This is the README file for the ecm library.

To use the library, you need to add the following line in your source file:

#include "ecm.h"

and link with -lecm.

The public interface is defined in the "ecm.h" file. It contains the following
functions:

int ecm_factor (mpz_t f, mpz_t n, double B1, ecm_params p)

   where n is the number to factor, f is the factor found (if any),
   B1 is the stage 1 bound, and p contains auxiliary parameters (see below).
   When p is NULL, default values for those parameters are chosen.

   The ecm_factor() function returns:

   * a positive value if a factor was found (1 for step 1, 2 for step 2),
   * zero when no factor was found,
   * a negative value when an error occurred.

void ecm_init (ecm_params p)

   Initialize the parameters to default values.

void ecm_clear (ecm_params p)

   Clear the parameters.

Detailed description of parameters (ecm_params):

* p->method is the factorization method (ECM_ECM for ECM, ECM_PM1 for P-1,
	ECM_PP1 for P+1). Default is ECM_ECM.
* p->x (if non zero) is the starting point (ECM, P-1, P+1). For ECM, we take
	as starting point (x0 : y0) where x0=x, y0=1; for P-1, we take x0;
	for P+1, we take x0 as starting point of the Lucas sequence.
	When ecm_factor() returns, p->x is the point obtained after stage 1.
* p->sigma (ECM only) is the "sigma" parameter. The elliptic curve chosen
	is b*y^2 = x^3 + a*x^2 + x where a = (v-u)^3*(3*u+v)/(4*u^3*v)-2,
	u = sigma^2-5, v = 4*sigma (Suyama's parametrization).
	The initial point (if p->x is zero) is taken as x0=u^3/v^3, y0=1
	(thus b is taken as x0^3 + a*x0^2 + x0).
* p->sigma_is_A (ECM only) indicates that p->sigma is the 'a' parameter
	from the elliptic curve.
* p->go is the initial group order to preload (default is 1).
* p->B1done tells that step 1 was already done up to B1done. This means that
	all prime powers <= B1done were dealt with. If for example B1done=100
	and B1=200, prime 2 was dealt with up to power 6, thus it remains to
	"multiply" once by 2 to go up to power 7. Of course, all primes p such
	that B1done < p <= B1 will be considered with power 1.
* p->B2min is the lower bound for stage 2, which will treat all primes p such
	that B2min <= p <= B2. If negative, B2min will be set to B1.
* p->B2 is the upper bound for stage 2 (default is automatically computed from
	B1, to optimize the efficiency of the method).
* p->k  is the number of blocks used in stage 2 (default is ECM_DEFAULT_K).
* p->S  defines the polynomial used for Brent-Suyama's extension in stage 2.
	If positive, the polynomial used is x^S; if negative, it is Dickson's
	polynomial of degree S with parameter a=-1, where D_{1,a}(x) = x,
	D_{2,a}(x) = x^2-2*a, and D_{k+2,a}(x) = x*D_{k+1,a}(x) - a*D_{k,a}(x),
	or equivalently D_{k,a}(2*sqrt(a)*cos(t)) = 2*a^(k/2)*cos(k*t).
        If zero, choice is automatic (and should be close to optimal).
	Default is ECM_DEFAULT_S.
* p->repr defines the representation used for modular arithmetic: 1 means
	the 'mpz' class from GMP, 2 means 'modmuln' (Montgomery's multiplication,
	quadratic implementation), 3 means 'redc' (Montgomery's multiplication,
	subquadratic implementation), -1 indicates not to use a special base-2
	representation (when the input number is a factor of 2^n +/- 1).
	Other values (including 0) mean the representation will be chosen
	automatically (hopefully in some optimal way).
* p->verbose is the verbosity level: 0 for no output, 1 for normal output
	(like default for GMP-ECM), 2 for diagnostic output without inter-
        mediate residues (like -v in GMP-ECM), 3 for diagnostic output with
        residues (like -v -v), 4 for high diagnostic output (-v -v -v), 
        and 5 for trace output (-v -v -v -v).
* p->os is the output stream used for verbose output. Default is stdout.
* p->es is the output stream used for errors. Default is stderr.
* p->TreeFilename if non NULL, is the file name to store the product tree
	of F (option -treefile f).
* p->maxmem is the maximum amount of memory in bytes that should be used in
        stage 2. Setting this value too low (< 10MB, say) will cause stage 2 
        to perform very poorly, or return with an error code.
* p->stage1time is the time already spent in stage 1 (useful to get a correct
	estimation of the expected time to find factors).
* p->rng is a random number generator state.
* p->use_ntt if equal to 1, use NTT in stage 2.
* p->(*stop_asap) pointer to function: if the function returns zero, continue
	normally, otherwise exit as soon as possible. May be NULL.