diff --git a/arith.go b/arith.go
index fc444cd..3e16e0d 100644
--- a/arith.go
+++ b/arith.go
@@ -113,6 +113,15 @@ func floatMod(x, y float64) float64 {
 	if y == 0 || math.IsInf(x, 0) || x != x || y != y {
 		return (x * y) / (x * y)
 	}
+	// whole numbers below 2^53, as code written before Lua had integers takes bits: exact
+	// as integers, where math.Mod loops over the bits of the quotient
+	if a, b := int64(x), int64(y); float64(a) == x && float64(b) == y && x < 0x1p53 && x > -0x1p53 && y < 0x1p53 && y > -0x1p53 {
+		m := intMod(a, b)
+		if m == 0 {
+			return math.Copysign(0, x) // as fmod: a zero remainder keeps the dividend's sign
+		}
+		return float64(m)
+	}
 	m := math.Mod(x, y)
 	if (m > 0 && y < 0) || (m < 0 && y != m && y > 0) {
 		m += y
diff --git a/bench/asmgate/baseline.txt b/bench/asmgate/baseline.txt
index 0d4a421..6003ce6 100644
--- a/bench/asmgate/baseline.txt
+++ b/bench/asmgate/baseline.txt
@@ -1,8 +1,8 @@
 # Stack accesses per hot opcode in (*executor).fast, outside write-barrier slow paths.
 # Opcodes not listed must have none. Written by go run ./bench/asmgate -update.
 amd64-v1 head 1
-amd64-v1 opGetField 7
-amd64-v1 opGetTable,opGetIndex 2
+amd64-v1 opGetField 6
+amd64-v1 opGetTable,opGetIndex 3
 amd64-v1 opJmp 3
 amd64-v1 opSelf 1
 amd64-v3 head 2
diff --git a/checked_gen.go b/checked_gen.go
index 03b54e0..21b1580 100644
--- a/checked_gen.go
+++ b/checked_gen.go
@@ -410,6 +410,14 @@ dispatch:
 				idx = uint64(uint8(i>>24)) - 1
 			} else if key := &regs[uint8(i>>24)]; key.p == tInt() {
 				idx = key.n - 1
+			} else if key.p == tFloat() {
+				// a float with a whole value, as arithmetic in code written for Lua 5.1 makes
+				// indexes: the integer key it normalises to
+				var whole bool
+				if idx, whole = wholeIndex(key.n); !whole {
+					e = exSlowOp
+					break dispatch
+				}
 			} else if key.n>>56 == kindString && !isScalar(key.p) && key.n&lenMask <= 16 && obj.n == kindTable<<56 && !isScalar(obj.p) {
 				// a short string key: hash it and probe inline, as hashString and keyEq would
 				t, n := (*Table)(obj.p), key.n&lenMask
@@ -507,6 +515,12 @@ dispatch:
 				idx = uint64(uint8(i>>16)) - 1
 			} else if key := &regs[uint8(i>>16)]; key.p == tInt() {
 				idx = key.n - 1
+			} else if key.p == tFloat() {
+				var whole bool
+				if idx, whole = wholeIndex(key.n); !whole {
+					e = exSlowOp
+					break dispatch
+				}
 			} else {
 				e = exSlowOp
 				break dispatch
@@ -582,6 +596,29 @@ dispatch:
 				} else {
 					setInt(&regs[uint8(i>>8)], uint64(q))
 				}
+			} else if (uint8(i) == opMod || uint8(i) == opModK) && (x.p == tFloat() || y.p == tFloat()) && isNum(x) && isNum(y) {
+				// a float remainder of whole numbers below 2^53, as code written before Lua had
+				// integers takes bits: exact as integers, where math.Mod loops over the quotient's
+				// bits. Two integers with a divisor below 1 are the driver's: the result is an integer
+				fx, fy := toFloat(x), toFloat(y)
+				a, b := int64(fx), int64(fy)
+				if float64(a) != fx || float64(b) != fy || b == 0 || fx >= 0x1p53 || fx <= -0x1p53 || fy >= 0x1p53 || fy <= -0x1p53 {
+					// not whole, too large, NaN, infinite, or a zero divisor. Spelt out: wholeInt
+					// here spills the loop
+					e = exSlowOp
+					break dispatch
+				}
+				m := a % b
+				if m != 0 && (m^b) < 0 { // round towards minus infinity
+					m += b
+				}
+				r := float64(m)
+				if m == 0 {
+					// as fmod: a zero remainder keeps the dividend's sign, which is bit 63 of an
+					// integer and of a float alike
+					r = math.Float64frombits(x.n & (1 << 63))
+				}
+				setFloat(&regs[uint8(i>>8)], r)
 			} else {
 				e = exSlowOp
 				break dispatch
diff --git a/exec_test.go b/exec_test.go
index a460a6f..ebf59bf 100644
--- a/exec_test.go
+++ b/exec_test.go
@@ -1020,3 +1020,72 @@ func TestWrapFailureKeepsNothing(t *testing.T) {
 	}
 	release(&rt.pool, ex)
 }
+
+// The remainder of floats with whole values, as code written for Lua 5.1 takes bits, is
+// computed as integers, inline and in the driver: the same as fmod gives, sign of a zero
+// included; values that are not whole, or too large, still go the long way.
+func TestFloatModWhole(t *testing.T) {
+	src := `
+		local function same(a, b) return a == b and (a ~= 0 or 1 / a == 1 / b) end
+		local K = 3.0
+		local cases = {
+			{ 7.0, 3.0, 1.0 }, { -7.0, 3.0, 2.0 }, { 7.0, -3.0, -2.0 }, { -7.0, -3.0, -1.0 },
+			{ 6.0, 3.0, 0.0 }, { -6.0, 3.0, -0.0 }, { 6.0, -3.0, 0.0 }, { -0.0, 3.0, -0.0 }, { 0.0, -3.0, 0.0 },
+			{ 7, 3.0, 1.0 }, { 7.0, 3, 1.0 }, { -6, 3.0, -0.0 }, { -5, -1.0, -0.0 }, { 6, -3.0, 0.0 }, { -7, 3.0, 2.0 },
+			{ 5.5, 2.0, 1.5 }, { 7.0, 2.5, 2.0 }, { 2^53, 3.0, 2.0 }, { 2^60, 7.0, 1.0 }, { 16777216.0 * 65536, 256.0, 0.0 },
+			{ 1e300, 7.0, 1.0 }, -- the last three go the long way, with the values C Lua gives
+		}
+		for i, c in ipairs(cases) do
+			local x, y, want = c[1], c[2], c[3]
+			local got = x % y
+			assert(same(got, want), i .. ": " .. tostring(x) .. " % " .. tostring(y) .. " = " .. tostring(got))
+			assert(math.type(got) == "float", i)
+		end
+		local x = 7.0
+		assert(same(x % 3.0, 1.0) and same(-x % 3.0, 2.0) and same((x - 13) % 3.0, -0.0)) -- the constant form, MODK
+		assert(same(K % 3, 0.0) and same(-K % 3, -0.0)) -- a float register with an integer constant
+		local nan = 7.0 % 0.0
+		assert(nan ~= nan)
+		local bitbuf, room = 0, 1 -- a bit buffer as inflate keeps one, in floats
+		for i = 1, 20 do bitbuf, room = bitbuf + (i % 256) * room, room * 256 end
+		local v = 0
+		for _ = 1, 50 do local p = 2 ^ 5; local r = bitbuf % p; v = v * 2 + r; bitbuf = (bitbuf - r) / p end
+		return v`
+	for _, checked := range []bool{true, false} {
+		res, err := runInEnv(t, MustNew(withLoop(checked)), src)
+		if err != nil || len(res) != 1 {
+			t.Fatalf("checked=%v: %v %v", checked, res, err)
+		}
+		if f, _ := res[0].Float(); f != 5181448545894400 { // as C Lua computes it
+			t.Errorf("checked=%v: bit buffer gave %v", checked, res[0])
+		}
+	}
+}
+
+// A float key with a whole value finds the integer key it normalises to, inline, in the
+// array part and in the hash part; one without, or past the integers, goes the long way.
+func TestFloatKeysInline(t *testing.T) {
+	src := `
+		local t = { 10, 20, 30, [0] = 5, [-1] = -5, [100] = 1000, [0.5] = "half", [2^53] = "big", [2^63] = "huge" }
+		assert(t[1.0] == 10 and t[3.0] == 30 and t[0.0] == 5 and t[-0.0] == 5 and t[-1.0] == -5 and t[100.0] == 1000)
+		assert(t[0.5] == "half" and t[2^53] == "big" and t[2^63] == "huge" and t[4.0] == nil and t[1e300] == nil)
+		local nan = 0 / 0
+		assert(t[nan] == nil)
+		t[2.0] = 22
+		t[0.0] = 55
+		t[100.0] = 1001
+		t[4.0] = 40 -- an append, as t[4] is
+		assert(t[2] == 22 and t[0] == 55 and t[100] == 1001 and t[4] == 40 and #t == 4)
+		local w = {}
+		for k = 1, 10 do w[k + 0.0] = k * k end
+		local s = 0
+		for k = 1, 10 do s = s + w[k] end
+		assert(s == 385 and #w == 10)
+		return "ok"`
+	for _, checked := range []bool{true, false} {
+		res, err := runInEnv(t, MustNew(withLoop(checked)), src)
+		if err != nil || len(res) != 1 || res[0].String() != "ok" {
+			t.Errorf("checked=%v: %v %v", checked, res, err)
+		}
+	}
+}
diff --git a/fast.go b/fast.go
index 6a9e719..b236c55 100644
--- a/fast.go
+++ b/fast.go
@@ -44,6 +44,19 @@ func strEqBytes(x, y *Value, n uintptr) bool {
 	return true
 }
 
+// wholeIndex returns the array index of a float key, from its bits, when its value is whole
+// and an integer: the key it normalises to, less one, as normKey gives it. The range is
+// tested on the float, as arm64 saturates int64(f) where amd64 gives the minimum. Small
+// enough to inline into fast; split in two, it spills the loop.
+func wholeIndex(bits uint64) (uint64, bool) {
+	f := math.Float64frombits(bits)
+	n := int64(f)
+	if float64(n) != f || f >= 0x1p63 || f < -0x1p63 {
+		return 0, false
+	}
+	return uint64(n) - 1, true
+}
+
 // isNum reports whether v is an integer or a float. Small enough to inline into fast.
 func isNum(v *Value) bool { return v.p == tInt() || v.p == tFloat() }
 
@@ -508,6 +521,14 @@ dispatch:
 				idx = uint64(uint8(i>>24)) - 1
 			} else if key := &regs[uint8(i>>24)]; key.p == tInt() {
 				idx = key.n - 1
+			} else if key.p == tFloat() {
+				// a float with a whole value, as arithmetic in code written for Lua 5.1 makes
+				// indexes: the integer key it normalises to
+				var whole bool
+				if idx, whole = wholeIndex(key.n); !whole {
+					e = exSlowOp
+					break dispatch
+				}
 			} else if key.n>>56 == kindString && !isScalar(key.p) && key.n&lenMask <= 16 && obj.n == kindTable<<56 && !isScalar(obj.p) {
 				// a short string key: hash it and probe inline, as hashString and keyEq would
 				t, n := (*Table)(obj.p), key.n&lenMask
@@ -605,6 +626,12 @@ dispatch:
 				idx = uint64(uint8(i>>16)) - 1
 			} else if key := &regs[uint8(i>>16)]; key.p == tInt() {
 				idx = key.n - 1
+			} else if key.p == tFloat() {
+				var whole bool
+				if idx, whole = wholeIndex(key.n); !whole {
+					e = exSlowOp
+					break dispatch
+				}
 			} else {
 				e = exSlowOp
 				break dispatch
@@ -680,6 +707,29 @@ dispatch:
 				} else {
 					setInt(&regs[uint8(i>>8)], uint64(q))
 				}
+			} else if (uint8(i) == opMod || uint8(i) == opModK) && (x.p == tFloat() || y.p == tFloat()) && isNum(x) && isNum(y) {
+				// a float remainder of whole numbers below 2^53, as code written before Lua had
+				// integers takes bits: exact as integers, where math.Mod loops over the quotient's
+				// bits. Two integers with a divisor below 1 are the driver's: the result is an integer
+				fx, fy := toFloat(x), toFloat(y)
+				a, b := int64(fx), int64(fy)
+				if float64(a) != fx || float64(b) != fy || b == 0 || fx >= 0x1p53 || fx <= -0x1p53 || fy >= 0x1p53 || fy <= -0x1p53 {
+					// not whole, too large, NaN, infinite, or a zero divisor. Spelt out: wholeInt
+					// here spills the loop
+					e = exSlowOp
+					break dispatch
+				}
+				m := a % b
+				if m != 0 && (m^b) < 0 { // round towards minus infinity
+					m += b
+				}
+				r := float64(m)
+				if m == 0 {
+					// as fmod: a zero remainder keeps the dividend's sign, which is bit 63 of an
+					// integer and of a float alike
+					r = math.Float64frombits(x.n & (1 << 63))
+				}
+				setFloat(&regs[uint8(i>>8)], r)
 			} else {
 				e = exSlowOp
 				break dispatch