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Copy pathmath.lua
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942 lines (808 loc) · 27.1 KB
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-- $Id: testes/math.lua $
-- 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))
do -- tests for different kinds of opcodes
local x, y
x = 1; assert(x // 0.0 == 1/0)
x = 1.0; assert(x // 0 == 1/0)
x = 3.5; assert(eqT(x // 1, 3.0))
assert(eqT(x // -1, -4.0))
x = 3.5; y = 1.5; assert(eqT(x // y, 2.0))
x = 3.5; y = -1.5; assert(eqT(x // y, -3.0))
end
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))
assert(not (4 <= NaN))
assert(not (4 < 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] == undef)
a[1] = 1
assert(not pcall(rawset, a, NaN, 1))
assert(a[NaN] == undef)
-- 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'")
local random, max, min = math.random, math.max, math.min
local function testnear (val, ref, tol)
return (math.abs(val - ref) < ref * tol)
end
-- low-level!! For the current implementation of random in Lua,
-- the first call after seed 1007 should return 0x7a7040a5a323c9d6
do
-- all computations assume at most 32-bit integers
local h = 0x7a7040a5 -- higher half
local l = 0xa323c9d6 -- lower half
math.randomseed(1007)
-- get the low 'intbits' of the 64-bit expected result
local res = (h << 32 | l) & ~(~0 << intbits)
assert(random(0) == res)
math.randomseed(1007, 0)
-- using lower bits to generate random floats; (the '% 2^32' converts
-- 32-bit integers to floats as unsigned)
local res
if floatbits <= 32 then
-- get all bits from the lower half
res = (l & ~(~0 << floatbits)) % 2^32
else
-- get 32 bits from the lower half and the rest from the higher half
res = ((h & ~(~0 << (floatbits - 32))) % 2^32) * 2^32 + (l % 2^32)
end
assert(random() * 2^floatbits == res)
end
math.randomseed(0, os.time())
do -- test random for floats
local randbits = math.min(floatbits, 64) -- at most 64 random bits
local mult = 2^randbits -- to make random float into an integral
local counts = {} -- counts for bits
for i = 1, randbits do counts[i] = 0 end
local up = -math.huge
local low = math.huge
local rounds = 100 * randbits -- 100 times for each bit
local totalrounds = 0
::doagain:: -- will repeat test until we get good statistics
for i = 0, rounds do
local t = random()
assert(0 <= t and t < 1)
up = max(up, t)
low = min(low, t)
assert(t * mult % 1 == 0) -- no extra bits
local bit = i % randbits -- bit to be tested
if (t * 2^bit) % 1 >= 0.5 then -- is bit set?
counts[bit + 1] = counts[bit + 1] + 1 -- increment its count
end
end
totalrounds = totalrounds + rounds
if not (eq(up, 1, 0.001) and eq(low, 0, 0.001)) then
goto doagain
end
-- all bit counts should be near 50%
local expected = (totalrounds / randbits / 2)
for i = 1, randbits do
if not testnear(counts[i], expected, 0.10) then
goto doagain
end
end
print(string.format("float random range in %d calls: [%f, %f]",
totalrounds, low, up))
end
do -- test random for full integers
local up = 0
local low = 0
local counts = {} -- counts for bits
for i = 1, intbits do counts[i] = 0 end
local rounds = 100 * intbits -- 100 times for each bit
local totalrounds = 0
::doagain:: -- will repeat test until we get good statistics
for i = 0, rounds do
local t = random(0)
up = max(up, t)
low = min(low, t)
local bit = i % intbits -- bit to be tested
-- increment its count if it is set
counts[bit + 1] = counts[bit + 1] + ((t >> bit) & 1)
end
totalrounds = totalrounds + rounds
local lim = maxint >> 10
if not (maxint - up < lim and low - minint < lim) then
goto doagain
end
-- all bit counts should be near 50%
local expected = (totalrounds / intbits / 2)
for i = 1, intbits do
if not testnear(counts[i], expected, 0.10) then
goto doagain
end
end
print(string.format(
"integer random range in %d calls: [minint + %.0fppm, maxint - %.0fppm]",
totalrounds, (minint - low) / minint * 1e6,
(maxint - up) / maxint * 1e6))
end
do
-- test distribution for a dice
local count = {0, 0, 0, 0, 0, 0}
local rep = 200
local totalrep = 0
::doagain::
for i = 1, rep * 6 do
local r = random(6)
count[r] = count[r] + 1
end
totalrep = totalrep + rep
for i = 1, 6 do
if not testnear(count[i], totalrep, 0.05) then
goto doagain
end
end
end
do
local function aux (x1, x2) -- test random for small intervals
local mark = {}; local count = 0 -- to check that all values appeared
while true do
local t = random(x1, x2)
assert(x1 <= t and t <= x2)
if not mark[t] then -- new value
mark[t] = true
count = count + 1
if count == x2 - x1 + 1 then -- all values appeared; OK
goto ok
end
end
end
::ok::
end
aux(-10,0)
aux(1, 6)
aux(1, 2)
aux(1, 32)
aux(-10, 10)
aux(-10,-10) -- unit set
aux(minint, minint) -- unit set
aux(maxint, maxint) -- unit set
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 = 100
local mark = {}; local count = 0 -- to count how many different values
::doagain::
for _ = 1, n do
local t = random(p1, p2)
if not mark[t] then -- new value
assert(p1 <= t and t <= p2)
max = math.max(max, t)
min = math.min(min, t)
mark[t] = true
count = count + 1
end
end
-- at least 80% of values are different
if not (count >= n * 0.8) then
goto doagain
end
-- min and max not too far from formal min and max
local diff = (p2 - p1) >> 4
if not (min < p1 + diff and max > p2 - diff) then
goto doagain
end
end
aux(0, maxint)
aux(1, maxint)
aux(minint, -1)
aux(minint // 2, maxint // 2)
aux(minint, maxint)
aux(minint + 1, maxint)
aux(minint, maxint - 1)
aux(0, 1 << (intbits - 5))
end
assert(not pcall(random, 1, 2, 3)) -- too many arguments
-- empty interval
assert(not pcall(random, minint + 1, minint))
assert(not pcall(random, maxint, maxint - 1))
assert(not pcall(random, maxint, minint))
print('OK')
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