1 /***************************************
2 $Header: /home/amb/routino/src/RCS/segmentsx.c,v 1.51 2010/04/28 17:27:02 amb Exp $
4 Extended Segment data type functions.
6 Part of the Routino routing software.
7 ******************/ /******************
8 This file Copyright 2008-2010 Andrew M. Bishop
10 This program is free software: you can redistribute it and/or modify
11 it under the terms of the GNU Affero General Public License as published by
12 the Free Software Foundation, either version 3 of the License, or
13 (at your option) any later version.
15 This program is distributed in the hope that it will be useful,
16 but WITHOUT ANY WARRANTY; without even the implied warranty of
17 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18 GNU Affero General Public License for more details.
20 You should have received a copy of the GNU Affero General Public License
21 along with this program. If not, see <http://www.gnu.org/licenses/>.
22 ***************************************/
33 #include "functions.h"
35 #include "segmentsx.h"
44 /*+ The command line '--slim' option. +*/
45 extern int option_slim;
47 /*+ The command line '--tmpdir' option or its default value. +*/
48 extern char *option_tmpdirname;
52 static int sort_by_id(SegmentX *a,SegmentX *b);
54 static distance_t DistanceX(NodeX *nodex1,NodeX *nodex2);
57 /*++++++++++++++++++++++++++++++++++++++
58 Allocate a new segment list (create a new file or open an existing one).
60 SegmentsX *NewSegmentList Returns the segment list.
62 int append Set to 1 if the file is to be opened for appending (now or later).
63 ++++++++++++++++++++++++++++++++++++++*/
65 SegmentsX *NewSegmentList(int append)
69 segmentsx=(SegmentsX*)calloc(1,sizeof(SegmentsX));
71 assert(segmentsx); /* Check calloc() worked */
73 segmentsx->filename=(char*)malloc(strlen(option_tmpdirname)+32);
76 sprintf(segmentsx->filename,"%s/segments.input.tmp",option_tmpdirname);
78 sprintf(segmentsx->filename,"%s/segments.%p.tmp",option_tmpdirname,segmentsx);
84 segmentsx->fd=AppendFile(segmentsx->filename);
86 size=SizeFile(segmentsx->filename);
88 segmentsx->xnumber=size/sizeof(SegmentX);
91 segmentsx->fd=OpenFile(segmentsx->filename);
97 /*++++++++++++++++++++++++++++++++++++++
100 SegmentsX *segmentsx The list to be freed.
102 int keep Set to 1 if the file is to be kept.
103 ++++++++++++++++++++++++++++++++++++++*/
105 void FreeSegmentList(SegmentsX *segmentsx,int keep)
108 DeleteFile(segmentsx->filename);
110 free(segmentsx->filename);
113 free(segmentsx->idata);
115 if(segmentsx->firstnode)
116 free(segmentsx->firstnode);
119 free(segmentsx->sdata);
125 /*++++++++++++++++++++++++++++++++++++++
126 Append a single segment to a segment list.
128 SegmentsX* segmentsx The set of segments to process.
130 way_t way The way that the segment belongs to.
132 node_t node1 The first node in the segment.
134 node_t node2 The second node in the segment.
136 distance_t distance The distance between the nodes (or just the flags).
137 ++++++++++++++++++++++++++++++++++++++*/
139 void AppendSegment(SegmentsX* segmentsx,way_t way,node_t node1,node_t node2,distance_t distance)
143 assert(!segmentsx->idata); /* Must not have idata filled in => unsorted */
145 segmentx.node1=node1;
146 segmentx.node2=node2;
148 segmentx.distance=distance;
150 WriteFile(segmentsx->fd,&segmentx,sizeof(SegmentX));
152 segmentsx->xnumber++;
156 /*++++++++++++++++++++++++++++++++++++++
157 Sort the segment list.
159 SegmentsX* segmentsx The set of segments to process.
160 ++++++++++++++++++++++++++++++++++++++*/
162 void SortSegmentList(SegmentsX* segmentsx)
166 /* Check the start conditions */
168 assert(!segmentsx->idata); /* Must not have idata filled in => unsorted */
170 /* Print the start message */
172 printf("Sorting Segments");
175 /* Close the files and re-open them (finished appending) */
177 CloseFile(segmentsx->fd);
178 segmentsx->fd=ReOpenFile(segmentsx->filename);
180 DeleteFile(segmentsx->filename);
182 fd=OpenFile(segmentsx->filename);
184 /* Sort by node indexes */
186 filesort_fixed(segmentsx->fd,fd,sizeof(SegmentX),(int (*)(const void*,const void*))sort_by_id,NULL);
188 segmentsx->number=segmentsx->xnumber;
190 /* Close the files and re-open them */
192 CloseFile(segmentsx->fd);
195 segmentsx->fd=ReOpenFile(segmentsx->filename);
197 /* Print the final message */
199 printf("\rSorted Segments: Segments=%d\n",segmentsx->xnumber);
204 /*++++++++++++++++++++++++++++++++++++++
205 Sort the segments into id order (node1 then node2).
207 int sort_by_id Returns the comparison of the node fields.
209 SegmentX *a The first segment.
211 SegmentX *b The second segment.
212 ++++++++++++++++++++++++++++++++++++++*/
214 static int sort_by_id(SegmentX *a,SegmentX *b)
216 node_t a_id1=a->node1;
217 node_t b_id1=b->node1;
223 else /* if(a_id1==b_id1) */
225 node_t a_id2=a->node2;
226 node_t b_id2=b->node2;
234 distance_t a_distance=a->distance;
235 distance_t b_distance=b->distance;
237 if(a_distance<b_distance)
239 else if(a_distance>b_distance)
248 /*++++++++++++++++++++++++++++++++++++++
249 Find the first segment index with a particular starting node.
251 index_t IndexFirstSegmentX Returns a pointer to the index of the first extended segment with the specified id.
253 SegmentsX* segmentsx The set of segments to process.
255 node_t node The node to look for.
256 ++++++++++++++++++++++++++++++++++++++*/
258 index_t IndexFirstSegmentX(SegmentsX* segmentsx,node_t node)
261 int end=segmentsx->number-1;
265 /* Check if the first node index exists */
267 if(segmentsx->firstnode)
269 index_t index=segmentsx->firstnode[node];
271 if(segmentsx->firstnode[node+1]==index)
277 assert(segmentsx->idata); /* Must have idata filled in => sorted by node 1 */
279 /* Binary search - search key exact match only is required.
281 * # <- start | Check mid and move start or end if it doesn't match
283 * # | Since an exact match is wanted we can set end=mid-1
284 * # <- mid | or start=mid+1 because we know that mid doesn't match.
286 * # | Eventually either end=start or end=start+1 and one of
287 * # <- end | start or end is the wanted one.
290 if(end<start) /* There are no nodes */
292 else if(node<segmentsx->idata[start]) /* Check key is not before start */
294 else if(node>segmentsx->idata[end]) /* Check key is not after end */
300 mid=(start+end)/2; /* Choose mid point */
302 if(segmentsx->idata[mid]<node) /* Mid point is too low */
304 else if(segmentsx->idata[mid]>node) /* Mid point is too high */
306 else /* Mid point is correct */
307 {found=mid; goto found;}
309 while((end-start)>1);
311 if(segmentsx->idata[start]==node) /* Start is correct */
312 {found=start; goto found;}
314 if(segmentsx->idata[end]==node) /* End is correct */
315 {found=end; goto found;}
322 while(found>0 && segmentsx->idata[found-1]==node)
329 /*++++++++++++++++++++++++++++++++++++++
330 Find the next segment index with a particular starting node.
332 index_t IndexNextSegmentX Returns the index of the next segment with the same id.
334 SegmentsX* segmentsx The set of segments to process.
336 index_t segindex The current segment index.
338 index_t nodeindex The node index.
339 ++++++++++++++++++++++++++++++++++++++*/
341 index_t IndexNextSegmentX(SegmentsX* segmentsx,index_t segindex,index_t nodeindex)
343 assert(segmentsx->firstnode); /* Must have firstnode filled in => segments updated */
345 if(++segindex==segmentsx->firstnode[nodeindex+1])
352 /*++++++++++++++++++++++++++++++++++++++
353 Lookup a particular segment.
355 SegmentX *LookupSegmentX Returns a pointer to the extended segment with the specified id.
357 SegmentsX* segmentsx The set of segments to process.
359 index_t index The segment index to look for.
361 int position The position in the cache to use.
362 ++++++++++++++++++++++++++++++++++++++*/
364 SegmentX *LookupSegmentX(SegmentsX* segmentsx,index_t index,int position)
366 assert(index!=NO_SEGMENT); /* Must be a valid segment */
370 SeekFile(segmentsx->fd,index*sizeof(SegmentX));
372 ReadFile(segmentsx->fd,&segmentsx->cached[position-1],sizeof(SegmentX));
374 return(&segmentsx->cached[position-1]);
378 return(&segmentsx->xdata[index]);
383 /*++++++++++++++++++++++++++++++++++++++
384 Remove bad segments (duplicated, zero length or missing nodes).
386 NodesX *nodesx The nodes to check.
388 SegmentsX *segmentsx The segments to modify.
389 ++++++++++++++++++++++++++++++++++++++*/
391 void RemoveBadSegments(NodesX *nodesx,SegmentsX *segmentsx)
393 int duplicate=0,loop=0,missing=0,good=0,total=0;
396 node_t prevnode1=NO_NODE,prevnode2=NO_NODE;
398 /* Print the start message */
400 printf("Checking: Segments=0 Duplicate=0 Loop=0 Missing-Node=0");
403 /* Allocate the array of indexes */
405 segmentsx->idata=(node_t*)malloc(segmentsx->xnumber*sizeof(node_t));
407 assert(segmentsx->idata); /* Check malloc() worked */
409 /* Modify the on-disk image */
411 DeleteFile(segmentsx->filename);
413 fd=OpenFile(segmentsx->filename);
414 SeekFile(segmentsx->fd,0);
416 while(!ReadFile(segmentsx->fd,&segmentx,sizeof(SegmentX)))
418 if(prevnode1==segmentx.node1 && prevnode2==segmentx.node2)
420 else if(segmentx.node1==segmentx.node2)
422 else if(IndexNodeX(nodesx,segmentx.node1)==NO_NODE ||
423 IndexNodeX(nodesx,segmentx.node2)==NO_NODE)
427 WriteFile(fd,&segmentx,sizeof(SegmentX));
429 segmentsx->idata[good]=segmentx.node1;
432 prevnode1=segmentx.node1;
433 prevnode2=segmentx.node2;
440 printf("\rChecking: Segments=%d Duplicate=%d Loop=%d Missing-Node=%d",total,duplicate,loop,missing);
445 /* Close the files and re-open them */
447 CloseFile(segmentsx->fd);
450 segmentsx->fd=ReOpenFile(segmentsx->filename);
452 segmentsx->number=good;
454 /* Print the final message */
456 printf("\rChecked: Segments=%d Duplicate=%d Loop=%d Missing-Node=%d \n",total,duplicate,loop,missing);
461 /*++++++++++++++++++++++++++++++++++++++
462 Measure the segments and replace node/way ids with indexes.
464 SegmentsX* segmentsx The set of segments to process.
466 NodesX *nodesx The list of nodes to use.
468 WaysX *waysx The list of ways to use.
469 ++++++++++++++++++++++++++++++++++++++*/
471 void UpdateSegments(SegmentsX* segmentsx,NodesX *nodesx,WaysX *waysx)
477 /* Print the start message */
479 printf("Measuring Segments: Segments=0");
482 /* Map into memory */
485 nodesx->xdata=MapFile(nodesx->filename);
487 /* Free the now-unneeded index */
489 free(segmentsx->idata);
490 segmentsx->idata=NULL;
492 /* Allocate the array of indexes */
494 segmentsx->firstnode=(index_t*)malloc((nodesx->number+1)*sizeof(index_t));
496 assert(segmentsx->firstnode); /* Check malloc() worked */
498 for(i=0;i<nodesx->number;i++)
499 segmentsx->firstnode[i]=NO_SEGMENT;
501 segmentsx->firstnode[nodesx->number]=segmentsx->number;
503 /* Modify the on-disk image */
505 DeleteFile(segmentsx->filename);
507 fd=OpenFile(segmentsx->filename);
508 SeekFile(segmentsx->fd,0);
510 while(!ReadFile(segmentsx->fd,&segmentx,sizeof(SegmentX)))
512 index_t node1=IndexNodeX(nodesx,segmentx.node1);
513 index_t node2=IndexNodeX(nodesx,segmentx.node2);
514 index_t way =IndexWayX (waysx ,segmentx.way);
516 NodeX *nodex1=LookupNodeX(nodesx,node1,1);
517 NodeX *nodex2=LookupNodeX(nodesx,node2,2);
519 /* Replace the node and way ids with their indexes */
521 segmentx.node1=node1;
522 segmentx.node2=node2;
525 /* Set the distance but preserve the ONEWAY_* flags */
527 segmentx.distance|=DISTANCE(DistanceX(nodex1,nodex2));
529 /* Set the first segment index in the nodes */
531 if(index<segmentsx->firstnode[node1])
532 segmentsx->firstnode[node1]=index;
534 /* Write the modified segment */
536 WriteFile(fd,&segmentx,sizeof(SegmentX));
542 printf("\rMeasuring Segments: Segments=%d",index);
547 /* Close the files and re-open them */
549 CloseFile(segmentsx->fd);
552 segmentsx->fd=ReOpenFile(segmentsx->filename);
554 /* Free the other now-unneeded indexes */
562 /* Unmap from memory */
565 nodesx->xdata=UnmapFile(nodesx->filename);
567 /* Print the final message */
569 printf("\rMeasured Segments: Segments=%d \n",segmentsx->number);
574 /*++++++++++++++++++++++++++++++++++++++
575 Make the segments all point the same way (node1<node2).
577 SegmentsX* segmentsx The set of segments to process.
578 ++++++++++++++++++++++++++++++++++++++*/
580 void RotateSegments(SegmentsX* segmentsx)
582 int index=0,rotated=0;
586 /* Check the start conditions */
588 assert(!segmentsx->idata); /* Must not have idata filled in => not sorted by node 1 */
590 /* Print the start message */
592 printf("Rotating Segments: Segments=0 Rotated=0");
595 /* Close the files and re-open them (finished appending) */
597 CloseFile(segmentsx->fd);
598 segmentsx->fd=ReOpenFile(segmentsx->filename);
600 DeleteFile(segmentsx->filename);
602 fd=OpenFile(segmentsx->filename);
604 /* Modify the file contents */
606 while(!ReadFile(segmentsx->fd,&segmentx,sizeof(SegmentX)))
608 if(segmentx.node1>segmentx.node2)
613 segmentx.node1=segmentx.node2;
616 if(segmentx.distance&(ONEWAY_2TO1|ONEWAY_1TO2))
617 segmentx.distance^=ONEWAY_2TO1|ONEWAY_1TO2;
622 WriteFile(fd,&segmentx,sizeof(SegmentX));
628 printf("\rRotating Segments: Segments=%d Rotated=%d",index,rotated);
633 /* Close the files and re-open them */
635 CloseFile(segmentsx->fd);
638 segmentsx->fd=ReOpenFile(segmentsx->filename);
640 /* Print the final message */
642 printf("\rRotated Segments: Segments=%d Rotated=%d \n",index,rotated);
647 /*++++++++++++++++++++++++++++++++++++++
648 Remove the duplicate segments.
650 SegmentsX* segmentsx The set of segments to process.
652 NodesX *nodesx The list of nodes to use.
654 WaysX *waysx The list of ways to use.
655 ++++++++++++++++++++++++++++++++++++++*/
657 void DeduplicateSegments(SegmentsX* segmentsx,NodesX *nodesx,WaysX *waysx)
659 int duplicate=0,good=0;
660 index_t firstindex=0,index=0;
662 SegmentX prevsegmentx[16],segmentx;
664 /* Print the start message */
666 printf("Deduplicating Segments: Segments=0 Duplicate=0");
669 /* Map into memory */
672 waysx->xdata=MapFile(waysx->filename);
674 /* Allocate the array of indexes */
676 segmentsx->firstnode=(index_t*)malloc((nodesx->number+1)*sizeof(index_t));
678 assert(segmentsx->firstnode); /* Check malloc() worked */
680 for(i=0;i<nodesx->number;i++)
681 segmentsx->firstnode[i]=NO_SEGMENT;
683 segmentsx->firstnode[nodesx->number]=segmentsx->number;
685 /* Modify the on-disk image */
687 DeleteFile(segmentsx->filename);
689 fd=OpenFile(segmentsx->filename);
690 SeekFile(segmentsx->fd,0);
692 while(!ReadFile(segmentsx->fd,&segmentx,sizeof(SegmentX)))
696 if(index && segmentx.node1==prevsegmentx[0].node1 &&
697 segmentx.node2==prevsegmentx[0].node2)
699 index_t previndex=firstindex;
701 while(previndex<index)
703 int offset=previndex-firstindex;
705 if(DISTFLAG(segmentx.distance)==DISTFLAG(prevsegmentx[offset].distance))
707 WayX *wayx1=LookupWayX(waysx,prevsegmentx[offset].way,1);
708 WayX *wayx2=LookupWayX(waysx, segmentx .way,2);
710 if(!WaysCompare(&wayx1->way,&wayx2->way))
721 assert((index-firstindex)<(sizeof(prevsegmentx)/sizeof(prevsegmentx[0])));
723 prevsegmentx[index-firstindex]=segmentx;
728 prevsegmentx[0]=segmentx;
733 WriteFile(fd,&segmentx,sizeof(SegmentX));
735 if(good<segmentsx->firstnode[segmentx.node1])
736 segmentsx->firstnode[segmentx.node1]=good;
745 printf("\rDeduplicating Segments: Segments=%d Duplicate=%d",index,duplicate);
750 /* Close the files and re-open them */
752 CloseFile(segmentsx->fd);
755 segmentsx->fd=ReOpenFile(segmentsx->filename);
757 segmentsx->number=good;
759 /* Fix-up the firstnode index for the missing nodes */
761 for(i=nodesx->number-1;i>=0;i--)
762 if(segmentsx->firstnode[i]==NO_SEGMENT)
763 segmentsx->firstnode[i]=segmentsx->firstnode[i+1];
765 /* Unmap from memory */
768 waysx->xdata=UnmapFile(waysx->filename);
770 /* Print the final message */
772 printf("\rDeduplicated Segments: Segments=%d Duplicate=%d Unique=%d\n",index,duplicate,index-duplicate);
777 /*++++++++++++++++++++++++++++++++++++++
778 Create the real segments data.
780 SegmentsX* segmentsx The set of segments to use.
782 WaysX* waysx The set of ways to use.
783 ++++++++++++++++++++++++++++++++++++++*/
785 void CreateRealSegments(SegmentsX *segmentsx,WaysX *waysx)
789 /* Check the start conditions */
791 assert(!segmentsx->sdata); /* Must not have sdata filled in => no real segments */
793 /* Print the start message */
795 printf("Creating Real Segments: Segments=0");
798 /* Map into memory */
802 segmentsx->xdata=MapFile(segmentsx->filename);
803 waysx->xdata=MapFile(waysx->filename);
806 /* Free the unneeded memory */
808 free(segmentsx->firstnode);
809 segmentsx->firstnode=NULL;
811 /* Allocate the memory */
813 segmentsx->sdata=(Segment*)malloc(segmentsx->number*sizeof(Segment));
815 assert(segmentsx->sdata); /* Check malloc() worked */
817 /* Loop through and fill */
819 for(i=0;i<segmentsx->number;i++)
821 SegmentX *segmentx=LookupSegmentX(segmentsx,i,1);
822 WayX *wayx=LookupWayX(waysx,segmentx->way,1);
824 segmentsx->sdata[i].node1=0;
825 segmentsx->sdata[i].node2=0;
826 segmentsx->sdata[i].next2=NO_NODE;
827 segmentsx->sdata[i].way=wayx->prop;
828 segmentsx->sdata[i].distance=segmentx->distance;
832 printf("\rCreating Real Segments: Segments=%d",i+1);
837 /* Unmap from memory */
841 segmentsx->xdata=UnmapFile(segmentsx->filename);
842 waysx->xdata=UnmapFile(waysx->filename);
845 /* Print the final message */
847 printf("\rCreating Real Segments: Segments=%d \n",segmentsx->number);
852 /*++++++++++++++++++++++++++++++++++++++
853 Assign the nodes indexes to the segments.
855 SegmentsX* segmentsx The set of segments to process.
857 NodesX *nodesx The list of nodes to use.
858 ++++++++++++++++++++++++++++++++++++++*/
860 void IndexSegments(SegmentsX* segmentsx,NodesX *nodesx)
864 /* Check the start conditions */
866 assert(nodesx->ndata); /* Must have ndata filled in => real nodes exist */
867 assert(segmentsx->sdata); /* Must have sdata filled in => real segments exist */
869 /* Print the start message */
871 printf("Indexing Nodes: Nodes=0");
874 /* Map into memory */
878 nodesx->xdata=MapFile(nodesx->filename);
879 segmentsx->xdata=MapFile(segmentsx->filename);
882 /* Index the segments */
884 for(i=0;i<nodesx->number;i++)
886 NodeX *nodex=LookupNodeX(nodesx,i,1);
887 Node *node =&nodesx->ndata[nodex->id];
888 index_t index=SEGMENT(node->firstseg);
892 SegmentX *segmentx=LookupSegmentX(segmentsx,index,1);
894 if(segmentx->node1==nodex->id)
896 segmentsx->sdata[index].node1=i;
900 if(index>=segmentsx->number)
903 segmentx=LookupSegmentX(segmentsx,index,1);
905 if(segmentx->node1!=nodex->id)
910 segmentsx->sdata[index].node2=i;
912 if(segmentsx->sdata[index].next2==NO_NODE)
915 index=segmentsx->sdata[index].next2;
922 printf("\rIndexing Nodes: Nodes=%d",i+1);
927 /* Unmap from memory */
931 nodesx->xdata=UnmapFile(nodesx->filename);
932 segmentsx->xdata=UnmapFile(segmentsx->filename);
935 /* Print the final message */
937 printf("\rIndexed Nodes: Nodes=%d \n",nodesx->number);
942 /*++++++++++++++++++++++++++++++++++++++
943 Save the segment list to a file.
945 SegmentsX* segmentsx The set of segments to save.
947 const char *filename The name of the file to save.
948 ++++++++++++++++++++++++++++++++++++++*/
950 void SaveSegmentList(SegmentsX* segmentsx,const char *filename)
955 int super_number=0,normal_number=0;
957 /* Check the start conditions */
959 assert(segmentsx->sdata); /* Must have sdata filled in => real segments */
961 /* Print the start message */
963 printf("Writing Segments: Segments=0");
966 /* Count the number of super-segments and normal segments */
968 for(i=0;i<segmentsx->number;i++)
970 if(IsSuperSegment(&segmentsx->sdata[i]))
972 if(IsNormalSegment(&segmentsx->sdata[i]))
976 /* Fill in a Segments structure with the offset of the real data in the file after
977 the Segment structure itself. */
979 segments=calloc(1,sizeof(Segments));
981 assert(segments); /* Check calloc() worked */
983 segments->number=segmentsx->number;
984 segments->snumber=super_number;
985 segments->nnumber=normal_number;
988 segments->segments=NULL;
990 /* Write out the Segments structure and then the real data. */
992 fd=OpenFile(filename);
994 WriteFile(fd,segments,sizeof(Segments));
996 for(i=0;i<segments->number;i++)
998 WriteFile(fd,&segmentsx->sdata[i],sizeof(Segment));
1002 printf("\rWriting Segments: Segments=%d",i+1);
1009 /* Print the final message */
1011 printf("\rWrote Segments: Segments=%d \n",segments->number);
1014 /* Free the fake Segments */
1020 /*++++++++++++++++++++++++++++++++++++++
1021 Calculate the distance between two nodes.
1023 distance_t DistanceX Returns the distance between the extended nodes.
1025 NodeX *nodex1 The starting node.
1027 NodeX *nodex2 The end node.
1028 ++++++++++++++++++++++++++++++++++++++*/
1030 static distance_t DistanceX(NodeX *nodex1,NodeX *nodex2)
1032 double dlon = latlong_to_radians(nodex1->longitude) - latlong_to_radians(nodex2->longitude);
1033 double dlat = latlong_to_radians(nodex1->latitude) - latlong_to_radians(nodex2->latitude);
1034 double lat1 = latlong_to_radians(nodex1->latitude);
1035 double lat2 = latlong_to_radians(nodex2->latitude);
1037 double a1,a2,a,sa,c,d;
1039 if(dlon==0 && dlat==0)
1042 a1 = sin (dlat / 2);
1043 a2 = sin (dlon / 2);
1044 a = (a1 * a1) + cos (lat1) * cos (lat2) * a2 * a2;
1047 {c = 2 * asin (sa);}
1049 {c = 2 * asin (1.0);}
1052 return km_to_distance(d);