Revision history for Math-AnyNum 0.41 2025-06-22 - Stricter validation of rational inputs provided to the `new` method. 0.40 2022-12-01 - Fixed the numification of integers on 32-bit systems with 64-bit Perl. 0.39 2022-06-11 [ADDITIONS] - Added the `addmod(a,b,m)`, `submod(a,b,m)` and `mulmod(a,b,m)` methods. - Added the `chebyshevTmod(n,x,m)` and `chebyshevUmod(n,x,m)` methods. - Added the `quadratic_powmod(a,b,w,n,m)` method. - Added the `idiv_ceil(a,b)`, `idiv_trunc(a,b)`, `idiv_round(a,b)` methods. - Added the `is_power_of(n,b)` method, which returns true if n is a power of b. [CHANGES] - Changed `idiv(a,b)` to do floor-division instead of truncated-division. - Return zero when k > n in subfactorial(n, k). [IMPROVEMENTS] - Extended `divmod()` to support an additional argument. - Optimization in `digits(n,b)` and `sumdigits(n,b)` for large n and b. - Faster computation of `chebyshevT(n,x)` and `chebyshevU(n,x)` for large n. - Less memory usage in `sumdigits(n,b=10)` for very large n. 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.