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lsystems_v7.c
1027 lines (712 loc) · 27 KB
/
lsystems_v7.c
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//////////////////////////////////////////////////////////////////////
//
// lsystems_v7.c
// Matt Zucker
//
//////////////////////////////////////////////////////////////////////
//
// Based on documentation in https://en.wikipedia.org/wiki/L-system and
// http://paulbourke.net/fractals/lsys/
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <ctype.h>
#include <math.h>
#include <time.h>
#ifdef _OPENMP
#include <omp.h>
#endif
//////////////////////////////////////////////////////////////////////
// for benchmarking
double get_time_as_double(void);
//////////////////////////////////////////////////////////////////////
// dynamic array
// dynamic array data type
typedef struct darray {
size_t elem_size;
size_t capacity;
size_t count;
unsigned char* data;
} darray_t;
// dynamic array functions
void darray_create(darray_t* darray, size_t elem_size, size_t capacity);
void darray_resize(darray_t* darray, size_t new_count);
void darray_extend(darray_t* darray, const void* elements, size_t count);
void darray_push_back(darray_t* darray, const void* elem);
void darray_pop_back(darray_t* darray, void* elem);
void* darray_elem_ptr(darray_t* darray, size_t idx);
const void* darray_const_elem_ptr(const darray_t* darray, size_t idx);
void darray_get(const darray_t* darray, size_t idx, void* dst);
void darray_set(darray_t* darray, size_t idx, const void* src);
void darray_clear(darray_t* darray);
void darray_destroy(darray_t* darray);
//////////////////////////////////////////////////////////////////////
// geometry utils
// 2D point
typedef struct point2d {
float x, y;
} point2d_t;
// 2D rotation
typedef struct rot2d {
float c, s;
} rot2d_t;
// 2D transformation
typedef struct xform {
point2d_t pos;
rot2d_t rot;
float angle;
} xform_t;
// identity transform
static const xform_t IDENTITY_XFORM = {
{ 0.f, 0.f, }, { 1.f, 0.f }, 0.f
};
// 2D geometry functions
int positive_mod(int ticks, int divisor);
point2d_t rotate_point(const rot2d_t R, const point2d_t p);
rot2d_t rotate_compose(const rot2d_t R2, const rot2d_t R1);
point2d_t translate_point(const point2d_t p, const point2d_t q);
xform_t xform_inverse(xform_t xform);
xform_t xform_compose(xform_t xform2, xform_t xform1);
point2d_t xform_transform_point(xform_t xform, point2d_t p);
//////////////////////////////////////////////////////////////////////
// L-System types/functions
// misc enums
enum {
LSYS_MAX_RULES = 128,
LSYS_MAX_CYCLE_LENGTH = 256,
LSYS_INIT_STRING_CAPACITY = 4096,
LSYS_INIT_STATES_CAPACITY = 64,
LSYS_INIT_SEGMENTS_CAPACITY = 1024
};
// line segment is 2 points
typedef struct lsys_segment {
point2d_t p0, p1;
} lsys_segment_t;
// rule tagged with string length for string replacement
typedef struct lsys_sized_string {
const char* replacement;
size_t length;
} lsys_sized_string_t;
// L-System datatype
typedef struct lsystem {
const char* name;
const char* start;
lsys_sized_string_t rules[LSYS_MAX_RULES];
unsigned char draw_chars[LSYS_MAX_RULES];
double turn_angle_rad;
int rotation_cycle_length;
rot2d_t rotations[LSYS_MAX_CYCLE_LENGTH];
} lsys_t;
// lsystem character + replacement pair, for defining L-Systems
typedef struct lsys_rule_def {
char symbol;
const char* replacement;
} lsys_rule_def_t;
// datatype for memoizing a single L-System rule
typedef struct lsys_memo {
size_t memo_iterations;
size_t segment_start;
size_t segment_count;
xform_t init_inverse;
xform_t delta_xform;
} lsys_memo_t;
// datatype for memoizing an entire L-system
typedef struct lsys_memo_set {
size_t total_iterations;
size_t min_memo_segments;
size_t min_parallel_segments;
lsys_memo_t* memos[LSYS_MAX_RULES];
} lsys_memo_set_t;
void lsys_create(lsys_t* lsys,
const char* name,
const char* start,
lsys_rule_def_t const rules[],
double turn_angle_deg,
const char* draw_chars);
void lsys_print(const lsys_t* lsys);
char* lsys_build_string(const lsys_t* lsys, size_t total_iterations);
darray_t* lsys_segments_from_string(const lsys_t* lsys,
const char* lstring);
darray_t* lsys_segments_recursive(const lsys_t* lsys,
size_t total_iterations,
size_t min_memo_segments,
size_t min_parallel_segments);
//////////////////////////////////////////////////////////////////////
// set up some known L-Systems
enum {
LSYS_SIERPINSKI_ARROWHEAD = 0, // depth 17 takes ~5 sec
LSYS_SIERPINSKI_TRIANGLE, // depth 16 takes ~3 sec
LSYS_DRAGON_CURVE, // depth 26 takes ~6 sec
LSYS_BARNSLEY_FERN, // depth 13 takes ~7 sec
LSYS_STICKS, // depth 16 takes ~4 sec
LSYS_HILBERT, // depth 13 takes ~3 sec
LSYS_PENTAPLEXITY, // depth 9 takes ~2 sec
NUM_KNOWN_LSYSTEMS
};
lsys_t KNOWN_LSYSTEMS[NUM_KNOWN_LSYSTEMS];
void initialize_known_lsystems(void);
//////////////////////////////////////////////////////////////////////
// options for running this program
typedef enum lsys_method {
LSYS_METHOD_RECURSION,
LSYS_METHOD_STRING
} lsys_method_t;
typedef struct options {
lsys_t* lsys;
size_t total_iterations;
size_t max_segments;
lsys_method_t method;
size_t min_memo_segments;
size_t min_parallel_segments;
} options_t;
void parse_options(int argc, char** argv, options_t* opts);
//////////////////////////////////////////////////////////////////////
double get_time_as_double(void) {
struct timespec tp;
clock_gettime(CLOCK_REALTIME, &tp);
return (double)tp.tv_sec + (double)tp.tv_nsec * 1e-9;
}
//////////////////////////////////////////////////////////////////////
int positive_mod(int ticks, int divisor) {
int rval = ticks % divisor;
if (ticks < 0) {
rval += divisor;
}
return rval;
}
point2d_t rotate_point(const rot2d_t R, const point2d_t p) {
return (point2d_t){
R.c * p.x - R.s * p.y,
R.s * p.x + R.c * p.y
};
}
rot2d_t rotate_compose(const rot2d_t R2, const rot2d_t R1) {
return (rot2d_t) {
R2.c * R1.c - R2.s * R1.s,
R2.s * R1.c + R2.c * R1.s,
};
}
point2d_t translate_point(const point2d_t p, const point2d_t q) {
return (point2d_t) { p.x + q.x, p.y + q.y };
}
xform_t xform_inverse(xform_t xform) {
rot2d_t rinv = { xform.rot.c, -xform.rot.s };
return (xform_t) {
.pos = rotate_point(rinv, (point2d_t){ -xform.pos.x, -xform.pos.y }),
.rot = rinv,
.angle = -xform.angle
};
}
xform_t xform_compose(xform_t xform2,
xform_t xform1) {
return (xform_t) {
.pos = translate_point(xform2.pos,
rotate_point(xform2.rot, xform1.pos)),
.rot = rotate_compose(xform2.rot, xform1.rot),
.angle = xform2.angle + xform1.angle
};
}
point2d_t xform_transform_point(xform_t xform,
point2d_t p) {
return translate_point(rotate_point(xform.rot, p), xform.pos);
}
//////////////////////////////////////////////////////////////////////
void darray_create(darray_t* darray, size_t elem_size, size_t capacity) {
size_t alloc_size = elem_size * capacity;
darray->elem_size = elem_size;
darray->count = 0;
darray->capacity = capacity;
darray->data = malloc(alloc_size);
}
void darray_resize(darray_t* darray, size_t new_count) {
if (new_count > darray->capacity) {
size_t new_capacity = darray->capacity;
while (new_capacity <= new_count) {
new_capacity *= 2;
}
size_t alloc_size = darray->elem_size * new_capacity;
darray->data = realloc(darray->data, alloc_size);
darray->capacity = new_capacity;
}
darray->count = new_count;
}
void darray_extend(darray_t* darray, const void* elements, size_t count) {
size_t offset = darray->elem_size * darray->count;
darray_resize(darray, darray->count + count);
memcpy(darray->data + offset, elements, count*darray->elem_size);
}
void darray_push_back(darray_t* darray, const void* elem) {
darray_extend(darray, elem, 1);
}
void* darray_elem_ptr(darray_t* darray, size_t idx) {
return darray->data + idx*darray->elem_size;
}
const void* darray_const_elem_ptr(const darray_t* darray, size_t idx) {
return darray->data + idx*darray->elem_size;
}
void darray_get(const darray_t* darray, size_t idx, void* dst) {
memcpy(dst, darray_const_elem_ptr(darray, idx), darray->elem_size);
}
void darray_set(darray_t* darray, size_t idx, const void* src) {
memcpy(darray_elem_ptr(darray, idx), src, darray->elem_size);
}
void darray_pop_back(darray_t* darray, void* dst) {
darray->count -= 1;
size_t offset = darray->count * darray->elem_size;
memcpy(dst, (const void*)darray->data + offset, darray->elem_size);
}
void darray_clear(darray_t* darray) {
darray->count = 0;
}
void darray_destroy(darray_t* darray) {
free(darray->data);
memset(darray, 0, sizeof(darray_t));
}
//////////////////////////////////////////////////////////////////////
void lsys_create(lsys_t* lsys,
const char* name,
const char* start,
lsys_rule_def_t const rules[],
double turn_angle_deg,
const char* draw_chars) {
lsys->name = name;
lsys->start = start;
memset(lsys->rules, 0, sizeof(lsys->rules));
memset(lsys->draw_chars, 0, sizeof(lsys->draw_chars));
for (const lsys_rule_def_t* src_rule=rules; src_rule->symbol; ++src_rule) {
lsys_sized_string_t* dst_rule = lsys->rules + (int)src_rule->symbol;
dst_rule->replacement = src_rule->replacement;
dst_rule->length = strlen(src_rule->replacement);
}
lsys->turn_angle_rad = turn_angle_deg * M_PI / 180.f;
for (int i=0; i<=LSYS_MAX_CYCLE_LENGTH; ++i) {
if (i > 0 && fmod(turn_angle_deg*i, 360.) == 0) {
lsys->rotation_cycle_length = i;
break;
}
float theta = lsys->turn_angle_rad * i;
lsys->rotations[i].c = cosf(theta);
lsys->rotations[i].s = sinf(theta);
}
if (draw_chars) {
lsys->draw_chars[0] = 1;
for (const char* c=draw_chars; *c; ++c) {
lsys->draw_chars[(int)*c] = 1;
}
}
}
void lsys_print(const lsys_t* lsys) {
printf("%s:\n", lsys->name);
printf(" start: %s\n", lsys->start);
printf(" rules:\n");
for (int i=0; i<LSYS_MAX_RULES; ++i) {
if (lsys->rules[i].replacement) {
printf(" %c -> %s\n", i, lsys->rules[i].replacement);
}
}
printf(" turn_angle_deg: %g\n", lsys->turn_angle_rad * 180.f / M_PI);
if (lsys->rotation_cycle_length) {
printf(" rotation_cycle_length: %d\n", lsys->rotation_cycle_length);
}
printf("\n");
}
char* lsys_build_string(const lsys_t* lsys, size_t total_iterations) {
darray_t string_darrays[2];
for (int i=0; i<2; ++i) {
darray_create(string_darrays + i, sizeof(char),
LSYS_INIT_STRING_CAPACITY);
}
int cur_idx = 0;
darray_extend(string_darrays + cur_idx,
lsys->start,
strlen(lsys->start));
for (int i=0; i<total_iterations; ++i) {
int next_idx = 1 - cur_idx;
darray_t* src_darray = string_darrays + cur_idx;
darray_t* dst_darray = string_darrays + next_idx;
darray_clear(dst_darray);
const char* start = (const char*)src_darray->data;
const char* end = start + src_darray->count;
for (const char* c=start; c!=end; ++c) {
const lsys_sized_string_t* rule = lsys->rules + (int)*c;
if (rule->replacement) {
darray_extend(dst_darray,
rule->replacement,
rule->length);
} else {
darray_push_back(dst_darray, c);
}
}
cur_idx = next_idx;
}
const char nul = '\0';
darray_push_back(string_darrays + cur_idx, &nul);
darray_destroy(string_darrays + (1 - cur_idx));
return (char*)string_darrays[cur_idx].data;
}
void _lsys_execute_symbol(const lsys_t* lsys,
const char symbol,
darray_t* segments,
xform_t* state,
darray_t* xform_stack) {
if (isalpha(symbol)) {
if (lsys->draw_chars[0] && !lsys->draw_chars[(int)symbol]) {
return;
}
float xnew = state->pos.x + state->rot.c;
float ynew = state->pos.y + state->rot.s;
lsys_segment_t seg = { { state->pos.x, state->pos.y},
{ xnew, ynew } };
darray_push_back(segments, &seg);
state->pos.x = xnew;
state->pos.y = ynew;
} else if (symbol == '+' || symbol == '-') {
if (lsys->rotation_cycle_length) {
int delta = (symbol == '+') ? 1 : -1;
int t = positive_mod((int)state->angle + delta,
lsys->rotation_cycle_length);
state->angle = t;
state->rot = lsys->rotations[t];
} else {
float delta = ( (symbol == '+') ?
lsys->turn_angle_rad : -lsys->turn_angle_rad );
state->angle += delta;
state->rot.c = cosf(state->angle);
state->rot.s = sinf(state->angle);
}
} else if (symbol == '[') {
darray_push_back(xform_stack, state);
} else if (symbol == ']') {
darray_pop_back(xform_stack, state);
} else {
fprintf(stderr, "invalid character in string: %c\n", symbol);
exit(1);
}
}
darray_t* lsys_segments_from_string(const lsys_t* lsys,
const char* lstring) {
darray_t* segments = malloc(sizeof(darray_t));
darray_create(segments, sizeof(lsys_segment_t),
LSYS_INIT_SEGMENTS_CAPACITY);
darray_t xform_stack;
darray_create(&xform_stack, sizeof(xform_t),
LSYS_INIT_STATES_CAPACITY);
xform_t cur_state = IDENTITY_XFORM;
for (const char* psymbol=lstring; *psymbol; ++psymbol) {
_lsys_execute_symbol(lsys, *psymbol, segments,
&cur_state, &xform_stack);
}
darray_destroy(&xform_stack);
return segments;
}
void _lsys_segments_r(const lsys_t* lsys,
const char* lstring,
size_t remaining_iterations,
darray_t* segments,
xform_t* cur_state,
darray_t* xform_stack,
lsys_memo_set_t* mset) {
for (const char* psymbol=lstring; *psymbol; ++psymbol) {
int symbol = *psymbol;
const lsys_sized_string_t* rule = lsys->rules + symbol;
if (remaining_iterations && rule->replacement) {
size_t segment_start = segments->count;
xform_t xform_start = *cur_state;
if (mset) {
lsys_memo_t* memo = mset->memos[symbol];
if (memo && memo->memo_iterations == remaining_iterations) {
xform_t update_xform =
xform_compose(*cur_state, memo->init_inverse);
darray_resize(segments, segment_start + memo->segment_count);
const lsys_segment_t* src =
darray_const_elem_ptr(segments, memo->segment_start);
lsys_segment_t* dst =
darray_elem_ptr(segments, segment_start);
#ifdef _OPENMP
int do_parallelize =
(memo->segment_count >= mset->min_parallel_segments);
#endif
#pragma omp parallel for if (do_parallelize)
for (size_t i=0; i<memo->segment_count; ++i) {
lsys_segment_t newsrc = {
xform_transform_point(update_xform, src[i].p0),
xform_transform_point(update_xform, src[i].p1)
};
dst[i] = newsrc;
}
*cur_state = xform_compose(*cur_state, memo->delta_xform);
continue;
}
}
_lsys_segments_r(lsys, rule->replacement,
remaining_iterations-1,
segments, cur_state, xform_stack,
mset);
if (mset && !mset->memos[symbol]) {
size_t segment_count = segments->count - segment_start;
if (segment_count > mset->min_memo_segments ||
remaining_iterations == mset->total_iterations - 2) {
lsys_memo_t* new_memo = malloc(sizeof(lsys_memo_t));
new_memo->memo_iterations = remaining_iterations;
new_memo->segment_start = segment_start;
new_memo->segment_count = segment_count;
new_memo->init_inverse = xform_inverse(xform_start);
new_memo->delta_xform = xform_compose(new_memo->init_inverse,
*cur_state);
mset->memos[symbol] = new_memo;
}
}
} else {
_lsys_execute_symbol(lsys, *psymbol, segments,
cur_state, xform_stack);
}
}
}
darray_t* lsys_segments_recursive(const lsys_t* lsys,
size_t total_iterations,
size_t min_memo_segments,
size_t min_parallel_segments) {
darray_t* segments = malloc(sizeof(darray_t));
darray_create(segments, sizeof(lsys_segment_t),
LSYS_INIT_SEGMENTS_CAPACITY);
darray_t xform_stack;
darray_create(&xform_stack, sizeof(xform_t),
LSYS_INIT_STATES_CAPACITY);
xform_t cur_state = IDENTITY_XFORM;
lsys_memo_set_t mset;
memset(&mset, 0, sizeof(mset));
mset.total_iterations = total_iterations;
mset.min_memo_segments = min_memo_segments;
mset.min_parallel_segments = min_parallel_segments;
_lsys_segments_r(lsys, lsys->start,
total_iterations, segments,
&cur_state, &xform_stack,
&mset);
for (int i=0; i<LSYS_MAX_RULES; ++i) {
if (mset.memos[i]) {
free(mset.memos[i]);
}
}
darray_destroy(&xform_stack);
return segments;
}
//////////////////////////////////////////////////////////////////////
// definitions for L-Systems from websites listed at top of file
void initialize_known_lsystems(void) {
lsys_create(KNOWN_LSYSTEMS + LSYS_SIERPINSKI_TRIANGLE,
"sierpinski_triangle", "F-G-G",
(lsys_rule_def_t[]){
{ 'F', "F-G+F+G-F" },
{ 'G', "GG" },
{ 0, 0 }
}, 120, NULL);
lsys_create(KNOWN_LSYSTEMS + LSYS_SIERPINSKI_ARROWHEAD,
"sierpinski_arrowhead", "A",
(lsys_rule_def_t[]){
{ 'A', "B-A-B" },
{ 'B', "A+B+A" },
{ 0, 0 }
}, 60, NULL);
lsys_create(KNOWN_LSYSTEMS + LSYS_DRAGON_CURVE,
"dragon_curve", "FX",
(lsys_rule_def_t[]){
{ 'X', "X+YF+" },
{ 'Y', "-FX-Y" },
{ 0, 0 }
}, 90, NULL);
lsys_create(KNOWN_LSYSTEMS + LSYS_BARNSLEY_FERN,
"barnsley_fern", "X",
(lsys_rule_def_t[]){
{ 'X', "F+[[X]-X]-F[-FX]+X" },
{ 'F', "FF" },
{ 0, 0 }
}, 25, NULL);
lsys_create(KNOWN_LSYSTEMS + LSYS_STICKS,
"sticks", "X",
(lsys_rule_def_t[]){
{ 'X', "F[+X]F[-X]+X" },
{ 'F', "FF" },
{ 0, 0 }
}, 20, "F");
lsys_create(KNOWN_LSYSTEMS + LSYS_HILBERT,
"hilbert", "L",
(lsys_rule_def_t[]){
{ 'L', "+RF-LFL-FR+" },
{ 'R', "-LF+RFR+FL-" },
{ 0, 0 }
}, 90, "F");
lsys_create(KNOWN_LSYSTEMS + LSYS_PENTAPLEXITY,
"pentaplexity", "F++F++F++F++F",
(lsys_rule_def_t[]){
{ 'F', "F++F++F+++++F-F++F" },
{ 0, 0 }
}, 36, NULL);
}
//////////////////////////////////////////////////////////////////////
void parse_options(int argc, char** argv, options_t* opts) {
int ok = 1;
int disable_precomputed_rotation = 0;
int disable_memoization = 0;
int disable_parallelization = 0;
memset(opts, 0, sizeof(options_t));
opts->max_segments = 100000;
int i=1;
int required_count = 0;
for (; i<argc; ++i) {
const char* arg = argv[i];
if (*arg && arg[0] != '-') {
if (required_count == 0) {
ok = 0;
for (int j=0; j<NUM_KNOWN_LSYSTEMS; ++j) {
if (!strcmp(arg, KNOWN_LSYSTEMS[j].name)) {
ok = 1;
opts->lsys = KNOWN_LSYSTEMS + j;
break;
}
}
if (!ok) { break; }
} else if (required_count == 1) {
int d;
if (sscanf(arg, "%d", &d) != 1 || d <= 0) {
ok = 0;
break;
}
opts->total_iterations = d;
} else {
ok = 0;
break;
}
++required_count;
} else if (!strcmp(arg, "-s")) {
opts->method = LSYS_METHOD_STRING;
} else if (!strcmp(arg, "-r")) {
opts->method = LSYS_METHOD_RECURSION;
} else if (!strcmp(arg, "-x")) {
if (++i == argc) { ok = 0; break; }
int d;
if (sscanf(argv[i], "%d", &d) != 1) {
ok = 0; break;
}
if (d >= -1) {
opts->max_segments = (size_t)d;
} else {
ok = 0;
break;
}
} else if (!strcmp(arg, "-M")) {
disable_memoization = 1;
#ifdef _OPENMP
} else if (!strcmp(arg, "-P")) {
disable_parallelization = 1;
#endif
} else if (!strcmp(arg, "-R")) {
disable_precomputed_rotation = 1;
} else {
fprintf(stderr, "error: unrecognized option %s\n\n", arg);
ok = 0;
break;
}
}
if (!ok || !opts->lsys || !opts->total_iterations) {
printf("usage: %s [options] LSYSTEM ITERATIONS\n"
"\n"
"where LSYSTEM is one of:\n", argv[0]);
for (int j=0; j<NUM_KNOWN_LSYSTEMS; ++j) {
printf(" * %s\n", KNOWN_LSYSTEMS[j].name);
}
printf("\n");
printf("options:\n");
printf(" -x MAXSEGMENTS maximum number of segments for output\n"
" -s use string building method\n"
" -r use recursive method (default)\n"
" -M disable memoization for recursive method\n"
#ifdef _OPENMP
" -P disable parallelization for memoization\n"
#endif
" -R don't precompute rotations\n"
"\n");
exit(1);
}
printf("using %s method\n",
opts->method == LSYS_METHOD_STRING ? "string" : "recursion");
if (opts->method == LSYS_METHOD_STRING) {
if (disable_memoization) {
printf("warning: disabling memoization has no effect for string method!\n");
}
}
int have_memo = (opts->method == LSYS_METHOD_RECURSION) && !disable_memoization;
if (!have_memo) {
if (disable_parallelization) {
printf("warning: disabling parallelization has no effect when not memoizing\n");
}
opts->min_memo_segments = (size_t)-1;
opts->min_parallel_segments = (size_t)-1;
if (opts->method == LSYS_METHOD_RECURSION) {
printf("memoization is disabled\n");
}
} else if (disable_parallelization) {
opts->min_memo_segments = 10000;
opts->min_parallel_segments = (size_t)-1;
printf("memoizing runs with > %d segments\n",
(int)opts->min_memo_segments);
} else {
opts->min_memo_segments = 100000;
opts->min_parallel_segments = 5000;
printf("memoizing runs with > %d segments and parallelizing when > %d segments\n",
(int)opts->min_memo_segments, (int)opts->min_parallel_segments);
}
if (disable_precomputed_rotation) {
printf("disabling precomputed rotation!\n");
opts->lsys->rotation_cycle_length = 0;
}
printf("\n");
lsys_print(opts->lsys);
}
//////////////////////////////////////////////////////////////////////
// main program
int main(int argc, char** argv) {
// initialize lsystems
initialize_known_lsystems();
// parse command-line options
options_t opts;
parse_options(argc, argv, &opts);
////////////////////////////////////////////////////////////
// now get the segments
double start = get_time_as_double();
darray_t* segments;
if (opts.method == LSYS_METHOD_STRING) {
char* lstring = lsys_build_string(opts.lsys,
opts.total_iterations);
segments = lsys_segments_from_string(opts.lsys, lstring);
free(lstring);
} else {
segments = lsys_segments_recursive(opts.lsys, opts.total_iterations,
opts.min_memo_segments,
opts.min_parallel_segments);
}
double elapsed = get_time_as_double() - start;
printf("generated %d segments in %.6f s (%.3f ns/segment).\n",
(int)segments->count, elapsed, 1e9 * elapsed/segments->count);
////////////////////////////////////////////////////////////
// either output or not
if (segments->count > opts.max_segments) {
printf("...maximum of %d segments exceeded, skipping output!\n",
(int)opts.max_segments);
} else {