| |
| |
| |
| |
| assert(math.type and math.type(1)=="integer", "Lua integer arithmetic required") |
| |
| local MAX=math.maxinteger |
| local function checked(a) |
| assert(math.type(a)=="integer" and a>=-MAX and a<=MAX,"integer range exceeded") |
| return a |
| end |
| local function imul(a,b) |
| checked(a);checked(b) |
| assert(b==0 or math.abs(a)<=MAX//math.abs(b),"integer multiplication overflow") |
| return a*b |
| end |
| local function iadd(a,b) |
| checked(a);checked(b) |
| if b>0 then assert(a<=MAX-b,"integer addition overflow") |
| elseif b<0 then assert(a>=-MAX-b,"integer addition overflow") end |
| return a+b |
| end |
| local function gcd(a,b) a=math.abs(a);b=math.abs(b);while b~=0 do a,b=b,a%b end;return a end |
| local function rat(a,b) |
| b=b or 1;checked(a);checked(b);assert(b~=0);if b<0 then a,b=-a,-b end |
| local g=gcd(a,b);return {a//g,b//g} |
| end |
| local function add(a,b) |
| local g=gcd(a[2],b[2]);return rat(iadd(imul(a[1],b[2]//g),imul(b[1],a[2]//g)),imul(a[2]//g,b[2])) |
| end |
| local function neg(a)return {-a[1],a[2]}end |
| local function sub(a,b)return add(a,neg(b))end |
| local function mul(a,b) |
| local g=gcd(a[1],b[2]);local h=gcd(b[1],a[2]) |
| return rat(imul(a[1]//g,b[1]//h),imul(a[2]//h,b[2]//g)) |
| end |
| local function div(a,b)return mul(a,rat(b[2],b[1]))end |
| local function eq(a,b)return a[1]==b[1]and a[2]==b[2]end |
| local function fmt(a)return tostring(a[1]).."/"..tostring(a[2])end |
| local Z=rat(0) |
| local function pder(a,dt) |
| local r={};for j=2,#a do r[j-1]=div(mul(rat(j-1),a[j]),dt)end |
| if #r==0 then r={Z}end;return r |
| end |
| local function padd(a,b) |
| local r={};for j=1,math.max(#a,#b)do r[j]=add(a[j]or Z,b[j]or Z)end;return r |
| end |
| local function pscale(a,s)local r={};for j,v in ipairs(a)do r[j]=mul(v,s)end;return r end |
| local function integral(a,dt) |
| local r=Z;for j,v in ipairs(a)do r=add(r,div(v,rat(j)))end;return mul(r,dt) |
| end |
| local function square(a) |
| local r={};for j=1,2*#a-1 do r[j]=Z end |
| for i,x in ipairs(a)do for j,y in ipairs(a)do r[i+j-1]=add(r[i+j-1],mul(x,y))end end |
| return r |
| end |
| local low,high=rat(2,5),rat(9) |
| local mean,T,ca=rat(403,83),rat(249,50),rat(1,5) |
| local segments={{rat(7,10),low,low},{rat(1),low,high},{rat(79,50),high,high}, |
| {rat(1),high,low},{rat(7,10),low,low}} |
| local force,heat,meanint=Z,Z,Z |
| for _,seg in ipairs(segments)do |
| local dt,l,h=seg[1],seg[2],seg[3];local diff=sub(h,l) |
| local q={l,Z,mul(rat(3),diff),mul(rat(-2),diff)} |
| local dq=pder(q,dt);local ddq=pder(dq,dt) |
| local x={sub(q[1],mean),q[2],q[3],q[4]} |
| local v=padd(padd(ddq,pscale(dq,ca)),x) |
| force=add(force,integral(square(v),dt)) |
| heat=add(heat,mul(ca,integral(square(dq),dt))) |
| meanint=add(meanint,integral(q,dt)) |
| end |
| force,heat,meanint=div(force,T),div(heat,T),div(meanint,T) |
| assert(eq(force,rat(1815714302,6027875)),"force certificate failed") |
| assert(eq(heat,rat(14792,2075)),"heat certificate failed") |
| assert(eq(meanint,mean),"mean certificate failed") |
| print("PASS: exact average force squared = "..fmt(force)) |
| print("PASS: exact average acoustic heat = "..fmt(heat)) |
| print("PASS: exact stiffness mean = "..fmt(meanint)) |
| print("All operations used normalized integer rational arithmetic with overflow guards.") |
|
|
