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Copyright 1996, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
2009 Free Software Foundation, Inc.
This file is part of the GNU MP Library.
The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.
The GNU MP Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library. If not, see
Changes between GMP version 4.3.0 and 4.3.1
* Fixed bug in mpn_gcdext, affecting also mpz_gcdext and mpz_invert.
The bug could cause a cofactor to have a leading zero limb, which
could lead to crashes or miscomputation later on.
* Fixed some minor documentation issues.
* None.
* Workarounds for various issues with Mac OS X's build tools.
* Recognise more IBM "POWER" processor variants.
Changes between GMP version 4.2.X and 4.3.0
* Fixed bug in mpz_perfect_power_p with recognition of negative perfect
powers that can be written both as an even and odd power.
* We might accidentally have added bugs since there is a large amount of
new code in this release.
* Vastly improved assembly code for x86-64 processors from AMD and Intel.
* Major improvements also for many other processor families, such as
Alpha, PowerPC, and Itanium.
* New sub-quadratic mpn_gcd and mpn_gcdext, as well as improved basecase
gcd code.
* The multiply FFT code has been slightly improved.
* Balanced multiplication now uses 4-way Toom in addition to schoolbook,
Karatsuba, 3-way Toom, and FFT.
* Unbalanced multiplication has been vastly improved.
* Improved schoolbook division by means of faster quotient approximation.
* Several new algorithms for division and mod by single limbs, giving
many-fold speedups.
* Improved nth root computations.
* The mpz_nextprime function uses sieving and is much faster.
* Countless minor tweaks.
* Updated support for fat binaries for x86_32 include current processors
* Lots of new mpn internal interfaces. Some of them will become public
in a future GMP release.
* Support for the 32-bit ABI under x86-apple-darwin.
* x86 CPU recognition code should now default better for future
* The experimental nails feature does not work in this release, but
it might be re-enabled in the future.
* The gmp_version variable now always contains three parts. For this
release, it is "4.3.0".
Changes between GMP version 4.2.3 and 4.2.4
* Fix bug with parsing exponent '+' sign in mpf.
* Fix an allocation bug in mpf_set_str, also affecting mpf_init_set_str, and
* None, except that proper processor recognition helps affected processors.
* Recognize new AMD processors.
Changes between GMP version 4.2.2 and 4.2.3
* Fix x86 CPU recognition code to properly identify recent AMD and Intel
64-bit processors.
* The >> operator of the C++ wrapper gmpxx.h now does floor rounding, not
* Inline semantics now follow the C99 standard, and works with recent GCC
* C++ bitwise logical operations work for more types.
* For C++, gmp.h now includes cstdio, improving compiler compatibility.
* Bases > 36 now work properly in mpf_set_str.
* None, except that proper processor recognition helps affected processors.
* The allocation functions now detect overflow of the mpz_t type. This means
that overflow will now cause an abort, except when the allocation
computation itself overflows. (Such overflow can probably only happen in
powering functions; we will detect powering overflow in the future.)
Changes between GMP version 4.2.1 and 4.2.2
* License is now LGPL version 3.
* Shared library numbers corrected for libcxx.
* Fixed serious bug in gmpxx.h where a=a+b*c would generate garbage.
Note that this only affects C++ programs.
* Fix crash in mpz_set_d for arguments with large negative exponent.
* Fix 32-bit ABI bug with Itanium assembly for popcount and hamdist.
* Fix assembly syntax problem for powerpc-ibm-aix with AIX native assembler.
* Fix problems with x86 --enable-fat, where the compiler where told to
generate code for the build machine, not plain i386 code as it should.
* Improved recognition of powerpc systems wrt Altivec/VMX capability.
* Misc minor fixes, mainly workarounds for compiler/assembler bugs.
* "Core 2" and Pentium 4 processors, running in 64-bit mode will get a
slight boost as they are now specifically recognized.
* New support for x86_64-solaris
* New, rudimentary support for x86-apple-darwin and x86_64-apple-darwin.
(Please see for more information.)
Changes between GMP version 4.2 and 4.2.1
* Shared library numbers corrected.
* Broken support for 32-bit AIX fixed.
* Misc minor fixes.
* Exact division (mpz_divexact) now falls back to plain division for large
* Support for some new systems.
Changes between GMP version 4.1.4 and 4.2
* Minor bug fixes and code generalizations.
* Expanded and improved test suite.
* Many minor optimizations, too many to mention here.
* Division now always subquadratic.
* Computation of n-factorial much faster.
* Added basic x86-64 assembly code.
* Floating-point output is now subquadratic for all bases.
* FFT multiply code now about 25% faster.
* Toom3 multiply code faster.
* Much improved configure.
* Workarounds for many more compiler bugs.
* Temporary allocations are now made on the stack only if small.
* New systems supported: HPPA-2.0 gcc, IA-64 HP-UX, PowerPC-64 Darwin,
Sparc64 GNU/Linux.
* New i386 fat binaries, selecting optimised code at runtime (--enable-fat).
* New build option: --enable-profiling=instrument.
* New memory function: mp_get_memory_functions.
* New Mersenne Twister random numbers: gmp_randinit_mt, also now used for
* New random functions: gmp_randinit_set, gmp_urandomb_ui, gmp_urandomm_ui.
* New integer functions: mpz_combit, mpz_rootrem.
* gmp_printf etc new type "M" for mp_limb_t.
* gmp_scanf and friends now accept C99 hex floats.
* Numeric input and output can now be in bases up to 62.
* Comparisons mpz_cmp_d, mpz_cmpabs_d, mpf_cmp_d recognise infinities.
* Conversions mpz_get_d, mpq_get_d, mpf_get_d truncate towards zero,
previously their behaviour was unspecified.
* Fixes for overflow issues with operands >= 2^31 bits.
* mpfr is gone, and will from now on be released only separately. Please see
Changes between GMP version 4.1.3 and 4.1.4
* Bug fix to FFT multiplication code (crash for huge operands).
* Bug fix to mpf_sub (miscomputation).
* Support for powerpc64-gnu-linux.
* Better support for AMD64 in 32-bit mode.
* Upwardly binary compatible with 4.1.3, 4.1.2, 4.1.1, 4.1, 4.0.1, 4.0,
and 3.x versions.
Changes between GMP version 4.1.2 and 4.1.3
* Bug fix for FFT multiplication code (miscomputation).
* Bug fix to K6 assembly code for gcd.
* Bug fix to IA-64 assembly code for population count.
* Portability improvements, most notably functional AMD64 support.
* mpz_export allows NULL for countp parameter.
* Many minor bug fixes.
* mpz_export allows NULL for countp parameter.
* Upwardly binary compatible with 4.1.2, 4.1.1, 4.1, 4.0.1, 4.0, and 3.x
Changes between GMP version 4.1.1 and 4.1.2
* Bug fixes.
Changes between GMP version 4.1 and 4.1.1
* Bug fixes.
* New systems supported: NetBSD and OpenBSD sparc64.
Changes between GMP version 4.0.1 and 4.1
* Bug fixes.
* Speed improvements.
* Upwardly binary compatible with 4.0, 4.0.1, and 3.x versions.
* Asymptotically fast conversion to/from strings (mpz, mpq, mpn levels), but
also major speed improvements for tiny operands.
* mpn_get_str parameter restrictions relaxed.
* Major speed improvements for HPPA 2.0 systems.
* Major speed improvements for UltraSPARC systems.
* Major speed improvements for IA-64 systems (but still sub-optimal code).
* Extended test suite.
* mpfr is back, with many bug fixes and portability improvements.
* New function: mpz_ui_sub.
* New functions: mpz_export, mpz_import.
* Optimization for nth root functions (mpz_root, mpz_perfect_power_p).
* Optimization for extended gcd (mpz_gcdext, mpz_invert, mpn_gcdext).
* Generalized low-level number format, reserving a `nails' part of each
limb. (Please note that this is really experimental; some functions
are likely to compute garbage when nails are enabled.)
* Nails-enabled Alpha 21264 assembly code, allowing up to 75% better
performance. (Use --enable-nails=4 to enable it.)
Changes between GMP version 4.0 and 4.0.1
* Bug fixes.
Changes between GMP version 3.1.1 and 4.0
* Bug fixes.
* Speed improvements.
* Upwardly binary compatible with 3.x versions.
* New CPU support: IA-64, Pentium 4.
* Improved CPU support: 21264, Cray vector systems.
* Support for all MIPS ABIs: o32, n32, 64.
* New systems supported: Darwin, SCO, Windows DLLs.
* New divide-and-conquer square root algorithm.
* New algorithms chapter in the manual.
* New malloc reentrant temporary memory method.
* New C++ class interface by Gerardo Ballabio (beta).
* Revamped configure, featuring ABI selection.
* Speed improvements for mpz_powm and mpz_powm_ui (mainly affecting small
* mpz_perfect_power_p now properly recognizes 0, 1, and negative perfect
* mpz_hamdist now supports negative operands.
* mpz_jacobi now accepts non-positive denominators.
* mpz_powm now supports negative exponents.
* mpn_mul_1 operand overlap requirements relaxed.
* Float input and output uses locale specific decimal point where available.
* New gmp_printf, gmp_scanf and related functions.
* New division functions: mpz_cdiv_q_2exp, mpz_cdiv_r_2exp, mpz_divexact_ui.
* New divisibility tests: mpz_divisible_p, mpz_divisible_ui_p,
mpz_divisible_2exp_p, mpz_congruent_p, mpz_congruent_ui_p,
* New Fibonacci function: mpz_fib2_ui.
* New Lucas number functions: mpz_lucnum_ui, mpz_lucnum2_ui.
* Other new integer functions: mpz_cmp_d, mpz_cmpabs_d, mpz_get_d_2exp,
mpz_init2, mpz_kronecker, mpz_lcm_ui, mpz_realloc2.
* New rational I/O: mpq_get_str, mpq_inp_str, mpq_out_str, mpq_set_str.
* Other new rational functions: mpq_abs, mpq_cmp_si, mpq_div_2exp,
mpq_mul_2exp, mpq_set_f.
* New float tests: mpf_integer_p, mpf_fits_sint_p, mpf_fits_slong_p,
mpf_fits_sshort_p, mpf_fits_uint_p, mpf_fits_ulong_p, mpf_fits_ushort_p.
* Other new float functions: mpf_cmp_d, mpf_get_default_prec, mpf_get_si,
mpf_get_ui, mpf_get_d_2exp.
* New random functions: gmp_randinit_default, gmp_randinit_lc_2exp_size.
* New demo expression string parser (see demos/expr).
* New preliminary perl interface (see demos/perl).
* Tuned algorithm thresholds for many more CPUs.
Changes between GMP version 3.1 and 3.1.1
* Bug fixes for division (rare), mpf_get_str, FFT, and miscellaneous minor
Changes between GMP version 3.0 and 3.1
* Bug fixes.
* Improved `make check' running more tests.
* Tuned algorithm cutoff points for many machines. This will improve speed for
a lot of operations, in some cases by a large amount.
* Major speed improvements: Alpha 21264.
* Some speed improvements: Cray vector computers, AMD K6 and Athlon, Intel P5
and Pentium Pro/II/III.
* The mpf_get_prec function now works as it did in GMP 2.
* New utilities for auto-tuning and speed measuring.
* Multiplication now optionally uses FFT for very large operands. (To enable
it, pass --enable-fft to configure.)
* Support for new systems: Solaris running on x86, FreeBSD 5, HP-UX 11, Cray
vector computers, Rhapsody, Nextstep/Openstep, MacOS.
* Support for shared libraries on 32-bit HPPA.
* New integer functions: mpz_mul_si, mpz_odd_p, mpz_even_p.
* New Kronecker symbol functions: mpz_kronecker_si, mpz_kronecker_ui,
mpz_si_kronecker, mpz_ui_kronecker.
* New rational functions: mpq_out_str, mpq_swap.
* New float functions: mpf_swap.
* New mpn functions: mpn_divexact_by3c, mpn_tdiv_qr.
* New EXPERIMENTAL function layer for accurate floating-point arithmetic, mpfr.
To try it, pass --enable-mpfr to configure. See the mpfr subdirectory for
more information; it is not documented in the main GMP manual.
Changes between GMP version 3.0 and 3.0.1
* Memory leaks in gmp_randinit and mpz_probab_prime_p fixed.
* Documentation for gmp_randinit fixed. Misc documentation errors fixed.
Changes between GMP version 2.0 and 3.0
* Source level compatibility with past releases (except mpn_gcd).
* Bug fixes.
* Much improved speed thanks to both host independent and host dependent
* Switch to autoconf/automake/libtool.
* Support for building libgmp as a shared library.
* Multiplication and squaring using 3-way Toom-Cook.
* Division using the Burnikel-Ziegler method.
* New functions computing binomial coefficients: mpz_bin_ui, mpz_bin_uiui.
* New function computing Fibonacci numbers: mpz_fib_ui.
* New random number generators: mpf_urandomb, mpz_rrandomb, mpz_urandomb,
mpz_urandomm, gmp_randclear, gmp_randinit, gmp_randinit_lc_2exp,
gmp_randseed, gmp_randseed_ui.
* New function for quickly extracting limbs: mpz_getlimbn.
* New functions performing integer size tests: mpz_fits_sint_p,
mpz_fits_slong_p, mpz_fits_sshort_p, mpz_fits_uint_p, mpz_fits_ulong_p,
* New mpf functions: mpf_ceil, mpf_floor, mpf_pow_ui, mpf_trunc.
* New mpq function: mpq_set_d.
* New mpz functions: mpz_addmul_ui, mpz_cmpabs, mpz_cmpabs_ui, mpz_lcm,
mpz_nextprime, mpz_perfect_power_p, mpz_remove, mpz_root, mpz_swap,
mpz_tdiv_ui, mpz_tstbit, mpz_xor.
* New mpn function: mpn_divexact_by3.
* New CPU support: DEC Alpha 21264, AMD K6 and Athlon, HPPA 2.0 and 64,
Intel Pentium Pro and Pentium-II/III, Sparc 64, PowerPC 64.
* Almost 10 times faster mpz_invert and mpn_gcdext.
* The interface of mpn_gcd has changed.
* Better support for MIPS R4x000 and R5000 under Irix 6.
* Improved support for SPARCv8 and SPARCv9 processors.
Changes between GMP version 2.0 and 2.0.2
* Many bug fixes.
Changes between GMP version 1.3.2 and 2.0
* Division routines in the mpz class have changed. There are three classes of
functions, that rounds the quotient to -infinity, 0, and +infinity,
respectively. The first class of functions have names that begin with
mpz_fdiv (f is short for floor), the second class' names begin with mpz_tdiv
(t is short for trunc), and the third class' names begin with mpz_cdiv (c is
short for ceil).
The old division routines beginning with mpz_m are similar to the new
mpz_fdiv, with the exception that some of the new functions return useful
The old function names can still be used. All the old functions names will
now do floor division, not trunc division as some of them used to. This was
changed to make the functions more compatible with common mathematical
The mpz_mod and mpz_mod_ui functions now compute the mathematical mod
function. I.e., the sign of the 2nd argument is ignored.
* The mpq assignment functions do not canonicalize their results. A new
function, mpq_canonicalize must be called by the user if the result is not
known to be canonical.
* The mpn functions are now documented. These functions are intended for
very time critical applications, or applications that need full control over
memory allocation. Note that the mpn interface is irregular and hard to
* New functions for arbitrary precision floating point arithmetic. Names
begin with `mpf_'. Associated type mpf_t.
* New and improved mpz functions, including much faster GCD, fast exact
division (mpz_divexact), bit scan (mpz_scan0 and mpz_scan1), and number
theoretical functions like Jacobi (mpz_jacobi) and multiplicative inverse
* New variable types (mpz_t and mpq_t) are available that makes syntax of
mpz and mpq calls nicer (no need for & before variables). The MP_INT and
MP_RAT types are still available for compatibility.
* Uses GNU configure. This makes it possible to choose target architecture
and CPU variant, and to compile into a separate object directory.
* Carefully optimized assembly for important inner loops. Support for DEC
Alpha, Amd 29000, HPPA 1.0 and 1.1, Intel Pentium and generic x86, Intel
i960, Motorola MC68000, MC68020, MC88100, and MC88110, Motorola/IBM
PowerPC, National NS32000, IBM POWER, MIPS R3000, R4000, SPARCv7,
SuperSPARC, generic SPARCv8, and DEC VAX. Some support also for ARM,
Clipper, IBM ROMP (RT), and Pyramid AP/XP.
* Faster. Thanks to the assembler code, new algorithms, and general tuning.
In particular, the speed on machines without GCC is improved.
* Support for machines without alloca.
* Now under the LGPL.
* mpq assignment functions do not canonicalize their results.
* mpz division functions round differently.
* mpz mod functions now really compute mod.
* mpz_powm and mpz_powm_ui now really use mod for reduction.
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