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lua/testes/math.lua
Roberto Ierusalimschy 1bf4b80f1a Floats formatted with "correct" precision 
Conversion float->string ensures that, for any float f,
tonumber(tostring(f)) == f, but still avoiding noise like 1.1
converting to "1.1000000000000001".
2024-08-02 15:09:30 -03:00

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-- $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
-- maximum exponent for a floating-point number
local maxexp = 0
do
local p = 2.0
while p < math.huge do
maxexp = maxexp + 1
p = p + p
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)
local msg = " %d-bit integers, %d-bit*2^%d floats"
print(string.format(msg, intbits, floatbits, maxexp))
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
local 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
local 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
local 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
print(string.format("random seeds: %d, %d", x, y))
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("testing precision of 'tostring'")
-- -===================================================================
--
-- number of decimal digits supported by float precision
local decdig = math.floor(floatbits * math.log(2, 10))
print(string.format(" %d-digit float numbers with full precision",
decdig))
-- number of decimal digits supported by integer precision
local Idecdig = math.floor(math.log(maxint, 10))
print(string.format(" %d-digit integer numbers with full precision",
Idecdig))
do
-- Any number should print so that reading it back gives itself:
-- tonumber(tostring(x)) == x
-- Mersenne fractions
local p = 1.0
for i = 1, maxexp do
p = p + p
local x = 1 / (p - 1)
assert(x == tonumber(tostring(x)))
end
-- some random numbers in [0,1)
for i = 1, 100 do
local x = math.random()
assert(x == tonumber(tostring(x)))
end
-- different numbers shold print differently.
-- check pairs of floats with minimum detectable difference
local p = floatbits - 1
for i = 1, maxexp - 1 do
for _, i in ipairs{-i, i} do
local x = 2^i
local diff = 2^(i - p) -- least significant bit for 'x'
local y = x + diff
local fy = tostring(y)
assert(x ~= y and tostring(x) ~= fy)
assert(tonumber(fy) == y)
end
end
-- "reasonable" numerals should be printed like themselves
-- create random float numerals with 5 digits, with a decimal point
-- inserted in all places. (With more than 5, things like "0.00001"
-- reformats like "1e-5".)
for i = 1, 1000 do
-- random numeral with 5 digits
local x = string.format("%.5d", math.random(0, 99999))
for i = 2, #x do
-- insert decimal point at position 'i'
local y = string.sub(x, 1, i - 1) .. "." .. string.sub(x, i, -1)
y = string.gsub(y, "^0*(%d.-%d)0*$", "%1") -- trim extra zeros
assert(y == tostring(tonumber(y)))
end
end
-- all-random floats
local Fsz = string.packsize("n") -- size of floats in bytes
for i = 1, 400 do
local s = string.pack("j", math.random(0)) -- a random string of bits
while #s < Fsz do -- make 's' long enough
s = s .. string.pack("j", math.random(0))
end
local n = string.unpack("n", s) -- read 's' as a float
s = tostring(n)
if string.find(s, "^%-?%d") then -- avoid NaN, inf, -inf
assert(tonumber(s) == n)
end
end
end
-- ]]==================================================================
print('OK')
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