Data commit

Task/Pathological-floating-point-problems/Icon/pathological-floating-point-problems.icon

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+#
+# Pathological floating point problems
+#
+procedure main()
+    sequence()
+    chaotic()
+end
+
+#
+# First task, sequence convergence
+#
+link printf
+procedure sequence()
+     local l := [2, -4]
+     local iters := [3, 4, 5, 6, 7, 8, 20, 30, 50, 100, 200]
+     local i, j, k
+     local n := 1
+
+     write("Sequence convergence")
+     # Demonstrate the convergence problem with various precision values
+     every k := (100 | 300) do {
+         n := 10^k
+         write("\n", k, " digits of intermediate precision")
+
+         # numbers are scaled up using large integer powers of 10
+         every i := !iters do {
+             l := [2 * n, -4 * n]
+             printf("i: %3d", i)
+
+             every j := 3 to i do {
+                 # build out a list of intermediate passes
+                 # order of scaling operations matters
+                 put(l, 111 * n - (1130 * n * n / l[j - 1]) +
+                        (3000 * n * n * n / (l[j - 1] * l[j - 2])))
+             }
+             # down scale the result to a real
+             # some precision may be lost in the final display
+             printf(" %20.16r\n", l[i] * 1.0 / n)
+         }
+     }
+end
+
+#
+# Task 2, chaotic bank of Euler
+#
+procedure chaotic()
+    local euler, e, scale, show, y, d
+
+    write("\nChaotic Banking Society of Euler")
+    # format the number for listing, string form, way overboard on digits
+    euler :=
+"2718281828459045235360287471352662497757247093699959574966967627724076630353_
+  547594571382178525166427427466391932003059921817413596629043572900334295260_
+  595630738132328627943490763233829880753195251019011573834187930702154089149_
+  934884167509244761460668082264800168477411853742345442437107539077744992069_
+  551702761838606261331384583000752044933826560297606737113200709328709127443_
+  747047230696977209310141692836819025515108657463772111252389784425056953696_
+  770785449969967946864454905987931636889230098793127736178215424999229576351_
+  482208269895193668033182528869398496465105820939239829488793320362509443117_
+  301238197068416140397019837679320683282376464804295311802328782509819455815_
+  301756717361332069811250996181881593041690351598888519345807273866738589422_
+  879228499892086805825749279610484198444363463244968487560233624827041978623_
+  209002160990235304369941849146314093431738143640546253152096183690888707016_
+  768396424378140592714563549061303107208510383750510115747704171898610687396_
+  9655212671546889570350354"
+
+    # precise math with long integers, string form just for pretty listing
+    e := integer(euler)
+
+    # 1000 digits after the decimal for scaling intermediates and service fee
+    scale := 10^1000
+
+    # initial deposit - $1
+    d := e - scale
+
+    # show balance with 16 digits
+    show := 10^16
+    write("Starting balance:       $", d * show / scale * 1.0 / show, "...")
+
+    # wait 25 years, with only a trivial $1 service fee
+    every y := 1 to 25 do {
+        d := d * y - scale
+    }
+
+    # show final balance with 4 digits after the decimal (truncation)
+    show := 10^4
+    write("Balance after ", y, " years: $", d * show / scale * 1.0 / show)
+end