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Released February 1, 2011
* Python 3 is now supported
* Dropped Python 2.4 compatibility
* Fixed Python 2.5 compatibility in matrix slicing code
* Implemented Python 3.2-compatible hashing, making mpmath numbers
hash compatible with extremely large integers and with fractions
in Python versions >= 3.2 (contributed by Case Vanhorsen)
Special functions:
* Implemented the von Mangoldt function (mangoldt())
* Implemented the "secondary zeta function" (secondzeta()) (contributed
by Juan Arias de Reyna).
* Implemented zeta zero counting (nzeros()) and the Backlund S function
(backlunds()) (contributed by Juan Arias de Reyna)
* Implemented derivatives of order 1-4 for siegelz() and siegeltheta()
(contributed by Juan Arias de Reyna)
* Improved Euler-Maclaurin summation for zeta() to give more accurate
results in the right half-plane when the reflection formula
cannot be used
* Implemented the Lerch transcendent (lerchphi())
* Fixed polygamma function to return a complex NaN at complex
infinity or NaN, instead of raising an unrelated exception.
Released September 24, 2010
Backends and distribution:
* Added Sage hooks for Cython versions of exp, ln, cos, sin,
hypergeometric series, and some related functions
* Fixed imports for gmpy2 compatibility (contributed by Case Van Horsen)
* Removed documentation from main mpmath package to save space (a separate
tar.gz file is now provided for the documentation sources)
* Fixed matplotlib version detection
* Converted files to Unix line endings
Special functions:
* Started adding plots of special functions to the documentation
* Added Anger and Weber functions (angerj(), webere())
* Added Lommel functions (lommels1(), lommels2())
* Added interval versions of gamma(), loggamma(), rgamma() and
* Rewritten Airy functions to improve speed and accuracy
* Support for arbitrary-order derivatives of airyai(), airybi()
* Added Airy function zeros (airyaizero(), airybizero())
* Added Scorer functions (scorergi(), scorerhi())
* Added computation of Bessel function zeros and Bessel function
derivative zeros (besseljzero(), besselyzero())
* Fixed besselj(mpc(n), z)
* Rewritten lambertw() to fix various subtle bugs and robustly handle
numerical difficulties near branch cuts and branch points.
* Fixed fp.lambertw() to behave the same on branch cuts on systems with
and without signed-zero floats
* Added Carlson symmetric incomplete elliptic integrals
(elliprf(), elliprc(), elliprj(), elliprd(), elliprg())
* Added Legendre incomplete elliptic integrals (ellipf(), ellippi(),
ellipe() with two arguments)
* Implemented Parabolic cylinder functions (pcfd(), pcfu(), pcfv(),
* Implemented Euler-Maclaurin summation for hypergeometric functions
of order (p,p-1) to support evaluation with z close to 1 in remaining cases
* Fixed a bug in hypergeometric series summation, causing occasional
inaccurate results and incorrect detection of zeros
* Fixed qfrom(m=...)
* Implemented generators diffs_exp(), diffs_prod() for composing
* Implemented Abel-Plana summation for infinite series (sumap())
Basic arithmetic and functions:
* Implemented matrix slice indexing, supporting submatrix
extraction and assignment (contributed by Ioannis Tziakos)
* Added missing constant fp.glaisher
* Fixed a bug preventing internal rational numbers from being
* Fixed bug in isnpint()
* Fixed a bug in cos_sin() for pure imaginary argument
* Slightly improved performance for elementary functions of pure
real or pure imaginary mpc inputs
* Fixed plot() with real-valued mpc instances
* Fixed cplot() to work with endpoints of other type than float/int
Released June 6, 2010
Basic transcendental functions:
* Reimplemented all elementary functions except log, reducing
overhead and giving asymptotic speedups at high precision
* Reimplemented gamma() and loggamma(), improving speed and
fixing accuracy in corner cases
* Added rgamma() (reciprocal gamma function)
* Added a stress test suite for the gamma function
* Provided top-level functions cos_sin() and cospi_sinpi() for fast
simultaneous computation
Riemann zeta function:
* New zetazeros() implementation, supporting arbitrarily large indices
(contributed by Juan Arias de Reyna)
* Tuned algorithm selection in zeta() for complex arguments
(contributed by Juan Arias de Reyna)
* Accelerated computation of zeta function series using sieving
Special functions:
* Added qfrom(), qbarfrom(), mfrom(), kfrom(), taufrom() for elliptic
argument conversion
* Merged jsn(), jcn(), jdn() -> ellipfun() and generalized it to compute
all 12 Jacobi elliptic functions
* Implemented the Klein j-invariant (kleinj())
* Implemented the q-Pochhammer symbol (qp())
* Implemented q-factorial (qfac()) and q--gamma (qgamma())
* Implemented q-hypergeometric series (qhyper())
* Implemented bilateral hypergeometric series (bihyper())
* Implemented Appell 2D hypergeometric series F2-F4 (appellf2()-appellf4())
* Implemented generalized 2D hypergeometric series (hyper2d())
* Fixed gammainc() for integer-valued complex argument (contributed by
Juan Arias de Reyna)
* Fixed asymptotic expansion of hyp1f1() (contributed by Juan Arias de Reyna)
Numerical calculus:
* Added support for multidimensional series in nsum()
* Made nprod() faster by default by extrapolating directly instead of
calling nsum()
* Changed some options for diff()/diffs()
* Made taylor() chop tiny coefficients by default
* Added support for partial derivatives in diff()
Interval arithmetic:
* All interval arithmetic functionality moved to a separate context
namespace (iv)
* Preliminary support for complex intervals (iv.mpc)
* Fixed interval cos/sin to support intervals overlapping zeros/extreme points
* Implemented interval atan2
* Implemented exp/log/cos/sin for complex intervals
* Some other interface changes to interval code
Utility functions:
* Made chop() use relative rather than absolute tolerance for
real/imaginary parts
* Optimized floor(), ceil(), isinf(), isnan(), isint()
* Implemented nint(), frac(), isnormal()
* Fixed and documented semantics for isinf(), isin(), isnan()
* Added utility functions autoprec(), maxcalls(), memoize()
Miscellaneous tweaks and fixes:
* Support complex conjugation in fdot()
* Added support for Cholesky decomposition of complex matrices
* Fixed a small precision bug in linear algebra functions
* Suppress NoConvergence exception when plotting
* Removed some dirty code to improve PyPy compatibility
* Fixed plotting to work with mpmath numbers in the interval specification
* Fixed fp arithmetic on systems where math.log and math.sqrt return NaN
instead of raising an exception
* Fixed fp.conj for Python 2.4 and 2.5
* Fixed quadrature to work with reversed infinite intervals such as [0,-inf]
* Renamed modf() -> fmod() for consistency
Released February 5, 2010
General changes:
* Fully separated the code into "low-level" and "high-level", permitting the
use of alternative contexts (the object provides the default
* Implemented a context for fast double-precision arithmetic using Python
types (mpmath.fp)
* Implemented hooks for importing a faster version of mp arithmetic from Sage
* Implemented optimized fp versions of certain functions (including erf, erfc,
gamma, digamma, ei, e1)
* Renamed and reorganized various internal modules and methods (including
merging low-level modules into mpmath.libmp). This should not affect most
external code using top-level imports.
* Implemented splot() for 3D surface plots (contributed by Jorn Baayen)
* Permit calling plot functions with custom axes (contributed by Jorn Baayen)
* Fixed lu_solve for overdetermined systems (contributed by Vinzent Steinberg)
* Added conjugate matrix transpose (contributed by Vinzent Steinberg)
* Implemented matrix functions (expm, cosm, sinm, sqrtm, logm, powm)
* Prettier printing of numbers with leading zeros at small precisions
* Made nstr pass on kwargs, permitting more formatting options
* Fixed wrong directed rounding of addition of numbers with large magnitude
* Fixed several docstring typos (contributed by Chris Smith)
* Fixed a bug that prevented caching of quadrature nodes to work optimally.
Special functions:
* Implemented fast evaluation for large imaginary heights of the Riemann zeta
function, Z function and derived functions using the Riemann-Siegel
(contributed by Juan Arias de Reyna)
* Unified the zeta() and hurwitz() functions, automatically selecting a fast
* Improved altzeta() to fall back to zeta() for large arguments
* Fixed accuracy of zeta(s) for s ~= 1
* Implemented exact evaluation of Euler numbers (contributed by Juan Arias
de Reyna)
* Implemented numerical evaluation of Euler numbers and Euler polynomials
(eulernum(), eulerpoly())
* Fixed bernpoly() and eulerpoly() to compute accurate values for large
* Fixed accuracy problems for hypergeometric functions with large parameters
* Faster evaluation of hypergeometric series using on-the-fly code generation
* Optimized hypercomb to detect certain zero terms symbolically
* Removed the djtheta function (jtheta() accepts a derivative parameter)
* Implemented li(x, offset=True) to compute the offset logarithmic integral
* Fixed wrong branch in Lambert W function for certain complex inputs
* Implemented the reflection formula for the Barnes G-function,
superfactorials, hyperfactorials, permitting large arguments in the left
* Implemented analytic continuation to |z| >= 1 for hypergeometric functions
pFq with p=q+1; added hyp3f2()
* Implemented Borel summation of divergent pFq functions with p > q+1
* Implemented automatic degree reduction of hypergeometric functions with
repeated parameters
* Added convenience functions expj(), expjpi()
* Use Mathematica's convention for the continuation of the Meijer G-function
* Added phase(), polar(), rect() functions for compatibility with the
Python 2.6 cmath module
* Implemented spherical harmonics (spherharm())
* Optimized ci(), si(), chi(), shi() for complex arguments by evaluating
them in terms of ei()
* Optimized hyp2f1 for z ~= -1
Released August 13, 2009
New special functions:
* The generalized exponential integral E_n (expint(), e1() for E_1)
* The generalized incomplete beta function (betainc())
* Whittaker functions (whitm(), whitw())
* Struve functions (struveh(), struvel())
* Kelvin functions (ber(), bei(), ker(), kei())
* Cyclotomic polynomials (cyclotomic())
* The Meijer G-function (meijerg())
* Clausen functions (clsin(), clcos())
* The Appell F1 hypergeometric function of two variables (appellf1())
* The Hurwitz zeta function, with nth order derivatives (hurwitz())
* Dirichlet L-series (dirichlet())
* Coulomb wave functions (coulombf(), coulombg(), coulombc())
* Associated Legendre functions of 1st and 2nd kind (legenp(), legenq())
* Hermite polynomials (hermite())
* Gegenbauer polynomials (gegenbauer())
* Associated Laguerre polynomials (laguerre())
* Hypergeometric functions hyp1f2(), hyp2f2(), hyp2f3(), hyp2f0(), hyperu()
Evaluation of hypergeometric functions:
* Added the function hypercomb() for evaluating expressions containing
hypergeometric series, with automatic handling of limits
* The available hypergeometric series (of orders up to and including 2F3)
implement asymptotic expansions with respect to the last argument z, allowing
fast and accurate evaluation anywhere in the complex plane. A massive number
of functions, including Bessel functions, error functions, etc., have been
updated to take advantage of this to support fast and accurate evaluation
anywhere in the complex plane.
* Fixed hyp2f1 to handle z close to and on the unit circle (supporting
evaluation anywhere in the complex plane)
* hyper() handles the 0F0 and 1F0 cases exactly
* hyper() eventually raises NoConvergence instead of getting stuck in
an infinite loop if given a divergent or extremely slowly convergent series
Other improvements and bug fixes to special functions:
* gammainc is much faster for large arguments and avoids catastrophic
* Implemented specialized code for ei(x), e1(x), expint(n,x) and gammainc(n,x)
for small integers n, making evaluation much faster
* Extended the domain of polylog
* Fixed accuracy for asin(x) near x = 1
* Fast evaluation of Bernoulli polynomials for large z
* Fixed Jacobi polynomials to handle some poles
* Some Bessel functions support computing nth order derivatives
* A set of "torture tests" for special functions is available as
* Implemented the differint() function for fractional differentiaton / iterated
* Added functions fadd, fsub, fneg, fmul, fdiv for high-level arithmetic with
controllable precision and rounding
* Added the function mag() for quick order-of-magnitude estimates of numbers
* Implemented powm1() for accurate calculation of x^y-1
* Improved speed and accuracy for raising a pure imaginary number to
an integer power
* nthroot() renamed to root(); root() optionally computes any of
the non-principal roots of a number
* Implemented unitroots() for generating all (primitive) roots of unity
* Added the mp.pretty option for nicer repr output
Released June 9, 2009
* It is now possible to create multiple context objects and use context-local
methods instead of global state/functions (e.g. mp2=mp.clone(); mp2.dps=50;
mp2.cos(3)). Not all functions have been converted to context methods, and
there are some bugs, so this feature is currently experimental.
* If mpmath is installed in Sage 4.0 or later, mpmath will now use sage.Integer
instead of Python long internally.
* Removed instances of old-style integer division from the codebase.
* can be run with -coverage to generate coverage statistics.
Types and basic arithmetic
* Fixed comparison with -inf.
* Changed repr format of the mpi interval type to make eval(repr(x)) == x.
* Improved printing of intervals, with configurable output format (contributed
by Vinzent Steinberg based on code by Don Peterson).
* Intervals supported by mpmathify() and nstr() (contributed by Vinzent
* mpc is now hashable.
* Added more formatting options to the internal function to_str.
* Faster pure-Python square root.
* Fix trailing whitespace giving wrong values in str->mpf conversion.
* Fixed nsum() with Euler-Maclaurin summation which would previously
ignore the starting index and sum from n=1.
* Implemented Newton's method for findroot() (contributed by Vinzent
Linear algebra
* Fixed LU_decomp() to recognize singular matrices (contributed by Jorn Baayen).
* The various norm functions were replaced by the generic vector norm
function norm(x,p) and the generic matrix norm function mnorm(x,p).
Special functions:
* Some internal caches were changed to always slightly overallocate
precision. This fixes worst-case behavior where previously the cached
value had to be recomputed on every function call.
* Fixed log(tiny number) returning nonsense at high precision.
* Fixed gamma() and derivative functions such as binomial() returning
wrong results at integer inputs being divisible by a large power of 2.
* Fixed asin() not to raise an exception at high precision (contributed
by Vinzent Steinberg).
* Optimized the AGM code for the natural logarithm, making the previously
used Newton method at intermediate precisions obsolete.
* The arithmetic-geometric mean function agm() is now an order of magnitude
faster at low precision.
* Faster implementations of ellipk() and ellipe().
* Analytic continuation of ellipe() to |x| >= 1 implemented.
* Implemented the log gamma function (loggamma()) with correct branch
cuts (slow, placeholder implementation).
* Fixed branch cuts of hyperfac().
* Implemented the Riemann-Siegel Z-function (siegelz()).
* Implemented the Riemann-Siegel theta function (siegeltheta()).
* Implemented calculation of Gram points (grampoint()).
* Implemented calculation of Riemann zeta function zeros (zetazero()).
* Implemented the prime counting function: a slow, exact version (primepi()).
and a fast approximate version (primepi2()) that gives a bounding interval.
* Implemented the Riemann R prime counting function (riemannr()).
* Implemented Bell numbers and polynomials (bell()).
* Implemented the expm1() function.
* Implemented the 'polyexponential function' (polyexp()).
* Implemented the twin prime constant (twinprime) and Mertens' constant
* Implemented the prime zeta function (primezeta()).
Released January 26, 2009
* Most of the documentation is now generated from docstrings
using Sphinx' autodoc feature, and proper LaTeX is used
for mathematical formulas. A large amount of new documentation
has been written.
* Improved gmpy backend. Using gmpy-1.04 gives a ~30% unit tests
speedup over 1.03, with speedups in the range of 2-3x for
specific operations (contributed by Case van Horsen and
Mario Pernici).
* Mpmath imports slightly faster due to not trying to
load the 'random' library
Numerical calculus, etc:
* Implemented a fast high-precision ODE solver (to replace the slow
and low-accuracy RK4 algorithm) (odefun())
* Created an intelligent function nsum() to replace sumrich/sumsh
* Implemented nprod() for computing infinite products
* Rewrote limit() to use the same adaptive extrapolation algorithm
as nsum()
* Multidimensional nonlinear solving with Newton's method
implemented in findroot() (contributed by Vinzent Steinberg)
* Simplified the implementation and interface of sumem()
* Reimplemented Shanks transformation for nsum using Wynn's epsilon
algorithm (shanks())
* Reimplemented Richardson extrapolation slightly more simply and
efficiently (richardson())
* Prevent shanks() from exiting prematurely by adding
random noise to zeros
* Removed the obsolete secant() function (see findroot())
* Implemented high-order derivatives (diff(), diffs())
* Implemented calculation of Taylor series (taylor())
* Implemented calculation of Fourier series (fourier(), fourierval())
* Implemented Pade approximation (pade()) (contributed by
Mario Pernici)
* Better cancel condition for findroot() (contributed by
Vinzent Steinberg)
* Some refactoring of numerical integration code
* Fix erroneous nodes for 0-th order Gauss-Legendre quadrature,
which was causing unnecessary slowness
* Quadrature nodes are cached for arbitrary intervals, giving a
30% speedup for repeated integrations
* Unified interface and added more options for identify(), pslq(), findpoly()
New special functions:
* Implemented polylogarithms (polylog())
* Implemented Bernoulli polynomials (bernpoly())
* Implemented the Barnes G-function (barnesg())
* Implemented double factorials (fac2())
* Implemented superfactorials (superfac())
* Implemented hyperfactorials (hyperfac())
* Replaced lower_gamma and upper_gamma with a more versatile
function gammainc() for computing the generalized (and optionally
regularized) incomplete gamma function
* Implemented sinc() and sincpi()
* Implemented Fibonacci numbers (fib())
* Implemented the Dirichlet eta function (altzeta())
* Implemented the inverse error function (erfinv())
* Jacobi theta functions and elliptic functions were essentially
rewritten from scratch, making them much faster and more
general. Renamed Jacobi theta functions: jacobi_theta -> jtheta,
etc. (contributed by Mario Pernici)
* Implemented derivatives of jtheta (djtheta) (contributed by
Mario Pernici)
* Implemented Bessel Y, I, K functions (bessely, besseli,
besselk; Bessel J functions were also renamed to besselj)
also renamed)
* Generalized Stieltjes constants can now be computed,
with stieltjes(n,a)
* Implemented Hankel functions (hankel1, hankel2)
Speed improvements and bugfixes to special functions:
* Fast logarithm at very high precision using the formula by
Sasaki and Kanada (contributed by Mario Pernici)
* Slightly faster logarithm at low precision (contributed by
Mario Pernici)
* Faster exponential function at high precision, using
Newton's method (contributed by Mario Pernici)
* Faster computation of ln2 and ln10 by means of binary splitting
(contributed by Mario Pernici)
* Fixed accuracy problems in sinpi() and cospi()
* Correct evaluation of beta() at limits
* Much faster evaluation of stieltjes(n), using an improved integral
* Fixed bernoulli() being inaccurate for large n and low precision,
and being needlessly slow for small n and huge precision
* Fixed accuracy of zeta(s) for large negative re(s)
* Fixed accuracy problems for asinh, atanh and tanh
* Fixed accuracy of airyai() for large x.real
* Fixed bug in nthroot() for very large arguments (contributed by
Mario Pernici)
* Fixed accuracy of log(x) for complex |x| ~= 1
* Fixed accuracy of exp(n), n a huge integer and prec >= 600
* Slightly faster hypergeometric functions with rational parameters
(contributed by Mario Pernici)
* Faster and more accurate calculation of ci(x), si(x)
* Faster and more accurate calculation of ei(x) for large x,
using an asymptotic expansion (contributed by Mario Pernici)
* Fixed accuracy bugs in theta functions (contributed by
Mario Pernici)
* The Lambert W function returns more appropriate values at infinities
Arithmetic and basic interface:
* Square roots are now rounded correctly
* Made float(huge) -> inf and float(1/huge) -> 0 instead of
raising OverflowError
* Renamed convert_lossless -> mpmathify
* mpmathify() accepts strings representing fractions or complex
numbers (contributed by Vinzent Steinberg)
* Fixed a bug in interval multiplication giving wrong signs
* Added monitor() to monitor function evaluation
* Implemented a chop() utility function for deletion of numerical noise
* Added re(), im(), conj(), fabs(), mpf.conjugate()
* Fixed the != operator for intervals
* Added functions fsum, fprod, fdot for efficient computation of
sums, products and dot products of lists of mpf:s or mpc:s
* Generation of Hilbert matrices (hilbert()) (contributed by
Vinzent Steinberg)
* Added lu_solve_mat() to solve a*x=b where a and b are matrices (contributed
by Mario Pernici)
* Implemented computation of matrix exponentials (exp_pade()) (contributed
by Mario Pernici)
* Prettier repr of complex matrices (contributed by Vinzent Steinberg)
* Speedups by using fdot and fsum (contributed by Vinzent Steinberg)
Released October 15, 2008
Interface / general:
* Mpmath now works with Python 2.6
* Implemented function plotting via 'plot' and 'cplot' (requires
* Removed global rounding mode (always rounding to nearest by default)
* Instead added 'prec', 'dps', 'rounding' keyword arguments to
standard functions, for optional fine-grained control over precision
and rounding
* Implemented isinf, isnan, isint, utility functions
* A large number of internal functions were moved and/or renamed to
improve consistency. This particularly affects low-level mpf
functions (lib.fadd -> libmpf.mpf_add, etc).
* Syntax for some operations was changed (see details below)
* The test runner ( was updated to support running
isolated tests and to allow a local import of mpmath
* Unit tests can now be run with import mpmath; mpmath.runtests()
* Implicit imports are no longer used internally in the main codebase.
(This will hopefully make the source easier to read, and can catch
installation problems more cleanly.)
Added linear algebra functions (contributed by Vinzent Steinberg):
* Provided a matrix class
* Computation of powers, inverses, determinants
* Linear system solving using LU, QR and Cholesky
* Vector and matrix norms
* Calculation of condition numbers
Improvements to interval arithmetic:
* Fixed rounding direction for negative numbers and related
spurious bugs
* Fix interval exponentiation (all cases should work now)
* Basic interval arithmetic is up to 10x faster
* sqrt, exp, log, sin, cos and a few other functions
accept interval arguments
* Intervals supported in matrices
Changes to root-finding code:
* secant renamed to findroot
* findroot was made more general; many useful alternative root-finding
algorithms were implemented (contributed by Vinzent Steinberg)
Improvements to special functions:
* Implemented polygamma functions
* Implemented harmonic numbers
* Implemented Stieltjes constants
* Made gamma more accurate for huge arguments and/or precision
* Made zeta more accurate in various cases
* Made zeta typically 2-5x faster
* Much more efficient computation of zeta for huge s (zeta(s) ~= 1)
* Optimized numerical calculation of Bernoulli numbers
* Fast exact calculation of huge Bernoulli numbers via zeta and the
von Staudt-Clausen theorem
* Using AGM to compute ellipk, which is much faster and works
in the entire complex plane
* Allow single-argument form agm(x) = agm(1,x)
* Faster and more accurate computation of erf
* Added fast and accurate implementation of erfc
* Normal probability functions npdf, ncdf
* Fixed directed rounding in corner cases for various functions
Improvements to numerical integration:
* Changed syntax for integration (quad(f, [a, b], options))
* Implemented Gauss-Legendre quadrature
* Direct support for triple integrals (quad(f, X, Y, Z))
* Interval can be a list of several points, to split integration
into subintervals
* Oscillatory quadrature uses Gauss-Legendre instead of tanh-sinh,
since this is typically faster
* Fixed minor rounding bug in tanh-sinh quadrature not giving
complete symmetry in the nodes
* Implemented quadrature rules in classes for improved extensibility
Various speed improvements:
* Up to 3x faster computation of log(x) at low precision, due to using
Taylor series with argument reduction and partial caching
* About 2x faster log(x) at very high precision due to more efficient
computation of exp in the Newton iteration
* Up to 10x faster computation of atan(x) at low to medium precision,
due to using Taylor series with argument reduction and partial caching
* Faster pickling due to using hex() instead of long()
* Optimized code for Khinchin's constant (2.5x faster at 1000 digits)
* Optimized code for Glaisher's constant (1.5x faster at 1000 digits)
* Faster algorithm for Euler's constant (10x faster at 10000 digits)
* Rewrote PSLQ to use fixed-point arithmetic, giving a ~7x speedup
in pslq, findpoly and identify
Miscellaneous bugfixes:
* Fixed nthroot for n = -1, 0, 1
* Fixed inf/2**n and nan/2**n returning zero
Released August 23, 2008
* gmpy mpzs are used instead of python ints when available, for
huge speedups at high precision (contributed by Case Van Horsen)
* using binary splitting to compute pi and e near-optimally
* mpmath includes __version__ information
* arange behaves more like range (contributed by Vinzent Steinberg)
* asymptotically faster trigonometric functions via Brent's trick
(contributed by Mario Pernici)
* asymptotically faster inverse trigonometric functions via Newton's
method (contributed by Mario Pernici)
* added Jacobi elliptic functions 1-4, sn, cn, dn (contributed by Mike
* polyval, polyroots and related functions now use the same order
for coefficients as scipy and matlab (i.e. the reverse order of what
was used previously in mpmath)
* fixed polyroots for degree-0 polynomials (contributed by Nimish Telang)
* added convenience functions (log10, degrees, radians, frexp, modf, ln,
arg, sign)
* added fast cbrt and nthroot functions for computing nth roots
(contributed by (Mario Pernici)
* added various exponential integrals (ei, li, si, ci, shi, chi, erfi)
* added airy functions (airyai, airybi)
* more __op__ and __rop__ methods return NotImplemented where
* external classes can define a special method _mpmath_ to interact
with mpmath numbers and functions
* fixed some corner cases in atan2
* faster rand()
Released April 20, 2008
New features:
* the full set of reciprocal trigonometric and hyperbolic functions
and their inverses (cotangent, secant, etc) is available
* oscillatory quadrature algorithm
* the PSLQ algorithm and constant recognition functions
* Richardson and Shanks transformations for computing limits and series
* Euler-Maclaurin summation of series
* basic ODE solvers (contributed by Ondrej Certik)
* the Lambert W function
* arithmetic-geometric mean function
* generic hypergeometric series and some special hypergeometric
functions (elliptic integrals, orthogonal polynomials)
* several more mathematical constants
* fast sequential computation of integer logarithms and Bernoulli
* Bessel function jv works for complex arguments and noninteger v
* support for trapping complex results
* using Sphinx to generate HTML documentation
Bugfixes, speed enhancements, and other improvements:
* compatibility tests should now pass on systems where Python is
compiled to use 80-bit registers for floating point operations
* fixed mpmath to work with some versions of Python 2.4 where a
list indexing bug is present in the Python core
* better algorithms for various complex elementary functions
(tan and tanh by Fredrik; sqrt, acos, asin, acosh and asinh
improved by Mario Pernici)
* multiplication and integer powers for complex numbers is faster
and more accurate
* miscellaneous speed improvements to complex arithmetic (contributed
by Mario Pernici)
* faster computation of cos and sin when only one of them is needed
(contributed by Mario Pernici)
* slightly faster square roots at low precision (contributed by
Mario Pernici)
* fixed computation of exp(n) for negative integers and x**y for
negative half integers y
* mpf ** complex now works
* faster generation of quadrature nodes (contributed by Mario Pernici)
* faster change of variables for quadrature
* comparisons and conversions have been optimized slightly.
comparisons with float(nan) also work as intended.
* str() is several times faster at very high precision
* implementations of most elementary functions moved to the lib
and libmpc modules for cleaner separation of functionality
* the rounding argument for lib and libmpc functions, and for
some functions also the the prec argument, are now optional,
resulting in cleaner and slightly faster lib code
* gamma and factorial are about 2x faster
* polyroots returns nicer results
* pickling now works for mpf and mpc instances
Released March 12, 2008
* the interface for switching precision and rounding modes has been
changed. instead of changing mpf.prec, there is a new object mp
which holds the precision as mp.prec. this change improves
flexibility in the implementation. it will unfortunately break
any existing code written for mpmath, but the broken code should
be trivial to update.
* the functions workprec, workdps, extraprec, extradps have been
introduced for switching precision in a more safe manner,
ensuring that the precision gets reset when finished. they can
be used with the 'with' statement available in python 2.5
* improved documentation (manual.html)
* the round-half-down and round-half-up modes have been deprecated,
since they added complexity without being particularly useful.
round-half-even has been renamed to round-nearest.
* implemented the functions nstr, nprint for printing numbers with
a small or custom number of digits
* accuracy of cos and sin near roots has been fixed. computing
sin(x) or cos(x) where x is huge is also much faster
* implemented a magical constant eps that gives the "machine"
* additional mathematical functions: implemented Catalan's constant
and Bessel functions J_n(x) for integer n and real x
* new functions diff and diffc for numerical differentiation
* implemented the ldexp function for fast multiplication by 2**n
* mpf uses rich comparison methods (contributed by Pearu Peterson)
* epydoc-friendly docstrings (contributed by Pearu Peterson)
* support creating mpf from float nan or inf
* fixed printing of complex numbers with negative imaginary part
* flattened package structure to simplify inclusion of mpmath in other
* external classes can interoperate with mpf and mpc instances
by defining _mpf_ or _mpc_ properties
* renamed lib.fpow -> lib.fpowi and implemented lib.fpow for general
real powers. <mpf> ** <mpf> should now be slightly faster and more
* the internal number representation has been changed to include
an explicit sign bit. as a result of this change and other small
tweaks, arithmetic is up to 20% faster and the total running
time for mpmath's unit tests has dropped 10%.
* miscellaneous speed improvements:
* <mpf> ** <int> is 2-3 times faster (contributed by Mario Pernici)
* <mpf> * <int> and <int> * <mpf> is roughly twice as fast
* <int> / <mpf> is roughly twice as fast (contributed by Mario
* exp and log are about 10% faster
* fast computation of e and exp(n) when precision is extremely high
Released January 13, 2008
* added the mpi type for interval arithmetic
* powers with integer exponents are computed with directed rounding
all the way through to preserve interval bounds more robustly
(however, the code is not fully tested and may have some bugs)
* string input to mpf.__new__() can now be unicode
* mpf.__eq__ now works in pypy
* infs and nans are now implemented in mpmath.lib, resulting in
considerable simplification of the mpf class implementation
* partial support for infs and nans in functions, e.g.
exp(inf) -> inf and exp(-inf) -> 0 now work.
* renamed several files. created mpmath.apps and moved tests into
the main mpmath directory
* wrote script to permit running unit tests without py.test available
* improved bit counting code in fadd, fmul and fdiv, plus other
small performance tweaks, resulting in a 20-30% speedup for
Released November 24, 2007
* added the quad module for arbitrary-precision numerical integration
* floor and ceil functions available
* implemented __mod__ and __rmod__ for the mpf class
* partial support for the special numbers +inf, -inf and nan
* faster multiplication and division (up to 40% faster with psyco)
* simplified syntax for conversion function (from_int instead of
from_int_exact, etc)
* renamed cgamma to euler
* more documentation strings
Released November 3, 2007
* new string conversion code (much faster; unlimited exponents)
* fixed bug in factorial (it gave the wrong value, though gamma worked)
* division now uses a rigorous algorithm for directed rounding
(mpmath previously used a heuristic that got the last bit wrong
in 1/10000 of cases)
* misc. performance improvements (arithmetic is 15% faster)
* refactored parts of the code; added many more docstrings and tests
* added a function rand() for generating full-precision random numbers
* rewrote the benchmark script to compare against Decimal and to
automatically generate timings with psyco both disabled and enabled
* rewrote unit tests to use py.test
Released October 5, 2007
* fixed high-precision accuracy problem in complex sqrt
* fixed high-precision accuracy problem in atan and complex log
* fixed directed rounding for sqrt (always rounded to nearest)
* implemented all hyperbolic and inverse functions (there are some
accuracy issues left to sort out)
* included gamma, factorial, erf, zeta incomplete gamma functions
* made sin and tan more accurate for complex input very close to 0
* more docstrings
* many more tests
* including a benchmark script
-- 0.2 --
Released October 2, 2007
* 50% faster exponential function
* faster mpf <-> int ops
* fixed import error in; added demos to source distribution
* __rmul__ was missing on mpf
* fixed bitcount bug also for -(2**n-1)
* more docstrings
* more tests; tests included in source distribution
* approximate equality testing (.ae method) supported
* implemented atan and atan2 functions
* tan works for both mpfs and mpcs
* complex logarithms and complex powers supported
* more details in README
-- 0.1 --
Released September 27, 2007
* imported code from SymPy's numerics module
* renamed functions and restructured various parts of the code
* fixed erroneous bitcount for 2**n-1 mantissa with directed rounding
* various small speed improvements and bug fixes
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