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TOP (GNU MP 6.2.1)
How to install and use the GNU multiple precision arithmetic library,version 6.2.1.
INITIALIZING INTEGERS (GNU MP 6.2.1) Initialize a NULL-terminated list of mpz_t variables, and set their values to 0. Function: void mpz_init2 (mpz_t x, mp_bitcnt_t n) Initialize x, with space for n -bit numbers, and set its value to 0. Calling this function instead of mpz_init or mpz_inits is never necessary; reallocation is handled automatically by GMP when needed.While n
CONVERTING INTEGERS (GNU MP 6.2.1) 5.4 Conversion Functions. This section describes functions for converting GMP integers to standard C types. Functions for converting to GMP integers are described in Assigning Integers and I/O of Integers.. Function: unsigned long int mpz_get_ui (const mpz_t op) Return the value of op as an unsigned long.. If op is too big to fit an unsigned long then just the least significant bits that do EXACT DIVISION (GNU MP 6.2.1) 15.2.5 Exact Division. A so-called exact division is when the dividend is known to be an exact multiple of the divisor. Jebelean’s exact division algorithm uses this knowledge to make some significant optimizations (see References).. The idea can be illustrated INTEGER COMPARISONS (GNU MP 6.2.1) 5.10 Comparison Functions. Compare op1 and op2. Return a positive value if op1 > op2, zero if op1 = op2, or a negative value if op1 < op2 . mpz_cmp_ui and mpz_cmp_si are macros and will evaluate their arguments more than once. mpz_cmp_d can be called with an infinity, but results are undefined for a NaN. Compare the absolute values ofop1 and op2.
PRIME TESTING ALGORITHM (GNU MP 6.2.1) 15.7.1 Prime Testing. The primality testing in mpz_probab_prime_p (see Number Theoretic Functions) first does some trial division by small factors and then uses the Miller-Rabin probabilistic primality testing algorithm, as described in Knuth section 4.5.4 algorithm P (see References).. For an odd input n, and with n = q*2^k+1 where q is odd, this algorithm selects a random base x and tests C++ INTERFACE INTEGERS (GNU MP 6.2.1) 12.2 C++ Interface Integers Function: mpz_class::mpz_class (type n) Construct an mpz_class.All the standard C++ types may be used, except long long and long double, and all the GMP C++ classes can be used, although conversions from mpq_class and mpf_class are explicit.Any necessary conversion follows the corresponding C function, for example double follows mpz_set_d (see Assigning Integers). SYSTEM EMULATION USING QEMU The PC emulation works well and doesn't suffer from major incompatibility problems from qemu release to qemu release. It is really simple to get started. Create 4GiB disk image: dd if=/dev/zero of=disk.img bs=1048576 count=4096. Install: qemu-system-i386 -hda disk.img -cdrom your-favourite-os-install.iso -boot d. Boot theinstalled system:
GMPLIB.ORG - THE GNU MP BIGNUM LIBRARY6.2.0 HTML6.2.0 PDFGMP-6.2.0.TAR.LZRELEASE NOTESDEVELOPERS' CORNERRESULTS The GMP computers are maintained by a single person on a volunteer basis. The ongoing Intel CPU bug debacle with Meltdown, Spectre, Foreshadow, MDS, the jCC/cache-line bug, Fallout, LVI, Portsmash, etc, etc, and the ME backdoor is making the main GMP server far from as secure as we'd like it to be. The system which runs this web server as well as mail server, mailing list server, firewall, etc INTRODUCTION TO GMP (GNU MP 6.2.1) The proper place for bug reports is gmp-bugs@gmplib.org.See Reporting Bugs for information about reporting bugs. 1.1 How to use this Manual. Everyone should read GMP Basics.If you need to install the library yourself, then read Installing GMP.If you have a system with multiple ABIs, then read ABI and ISA, for the compiler options that must be used on applications.TOP (GNU MP 6.2.1)
How to install and use the GNU multiple precision arithmetic library,version 6.2.1.
INITIALIZING INTEGERS (GNU MP 6.2.1) Initialize a NULL-terminated list of mpz_t variables, and set their values to 0. Function: void mpz_init2 (mpz_t x, mp_bitcnt_t n) Initialize x, with space for n -bit numbers, and set its value to 0. Calling this function instead of mpz_init or mpz_inits is never necessary; reallocation is handled automatically by GMP when needed.While n
CONVERTING INTEGERS (GNU MP 6.2.1) 5.4 Conversion Functions. This section describes functions for converting GMP integers to standard C types. Functions for converting to GMP integers are described in Assigning Integers and I/O of Integers.. Function: unsigned long int mpz_get_ui (const mpz_t op) Return the value of op as an unsigned long.. If op is too big to fit an unsigned long then just the least significant bits that do EXACT DIVISION (GNU MP 6.2.1) 15.2.5 Exact Division. A so-called exact division is when the dividend is known to be an exact multiple of the divisor. Jebelean’s exact division algorithm uses this knowledge to make some significant optimizations (see References).. The idea can be illustrated INTEGER COMPARISONS (GNU MP 6.2.1) 5.10 Comparison Functions. Compare op1 and op2. Return a positive value if op1 > op2, zero if op1 = op2, or a negative value if op1 < op2 . mpz_cmp_ui and mpz_cmp_si are macros and will evaluate their arguments more than once. mpz_cmp_d can be called with an infinity, but results are undefined for a NaN. Compare the absolute values ofop1 and op2.
PRIME TESTING ALGORITHM (GNU MP 6.2.1) 15.7.1 Prime Testing. The primality testing in mpz_probab_prime_p (see Number Theoretic Functions) first does some trial division by small factors and then uses the Miller-Rabin probabilistic primality testing algorithm, as described in Knuth section 4.5.4 algorithm P (see References).. For an odd input n, and with n = q*2^k+1 where q is odd, this algorithm selects a random base x and tests C++ INTERFACE INTEGERS (GNU MP 6.2.1) 12.2 C++ Interface Integers Function: mpz_class::mpz_class (type n) Construct an mpz_class.All the standard C++ types may be used, except long long and long double, and all the GMP C++ classes can be used, although conversions from mpq_class and mpf_class are explicit.Any necessary conversion follows the corresponding C function, for example double follows mpz_set_d (see Assigning Integers). SYSTEM EMULATION USING QEMU The PC emulation works well and doesn't suffer from major incompatibility problems from qemu release to qemu release. It is really simple to get started. Create 4GiB disk image: dd if=/dev/zero of=disk.img bs=1048576 count=4096. Install: qemu-system-i386 -hda disk.img -cdrom your-favourite-os-install.iso -boot d. Boot theinstalled system:
INTRODUCTION TO GMP (GNU MP 6.2.1) The proper place for bug reports is gmp-bugs@gmplib.org.See Reporting Bugs for information about reporting bugs. 1.1 How to use this Manual. Everyone should read GMP Basics.If you need to install the library yourself, then read Installing GMP.If you have a system with multiple ABIs, then read ABI and ISA, for the compiler options that must be used on applications.TOP (GNU MP 6.2.1)
How to install and use the GNU multiple precision arithmetic library,version 6.2.1.
BUILD OPTIONS (GNU MP 6.2.1) Build Options (GNU MP 6.2.1) Tools. ‘ configure ’ requires various Unix-like tools. See Notes for Particular Systems, for some options on non-Unix systems. It might be possible to build without the help of ‘ configure ’, certainly all the code is there, but unfortunately you’ll be on your own. Build Directory. FORMATTED OUTPUT STRINGS (GNU MP 6.2.1) ‘o’, ‘x’ and ‘X’ are unsigned for the standard C types, but for types ‘Z’, ‘Q’ and ‘N’ they are signed. ‘u’ is not meaningful for ‘Z’, ‘Q’ and ‘N’. ‘M’ is a proxy for the C library ‘l’ or ‘L’, according to the size of mp_limb_t.Unsigned conversions will be usual, but a signed conversion can be used and will interpret the value as a twos EXACT DIVISION (GNU MP 6.2.1) 15.2.5 Exact Division. A so-called exact division is when the dividend is known to be an exact multiple of the divisor. Jebelean’s exact division algorithm uses this knowledge to make some significant optimizations (see References).. The idea can be illustrated INTEGER DIVISION (GNU MP 6.2.1) Function: void mpz_tdiv_r_2exp (mpz_t r, const mpz_t n, mp_bitcnt_t b) Divide n by d, forming a quotient q and/or remainder r. For the 2exp functions, d=2^b . The rounding is in three styles, each suiting different applications. cdiv rounds q up towards +infinity, and r will have the opposite sign to d. CONCEPT INDEX (GNU MP 6.2.1) How to install and use the GNU multiple precision arithmetic library,version 6.2.1.
RANDOM STATE INITIALIZATION (GNU MP 6.2.1) This algorithm is fast and has good randomness properties. Function: void gmp_randinit_lc_2exp (gmp_randstate_t state, const mpz_t a, unsigned long c, mp_bitcnt_t m2exp) Initialize state with a linear congruential algorithm X = (a*X + c) mod 2^m2exp . The low bits of X in this algorithm are not very random. The least significant bit willhave a
C++ INTERFACE RATIONALS (GNU MP 6.2.1) 12.3 C++ Interface Rationals. In all the following constructors, if a fraction is given then it should be in canonical form, or if not then mpq_class::canonicalize called.. Function: mpq_class::mpq_class (type op) Function: mpq_class::mpq_class (integer num, integer den) Construct an mpq_class.The initial value can be a single value of any type (conversion from mpf_class is explicit), or a C++ INTERFACE FLOATS (GNU MP 6.2.1) Function: explicit mpf_class::mpf_class (const mpf_t f) Function: mpf_class::mpf_class (const mpf_t f, mp_bitcnt_t prec) Construct an mpf_class from an mpf_t.The value in f is copied into the new mpf_class, there won’t be any permanent association between it and f.. If prec is given, the initial precision is that value, in bits. If prec is not given, then the initial precision is that of f. GMPLIB.ORG - THE GNU MP BIGNUM LIBRARY6.2.0 HTML6.2.0 PDFGMP-6.2.0.TAR.LZRELEASE NOTESDEVELOPERS' CORNERRESULTS The GMP computers are maintained by a single person on a volunteer basis. The ongoing Intel CPU bug debacle with Meltdown, Spectre, Foreshadow, MDS, the jCC/cache-line bug, Fallout, LVI, Portsmash, etc, etc, and the ME backdoor is making the main GMP server far from as secure as we'd like it to be. The system which runs this web server as well as mail server, mailing list server, firewall, etc INTEGER FUNCTIONS (GNU MP 6.2.1) 5 Integer Functions. This chapter describes the GMP functions for performing integer arithmetic. These functions start with the prefix mpz_ . GMP integers are stored in objects of type mpz_t . • Initializing Integers. • Assigning Integers. • Simultaneous Integer Init & Assign. BUILD OPTIONS (GNU MP 6.2.1) Build Options (GNU MP 6.2.1) Tools. ‘ configure ’ requires various Unix-like tools. See Notes for Particular Systems, for some options on non-Unix systems. It might be possible to build without the help of ‘ configure ’, certainly all the code is there, but unfortunately you’ll be on your own. Build Directory. INITIALIZING INTEGERS (GNU MP 6.2.1) Initialize a NULL-terminated list of mpz_t variables, and set their values to 0. Function: void mpz_init2 (mpz_t x, mp_bitcnt_t n) Initialize x, with space for n -bit numbers, and set its value to 0. Calling this function instead of mpz_init or mpz_inits is never necessary; reallocation is handled automatically by GMP when needed.While n
INTEGER COMPARISONS (GNU MP 6.2.1) 5.10 Comparison Functions. Compare op1 and op2. Return a positive value if op1 > op2, zero if op1 = op2, or a negative value if op1 < op2 . mpz_cmp_ui and mpz_cmp_si are macros and will evaluate their arguments more than once. mpz_cmp_d can be called with an infinity, but results are undefined for a NaN. Compare the absolute values ofop1 and op2.
REPORTING BUGS (GNU MP 6.2.1) 4 Reporting Bugs. If you think you have found a bug in the GMP library, please investigate it and report it. We have made this library available to you, and it is not too much to ask you to reportthe bugs you find.
C++ INTERFACE INTERNALS (GNU MP 6.2.1) 16.5 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 implementationcannot provide.
CUSTOM ALLOCATION (GNU MP 6.2.1) How to install and use the GNU multiple precision arithmetic library,version 6.2.1.
SYSTEM EMULATION USING QEMU The PC emulation works well and doesn't suffer from major incompatibility problems from qemu release to qemu release. It is really simple to get started. Create 4GiB disk image: dd if=/dev/zero of=disk.img bs=1048576 count=4096. Install: qemu-system-i386 -hda disk.img -cdrom your-favourite-os-install.iso -boot d. Boot theinstalled system:
ELIMINATING BRANCHES USING A SUPEROPTIMIZER AND THE GNU C the sign bit into the entire word (thus yielding –1 ifais negative, and 0 ifais greater than or equal to 0) and then add 1 to get the desired result. The difference between sequence two and three is GMPLIB.ORG - THE GNU MP BIGNUM LIBRARY6.2.0 HTML6.2.0 PDFGMP-6.2.0.TAR.LZRELEASE NOTESDEVELOPERS' CORNERRESULTS The GMP computers are maintained by a single person on a volunteer basis. The ongoing Intel CPU bug debacle with Meltdown, Spectre, Foreshadow, MDS, the jCC/cache-line bug, Fallout, LVI, Portsmash, etc, etc, and the ME backdoor is making the main GMP server far from as secure as we'd like it to be. The system which runs this web server as well as mail server, mailing list server, firewall, etc INTEGER FUNCTIONS (GNU MP 6.2.1) 5 Integer Functions. This chapter describes the GMP functions for performing integer arithmetic. These functions start with the prefix mpz_ . GMP integers are stored in objects of type mpz_t . • Initializing Integers. • Assigning Integers. • Simultaneous Integer Init & Assign. BUILD OPTIONS (GNU MP 6.2.1) Build Options (GNU MP 6.2.1) Tools. ‘ configure ’ requires various Unix-like tools. See Notes for Particular Systems, for some options on non-Unix systems. It might be possible to build without the help of ‘ configure ’, certainly all the code is there, but unfortunately you’ll be on your own. Build Directory. INITIALIZING INTEGERS (GNU MP 6.2.1) Initialize a NULL-terminated list of mpz_t variables, and set their values to 0. Function: void mpz_init2 (mpz_t x, mp_bitcnt_t n) Initialize x, with space for n -bit numbers, and set its value to 0. Calling this function instead of mpz_init or mpz_inits is never necessary; reallocation is handled automatically by GMP when needed.While n
INTEGER COMPARISONS (GNU MP 6.2.1) 5.10 Comparison Functions. Compare op1 and op2. Return a positive value if op1 > op2, zero if op1 = op2, or a negative value if op1 < op2 . mpz_cmp_ui and mpz_cmp_si are macros and will evaluate their arguments more than once. mpz_cmp_d can be called with an infinity, but results are undefined for a NaN. Compare the absolute values ofop1 and op2.
REPORTING BUGS (GNU MP 6.2.1) 4 Reporting Bugs. If you think you have found a bug in the GMP library, please investigate it and report it. We have made this library available to you, and it is not too much to ask you to reportthe bugs you find.
C++ INTERFACE INTERNALS (GNU MP 6.2.1) 16.5 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 implementationcannot provide.
CUSTOM ALLOCATION (GNU MP 6.2.1) How to install and use the GNU multiple precision arithmetic library,version 6.2.1.
SYSTEM EMULATION USING QEMU The PC emulation works well and doesn't suffer from major incompatibility problems from qemu release to qemu release. It is really simple to get started. Create 4GiB disk image: dd if=/dev/zero of=disk.img bs=1048576 count=4096. Install: qemu-system-i386 -hda disk.img -cdrom your-favourite-os-install.iso -boot d. Boot theinstalled system:
ELIMINATING BRANCHES USING A SUPEROPTIMIZER AND THE GNU C the sign bit into the entire word (thus yielding –1 ifais negative, and 0 ifais greater than or equal to 0) and then add 1 to get the desired result. The difference between sequence two and three is INTRODUCTION TO GMP (GNU MP 6.2.1) The proper place for bug reports is gmp-bugs@gmplib.org.See Reporting Bugs for information about reporting bugs. 1.1 How to use this Manual. Everyone should read GMP Basics.If you need to install the library yourself, then read Installing GMP.If you have a system with multiple ABIs, then read ABI and ISA, for the compiler options that must be used on applications.TOP (GNU MP 6.2.1)
How to install and use the GNU multiple precision arithmetic library,version 6.2.1.
INITIALIZING RATIONALS (GNU MP 6.2.1) 6.1 Initialization and Assignment Functions Function: void mpq_init (mpq_t x) Initialize x and set it to 0/1. Each variable should normally only be initialized once, or at least cleared out (using the function mpq_clear) between each initialization.. Function: void mpq_inits (mpq_t x, ) Initialize a NULL-terminated list of mpq_t variables, and set their values to 0/1. CONVERTING INTEGERS (GNU MP 6.2.1) 5.4 Conversion Functions. This section describes functions for converting GMP integers to standard C types. Functions for converting to GMP integers are described in Assigning Integers and I/O of Integers.. Function: unsigned long int mpz_get_ui (const mpz_t op) Return the value of op as an unsigned long.. If op is too big to fit an unsigned long then just the least significant bits that doGMPBENCH RESULTS
GMPbench results. We have run the benchmark on the highest-frequency CPU of each type to which we have convenient access. Scaling to lower or higher frequencies should work well, since GMP mainly works off thecaches.
INTEGER DIVISION (GNU MP 6.2.1) Function: void mpz_tdiv_r_2exp (mpz_t r, const mpz_t n, mp_bitcnt_t b) Divide n by d, forming a quotient q and/or remainder r. For the 2exp functions, d=2^b . The rounding is in three styles, each suiting different applications. cdiv rounds q up towards +infinity, and r will have the opposite sign to d. FORMATTED OUTPUT STRINGS (GNU MP 6.2.1) ‘o’, ‘x’ and ‘X’ are unsigned for the standard C types, but for types ‘Z’, ‘Q’ and ‘N’ they are signed. ‘u’ is not meaningful for ‘Z’, ‘Q’ and ‘N’. ‘M’ is a proxy for the C library ‘l’ or ‘L’, according to the size of mp_limb_t.Unsigned conversions will be usual, but a signed conversion can be used and will interpret the value as a twos C++ INTERFACE FLOATS (GNU MP 6.2.1) Function: explicit mpf_class::mpf_class (const mpf_t f) Function: mpf_class::mpf_class (const mpf_t f, mp_bitcnt_t prec) Construct an mpf_class from an mpf_t.The value in f is copied into the new mpf_class, there won’t be any permanent association between it and f.. If prec is given, the initial precision is that value, in bits. If prec is not given, then the initial precision is that of f. TOOM 4-WAY MULTIPLICATION (GNU MP 6.2.1) 15.1.4 Toom 4-Way Multiplication. Karatsuba and Toom-3 split the operands into 2 and 3 coefficients, respectively. Toom-4 analogously splits the operands into 4 coefficients. Using the notation from the section on Toom-3 multiplication, we form two polynomials: X (t) and Y (t) are evaluated and multiplied at 7 points, giving values of W (t)at
ELIMINATING BRANCHES USING A SUPEROPTIMIZER AND THE GNU C the sign bit into the entire word (thus yielding –1 ifais negative, and 0 ifais greater than or equal to 0) and then add 1 to get the desired result. The difference between sequence two and three is GMPLIB.ORG - THE GNU MP BIGNUM LIBRARY6.2.0 HTML6.2.0 PDFGMP-6.2.0.TAR.LZRELEASE NOTESDEVELOPERS' CORNERRESULTS The GMP computers are maintained by a single person on a volunteer basis. The ongoing Intel CPU bug debacle with Meltdown, Spectre, Foreshadow, MDS, the jCC/cache-line bug, Fallout, LVI, Portsmash, etc, etc, and the ME backdoor is making the main GMP server far from as secure as we'd like it to be. The system which runs this web server as well as mail server, mailing list server, firewall, etc INTEGER FUNCTIONS (GNU MP 6.2.1) 5 Integer Functions. This chapter describes the GMP functions for performing integer arithmetic. These functions start with the prefix mpz_ . GMP integers are stored in objects of type mpz_t . • Initializing Integers. • Assigning Integers. • Simultaneous Integer Init & Assign. BUILD OPTIONS (GNU MP 6.2.1) Build Options (GNU MP 6.2.1) Tools. ‘ configure ’ requires various Unix-like tools. See Notes for Particular Systems, for some options on non-Unix systems. It might be possible to build without the help of ‘ configure ’, certainly all the code is there, but unfortunately you’ll be on your own. Build Directory. INITIALIZING INTEGERS (GNU MP 6.2.1) Initialize a NULL-terminated list of mpz_t variables, and set their values to 0. Function: void mpz_init2 (mpz_t x, mp_bitcnt_t n) Initialize x, with space for n -bit numbers, and set its value to 0. Calling this function instead of mpz_init or mpz_inits is never necessary; reallocation is handled automatically by GMP when needed.While n
INTEGER COMPARISONS (GNU MP 6.2.1) 5.10 Comparison Functions. Compare op1 and op2. Return a positive value if op1 > op2, zero if op1 = op2, or a negative value if op1 < op2 . mpz_cmp_ui and mpz_cmp_si are macros and will evaluate their arguments more than once. mpz_cmp_d can be called with an infinity, but results are undefined for a NaN. Compare the absolute values ofop1 and op2.
REPORTING BUGS (GNU MP 6.2.1) 4 Reporting Bugs. If you think you have found a bug in the GMP library, please investigate it and report it. We have made this library available to you, and it is not too much to ask you to reportthe bugs you find.
C++ INTERFACE INTERNALS (GNU MP 6.2.1) 16.5 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 implementationcannot provide.
CUSTOM ALLOCATION (GNU MP 6.2.1) How to install and use the GNU multiple precision arithmetic library,version 6.2.1.
SYSTEM EMULATION USING QEMU The PC emulation works well and doesn't suffer from major incompatibility problems from qemu release to qemu release. It is really simple to get started. Create 4GiB disk image: dd if=/dev/zero of=disk.img bs=1048576 count=4096. Install: qemu-system-i386 -hda disk.img -cdrom your-favourite-os-install.iso -boot d. Boot theinstalled system:
ELIMINATING BRANCHES USING A SUPEROPTIMIZER AND THE GNU C the sign bit into the entire word (thus yielding –1 ifais negative, and 0 ifais greater than or equal to 0) and then add 1 to get the desired result. The difference between sequence two and three is GMPLIB.ORG - THE GNU MP BIGNUM LIBRARY6.2.0 HTML6.2.0 PDFGMP-6.2.0.TAR.LZRELEASE NOTESDEVELOPERS' CORNERRESULTS The GMP computers are maintained by a single person on a volunteer basis. The ongoing Intel CPU bug debacle with Meltdown, Spectre, Foreshadow, MDS, the jCC/cache-line bug, Fallout, LVI, Portsmash, etc, etc, and the ME backdoor is making the main GMP server far from as secure as we'd like it to be. The system which runs this web server as well as mail server, mailing list server, firewall, etc INTEGER FUNCTIONS (GNU MP 6.2.1) 5 Integer Functions. This chapter describes the GMP functions for performing integer arithmetic. These functions start with the prefix mpz_ . GMP integers are stored in objects of type mpz_t . • Initializing Integers. • Assigning Integers. • Simultaneous Integer Init & Assign. BUILD OPTIONS (GNU MP 6.2.1) Build Options (GNU MP 6.2.1) Tools. ‘ configure ’ requires various Unix-like tools. See Notes for Particular Systems, for some options on non-Unix systems. It might be possible to build without the help of ‘ configure ’, certainly all the code is there, but unfortunately you’ll be on your own. Build Directory. INITIALIZING INTEGERS (GNU MP 6.2.1) Initialize a NULL-terminated list of mpz_t variables, and set their values to 0. Function: void mpz_init2 (mpz_t x, mp_bitcnt_t n) Initialize x, with space for n -bit numbers, and set its value to 0. Calling this function instead of mpz_init or mpz_inits is never necessary; reallocation is handled automatically by GMP when needed.While n
INTEGER COMPARISONS (GNU MP 6.2.1) 5.10 Comparison Functions. Compare op1 and op2. Return a positive value if op1 > op2, zero if op1 = op2, or a negative value if op1 < op2 . mpz_cmp_ui and mpz_cmp_si are macros and will evaluate their arguments more than once. mpz_cmp_d can be called with an infinity, but results are undefined for a NaN. Compare the absolute values ofop1 and op2.
REPORTING BUGS (GNU MP 6.2.1) 4 Reporting Bugs. If you think you have found a bug in the GMP library, please investigate it and report it. We have made this library available to you, and it is not too much to ask you to reportthe bugs you find.
C++ INTERFACE INTERNALS (GNU MP 6.2.1) 16.5 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 implementationcannot provide.
CUSTOM ALLOCATION (GNU MP 6.2.1) How to install and use the GNU multiple precision arithmetic library,version 6.2.1.
SYSTEM EMULATION USING QEMU The PC emulation works well and doesn't suffer from major incompatibility problems from qemu release to qemu release. It is really simple to get started. Create 4GiB disk image: dd if=/dev/zero of=disk.img bs=1048576 count=4096. Install: qemu-system-i386 -hda disk.img -cdrom your-favourite-os-install.iso -boot d. Boot theinstalled system:
ELIMINATING BRANCHES USING A SUPEROPTIMIZER AND THE GNU C the sign bit into the entire word (thus yielding –1 ifais negative, and 0 ifais greater than or equal to 0) and then add 1 to get the desired result. The difference between sequence two and three is INTRODUCTION TO GMP (GNU MP 6.2.1) The proper place for bug reports is gmp-bugs@gmplib.org.See Reporting Bugs for information about reporting bugs. 1.1 How to use this Manual. Everyone should read GMP Basics.If you need to install the library yourself, then read Installing GMP.If you have a system with multiple ABIs, then read ABI and ISA, for the compiler options that must be used on applications.TOP (GNU MP 6.2.1)
How to install and use the GNU multiple precision arithmetic library,version 6.2.1.
INITIALIZING RATIONALS (GNU MP 6.2.1) 6.1 Initialization and Assignment Functions Function: void mpq_init (mpq_t x) Initialize x and set it to 0/1. Each variable should normally only be initialized once, or at least cleared out (using the function mpq_clear) between each initialization.. Function: void mpq_inits (mpq_t x, ) Initialize a NULL-terminated list of mpq_t variables, and set their values to 0/1. CONVERTING INTEGERS (GNU MP 6.2.1) 5.4 Conversion Functions. This section describes functions for converting GMP integers to standard C types. Functions for converting to GMP integers are described in Assigning Integers and I/O of Integers.. Function: unsigned long int mpz_get_ui (const mpz_t op) Return the value of op as an unsigned long.. If op is too big to fit an unsigned long then just the least significant bits that doGMPBENCH RESULTS
GMPbench results. We have run the benchmark on the highest-frequency CPU of each type to which we have convenient access. Scaling to lower or higher frequencies should work well, since GMP mainly works off thecaches.
INTEGER DIVISION (GNU MP 6.2.1) Function: void mpz_tdiv_r_2exp (mpz_t r, const mpz_t n, mp_bitcnt_t b) Divide n by d, forming a quotient q and/or remainder r. For the 2exp functions, d=2^b . The rounding is in three styles, each suiting different applications. cdiv rounds q up towards +infinity, and r will have the opposite sign to d. FORMATTED OUTPUT STRINGS (GNU MP 6.2.1) ‘o’, ‘x’ and ‘X’ are unsigned for the standard C types, but for types ‘Z’, ‘Q’ and ‘N’ they are signed. ‘u’ is not meaningful for ‘Z’, ‘Q’ and ‘N’. ‘M’ is a proxy for the C library ‘l’ or ‘L’, according to the size of mp_limb_t.Unsigned conversions will be usual, but a signed conversion can be used and will interpret the value as a twos C++ INTERFACE FLOATS (GNU MP 6.2.1) Function: explicit mpf_class::mpf_class (const mpf_t f) Function: mpf_class::mpf_class (const mpf_t f, mp_bitcnt_t prec) Construct an mpf_class from an mpf_t.The value in f is copied into the new mpf_class, there won’t be any permanent association between it and f.. If prec is given, the initial precision is that value, in bits. If prec is not given, then the initial precision is that of f. TOOM 4-WAY MULTIPLICATION (GNU MP 6.2.1) 15.1.4 Toom 4-Way Multiplication. Karatsuba and Toom-3 split the operands into 2 and 3 coefficients, respectively. Toom-4 analogously splits the operands into 4 coefficients. Using the notation from the section on Toom-3 multiplication, we form two polynomials: X (t) and Y (t) are evaluated and multiplied at 7 points, giving values of W (t)at
ELIMINATING BRANCHES USING A SUPEROPTIMIZER AND THE GNU C the sign bit into the entire word (thus yielding –1 ifais negative, and 0 ifais greater than or equal to 0) and then add 1 to get the desired result. The difference between sequence two and three is GMP «Arithmetic without limitations»The GNU
Multiple Precision
Arithmetic Library
Last modified: 2021-02-05Documentation:
6.2.1 HTML | 6.2.1 PDFDownload:
gmp-6.2.1.tar.lz |
Release notes
NEW 2020-11-14
Development:
Developers' corner
GMPbench:
Results | Download benchmark sourcesFun:
Compute billions of digits of π using GMP!Security:
GMP server security policyPage contents:
-------------------------What is GMP?
Function categories
Download
Reporting bugs
Mailing lists
Current release statusFuture releases
The GMP computers are maintained by a single person on a volunteer basis. The ongoing Intel CPU bug debacle with Meltdown,
Spectre
,
Foreshadow
,
MDS ,
the jCC/cache-line bug, Fallout, LVI, Portsmash, etc, etc, and the ME backdoor is making the main GMP server far from as secure as we'd likeit to be.
The system which runs this web server as well as mail server, mailing list server, firewall, etc, has an Intel E5-1650 v2 which is affected by most of the bugs/backdoors mentioned above. Please keep that in mind when using the resources here. Please understand that we don't take security lightly, but that we effectively are DoS'edby
sloppy/malicious engineering. Thanks to a very generous donation from Christian Calderon, the GMP project now has a brand new, AMD Epyc server which will replace the old server. This is great for GMP, not only because of the old server's hardware security issues, but also since the new server is 3x more powerful than the old one. The new server will be replacing the old server as soon as we have had time to install all subsystems, which we expect will happen by midApril.
Here are the specs of the system Christian has given us: > * Supermicro barebone 1114S-WTRT > * AMD Epyc 7402P 24-core CPU > * 256 GiB of ECC RAM > * 1.6 TB PCIe SSD disk (Samsung PM1735)WHAT IS GMP?
GMP is a free library for arbitrary precision arithmetic, operating on signed integers, rational numbers, and floating-point numbers. There is no practical limit to the precision except the ones implied by the available memory in the machine GMP runs on. GMP has a rich set of functions, and the functions have a regular interface. The main target applications for GMP are cryptography applications and research, Internet security applications, algebra systems, computational algebra research, etc. GMP is carefully designed to be as fast as possible, both for small operands and for huge operands. The speed is achieved by using fullwords as the basic arithmetic type, by using fast algorithms, with highly optimised assembly code for the most common inner loops for a lot of CPUs, and by a general emphasis on speed. The first GMP release was made in 1991. It is continually developed and maintained, with a new release about once a year. Since version 6, GMP is distributed under the dual licenses, GNU LGPLv3 and GNU GPL v2
. These licenses make the library free to use, share, and improve, and allow you to pass on the result. The GNU licenses give freedoms, but also set firm restrictions on the use with non-free programs. GMP is part of the GNU project. For more information about the GNU project, please see the official GNU web site. GMP's main target platforms are Unix-type systems, such as GNU/Linux, Solaris, HP-UX, Mac OS X/Darwin, BSD, AIX, etc. It also is known to work on Windows in both 32-bit and 64-bit mode. GMP is brought to you by a team listed in the manual.
GMP is carefully developed and maintained, both technically and legally. We of course inspect and test contributed code carefully, but equally importantly we make sure we have the legal right to distribute the contributions, meaning users can safely use GMP. To achieve this, we will ask contributors to sign paperwork where they allow us to distribute their work. ------------------------- GMP FUNCTION CATEGORIES There are several categories of functions in GMP: * High-level signed integer arithmetic functions (mpz). There are about 150 arithmetic and logic functions in this category. * High-level rational arithmetic functions (mpq). This category consists of about 35 functions, but all mpz functions can be used too, by applying them to the numerator and denominator separately. * High-level floating-point arithmetic functions (mpf). This is the GMP function category to use if the C type `double' doesn't give enough precision for an application. There are about 70 functions in this category. New projects should strongly consider using the much more complete GMP extension library mpfrinstead of mpf.
* C++ class based interface to all of the above. (The C functions and types can of course be used directly from C++ too.) * Low-level positive-integer, hard-to-use, very low overhead functions are found in the mpn category. No memory management is performed; the caller must ensure enough space is available for the results. The set of functions is not always regular, nor is the calling interface. These functions accept input arguments in the form of pairs consisting of a pointer to the least significant word, and an integral size telling how many limbs (= words) there are in that argument. The functions in the other categories call mpn for almost all their calculations. Of these functions about 60 are public. ------------------------- DOWNLOAD THE LATEST RELEASE OF GMP> GMP 6.2.1
> LZ, 2020558 BYTES > XZ, 2027316 BYTES > ZSTD, 2101289 BYTES>
> Main site, gmplib.org, via https > gmp-6.2.1.tar.lz > gmp-6.2.1.tar.xz > gmp-6.2.1.tar.zst>
> USA, ftp.gnu.org, via https > gmp-6.2.1.tar.lz > gmp-6.2.1.tar.xz > gmp-6.2.1.tar.zst>
To try to verify that the file you have downloaded has not been tampered with, you can check that the GnuPG signature matches the contents of the file. Use your GnuPG softwareor a key server
directly to get the key that was used for creating the signature. Starting from the repackaging of gmp-5.1.0 as gmp-5.1.0a.tar.* the following key is used to sign GMP releases: > Key ID: 0x28C67298 > Key type: 2560 bit RSA > Fingerprint: 343C 2FF0 FBEE 5EC2 EDBE F399 F359 9FF8 28C6 7298 Instead of using a release, you may also get the latest code from the GMP repositories . This will require some more work compared to using a release. ------------------------- REPORTING BUGS IN GMP Please first see the manual on how to report bugs. The proper address for bug reports is gmp-bugs at gmplib.org. Most problems with GMP these days are due to problems not in GMP, but with the compiler used for compiling the GMP sources. This is a major concern to the GMP project, since an incorrect computation is an incorrect computation, whether caused by a GMP bug or a compiler bug. We fight this by making the GMP testsuite have great coverage, so that it should catch every possible miscompilation. -------------------------GMP MAILING LISTS
> LIST
> SUBSCRIBE URL > ARCHIVE URL > PURPOSE>
> gmp-bugs > gmplib.org/mailman/listinfo/gmp-bugs>
> gmplib.org/list-archives/gmp-bugs/ > Bug reports (not questions!). See manual> .
>
> gmp-announce > gmplib.org/mailman/listinfo/gmp-announce>
> gmplib.org/list-archives/gmp-announce/>
> Announcements from the developers (very little traffic)>
> gmp-discuss > gmplib.org/mailman/listinfo/gmp-discuss>
> gmplib.org/list-archives/gmp-discuss/>
> Questions, Help, Discussions>
> gmp-devel > gmplib.org/mailman/listinfo/gmp-devel>
> gmplib.org/list-archives/gmp-devel/ > Technical discussions between developers>
> gmp-commit > gmplib.org/mailman/listinfo/gmp-commit>
> gmplib.org/list-archives/gmp-commit/>
> Commit messages Note that we perform spam and virus filtering of these lists. The lists have been 100% spam-free during the last years. We're blocking all mail from PR China, since 99% of the spam arriving to the GMP moderators emanates from PR China. If you are affected but have a legitimate reason to send mail to the GMP project, e.g., if you work at a university or corporation with an interest in GMP, please let us know; we will open access for you. ------------------------- STATUS OF THE CURRENT RELEASE The current stable release is 6.2.1, released 2020-11-14. ISSUES WITH GMP 6.2.1: * While we added support for Apple's new Arm based computers, our support has a problem. The problem is that Apple reserves CPU register x18, but GMP's mpn/arm64 assembly code uses that register. While GMP runs fine in our tests, we expect things to go awry in some execution situation. (Apple has not been kind enough to specify how they use x18. Therefore, we don't know what the consequences of using x18 mightbe.)
ISSUES WITH GMP 6.2.0: * MacOS Xcode 11 prior to 11.3 miscompiles GMP, leading to crashesand miscomputation.
ISSUES WITH GMP 6.1.2: * MacOS Xcode 11 prior to 11.3 miscompiles GMP, leading to crashesand miscomputation.
ISSUES WITH GMP 6.1.1: * There are several issues with mini-gmp. Please see the special mini-gmp-status page. ISSUES WITH GMP 6.1.0: * An assembly file which is used for Intel Broadwell and Intel Skylake (except crippled Pentiums and Celerons without BMI2) will not work correctly for Windoze. Patch. * See also issues for subsequent releases above. ISSUES WITH GMP 6.0.0:*
* See also issues for subsequent releases above. ISSUES WITH GMP 5.1.3: * The documentation of mpn_set_str is incorrect and incomplete wrt allocation requirements. Patch. * See also issues for subsequent releases above. ISSUES WITH GMP 5.1.2: * The functions mpn_sbpi1_div_qr_sec and mpn_sbpi1_div_r_sec compute incorrect results for some operands. With uniformly distributed random operands, the error is very hard to trigger, and for the intended use of these functions, operands can be expected to appear as such random operands from these functions' perspective. Patch. * The internal function mpn_divrem_2 on Itanium clobbers two callee-saves registers. This can lead to miscomputations or crashes inthe callers. Patch.
* See also issues for subsequent releases above. ISSUES WITH GMP 5.1.1: * Windows only: A 64-bit build for AMD Bulldozer and Piledriver chips, or a fat 64-bit build running on these chips, will not workcorrectly. Patch.
* The function mpz_powm_ui computes garbage if the base argument is over 15000 decimal or the mod argument is at least 7500 decimal digits. No other GMP powm function is affected. Patch. * See also issues for subsequent releases above. ISSUES WITH GMP 5.1.0: * The mini-gmp.c file, which implements a subset of mpn and mpz, was not properly tested and contained a number of bugs. Please do not use the 5.1.0 version of mini-gmp.c. Note that these bugs do not affectGMP itself.
* The included top-level Makefile.in has an automake-generated distcheck target which creates a world-writable directory. This target is not used in the GMP release process, but it is a potential security problem affecting users who invoke this make target. This problem (and no other) is corrected in the gmp-5.1.0a.tar.* set of files. * See also issues for subsequent releases above. For patches to older GMP versions, please see the Info on older GMPreleases .
-------------------------FUTURE RELEASES
Please see the GMPng page for information on what we'reworking on.
Please send comments about this page to gmp-discussat gmplib.org
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