AP_Scripting: add math and strings test scripts

2020-03-14 16:37:18 +00:00 · 2020-03-14 16:37:18 +00:00 · 524d59ad78
parent 32276d9725
commit 524d59ad78
2 changed files with 1205 additions and 0 deletions
--- a/libraries/AP_Scripting/tests/math.lua
+++ b/libraries/AP_Scripting/tests/math.lua
@ -0,0 +1,836 @@
+-- $Id: math.lua,v 1.77 2016/06/23 15:17:20 roberto Exp roberto $
+
+--[[
+*****************************************************************************
+* Copyright (C) 1994-2016 Lua.org, PUC-Rio.
+*
+* Permission is hereby granted, free of charge, to any person obtaining
+* a copy of this software and associated documentation files (the
+* "Software"), to deal in the Software without restriction, including
+* without limitation the rights to use, copy, modify, merge, publish,
+* distribute, sublicense, and/or sell copies of the Software, and to
+* permit persons to whom the Software is furnished to do so, subject to
+* the following conditions:
+*
+* The above copyright notice and this permission notice shall be
+* included in all copies or substantial portions of the Software.
+*
+* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
+* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
+* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
+* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+*****************************************************************************
+]]
+
+-- This code is copied from https://github.com/lua/tests and slightly modified to work within ArduPilot
+
+gcs:send_text(6, "testing numbers and math lib")
+
+local minint = math.mininteger
+local maxint = math.maxinteger
+
+local intbits = math.floor(math.log(maxint, 2) + 0.5) + 1
+assert((1 << intbits) == 0)
+
+assert(minint == 1 << (intbits - 1))
+assert(maxint == minint - 1)
+
+-- number of bits in the mantissa of a floating-point number
+local floatbits = 24
+do
+  local p = 2.0^floatbits
+  while p < p + 1.0 do
+    p = p * 2.0
+    floatbits = floatbits + 1
+  end
+end
+
+local function isNaN (x)
+  return (x ~= x)
+end
+
+assert(isNaN(0/0))
+assert(not isNaN(1/0))
+
+
+do
+  local x = 2.0^floatbits
+  assert(x > x - 1.0 and x == x + 1.0)
+
+  gcs:send_text(6, string.format("%d-bit integers, %d-bit (mantissa) floats",
+                       intbits, floatbits))
+end
+
+assert(math.type(0) == "integer" and math.type(0.0) == "float"
+       and math.type("10") == nil)
+
+
+local function checkerror (msg, f, ...)
+  local s, err = pcall(f, ...)
+  assert(not s and string.find(err, msg))
+end
+
+local msgf2i = "number.* has no integer representation"
+
+-- float equality
+function eq (a,b,limit)
+  if not limit then
+    if floatbits >= 50 then limit = 1E-11
+    else limit = 1E-5
+    end
+  end
+  -- a == b needed for +inf/-inf
+  return a == b or math.abs(a-b) <= limit
+end
+
+
+-- equality with types
+function eqT (a,b)
+  return a == b and math.type(a) == math.type(b)
+end
+
+
+-- basic float notation
+assert(0e12 == 0 and .0 == 0 and 0. == 0 and .2e2 == 20 and 2.E-1 == 0.2)
+
+do
+  local a,b,c = "2", " 3e0 ", " 10  "
+  assert(a+b == 5 and -b == -3 and b+"2" == 5 and "10"-c == 0)
+  assert(type(a) == 'string' and type(b) == 'string' and type(c) == 'string')
+  assert(a == "2" and b == " 3e0 " and c == " 10  " and -c == -"  10 ")
+  assert(c%a == 0 and a^b == 08)
+  a = 0
+  assert(a == -a and 0 == -0)
+end
+
+do
+  local x = -1
+  local mz = 0/x   -- minus zero
+  t = {[0] = 10, 20, 30, 40, 50}
+  assert(t[mz] == t[0] and t[-0] == t[0])
+end
+
+do   -- tests for 'modf'
+  local a,b = math.modf(3.5)
+  assert(a == 3.0 and b == 0.5)
+  a,b = math.modf(-2.5)
+  assert(a == -2.0 and b == -0.5)
+  a,b = math.modf(-3e23)
+  assert(a == -3e23 and b == 0.0)
+  a,b = math.modf(3e35)
+  assert(a == 3e35 and b == 0.0)
+  a,b = math.modf(-1/0)   -- -inf
+  assert(a == -1/0 and b == 0.0)
+  a,b = math.modf(1/0)   -- inf
+  assert(a == 1/0 and b == 0.0)
+  a,b = math.modf(0/0)   -- NaN
+  assert(isNaN(a) and isNaN(b))
+  a,b = math.modf(3)  -- integer argument
+  assert(eqT(a, 3) and eqT(b, 0.0))
+  a,b = math.modf(minint)
+  assert(eqT(a, minint) and eqT(b, 0.0))
+end
+
+assert(math.huge > 10e30)
+assert(-math.huge < -10e30)
+
+
+-- integer arithmetic
+assert(minint < minint + 1)
+assert(maxint - 1 < maxint)
+assert(0 - minint == minint)
+assert(minint * minint == 0)
+assert(maxint * maxint * maxint == maxint)
+
+
+-- testing floor division and conversions
+
+for _, i in pairs{-16, -15, -3, -2, -1, 0, 1, 2, 3, 15} do
+  for _, j in pairs{-16, -15, -3, -2, -1, 1, 2, 3, 15} do
+    for _, ti in pairs{0, 0.0} do     -- try 'i' as integer and as float
+      for _, tj in pairs{0, 0.0} do   -- try 'j' as integer and as float
+        local x = i + ti
+        local y = j + tj
+          assert(i//j == math.floor(i/j))
+      end
+    end
+  end
+end
+
+assert(1//0.0 == 1/0)
+assert(-1 // 0.0 == -1/0)
+assert(eqT(3.5 // 1.5, 2.0))
+assert(eqT(3.5 // -1.5, -3.0))
+
+assert(maxint // maxint == 1)
+assert(maxint // 1 == maxint)
+assert((maxint - 1) // maxint == 0)
+assert(maxint // (maxint - 1) == 1)
+assert(minint // minint == 1)
+assert(minint // minint == 1)
+assert((minint + 1) // minint == 0)
+assert(minint // (minint + 1) == 1)
+assert(minint // 1 == minint)
+
+assert(minint // -1 == -minint)
+assert(minint // -2 == 2^(intbits - 2))
+assert(maxint // -1 == -maxint)
+
+
+-- negative exponents
+do
+  assert(2^-3 == 1 / 2^3)
+  assert(eq((-3)^-3, 1 / (-3)^3))
+  for i = -3, 3 do    -- variables avoid constant folding
+      for j = -3, 3 do
+        -- domain errors (0^(-n)) are not portable
+        if not _port or i ~= 0 or j > 0 then
+          assert(eq(i^j, 1 / i^(-j)))
+       end
+    end
+  end
+end
+
+-- comparison between floats and integers (border cases)
+if floatbits < intbits then
+  assert(2.0^floatbits == (1 << floatbits))
+  assert(2.0^floatbits - 1.0 == (1 << floatbits) - 1.0)
+  assert(2.0^floatbits - 1.0 ~= (1 << floatbits))
+  -- float is rounded, int is not
+  assert(2.0^floatbits + 1.0 ~= (1 << floatbits) + 1)
+else   -- floats can express all integers with full accuracy
+  assert(maxint == maxint + 0.0)
+  assert(maxint - 1 == maxint - 1.0)
+  assert(minint + 1 == minint + 1.0)
+  assert(maxint ~= maxint - 1.0)
+end
+assert(maxint + 0.0 == 2.0^(intbits - 1) - 1.0)
+assert(minint + 0.0 == minint)
+assert(minint + 0.0 == -2.0^(intbits - 1))
+
+
+-- order between floats and integers
+assert(1 < 1.1); assert(not (1 < 0.9))
+assert(1 <= 1.1); assert(not (1 <= 0.9))
+assert(-1 < -0.9); assert(not (-1 < -1.1))
+assert(1 <= 1.1); assert(not (-1 <= -1.1))
+assert(-1 < -0.9); assert(not (-1 < -1.1))
+assert(-1 <= -0.9); assert(not (-1 <= -1.1))
+assert(minint <= minint + 0.0)
+assert(minint + 0.0 <= minint)
+assert(not (minint < minint + 0.0))
+assert(not (minint + 0.0 < minint))
+assert(maxint < minint * -1.0)
+assert(maxint <= minint * -1.0)
+
+do
+  local fmaxi1 = 2^(intbits - 1)
+  assert(maxint < fmaxi1)
+  assert(maxint <= fmaxi1)
+  assert(not (fmaxi1 <= maxint))
+  assert(minint <= -2^(intbits - 1))
+  assert(-2^(intbits - 1) <= minint)
+end
+
+if floatbits < intbits then
+  gcs:send_text(6, "testing order (floats can't represent all int)")
+  local fmax = 2^floatbits
+  local ifmax = fmax | 0
+  assert(fmax < ifmax + 1)
+  assert(fmax - 1 < ifmax)
+  assert(-(fmax - 1) > -ifmax)
+  assert(not (fmax <= ifmax - 1))
+  assert(-fmax > -(ifmax + 1))
+  assert(not (-fmax >= -(ifmax - 1)))
+
+  assert(fmax/2 - 0.5 < ifmax//2)
+  assert(-(fmax/2 - 0.5) > -ifmax//2)
+
+  assert(maxint < 2^intbits)
+  assert(minint > -2^intbits)
+  assert(maxint <= 2^intbits)
+  assert(minint >= -2^intbits)
+else
+  gcs:send_text(6, "testing order (floats can represent all ints)")
+  assert(maxint < maxint + 1.0)
+  assert(maxint < maxint + 0.5)
+  assert(maxint - 1.0 < maxint)
+  assert(maxint - 0.5 < maxint)
+  assert(not (maxint + 0.0 < maxint))
+  assert(maxint + 0.0 <= maxint)
+  assert(not (maxint < maxint + 0.0))
+  assert(maxint + 0.0 <= maxint)
+  assert(maxint <= maxint + 0.0)
+  assert(not (maxint + 1.0 <= maxint))
+  assert(not (maxint + 0.5 <= maxint))
+  assert(not (maxint <= maxint - 1.0))
+  assert(not (maxint <= maxint - 0.5))
+
+  assert(minint < minint + 1.0)
+  assert(minint < minint + 0.5)
+  assert(minint <= minint + 0.5)
+  assert(minint - 1.0 < minint)
+  assert(minint - 1.0 <= minint)
+  assert(not (minint + 0.0 < minint))
+  assert(not (minint + 0.5 < minint))
+  assert(not (minint < minint + 0.0))
+  assert(minint + 0.0 <= minint)
+  assert(minint <= minint + 0.0)
+  assert(not (minint + 1.0 <= minint))
+  assert(not (minint + 0.5 <= minint))
+  assert(not (minint <= minint - 1.0))
+end
+
+do
+  local NaN = 0/0
+  assert(not (NaN < 0))
+  assert(not (NaN > minint))
+  assert(not (NaN <= -9))
+  assert(not (NaN <= maxint))
+  assert(not (NaN < maxint))
+  assert(not (minint <= NaN))
+  assert(not (minint < NaN))
+end
+
+
+-- avoiding errors at compile time
+--local function checkcompt (msg, code)
+--  checkerror(msg, assert(load(code)))
+--end
+--checkcompt("divide by zero", "return 2 // 0")
+--checkcompt(msgf2i, "return 2.3 >> 0")
+--checkcompt(msgf2i, ("return 2.0^%d & 1"):format(intbits - 1))
+--checkcompt("field 'huge'", "return math.huge << 1")
+--checkcompt(msgf2i, ("return 1 | 2.0^%d"):format(intbits - 1))
+--checkcompt(msgf2i, "return 2.3 ~ '0.0'")
+
+
+-- testing overflow errors when converting from float to integer (runtime)
+local function f2i (x) return x | x end
+checkerror(msgf2i, f2i, math.huge)     -- +inf
+checkerror(msgf2i, f2i, -math.huge)    -- -inf
+checkerror(msgf2i, f2i, 0/0)           -- NaN
+
+if floatbits < intbits then
+  -- conversion tests when float cannot represent all integers
+  assert(maxint + 1.0 == maxint + 0.0)
+  assert(minint - 1.0 == minint + 0.0)
+  checkerror(msgf2i, f2i, maxint + 0.0)
+  assert(f2i(2.0^(intbits - 2)) == 1 << (intbits - 2))
+  assert(f2i(-2.0^(intbits - 2)) == -(1 << (intbits - 2)))
+  assert((2.0^(floatbits - 1) + 1.0) // 1 == (1 << (floatbits - 1)) + 1)
+  -- maximum integer representable as a float
+  local mf = maxint - (1 << (floatbits - intbits)) + 1
+  assert(f2i(mf + 0.0) == mf)  -- OK up to here
+  mf = mf + 1
+  assert(f2i(mf + 0.0) ~= mf)   -- no more representable
+else
+  -- conversion tests when float can represent all integers
+  assert(maxint + 1.0 > maxint)
+  assert(minint - 1.0 < minint)
+  assert(f2i(maxint + 0.0) == maxint)
+  checkerror("no integer rep", f2i, maxint + 1.0)
+  checkerror("no integer rep", f2i, minint - 1.0)
+end
+
+-- 'minint' should be representable as a float no matter the precision
+assert(f2i(minint + 0.0) == minint)
+
+
+-- testing numeric strings
+
+assert("2" + 1 == 3)
+assert("2 " + 1 == 3)
+assert(" -2 " + 1 == -1)
+assert(" -0xa " + 1 == -9)
+
+
+-- Literal integer Overflows (new behavior in 5.3.3)
+do
+  -- no overflows
+  assert(eqT(tonumber(tostring(maxint)), maxint))
+  assert(eqT(tonumber(tostring(minint)), minint))
+
+  -- add 1 to last digit as a string (it cannot be 9...)
+  local function incd (n)
+    local s = string.format("%d", n)
+    s = string.gsub(s, "%d$", function (d)
+          assert(d ~= '9')
+          return string.char(string.byte(d) + 1)
+        end)
+    return s
+  end
+
+  -- 'tonumber' with overflow by 1
+  assert(eqT(tonumber(incd(maxint)), maxint + 1.0))
+  assert(eqT(tonumber(incd(minint)), minint - 1.0))
+
+  -- large numbers
+  assert(eqT(tonumber("1"..string.rep("0", 30)), 1e30))
+  assert(eqT(tonumber("-1"..string.rep("0", 30)), -1e30))
+
+  -- hexa format still wraps around
+  assert(eqT(tonumber("0x1"..string.rep("0", 30)), 0))
+
+  -- lexer in the limits
+  --assert(minint == load("return " .. minint)())
+  --assert(eqT(maxint, load("return " .. maxint)()))
+
+  assert(eqT(10000000000000000000000.0, 10000000000000000000000))
+  assert(eqT(-10000000000000000000000.0, -10000000000000000000000))
+end
+
+
+-- testing 'tonumber'
+
+-- 'tonumber' with numbers
+assert(tonumber(3.4) == 3.4)
+assert(eqT(tonumber(3), 3))
+assert(eqT(tonumber(maxint), maxint) and eqT(tonumber(minint), minint))
+assert(tonumber(1/0) == 1/0)
+
+-- 'tonumber' with strings
+assert(tonumber("0") == 0)
+assert(tonumber("") == nil)
+assert(tonumber("  ") == nil)
+assert(tonumber("-") == nil)
+assert(tonumber("  -0x ") == nil)
+assert(tonumber{} == nil)
+assert(tonumber'+0.01' == 1/100 and tonumber'+.01' == 0.01 and
+       tonumber'.01' == 0.01    and tonumber'-1.' == -1 and
+       tonumber'+1.' == 1)
+assert(tonumber'+ 0.01' == nil and tonumber'+.e1' == nil and
+       tonumber'1e' == nil     and tonumber'1.0e+' == nil and
+       tonumber'.' == nil)
+assert(tonumber('-012') == -010-2)
+assert(tonumber('-1.2e2') == - - -120)
+
+assert(tonumber("0xffffffffffff") == (1 << (4*12)) - 1)
+assert(tonumber("0x"..string.rep("f", (intbits//4))) == -1)
+assert(tonumber("-0x"..string.rep("f", (intbits//4))) == 1)
+
+-- testing 'tonumber' with base
+assert(tonumber('  001010  ', 2) == 10)
+assert(tonumber('  001010  ', 10) == 001010)
+assert(tonumber('  -1010  ', 2) == -10)
+assert(tonumber('10', 36) == 36)
+assert(tonumber('  -10  ', 36) == -36)
+assert(tonumber('  +1Z  ', 36) == 36 + 35)
+assert(tonumber('  -1z  ', 36) == -36 + -35)
+assert(tonumber('-fFfa', 16) == -(10+(16*(15+(16*(15+(16*15)))))))
+assert(tonumber(string.rep('1', (intbits - 2)), 2) + 1 == 2^(intbits - 2))
+assert(tonumber('ffffFFFF', 16)+1 == (1 << 32))
+assert(tonumber('0ffffFFFF', 16)+1 == (1 << 32))
+assert(tonumber('-0ffffffFFFF', 16) - 1 == -(1 << 40))
+for i = 2,36 do
+  local i2 = i * i
+  local i10 = i2 * i2 * i2 * i2 * i2      -- i^10
+  assert(tonumber('\t10000000000\t', i) == i10)
+end
+
+if not _soft then
+  -- tests with very long numerals
+  assert(tonumber("0x"..string.rep("f", 13)..".0") == 2.0^(4*13) - 1)
+  assert(tonumber("0x"..string.rep("f", 150)..".0") == 2.0^(4*150) - 1)
+  assert(tonumber("0x"..string.rep("f", 300)..".0") == 2.0^(4*300) - 1)
+  assert(tonumber("0x"..string.rep("f", 500)..".0") == 2.0^(4*500) - 1)
+  assert(tonumber('0x3.' .. string.rep('0', 1000)) == 3)
+  assert(tonumber('0x' .. string.rep('0', 1000) .. 'a') == 10)
+  assert(tonumber('0x0.' .. string.rep('0', 13).."1") == 2.0^(-4*14))
+  assert(tonumber('0x0.' .. string.rep('0', 150).."1") == 2.0^(-4*151))
+  assert(tonumber('0x0.' .. string.rep('0', 300).."1") == 2.0^(-4*301))
+  assert(tonumber('0x0.' .. string.rep('0', 500).."1") == 2.0^(-4*501))
+
+  assert(tonumber('0xe03' .. string.rep('0', 1000) .. 'p-4000') == 3587.0)
+  assert(tonumber('0x.' .. string.rep('0', 1000) .. '74p4004') == 0x7.4)
+end
+
+-- testing 'tonumber' for invalid formats
+--[[
+local function f (...)
+  if select('#', ...) == 1 then
+    return (...)
+  else
+    return "***"
+  end
+end
+
+assert(f(tonumber('fFfa', 15)) == nil)
+assert(f(tonumber('099', 8)) == nil)
+assert(f(tonumber('1\0', 2)) == nil)
+assert(f(tonumber('', 8)) == nil)
+assert(f(tonumber('  ', 9)) == nil)
+assert(f(tonumber('  ', 9)) == nil)
+assert(f(tonumber('0xf', 10)) == nil)
+
+assert(f(tonumber('inf')) == nil)
+assert(f(tonumber(' INF ')) == nil)
+assert(f(tonumber('Nan')) == nil)
+assert(f(tonumber('nan')) == nil)
+
+assert(f(tonumber('  ')) == nil)
+assert(f(tonumber('')) == nil)
+assert(f(tonumber('1  a')) == nil)
+assert(f(tonumber('1  a', 2)) == nil)
+assert(f(tonumber('1\0')) == nil)
+assert(f(tonumber('1 \0')) == nil)
+assert(f(tonumber('1\0 ')) == nil)
+assert(f(tonumber('e1')) == nil)
+assert(f(tonumber('e  1')) == nil)
+assert(f(tonumber(' 3.4.5 ')) == nil)
+]]
+
+-- testing 'tonumber' for invalid hexadecimal formats
+
+assert(tonumber('0x') == nil)
+assert(tonumber('x') == nil)
+assert(tonumber('x3') == nil)
+assert(tonumber('0x3.3.3') == nil)   -- two decimal points
+assert(tonumber('00x2') == nil)
+assert(tonumber('0x 2') == nil)
+assert(tonumber('0 x2') == nil)
+assert(tonumber('23x') == nil)
+assert(tonumber('- 0xaa') == nil)
+assert(tonumber('-0xaaP ') == nil)   -- no exponent
+assert(tonumber('0x0.51p') == nil)
+assert(tonumber('0x5p+-2') == nil)
+
+
+-- testing hexadecimal numerals
+
+assert(0x10 == 16 and 0xfff == 2^12 - 1 and 0XFB == 251)
+assert(0x0p12 == 0 and 0x.0p-3 == 0)
+assert(0xFFFFFFFF == (1 << 32) - 1)
+assert(tonumber('+0x2') == 2)
+assert(tonumber('-0xaA') == -170)
+assert(tonumber('-0xffFFFfff') == -(1 << 32) + 1)
+
+-- possible confusion with decimal exponent
+assert(0E+1 == 0 and 0xE+1 == 15 and 0xe-1 == 13)
+
+
+-- floating hexas
+
+assert(tonumber('  0x2.5  ') == 0x25/16)
+assert(tonumber('  -0x2.5  ') == -0x25/16)
+assert(tonumber('  +0x0.51p+8  ') == 0x51)
+assert(0x.FfffFFFF == 1 - '0x.00000001')
+assert('0xA.a' + 0 == 10 + 10/16)
+assert(0xa.aP4 == 0XAA)
+assert(0x4P-2 == 1)
+assert(0x1.1 == '0x1.' + '+0x.1')
+assert(0Xabcdef.0 == 0x.ABCDEFp+24)
+
+
+assert(1.1 == 1.+.1)
+assert(100.0 == 1E2 and .01 == 1e-2)
+assert(1111111111 - 1111111110 == 1000.00e-03)
+assert(1.1 == '1.'+'.1')
+assert(tonumber'1111111111' - tonumber'1111111110' ==
+       tonumber"  +0.001e+3 \n\t")
+
+assert(0.1e-30 > 0.9E-31 and 0.9E30 < 0.1e31)
+
+assert(0.123456 > 0.123455)
+
+assert(tonumber('+1.23E18') == 1.23*10.0^18)
+
+-- testing order operators
+assert(not(1<1) and (1<2) and not(2<1))
+assert(not('a'<'a') and ('a'<'b') and not('b'<'a'))
+assert((1<=1) and (1<=2) and not(2<=1))
+assert(('a'<='a') and ('a'<='b') and not('b'<='a'))
+assert(not(1>1) and not(1>2) and (2>1))
+assert(not('a'>'a') and not('a'>'b') and ('b'>'a'))
+assert((1>=1) and not(1>=2) and (2>=1))
+assert(('a'>='a') and not('a'>='b') and ('b'>='a'))
+assert(1.3 < 1.4 and 1.3 <= 1.4 and not (1.3 < 1.3) and 1.3 <= 1.3)
+
+-- testing mod operator
+assert(eqT(-4 % 3, 2))
+assert(eqT(4 % -3, -2))
+assert(eqT(-4.0 % 3, 2.0))
+assert(eqT(4 % -3.0, -2.0))
+assert(math.pi - math.pi % 1 == 3)
+assert(math.pi - math.pi % 0.001 == 3.141)
+
+assert(eqT(minint % minint, 0))
+assert(eqT(maxint % maxint, 0))
+assert((minint + 1) % minint == minint + 1)
+assert((maxint - 1) % maxint == maxint - 1)
+assert(minint % maxint == maxint - 1)
+
+assert(minint % -1 == 0)
+assert(minint % -2 == 0)
+assert(maxint % -2 == -1)
+
+-- testing unsigned comparisons
+assert(math.ult(3, 4))
+assert(not math.ult(4, 4))
+assert(math.ult(-2, -1))
+assert(math.ult(2, -1))
+assert(not math.ult(-2, -2))
+assert(math.ult(maxint, minint))
+assert(not math.ult(minint, maxint))
+
+
+assert(eq(math.sin(-9.8)^2 + math.cos(-9.8)^2, 1))
+assert(eq(math.tan(math.pi/4), 1))
+assert(eq(math.sin(math.pi/2), 1) and eq(math.cos(math.pi/2), 0))
+assert(eq(math.atan(1), math.pi/4) and eq(math.acos(0), math.pi/2) and
+       eq(math.asin(1), math.pi/2))
+assert(eq(math.deg(math.pi/2), 90) and eq(math.rad(90), math.pi/2))
+assert(math.abs(-10.43) == 10.43)
+assert(eqT(math.abs(minint), minint))
+assert(eqT(math.abs(maxint), maxint))
+assert(eqT(math.abs(-maxint), maxint))
+assert(eq(math.atan(1,0), math.pi/2))
+assert(math.fmod(10,3) == 1)
+assert(eq(math.sqrt(10)^2, 10))
+assert(eq(math.log(2, 10), math.log(2)/math.log(10)))
+assert(eq(math.log(2, 2), 1))
+assert(eq(math.log(9, 3), 2))
+assert(eq(math.exp(0), 1))
+assert(eq(math.sin(10), math.sin(10%(2*math.pi))))
+
+
+assert(tonumber(' 1.3e-2 ') == 1.3e-2)
+assert(tonumber(' -1.00000000000001 ') == -1.00000000000001)
+
+-- testing constant limits
+-- 2^23 = 8388608
+assert(8388609 + -8388609 == 0)
+assert(8388608 + -8388608 == 0)
+assert(8388607 + -8388607 == 0)
+
+
+
+do   -- testing floor & ceil
+  assert(eqT(math.floor(3.4), 3))
+  assert(eqT(math.ceil(3.4), 4))
+  assert(eqT(math.floor(-3.4), -4))
+  assert(eqT(math.ceil(-3.4), -3))
+  assert(eqT(math.floor(maxint), maxint))
+  assert(eqT(math.ceil(maxint), maxint))
+  assert(eqT(math.floor(minint), minint))
+  assert(eqT(math.floor(minint + 0.0), minint))
+  assert(eqT(math.ceil(minint), minint))
+  assert(eqT(math.ceil(minint + 0.0), minint))
+  assert(math.floor(1e50) == 1e50)
+  assert(math.ceil(1e50) == 1e50)
+  assert(math.floor(-1e50) == -1e50)
+  assert(math.ceil(-1e50) == -1e50)
+  for _, p in pairs{31,32,63,64} do
+    assert(math.floor(2^p) == 2^p)
+    assert(math.floor(2^p + 0.5) == 2^p)
+    assert(math.ceil(2^p) == 2^p)
+    assert(math.ceil(2^p - 0.5) == 2^p)
+  end
+  checkerror("number expected", math.floor, {})
+  checkerror("number expected", math.ceil, print)
+  assert(eqT(math.tointeger(minint), minint))
+  assert(eqT(math.tointeger(minint .. ""), minint))
+  assert(eqT(math.tointeger(maxint), maxint))
+  assert(eqT(math.tointeger(maxint .. ""), maxint))
+  assert(eqT(math.tointeger(minint + 0.0), minint))
+  assert(math.tointeger(0.0 - minint) == nil)
+  assert(math.tointeger(math.pi) == nil)
+  assert(math.tointeger(-math.pi) == nil)
+  assert(math.floor(math.huge) == math.huge)
+  assert(math.ceil(math.huge) == math.huge)
+  assert(math.tointeger(math.huge) == nil)
+  assert(math.floor(-math.huge) == -math.huge)
+  assert(math.ceil(-math.huge) == -math.huge)
+  assert(math.tointeger(-math.huge) == nil)
+  assert(math.tointeger("34.0") == 34)
+  assert(math.tointeger("34.3") == nil)
+  assert(math.tointeger({}) == nil)
+  assert(math.tointeger(0/0) == nil)    -- NaN
+end
+
+
+-- testing fmod for integers
+for i = -6, 6 do
+  for j = -6, 6 do
+    if j ~= 0 then
+      local mi = math.fmod(i, j)
+      local mf = math.fmod(i + 0.0, j)
+      assert(mi == mf)
+      assert(math.type(mi) == 'integer' and math.type(mf) == 'float')
+      if (i >= 0 and j >= 0) or (i <= 0 and j <= 0) or mi == 0 then
+        assert(eqT(mi, i % j))
+      end
+    end
+  end
+end
+assert(eqT(math.fmod(minint, minint), 0))
+assert(eqT(math.fmod(maxint, maxint), 0))
+assert(eqT(math.fmod(minint + 1, minint), minint + 1))
+assert(eqT(math.fmod(maxint - 1, maxint), maxint - 1))
+
+checkerror("zero", math.fmod, 3, 0)
+
+
+do    -- testing max/min
+  checkerror("value expected", math.max)
+  checkerror("value expected", math.min)
+  assert(eqT(math.max(3), 3))
+  assert(eqT(math.max(3, 5, 9, 1), 9))
+  assert(math.max(maxint, 10e60) == 10e60)
+  assert(eqT(math.max(minint, minint + 1), minint + 1))
+  assert(eqT(math.min(3), 3))
+  assert(eqT(math.min(3, 5, 9, 1), 1))
+  assert(math.min(3.2, 5.9, -9.2, 1.1) == -9.2)
+  assert(math.min(1.9, 1.7, 1.72) == 1.7)
+  assert(math.min(-10e60, minint) == -10e60)
+  assert(eqT(math.min(maxint, maxint - 1), maxint - 1))
+  assert(eqT(math.min(maxint - 2, maxint, maxint - 1), maxint - 2))
+end
+-- testing implicit convertions
+
+local a,b = '10', '20'
+assert(a*b == 200 and a+b == 30 and a-b == -10 and a/b == 0.5 and -b == -20)
+assert(a == '10' and b == '20')
+
+
+do
+  gcs:send_text(6, "testing -0 and NaN")
+  local mz, z = -0.0, 0.0
+  assert(mz == z)
+  assert(1/mz < 0 and 0 < 1/z)
+  local a = {[mz] = 1}
+  assert(a[z] == 1 and a[mz] == 1)
+  a[z] = 2
+  assert(a[z] == 2 and a[mz] == 2)
+  local inf = math.huge * 2 + 1
+  mz, z = -1/inf, 1/inf
+  assert(mz == z)
+  assert(1/mz < 0 and 0 < 1/z)
+  local NaN = inf - inf
+  assert(NaN ~= NaN)
+  assert(not (NaN < NaN))
+  assert(not (NaN <= NaN))
+  assert(not (NaN > NaN))
+  assert(not (NaN >= NaN))
+  assert(not (0 < NaN) and not (NaN < 0))
+  local NaN1 = 0/0
+  assert(NaN ~= NaN1 and not (NaN <= NaN1) and not (NaN1 <= NaN))
+  local a = {}
+  assert(not pcall(rawset, a, NaN, 1))
+  assert(a[NaN] == nil)
+  a[1] = 1
+  assert(not pcall(rawset, a, NaN, 1))
+  assert(a[NaN] == nil)
+  -- strings with same binary representation as 0.0 (might create problems
+  -- for constant manipulation in the pre-compiler)
+  local a1, a2, a3, a4, a5 = 0, 0, "\0\0\0\0\0\0\0\0", 0, "\0\0\0\0\0\0\0\0"
+  assert(a1 == a2 and a2 == a4 and a1 ~= a3)
+  assert(a3 == a5)
+end
+
+
+gcs:send_text(6, "testing 'math.random'")
+math.randomseed(0)
+
+do   -- test random for floats
+  local max = -math.huge
+  local min = math.huge
+  for i = 0, 20000 do
+    local t = math.random()
+    assert(0 <= t and t < 1)
+    max = math.max(max, t)
+    min = math.min(min, t)
+    if eq(max, 1, 0.001) and eq(min, 0, 0.001) then
+      goto ok
+    end
+  end
+  -- loop ended without satisfing condition
+  assert(false)
+ ::ok::
+end
+
+do
+  local function aux (p, lim)   -- test random for small intervals
+    local x1, x2
+    if #p == 1 then x1 = 1; x2 = p[1]
+    else x1 = p[1]; x2 = p[2]
+    end
+    local mark = {}; local count = 0   -- to check that all values appeared
+    for i = 0, lim or 2000 do
+      local t = math.random(table.unpack(p))
+      assert(x1 <= t and t <= x2)
+      if not mark[t] then  -- new value
+        mark[t] = true
+        count = count + 1
+      end
+      if count == x2 - x1 + 1 then   -- all values appeared; OK
+        goto ok
+      end
+    end
+    -- loop ended without satisfing condition
+    assert(false)
+   ::ok::
+  end
+
+  aux({-10,0})
+  aux({6})
+  aux({-10, 10})
+  aux({minint, minint})
+  aux({maxint, maxint})
+  aux({minint, minint + 9})
+  aux({maxint - 3, maxint})
+end
+
+do
+  local function aux(p1, p2)       -- test random for large intervals
+    local max = minint
+    local min = maxint
+    local n = 200
+    local mark = {}; local count = 0   -- to count how many different values
+    for _ = 1, n do
+      local t = math.random(p1, p2)
+      max = math.max(max, t)
+      min = math.min(min, t)
+      if not mark[t] then  -- new value
+        mark[t] = true
+        count = count + 1
+      end
+    end
+    -- at least 80% of values are different
+    assert(count >= n * 0.8)
+    -- min and max not too far from formal min and max
+    local diff = (p2 - p1) // 8
+    assert(min < p1 + diff and max > p2 - diff)
+  end
+  aux(0, maxint)
+  aux(1, maxint)
+  aux(minint, -1)
+  aux(minint // 2, maxint // 2)
+end
+
+for i=1,100 do
+  assert(math.random(maxint) > 0)
+  assert(math.random(minint, -1) < 0)
+end
+
+assert(not pcall(math.random, 1, 2, 3))    -- too many arguments
+
+-- empty interval
+assert(not pcall(math.random, minint + 1, minint))
+assert(not pcall(math.random, maxint, maxint - 1))
+assert(not pcall(math.random, maxint, minint))
+
+-- interval too large
+assert(not pcall(math.random, minint, 0))
+assert(not pcall(math.random, -1, maxint))
+assert(not pcall(math.random, minint // 2, maxint // 2 + 1))
+
+function update()
+  gcs:send_text(6, 'Math tests passed')
+  return update, 1000
+end
+
+return update()
--- a/libraries/AP_Scripting/tests/strings.lua
+++ b/libraries/AP_Scripting/tests/strings.lua
@ -0,0 +1,369 @@
+-- $Id: strings.lua,v 1.86 2016/11/07 13:11:28 roberto Exp roberto $
+
+--[[
+*****************************************************************************
+* Copyright (C) 1994-2016 Lua.org, PUC-Rio.
+*
+* Permission is hereby granted, free of charge, to any person obtaining
+* a copy of this software and associated documentation files (the
+* "Software"), to deal in the Software without restriction, including
+* without limitation the rights to use, copy, modify, merge, publish,
+* distribute, sublicense, and/or sell copies of the Software, and to
+* permit persons to whom the Software is furnished to do so, subject to
+* the following conditions:
+*
+* The above copyright notice and this permission notice shall be
+* included in all copies or substantial portions of the Software.
+*
+* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
+* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
+* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
+* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+*****************************************************************************
+]]
+
+-- This code is copied from https://github.com/lua/tests and slightly modified to work within ArduPilot
+
+gcs:send_text(6, 'testing strings and string library')
+
+local maxi, mini = math.maxinteger, math.mininteger
+
+
+local function checkerror (msg, f, ...)
+  local s, err = pcall(f, ...)
+  assert(not s and string.find(err, msg))
+end
+
+
+-- testing string comparisons
+assert('alo' < 'alo1')
+assert('' < 'a')
+assert('alo\0alo' < 'alo\0b')
+assert('alo\0alo\0\0' > 'alo\0alo\0')
+assert('alo' < 'alo\0')
+assert('alo\0' > 'alo')
+assert('\0' < '\1')
+assert('\0\0' < '\0\1')
+assert('\1\0a\0a' <= '\1\0a\0a')
+assert(not ('\1\0a\0b' <= '\1\0a\0a'))
+assert('\0\0\0' < '\0\0\0\0')
+assert(not('\0\0\0\0' < '\0\0\0'))
+assert('\0\0\0' <= '\0\0\0\0')
+assert(not('\0\0\0\0' <= '\0\0\0'))
+assert('\0\0\0' <= '\0\0\0')
+assert('\0\0\0' >= '\0\0\0')
+assert(not ('\0\0b' < '\0\0a\0'))
+
+-- testing string.sub
+assert(string.sub("123456789",2,4) == "234")
+assert(string.sub("123456789",7) == "789")
+assert(string.sub("123456789",7,6) == "")
+assert(string.sub("123456789",7,7) == "7")
+assert(string.sub("123456789",0,0) == "")
+assert(string.sub("123456789",-10,10) == "123456789")
+assert(string.sub("123456789",1,9) == "123456789")
+assert(string.sub("123456789",-10,-20) == "")
+assert(string.sub("123456789",-1) == "9")
+assert(string.sub("123456789",-4) == "6789")
+assert(string.sub("123456789",-6, -4) == "456")
+assert(string.sub("123456789", mini, -4) == "123456")
+assert(string.sub("123456789", mini, maxi) == "123456789")
+assert(string.sub("123456789", mini, mini) == "")
+assert(string.sub("\000123456789",3,5) == "234")
+assert(("\000123456789"):sub(8) == "789")
+
+-- testing string.find
+assert(string.find("123456789", "345") == 3)
+a,b = string.find("123456789", "345")
+assert(string.sub("123456789", a, b) == "345")
+assert(string.find("1234567890123456789", "345", 3) == 3)
+assert(string.find("1234567890123456789", "345", 4) == 13)
+assert(string.find("1234567890123456789", "346", 4) == nil)
+assert(string.find("1234567890123456789", ".45", -9) == 13)
+assert(string.find("abcdefg", "\0", 5, 1) == nil)
+assert(string.find("", "") == 1)
+assert(string.find("", "", 1) == 1)
+assert(not string.find("", "", 2))
+assert(string.find('', 'aaa', 1) == nil)
+assert(('alo(.)alo'):find('(.)', 1, 1) == 4)
+
+assert(string.len("") == 0)
+assert(string.len("\0\0\0") == 3)
+assert(string.len("1234567890") == 10)
+
+assert(#"" == 0)
+assert(#"\0\0\0" == 3)
+assert(#"1234567890" == 10)
+
+-- testing string.byte/string.char
+assert(string.byte("a") == 97)
+assert(string.byte("\xe4") > 127)
+assert(string.byte(string.char(255)) == 255)
+assert(string.byte(string.char(0)) == 0)
+assert(string.byte("\0") == 0)
+assert(string.byte("\0\0alo\0x", -1) == string.byte('x'))
+assert(string.byte("ba", 2) == 97)
+assert(string.byte("\n\n", 2, -1) == 10)
+assert(string.byte("\n\n", 2, 2) == 10)
+assert(string.byte("") == nil)
+assert(string.byte("hi", -3) == nil)
+assert(string.byte("hi", 3) == nil)
+assert(string.byte("hi", 9, 10) == nil)
+assert(string.byte("hi", 2, 1) == nil)
+assert(string.char() == "")
+assert(string.char(0, 255, 0) == "\0\255\0")
+assert(string.char(0, string.byte("\xe4"), 0) == "\0\xe4\0")
+assert(string.char(string.byte("\xe4l\0<EFBFBD>u", 1, -1)) == "\xe4l\0<EFBFBD>u")
+assert(string.char(string.byte("\xe4l\0<EFBFBD>u", 1, 0)) == "")
+assert(string.char(string.byte("\xe4l\0<EFBFBD>u", -10, 100)) == "\xe4l\0<EFBFBD>u")
+
+assert(string.upper("ab\0c") == "AB\0C")
+assert(string.lower("\0ABCc%$") == "\0abcc%$")
+assert(string.rep('teste', 0) == '')
+assert(string.rep('t<EFBFBD>s\00t<EFBFBD>', 2) == 't<EFBFBD>s\0t<EFBFBD>t<EFBFBD>s\000t<EFBFBD>')
+assert(string.rep('', 10) == '')
+
+if string.packsize("i") == 4 then
+  -- result length would be 2^31 (int overflow)
+  checkerror("too large", string.rep, 'aa', (1 << 30))
+  checkerror("too large", string.rep, 'a', (1 << 30), ',')
+end
+
+-- repetitions with separator
+assert(string.rep('teste', 0, 'xuxu') == '')
+assert(string.rep('teste', 1, 'xuxu') == 'teste')
+assert(string.rep('\1\0\1', 2, '\0\0') == '\1\0\1\0\0\1\0\1')
+assert(string.rep('', 10, '.') == string.rep('.', 9))
+assert(not pcall(string.rep, "aa", maxi // 2 + 10))
+assert(not pcall(string.rep, "", maxi // 2 + 10, "aa"))
+
+assert(string.reverse"" == "")
+assert(string.reverse"\0\1\2\3" == "\3\2\1\0")
+assert(string.reverse"\0001234" == "4321\0")
+
+for i=0,30 do assert(string.len(string.rep('a', i)) == i) end
+
+assert(type(tostring(nil)) == 'string')
+assert(type(tostring(12)) == 'string')
+assert(string.find(tostring{}, 'table:'))
+assert(#tostring('\0') == 1)
+assert(tostring(true) == "true")
+assert(tostring(false) == "false")
+assert(tostring(-1203) == "-1203")
+assert(tostring(1203.125) == "1203.125")
+assert(tostring(-0.5) == "-0.5")
+assert(tostring(-32767) == "-32767")
+if math.tointeger(2147483647) then   -- no overflow? (32 bits)
+  assert(tostring(-2147483647) == "-2147483647")
+end
+if math.tointeger(4611686018427387904) then   -- no overflow? (64 bits)
+  assert(tostring(4611686018427387904) == "4611686018427387904")
+  assert(tostring(-4611686018427387904) == "-4611686018427387904")
+end
+
+if tostring(0.0) == "0.0" then   -- "standard" coercion float->string
+  assert('' .. 12 == '12' and 12.0 .. '' == '12.0')
+  assert(tostring(-1203 + 0.0) == "-1203.0")
+else   -- compatible coercion
+  assert(tostring(0.0) == "0")
+  assert('' .. 12 == '12' and 12.0 .. '' == '12')
+  assert(tostring(-1203 + 0.0) == "-1203")
+end
+
+
+x = '"<22>lo"\n\\'
+assert(string.format('%q%s', x, x) == '"\\"<22>lo\\"\\\n\\\\""<22>lo"\n\\')
+assert(string.format('%q', "\0") == [["\0"]])
+--assert(load(string.format('return %q', x))() == x)
+x = "\0\1\0023\5\0009"
+--assert(load(string.format('return %q', x))() == x)
+assert(string.format("\0%c\0%c%x\0", string.byte("\xe4"), string.byte("b"), 140) ==
+              "\0\xe4\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))
+assert(string.format("%s\0 is not \0%s", 'not be', 'be') == 'not be\0 is not \0be')
+assert(string.format("%%%d %010d", 10, 23) == "%10 0000000023")
+assert(tonumber(string.format("%f", 10.3)) == 10.3)
+x = string.format('"%-50s"', 'a')
+assert(#x == 52)
+assert(string.sub(x, 1, 4) == '"a  ')
+
+assert(string.format("-%.20s.20s", string.rep("%", 2000)) ==
+                     "-"..string.rep("%", 20)..".20s")
+assert(string.format('"-%20s.20s"', string.rep("%", 2000)) ==
+       string.format("%q", "-"..string.rep("%", 2000)..".20s"))
+
+--[[
+do
+  local function checkQ (v)
+    local s = string.format("%q", v)
+    local nv = load("return " .. s)()
+    assert(v == nv and math.type(v) == math.type(nv))
+  end
+  checkQ("\0\0\1\255\u{234}")
+  checkQ(math.maxinteger)
+  checkQ(math.mininteger)
+  checkQ(math.pi)
+  checkQ(0.1)
+  checkQ(true)
+  checkQ(nil)
+  checkQ(false)
+  checkerror("no literal", string.format, "%q", {})
+end
+]]
+
+assert(string.format("\0%s\0", "\0\0\1") == "\0\0\0\1\0")
+checkerror("contains zeros", string.format, "%10s", "\0")
+
+-- format x tostring
+assert(string.format("%s %s", nil, true) == "nil true")
+assert(string.format("%s %.4s", false, true) == "false true")
+assert(string.format("%.3s %.3s", false, true) == "fal tru")
+--local m = setmetatable({}, {__tostring = function () return "hello" end,
+--                            __name = "hi"})
+--assert(string.format("%s %.10s", m, m) == "hello hello")
+--getmetatable(m).__tostring = nil   -- will use '__name' from now on
+--assert(string.format("%.4s", m) == "hi: ")
+
+--getmetatable(m).__tostring = function () return {} end
+--checkerror("'__tostring' must return a string", tostring, m)
+
+
+assert(string.format("%x", 0.0) == "0")
+assert(string.format("%02x", 0.0) == "00")
+assert(string.format("%08X", 0xFFFFFFFF) == "FFFFFFFF")
+assert(string.format("%+08d", 31501) == "+0031501")
+assert(string.format("%+08d", -30927) == "-0030927")
+
+
+do    -- longest number that can be formatted
+  local i = 1
+  local j = 10000
+  while i + 1 < j do   -- binary search for maximum finite float
+    local m = (i + j) // 2
+    if 10^m < math.huge then i = m else j = m end
+  end
+  assert(10^i < math.huge and 10^j == math.huge)
+  local s = string.format('%.99f', -(10^i))
+  assert(string.len(s) >= i + 101)
+  assert(tonumber(s) == -(10^i))
+end
+
+
+-- testing large numbers for format
+do   -- assume at least 32 bits
+  local max, min = 0x7fffffff, -0x80000000    -- "large" for 32 bits
+  assert(string.sub(string.format("%8x", -1), -8) == "ffffffff")
+  assert(string.format("%x", max) == "7fffffff")
+  assert(string.sub(string.format("%x", min), -8) == "80000000")
+  assert(string.format("%d", max) ==  "2147483647")
+  assert(string.format("%d", min) == "-2147483648")
+  assert(string.format("%u", 0xffffffff) == "4294967295")
+  assert(string.format("%o", 0xABCD) == "125715")
+
+  max, min = 0x7fffffffffffffff, -0x8000000000000000
+  if max > 2.0^53 then  -- only for 64 bits
+    assert(string.format("%x", (2^52 | 0) - 1) == "fffffffffffff")
+    assert(string.format("0x%8X", 0x8f000003) == "0x8F000003")
+    assert(string.format("%d", 2^53) == "9007199254740992")
+    assert(string.format("%i", -2^53) == "-9007199254740992")
+    assert(string.format("%x", max) == "7fffffffffffffff")
+    assert(string.format("%x", min) == "8000000000000000")
+    assert(string.format("%d", max) ==  "9223372036854775807")
+    assert(string.format("%d", min) == "-9223372036854775808")
+    assert(string.format("%u", ~(-1 << 64)) == "18446744073709551615")
+    assert(tostring(1234567890123) == '1234567890123')
+  end
+end
+
+
+do gcs:send_text(6, "testing 'format %a %A'")
+  local function matchhexa (n)
+    local s = string.format("%a", n)
+    -- result matches ISO C requirements
+    assert(string.find(s, "^%-?0x[1-9a-f]%.?[0-9a-f]*p[-+]?%d+$"))
+    assert(tonumber(s) == n)  -- and has full precision
+    s = string.format("%A", n)
+    assert(string.find(s, "^%-?0X[1-9A-F]%.?[0-9A-F]*P[-+]?%d+$"))
+    assert(tonumber(s) == n)
+  end
+  for _, n in ipairs{0.1, -0.1, 1/3, -1/3, 1e30, -1e30,
+                     -45/247, 1, -1, 2, -2, 3e-20, -3e-20} do
+    matchhexa(n)
+  end
+
+  assert(string.find(string.format("%A", 0.0), "^0X0%.?0?P%+?0$"))
+  assert(string.find(string.format("%a", -0.0), "^%-0x0%.?0?p%+?0$"))
+
+  if not _port then   -- test inf, -inf, NaN, and -0.0
+    assert(string.find(string.format("%a", 1/0), "^inf"))
+    assert(string.find(string.format("%A", -1/0), "^%-INF"))
+    assert(string.find(string.format("%a", 0/0), "^%-?nan"))
+    assert(string.find(string.format("%a", -0.0), "^%-0x0"))
+  end
+  
+  if not pcall(string.format, "%.3a", 0) then
+    (Message or print)("\n >>> modifiers for format '%a' not available <<<\n")
+  else
+    assert(string.find(string.format("%+.2A", 12), "^%+0X%x%.%x0P%+?%d$"))
+    assert(string.find(string.format("%.4A", -12), "^%-0X%x%.%x000P%+?%d$"))
+  end
+end
+
+
+-- errors in format
+
+local function check (fmt, msg)
+  checkerror(msg, string.format, fmt, 10)
+end
+
+local aux = string.rep('0', 600)
+check("%100.3d", "too long")
+check("%1"..aux..".3d", "too long")
+check("%1.100d", "too long")
+check("%10.1"..aux.."004d", "too long")
+check("%t", "invalid option")
+check("%"..aux.."d", "repeated flags")
+check("%d %d", "no value")
+
+
+--assert(load("return 1\n--comment without ending EOL")() == 1)
+
+
+checkerror("table expected", table.concat, 3)
+assert(table.concat{} == "")
+assert(table.concat({}, 'x') == "")
+assert(table.concat({'\0', '\0\1', '\0\1\2'}, '.\0.') == "\0.\0.\0\1.\0.\0\1\2")
+local a = {}; for i=1,300 do a[i] = "xuxu" end
+assert(table.concat(a, "123").."123" == string.rep("xuxu123", 300))
+assert(table.concat(a, "b", 20, 20) == "xuxu")
+assert(table.concat(a, "", 20, 21) == "xuxuxuxu")
+assert(table.concat(a, "x", 22, 21) == "")
+assert(table.concat(a, "3", 299) == "xuxu3xuxu")
+assert(table.concat({}, "x", maxi, maxi - 1) == "")
+assert(table.concat({}, "x", mini + 1, mini) == "")
+assert(table.concat({}, "x", maxi, mini) == "")
+assert(table.concat({[maxi] = "alo"}, "x", maxi, maxi) == "alo")
+assert(table.concat({[maxi] = "alo", [maxi - 1] = "y"}, "-", maxi - 1, maxi)
+       == "y-alo")
+
+assert(not pcall(table.concat, {"a", "b", {}}))
+
+a = {"a","b","c"}
+assert(table.concat(a, ",", 1, 0) == "")
+assert(table.concat(a, ",", 1, 1) == "a")
+assert(table.concat(a, ",", 1, 2) == "a,b")
+assert(table.concat(a, ",", 2) == "b,c")
+assert(table.concat(a, ",", 3) == "c")
+assert(table.concat(a, ",", 4) == "")
+
+function update()
+  gcs:send_text(6, 'String tests passed')
+  return update, 1000
+end
+
+return update()