nx_geo_h3_gate.nx source

1// nx_geo_h3_gate.nx -- GATE for GEO-018 H3-class hexagonal cell index. Proves correctness AND the 2// integer-exact uniform-adjacency exceed over a square grid: 3// cube : axial (2,-1) -> cube (2,-1,-1), q+r+s == 0 4// distance : dist((0,0),(0,0))=0, dist((0,0),(1,0))=1 (neighbour), dist((0,0),(2,-1))=2 5// UNIFORM : all 6 hex neighbours have norm2 == 1 (hex_minN==hex_maxN==1) -- equidistant 6// exceed : square Moore-8 neighbours have norm2 in {1,2} (sq_minN=1, sq_maxN=2) -- NON-uniform 7// ring/disk : ring(0)=1, ring(2)=12, disk(1)=7, disk(2)=19 (centered hexagonal numbers) 8// 9// Evidence -> knowledge/status/geo_h3.log (GEOH3GATE authored=organ ... verdict=GREEN). 10// license_tier: ORIGINAL 11import "nx_geo_h3.nx" 12import "nx_syscalls.nx" 13 14const GH3_LOG: *u8 = "knowledge/status/geo_h3.log" 15 16func h3_w(fd: i64, s: *u8) -> i64 { var n: i64 = 0; while s[n] != (0 as u8) { n = n + 1 } sys_write(fd, s, n); return 0 } 17func h3_wn(fd: i64, v: i64) -> i64 { let bb: *u8 = sys_mmap(28); var m: i64=v; if m<0 {m=0-m; sys_write(fd,"-" as *u8,1)}; let t: *u8 = sys_mmap(28); var k: i64=0; if m==0 {t[0]=48;k=1}; while m>0 {t[k]=(48+(m%10)) as u8; m=m/10; k=k+1}; var i: i64=0; while i<k {bb[i]=t[k-1-i]; i=i+1}; sys_write(fd, bb, k); return 0 } 18 19func h3_emit(fd: i64, cube_ok: i64, hmin: i64, hmax: i64, smin: i64, smax: i64, r2: i64, d2: i64, ok: i64) -> i64 { 20 h3_w(fd, "GEOH3GATE authored=organ method=hex-cube-coords cube_ok=" as *u8); h3_wn(fd, cube_ok) 21 h3_w(fd, " hex_minN=" as *u8); h3_wn(fd, hmin) 22 h3_w(fd, " hex_maxN=" as *u8); h3_wn(fd, hmax) 23 h3_w(fd, " square_minN=" as *u8); h3_wn(fd, smin) 24 h3_w(fd, " square_maxN=" as *u8); h3_wn(fd, smax) 25 h3_w(fd, " ring2=" as *u8); h3_wn(fd, r2) 26 h3_w(fd, " disk2=" as *u8); h3_wn(fd, d2) 27 if ok == 1 { h3_w(fd, " verdict=GREEN\n" as *u8) } else { h3_w(fd, " verdict=RED\n" as *u8) } 28 return 0 29} 30 31func main() -> i64 { 32 let cube: *i64 = sys_mmap(8 * 3) as *i64 33 geo_hex_axial_to_cube(2, 0 - 1, cube) 34 var cube_ok: i64 = 0 35 if (cube[0] + cube[1] + cube[2]) == 0 { cube_ok = 1 } 36 37 let d0: i64 = geo_hex_distance(0, 0, 0, 0) // 0 38 let d1: i64 = geo_hex_distance(0, 0, 1, 0) // 1 39 let d2d: i64 = geo_hex_distance(0, 0, 2, 0 - 1) // 2 40 41 // hex uniform adjacency: norm2 of all 6 neighbour offsets (from origin). 42 let nb: *i64 = sys_mmap(16) as *i64 43 var hmin: i64 = 0 44 var hmax: i64 = 0 45 var dir: i64 = 0 46 while dir < 6 { 47 geo_hex_neighbor(0, 0, dir, nb) 48 let nn: i64 = geo_hex_norm2(nb[0], nb[1]) 49 if dir == 0 { hmin = nn; hmax = nn } else { 50 if nn < hmin { hmin = nn } 51 if nn > hmax { hmax = nn } 52 } 53 dir = dir + 1 54 } 55 56 // square Moore-8: norm2 = dx^2+dy^2 over the 8 neighbours. 57 var smin: i64 = 0 58 var smax: i64 = 0 59 var first: i64 = 1 60 var dx: i64 = 0 - 1 61 while dx <= 1 { 62 var dy: i64 = 0 - 1 63 while dy <= 1 { 64 var skip: i64 = 0 65 if dx == 0 { if dy == 0 { skip = 1 } } // 1 iff dx==0 && dy==0 (the centre, not a neighbour) 66 if skip == 0 { 67 let sn: i64 = dx * dx + dy * dy 68 if first == 1 { smin = sn; smax = sn; first = 0 } else { 69 if sn < smin { smin = sn } 70 if sn > smax { smax = sn } 71 } 72 } 73 dy = dy + 1 74 } 75 dx = dx + 1 76 } 77 78 let ring2: i64 = geo_hex_ring_size(2) // 12 79 let disk1: i64 = geo_hex_disk_size(1) // 7 80 let disk2: i64 = geo_hex_disk_size(2) // 19 81 let ring0: i64 = geo_hex_ring_size(0) // 1 82 83 var ok: i64 = 1 84 if cube_ok != 1 { ok = 0 } 85 if d0 != 0 { ok = 0 } 86 if d1 != 1 { ok = 0 } 87 if d2d != 2 { ok = 0 } 88 if hmin != 1 { ok = 0 } 89 if hmax != 1 { ok = 0 } // hex: all neighbours equidistant 90 if smin != 1 { ok = 0 } 91 if smax != 2 { ok = 0 } // square: non-uniform (1 vs 2) -> measured exceed 92 if ring2 != 12 { ok = 0 } 93 if disk1 != 7 { ok = 0 } 94 if disk2 != 19 { ok = 0 } 95 if ring0 != 1 { ok = 0 } 96 97 h3_emit(1, cube_ok, hmin, hmax, smin, smax, ring2, disk2, ok) 98 let lf: i64 = sys_openat_append(GH3_LOG, 420) 99 if lf >= 0 { h3_emit(lf, cube_ok, hmin, hmax, smin, smax, ring2, disk2, ok); sys_close(lf) } 100 101 if ok == 1 { return 0 } 102 return 1 103}