blob: b010ff6c3ada68c2b7b270c1dfea36b8c0413f3d [file] [log] [blame]
 -- \$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(eqT(4 % -5, -1)) assert(eqT(4 % -5.0, -1.0)) assert(eqT(4 % 5, 4)) assert(eqT(4 % 5.0, 4.0)) assert(eqT(-4 % -5, -4)) assert(eqT(-4 % -5.0, -4.0)) assert(eqT(-4 % 5, 1)) assert(eqT(-4 % 5.0, 1.0)) assert(eqT(4.25 % 4, 0.25)) assert(eqT(10.0 % 2, 0.0)) assert(eqT(-10.0 % 2, 0.0)) assert(eqT(-10.0 % -2, 0.0)) assert(math.pi - math.pi % 1 == 3) assert(math.pi - math.pi % 0.001 == 3.141) do -- very small numbers local i, j = 0, 20000 while i < j do local m = (i + j) // 2 if 10^-m > 0 then i = m + 1 else j = m end end -- 'i' is the smallest possible ten-exponent local b = 10^-(i - (i // 10)) -- a very small number assert(b > 0 and b * b == 0) local delta = b / 1000 assert(eq((2.1 * b) % (2 * b), (0.1 * b), delta)) assert(eq((-2.1 * b) % (2 * b), (2 * b) - (0.1 * b), delta)) assert(eq((2.1 * b) % (-2 * b), (0.1 * b) - (2 * b), delta)) assert(eq((-2.1 * b) % (-2 * b), (-0.1 * b), delta)) end -- basic consistency between integer modulo and float modulo for i = -10, 10 do for j = -10, 10 do if j ~= 0 then assert((i + 0.0) % j == i % j) end end end for i = 0, 10 do for j = -10, 10 do if j ~= 0 then assert((2^i) % j == (1 << i) % j) end end end do -- precision of module for large numbers local i = 10 while (1 << i) > 0 do assert((1 << i) % 3 == i % 2 + 1) i = i + 1 end i = 10 while 2^i < math.huge do assert(2^i % 3 == i % 2 + 1) i = i + 1 end end 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 higher 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 higher half res = (h >> (32 - floatbits)) % 2^32 else -- get 32 bits from the higher half and the rest from the lower half res = (h % 2^32) * 2^(floatbits - 32) + ((l >> (64 - floatbits)) % 2^32) end local rand = random() assert(eq(rand, 0x0.7a7040a5a323c9d6, 2^-floatbits)) assert(rand * 2^floatbits == res) end math.randomseed() 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')