| -- $Id: testes/math.lua $ |
| -- See Copyright Notice in file all.lua |
| |
| print("testing numbers and math lib") |
| |
| local minint <const> = math.mininteger |
| local maxint <const> = math.maxinteger |
| |
| local intbits <const> = 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 not math.type("10")) |
| |
| |
| 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 <const> = 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(not tonumber("")) |
| assert(not tonumber(" ")) |
| assert(not tonumber("-")) |
| assert(not tonumber(" -0x ")) |
| assert(not tonumber{}) |
| 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(not tonumber'+ 0.01' and not tonumber'+.e1' and |
| not tonumber'1e' and not tonumber'1.0e+' and |
| not tonumber'.') |
| 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(not f(tonumber('fFfa', 15))) |
| assert(not f(tonumber('099', 8))) |
| assert(not f(tonumber('1\0', 2))) |
| assert(not f(tonumber('', 8))) |
| assert(not f(tonumber(' ', 9))) |
| assert(not f(tonumber(' ', 9))) |
| assert(not f(tonumber('0xf', 10))) |
| |
| assert(not f(tonumber('inf'))) |
| assert(not f(tonumber(' INF '))) |
| assert(not f(tonumber('Nan'))) |
| assert(not f(tonumber('nan'))) |
| |
| assert(not f(tonumber(' '))) |
| assert(not f(tonumber(''))) |
| assert(not f(tonumber('1 a'))) |
| assert(not f(tonumber('1 a', 2))) |
| assert(not f(tonumber('1\0'))) |
| assert(not f(tonumber('1 \0'))) |
| assert(not f(tonumber('1\0 '))) |
| assert(not f(tonumber('e1'))) |
| assert(not f(tonumber('e 1'))) |
| assert(not f(tonumber(' 3.4.5 '))) |
| |
| |
| -- testing 'tonumber' for invalid hexadecimal formats |
| |
| assert(not tonumber('0x')) |
| assert(not tonumber('x')) |
| assert(not tonumber('x3')) |
| assert(not tonumber('0x3.3.3')) -- two decimal points |
| assert(not tonumber('00x2')) |
| assert(not tonumber('0x 2')) |
| assert(not tonumber('0 x2')) |
| assert(not tonumber('23x')) |
| assert(not tonumber('- 0xaa')) |
| assert(not tonumber('-0xaaP ')) -- no exponent |
| assert(not tonumber('0x0.51p')) |
| assert(not tonumber('0x5p+-2')) |
| |
| |
| -- 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(not math.tointeger(0.0 - minint)) |
| assert(not math.tointeger(math.pi)) |
| assert(not math.tointeger(-math.pi)) |
| assert(math.floor(math.huge) == math.huge) |
| assert(math.ceil(math.huge) == math.huge) |
| assert(not math.tointeger(math.huge)) |
| assert(math.floor(-math.huge) == -math.huge) |
| assert(math.ceil(-math.huge) == -math.huge) |
| assert(not math.tointeger(-math.huge)) |
| assert(math.tointeger("34.0") == 34) |
| assert(not math.tointeger("34.3")) |
| assert(not math.tointeger({})) |
| assert(not math.tointeger(0/0)) -- 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 conversions |
| |
| 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 <const> = -0.0 |
| local z <const> = 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 |
| local mz <const> = -1/inf |
| local z <const> = 1/inf |
| assert(mz == z) |
| assert(1/mz < 0 and 0 < 1/z) |
| local NaN <const> = 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 <const> = 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 should work with 32-bit integers |
| local h <const> = 0x7a7040a5 -- higher half |
| local l <const> = 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 |
| |
| do |
| -- testing return of 'randomseed' |
| local x, y = math.randomseed() |
| local res = math.random(0) |
| x, y = math.randomseed(x, y) -- should repeat the state |
| assert(math.random(0) == res) |
| math.randomseed(x, y) -- again should repeat the state |
| assert(math.random(0) == res) |
| -- keep the random seed for following tests |
| end |
| |
| 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, 13) |
| aux(1, 31) |
| aux(1, 32) |
| aux(1, 33) |
| 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(3, maxint // 3) |
| 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') |