reorganize singular_values, do one precomputation and then only compute unique traces
This commit is contained in:
Florian Stecker
parent
6c12f49db8
commit
2735281300
2
Makefile
2
Makefile
@ -1,7 +1,7 @@
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HEADERS=linalg.h mat.h coxeter.h enumerate_triangle_group.h
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#SPECIAL_OPTIONS=-O0 -g -D_DEBUG
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SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
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SPECIAL_OPTIONS=-O3 -pg -g -funroll-loops -fno-inline
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#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
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#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -mavx512f -mavx512cd -mavx512er -mavx512pf # KNL
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#SPECIAL_OPTIONS=
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@ -9,17 +9,21 @@ main = do
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listWordsUpToLength :: Int -> IO ()
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listWordsUpToLength n = do
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putStrLn $ unlines [printf "%s %d/%d %f %s"
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putStr $ unlines [printf "%s %d/%d %f"
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w
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(p `div` gcd p q)
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(q `div` gcd p q)
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(sqrt 3 / 2 * fromIntegral p / (fromIntegral q + fromIntegral p / 2) :: Double)
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(slopeWord "bca" (orthogonalSlope (p,q))) |
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(atan (sqrt 3 / (2*q_/p_ + 1))) |
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((p,q),w) <- wordlist (n `div` 2, n `div` 2),
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let p_ = fromIntegral p :: Double,
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let q_ = fromIntegral q :: Double,
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length w <= n,
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let x = 2*q + p,
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let y = 2*p + q]
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-- (sqrt 3 / 2 * fromIntegral p / (fromIntegral q + fromIntegral p / 2) :: Double) |
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-- (slopeWord "bca" (orthogonalSlope (p,q))) |
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wordlist :: (Int,Int) -> [((Int,Int),String)]
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wordlist (pmax,qmax) = nub $
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sortBy (comparing sl)
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@ -7,6 +7,7 @@ typedef struct _groupelement {
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int id;
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int letter;
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struct _groupelement *parent;
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int need_to_compute; // optimization flag; if 0, will skip matrix computation
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int length;
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struct _groupelement *inverse;
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@ -1,13 +1,12 @@
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#include "enumerate_triangle_group.h"
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#include "linalg.h"
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int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues)
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int solve_characteristic_polynomial(mps_context *solv, mps_monomial_poly *poly, mpq_t tr, mpq_t trinv, double *eigenvalues)
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{
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mpq_t coeff1, coeff2, zero;
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cplx_t *roots;
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double radii[3];
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double *radii_p[3];
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mps_monomial_poly *poly;
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mps_boolean errors;
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int result = 0;
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@ -15,7 +14,6 @@ int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, do
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mpq_set(coeff1, trinv);
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mpq_sub(coeff2, zero, tr);
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poly = mps_monomial_poly_new(solv, 3);
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mps_monomial_poly_set_coefficient_int(solv, poly, 0, -1, 0);
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mps_monomial_poly_set_coefficient_q(solv, poly, 1, coeff1, zero);
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mps_monomial_poly_set_coefficient_q(solv, poly, 2, coeff2, zero);
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@ -215,7 +213,7 @@ char *print_word(groupelement_t *g, char *str)
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return str;
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}
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void enumerate(group_t *group, mat *matrices, int p1, int p2, int p3, mpq_t s, mpq_t t)
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void enumerate(group_t *group, mat *matrices, int p1, int p2, int p3, mpq_t s, mpq_t q)
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{
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mat_workspace *ws;
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mat tmp;
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@ -228,7 +226,7 @@ void enumerate(group_t *group, mat *matrices, int p1, int p2, int p3, mpq_t s, m
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mat_init(gen[i], 3);
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mat_init(tmp, 3);
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initialize_triangle_generators(ws, gen, p1, p2, p3, s, t);
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initialize_triangle_generators(ws, gen, p1, p2, p3, s, q);
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mat_identity(matrices[0]);
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for(int i = 1; i < group->size; i++) {
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@ -236,6 +234,8 @@ void enumerate(group_t *group, mat *matrices, int p1, int p2, int p3, mpq_t s, m
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continue;
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if(!group->elements[i].inverse)
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continue;
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if(!group->elements[i].need_to_compute)
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continue;
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int parent = group->elements[i].parent->id;
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int grandparent = group->elements[i].parent->parent->id;
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@ -6,7 +6,7 @@
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#include <mps/mps.h>
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int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues);
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int solve_characteristic_polynomial(mps_context *solv, mps_monomial_poly *poly, mpq_t tr, mpq_t trinv, double *eigenvalues);
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void continued_fraction_approximation(mpq_t out, double in, int level);
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void quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e);
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// p1,p2,p3 are only allowed to be 2,3,4,6
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@ -3,9 +3,12 @@
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#include "mat.h"
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#include "enumerate_triangle_group.h"
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#include <time.h>
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#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
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//#define DEBUG(msg, ...) fprintf(stderr, msg, ##__VA_ARGS__)
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#define DEBUG(msg, ...)
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#define DEBUG(msg, ...) fprintf(stderr, "[%10.3f] " msg, runtime(), ##__VA_ARGS__);
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//#define DEBUG(msg, ...)
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struct result {
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int id;
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@ -31,7 +34,17 @@ static int compare_result(const void *a_, const void *b_)
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return d;
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}
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static int compare_result_with_id(const void *a_, const void *b_)
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static int compare_result_by_id(const void *a_, const void *b_)
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{
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int d = 0;
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struct result **a = (struct result **)a_;
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struct result **b = (struct result **)b_;
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return (*a)->id - (*b)->id;
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}
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static int compare_result_by_tr_trinv_id(const void *a_, const void *b_)
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{
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int d = 0;
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@ -62,128 +75,73 @@ static int compare_result_by_slope(const void *a_, const void *b_)
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return slopea > slopeb ? -1 : slopea < slopeb ? 1 : 0;
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}
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int main(int argc, char *argv[])
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struct timespec starttime;
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static void start_timer()
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{
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mpq_t s, q, t, tmp;
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double sapprox, tapprox, qapprox, tqfactor;
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mat *matrices;
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group_t *group;
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int index;
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clock_gettime(CLOCK_MONOTONIC, &starttime);
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}
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static double runtime()
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{
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struct timespec curtime;
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double diff;
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clock_gettime(CLOCK_MONOTONIC, &curtime);
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return (curtime.tv_sec - starttime.tv_sec) + (curtime.tv_nsec - starttime.tv_nsec) / 1e9;
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}
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int compute_invariants(group_t *group, mat *matrices, struct result **invariants, int *n, int unique)
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{
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mpq_t tmp;
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mps_context *solver;
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int acc = 100;
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int n, nuniq, nmax;
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mps_monomial_poly *poly;
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int index;
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int ntraces = *n, nuniq;
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int retval;
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double evs[3];
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int max_slope_id;
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double max_slope;
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char buf[100];
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char buf2[100];
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struct result *invariants;
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struct result **distinct_invariants;
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if(argc < 4) {
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fprintf(stderr, "Usage: %s <N> <s> <q>\n", argv[0]);
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exit(1);
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// DEBUG("Compute traces\n");
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for(int i = 0; i < ntraces; i++) {
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int id = invariants[i]->id;
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int invid = group->elements[id].inverse->id;
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mat_trace(invariants[i]->tr, matrices[id]);
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mat_trace(invariants[i]->trinv, matrices[invid]);
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}
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nmax = atoi(argv[1]);
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if(!unique)
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nuniq = ntraces;
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else {
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// DEBUG("Get unique traces\n");
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qsort(invariants, ntraces, sizeof(struct result*), compare_result);
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DEBUG("Allocate\n");
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mpq_inits(s, q, t, tmp, NULL);
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matrices = malloc(nmax*sizeof(mat));
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for(int i = 0; i < nmax; i++)
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mat_init(matrices[i], 3);
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invariants = malloc(nmax*sizeof(struct result));
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distinct_invariants = malloc(nmax*sizeof(struct result));
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for(int i = 0; i < nmax; i++) {
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mpq_init(invariants[i].tr);
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mpq_init(invariants[i].trinv);
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distinct_invariants[i] = &invariants[i];
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nuniq = 0;
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for(int i = 0; i < ntraces; i++) {
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if(i == 0 || compare_result(&invariants[i], &invariants[nuniq-1]) != 0) {
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invariants[nuniq] = invariants[i];
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invariants[nuniq]->count = 1;
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nuniq++;
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} else {
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invariants[nuniq-1]->count++;
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int oldlength = group->elements[invariants[nuniq-1]->id].length;
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int newlength = group->elements[invariants[i]->id].length;
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if(newlength < oldlength)
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invariants[nuniq-1]->id = invariants[i]->id;
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}
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}
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}
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DEBUG("Solve characteristic polynomials\n");
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solver = mps_context_new();
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poly = mps_monomial_poly_new(solver, 3);
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mps_context_set_output_prec(solver, 20); // relative precision
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mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
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DEBUG("Approximate parameters\n");
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// get approximate s and q values
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sapprox = atof(argv[2]);
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qapprox = atof(argv[3]);
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// tapprox = atof(argv[3]);
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// tqfactor = pow((sapprox*sapprox-sapprox+1)*(sapprox*sapprox-sapprox+1)*(sapprox*sapprox+1), 1/6.0);
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// qapprox = tapprox/tqfactor;
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for(int i = 0; ; i++) {
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continued_fraction_approximation(tmp, sapprox, i);
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if(fabs(mpq_get_d(t)-sapprox) < 1e-10
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|| (mpz_cmpabs_ui(mpq_numref(tmp),acc) > 0 && mpz_cmpabs_ui(mpq_denref(tmp),acc) > 0))
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break;
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mpq_set(s, tmp);
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}
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mpq_canonicalize(s);
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for(int i = 0; ; i++) {
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continued_fraction_approximation(tmp, qapprox, i);
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if(fabs(mpq_get_d(t)-qapprox) < 1e-10
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|| (mpz_cmpabs_ui(mpq_numref(tmp),acc) > 0 && mpz_cmpabs_ui(mpq_denref(tmp),acc) > 0))
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break;
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mpq_set(q, tmp);
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}
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mpq_canonicalize(q);
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tqfactor = pow((mpq_get_d(s)*mpq_get_d(s)-mpq_get_d(s)+1)*(mpq_get_d(s)*mpq_get_d(s)-mpq_get_d(s)+1)*(mpq_get_d(s)*mpq_get_d(s)+1), 1/6.0);
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// group
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// order of the triangle reflection generators: a, b, c
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// order of the rotation orders: bc, ac, ab
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DEBUG("Generate group\n");
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group = coxeter_init_triangle(4, 3, 3, nmax);
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DEBUG("Compute matrices\n");
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enumerate(group, matrices, 4, 3, 3, s, q);
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n = 0;
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DEBUG("Compute traces\n");
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for(int i = 0; i < nmax; i++) {
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if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
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continue;
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invariants[i].id = i;
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mat_trace(invariants[i].tr, matrices[i]);
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mat_trace(invariants[i].trinv, matrices[group->elements[i].inverse->id]);
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distinct_invariants[n++] = &invariants[i];
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}
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DEBUG("Get unique traces\n");
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qsort(distinct_invariants, n, sizeof(struct result*), compare_result);
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nuniq = 0;
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for(int i = 0; i < n; i++) {
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if(i == 0 || compare_result(&distinct_invariants[i], &distinct_invariants[nuniq-1]) != 0) {
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distinct_invariants[nuniq] = distinct_invariants[i];
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distinct_invariants[nuniq]->count = 1;
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nuniq++;
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} else {
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distinct_invariants[nuniq-1]->count++;
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int oldlength = group->elements[distinct_invariants[nuniq-1]->id].length;
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int newlength = group->elements[distinct_invariants[i]->id].length;
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if(newlength < oldlength)
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distinct_invariants[nuniq-1]->id = distinct_invariants[i]->id;
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}
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// gmp_printf("%d %d %s\n", i, nuniq-1, print_word(&group->elements[i], buf));
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}
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max_slope = 0;
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int max_slope_index;
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DEBUG("Solve characteristic polynomials\n");
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for(int i = 0; i < nuniq; i++) {
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retval = solve_characteristic_polynomial(solver, distinct_invariants[i]->tr, distinct_invariants[i]->trinv, evs);
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retval = solve_characteristic_polynomial(solver, poly, invariants[i]->tr, invariants[i]->trinv, evs);
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retval = 0;evs[0] = 2;evs[1] = 1;evs[2] = 0.5; // fake solving the polynomial for memory leak test
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if(retval == 1) {
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fprintf(stderr, "Error! Could not solve polynomial.\n");
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continue;
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@ -201,43 +159,193 @@ int main(int argc, char *argv[])
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double x = log(fabs(evs[0]));
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double y = -log(fabs(evs[2]));
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distinct_invariants[i]->x = x;
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distinct_invariants[i]->y = y;
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invariants[i]->x = x;
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invariants[i]->y = y;
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if(y/x > max_slope && (x > 0.1 || y > 0.1)) {
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max_slope_index = distinct_invariants[i] - invariants;
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if(y/x > max_slope + 1e-12 && (x > 0.1 || y > 0.1)) {
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max_slope_id = invariants[i]->id;
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max_slope = y/x;
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} else if(y/x > max_slope - 1e-12 && (x > 0.1 || y > 0.1)) {
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// DEBUG("%s didn't quite make it\n",
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// print_word(&group->elements[invariants[i]->id], buf));
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}
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}
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mps_context_free(solver);
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qsort(invariants, nuniq, sizeof(struct result*), compare_result_by_id);
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*n = nuniq;
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return max_slope_id;
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}
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long check_memory_usage(mat *matrices, int n)
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{
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mpq_t x;
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long total;
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for(int i = 0; i < n; i++)
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{
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LOOP(j,3) LOOP(k,3) {
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total += mpq_numref(M(matrices[i], j, k))->_mp_size;
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total += mpq_denref(M(matrices[i], j, k))->_mp_size;
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}
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}
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qsort(distinct_invariants, nuniq, sizeof(struct result*), compare_result_by_slope);
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return total;
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}
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gmp_fprintf(stdout, "\"s = %Qd = %.3f, q = %Qd, t = %.3f\"\n", s, mpq_get_d(s), q, mpq_get_d(q)*tqfactor);
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int main(int argc, char *argv[])
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{
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mpq_t s, q, t, tmp;
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int p1, p2, p3;
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int sstart, send, sdenom, qstart, qend, qdenom;
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mat *matrices;
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group_t *group;
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int nmax, n;
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int max_slope_id;
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char buf[100];
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char buf2[100];
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struct result *invariants;
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struct result **distinct_invariants;
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// printf("- 0 0 - - - - 0.5\n");
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int cumulative = 0;
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double slope;
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for(int i = 0; i < nuniq; i++) {
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slope = distinct_invariants[i]->y/distinct_invariants[i]->x;
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start_timer();
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mpq_inits(s, q, t, tmp, NULL);
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if(argc < 11) {
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fprintf(stderr, "Usage: %s <N> <p1> <p2> <p3> <s start> <s end> <s denom> <q start> <q end> <q denom>\n", argv[0]);
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exit(1);
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}
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nmax = atoi(argv[1]);
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p1 = atoi(argv[2]);
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p2 = atoi(argv[3]);
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p3 = atoi(argv[4]);
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sstart = atoi(argv[5]);
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send = atoi(argv[6]);
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sdenom = atoi(argv[7]);
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qstart = atoi(argv[8]);
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qend = atoi(argv[9]);
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qdenom = atoi(argv[10]);
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DEBUG("Allocate\n");
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matrices = malloc(nmax*sizeof(mat));
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for(int i = 0; i < nmax; i++)
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mat_init(matrices[i], 3);
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invariants = malloc(nmax*sizeof(struct result));
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distinct_invariants = malloc(nmax*sizeof(struct result));
|
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for(int i = 0; i < nmax; i++) {
|
||||
mpq_init(invariants[i].tr);
|
||||
mpq_init(invariants[i].trinv);
|
||||
}
|
||||
|
||||
// order of the triangle reflection generators: a, b, c
|
||||
// order of the rotation orders: bc, ac, ab
|
||||
DEBUG("Generate group\n");
|
||||
group = coxeter_init_triangle(p1, p2, p3, nmax);
|
||||
|
||||
// first run; compute all matrices
|
||||
for(int i = 0; i < group->size; i++)
|
||||
group->elements[i].need_to_compute = 1;
|
||||
|
||||
// use very generic values for the pilot run unless sstart=send and qstart=qend
|
||||
if(sstart == send && qstart == qend) {
|
||||
mpq_set_ui(s, sstart, sdenom);
|
||||
mpq_set_ui(q, qstart, qdenom);
|
||||
DEBUG("Single run for s = %d/%d, q = %d/%d\n", sstart, sdenom, qstart, qdenom);
|
||||
} else {
|
||||
mpq_set_ui(s, 4, 100);
|
||||
mpq_set_ui(q, 7, 100);
|
||||
DEBUG("Initial run for s = %d/%d, q = %d/%d\n", 4, 100, 7, 100);
|
||||
}
|
||||
|
||||
DEBUG("Compute matrices\n");
|
||||
enumerate(group, matrices, p1, p2, p3, s, q);
|
||||
|
||||
// prepare array of ids
|
||||
n = 0;
|
||||
for(int i = 0; i < group->size; i++)
|
||||
{
|
||||
if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
|
||||
continue;
|
||||
invariants[i].id = i;
|
||||
distinct_invariants[n++] = &invariants[i];
|
||||
}
|
||||
|
||||
DEBUG("Compute invariants\n");
|
||||
max_slope_id = compute_invariants(group, matrices, distinct_invariants, &n, 1);
|
||||
|
||||
// prepare for next time; don't need to change ids in distinct_invariants!
|
||||
for(int i = 0; i < group->size; i++)
|
||||
group->elements[i].need_to_compute = 0;
|
||||
group->elements[0].need_to_compute = 1;
|
||||
int multiplication_count = 1;
|
||||
for(int i = 0; i < n; i++) {
|
||||
groupelement_t *cur = &group->elements[distinct_invariants[i]->id];
|
||||
while(cur->need_to_compute == 0) {
|
||||
cur->need_to_compute = 1;
|
||||
multiplication_count++;
|
||||
cur = cur->parent->parent; // also need to compute its even-length ancestors
|
||||
}
|
||||
cur = group->elements[distinct_invariants[i]->id].inverse;
|
||||
while(cur->need_to_compute == 0) {
|
||||
cur->need_to_compute = 1;
|
||||
multiplication_count++;
|
||||
cur = cur->parent->parent;
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
DEBUG("Would have needed %d matrix multiplications for %d unique traces up to reflection length %d\n", multiplication_count, n, group->elements[group->size-1].length);
|
||||
|
||||
if(sstart != send || qstart != qend) {
|
||||
for(int sloop = sstart; sloop <= send; sloop++) {
|
||||
for(int qloop = qstart; qloop <= qend; qloop++) {
|
||||
DEBUG("Loop for s = %d/%d, q = %d/%d\n", sloop, sdenom, qloop, qdenom);
|
||||
mpq_set_ui(s, sloop, sdenom);
|
||||
mpq_set_ui(q, qloop, qdenom);
|
||||
DEBUG("Compute matrices\n");
|
||||
enumerate(group, matrices, p1, p2, p3, s, q);
|
||||
DEBUG("Compute invariants\n");
|
||||
max_slope_id = compute_invariants(group, matrices, distinct_invariants, &n, 0);
|
||||
// output
|
||||
gmp_printf("%Qd %Qd %s\n", s, q,
|
||||
print_word(&group->elements[max_slope_id], buf));
|
||||
fflush(stdout);
|
||||
}
|
||||
}
|
||||
} else {
|
||||
// output
|
||||
for(int i = 0; i < n; i++) {
|
||||
double slope = distinct_invariants[i]->y/distinct_invariants[i]->x;
|
||||
|
||||
// exclude tr = trinv = 2/1/0/-1/3
|
||||
mpq_set_si(tmp, 2, 1);
|
||||
if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
|
||||
mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
|
||||
continue;
|
||||
mpq_set_si(tmp, 1, 1);
|
||||
if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 && mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0) {
|
||||
if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
|
||||
mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
|
||||
continue;
|
||||
}
|
||||
mpq_set_si(tmp, 0, 1);
|
||||
if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 && mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0) {
|
||||
if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
|
||||
mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
|
||||
continue;
|
||||
}
|
||||
mpq_set_si(tmp, -1, 1);
|
||||
if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 && mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0) {
|
||||
if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
|
||||
mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
|
||||
continue;
|
||||
}
|
||||
mpq_set_si(tmp, 3, 1);
|
||||
if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 && mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0) {
|
||||
if(mpq_cmp(distinct_invariants[i]->tr, tmp) == 0 &&
|
||||
mpq_cmp(distinct_invariants[i]->trinv, tmp) == 0)
|
||||
continue;
|
||||
}
|
||||
|
||||
cumulative += distinct_invariants[i]->count;
|
||||
gmp_printf("%d %d %s %f\n",
|
||||
distinct_invariants[i]->id, distinct_invariants[i]->count,
|
||||
print_word(&group->elements[distinct_invariants[i]->id], buf),
|
||||
slope
|
||||
);
|
||||
|
||||
/*
|
||||
gmp_printf("%d %d %d %Qd %Qd %f %f %f %f %f %s\n",
|
||||
distinct_invariants[i]->id, distinct_invariants[i]->count, cumulative,
|
||||
distinct_invariants[i]->tr, distinct_invariants[i]->trinv,
|
||||
@ -245,8 +353,10 @@ int main(int argc, char *argv[])
|
||||
distinct_invariants[i]->x, distinct_invariants[i]->y, slope,
|
||||
print_word(&group->elements[distinct_invariants[i]->id], buf)
|
||||
);
|
||||
*/
|
||||
}
|
||||
|
||||
}
|
||||
// printf("- 0 %d - - - - 2.0\n", cumulative);
|
||||
|
||||
DEBUG("Clean up\n");
|
||||
for(int i = 0; i < nmax; i++) {
|
||||
@ -260,5 +370,4 @@ int main(int argc, char *argv[])
|
||||
free(matrices);
|
||||
coxeter_clear(group);
|
||||
mpq_clears(s, q, t, tmp, NULL);
|
||||
mps_context_free(solver);
|
||||
}
|
||||
|
||||
@ -33,6 +33,7 @@ int main(int argc, char *argv[])
|
||||
mat_workspace *ws;
|
||||
mat gen[6];
|
||||
mps_context *solver;
|
||||
mps_monomial_poly *poly;
|
||||
mat element, inverse;
|
||||
int letter1, letter2, letter;
|
||||
mpq_t tr, trinv;
|
||||
@ -68,6 +69,7 @@ int main(int argc, char *argv[])
|
||||
mat_init(inverse, 3);
|
||||
|
||||
solver = mps_context_new();
|
||||
poly = mps_monomial_poly_new(solver, 3);
|
||||
mps_context_set_output_prec(solver, 20); // relative precision
|
||||
mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
|
||||
|
||||
@ -112,7 +114,7 @@ int main(int argc, char *argv[])
|
||||
mat_trace(tr, element);
|
||||
mat_trace(trinv, inverse);
|
||||
|
||||
retval = solve_characteristic_polynomial(solver, tr, trinv, evs);
|
||||
retval = solve_characteristic_polynomial(solver, poly, tr, trinv, evs);
|
||||
if(retval == 1) {
|
||||
fprintf(stderr, "Error! Could not solve polynomial.\n");
|
||||
return 1;
|
||||
@ -150,7 +152,7 @@ int main(int argc, char *argv[])
|
||||
}
|
||||
|
||||
if(mode != 2)
|
||||
gmp_printf("%s %.9f\n", argv[w+3], slope);
|
||||
gmp_printf("%s %.9f %Qd %Qd\n", argv[w+3], slope, tr, trinv);
|
||||
}
|
||||
|
||||
if(mode != 0)
|
||||
|
||||
Loading…
Reference in New Issue
Block a user