vailable at `_mp_d', and secondly when `mpf_set_prec_raw' lowers `_mp_prec' it leaves `_mp_size' unchanged and so the size can be arbitrarily bigger than `_mp_prec'. Rounding All rounding is done on limb boundaries. Calculating `_mp_prec' limbs with the high non-zero will ensure the application requested minimum precision is obtained. The use of simple "trunc" rounding towards zero is efficient, since there's no need to examine extra limbs and increment or decrement. Bit Shifts Since the exponent is in limbs, there are no bit shifts in basic operations like `mpf_add' and `mpf_mul'. When differing exponents are encountered all that's needed is to adjust pointers to line up the relevant limbs. Of course `mpf_mul_2exp' and `mpf_div_2exp' will require bit shifts, but the choice is between an exponent in limbs which requires shifts there, or one in bits which requires them almost everywhere else. Use of `_mp_prec+1' Limbs The extra limb on `_mp_d' (`_mp_prec+1' rather than just `_mp_prec') helps when an `mpf' routine might get a carry from its operation. `mpf_add' for instance will do an `mpn_add' of `_mp_prec' limbs. If there's no carry then that's the result, but if there is a carry then it's stored in the extra limb of space and `_mp_size' becomes `_mp_prec+1'. Whenever `_mp_prec+1' limbs are held in a variable, the low limb is not needed for the intended precision, only the `_mp_prec' high limbs. But zeroing it out or moving the rest down is unnecessary. Subsequent routines reading the value will simply take the high limbs they need, and this will be `_mp_prec' if their target has that same precision. This is no more than a pointer adjustment, and must be checked anyway since the destination precision can be different from the sources. Copy functions like `mpf_set' will retain a full `_mp_prec+1' limbs if available. This ensures that a variable which has `_mp_size' equal to `_mp_prec+1' will get its full exact value copied. Strictly speaking this is unnecessary since only `_mp_prec' limbs are needed for the application's requested precision, but it's considered that an `mpf_set' from one variable into another of the same precision ought to produce an exact copy. Application Precisions `__GMPF_BITS_TO_PREC' converts an application requested precision to an `_mp_prec'. The value in bits is rounded up to a whole limb then an extra limb is added since the most significant limb of `_mp_d' is only non-zero and therefore might contain only one bit. `__GMPF_PREC_TO_BITS' does the reverse conversion, and removes the extra limb from `_mp_prec' before converting to bits. The net effect of reading back with `mpf_get_prec' is simply the precision rounded up to a multiple of `mp_bits_per_limb'. Note that the extra limb added here for the high only being non-zero is in addition to the extra limb allocated to `_mp_d'. For example with a 32-bit limb, an application request for 250 bits will be rounded up to 8 limbs, then an extra added for the high being only non-zero, giving an `_mp_prec' of 9. `_mp_d' then gets 10 limbs allocated. Reading back with `mpf_get_prec' will take `_mp_prec' subtract 1 limb and multiply by 32, giving 256 bits. Strictly speaking, the fact the high limb has at least one bit means that a float with, say, 3 limbs of 32-bits each will be holding at least 65 bits, but for the purposes of `mpf_t' it's considered simply to be 64 bits, a nice multiple of the limb size.  File: gmp.info, Node: Raw Output Internals, Next: C++ Interface Internals, Prev: Float Internals, Up: Internals 17.4 Raw Output Internals ========================= `mpz_out_raw' uses the following format. +------+------------------------+ | size | data bytes | +------+------------------------+ The size is 4 bytes written most significant byte first, being the number of subsequent data bytes, or the twos complement negative of that when a negative integer is represented. The data bytes are the absolute value of the integer, written most significant byte first. The most significant data byte is always non-zero, so the output is the same on all systems, irrespective of limb size. In GMP 1, leading zero bytes were written to pad the data bytes to a multiple of the limb size. `mpz_inp_raw' will still accept this, for compatibility. The use of "big endian" for both the size and data fields is deliberate, it makes the data easy to read in a hex dump of a file. Unfortunately it also means that the limb data must be reversed when reading or writing, so neither a big endian nor little endian system can just read and write `_mp_d'.  File: gmp.info, Node: C++ Interface Internals, Prev: Raw Output Internals, Up: Internals 17.5 C++ Interface Internals ============================ A system of expression templates is used to ensure something like `a=b+c' turns into a simple call to `mpz_add' etc. For `mpf_class' the scheme also ensures the precision of the final destination is used for any temporaries within a statement like `f=w*x+y*z'. These are important features which a naive implementation cannot provide. A simplified description of the scheme follows. The true scheme is complicated by the fact that expressions have different return types. For detailed information, refer to the source code. To perform an operation, say, addition, we first define a "function object" evaluating it, struct __gmp_binary_plus { static void eval(mpf_t f, mpf_t g, mpf_t h) { mpf_add(f, g, h); } }; And an "additive expression" object, __gmp_expr<__gmp_binary_expr > operator+(const mpf_class &f, const mpf_class &g) { return __gmp_expr <__gmp_binary_expr >(f, g); } The seemingly redundant `__gmp_expr<__gmp_binary_expr<...>>' is used to encapsulate any possible kind of expression into a single template type. In fact even `mpf_class' etc are `typedef' specializations of `__gmp_expr'. Next we define assignment of `__gmp_expr' to `mpf_class'. template mpf_class & mpf_class::operator=(const __gmp_expr &expr) { expr.eval(this->get_mpf_t(), this->precision()); return *this; } template void __gmp_expr<__gmp_binary_expr >::eval (mpf_t f, mp_bitcnt_t precision) { Op::eval(f, expr.val1.get_mpf_t(), expr.val2.get_mpf_t()); } where `expr.val1' and `expr.val2' are references to the expression's operands (here `expr' is the `__gmp_binary_expr' stored within the `__gmp_expr'). This way, the expression is actually evaluated only at the time of assignment, when the required precision (that of `f') is known. Furthermore the target `mpf_t' is now available, thus we can call `mpf_add' directly with `f' as the output argument. Compound expressions are handled by defining operators taking subexpressions as their arguments, like this: template __gmp_expr <__gmp_binary_expr<__gmp_expr, __gmp_expr, __gmp_binary_plus> > operator+(const __gmp_expr &expr1, const __gmp_expr &expr2) { return __gmp_expr <__gmp_binary_expr<__gmp_expr, __gmp_expr, __gmp_binary_plus> > (expr1, expr2); } And the corresponding specializations of `__gmp_expr::eval': template void __gmp_expr <__gmp_binary_expr<__gmp_expr, __gmp_expr, Op> >::eval (mpf_t f, mp_bitcnt_t precision) { // declare two temporaries mpf_class temp1(expr.val1, precision), temp2(expr.val2, precision); Op::eval(f, temp1.get_mpf_t(), temp2.get_mpf_t()); } The expression is thus recursively evaluated to any level of complexity and all subexpressions are evaluated to the precision of `f'.  File: gmp.info, Node: Contributors, Next: References, Prev: Internals, Up: Top Appendix A Contributors *********************** Torbjo"rn Granlund wrote the original GMP library and is still the main developer. Code not explicitly attributed to others, was contributed by Torbjo"rn. Several other individuals and organizations have contributed GMP. Here is a list in chronological order on first contribution: Gunnar Sjo"din and Hans Riesel helped with mathematical problems in early versions of the library. Richard Stallman helped with the interface design and revised the first version of this manual. Brian Beuning and Doug Lea helped with testing of early versions of the library and made creative suggestions. John Amanatides of York University in Canada contributed the function `mpz_probab_prime_p'. Paul Zimmermann wrote the REDC-based mpz_powm code, the Scho"nhage-Strassen FFT multiply code, and the Karatsuba square root code. He also improved the Toom3 code for GMP 4.2. Paul sparked the development of GMP 2, with his comparisons between bignum packages. The ECMNET project Paul is organizing was a driving force behind many of the optimizations in GMP 3. Paul also wrote the new GMP 4.3 nth root code (with Torbjo"rn). Ken Weber (Kent State University, Universidade Federal do Rio Grande do Sul) contributed now defunct versions of `mpz_gcd', `mpz_divexact', `mpn_gcd', and `mpn_bdivmod', partially supported by CNPq (Brazil) grant 301314194-2. Per Bothner of Cygnus Support helped to set up GMP to use Cygnus' configure. He has also made valuable suggestions and tested numerous intermediary releases. Joachim Hollman was involved in the design of the `mpf' interface, and in the `mpz' design revisions for version 2. Bennet Yee contributed the initial versions of `mpz_jacobi' and `mpz_legendre'. Andreas Schwab contributed the files `mpn/m68k/lshift.S' and `mpn/m68k/rshift.S' (now in `.asm' form). Robert Harley of Inria, France and David Seal of ARM, England, suggested clever improvements for population count. Robert also wrote highly optimized Karatsuba and 3-way Toom multiplication functions for GMP 3, and contributed the ARM assembly code. Torsten Ekedahl of the Mathematical department of Stockholm University provided significant inspiration during several phases of the GMP development. His mathematical expertise helped improve several algorithms. Linus Nordberg wrote the new configure system based on autoconf and implemented the new random functions. Kevin Ryde worked on a large number of things: optimized x86 code, m4 asm macros, parameter tuning, speed measuring, the configure system, function inlining, divisibility tests, bit scanning, Jacobi symbols, Fibonacci and Lucas number functions, printf and scanf functions, perl interface, demo expression parser, the algorithms chapter in the manual, `gmpasm-mode.el', and various miscellaneous improvements elsewhere. Kent Boortz made the Mac OS 9 port. Steve Root helped write the optimized alpha 21264 assembly code. Gerardo Ballabio wrote the `gmpxx.h' C++ class interface and the C++ `istream' input routines. Jason Moxham rewrote `mpz_fac_ui'. Pedro Gimeno implemented the Mersenne Twister and made other random number improvements. Niels Mo"ller wrote the sub-quadratic GCD and extended GCD code, the quadratic Hensel division code, and (with Torbjo"rn) the new divide and conquer division code for GMP 4.3. Niels also helped implement the new Toom multiply code for GMP 4.3 and implemented helper functions to simplify Toom evaluations for GMP 5.0. He wrote the original version of mpn_mulmod_bnm1. Alberto Zanoni and Marco Bodrato suggested the unbalanced multiply strategy, and found the optimal strategies for evaluation and interpolation in Toom multiplication. Marco Bodrato helped implement the new Toom multiply code for GMP 4.3 and implemented most of the new Toom multiply and squaring code for 5.0. He is the main author of the current mpn_mulmod_bnm1 and mpn_mullo_n. Marco also wrote the functions mpn_invert and mpn_invertappr. David Harvey suggested the internal function `mpn_bdiv_dbm1', implementing division relevant to Toom multiplication. He also worked on fast assembly sequences, in particular on a fast AMD64 `mpn_mul_basecase'. Martin Boij wrote `mpn_perfect_power_p'. (This list is chronological, not ordered after significance. If you have contributed to GMP but are not listed above, please tell about the omission!) The development of floating point functions of GNU MP 2, were supported in part by the ESPRIT-BRA (Basic Research Activities) 6846 project POSSO (POlynomial System SOlving). The development of GMP 2, 3, and 4 was supported in part by the IDA Center for Computing Sciences. Thanks go to Hans Thorsen for donating an SGI system for the GMP test system environment.  File: gmp.info, Node: References, Next: GNU Free Documentation License, Prev: Contributors, Up: Top Appendix B References ********************* B.1 Books ========= * Jonathan M. Borwein and Peter B. Borwein, "Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity", Wiley, 1998. * Richard Crandall and Carl Pomerance, "Prime Numbers: A Computational Perspective", 2nd edition, Springer-Verlag, 2005. `http://math.dartmouth.edu/~carlp/' * Henri Cohen, "A Course in Computational Algebraic Number Theory", Graduate Texts in Mathematics number 138, Springer-Verlag, 1993. `http://www.math.u-bordeaux.fr/~cohen/' * Donald E. Knuth, "The Art of Computer Programming", volume 2, "Seminumerical Algorithms", 3rd edition, Addison-Wesley, 1998. `http://www-cs-faculty.stanford.edu/~knuth/taocp.html' * John D. Lipson, "Elements of Algebra and Algebraic Computing", The Benjamin Cummings Publishing Company Inc, 1981. * Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, "Handbook of Applied Cryptography", `http://www.cacr.math.uwaterloo.ca/hac/' * Richard M. Stallman and the GCC Developer Community, "Using the GNU Compiler Collection", Free Software Foundation, 2008, available online `http://gcc.gnu.org/onlinedocs/', and in the GCC package `ftp://ftp.gnu.org/gnu/gcc/' B.2 Papers ========== * Yves Bertot, Nicolas Magaud and Paul Zimmermann, "A Proof of GMP Square Root", Journal of Automated Reasoning, volume 29, 2002, pp. 225-252. Also available online as INRIA Research Report 4475, June 2001, `http://www.inria.fr/rrrt/rr-4475.html' * Christoph Burnikel and Joachim Ziegler, "Fast Recursive Division", Max-Planck-Institut fuer Informatik Research Report MPI-I-98-1-022, `http://data.mpi-sb.mpg.de/internet/reports.nsf/NumberView/1998-1-022' * Torbjo"rn Granlund and Peter L. Montgomery, "Division by Invariant Integers using Multiplication", in Proceedings of the SIGPLAN PLDI'94 Conference, June 1994. Also available `ftp://ftp.cwi.nl/pub/pmontgom/divcnst.psa4.gz' (and .psl.gz). * Niels Mo"ller and Torbjo"rn Granlund, "Improved division by invariant integers", to appear. * Torbjo"rn Granlund and Niels Mo"ller, "Division of integers large and small", to appear. * Tudor Jebelean, "An algorithm for exact division", Journal of Symbolic Computation, volume 15, 1993, pp. 169-180. Research report version available `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-35.ps.gz' * Tudor Jebelean, "Exact Division with Karatsuba Complexity - Extended Abstract", RISC-Linz technical report 96-31, `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1996/96-31.ps.gz' * Tudor Jebelean, "Practical Integer Division with Karatsuba Complexity", ISSAC 97, pp. 339-341. Technical report available `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1996/96-29.ps.gz' * Tudor Jebelean, "A Generalization of the Binary GCD Algorithm", ISSAC 93, pp. 111-116. Technical report version available `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1993/93-01.ps.gz' * Tudor Jebelean, "A Double-Digit Lehmer-Euclid Algorithm for Finding the GCD of Long Integers", Journal of Symbolic Computation, volume 19, 1995, pp. 145-157. Technical report version also available `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-69.ps.gz' * Werner Krandick and Tudor Jebelean, "Bidirectional Exact Integer Division", Journal of Symbolic Computation, volume 21, 1996, pp. 441-455. Early technical report version also available `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1994/94-50.ps.gz' * Makoto Matsumoto and Takuji Nishimura, "Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator", ACM Transactions on Modelling and Computer Simulation, volume 8, January 1998, pp. 3-30. Available online `http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.ps.gz' (or .pdf) * R. Moenck and A. Borodin, "Fast Modular Transforms via Division", Proceedings of the 13th Annual IEEE Symposium on Switching and Automata Theory, October 1972, pp. 90-96. Reprinted as "Fast Modular Transforms", Journal of Computer and System Sciences, volume 8, number 3, June 1974, pp. 366-386. * Niels Mo"ller, "On Scho"nhage's algorithm and subquadratic integer GCD computation", in Mathematics of Computation, volume 77, January 2008, pp. 589-607. * Peter L. Montgomery, "Modular Multiplication Without Trial Division", in Mathematics of Computation, volume 44, number 170, April 1985. * Arnold Scho"nhage and Volker Strassen, "Schnelle Multiplikation grosser Zahlen", Computing 7, 1971, pp. 281-292. * Kenneth Weber, "The accelerated integer GCD algorithm", ACM Transactions on Mathematical Software, volume 21, number 1, March 1995, pp. 111-122. * Paul Zimmermann, "Karatsuba Square Root", INRIA Research Report 3805, November 1999, `http://www.inria.fr/rrrt/rr-3805.html' * Paul Zimmermann, "A Proof of GMP Fast Division and Square Root Implementations", `http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz' * Dan Zuras, "On Squaring and Multiplying Large Integers", ARITH-11: IEEE Symposium on Computer Arithmetic, 1993, pp. 260 to 271. Reprinted as "More on Multiplying and Squaring Large Integers", IEEE Transactions on Computers, volume 43, number 8, August 1994, pp. 899-908.  File: gmp.info, Node: GNU Free Documentation License, Next: Concept Index, Prev: References, Up: Top Appendix C GNU Free Documentation License ***************************************** Version 1.3, 3 November 2008 Copyright (C) 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc. `http://fsf.org/' Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 0. PREAMBLE The purpose of this License is to make a manual, textbook, or other functional and useful document "free" in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially. Secondarily, this License preserves for the author and publisher a way to get credit for their work, while not being considered responsible for modifications made by others. 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The operator of an MMC Site may republish an MMC contained in the site under CC-BY-SA on the same site at any time before August 1, 2009, provided the MMC is eligible for relicensing. ADDENDUM: How to use this License for your documents ==================================================== To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page: Copyright (C) YEAR YOUR NAME. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled ``GNU Free Documentation License''. If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the "with...Texts." line with this: with the Invariant Sections being LIST THEIR TITLES, with the Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST. If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation. If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.  File: gmp.info, Node: Concept Index, Next: Function Index, Prev: GNU Free Documentation License, Up: Top Concept Index ************* [index] * Menu: * #include: Headers and Libraries. (line 6) * --build: Build Options. (line 52) * --disable-fft: Build Options. (line 317) * --disable-shared: Build Options. (line 45) * --disable-static: Build Options. (line 45) * --enable-alloca: Build Options. (line 278) * --enable-assert: Build Options. (line 327) * --enable-cxx: Build Options. (line 230) * --enable-fat: Build Options. (line 164) * --enable-mpbsd: Build Options. (line 322) * --enable-profiling <1>: Profiling. (line 6) * --enable-profiling: Build Options. (line 331) * --exec-prefix: Build Options. (line 32) * --host: Build Options. (line 66) * --prefix: Build Options. (line 32) * -finstrument-functions: Profiling. (line 66) * 2exp functions: Efficiency. (line 43) * 68000: Notes for Particular Systems. (line 80) * 80x86: Notes for Particular Systems. (line 126) * ABI <1>: Build Options. (line 171) * ABI: ABI and ISA. (line 6) * About this manual: Introduction to GMP. (line 58) * AC_CHECK_LIB: Autoconf. (line 11) * AIX <1>: ABI and ISA. (line 184) * AIX <2>: Notes for Particular Systems. (line 7) * AIX: ABI and ISA. (line 169) * Algorithms: Algorithms. (line 6) * alloca: Build Options. (line 278) * Allocation of memory: Custom Allocation. (line 6) * AMD64: ABI and ISA. (line 44) * Anonymous FTP of latest version: Introduction to GMP. (line 38) * Application Binary Interface: ABI and ISA. (line 6) * Arithmetic functions <1>: Float Arithmetic. (line 6) * Arithmetic functions <2>: Integer Arithmetic. (line 6) * Arithmetic functions: Rational Arithmetic. (line 6) * ARM: Notes for Particular Systems. (line 20) * Assembly cache handling: Assembly Cache Handling. (line 6) * Assembly carry propagation: Assembly Carry Propagation. (line 6) * Assembly code organisation: Assembly Code Organisation. (line 6) * Assembly coding: Assembly Coding. (line 6) * Assembly floating Point: Assembly Floating Point. (line 6) * Assembly loop unrolling: Assembly Loop Unrolling. (line 6) * Assembly SIMD: Assembly SIMD Instructions. (line 6) * Assembly software pipelining: Assembly Software Pipelining. (line 6) * Assembly writing guide: Assembly Writing Guide. (line 6) * Assertion checking <1>: Debugging. (line 79) * Assertion checking: Build Options. (line 327) * Assignment functions <1>: Assigning Floats. (line 6) * Assignment functions <2>: Initializing Rationals. (line 6) * Assignment functions <3>: Simultaneous Integer Init & Assign. (line 6) * Assignment functions <4>: Simultaneous Float Init & Assign. (line 6) * Assignment functions: Assigning Integers. (line 6) * Autoconf: Autoconf. (line 6) * Basics: GMP Basics. (line 6) * Berkeley MP compatible functions <1>: Build Options. (line 322) * Berkeley MP compatible functions: BSD Compatible Functions. (line 6) * Binomial coefficient algorithm: Binomial Coefficients Algorithm. (line 6) * Binomial coefficient functions: Number Theoretic Functions. (line 100) * Binutils strip: Known Build Problems. (line 28) * Bit manipulation functions: Integer Logic and Bit Fiddling. (line 6) * Bit scanning functions: Integer Logic and Bit Fiddling. (line 38) * Bit shift left: Integer Arithmetic. (line 35) * Bit shift right: Integer Division. (line 53) * Bits per limb: Useful Macros and Constants. (line 7) * BSD MP compatible functions <1>: Build Options. (line 322) * BSD MP compatible functions: BSD Compatible Functions. (line 6) * Bug reporting: Reporting Bugs. (line 6) * Build directory: Build Options. (line 19) * Build notes for binary packaging: Notes for Package Builds. (line 6) * Build notes for particular systems: Notes for Particular Systems. (line 6) * Build options: Build Options. (line 6) * Build problems known: Known Build Problems. (line 6) * Build system: Build Options. (line 52) * Building GMP: Installing GMP. (line 6) * Bus error: Debugging. (line 7) * C compiler: Build Options. (line 182) * C++ compiler: Build Options. (line 254) * C++ interface: C++ Class Interface. (line 6) * C++ interface internals: C++ Interface Internals. (line 6) * C++ istream input: C++ Formatted Input. (line 6) * C++ ostream output: C++ Formatted Output. (line 6) * C++ support: Build Options. (line 230) * CC: Build Options. (line 182) * CC_FOR_BUILD: Build Options. (line 217) * CFLAGS: Build Options. (line 182) * Checker: Debugging. (line 115) * checkergcc: Debugging. (line 122) * Code organisation: Assembly Code Organisation. (line 6) * Compaq C++: Notes for Particular Systems. (line 25) * Comparison functions <1>: Integer Comparisons. (line 6) * Comparison functions <2>: Comparing Rationals. (line 6) * Comparison functions: Float Comparison. (line 6) * Compatibility with older versions: Compatibility with older versions. (line 6) * Conditions for copying GNU MP: Copying. (line 6) * Configuring GMP: Installing GMP. (line 6) * Congruence algorithm: Exact Remainder. (line 29) * Congruence functions: Integer Division. (line 124) * Constants: Useful Macros and Constants. (line 6) * Contributors: Contributors. (line 6) * Conventions for parameters: Parameter Conventions. (line 6) * Conventions for variables: Variable Conventions. (line 6) * Conversion functions <1>: Converting Integers. (line 6) * Conversion functions <2>: Converting Floats. (line 6) * Conversion functions: Rational Conversions. (line 6) * Copying conditions: Copying. (line 6) * CPPFLAGS: Build Options. (line 208) * CPU types <1>: Introduction to GMP. (line 24) * CPU types: Build Options. (line 108) * Cross compiling: Build Options. (line 66) * Custom allocation: Custom Allocation. (line 6) * CXX: Build Options. (line 254) * CXXFLAGS: Build Options. (line 254) * Cygwin: Notes for Particular Systems. (line 43) * Darwin: Known Build Problems. (line 51) * Debugging: Debugging. (line 6) * Demonstration programs: Demonstration Programs. (line 6) * Digits in an integer: Miscellaneous Integer Functions. (line 23) * Divisibility algorithm: Exact Remainder. (line 29) * Divisibility functions: Integer Division. (line 124) * Divisibility testing: Efficiency. (line 91) * Division algorithms: Division Algorithms. (line 6) * Division functions <1>: Rational Arithmetic. (line 22) * Division functions <2>: Integer Division. (line 6) * Division functions: Float Arithmetic. (line 33) * DJGPP <1>: Notes for Particular Systems. (line 43) * DJGPP: Known Build Problems. (line 18) * DLLs: Notes for Particular Systems. (line 56) * DocBook: Build Options. (line 354) * Documentation formats: Build Options. (line 347) * Documentation license: GNU Free Documentation License. (line 6) * DVI: Build Options. (line 350) * Efficiency: Efficiency. (line 6) * Emacs: Emacs. (line 6) * Exact division functions: Integer Division. (line 102) * Exact remainder: Exact Remainder. (line 6) * Example programs: Demonstration Programs. (line 6) * Exec prefix: Build Options. (line 32) * Execution profiling <1>: Profiling. (line 6) * Execution profiling: Build Options. (line 331) * Exponentiation functions <1>: Integer Exponentiation. (line 6) * Exponentiation functions: Float Arithmetic. (line 41) * Export: Integer Import and Export. (line 45) * Expression parsing demo: Demonstration Programs. (line 18) * Extended GCD: Number Theoretic Functions. (line 45) * Factor removal functions: Number Theoretic Functions. (line 90) * Factorial algorithm: Factorial Algorithm. (line 6) * Factorial functions: Number Theoretic Functions. (line 95) * Factorization demo: Demonstration Programs. (line 25) * Fast Fourier Transform: FFT Multiplication. (line 6) * Fat binary: Build Options. (line 164) * FFT multiplication <1>: FFT Multiplication. (line 6) * FFT multiplication: Build Options. (line 317) * Fibonacci number algorithm: Fibonacci Numbers Algorithm. (line 6) * Fibonacci sequence functions: Number Theoretic Functions. (line 108) * Float arithmetic functions: Float Arithmetic. (line 6) * Float assignment functions <1>: Simultaneous Float Init & Assign. (line 6) * Float assignment functions: Assigning Floats. (line 6) * Float comparison functions: Float Comparison. (line 6) * Float conversion functions: Converting Floats. (line 6) * Float functions: Floating-point Functions. (line 6) * Float initialization functions <1>: Simultaneous Float Init & Assign. (line 6) * Float initialization functions: Initializing Floats. (line 6) * Float input and output functions: I/O of Floats. (line 6) * Float internals: Float Internals. (line 6) * Float miscellaneous functions: Miscellaneous Float Functions. (line 6) * Float random number functions: Miscellaneous Float Functions. (line 27) * Float rounding functions: Miscellaneous Float Functions. (line 9) * Float sign tests: Float Comparison. (line 33) * Floating point mode: Notes for Particular Systems. (line 34) * Floating-point functions: Floating-point Functions. (line 6) * Floating-point number: Nomenclature and Types. (line 21) * fnccheck: Profiling. (line 77) * Formatted input: Formatted Input. (line 6) * Formatted output: Formatted Output. (line 6) * Free Documentation License: GNU Free Documentation License. (line 6) * frexp <1>: Converting Floats. (line 23) * frexp: Converting Integers. (line 42) * FTP of latest version: Introduction to GMP. (line 38) * Function classes: Function Classes. (line 6) * FunctionCheck: Profiling. (line 77) * GCC Checker: Debugging. (line 115) * GCD algorithms: Greatest Common Divisor Algorithms. (line 6) * GCD extended: Number Theoretic Functions. (line 45) * GCD functions: Number Theoretic Functions. (line 30) * GDB: Debugging. (line 58) * Generic C: Build Options. (line 153) * GMP Perl module: Demonstration Programs. (line 35) * GMP version number: Useful Macros and Constants. (line 12) * gmp.h: Headers and Libraries. (line 6) * gmpxx.h: C++ Interface General. (line 8) * GNU Debugger: Debugging. (line 58) * GNU Free Documentation License: GNU Free Documentation License. (line 6) * GNU strip: Known Build Problems. (line 28) * gprof: Profiling. (line 41) * Greatest common divisor algorithms: Greatest Common Divisor Algorithms. (line 6) * Greatest common divisor functions: Number Theoretic Functions. (line 30) * Hardware floating point mode: Notes for Particular Systems. (line 34) * Headers: Headers and Libraries. (line 6) * Heap problems: Debugging. (line 24) * Home page: Introduction to GMP. (line 34) * Host system: Build Options. (line 66) * HP-UX: ABI and ISA. (line 107) * HPPA: ABI and ISA. (line 68) * I/O functions <1>: I/O of Integers. (line 6) * I/O functions <2>: I/O of Rationals. (line 6) * I/O functions: I/O of Floats. (line 6) * i386: Notes for Particular Systems. (line 126) * IA-64: ABI and ISA. (line 107) * Import: Integer Import and Export. (line 11) * In-place operations: Efficiency. (line 57) * Include files: Headers and Libraries. (line 6) * info-lookup-symbol: Emacs. (line 6) * Initialization functions <1>: Initializing Integers. (line 6) * Initialization functions <2>: Initializing Rationals. (line 6) * Initialization functions <3>: Random State Initialization.