working version of Q extensions
This commit is contained in:
Florian Stecker
parent
1f92d1af9c
commit
51f7b98ccb
15
Makefile
15
Makefile
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@ -1,8 +1,8 @@
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HEADERS=linalg.h mat.h coxeter.h enumerate_triangle_group.h parallel.h
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HEADERS=linalg.h mat.h coxeter.h enumerate_triangle_group.h parallel.h qext.h
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#SPECIAL_OPTIONS=-O0 -g -D_DEBUG -DQEXT_SQRT5
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SPECIAL_OPTIONS=-O0 -g -D_DEBUG -DQEXT
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#SPECIAL_OPTIONS=-O3 -pg -g -funroll-loops -fno-inline
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SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -DQEXT_SQRT5
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#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -DQEXT
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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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@ -19,8 +19,8 @@ billiard_words: billiard_words.hs
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singular_values: singular_values.o coxeter.o mat.o enumerate_triangle_group.o parallel.o
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mpicc $(OPTIONS) -o singular_values coxeter.o singular_values.o mat.o enumerate_triangle_group.o parallel.o -lm -lgmp -lmps
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singular_values_barbot: singular_values_barbot.o coxeter.o mat.o enumerate_triangle_group.o parallel.o
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mpicc $(OPTIONS) -o singular_values_barbot coxeter.o singular_values_barbot.o mat.o enumerate_triangle_group.o parallel.o -lm -lgmp -lmps
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singular_values_barbot: singular_values_barbot.o coxeter.o mat.o enumerate_triangle_group.o parallel.o qext.o
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mpicc $(OPTIONS) -o singular_values_barbot coxeter.o singular_values_barbot.o mat.o enumerate_triangle_group.o parallel.o qext.o -lm -lgmp -lmps
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#singular_values_mpi: singular_values_mpi.o coxeter.o mat.o
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# mpicc $(OPTIONS) -o singular_values_mpi coxeter.o singular_values_mpi.o mat.o -lm -lgmp -lmps
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@ -55,5 +55,8 @@ mat.o: mat.c $(HEADERS)
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parallel.o: parallel.c $(HEADERS)
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gcc $(OPTIONS) -c parallel.c
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qext.o: qext.c $(HEADERS)
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gcc $(OPTIONS) -c qext.c
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clean:
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rm -f singular_values singular_values_barbot special_element singular_values_mpi coxeter.o linalg.o singular_values.o singular_values_barbot.o singular_values_mpi.o mat.o special_element.o convert.hi convert.o convert billiard_words.hi billiard_words.o billiard_words enumerate_triangle_group.o parallel.o
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rm -f singular_values singular_values_barbot special_element singular_values_mpi coxeter.o linalg.o singular_values.o singular_values_barbot.o singular_values_mpi.o mat.o special_element.o convert.hi convert.o convert billiard_words.hi billiard_words.o billiard_words enumerate_triangle_group.o parallel.o qext.o
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@ -129,33 +129,38 @@ void discriminant(NUMBER out, NUMBER x, NUMBER y)
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CLEAR(x2);CLEAR(x3);CLEAR(y2);CLEAR(y3);CLEAR(tmp);
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}
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void generators_triangle_rotation_generic(mat *gen, NUMBER rho1, NUMBER rho2, NUMBER rho3, NUMBER s, NUMBER q)
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void generators_triangle_rotation_generic(mat *gen, NUMBER rho1, NUMBER rho2, NUMBER rho3, mpq_t s, mpq_t q)
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{
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mat_workspace *ws;
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mat r1,r2,r3;
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NUMBER b1,c1,a2,c2,a3,b3;
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NUMBER sinv;
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mpq_t sinv, qinv;
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ws = mat_workspace_init(3);
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INIT(sinv);INIT(b1);INIT(c1);INIT(a2);INIT(c2);INIT(a3);INIT(b3);
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INIT(b1);INIT(c1);INIT(a2);INIT(c2);INIT(a3);INIT(b3);
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mpq_init(sinv);
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mpq_init(qinv);
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mat_init(r1, 3);
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mat_init(r2, 3);
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mat_init(r3, 3);
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// sinv = s^{-1}
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SET_INT(sinv, 1);
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DIV(sinv, sinv, s);
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mpq_inv(sinv, s);
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mpq_inv(qinv, q);
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// c1 = rho2 q, a2 = rho3 q, b3 = rho1 q, b1 = c2 = a3 = 1/q
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MUL(c1, rho2, q);
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MUL(a2, rho3, q);
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MUL(b3, rho1, q);
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SET_Q(c1, q);
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SET_Q(a2, q);
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SET_Q(b3, q);
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MUL(c1, c1, rho2);
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MUL(a2, a2, rho3);
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MUL(b3, b3, rho1);
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SET_INT(b1, 1);
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SET_INT(c2, 1);
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SET_INT(a3, 1);
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DIV(b1, b1, q);
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DIV(c2, c2, q);
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DIV(a3, a3, q);
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SET_Q(b1, qinv);
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SET_Q(c2, qinv);
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SET_Q(a3, qinv);
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mat_zero(r1);
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mat_zero(r2);
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@ -183,17 +188,17 @@ void generators_triangle_rotation_generic(mat *gen, NUMBER rho1, NUMBER rho2, NU
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// gen[0] = diag(1,s^{-1},s)
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SET_INT(*mat_ref(gen[0], 0, 0), 1);
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mat_set(gen[0], 1, 1, sinv);
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mat_set(gen[0], 2, 2, s);
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SET_Q (*mat_ref(gen[0], 1, 1), sinv);
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SET_Q (*mat_ref(gen[0], 2, 2), s);
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// gen[1] = diag(s,1,s^{-1})
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mat_set(gen[1], 0, 0, s);
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SET_Q (*mat_ref(gen[1], 0, 0), s);
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SET_INT(*mat_ref(gen[1], 1, 1), 1);
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mat_set(gen[1], 2, 2, sinv);
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SET_Q (*mat_ref(gen[1], 2, 2), sinv);
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// gen[3] = diag(s^{-1},s,1)
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mat_set(gen[2], 0, 0, sinv);
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mat_set(gen[2], 1, 1, s);
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// gen[2] = diag(s^{-1},s,1)
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SET_Q (*mat_ref(gen[2], 0, 0), sinv);
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SET_Q (*mat_ref(gen[2], 1, 1), s);
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SET_INT(*mat_ref(gen[2], 2, 2), 1);
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// gen[0] = r2 * gen[0] * r3
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@ -214,7 +219,9 @@ void generators_triangle_rotation_generic(mat *gen, NUMBER rho1, NUMBER rho2, NU
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mat_pseudoinverse(ws, gen[5], gen[2]);
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mat_workspace_clear(ws);
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CLEAR(sinv);CLEAR(b1);CLEAR(c1);CLEAR(a2);CLEAR(c2);CLEAR(a3);CLEAR(b3);
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CLEAR(b1);CLEAR(c1);CLEAR(a2);CLEAR(c2);CLEAR(a3);CLEAR(b3);
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mpq_clear(sinv);
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mpq_clear(qinv);
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mat_clear(r1);
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mat_clear(r2);
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mat_clear(r3);
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@ -239,31 +246,29 @@ void generators_triangle_rotation_2346_rational(mat *gen, int p1, int p2, int p3
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}
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#endif
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#ifdef QEXT_SQRT5
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#ifdef QEXT
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void generators_triangle_rotation_555_barbot(mat *gen, mpq_t s_, mpq_t q_)
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{
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NUMBER rho, c, one, s, q;
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INIT(rho);INIT(c);INIT(one);INIT(s);INIT(q);
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NUMBER rho, c, one, s;
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INIT(rho);INIT(c);INIT(one);INIT(s);
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// c = - (1+sqrt(5))/2
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mpq_set_si(c[0], -1, 2);
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mpq_set_si(c[1], -1, 2);
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mpq_set_si(c->a[0], -1, 2);
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mpq_set_si(c->a[1], -1, 2);
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SET_ONE(one);
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mpq_set(s[0], s_);
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mpq_set_ui(s[1], 0, 1);
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mpq_set(q[0], q_);
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mpq_set_ui(q[1], 0, 1);
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SET_Q(s, s_);
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// rho = s^2 + cs + 1
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SET(rho, one);
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MUL(rho, rho, s);
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ADD(rho, rho, c);
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MUL(rho, rho, s);
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ADD(rho, rho, one);
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generators_triangle_rotation_generic(gen, rho, rho, rho, s, q);
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generators_triangle_rotation_generic(gen, rho, rho, rho, s_, q_);
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CLEAR(rho);CLEAR(c);CLEAR(one);CLEAR(s);CLEAR(q);
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CLEAR(rho);CLEAR(c);CLEAR(one);CLEAR(s);
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}
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#endif
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@ -10,15 +10,15 @@
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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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// geneartors
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void generators_triangle_rotation_generic(mat *gen, NUMBER rho1, NUMBER rho2, NUMBER rho3, NUMBER s, NUMBER q);
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// generators
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void generators_triangle_rotation_generic(mat *gen, NUMBER rho1, NUMBER rho2, NUMBER rho3, mpq_t s, mpq_t q);
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#ifdef QEXT_TRIVIAL
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void generators_triangle_rotation_2346_rational(mat *gen, int p1, int p2, int p3, mpq_t s, mpq_t q);
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#endif
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#ifdef QEXT_SQRT5
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void generators_triangle_rotation_555_barbot(mat *gen, mpq_t s, mpq_t q);
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#ifdef QEXT
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void generators_triangle_rotation_555_barbot(mat *gen, mpq_t s_, mpq_t q_);
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#endif
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// general functions
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128
mat.h
128
mat.h
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@ -8,119 +8,25 @@
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// library for matrix computations in variable rings (based on GMP types)
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#ifdef QEXT_SQRT5
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#ifdef QEXT
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typedef mpq_t NUMBER [2];
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#define INIT(x) do { mpq_init((x)[0]); mpq_init((x)[1]); } while(0)
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#define CLEAR(x) do { mpq_clear((x)[0]); mpq_clear((x)[1]); } while(0)
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#define SET(x,y) do { mpq_set((x)[0],(y)[0]); mpq_set((x)[1],(y)[1]); } while(0)
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#define SET_INT(x,y) do { mpq_set_si((x)[0],(y),1); mpq_set_si((x)[1],0,1); } while(0)
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#define SET_ZERO(x) SET_INT(x,0)
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#define SET_ONE(x) SET_INT(x,1)
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#define ADD(x,y,z) do { mpq_add((x)[0],(y)[0],(z)[0]); mpq_add((x)[1],(y)[1],(z)[1]); } while(0)
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#define SUB(x,y,z) do { mpq_sub((x)[0],(y)[0],(z)[0]); mpq_sub((x)[1],(y)[1],(z)[1]); } while(0)
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#define MUL multiply_sqrt5
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#define DIV divide_sqrt5
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#define CMP compare_sqrt5
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#define PRINT(x) gmp_printf("%Qd + %Qd*sqrt(5)", (x)[0], (x)[1])
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#define SPRINT(buf, x) gmp_sprintf(buf, "%Qd+%Qd*sqrt(5)", (x)[0], (x)[1])
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#include "qext.h"
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static void multiply_sqrt5(NUMBER out, NUMBER a, NUMBER b)
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{
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// could be in place!!!
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mpq_t tmp, result[2];
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mpq_inits(tmp, result[0], result[1], 0);
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mpq_mul(result[0], a[1], b[1]);
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mpq_set_si(tmp, 5, 1);
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mpq_mul(result[0], result[0], tmp);
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mpq_mul(tmp, a[0], b[0]);
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mpq_add(result[0], result[0], tmp);
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mpq_mul(result[1], a[1], b[0]);
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mpq_mul(tmp, a[0], b[1]);
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mpq_add(result[1], result[1], tmp);
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mpq_set(out[0], result[0]);
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mpq_set(out[1], result[1]);
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mpq_clears(tmp, result[0], result[1], 0);
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}
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static void divide_sqrt5(NUMBER out, NUMBER a, NUMBER b)
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{
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mpq_t denom, num, tmp, neg5, result[2];
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mpq_inits(denom, num, tmp, neg5, result[0], result[1], 0);
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mpq_set_si(neg5, -5, 1);
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mpq_mul(denom, b[1], b[1]);
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mpq_mul(denom, denom, neg5);
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mpq_mul(tmp, b[0], b[0]);
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mpq_add(denom, denom, tmp);
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mpq_mul(num, a[1], b[1]);
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mpq_mul(num, num, neg5);
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mpq_mul(tmp, a[0], b[0]);
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mpq_add(num, num, tmp);
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mpq_div(result[0], num, denom);
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mpq_mul(num, a[1], b[0]);
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mpq_mul(tmp, a[0], b[1]);
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mpq_sub(num, num, tmp);
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mpq_div(result[1], num, denom);
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mpq_set(out[0], result[0]);
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mpq_set(out[1], result[1]);
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mpq_clears(denom, num, tmp, neg5, result[0], result[1], 0);
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}
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static int compare_sqrt5(NUMBER x, NUMBER y)
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{
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int result;
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mpq_t p, q, p2, q2, c5;
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mpq_inits(p, q, p2, q2, c5, 0);
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mpq_sub(p, x[0], y[0]);
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mpq_sub(q, x[1], y[1]);
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/*
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want to know if p + sqrt(5) q > 0
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if p>0 and q>0: always true
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if p>0 and q<0: equivalent to |p|^2 > 5 |q|^2
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if p<0 and q>0: equivalent to |p|^2 < 5 |q|^2
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if p<0 and q<0: always false
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*/
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if(mpq_sgn(p) > 0 && mpq_sgn(q) > 0) {
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result = 1;
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goto done;
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}
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if(mpq_sgn(p) < 0 && mpq_sgn(q) < 0) {
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result = -1;
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goto done;
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}
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mpq_mul(p2, p, p);
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mpq_mul(q2, q, q);
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mpq_set_si(c5, 5, 1);
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mpq_mul(q2, q2, c5);
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if(mpq_sgn(p) > 0)
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result = mpq_cmp(p2, q2); // this can't be zero, or else |p/q| = sqrt(5), but it's irrational
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else if(mpq_sgn(p) < 0)
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result = -mpq_cmp(p2, q2); // this can be zero if p = 0 and q = 0
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else // p = 0
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return mpq_sgn(q);
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done:
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mpq_clears(p, q, p2, q2, c5, 0);
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return result;
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}
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#define NUMBER qext_number
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#define INIT qext_init
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#define CLEAR qext_clear
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#define SET qext_set
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#define SET_INT qext_set_int
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#define SET_Q qext_set_q
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#define SET_ZERO(x) qext_set_int((x),0)
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#define SET_ONE(x) qext_set_int((x),1)
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#define ADD qext_add
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#define SUB qext_sub
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#define MUL qext_mul
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// #define DIV qext_div
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#define CMP qext_cmp
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#define PRINT qext_print
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#define SNPRINT qext_snprint
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#endif
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54
qext.c
54
qext.c
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@ -1,15 +1,26 @@
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#include "qext.h"
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const int qext_coefficients[QEXT_RANK+1] = {36, 0, -8, 0, 1};
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int qext_rank;
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mpq_t *qext_coefficient;
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#include <stdio.h>
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#include <malloc.h>
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#define LOOP(i,n) for(int i = 0; i < (n); i++)
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void qext_setup(int rank, const int *coeffs)
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{
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qext_rank = rank;
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qext_coefficient = malloc(rank*sizeof(mpq_t));
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LOOP(i, rank) {
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mpq_init(qext_coefficient[i]);
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mpq_set_si(qext_coefficient[i], -coeffs[i], coeffs[rank]);
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}
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}
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void qext_init(qext_number x)
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{
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x->rk = QEXT_RANK;
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x->rk = qext_rank;
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x->a = malloc(x->rk*sizeof(mpq_t));
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LOOP(i, x->rk) mpq_init(x->a[i]);
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}
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@ -32,6 +43,13 @@ void qext_set_int(qext_number x, int y)
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mpq_set_ui(x->a[i], 0, 1);
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}
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void qext_set_q(qext_number x, mpq_t y)
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{
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mpq_set(x->a[0], y);
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for(int i = 1; i < x->rk; i++)
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mpq_set_ui(x->a[i], 0, 1);
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}
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void qext_add(qext_number result, qext_number x, qext_number y)
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{
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LOOP(i, x->rk) mpq_add(result->a[i], x->a[i], y->a[i]);
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@ -83,21 +101,13 @@ int qext_cmp(qext_number x, qext_number y)
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void qext_mul(qext_number out, qext_number x, qext_number y)
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{
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static initialized = 0;
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static mpq_t result[2*x->rk-1];
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static mpq_t coefficient[x->rk];
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static mpq_t tmp;
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mpq_t result[2*x->rk-1];
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mpq_t tmp;
|
||||
|
||||
if(!initialized) {
|
||||
run_before = 1;
|
||||
mpq_init(tmp);
|
||||
LOOP(i, 2*x->rk-1) {
|
||||
mpq_init(result[i]);
|
||||
}
|
||||
LOOP(i, x->rk) {
|
||||
mpq_init(coefficient[i]);
|
||||
mpq_set_si(coefficient[i], -qext_coefficients[i], qext_coefficients[x->rk]);
|
||||
}
|
||||
mpq_init(tmp);
|
||||
LOOP(i, 2*x->rk-1) {
|
||||
mpq_init(result[i]);
|
||||
mpq_set_ui(result[i], 0, 1);
|
||||
}
|
||||
|
||||
// rk*rk multiplications + (rk-1)*rk multiplications with fixed coefficients
|
||||
|
|
@ -105,8 +115,6 @@ void qext_mul(qext_number out, qext_number x, qext_number y)
|
|||
// degree 2: 4+2
|
||||
// degree 4: 16+12, including 6 times 0*
|
||||
|
||||
LOOP(i, 2*x->rk-1) mpq_set_ui(result[i], 0, 1);
|
||||
|
||||
LOOP(i, x->rk) LOOP(j, x->rk) {
|
||||
mpq_mul(tmp, x->a[i], y->a[j]);
|
||||
mpq_add(result[i+j], result[i+j], tmp);
|
||||
|
|
@ -114,18 +122,18 @@ void qext_mul(qext_number out, qext_number x, qext_number y)
|
|||
|
||||
for(int i = x->rk-2; i >= 0; i--) {
|
||||
LOOP(j, x->rk) {
|
||||
mpq_mul(tmp, coefficient[j], result[x->rk+i]);
|
||||
mpq_mul(tmp, qext_coefficient[j], result[x->rk+i]);
|
||||
mpq_add(result[i+j], result[i+j], tmp);
|
||||
}
|
||||
}
|
||||
|
||||
LOOP(i, x->rk) mpq_set(out->a[i], result[i]);
|
||||
|
||||
/*
|
||||
LOOP(i, 2*x->rk-1) mpq_clear(result[i]);
|
||||
LOOP(i, x->rk) mpq_clear(coefficient[i]);
|
||||
mpq_clear(tmp);
|
||||
*/
|
||||
}
|
||||
|
||||
void qext_div(qext_number out, qext_number x, qext_number y);
|
||||
void qext_div(qext_number out, qext_number x, qext_number y)
|
||||
{
|
||||
// todo: implement this by solving a linear system
|
||||
}
|
||||
|
|
|
|||
16
qext.h
16
qext.h
|
|
@ -3,8 +3,6 @@
|
|||
|
||||
#include <gmp.h>
|
||||
|
||||
#define QEXT_RANK 4
|
||||
|
||||
struct qext_number_internal {
|
||||
int rk;
|
||||
mpq_t *a;
|
||||
|
|
@ -12,26 +10,18 @@ struct qext_number_internal {
|
|||
|
||||
typedef struct qext_number_internal qext_number[1];
|
||||
|
||||
void qext_setup(int rank, const int *coeffs);
|
||||
void qext_init(qext_number x);
|
||||
void qext_clear(qext_number x);
|
||||
void qext_set(qext_number x, qext_number y);
|
||||
void qext_set_int(qext_number x, int y);
|
||||
void qext_set_q(qext_number x, mpq_t y);
|
||||
void qext_add(qext_number result, qext_number x, qext_number y);
|
||||
void qext_sub(qext_number result, qext_number x, qext_number y);
|
||||
void qext_mul(qext_number out, qext_number x, qext_number y);
|
||||
void qext_div(qext_number out, qext_number x, qext_number y);
|
||||
int qext_cmp(qext_number x, qext_number y);
|
||||
void qext_print(qext_number x);
|
||||
void qext_sprint(qext_number x);
|
||||
|
||||
static void qext_set_zero(qext_number x)
|
||||
{
|
||||
qext_set_int(x, 0);
|
||||
}
|
||||
|
||||
static void qext_set_one(qext_number x)
|
||||
{
|
||||
qext_set_int(x, 1);
|
||||
}
|
||||
void qext_snprint(char *str, size_t len, qext_number x);
|
||||
|
||||
#endif
|
||||
|
|
|
|||
|
|
@ -145,12 +145,15 @@ int invariants_trace_loxodromic(group_t *group, mat *matrices, struct result **i
|
|||
|
||||
// check if loxodromic
|
||||
NUMBER disc, zero;
|
||||
double disc_real;
|
||||
INIT(disc);
|
||||
INIT(zero);
|
||||
SET_ZERO(zero);
|
||||
for(int i = 0; i < nuniq; i++) {
|
||||
discriminant(disc, invariants[i]->tr, invariants[i]->trinv);
|
||||
invariants[i]->disc_sign = CMP(disc, zero);
|
||||
disc_real = mpq_get_d(disc->a[0]) + sqrt(5)*mpq_get_d(disc->a[1]);
|
||||
gmp_printf("%Qd %Qd %f\n", disc->a[0], disc->a[1], disc_real);
|
||||
invariants[i]->disc_sign = disc_real > 0 ? 1 : disc_real < 0 ? -1 : 0;
|
||||
}
|
||||
CLEAR(disc);
|
||||
CLEAR(zero);
|
||||
|
|
@ -417,6 +420,9 @@ int main(int argc, char *argv[])
|
|||
g->qend = atoi(argv[9]);
|
||||
g->qdenom = atoi(argv[10]);
|
||||
|
||||
const int coefficients[] = {-5, 0, 1};
|
||||
qext_setup(2, coefficients);
|
||||
|
||||
// initialize
|
||||
parallel_context *ctx = parallel_init();
|
||||
parallel_set_datasize_and_callbacks(ctx, init_node, do_computation, destroy_node,
|
||||
|
|
@ -537,13 +543,13 @@ int main(int argc, char *argv[])
|
|||
mpq_clear(tmp);
|
||||
*/
|
||||
|
||||
SPRINT(buf, n.distinct_invariants[i]->tr);
|
||||
SPRINT(buf2, n.distinct_invariants[i]->trinv);
|
||||
printf("%d %s %f %f %d\n",
|
||||
SNPRINT(buf, sizeof(buf), n.distinct_invariants[i]->tr);
|
||||
SNPRINT(buf2, sizeof(buf2), n.distinct_invariants[i]->trinv);
|
||||
printf("%d %s %d\n",
|
||||
n.distinct_invariants[i]->id,
|
||||
print_word(&n.group->elements[n.distinct_invariants[i]->id], buf3),
|
||||
mpq_get_d(n.distinct_invariants[i]->tr[0])+sqrt(5)*mpq_get_d(n.distinct_invariants[i]->tr[1]),
|
||||
mpq_get_d(n.distinct_invariants[i]->trinv[0])+sqrt(5)*mpq_get_d(n.distinct_invariants[i]->trinv[1]),
|
||||
// mpq_get_d(n.distinct_invariants[i]->tr[0])+sqrt(5)*mpq_get_d(n.distinct_invariants[i]->tr[1]),
|
||||
// mpq_get_d(n.distinct_invariants[i]->trinv[0])+sqrt(5)*mpq_get_d(n.distinct_invariants[i]->trinv[1]),
|
||||
n.distinct_invariants[i]->disc_sign);
|
||||
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue