gmp
gmp is library providing Ruby bindings to GMP library. Here is the introduction paragraph at gmplib.org/#WHAT :
-
“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.
-
GMP is faster than any other bignum library. The advantage for GMP increases with the operand sizes for many operations, since GMP uses asymptotically faster algorithms.
-
The first GMP release was made in 1991. It is continually developed and maintained, with a new release about once a year.
-
GMP is distributed under the GNU LGPL. This license makes the library free to use, share, and improve, and allows you to pass on the result. The license gives freedoms, but also sets 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 Windoze in 32-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.“
Only GMP 4 or newer is supported. The following environments have been tested by me:
gmp gem 0.1.4.2 on:
+-------------------------------------+-------------------+-----------+
| Platform | Ruby | GMP |
+-------------------------------------+-------------------+-----------+
| Cygwin on x86 | (MRI) Ruby 1.8.7 | GMP 4.3.1 |
| Linux (LinuxMint 7) on x86 (32-bit) | (MRI) Ruby 1.8.7 | GMP 4.3.1 |
| Mac OS X 10.5.7 on x86 (32-bit) | (MRI) Ruby 1.8.6 | GMP 4.3.1 |
| Mac OS X 10.5.7 on x86 (32-bit) | (MRI) Ruby 1.9.1 | GMP 4.3.1 |
+-------------------------------------+-------------------+-----------+
Note: To get this running on Mac OS X (32-bit), I compiled GMP 4.3.1 with:
./configure ABI=32 --disable-dependency-tracking
Authors
-
Tomasz Wegrzanowski
-
srawlins
Classes
It provides module GMP with following classes:
-
GMP::Z - infinite precision integer numbers
-
GMP::Q - infinite precision rational numbers
-
GMP::F - arbitrary precision floating point numbers
Numbers are created by using new(). Constructors can take following arguments:
GMP::Z.new()
GMP::Z.new(GMP::Z)
GMP::Z.new(FixNum)
GMP::Z.new(BigNum)
GMP::Z.new(String)
GMP::Q.new()
GMP::Q.new(GMP::Q)
GMP::Q.new(String)
GMP::Q.new(any GMP::Z initializer)
GMP::Q.new(any GMP::Z initializer, any GMP::Z initializer)
GMP::F.new()
GMP::F.new(GMP::Z, precision=0)
GMP::F.new(GMP::Q, precision=0)
GMP::F.new(GMP::F)
GMP::F.new(GMP::F, precision)
GMP::F.new(String, precision=0)
GMP::F.new(FixNum, precision=0)
GMP::F.new(BigNum, precision=0)
GMP::F.new(Float, precision=0)
You can also call them as:
GMP.Z(args)
GMP.Q(args)
GMP.F(args)
Methods
GMP::Z, GMP::Q and GMP::F
+ addition
- substraction
* multiplication
to_s convert to string. For GMP::Z, this method takes
one optional argument, a base. The base can be a
Fixnum in the ranges [2, 62] or [-36, -2] or a
Symbol: :bin, :oct, :dec, or :hex.
-@ negation
neg! in-place negation
abs absolute value
asb! in-place absolute value
coerce promotion of arguments
== equality test
<=>,>=,>,<=,< comparisions
class methods of GMP::Z
fac(n) factorial of n
fib(n) nth fibonacci number
pow(n,m) n to mth power
GMP::Z and GMP::Q
swap efficiently swap contents of two objects, there
is no GMP::F.swap because various GMP::F objects
may have different precisions, which would make
them unswapable
GMP::Z
add! in-place addition
sub! in-place subtraction
tdiv,fdiv,cdiv truncate, floor and ceil division
tmod,fmod,cmod truncate, floor and ceil modulus
[],[]= testing and setting bits (as booleans)
scan0,scan1 starting at bitnr (1st arg), scan for a 0 or 1
(respectively), then return the index of the
first instance.
com 2's complement
com! in-place 2's complement
&,|,^ logical operations: and, or, xor
** power
powmod power modulo
even? is even
odd? is odd
<< shift left
>> shift right, floor
tshr shift right, truncate
lastbits_pos(n) last n bits of object, modulo if negative
lastbits_sgn(n) last n bits of object, preserve sign
power? is perfect power
square? is perfect square
sqrt square root
sqrt! change the object into its square root
sqrtrem square root, remainder
root(n) nth root
jacobi jacobi symbol
legendre legendre symbol
probab_prime? 0 if composite, 1 if probably prime, 2 if
certainly prime
nextprime next *probable* prime
nextprime! change the object into its next *probable* prime
popcount the number of bits equal to 1
to_i convert to FixNum or BigNum
remove(n) remove all occurences of factor n
GMP::Q and GMP::F
/ division
GMP::Q
num numerator
den denominator
inv inversion
inv! in-place inversion
floor,ceil,trunc nearest integer
class methods of GMP::F
default_prec get default precision
default_prec= set default precision
GMP::F
prec get precision
floor,ceil,trunc nearest integer, GMP::F is returned, not GMP::Z
floor!,ceil!,trunc! in-place nearest integer
GMP::F (only if MPFR is available)
exp e^object
expm1 the same as (object.exp) - 1, with better precision
log natural logarithm of object
log2 binary logarithm of object
log10 decimal logarithm of object
log1p the same as (object + 1).log, with better precision
sqrt square root of the object
cos \
sin |
tan |
acos |
asin |
atan | trigonometric functions
cosh | of the object
sinh |
tanh |
aconh |
asinh |
atanh /
nan? \
infinite? | type of floating point number
finite? |
number? /
** power
Known Issues
-
GMP::Z#pow does not appear to be working at all. Looking at the code, I don’t think it ever did.
Precision
Precision can be explicitely set as second argument for GMP::F.new().
If there is no explicit precision, highest precision of all GMP::F arguments is used. That doesn’t ensure that result will be exact. For details, consult any paper about floating point arithmetics.
Default precision can be explicitely set by passing 0 to GMP::F.new(). In particular, you can set precision of copy of GMP::F object by:
new_obj = GMP::F.new(old_obj, 0)
Precision argument, and default_precision will be rounded up to whatever GMP thinks is appropriate.
Todo
These are inherited from Tomasz. I will go through these and see which are still relevant.
-
mpz_fits_* and 31 vs. 32 integer variables
-
all appropriate module and class methods if there are any to add
-
fix all sign issues (don’t know what these are)
-
floats with precision control
-
random numbers
-
to_s vs. inspect
-
check if mpz_addmul_ui would optimize some statements
-
some system that allows using denref and numref as normal ruby objects
-
should we allocate global temporary variables like Perl GMP does?
-
takeover code that replaces all Bignums with GMP::Z
-
better bignum parser
-
zero-copy method for strings generation
-
put rb_raise into nice macros
-
benchmarks against Python GMP (gmpy? Is this still active?) and Perl GMP (I can’t find this either!)
-
dup methods
-
integrate F into system
-
should Z.[] bits be 0/1 or true/false, 0 is true, what might badly surprise users
-
any2small_integer()
-
check asm output, especially local memory efficiency
-
it might be better to use ‘register’ for some local variables
-
powm with negative exponents
-
check if different sorting of operatations gives better cache usage
-
GMP::* op RubyFloat and RubyFloat op GMP::*
-
sort checks
-
check all new GMP4 operations
-
GMP::Q.to_s(base), GMP::F.to_s(base)