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qpms/qpms/latticegens.c

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#include "lattices.h"
#include <limits.h>
#include <math.h>
#include <string.h>
#define MIN(x,y) ((x)<(y)?(x):(y))
// generic converting extractors
PGenPolReturnData PGen_next_pol_from_cart2(PGen *g) {
const PGenCart2ReturnData c = PGen_next_cart2(g);
if (c.flags & PGEN_DONE)
return PGenPolDoneVal;
else {
PGenPolReturnData p;
p.flags = (c.flags & ~QPMS_COORDS_BITRANGE) | QPMS_COORDS_POL;
p.point_pol = cart2pol(c.point_cart2);
return p;
}
}
PGenCart2ReturnData PGen_next_cart2_from_pol(PGen *g) {
const PGenPolReturnData p = PGen_next_pol(g);
if (p.flags & PGEN_DONE)
return PGenCart2DoneVal;
else {
PGenCart2ReturnData c;
c.flags = (p.flags & ~QPMS_COORDS_BITRANGE) | QPMS_COORDS_CART2;
c.point_cart2 = pol2cart(p.point_pol);
return c;
}
}
PGenSphReturnData PGen_next_sph_from_cart3(PGen *g) {
const PGenCart3ReturnData c = PGen_next_cart3(g);
if (c.flags & PGEN_DONE)
return PGenSphDoneVal;
else {
PGenSphReturnData s;
s.flags = (c.flags & ~QPMS_COORDS_BITRANGE) | QPMS_COORDS_SPH;
s.point_sph = cart2sph(c.point_cart3);
return s;
}
}
PGenCart3ReturnData PGen_next_cart3_from_cart2xy(PGen *g) {
const PGenCart2ReturnData c2 = PGen_next_cart2(g);
if (c2.flags & PGEN_DONE)
return PGenCart3DoneVal;
else {
PGenCart3ReturnData c3;
c3.flags = (c2.flags & ~QPMS_COORDS_BITRANGE) | QPMS_COORDS_CART3;
c3.point_cart3 = cart22cart3xy(c2.point_cart2);
return c3;
}
}
PGenSphReturnData PGen_next_sph_from_cart2(PGen *g) {
const PGenCart2ReturnData c = PGen_next_cart2(g);
if (c.flags & PGEN_DONE)
return PGenSphDoneVal;
else {
PGenSphReturnData s;
s.flags = (c.flags & ~QPMS_COORDS_BITRANGE) | QPMS_COORDS_SPH;
s.point_sph = cart22sph(c.point_cart2);
return s;
}
}
PGenCart3ReturnData PGen_next_cart3_from_sph(PGen *g) {
const PGenSphReturnData s = PGen_next_sph(g);
if (s.flags & PGEN_DONE)
return PGenCart3DoneVal;
else {
PGenCart3ReturnData c;
c.flags = (s.flags & ~QPMS_COORDS_BITRANGE) | QPMS_COORDS_CART3;
c.point_cart3 = sph2cart(s.point_sph);
return c;
}
}
// here, various "classes" of the PGenSph point generators are implemented.
// const PGenSphReturnData PGenSphDoneVal = {PGEN_DONE, {0,0,0}}; // defined already in lattices.h
// const PGenCart3ReturnData PGenCart3DoneVal = {PGEN_DONE, {0,0,0}}; // defined already in lattices.h
// General structure of a generator implementation looks like this:
#if 0
//==== PGen_NAME ====
extern const PGenClassInfo PGen_NAME; // forward declaration needed by constructor (may be placed in header file instead)
// Internal state structure
typedef struct PGen_NAME_StateData {
...
} PGen_NAME_StateData;
// Constructor
PGenSph PGen_NAME_new(...) {
g->stateData = malloc(sizeof(PGen_NAME_StateData));
...
PGenSph g = {&PGen_NAME, (void *) stateData};
return g;
}
// Dectructor
void PGen_NAME_destructor(PGen *g) {
...
free(g->stateData);
g->stateData = NULL;
}
// Extractor, spherical coordinate output
PGenSphReturnData PGen_NAME_next_sph(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenSphDoneVal;
else {
PGen_NAME_StateData *s = (PGen_NAME_StateData *) g->stateData;
if (... /* there are still points to be generated */) {
...
PGenSphReturnData retval = {.../*flags*/, .../*thePoint*/};
return retval;
} else {
PGen_destroy(g);
return PGenSphDoneVal;
}
}
}
// Extractor, 3D cartesian coordinate output
PGenCart3ReturnData PGen_NAME_next_cart3(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenCart3DoneVal;
else {
PGen_NAME_StateData *s = (PGen_NAME_StateData *) g->stateData;
if (... /* there are still points to be generated */) {
...
PGenCart3ReturnData retval = {.../*flags*/, .../*thePoint*/};
return retval;
} else {
PGen_destroy(g);
return PGenCart3DoneVal;
}
}
}
// Class metadata structure; TODO maybe this can rather be done by macro.
const PGenClassInfo PGen_NAME = {
"PGen_NAME",
?, //dimensionality
PGEN_COORDS_????, // native coordinate system
// some of the _next_... fun pointers can be NULL
PGen_NAME_next,
PGen_NAME_next_z,
PGen_NAME_next_pol,
PGen_NAME_next_sph,
PGen_NAME_next_cart2,
PGen_NAME_next_cart3,
PGen_NAME_fetch,
PGen_NAME_fetch_z,
PGen_NAME_fetch_pol,
PGen_NAME_fetch_sph,
PGen_NAME_fetch_cart2,
PGen_NAME_fetch_cart3,
PGen_NAME_destructor
};
#endif // 0
//==== PGenSph_FromPoint2DArray ====
// Internal state structure
typedef struct PGen_FromPoint2DArray_StateData {
const point2d *base;
size_t len;
size_t currentIndex;
}PGen_FromPoint2DArray_StateData;
// Constructor
PGen PGen_FromPoint2DArray_new(const point2d *points, size_t len) {
PGen_FromPoint2DArray_StateData *stateData = malloc(sizeof(PGen_FromPoint2DArray_StateData));
stateData->base = points;
stateData->len = len;
stateData->currentIndex = 0;
PGen g = {&PGen_FromPoint2DArray, (void *) stateData};
return g;
}
// Destructor
void PGen_FromPoint2DArray_destructor(PGen *g) {
free(g->stateData);
g->stateData = NULL;
}
// Extractor, 2D cartesian (native)
PGenCart2ReturnData PGen_FromPoint2DArray_next_cart2(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenCart2DoneVal;
else {
PGen_FromPoint2DArray_StateData *s = (PGen_FromPoint2DArray_StateData *) g->stateData;
if (s->currentIndex < s->len) {
cart2_t thePoint = s->base[s->currentIndex];
++(s->currentIndex);
PGenCart2ReturnData retval = {(PGEN_NOTDONE | PGEN_AT_XY | PGEN_COORDS_CART2), thePoint};
return retval;
} else {
PGen_destroy(g);
return PGenCart2DoneVal;
}
}
}
// Extractor, spherical
PGenSphReturnData PGen_FromPoint2DArray_next_sph(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenSphDoneVal;
else {
PGen_FromPoint2DArray_StateData *s = (PGen_FromPoint2DArray_StateData *) g->stateData;
if (s->currentIndex < s->len) {
sph_t thePoint = cart22sph(s->base[s->currentIndex]);
++(s->currentIndex);
PGenSphReturnData retval = {(PGEN_AT_XY | PGEN_COORDS_SPH), thePoint};
return retval;
} else {
PGen_destroy(g);
return PGenSphDoneVal;
}
}
}
const PGenClassInfo PGen_FromPoint2DArray = {
"PGen_FromPoint2DArray",
2, // dimensionality
PGEN_COORDS_CART2,
NULL,//PGen_FromPoint2DArray_next,
NULL,
NULL,//PGen_FromPoint2DArray_next_pol,
PGen_FromPoint2DArray_next_sph,
PGen_FromPoint2DArray_next_cart2,
NULL,//PGen_FromPoint2DArray_next_cart3,
NULL,//PGen_FromPoint2DArray_fetch,
NULL,//PGen_FromPoint2DArray_fetch_z,
NULL,//PGen_FromPoint2DArray_fetch_pol,
NULL,//PGen_FromPoint2DArray_fetch_sph,
NULL,//PGen_FromPoint2DArray_fetch_cart2,
NULL,//PGen_FromPoint2DArray_fetch_cart3,
PGen_FromPoint2DArray_destructor,
};
//==== PGen_1D ====
//equidistant points along the z-axis;
extern const PGenClassInfo PGen_1D; // forward declaration needed by constructor (may be placed in header file instead)
/* // This had to go to the header file:
enum PGen_1D_incrementDirection{
//PGEN1D_POSITIVE_INC, // not implemented
//PGEN1D_NEGATIVE_INC, // not implemented
PGEN1D_INC_FROM_ORIGIN,
PGEN1D_INC_TOWARDS_ORIGIN
};
*/
// Internal state structure
typedef struct PGen_1D_StateData {
long ptindex;
//long stopindex;
double minR, maxR;
bool inc_minR, inc_maxR;
double a; // lattice period
double offset; // offset of the zeroth lattice point from origin (will be normalised to interval [-a/2,a/2]
enum PGen_1D_incrementDirection incdir;
//bool skip_origin;
} PGen_1D_StateData;
static inline long ptindex_inc(long i) {
if (i > 0)
return -i;
else
return -i + 1;
}
static inline long ptindex_dec(long i) {
if (i > 0)
return -i + 1;
else
return -i;
}
// Constructor, specified by maximum and maximum absolute value
PGen PGen_1D_new_minMaxR(double period, double offset, double minR, bool inc_minR, double maxR, bool inc_maxR,
PGen_1D_incrementDirection incdir) {
PGen_1D_StateData *s = malloc(sizeof(PGen_1D_StateData));
s->minR = minR;
s->maxR = maxR;
s->inc_minR = inc_minR;
s->inc_maxR = inc_maxR;
s->incdir = incdir;
period = fabs(period);
double offset_normalised = offset - period * floor(offset / period); // shift to interval [0, period]
if (offset_normalised > period / 2) offset_normalised -= period; // and to interval [-period/2, period/2]
s->offset = offset_normalised;
if (offset_normalised > 0) // reverse the direction so that the conditions in _next() are hit in correct order
period *= -1;
switch(s->incdir) {
double curR;
case PGEN_1D_INC_FROM_ORIGIN:
s->ptindex = floor(minR / fabs(period));
while ( (curR = fabs(s->offset + s->ptindex * period)) < minR || (!inc_minR && curR <= minR))
s->ptindex = ptindex_inc(s->ptindex);
break;
case PGEN_1D_INC_TOWARDS_ORIGIN:
s->ptindex = - ceil(maxR / fabs(period));
while ( (curR = fabs(s->offset + s->ptindex * period)) > maxR || (!inc_minR && curR >= maxR))
s->ptindex = ptindex_dec(s->ptindex);
break;
default:
QPMS_WTF;
}
s->a = period;
PGen g = {&PGen_1D, (void *) s};
return g;
}
// Dectructor
void PGen_1D_destructor(PGen *g) {
free(g->stateData);
g->stateData = NULL;
}
// Extractor 1D number
PGenZReturnData PGen_1D_next_z(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenZDoneVal;
PGen_1D_StateData *s = (PGen_1D_StateData *) g->stateData;
const double zval = s->ptindex * s->a + s->offset;
const double r = fabs(zval);
bool theEnd = false;
switch (s->incdir) {
case PGEN_1D_INC_FROM_ORIGIN:
if (r < s->maxR || (s->inc_maxR && r == s->maxR))
s->ptindex = ptindex_inc(s->ptindex);
else theEnd = true;
break;
case PGEN_1D_INC_TOWARDS_ORIGIN:
if (r > s->minR || (s->inc_minR && r == s->minR)) {
if (s->ptindex == 0) // handle "underflow"
s->minR = INFINITY;
else
s->ptindex = ptindex_dec(s->ptindex);
} else theEnd = true;
break;
default:
QPMS_INVALID_ENUM(s->incdir);
}
if (!theEnd) {
const PGenZReturnData retval = {PGEN_NOTDONE | PGEN_AT_Z, zval};
return retval;
} else {
PGen_destroy(g);
return PGenZDoneVal;
}
}
// Extractor spherical coordinates // TODO remove/simplify
PGenSphReturnData PGen_1D_next_sph(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenSphDoneVal;
PGen_1D_StateData *s = (PGen_1D_StateData *) g->stateData;
const double zval = s->ptindex * s->a + s->offset;
const double r = fabs(zval);
bool theEnd = false;
switch (s->incdir) {
case PGEN_1D_INC_FROM_ORIGIN:
if (r < s->maxR || (s->inc_maxR && r == s->maxR))
s->ptindex = ptindex_inc(s->ptindex);
else theEnd = true;
break;
case PGEN_1D_INC_TOWARDS_ORIGIN:
if (r > s->minR || (s->inc_minR && r == s->minR)) {
if (s->ptindex == 0) // handle "underflow"
s->minR = INFINITY;
else
s->ptindex = ptindex_dec(s->ptindex);
} else theEnd = true;
break;
default:
QPMS_INVALID_ENUM(s->incdir);
}
if (!theEnd) {
const PGenSphReturnData retval = {PGEN_NOTDONE | PGEN_AT_Z | PGEN_COORDS_SPH,
{r, zval >= 0 ? 0 : M_PI, 0}};
return retval;
} else {
PGen_destroy(g);
return PGenSphDoneVal;
}
}
// Class metadata structure; TODO maybe this can rather be done by macro.
const PGenClassInfo PGen_1D = {
"PGen_1D",
1, // dimensionality
PGEN_COORDS_CART1,
NULL, //PGen_1D_next,
PGen_1D_next_z,
NULL,//PGen_1D_next_pol,
PGen_1D_next_sph,
NULL,//PGen_1D_next_cart2,
NULL,//PGen_1D_next_cart3,
NULL,//PGen_1D_fetch,
NULL,//PGen_1D_fetch_z,
NULL,//PGen_1D_fetch_pol,
NULL,//PGen_1D_fetch_sph,
NULL,//PGen_1D_fetch_cart2,
NULL,//PGen_1D_fetch_cart3,
PGen_1D_destructor
};
//==== PGen_xyWeb ====
// 2D lattice generator in the "spiderweb" style, generated in the "perimetre" order,
// not strictly ordered (or limited) by distance from origin.
// The minR and maxR here refer to the TODO WWHAT
extern const PGenClassInfo PGen_xyWeb; // forward declaration needed by constructor (may be placed in header file instead)
// Internal state structure
typedef struct PGen_xyWeb_StateData {
long i, j;
unsigned short phase; // 0 to 5
long layer;
long last_layer; // generation stops when layer > last_layer
double layer_min_height; // this * layer is what minR and maxR are compared to
double minR, maxR;
bool inc_minR, inc_maxR;
cart2_t b1, b2; // lattice vectors
cart2_t offset; // offset of the zeroth lattice point from origin (TODO will be normalised to the WS cell)
// TODO type rectangular vs. triangular
LatticeFlags lf;
} PGen_xyWeb_StateData;
// Constructor
PGen PGen_xyWeb_new(cart2_t b1, cart2_t b2, double rtol, cart2_t offset, double minR, bool inc_minR, double maxR, bool inc_maxR) {
PGen_xyWeb_StateData *s = malloc(sizeof(PGen_xyWeb_StateData));
s->minR = minR; s->maxR = maxR;
s->inc_minR = inc_minR;
s->inc_maxR = inc_maxR;
l2d_reduceBasis(b1, b2, &(s->b1), &(s->b2));
s->offset = offset; // TODO shorten into the WS cell ?
s->lf = l2d_detectRightAngles(s->b1, s->b2, rtol);
s->layer_min_height = l2d_hexWebInCircleRadius(s->b1, s->b2);
s->layer = ceil(s->minR/s->layer_min_height);
if(!inc_minR && (s->layer * s->layer_min_height) <= minR)
++(s->layer);
s->i = s->layer; s->j = 0; s->phase = 0; // init indices
s->last_layer = floor(s->maxR/s->layer_min_height);
if(!inc_maxR && (s->last_layer * s->layer_min_height) >= maxR)
--(s->last_layer);
PGen g = {&PGen_xyWeb, (void *) s};
return g;
}
// Destructor
void PGen_xyWeb_destructor(PGen *g) {
free(g->stateData);
g->stateData = NULL;
}
// Extractor (2D cartesian, native)
PGenCart2ReturnData PGen_xyWeb_next_cart2(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenCart2DoneVal;
else {
PGen_xyWeb_StateData * const s = (PGen_xyWeb_StateData *) g->stateData;
assert(s->layer >= 0);
if (s->layer <= s->last_layer) {
const cart2_t thePoint = cart2_add(s->offset,
cart2_add(cart2_scale(s->i, s->b1), cart2_scale(s->j, s->b2)));
if(s->layer == 0) { // origin is unique, proceed with next layer
++s->layer;
s->phase = 0;
s->i = s->layer;
s->j = 0;
}
else if(s->lf & ORTHOGONAL_01) {
// rectangular or square lattice, four perimeters
switch(s->phase) {
case 0: // initial i = l, j = 0
--s->i;
++s->j;
if(s->i <= 0) ++s->phase;
break;
case 1: // initial i = 0, j = l
--s->i;
--s->j;
if(s->j <= 0) ++s->phase;
break;
case 2: // initial i = -l, j = 0
++s->i;
--s->j;
if(s->i >= 0) ++s->phase;
break;
case 3: // initial i = 0, j = -l
++s->i;
++s->j;
if(s->j >= 0) ++s->phase;
break;
default:
QPMS_WTF;
}
if(s->phase == 4) { // phase overflow, start new layer
++s->layer;
s->phase = 0;
s->i = s->layer;
s->j = 0;
}
} else { // non-rectangular lattice, six perimeters
switch(s->phase) {
case 0:
--s->i;
++s->j;
if(s->i <= 0) ++s->phase;
break;
case 1:
--s->i;
if(s->i + s->j <= 0) ++s->phase;
break;
case 2:
--s->j;
if(s->j <= 0) ++s->phase;
break;
case 3:
++s->i;
--s->j;
if(s->i >= 0) ++s->phase;
break;
case 4:
++s->i;
if(s->i + s->j >= 0) ++s->phase;
break;
case 5:
++s->j;
if(s->j >= 0) ++s->phase;
break;
default:
QPMS_WTF;
}
if(s->phase == 6) { // phase overflow, start next layer
++s->layer;
s->phase = 0;
s->i = s->layer;
s->j = 0;
}
}
PGenCart2ReturnData retval = {(PGEN_NOTDONE | PGEN_AT_XY | PGEN_COORDS_CART2), thePoint};
return retval;
} else {
PGen_destroy(g);
return PGenCart2DoneVal;
}
}
}
// Class metadata structure; TODO maybe this can rather be done by macro.
const PGenClassInfo PGen_xyWeb = {
"PGen_xyWeb",
2,
PGEN_COORDS_CART2,
NULL,//PGen_xyWeb_next, // FIXME I should really implement this.
NULL,//PGen_xyWeb_next_z,
PGen_next_pol_from_cart2, //NULL,//PGen_xyWeb_next_pol,
PGen_next_sph_from_cart2, //NULL,//PGen_xyWeb_next_sph,
PGen_xyWeb_next_cart2, // native
PGen_next_cart3_from_cart2xy, //NULL,//PGen_xyWeb_next_cart3,
NULL,//PGen_xyWeb_fetch, // FIXME I should really implement this
NULL,//PGen_xyWeb_fetch_z,
NULL,//PGen_xyWeb_fetch_pol,
NULL,//PGen_xyWeb_fetch_sph,
NULL,//PGen_xyWeb_fetch_cart2,
NULL,//PGen_xyWeb_fetch_cart3,
PGen_xyWeb_destructor
};
size_t PGen_xyWeb_sizecap(cart2_t b1, cart2_t b2, double rtol, cart2_t offset,
double minR, bool inc_minR, double maxR, bool inc_maxR)
{
l2d_reduceBasis(b1, b2, &b1, &b2);
LatticeFlags lf = l2d_detectRightAngles(b1, b2, rtol);
double layer_min_height = l2d_hexWebInCircleRadius(b1, b2);
long layer = ceil(minR / layer_min_height);
if(!inc_minR && (layer * layer_min_height) <= minR)
++layer;
long last_layer = floor(maxR / layer_min_height);
if(!inc_maxR && (last_layer * layer_min_height) >= maxR)
--(last_layer);
// TODO less crude estimate (this one should be safe, however)
return ((lf & ORTHOGONAL_01) ? 4 : 6) * (last_layer - layer + 1);
}
//==== PGen_LatticeRadialHeap ====
extern const PGenClassInfo PGen_LatticeRadialHeap; // forward declaration needed by constructor (may be placed in header file instead)
// Internal state structure
typedef struct PGen_LatticeRadialHeap_StateData {
int ldim; // 2 or 3, must
int sdim;
int layer;
// Minimal distance of a point from the origin in the last layer (if the top of the heap exceeds this, a new layer must be evaluated
double layer_min_r;
size_t heap_len;
size_t heap_capacity;
double *r_heap;
int *coord_heap;
double b[0]; // basis vectors and offset
double offset_r;
double minR, maxR;
bool inc_minR, inc_maxR;
} PGen_LatticeRadialHeap_StateData;
static inline double nd2norm(const double a[], int d) {
double n = 0;
for(int i = 0; i < d; ++i)
n += a[i]*a[i];
return sqrt(n);
}
// General Constructor
PGen_LatticeRadialHeap_StateData *PGen_LatticeRadialHeap_new(int ldim, int sdim, double bvectors[],
double offset[], double minR, double maxR,
bool inc_minR, bool inc_maxR) {
QPMS_UNTESTED;
PGen_LatticeRadialHeap_StateData *s =
malloc(sizeof(PGen_LatticeRadialHeap_StateData) + (ldim + 1) * sdim * sizeof(double));
s->ldim = ldim;
s->sdim = sdim;
memcpy(s->b, bvectors, ldim * sdim * sizeof(double));
if (offset) {
memcpy(s->b + ldim * sdim, offset, sdim * sizeof(double));
s->offset_r = nd2norm(s->b + ldim*sdim, sdim);
} else {
for (size_t i = 0; i < sdim; ++i)
s->b[ldim*sdim + i] = 0;
s->offset_r = 0;
}
s->heap_len = 0;
s->heap_capacity = 1024;
QPMS_CRASHING_MALLOC(s->r_heap, sizeof(*s->r_heap) * s->heap_capacity);
QPMS_CRASHING_MALLOC(s->coord_heap, sizeof(*s->coord_heap) * ldim * s->heap_capacity);
s->layer = -1;
s->layer_min_r = -INFINITY;
s->inc_minR = inc_minR; s->inc_maxR = inc_maxR;
return s;
}
// 2D constructor
PGen PGen_LatticeRadialHeap2D_new(cart2_t b1, cart2_t b2, cart2_t offset,
double minR, bool inc_minR, double maxR, bool inc_maxR) {
double bvectors[4];
double offset_a[2];
cart2_to_double_array(&bvectors[0], b1);
cart2_to_double_array(&bvectors[2], b2);
cart2_to_double_array(offset_a, offset);
PGen g = {.c = &PGen_LatticeRadialHeap2D,
.stateData = PGen_LatticeRadialHeap_new(2, 2, bvectors, offset_a,
minR, maxR, inc_minR, inc_maxR)};
return g;
}
// 3D constructor
PGen PGen_LatticeRadialHeap3D_new(const cart3_t *b1, const cart3_t *b2, const cart3_t *b3,
const cart3_t *offset, double minR, bool inc_minR, double maxR, bool inc_maxR) {
double bvectors[9];
double offset_a[3];
int ldim = 0;
if (b1) {cart3_to_double_array(&bvectors[3*ldim], *b1); ++ldim;}
if (b2) {cart3_to_double_array(&bvectors[3*ldim], *b2); ++ldim;}
if (b3) {cart3_to_double_array(&bvectors[3*ldim], *b3); ++ldim;}
QPMS_ENSURE(ldim > 0, "At least one basis vector must be specified (non-NULL)");
PGen g = {.c = &PGen_LatticeRadialHeap3D,
.stateData = PGen_LatticeRadialHeap_new(ldim, 3, bvectors,
offset ? (cart3_to_double_array(offset_a, *offset), offset_a) : NULL,
minR, maxR, inc_minR, inc_maxR)};
return g;
}
// Increment a counter array with constant sum; in the beginning, both counter[] and counter_cumsum[]
// are expected to be init'd to {thesum, 0, 0, ..., 0}
// Everything is expected to be positive (although the types are signed)
static inline _Bool counter_increment(const int ldim, int counter[],
int counter_cumsum[], const int thesum) {
for(int i = 1; i < ldim; ++i) {
if(counter_cumsum[i] < thesum) { // Can increment this, do it.
++counter[i];
++counter_cumsum[i];
for(int j = i - 1; j > 0; --j) { // Zero the preceding ones
counter[j] = 0;
counter_cumsum[j] = counter_cumsum[i];
}
// Determine the last digit
counter[0] = thesum - counter_cumsum[1];
return 1; // Incremented successfully
}
}
return 0; // Could not increment (counter exhausted)
}
// Assuming the counter is initialised to all non-negative values, step through
// all the possible sign combinations. In the end, return them back to non-negative
// and return false.
static inline _Bool counter_signcycle(const int ldim, int counter[]) {
for(int i = 0; i < ldim; ++i) { // Flip signs until a sign flipped to negative (cool, right?)
counter[i] = -counter[i];
if (counter[i] < 0)
return 1;
}
return 0;
}
static inline double PGen_LatticeRadialHeap_nextlayer(PGen_LatticeRadialHeap_StateData *s) {
double mindist = 0;
s->layer++;
double minr = +INFINITY;
const int ldim = s->ldim;
const int sdim = s->sdim;
int *counter, *counter_cumsum, *tmp;
QPMS_CRASHING_CALLOC(counter, s->ldim * 2, sizeof(*counter));
counter_cumsum = counter + s->ldim;
counter[0] = s->layer;
counter_cumsum[0] = s->layer;
do {
if (s->heap_len >= s->heap_capacity - 1) { // Check heap capacity
s->heap_capacity = s->heap_capacity >= 1024 ? s->heap_capacity * 2 : 1024;
QPMS_CRASHING_REALLOC(s->r_heap, sizeof(*s->r_heap) * s->heap_capacity);
QPMS_CRASHING_REALLOC(s->coord_heap, sizeof(*s->coord_heap) * ldim * s->heap_capacity);
}
double r = 0;
for(int i = 0; i < s->sdim; ++i) { // calculate r
double component = s->b[ldim * sdim + i]; // offset
for (int j = 0; j < s->ldim; ++j)
component += s->b[j * sdim + i] * counter[j];
r += component * component;
}
r = sqrt(r);
minr = MIN(r, minr);
// Add to the heaps
int position = s->heap_len++;
s->r_heap[position] = r;
memcpy(&s->coord_heap[ldim * position], counter, sizeof(*s->coord_heap) * ldim);
// bubble-up
while(position > 0) {
int parent = (position - 1) / 2;
if (s->r_heap[parent] > r) { // swap
s->r_heap[position] = s->r_heap[parent];
memcpy(&s->coord_heap[ldim * position], &s->coord_heap[ldim * parent], sizeof(*s->coord_heap) * ldim);
s->r_heap[parent] = r;
memcpy(&s->coord_heap[ldim * parent], counter, sizeof(*s->coord_heap) * ldim);
position = parent;
}
else break;
}
} while (counter_signcycle(s->ldim, counter)
|| counter_increment(s->ldim, counter, counter_cumsum, s->layer));
free(counter);
return minr;
}
// sdim-independent generator method, returns the integer lattice coordinates
// N.B. This ALWAYS produces, not checking against maxR or destructing the generator itself
// (although it does discard the points with distance smaller (or equal) than minR)
// TODO maybe I want to return (double) r instead of (int) 0
int PGen_LatticeRadialHeap_fillNext_intcoords(PGen_LatticeRadialHeap_StateData *s, int target[]) {
bool hit = false;
while(!hit) {
// Ensure that we have sufficiently filled heap
while (s->heap_len < 1 || s->r_heap[0] + s->offset_r > s->layer_min_r)
s->layer_min_r = PGen_LatticeRadialHeap_nextlayer(s);
double r = s->r_heap[0];
hit = (r > s->minR || (s->inc_minR && r == s->minR));
if (hit) memcpy(target, s->coord_heap, s->ldim * sizeof(*target));
// Heap extract anyway
// Move last element to root
--(s->heap_len);
s->r_heap[0] = s->r_heap[s->heap_len];
memmove(s->coord_heap, &s->coord_heap[s->ldim * s->heap_len], s->ldim * sizeof(*s->coord_heap));
// Bubble down
int pos = 0;
while(1) {
int largest = pos, kidL = 2*pos+1, kidR = 2*pos+2;
if (kidL < s->heap_len && s->r_heap[kidL] > s->r_heap[largest])
largest = kidL;
if (kidR < s->heap_len && s->r_heap[kidR] > s->r_heap[largest])
largest = kidR;
if (largest == pos)
break;
else { // swap
s->r_heap[pos] = s->r_heap[largest];
s->r_heap[largest] = r;
memcpy(&s->coord_heap[s->ldim * pos], &s->coord_heap[s->ldim * largest], s->ldim * sizeof(*s->coord_heap));
memcpy(&s->coord_heap[s->ldim * largest], &s->coord_heap[s->ldim * s->heap_len /*it's still there*/],
s->ldim * sizeof(*s->coord_heap));
}
}
}
return 0;
}
// sdim-independent generator method, fills the point's cartesian coordinates, including the offset
// N.B. This ALWAYS produces, returning 0 if maxR not exceeded, else -2
// (it does discard the points with distance smaller (or equal) than minR)
#define LRH_STACKBUFSIZ 3 // Avoid heap allocation for typical dimensions
int PGen_LatticeRadialHeap_fillNext_cart(PGen *g, double target[]) {
if (g->stateData == NULL) // already destroyed
return -1; // LPTODO some other return value?
else {
PGen_LatticeRadialHeap_StateData * const s = g->stateData;
int stackbuf[LRH_STACKBUFSIZ];
int *buf;
if (s->sdim > LRH_STACKBUFSIZ) {
QPMS_CRASHING_MALLOC(buf, s->sdim * sizeof(*buf));
} else
buf = stackbuf;
QPMS_ENSURE_SUCCESS(PGen_LatticeRadialHeap_fillNext_intcoords(s, buf));
// Calculate the actual point
double r = 0;
for(int i = 0; i < s->sdim; ++i) { // calculate r
double component = s->b[s->ldim * s->sdim + i]; // offset
for (int j = 0; j < s->ldim; ++j)
component += s->b[j * s->sdim + i] * buf[j];
r += component * component;
target[i] = component;
}
r = sqrt(r);
if (s->sdim > LRH_STACKBUFSIZ) free(buf);
if (r < s->maxR || (r == s->maxR && s->inc_maxR))
return 0;
else
return -2;
}
}
// Destructor
void PGen_LatticeRadialHeap_destructor(PGen *g) {
PGen_LatticeRadialHeap_StateData *s = g->stateData;
free(s->r_heap);
free(s->coord_heap);
free(g->stateData);
g->stateData = NULL;
}
// Extractor, 2D cartesian coordinate output
PGenCart2ReturnData PGen_LatticeRadialHeap2D_next_cart2(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenCart2DoneVal;
else {
PGen_LatticeRadialHeap_StateData *s = (PGen_LatticeRadialHeap_StateData *) g->stateData;
QPMS_ENSURE(s->sdim <= 2, "Attemted to get a 2D point from %nD generator.", (int)(s->sdim));
double target[2] = {0,0};
if (PGen_LatticeRadialHeap_fillNext_cart(g, target) == 0 /* there are still points to be generated */) {
PGenCart2ReturnData retval = {PGEN_COORDS_CART2 | PGEN_NOTDONE, cart2_from_double_array(target)};
return retval;
} else { // Maybe more checking for errors?
PGen_destroy(g);
return PGenCart2DoneVal;
}
}
}
// Extractor, 3D cartesian coordinate output
PGenCart3ReturnData PGen_LatticeRadialHeap3D_next_cart3(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenCart3DoneVal;
else {
PGen_LatticeRadialHeap_StateData *s = (PGen_LatticeRadialHeap_StateData *) g->stateData;
QPMS_ENSURE(s->sdim <= 3, "Attemted to get a 3D point from %nD generator.", (int)(s->sdim));
double target[3] = {0,0,0};
if (PGen_LatticeRadialHeap_fillNext_cart(g, target) == 0 /* there are still points to be generated */) {
PGenCart3ReturnData retval = {PGEN_COORDS_CART3 | PGEN_NOTDONE, cart3_from_double_array(target)};
return retval;
} else { // Maybe more checking for errors?
PGen_destroy(g);
return PGenCart3DoneVal;
}
}
}
// Class metadata structure; TODO maybe this can rather be done by macro.
const PGenClassInfo PGen_LatticeRadialHeap2D = {
"PGen_LatticeRadialHeap2D", // 2D labels the space, not lattice dimension
2, //dimensionality
PGEN_COORDS_CART2, // native coordinate system
// some of the _next_... fun pointers can be NULL
NULL, //PGen_LatticeRadialHeap2D_next,
NULL, //PGen_LatticeRadialHeap2D_next_z,
PGen_next_pol_from_cart2, // NULL, //PGen_LatticeRadialHeap2D_next_pol,
PGen_next_sph_from_cart2, // NULL, //PGen_LatticeRadialHeap2D_next_sph,
PGen_LatticeRadialHeap2D_next_cart2,
PGen_next_cart3_from_cart2xy, // NULL, //PGen_LatticeRadialHeap2D_next_cart3,
NULL, //PGen_LatticeRadialHeap2D_fetch,
NULL, //PGen_LatticeRadialHeap2D_fetch_z,
NULL, //PGen_LatticeRadialHeap2D_fetch_pol,
NULL, //PGen_LatticeRadialHeap2D_fetch_sph,
NULL, //PGen_LatticeRadialHeap2D_fetch_cart2,
NULL, //PGen_LatticeRadialHeap2D_fetch_cart3,
PGen_LatticeRadialHeap_destructor
};
// Class metadata structure; TODO maybe this can rather be done by macro.
const PGenClassInfo PGen_LatticeRadialHeap3D = {
"PGen_LatticeRadialHeap3D", // 3D labels the space, not lattice dimension
3, //dimensionality
PGEN_COORDS_CART3, // native coordinate system
// some of the _next_... fun pointers can be NULL
NULL, //PGen_LatticeRadialHeap3D_next,
NULL, //PGen_LatticeRadialHeap3D_next_z,
NULL, //PGen_LatticeRadialHeap3D_next_pol,
PGen_next_sph_from_cart3, // NULL, //PGen_LatticeRadialHeap3D_next_sph,
NULL, //PGen_LatticeRadialHeap3D_next_cart2,
PGen_LatticeRadialHeap3D_next_cart3,
NULL, //PGen_LatticeRadialHeap3D_fetch,
NULL, //PGen_LatticeRadialHeap3D_fetch_z,
NULL, //PGen_LatticeRadialHeap3D_fetch_pol,
NULL, //PGen_LatticeRadialHeap3D_fetch_sph,
NULL, //PGen_LatticeRadialHeap3D_fetch_cart2,
NULL, //PGen_LatticeRadialHeap3D_fetch_cart3,
PGen_LatticeRadialHeap_destructor
};
//==== PGen_shifted ====
// Meta-generator that takes another generator and generates points shifted by a constant
extern const PGenClassInfo PGen_shifted; // forward declaration needed by constructor (may be placed in header file instead)
// Internal state structure
typedef struct PGen_shifted_StateData {
PGen orig;
cart3_t shift;
} PGen_shifted_StateData;
// Constructor
PGen PGen_shifted_new(PGen orig, cart3_t shift) {
PGen_shifted_StateData *s = malloc(sizeof(PGen_shifted_StateData));
s->shift = shift;
s->orig = orig;
PGen g = {&PGen_shifted, (void *) s};
return g;
}
// Dectructor
void PGen_shifted_destructor(PGen *g) {
PGen_shifted_StateData *s = g->stateData;
if(s->orig.stateData) PGen_destroy(&(s->orig));
free(g->stateData);
g->stateData = NULL;
}
// Extractor, 3D cartesian coordinate output
PGenCart3ReturnData PGen_shifted_next_cart3(PGen *g) {
if (g->stateData == NULL) // already destroyed
return PGenCart3DoneVal;
else {
PGen_shifted_StateData *s = (PGen_shifted_StateData *) g->stateData;
PGenCart3ReturnData retdata = PGen_next_cart3(&(s->orig));
if ((retdata.flags & PGEN_NOTDONE)) {
retdata.point_cart3 = cart3_add(retdata.point_cart3, s->shift);
retdata.flags = PGEN_COORDS_CART3 | PGEN_NOTDONE; //TODO more advanced flags?
return retdata;
} else {
PGen_destroy(g);
return retdata;
}
}
}
// Class metadata structure; TODO maybe this can rather be done by macro.
const PGenClassInfo PGen_shifted = {
"PGen_shifted",
3, //dimensionality
PGEN_COORDS_CART3, // native coordinate system
// some of the _next_... fun pointers can be NULL
NULL, //PGen_shifted_next,
NULL, //PGen_shifted_next_z,
NULL, //PGen_shifted_next_pol,
PGen_next_sph_from_cart3, //PGen_shifted_next_sph,
NULL, //PGen_shifted_next_cart2,
PGen_shifted_next_cart3, // native
NULL, //PGen_shifted_fetch,
NULL, //PGen_shifted_fetch_z,
NULL, //PGen_shifted_fetch_pol,
NULL, //PGen_shifted_fetch_sph,
NULL, //PGen_shifted_fetch_cart2,
NULL, //PGen_shifted_fetch_cart3, // TODO at least this
PGen_shifted_destructor
};
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