cluna 1.1.0

-- $Id: math.lua,v 1.78 2016/11/07 13:11:28 roberto Exp $
-- See Copyright Notice in file all.lua

print("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)

  print(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
  print("testing order (floats cannot represent all integers)")
  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
  print("testing order (floats can represent all integers)")
  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)

-- non-portable tests because Windows C library cannot compute
-- fmod(1, huge) correctly
if not _port then
  local function anan(x) assert(isNaN(x)) end -- assert Not a Number
  anan(0.0 % 0)
  anan(1.3 % 0)
  anan(math.huge % 1)
  anan(math.huge % 1e30)
  anan(-math.huge % 1e30)
  anan(-math.huge % -1e30)
  assert(1 % math.huge == 1)
  assert(1e30 % math.huge == 1e30)
  assert(1e30 % -math.huge == -math.huge)
  assert(-1 % math.huge == math.huge)
  assert(-1 % -math.huge == -1)
end


-- 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
  print("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


print("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

    end
  end
  -- loop ended without satisfing condition
  assert(false)
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

      end
    end
    -- loop ended without satisfing condition
    assert(false)
  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))


print('OK')