print("testing numbers and math lib")


-- 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
  local a, b = math.modf(3.5)
  assert(a == 3 and b == 0.5)
  assert(math.huge > 10e30)
  assert(-math.huge < -10e30)
end

function f(...)
  if select('#', ...) == 1 then
    return (...)
  else
    return "***"
  end
end

-- testing numeric strings

assert("2" + 1 == 3)
assert("2 " + 1 == 3)
assert(" -2 " + 1 == -1)
assert(" -0xa " + 1 == -9)


-- testing 'tonumber'
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") == 2 ^ (4 * 12) - 1)
assert(tonumber("0x" .. string.rep("f", 150)) == 2 ^ (4 * 150) - 1)
assert(tonumber('0x3.' .. string.rep('0', 100)) == 3)
assert(tonumber('0x0.' .. string.rep('0', 150) .. "1") == 2 ^ (-4 * 151))

-- 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', 42), 2) + 1 == 2 ^ 42)
assert(tonumber(string.rep('1', 34), 2) + 1 == 2 ^ 34)
assert(tonumber('ffffFFFF', 16) + 1 == 2 ^ 32)
assert(tonumber('0ffffFFFF', 16) + 1 == 2 ^ 32)
assert(tonumber('-0ffffffFFFF', 16) - 1 == -2 ^ 40)
for i = 2, 36 do
  assert(tonumber('\t10000000000\t', i) == i ^ 10)
end

-- testing 'tonumber' fo invalid formats
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\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('00x2') == nil)
assert(tonumber('0x 2') == nil)
assert(tonumber('0 x2') == nil)
assert(tonumber('23x') == nil)
assert(tonumber('- 0xaa') == 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 == 2 ^ 32 - 1)
assert(tonumber('+0x2') == 2)
assert(tonumber('-0xaA') == -170)
assert(tonumber('-0xffFFFfff') == -2 ^ 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(tonumber('0x0.51p') == nil)
assert(tonumber('0x5p+-2') == nil)
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(1.1 == 1. + .1)
assert(100.0 == 1E2 and .01 == 1e-2)
assert(1111111111111111 - 1111111111111110 == 1000.00e-03)
--     1234567890123456
assert(1.1 == '1.' + '.1')
assert('1111111111111111' - '1111111111111110' == tonumber "  +0.001e+3 \n\t")

function eq(a, b, limit)
  if not limit then limit = 10E-10 end
  return math.abs(a - b) <= limit
end

assert(0.1e-30 > 0.9E-31 and 0.9E30 < 0.1e31)

assert(0.123456 > 0.123455)

assert(tonumber('+1.23E18') == 1.23 * 10 ^ 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'))

-- testing mod operator
assert(-4 % 3 == 2)
assert(4 % -3 == -2)
assert(math.pi - math.pi % 1 == 3)
assert(math.pi - math.pi % 0.001 == 3.141)

local function testbit(a, n)
  return a / 2 ^ n % 2 >= 1
end

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) == 10)
assert(eq(math.atan2(1, 0), math.pi / 2))
assert(math.ceil(4.5) == 5.0)
assert(math.floor(4.5) == 4.0)
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))))
local v, e = math.frexp(math.pi)
assert(eq(math.ldexp(v, e), math.pi))

assert(eq(math.tanh(3.5), math.sinh(3.5) / math.cosh(3.5)))

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)

-- 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')


if not _port then
  print("testing -0 and NaN")
  local mz, z = -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)
  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(function() a[NaN] = 1 end))
  assert(a[NaN] == nil)
  a[1] = 1
  assert(not pcall(function() a[NaN] = 1 end))
  assert(a[NaN] == nil)
  -- string with same binary representation as 0.0 (may 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


if not _port then
  print("testing 'math.random'")
  math.randomseed(0)

  local function aux(x1, x2, p)
    local Max = -math.huge
    local Min = math.huge
    for i = 0, 20000 do
      local t = math.random(table.unpack(p))
      Max = math.max(Max, t)
      Min = math.min(Min, t)
      if eq(Max, x2, 0.001) and eq(Min, x1, 0.001) then
      end
    end
    -- loop ended without satisfing condition
    assert(false)
    assert(x1 <= Min and Max <= x2)
  end

  aux(0, 1, {})
  aux(-10, 0, { -10, 0 })
end

for i = 1, 10 do
  local t = math.random(5)
  assert(1 <= t and t <= 5)
end


print('OK')