Initial data commit

Task/Numeric-error-propagation/Icon/numeric-error-propagation.icon

@@ -0,0 +1,43 @@
+record num(val,err)
+
+procedure main(a)
+    x1 := num(100.0, 1.1)
+    y1 := num(50.0,  1.2)
+    x2 := num(200.0, 2.2)
+    y2 := num(100.0, 2.3)
+    d := pow(add(pow(sub(x1,x2),2),pow(sub(y1,y2),2)),0.5)
+    write("d = [",d.val,", ",d.err,"]")
+end
+
+procedure add(a,b)
+    return (numeric(a)+numeric(b)) |
+           num(numeric(a)+b.val, b.err) |
+           num(a.val+numeric(b), a.err) |
+           num(a.val+b.val, (a.err^2 + b.err^2) ^ 0.5)
+end
+
+procedure sub(a,b)
+    return (numeric(a)-numeric(b)) |
+           num(numeric(a)-b.val, b.err) |
+           num(a.val-numeric(b), a.err) |
+           num(a.val-b.val, (a.err^2 + b.err^2) ^ 0.5)
+end
+
+procedure mul(a,b)
+    return (numeric(a)*numeric(b)) |
+           num(numeric(a)*b.val, abs(a*b.err)) |
+           num(a.val*numeric(b), abs(b*a.err)) |
+           num(f := a.val*b.val, ((f^2*((a.err/a.val)^2+(b.err/b.val)^2))^0.5))
+end
+
+procedure div(a,b)
+    return (numeric(a)/numeric(b)) |
+           num(numeric(a)/b.val, abs(a*b.err)) |
+           num(a.val/numeric(b), abs(b*a.err)) |
+           num(f := a.val/b.val, ((f^2*((a.err/a.val)^2+(b.err/b.val)^2))^0.5))
+end
+
+procedure pow(a,b)
+    return (numeric(a)^numeric(b)) |
+           num(f := a.val^numeric(b), abs(f*b*(a.err/a.val)))
+end