michael@0: 
michael@0: function f56(x) {
michael@0:   var a = x >>> 0; // Range = [0 .. UINT32_MAX] (bits = 32)
michael@0:   var b = 0x800000; // == 2^23 (bits = 24)
michael@0:   if (a > 0) {
michael@0:     // Beta node: Range [1 .. UINT32_MAX] (bits = 32)
michael@0:     var c = a * b; // Range = [0 .. +inf] (bits = a.bits + b.bits - 1 = 55)
michael@0:     var d = c + 1; // Range = [0 .. +inf] (bits = c.bits + 1 = 56)
michael@0:     return (d | 0) & 1;
michael@0:   } else {
michael@0:     return 1;
michael@0:   }
michael@0: }
michael@0: 
michael@0: function f55(x) {
michael@0:   var a = x >>> 0; // Range = [0 .. UINT32_MAX] (bits = 32)
michael@0:   var b = 0x400000; // == 2^22 (bits = 23)
michael@0:   if (a > 0) {
michael@0:     // Beta node: Range [1 .. UINT32_MAX] (bits = 32)
michael@0:     var c = a * b; // Range = [0 .. +inf] (bits = a.bits + b.bits - 1 = 54)
michael@0:     var d = c + 1; // Range = [0 .. +inf] (bits = c.bits + 1 = 55)
michael@0:     return (d | 0) & 1;
michael@0:   } else {
michael@0:     return 1;
michael@0:   }
michael@0: }
michael@0: 
michael@0: // Still returns 1, because the top-level bit is not represented.
michael@0: function f54(x) {
michael@0:   var a = x >>> 0; // Range = [0 .. UINT32_MAX] (bits = 32)
michael@0:   var b = 0x200000; // == 2^21 (bits = 22)
michael@0:   if (a > 0) {
michael@0:     // Beta node: Range [1 .. UINT32_MAX] (bits = 32)
michael@0:     var c = a * b; // Range = [0 .. +inf] (bits = a.bits + b.bits - 1 = 53)
michael@0:     var d = c + 1; // Range = [1 .. +inf] (bits = c.bits + 1 = 54)
michael@0:     return (d | 0) & 1;
michael@0:   } else {
michael@0:     return 1;
michael@0:   }
michael@0: }
michael@0: 
michael@0: // Can safely truncate after these operations. (the mantissa has 53 bits)
michael@0: function f53(x) {
michael@0:   var a = x >>> 0; // Range = [0 .. UINT32_MAX] (bits = 32)
michael@0:   var b = 0x100000; // == 2^20 (bits = 21)
michael@0:   if (a > 0) {
michael@0:     // Beta node: Range [1 .. UINT32_MAX] (bits = 32)
michael@0:     var c = a * b; // Range = [0 .. +inf] (bits = a.bits + b.bits - 1 = 52)
michael@0:     var d = c + 1; // Range = [1 .. +inf] (bits = c.bits + 1 = 53)
michael@0:     return (d | 0) & 1;
michael@0:   } else {
michael@0:     return 1;
michael@0:   }
michael@0: }
michael@0: 
michael@0: function f52(x) {
michael@0:   var a = x >>> 0; // Range = [0 .. UINT32_MAX] (bits = 32)
michael@0:   var b = 0x80000; // == 2^19 (bits = 20)
michael@0:   if (a > 0) {
michael@0:     // Beta node: Range [1 .. UINT32_MAX] (bits = 32)
michael@0:     var c = a * b; // Range = [0 .. +inf] (bits = a.bits + b.bits - 1 = 51)
michael@0:     var d = c + 1; // Range = [1 .. +inf] (bits = c.bits + 1 = 52)
michael@0:     return (d | 0) & 1;
michael@0:   } else {
michael@0:     return 1;
michael@0:   }
michael@0: }
michael@0: 
michael@0: function f51(x) {
michael@0:   var a = x >>> 0; // Range = [0 .. UINT32_MAX] (bits = 32)
michael@0:   var b = 0x40000; // == 2^18 (bits = 19)
michael@0:   if (a > 0) {
michael@0:     // Beta node: Range [1 .. UINT32_MAX] (bits = 32)
michael@0:     var c = a * b; // Range = [0 .. +inf] (bits = a.bits + b.bits - 1 = 50)
michael@0:     var d = c + 1; // Range = [1 .. +inf] (bits = c.bits + 1 = 51)
michael@0:     return (d | 0) & 1;
michael@0:   } else {
michael@0:     return 1;
michael@0:   }
michael@0: }
michael@0: 
michael@0: var e = Math.pow(2, 32);
michael@0: for (var i = 1; i < e; i = i * 1.5) {
michael@0:     var x = i >>> 0;
michael@0:     assertEq(f56(x) , (x >= Math.pow(2, 30)) ? 0 : 1);
michael@0:     assertEq(f55(x), (x >= Math.pow(2, 31)) ? 0 : 1);
michael@0:     assertEq(f54(x), 1);
michael@0:     assertEq(f53(x), 1);
michael@0:     assertEq(f52(x), 1);
michael@0:     assertEq(f51(x), 1);
michael@0: }