diff --git a/_glua-tests/base.lua b/_glua-tests/base.lua
index 2bc64a8b..297a21be 100644
--- a/_glua-tests/base.lua
+++ b/_glua-tests/base.lua
@@ -46,3 +46,33 @@ local ok, a, b = xpcall(function()
      return err .. "!", "b"
   end)
 assert(not ok and string.find(a, "error!!") and b == nil)
+
+-- numbers convert to text with the reference Lua 5.1 "%.14g" rendering
+assert(tostring(100) == "100")
+assert(tostring(0.1) == "0.1")
+assert(tostring(0.1 + 0.2) == "0.3")
+assert(tostring(1e-10) == "1e-10")
+assert(tostring(1e15) == "1e+15")
+assert(tostring(2^53) == "9.007199254741e+15")
+assert(tostring(123456789012345678) == "1.2345678901235e+17")
+assert(tostring(1/0) == "inf")
+assert(tostring(-1/0) == "-inf")
+local nan = 0/0
+local s1, s2 = tostring(nan), tostring(-nan)
+assert(s1 == "nan" or s1 == "-nan")
+assert(s2 == "nan" or s2 == "-nan")
+assert(s1 ~= s2)
+
+-- negative zero renders with its sign
+local zero = 0.0
+local negzero = -zero
+assert(tostring(zero) == "0")
+assert(tostring(negzero) == "-0")
+assert(tostring(negzero * 1) == "-0")
+
+-- the same rendering applies to concatenation and table.concat
+assert((1e15 .. "") == "1e+15")
+assert((2^53 .. "x") == "9.007199254741e+15x")
+assert((1.5 .. "") == "1.5")
+assert(("" .. negzero) == "-0")
+assert(table.concat({1e15, 2^53}, ",") == "1e+15,9.007199254741e+15")
diff --git a/_glua-tests/math.lua b/_glua-tests/math.lua
index 871d4041..7915c6d1 100644
--- a/_glua-tests/math.lua
+++ b/_glua-tests/math.lua
@@ -10,3 +10,14 @@ local ok, msg = pcall(function()
   math.min()
 end)
 assert(not ok and string.find(msg, "wrong number of arguments"))
+
+-- math.huge is the positive infinity, as in reference Lua 5.1
+assert(math.huge == 1/0)
+assert(-math.huge == -1/0)
+assert(math.huge > 1e308)
+assert(tostring(math.huge) == "inf")
+assert(tostring(-math.huge) == "-inf")
+
+-- the fractional part returned by math.modf prints like the reference
+local _, fr = math.modf(3.7)
+assert(tostring(fr) == "0.7")
diff --git a/_glua-tests/strings.lua b/_glua-tests/strings.lua
index 273226d9..ab4a25d4 100644
--- a/_glua-tests/strings.lua
+++ b/_glua-tests/strings.lua
@@ -11,3 +11,57 @@ assert(ret1 == 1)
 assert(ret2 == 3)
 assert(ret3 == "aaa")
 assert(ret4 == 4)
+
+-- string.format: Lua 5.1 semantics for %s, %c and %q
+
+-- %s accepts only strings and numbers
+assert(string.format("%s", 12) == "12")
+assert(string.format("%s|%s", 12, 0.5) == "12|0.5")
+assert(string.format("%s", 1e15) == "1e+15")
+assert(not pcall(string.format, "%s", nil))
+assert(not pcall(string.format, "%s", true))
+assert(not pcall(string.format, "%s", {}))
+
+-- %s stops at an embedded NUL byte ...
+local withnul = "a" .. string.char(0) .. "b"
+assert(#string.format("%s", withnul) == 1)
+-- ... unless the string is 100 bytes or longer and no precision is given,
+-- in which case it is passed through whole
+local long = string.rep("x", 60) .. string.char(0) .. string.rep("y", 60)
+assert(#string.format("%s", long) == 121)
+assert(#string.format("%.9s", long) == 9)
+local plain = string.rep("ab", 60)
+assert(string.format("%99s", plain) == plain)
+assert(#string.format("%99s", "x") == 99)
+assert(string.format("%.4s", plain) == "abab")
+
+-- %s width and precision count bytes, not characters
+local twobyte = string.char(195, 169) -- a two-byte UTF-8 sequence
+assert(#string.format("%.1s", twobyte) == 1)
+assert(#string.format("%.2s", twobyte) == 2)
+assert(string.format("%3s|", twobyte) == " " .. twobyte .. "|")
+assert(#string.format("%4s", twobyte .. twobyte) == 4)
+
+-- %c writes its value as a single byte; byte zero adds nothing
+assert(string.format("%c", 72) == "H")
+assert(string.format("a%cb", 0) == "ab")
+assert(#string.format("%c", 256) == 0)
+assert(string.format("%-3c|", 65) == "A  |")
+
+-- %q escapes: '"', '\\' and newline keep their backslash (the newline stays
+-- a real newline), '\r' becomes \r, NUL becomes the three-digit \000;
+-- %q also accepts numbers and ignores any width
+assert(string.format("%q", "a\nb") == '"a\\\nb"')
+assert(string.format("%q", "a\rb") == '"a\\rb"')
+assert(string.format("%q", "x" .. string.char(0) .. "y") == '"x\\000y"')
+assert(string.format("%q", 42) == '"42"')
+assert(string.format("%5q", "x") == '"x"')
+assert(#string.format("%q", string.rep("x", 150)) == 152)
+assert(not pcall(string.format, "%q", {}))
+
+-- %q output always round-trips through loadstring
+for i = 0, 255 do
+  local orig = "a" .. string.char(i) .. "b"
+  local f = loadstring("return " .. string.format("%q", orig))
+  assert(f ~= nil and f() == orig)
+end
diff --git a/_lua5.1-tests/strings.lua b/_lua5.1-tests/strings.lua
index 9172f563..c607a841 100644
--- a/_lua5.1-tests/strings.lua
+++ b/_lua5.1-tests/strings.lua
@@ -99,10 +99,10 @@ assert(tostring(false) == "false")
 print('+')
 
 x = '"ílo"\n\\'
--- assert(string.format('%q%s', x, x) == '"\\"ílo\\"\\\n\\\\""ílo"\n\\')
--- assert(string.format('%q', "\0") == [["\000"]])
---assert(string.format("\0%c\0%c%x\0", string.byte("á"), string.byte("b"), 140) ==
---              "\0á\0b8c\0")
+assert(string.format('%q%s', x, x) == '"\\"ílo\\"\\\n\\\\""ílo"\n\\')
+assert(string.format('%q', "\0") == [["\000"]])
+assert(string.format("\0%c\0%c%x\0", string.byte("á"), string.byte("b"), 140) ==
+              "\0á\0b8c\0")
 assert(string.format('') == "")
 assert(string.format("%c",34)..string.format("%c",48)..string.format("%c",90)..string.format("%c",100) ==
        string.format("%c%c%c%c", 34, 48, 90, 100))
diff --git a/alloc.go b/alloc.go
index 7a8cd63a..4b994955 100644
--- a/alloc.go
+++ b/alloc.go
@@ -1,6 +1,7 @@
 package lua
 
 import (
+	"math"
 	"reflect"
 	"unsafe"
 )
@@ -55,8 +56,10 @@ func newAllocator(size int) *allocator {
 // The downside of this is that all of the floats on a given block have to become eligible for gc before the block
 // as a whole can be gc-ed.
 func (al *allocator) LNumber2I(v LNumber) LValue {
-	// first check for shared preloaded numbers
-	if v >= 0 && v < preloadLimit && float64(v) == float64(int64(v)) {
+	// first check for shared preloaded numbers; negative zero compares equal
+	// to zero but must not share the preloaded +0, or it loses its sign
+	// (tostring(-0.0) is "-0" in Lua 5.1)
+	if v >= 0 && v < preloadLimit && float64(v) == float64(int64(v)) && !math.Signbit(float64(v)) {
 		return preloads[int(v)]
 	}
 
diff --git a/mathlib.go b/mathlib.go
index e612f2f0..28540591 100644
--- a/mathlib.go
+++ b/mathlib.go
@@ -8,7 +8,7 @@ import (
 func OpenMath(L *LState) int {
 	mod := L.RegisterModule(MathLibName, mathFuncs).(*LTable)
 	mod.RawSetString("pi", LNumber(math.Pi))
-	mod.RawSetString("huge", LNumber(math.MaxFloat64))
+	mod.RawSetString("huge", LNumber(math.Inf(1)))
 	L.Push(mod)
 	return 1
 }
diff --git a/stringlib.go b/stringlib.go
index f484c2b3..2f144ac9 100644
--- a/stringlib.go
+++ b/stringlib.go
@@ -133,15 +133,144 @@ func strFind(L *LState) int {
 	return md.CaptureLength()/2 + 1
 }
 
+// strFormatQuoted implements the %q conversion the way Lua 5.1's addquoted
+// (lstrlib.c) does: '"', '\\' and newline keep a backslash (the newline stays
+// a real newline byte), '\r' becomes \r, a NUL byte becomes the three-digit
+// \000, and every other byte is copied through untouched.
+func strFormatQuoted(buf *[]byte, s string) {
+	*buf = append(*buf, '"')
+	for i := 0; i < len(s); i++ {
+		c := s[i]
+		switch c {
+		case '"', '\\', '\n':
+			*buf = append(*buf, '\\', c)
+		case '\r':
+			*buf = append(*buf, '\\', 'r')
+		case 0:
+			*buf = append(*buf, '\\', '0', '0', '0')
+		default:
+			*buf = append(*buf, c)
+		}
+	}
+	*buf = append(*buf, '"')
+}
+
+func strFormatPad(buf *[]byte, item string, width int, leftAlign bool) {
+	pad := width - len(item)
+	if !leftAlign {
+		for ; pad > 0; pad-- {
+			*buf = append(*buf, ' ')
+		}
+	}
+	*buf = append(*buf, item...)
+	if leftAlign {
+		for ; pad > 0; pad-- {
+			*buf = append(*buf, ' ')
+		}
+	}
+}
+
 func strFormat(L *LState) int {
 	str := L.CheckString(1)
-	args := make([]interface{}, L.GetTop()-1)
-	top := L.GetTop()
-	for i := 2; i <= top; i++ {
-		args[i-2] = L.Get(i)
+	arg := 1
+	out := make([]byte, 0, len(str)+16)
+	i := 0
+	for i < len(str) {
+		c := str[i]
+		if c != '%' {
+			out = append(out, c)
+			i++
+			continue
+		}
+		spec := i
+		i++
+		if i < len(str) && str[i] == '%' {
+			out = append(out, '%')
+			i++
+			continue
+		}
+		leftAlign := false
+		for i < len(str) && strings.IndexByte("-+ #0", str[i]) >= 0 {
+			if str[i] == '-' {
+				leftAlign = true
+			}
+			i++
+		}
+		width := -1
+		for i < len(str) && str[i] >= '0' && str[i] <= '9' {
+			if width < 0 {
+				width = 0
+			}
+			width = width*10 + int(str[i]-'0')
+			i++
+		}
+		prec := -1
+		if i < len(str) && str[i] == '.' {
+			i++
+			prec = 0
+			for i < len(str) && str[i] >= '0' && str[i] <= '9' {
+				prec = prec*10 + int(str[i]-'0')
+				i++
+			}
+		}
+		if i >= len(str) {
+			L.RaiseError("invalid format string to 'format'")
+		}
+		d := str[i]
+		i++
+		arg++
+		switch d {
+		case 's':
+			var ss string
+			switch v := L.Get(arg).(type) {
+			case LString:
+				ss = string(v)
+			case LNumber:
+				ss = v.String()
+			default:
+				L.TypeError(arg, LTString)
+			}
+			// Lua 5.1's str_format keeps a string with no precision and
+			// length >= 100 whole (too long for its C sprintf buffer), so
+			// only shorter strings are cut at the first NUL byte the way
+			// C sprintf's %s would cut them.
+			if prec < 0 && len(ss) >= 100 {
+				strFormatPad(&out, ss, width, leftAlign)
+				break
+			}
+			if i0 := strings.IndexByte(ss, 0); i0 >= 0 {
+				ss = ss[:i0]
+			}
+			if prec >= 0 && len(ss) > prec {
+				ss = ss[:prec]
+			}
+			strFormatPad(&out, ss, width, leftAlign)
+		case 'q':
+			var qs string
+			switch v := L.Get(arg).(type) {
+			case LString:
+				qs = string(v)
+			case LNumber:
+				qs = v.String()
+			default:
+				L.TypeError(arg, LTString)
+			}
+			strFormatQuoted(&out, qs)
+		case 'c':
+			// Lua 5.1 writes (char)n through sprintf and measures the
+			// result with strlen, so %c emits a single byte and a zero
+			// byte adds nothing.
+			n := int64(L.CheckNumber(arg))
+			item := ""
+			if b := byte(n); b != 0 {
+				item = string([]byte{b})
+			}
+			strFormatPad(&out, item, width, leftAlign)
+		default:
+			out = append(out, []byte(fmt.Sprintf(str[spec:i], L.Get(arg)))...)
+		}
 	}
-	npat := strings.Count(str, "%") - strings.Count(str, "%%")
-	L.Push(LString(fmt.Sprintf(str, args[:intMin(npat, len(args))]...)))
+	L.Push(LString(string(out)))
 	return 1
 }
 
diff --git a/value.go b/value.go
index 4156e9d5..5a979d79 100644
--- a/value.go
+++ b/value.go
@@ -3,6 +3,7 @@ package lua
 import (
 	"context"
 	"fmt"
+	"math"
 	"os"
 )
 
@@ -111,11 +112,24 @@ func (st LString) Format(f fmt.State, c rune) {
 	}
 }
 
+// String renders the number the way the reference Lua 5.1 interpreter does:
+// lua_number2str uses LUAI_NUMFMT "%.14g" (luaconf.h), and infinities and
+// NaNs print as C's printf spells them ("inf", "-inf", "nan", "-nan").
 func (nm LNumber) String() string {
-	if isInteger(nm) {
-		return fmt.Sprint(int64(nm))
+	f := float64(nm)
+	if math.IsInf(f, 1) {
+		return "inf"
 	}
-	return fmt.Sprint(float64(nm))
+	if math.IsInf(f, -1) {
+		return "-inf"
+	}
+	if math.IsNaN(f) {
+		if math.Signbit(f) {
+			return "-nan"
+		}
+		return "nan"
+	}
+	return fmt.Sprintf("%.14g", f)
 }
 
 func (nm LNumber) Type() LValueType { return LTNumber }