: returns a true value when all the prime factors of `n` are <= `k`
            - polymod(n, a, b, c, ...)  :: computes the polymod of `n` against a list of numbers.
            - subfactorial(n,k)         :: computes the number of derangements of a set with `n` elements with `k` fixed points.
            - multinomial(a, b, c, ...) :: computes the multinomial coefficient.

        [IMPROVEMENTS]

            - Minor performance improvement in the `mod(n,k)` method when `k` fits into a native unsigned integer.

        [OTHER]

            - Using the integer limits from Math::GMPq instead of POSIX. This makes POSIX no longer needed.

0.21    2018-01-25

        - Extended the `complex()` function to accept an additional argument, which specifies the imaginary part.
        - Reimplemented the `rat_approx()` method for much better performance (~3x faster).
        - More efficient conversion of Math::GComplex objects with Math::AnyNum components.

0.20    2018-01-05

        - Added parsing support for complex numbers in Cartesian form, such as "(3 4)" for "3+4i".
        - Fixed the result of the `atan2(x, y)` function, when `x` and `y` are complex numbers.

0.19    2017-12-09

        - Fixed some tests under mpfr-4.0.0.
        - `mpfr_root()` is deprecated since mpfr-4.0.0 and is no longer used under mpfr >= 4.0.0.
        - Using `mpfr_z_sub()` when mpfr >= 3.1.0 is available.
        - Using `mpfr_beta()` when mpfr >= 4.0.0 is available.

0.18    2017-11-22

        - Extended the `digits()` method to support arbitrary large bases.

            + Additionally, it returns the digits in reverse order, matching the output of the `.digits()` method from Ruby.

        - Fixed a minor issue in `rat(str)` to return NaN when `str` cannot be parsed as a fraction.
        - Fixed `polygonal_root(n, NaN)` to return `NaN` instead of `n`.
        - Minor optimizations for `x <=> 0`, `x == 0` and `x != 0`, when `0` is a native integer.

0.17    2017-11-04

        - Optimized `is_div(n, k)` when `n` and `k` are integers.
        - Optimized `kronecker(n, k)` when `k` is a native integer.
        - Improvements in `__bernfrac__(n)`, using a more optimized sieve for prime numbers.
        - Minor simplifications inside `faulhaber_sum(n)`.

0.16    2017-10-17

        - Fixed the numification of signed and unsigned integers close to the native integer limits.

0.15    2017-10-08

        - Bug-fix in `gcd(x, -y)` and `lcm(x, -y)`, when `y` is a native integer.
        - Minor internal optimizations.

0.14    2017-09-26

        [BUG-FIXES]

        - Fixed the sign in the results returned by the second-polygonal functions `polygonal_root2(n,k)` and `ipolygonal_root2(n,k)`.

0.13    2017-09-26

        [ADDITIONS]

        - acmp(x, y): absolute comparison of `x` and `y`.
        - polygonal(n, k): returns the nth k-gonal number.
        - polygonal_root(n, k): returns the k-gonal root of `n`.
        - polygonal_root2(n, k): returns the second k-gonal root of `n`.
        - ipolygonal_root(n, k): returns the integer k-gonal root of `n`.
        - ipolygonal_root2(n, k): returns the second integer k-gonal root of `n`.
        - is_polygonal(n, k): returns 1 when `n` is a k-gonal number.
        - is_polygonal2(n, k): returns 1 when `n` is a second k-gonal number.
        - faulhaber_sum(n, p): computes 1^p + 2^p + 3^p + ... + n^p, using Faulhaber's formula.

0.12    2017-09-18

        [ADDITIONS]

        - Added the `rat_approx(n)` function, which returns the smallest rational approximation for a given real number `n`.

        [IMPROVEMENTS]

        - The newly added functions in Math::MPFR-3.36, Rmpfr_q_div() and Rmpfr_z_div(), are now used by Math::AnyNum.

        [PERFORMANCE OPTIMIZATIONS]

        - Re-implemented all the methods without Class::Multimethods, which makes Math::AnyNum ~35% faster.
        - Many internal simplifications and optimizations.

0.11    2017-07-11

        [IMPROVEMENTS]

        - Extended the `rising_factorial(n, k)` and `falling_factorial(n, k)` for negative values of `k`.

        [PERFORMANCE IMPROVEMENTS]

        - Optimized `eta(n)` and `zeta(n)` for values of `n` that fit inside a native unsigned integer.

        [OTHER]

        - Fixed the number of skipped tests under old versions of GMP in t/integer_functions.t.

0.10    2017-07-09

        [ADDITIONS]

        - Added the `exp2(x)` and `exp10(x)` functions.
        - Added the `ipow2(x)` and `ipow10(x)` functions.
        - Added the `falling_factorial(n, k)` and `rising_factorial(n, k)` functions.

        [PERFORMANCE IMPROVEMENTS]

        - Faster stringification of floating-point numbers (including complex numbers).
        - Optimization in `mfactorial(n, m)` for native integers.
        - Optimization in `binomial(n, k)` for values of `n` that fit inside a native unsigned integer.

        [FIXES]

        - Fixed `eta(NaN)` to return `NaN` instead of `log(2)`.
        - Fixed `atanh(NaN)` to return `NaN` instead of `NaN+NaNi`.
        - Fixed the return value of `lgrt(+i)` and `lgrt(-i)`.

0.09    2017-05-30

        [ADDITIONS]

        - Added the `is_coprime(n, k)` function.

        [IMPROVEMENTS]

        - Minor simplification for `eta(1)`.
        - Minor optimization in `rand()` without arguments (when exported).
        - Extended the `rat(str)` function to parse a given decimal expansion as an exact fraction.
        - Re-implemented the `ilog(x, y)` function for better performance and to correctly handle arbitrary large integers.

        [PERFORMANCE IMPROVEMENTS]

        - ~4x faster algorithm in `bernfrac(n)`, due to Kevin J. McGown.

0.08    2017-05-08

        [PERFORMANCE IMPROVEMENTS]

        - Many internal simplifications and optimizations, which makes `Math::AnyNum` up to 30% faster.

        [FIXES]

        - Fixes a rounding error in ilog(n,b) when n is very large or when n is not a power of b.

0.07    2017-04-28

        [IMPROVEMENTS]

        - Minor optimization in `numify()` for integers and rationals.
        - Added checks for exact divisibility of two integers.
        - Optimized the gcd() and lcm() functions when the second argument is a native integer.
        - Documentation improvements.

        [FIXES]

        - Fixed the creation of very large constant integers in `:overload` mode.
        - Fixed the creation of binary, octal and hexadecimal constants that contain underscores (in `:overload` mode).

0.06    2017-04-18

        [ADDITIONS]

        - Added the `nude(x)` function.
        - Added the `conj(x)` function.
        - Added the `norm(x)` function.
        - Added the `reals(x)` function.
        - Added the `as_dec(x,y)` function.

        [IMPROVEMENTS]

        - Extended the `agm()` function to support complex numbers.
        - Extended the `as_frac()` function to accept an optional base.
        - Functions `inv(x)` and `neg(x)` are exportable.
        - Math::AnyNum->new() is considerably faster.
        - Many internal simplifications and optimizations.

        [FIXES]

        - Fixed a typo in `is_inf()` and `is_ninf()`.

0.05    2017-04-09

        [FIXES]

        - Fixed the (in)equality checks when one of the operands is NaN.
        - Comparing anything to NaN, now returns `undef` instead of `0`.

        [IMPROVEMENTS]

        - Refactored the method `is_power` to handle scalar arguments more efficiently.
        - Optimized the `root` and `iroot` method when the second argument is a scalar.

0.04    2017-04-08

        [FIXES]

        - Fixed some tests under GMP < 5.1.0 (thanks to Slaven Rezić; https://github.com/trizen/Math-AnyNum/issues/1).
        - Workaround in log10() with MPC < 1.0 (thanks to Slaven Rezić; https://github.com/trizen/Math-AnyNum/issues/1).

0.03    2017-04-08

        [IMPROVEMENTS]

        - Minor optimization in overloaded '-' and '/'.

        [FIXES]

        - Workaround for Math::GMPq::Rmpq_cmp_z() with a version of GMP older than 6.1.0. (https://rt.cpan.org/Public/Bug/Display.html?id=120910)
        - Minor-fix in the stringification of Math::MPFR objects with exponents and trailing zeros.

0.02    2017-04-03

        Require perl>=5.014.

0.01    2017-04-03

        First release.
