nx_research_dynamics2_gate.nx source

1// nx_research_dynamics2_gate.nx -- the time-stepping dynamics substrate scales to a MULTI-DOF system: two 2// unit masses coupled by three unit springs (wall-m1, m1-m2, m2-wall). a1 = -2x1+x2, a2 = x1-2x2 (k=1). 3// Start mass 1 displaced (x1=A, x2=0, at rest): energy SLOSHES back and forth between the masses (the normal-mode 4// beat) -- yet the TOTAL energy is conserved by the symplectic leapfrog and DRIFTS under forward-Euler. Same 5// conservation verifier + liar-kill as the single oscillator, now on a coupled system with real energy exchange. 6// Fixed-point integers (no float), deterministic. GREEN iff 6/6. license_tier: ORIGINAL 7import "nx_syscalls.nx" 8 9func g_w(s: *u8) -> i64 { var n: i64=0; while s[n]!=(0 as u8){n=n+1} sys_write(1,s,n); return 0 } 10func g_n(v: i64) -> i64 { var m: i64=v; if m<0{g_w("-");m=0-m} let t:*u8=sys_mmap(24); var k:i64=0; if m==0{t[0]=48 as u8;k=1}; while m>0{t[k]=(48+(m%10)) as u8;m=m/10;k=k+1}; var i:i64=0; let o:*u8=sys_mmap(24); while i<k{o[i]=t[k-1-i];i=i+1}; sys_write(1,o,k); return 0 } 11func g_row(id: *u8, ok: i64, pass: *i64) -> i64 { g_w(" "); g_w(id); g_w(": "); if ok==1 { g_w("OK\n"); pass[0]=pass[0]+1 } else { g_w("FAIL\n") } return 0 } 12func iabs(x: i64) -> i64 { if x<0 { return 0-x } return x } 13func permille(dev: i64, E0: i64) -> i64 { return dev*1000/E0 } 14// total energy of the coupled system (drop uniform 1/2; k=1): v1^2+v2^2 + x1^2 + (x1-x2)^2 + x2^2. 15func energy2(x1: i64, x2: i64, v1: i64, v2: i64) -> i64 { let d: i64=x1-x2; return v1*v1+v2*v2 + x1*x1 + d*d + x2*x2 } 16 17// leapfrog (velocity-Verlet). out[0]=max total-energy deviation, out[1]=max|x2| (energy reaching mass 2). 18func sim_lf2(x10: i64, x20: i64, D: i64, N: i64, out: *i64) -> i64 { 19 var x1: i64=x10; var x2: i64=x20; var v1: i64=0; var v2: i64=0 20 let E0: i64=energy2(x1,x2,v1,v2) 21 var maxdev: i64=0; var maxx2: i64=iabs(x20) 22 var i: i64=0 23 while i<N { 24 let a1: i64 = 0-2*x1+x2; let a2: i64 = x1-2*x2 25 let vh1: i64 = v1 + a1/(2*D); let vh2: i64 = v2 + a2/(2*D) 26 x1 = x1 + vh1/D; x2 = x2 + vh2/D 27 let a1n: i64 = 0-2*x1+x2; let a2n: i64 = x1-2*x2 28 v1 = vh1 + a1n/(2*D); v2 = vh2 + a2n/(2*D) 29 let E: i64 = energy2(x1,x2,v1,v2) 30 let dd: i64 = iabs(E-E0); if dd>maxdev { maxdev=dd } 31 if iabs(x2)>maxx2 { maxx2=iabs(x2) } 32 i=i+1 33 } 34 out[0]=maxdev; out[1]=maxx2 35 return 0 36} 37// forward-Euler. out[0]=max total-energy deviation. 38func sim_eu2(x10: i64, x20: i64, D: i64, N: i64, out: *i64) -> i64 { 39 var x1: i64=x10; var x2: i64=x20; var v1: i64=0; var v2: i64=0 40 let E0: i64=energy2(x1,x2,v1,v2) 41 var maxdev: i64=0 42 var i: i64=0 43 while i<N { 44 let a1: i64 = 0-2*x1+x2; let a2: i64 = x1-2*x2 45 let nx1: i64 = x1 + v1/D; let nx2: i64 = x2 + v2/D 46 let nv1: i64 = v1 + a1/D; let nv2: i64 = v2 + a2/D 47 x1=nx1; x2=nx2; v1=nv1; v2=nv2 48 let E: i64 = energy2(x1,x2,v1,v2) 49 let dd: i64 = iabs(E-E0); if dd>maxdev { maxdev=dd } 50 i=i+1 51 } 52 out[0]=maxdev 53 return 0 54} 55 56func main() -> i64 { 57 let pass: *i64 = sys_mmap(8) as *i64; pass[0]=0 58 g_w("=== NX-RESEARCH-DYNAMICS2 GATE (coupled oscillators: energy sloshes between masses, total conserved) ===\n") 59 let SC: i64=1000000; let D: i64=64; let N: i64=6000 60 let E0: i64=energy2(SC,0,0,0) 61 62 let lp: *i64=sys_mmap(8*8) as *i64; sim_lf2(SC,0,D,N,lp) 63 let eu: *i64=sys_mmap(8*8) as *i64; sim_eu2(SC,0,D,N,eu) 64 let lp_pm: i64=permille(lp[0],E0); let eu_pm: i64=permille(eu[0],E0); let lp_maxx2: i64=lp[1] 65 66 g_w(" steps="); g_n(N); g_w(" dt=1/"); g_n(D); g_w(" E0="); g_n(E0); g_w("\n") 67 g_w(" leapfrog: totalEdev_permille="); g_n(lp_pm); g_w(" max|x2|/SC*1000="); g_n(lp_maxx2/(SC/1000)); g_w("\n") 68 g_w(" euler: totalEdev_permille="); g_n(eu_pm); g_w("\n") 69 70 g_row("SETUP: coupled 2-mass / 3-spring system builds with E0 from a displaced mass 1" as *u8, (E0>0) as i64, pass) 71 g_row("ENERGY-EXCHANGE: energy sloshes to mass 2 (initially at rest, it reaches >half amplitude)" as *u8, (lp_maxx2 > SC/2) as i64, pass) 72 g_row("CONSERVATION: symplectic leapfrog keeps TOTAL energy bounded (< 5%) despite the exchange" as *u8, (lp_pm < 50) as i64, pass) 73 g_row("DRIFT-DETECT: forward-Euler drifts the total energy (> 15%)" as *u8, (eu_pm > 150) as i64, pass) 74 g_row("DISCRIMINATION: leapfrog total-energy deviation far below Euler's (symplectic measurably better)" as *u8, (eu_pm > lp_pm*5) as i64, pass) 75 var liar: i64=0; if lp_pm < 50 { if eu_pm >= 50 { liar=1 } } 76 g_row("LIAR-KILL: Euler's coupled trajectory FAILS the energy-conservation bar leapfrog passes" as *u8, liar, pass) 77 78 g_w("RESEARCH-DYNAMICS2-GATE rows=6 pass="); g_n(pass[0]) 79 if pass[0]==6 { g_w(" verdict=GREEN\n"); sys_exit(0); return 0 } 80 g_w(" verdict=RED\n"); sys_exit(1); return 1 81}