@@ -0,0 +1,1024 @@
1+-- $Id: testes/math.lua $
2+-- See Copyright Notice in file all.lua
4+print("testing numbers and math lib")
6+local minint <const> = math.mininteger
7+local maxint <const> = math.maxinteger
9+local intbits <const> = math.floor(math.log(maxint, 2) + 0.5) + 1
10+assert((1 << intbits) == 0)
12+assert(minint == 1 << (intbits - 1))
13+assert(maxint == minint - 1)
15+-- number of bits in the mantissa of a floating-point number
18+ local p = 2.0^floatbits
21+ floatbits = floatbits + 1
25+local function isNaN (x)
30+assert(not isNaN(1/0))
34+ local x = 2.0^floatbits
35+ assert(x > x - 1.0 and x == x + 1.0)
37+ print(string.format("%d-bit integers, %d-bit (mantissa) floats",
41+assert(math.type(0) == "integer" and math.type(0.0) == "float"
42+ and not math.type("10"))
45+local function checkerror (msg, f, ...)
46+ local s, err = pcall(f, ...)
47+ assert(not s and string.find(err, msg))
50+local msgf2i = "number.* has no integer representation"
53+local function eq (a,b,limit)
55+ if floatbits >= 50 then limit = 1E-11
59+ -- a == b needed for +inf/-inf
60+ return a == b or math.abs(a-b) <= limit
64+-- equality with types
65+local function eqT (a,b)
66+ return a == b and math.type(a) == math.type(b)
70+-- basic float notation
71+assert(0e12 == 0 and .0 == 0 and 0. == 0 and .2e2 == 20 and 2.E-1 == 0.2)
74+ local a,b,c = "2", " 3e0 ", " 10 "
75+ assert(a+b == 5 and -b == -3 and b+"2" == 5 and "10"-c == 0)
76+ assert(type(a) == 'string' and type(b) == 'string' and type(c) == 'string')
77+ assert(a == "2" and b == " 3e0 " and c == " 10 " and -c == -" 10 ")
78+ assert(c%a == 0 and a^b == 08)
80+ assert(a == -a and 0 == -0)
85+ local mz = 0/x -- minus zero
86+ local t = {[0] = 10, 20, 30, 40, 50}
87+ assert(t[mz] == t[0] and t[-0] == t[0])
90+do -- tests for 'modf'
91+ local a,b = math.modf(3.5)
92+ assert(a == 3.0 and b == 0.5)
93+ a,b = math.modf(-2.5)
94+ assert(a == -2.0 and b == -0.5)
95+ a,b = math.modf(-3e23)
96+ assert(a == -3e23 and b == 0.0)
97+ a,b = math.modf(3e35)
98+ assert(a == 3e35 and b == 0.0)
99+ a,b = math.modf(-1/0) -- -inf
100+ assert(a == -1/0 and b == 0.0)
101+ a,b = math.modf(1/0) -- inf
102+ assert(a == 1/0 and b == 0.0)
103+ a,b = math.modf(0/0) -- NaN
104+ assert(isNaN(a) and isNaN(b))
105+ a,b = math.modf(3) -- integer argument
106+ assert(eqT(a, 3) and eqT(b, 0.0))
107+ a,b = math.modf(minint)
108+ assert(eqT(a, minint) and eqT(b, 0.0))
111+assert(math.huge > 10e30)
112+assert(-math.huge < -10e30)
115+-- integer arithmetic
116+assert(minint < minint + 1)
117+assert(maxint - 1 < maxint)
118+assert(0 - minint == minint)
119+assert(minint * minint == 0)
120+assert(maxint * maxint * maxint == maxint)
123+-- testing floor division and conversions
125+for _, i in pairs{-16, -15, -3, -2, -1, 0, 1, 2, 3, 15} do
126+ for _, j in pairs{-16, -15, -3, -2, -1, 1, 2, 3, 15} do
127+ for _, ti in pairs{0, 0.0} do -- try 'i' as integer and as float
128+ for _, tj in pairs{0, 0.0} do -- try 'j' as integer and as float
131+ assert(i//j == math.floor(i/j))
137+assert(1//0.0 == 1/0)
138+assert(-1 // 0.0 == -1/0)
139+assert(eqT(3.5 // 1.5, 2.0))
140+assert(eqT(3.5 // -1.5, -3.0))
142+do -- tests for different kinds of opcodes
144+ x = 1; assert(x // 0.0 == 1/0)
145+ x = 1.0; assert(x // 0 == 1/0)
146+ x = 3.5; assert(eqT(x // 1, 3.0))
147+ assert(eqT(x // -1, -4.0))
149+ x = 3.5; y = 1.5; assert(eqT(x // y, 2.0))
150+ x = 3.5; y = -1.5; assert(eqT(x // y, -3.0))
153+assert(maxint // maxint == 1)
154+assert(maxint // 1 == maxint)
155+assert((maxint - 1) // maxint == 0)
156+assert(maxint // (maxint - 1) == 1)
157+assert(minint // minint == 1)
158+assert(minint // minint == 1)
159+assert((minint + 1) // minint == 0)
160+assert(minint // (minint + 1) == 1)
161+assert(minint // 1 == minint)
163+assert(minint // -1 == -minint)
164+assert(minint // -2 == 2^(intbits - 2))
165+assert(maxint // -1 == -maxint)
168+-- negative exponents
170+ assert(2^-3 == 1 / 2^3)
171+ assert(eq((-3)^-3, 1 / (-3)^3))
172+ for i = -3, 3 do -- variables avoid constant folding
174+ -- domain errors (0^(-n)) are not portable
175+ if not _port or i ~= 0 or j > 0 then
176+ assert(eq(i^j, 1 / i^(-j)))
182+-- comparison between floats and integers (border cases)
183+if floatbits < intbits then
184+ assert(2.0^floatbits == (1 << floatbits))
185+ assert(2.0^floatbits - 1.0 == (1 << floatbits) - 1.0)
186+ assert(2.0^floatbits - 1.0 ~= (1 << floatbits))
187+ -- float is rounded, int is not
188+ assert(2.0^floatbits + 1.0 ~= (1 << floatbits) + 1)
189+else -- floats can express all integers with full accuracy
190+ assert(maxint == maxint + 0.0)
191+ assert(maxint - 1 == maxint - 1.0)
192+ assert(minint + 1 == minint + 1.0)
193+ assert(maxint ~= maxint - 1.0)
195+assert(maxint + 0.0 == 2.0^(intbits - 1) - 1.0)
196+assert(minint + 0.0 == minint)
197+assert(minint + 0.0 == -2.0^(intbits - 1))
200+-- order between floats and integers
201+assert(1 < 1.1); assert(not (1 < 0.9))
202+assert(1 <= 1.1); assert(not (1 <= 0.9))
203+assert(-1 < -0.9); assert(not (-1 < -1.1))
204+assert(1 <= 1.1); assert(not (-1 <= -1.1))
205+assert(-1 < -0.9); assert(not (-1 < -1.1))
206+assert(-1 <= -0.9); assert(not (-1 <= -1.1))
207+assert(minint <= minint + 0.0)
208+assert(minint + 0.0 <= minint)
209+assert(not (minint < minint + 0.0))
210+assert(not (minint + 0.0 < minint))
211+assert(maxint < minint * -1.0)
212+assert(maxint <= minint * -1.0)
215+ local fmaxi1 = 2^(intbits - 1)
216+ assert(maxint < fmaxi1)
217+ assert(maxint <= fmaxi1)
218+ assert(not (fmaxi1 <= maxint))
219+ assert(minint <= -2^(intbits - 1))
220+ assert(-2^(intbits - 1) <= minint)
223+if floatbits < intbits then
224+ print("testing order (floats cannot represent all integers)")
225+ local fmax = 2^floatbits
226+ local ifmax = fmax | 0
227+ assert(fmax < ifmax + 1)
228+ assert(fmax - 1 < ifmax)
229+ assert(-(fmax - 1) > -ifmax)
230+ assert(not (fmax <= ifmax - 1))
231+ assert(-fmax > -(ifmax + 1))
232+ assert(not (-fmax >= -(ifmax - 1)))
234+ assert(fmax/2 - 0.5 < ifmax//2)
235+ assert(-(fmax/2 - 0.5) > -ifmax//2)
237+ assert(maxint < 2^intbits)
238+ assert(minint > -2^intbits)
239+ assert(maxint <= 2^intbits)
240+ assert(minint >= -2^intbits)
242+ print("testing order (floats can represent all integers)")
243+ assert(maxint < maxint + 1.0)
244+ assert(maxint < maxint + 0.5)
245+ assert(maxint - 1.0 < maxint)
246+ assert(maxint - 0.5 < maxint)
247+ assert(not (maxint + 0.0 < maxint))
248+ assert(maxint + 0.0 <= maxint)
249+ assert(not (maxint < maxint + 0.0))
250+ assert(maxint + 0.0 <= maxint)
251+ assert(maxint <= maxint + 0.0)
252+ assert(not (maxint + 1.0 <= maxint))
253+ assert(not (maxint + 0.5 <= maxint))
254+ assert(not (maxint <= maxint - 1.0))
255+ assert(not (maxint <= maxint - 0.5))
257+ assert(minint < minint + 1.0)
258+ assert(minint < minint + 0.5)
259+ assert(minint <= minint + 0.5)
260+ assert(minint - 1.0 < minint)
261+ assert(minint - 1.0 <= minint)
262+ assert(not (minint + 0.0 < minint))
263+ assert(not (minint + 0.5 < minint))
264+ assert(not (minint < minint + 0.0))
265+ assert(minint + 0.0 <= minint)
266+ assert(minint <= minint + 0.0)
267+ assert(not (minint + 1.0 <= minint))
268+ assert(not (minint + 0.5 <= minint))
269+ assert(not (minint <= minint - 1.0))
273+ local NaN <const> = 0/0
274+ assert(not (NaN < 0))
275+ assert(not (NaN > minint))
276+ assert(not (NaN <= -9))
277+ assert(not (NaN <= maxint))
278+ assert(not (NaN < maxint))
279+ assert(not (minint <= NaN))
280+ assert(not (minint < NaN))
281+ assert(not (4 <= NaN))
282+ assert(not (4 < NaN))
286+-- avoiding errors at compile time
287+local function checkcompt (msg, code)
288+ checkerror(msg, assert(load(code)))
290+checkcompt("divide by zero", "return 2 // 0")
291+checkcompt(msgf2i, "return 2.3 >> 0")
292+checkcompt(msgf2i, ("return 2.0^%d & 1"):format(intbits - 1))
293+checkcompt("field 'huge'", "return math.huge << 1")
294+checkcompt(msgf2i, ("return 1 | 2.0^%d"):format(intbits - 1))
295+checkcompt(msgf2i, "return 2.3 ~ 0.0")
298+-- testing overflow errors when converting from float to integer (runtime)
299+local function f2i (x) return x | x end
300+checkerror(msgf2i, f2i, math.huge) -- +inf
301+checkerror(msgf2i, f2i, -math.huge) -- -inf
302+checkerror(msgf2i, f2i, 0/0) -- NaN
304+if floatbits < intbits then
305+ -- conversion tests when float cannot represent all integers
306+ assert(maxint + 1.0 == maxint + 0.0)
307+ assert(minint - 1.0 == minint + 0.0)
308+ checkerror(msgf2i, f2i, maxint + 0.0)
309+ assert(f2i(2.0^(intbits - 2)) == 1 << (intbits - 2))
310+ assert(f2i(-2.0^(intbits - 2)) == -(1 << (intbits - 2)))
311+ assert((2.0^(floatbits - 1) + 1.0) // 1 == (1 << (floatbits - 1)) + 1)
312+ -- maximum integer representable as a float
313+ local mf = maxint - (1 << (floatbits - intbits)) + 1
314+ assert(f2i(mf + 0.0) == mf) -- OK up to here
316+ assert(f2i(mf + 0.0) ~= mf) -- no more representable
318+ -- conversion tests when float can represent all integers
319+ assert(maxint + 1.0 > maxint)
320+ assert(minint - 1.0 < minint)
321+ assert(f2i(maxint + 0.0) == maxint)
322+ checkerror("no integer rep", f2i, maxint + 1.0)
323+ checkerror("no integer rep", f2i, minint - 1.0)
326+-- 'minint' should be representable as a float no matter the precision
327+assert(f2i(minint + 0.0) == minint)
330+-- testing numeric strings
333+assert("2 " + 1 == 3)
334+assert(" -2 " + 1 == -1)
335+assert(" -0xa " + 1 == -9)
338+-- Literal integer Overflows (new behavior in 5.3.3)
341+ assert(eqT(tonumber(tostring(maxint)), maxint))
342+ assert(eqT(tonumber(tostring(minint)), minint))
344+ -- add 1 to last digit as a string (it cannot be 9...)
345+ local function incd (n)
346+ local s = string.format("%d", n)
347+ s = string.gsub(s, "%d$", function (d)
349+ return string.char(string.byte(d) + 1)
354+ -- 'tonumber' with overflow by 1
355+ assert(eqT(tonumber(incd(maxint)), maxint + 1.0))
356+ assert(eqT(tonumber(incd(minint)), minint - 1.0))
359+ assert(eqT(tonumber("1"..string.rep("0", 30)), 1e30))
360+ assert(eqT(tonumber("-1"..string.rep("0", 30)), -1e30))
362+ -- hexa format still wraps around
363+ assert(eqT(tonumber("0x1"..string.rep("0", 30)), 0))
365+ -- lexer in the limits
366+ assert(minint == load("return " .. minint)())
367+ assert(eqT(maxint, load("return " .. maxint)()))
369+ assert(eqT(10000000000000000000000.0, 10000000000000000000000))
370+ assert(eqT(-10000000000000000000000.0, -10000000000000000000000))
374+-- testing 'tonumber'
376+-- 'tonumber' with numbers
377+assert(tonumber(3.4) == 3.4)
378+assert(eqT(tonumber(3), 3))
379+assert(eqT(tonumber(maxint), maxint) and eqT(tonumber(minint), minint))
380+assert(tonumber(1/0) == 1/0)
382+-- 'tonumber' with strings
383+assert(tonumber("0") == 0)
384+assert(not tonumber(""))
385+assert(not tonumber(" "))
386+assert(not tonumber("-"))
387+assert(not tonumber(" -0x "))
388+assert(not tonumber{})
389+assert(tonumber'+0.01' == 1/100 and tonumber'+.01' == 0.01 and
390+ tonumber'.01' == 0.01 and tonumber'-1.' == -1 and
392+assert(not tonumber'+ 0.01' and not tonumber'+.e1' and
393+ not tonumber'1e' and not tonumber'1.0e+' and
395+assert(tonumber('-012') == -010-2)
396+assert(tonumber('-1.2e2') == - - -120)
398+assert(tonumber("0xffffffffffff") == (1 << (4*12)) - 1)
399+assert(tonumber("0x"..string.rep("f", (intbits//4))) == -1)
400+assert(tonumber("-0x"..string.rep("f", (intbits//4))) == 1)
402+-- testing 'tonumber' with base
403+assert(tonumber(' 001010 ', 2) == 10)
404+assert(tonumber(' 001010 ', 10) == 001010)
405+assert(tonumber(' -1010 ', 2) == -10)
406+assert(tonumber('10', 36) == 36)
407+assert(tonumber(' -10 ', 36) == -36)
408+assert(tonumber(' +1Z ', 36) == 36 + 35)
409+assert(tonumber(' -1z ', 36) == -36 + -35)
410+assert(tonumber('-fFfa', 16) == -(10+(16*(15+(16*(15+(16*15)))))))
411+assert(tonumber(string.rep('1', (intbits - 2)), 2) + 1 == 2^(intbits - 2))
412+assert(tonumber('ffffFFFF', 16)+1 == (1 << 32))
413+assert(tonumber('0ffffFFFF', 16)+1 == (1 << 32))
414+assert(tonumber('-0ffffffFFFF', 16) - 1 == -(1 << 40))
417+ local i10 = i2 * i2 * i2 * i2 * i2 -- i^10
418+ assert(tonumber('\t10000000000\t', i) == i10)
422+ -- tests with very long numerals
423+ assert(tonumber("0x"..string.rep("f", 13)..".0") == 2.0^(4*13) - 1)
424+ assert(tonumber("0x"..string.rep("f", 150)..".0") == 2.0^(4*150) - 1)
425+ assert(tonumber("0x"..string.rep("f", 300)..".0") == 2.0^(4*300) - 1)
426+ assert(tonumber("0x"..string.rep("f", 500)..".0") == 2.0^(4*500) - 1)
427+ assert(tonumber('0x3.' .. string.rep('0', 1000)) == 3)
428+ assert(tonumber('0x' .. string.rep('0', 1000) .. 'a') == 10)
429+ assert(tonumber('0x0.' .. string.rep('0', 13).."1") == 2.0^(-4*14))
430+ assert(tonumber('0x0.' .. string.rep('0', 150).."1") == 2.0^(-4*151))
431+ assert(tonumber('0x0.' .. string.rep('0', 300).."1") == 2.0^(-4*301))
432+ assert(tonumber('0x0.' .. string.rep('0', 500).."1") == 2.0^(-4*501))
434+ assert(tonumber('0xe03' .. string.rep('0', 1000) .. 'p-4000') == 3587.0)
435+ assert(tonumber('0x.' .. string.rep('0', 1000) .. '74p4004') == 0x7.4)
438+-- testing 'tonumber' for invalid formats
440+local function f (...)
441+ if select('#', ...) == 1 then
448+assert(not f(tonumber('fFfa', 15)))
449+assert(not f(tonumber('099', 8)))
450+assert(not f(tonumber('1\0', 2)))
451+assert(not f(tonumber('', 8)))
452+assert(not f(tonumber(' ', 9)))
453+assert(not f(tonumber(' ', 9)))
454+assert(not f(tonumber('0xf', 10)))
456+assert(not f(tonumber('inf')))
457+assert(not f(tonumber(' INF ')))
458+assert(not f(tonumber('Nan')))
459+assert(not f(tonumber('nan')))
461+assert(not f(tonumber(' ')))
462+assert(not f(tonumber('')))
463+assert(not f(tonumber('1 a')))
464+assert(not f(tonumber('1 a', 2)))
465+assert(not f(tonumber('1\0')))
466+assert(not f(tonumber('1 \0')))
467+assert(not f(tonumber('1\0 ')))
468+assert(not f(tonumber('e1')))
469+assert(not f(tonumber('e 1')))
470+assert(not f(tonumber(' 3.4.5 ')))
473+-- testing 'tonumber' for invalid hexadecimal formats
475+assert(not tonumber('0x'))
476+assert(not tonumber('x'))
477+assert(not tonumber('x3'))
478+assert(not tonumber('0x3.3.3')) -- two decimal points
479+assert(not tonumber('00x2'))
480+assert(not tonumber('0x 2'))
481+assert(not tonumber('0 x2'))
482+assert(not tonumber('23x'))
483+assert(not tonumber('- 0xaa'))
484+assert(not tonumber('-0xaaP ')) -- no exponent
485+assert(not tonumber('0x0.51p'))
486+assert(not tonumber('0x5p+-2'))
489+-- testing hexadecimal numerals
491+assert(0x10 == 16 and 0xfff == 2^12 - 1 and 0XFB == 251)
492+assert(0x0p12 == 0 and 0x.0p-3 == 0)
493+assert(0xFFFFFFFF == (1 << 32) - 1)
494+assert(tonumber('+0x2') == 2)
495+assert(tonumber('-0xaA') == -170)
496+assert(tonumber('-0xffFFFfff') == -(1 << 32) + 1)
498+-- possible confusion with decimal exponent
499+assert(0E+1 == 0 and 0xE+1 == 15 and 0xe-1 == 13)
504+assert(tonumber(' 0x2.5 ') == 0x25/16)
505+assert(tonumber(' -0x2.5 ') == -0x25/16)
506+assert(tonumber(' +0x0.51p+8 ') == 0x51)
507+assert(0x.FfffFFFF == 1 - '0x.00000001')
508+assert('0xA.a' + 0 == 10 + 10/16)
509+assert(0xa.aP4 == 0XAA)
511+assert(0x1.1 == '0x1.' + '+0x.1')
512+assert(0Xabcdef.0 == 0x.ABCDEFp+24)
516+assert(100.0 == 1E2 and .01 == 1e-2)
517+assert(1111111111 - 1111111110 == 1000.00e-03)
518+assert(1.1 == '1.'+'.1')
519+assert(tonumber'1111111111' - tonumber'1111111110' ==
520+ tonumber" +0.001e+3 \n\t")
522+assert(0.1e-30 > 0.9E-31 and 0.9E30 < 0.1e31)
524+assert(0.123456 > 0.123455)
526+assert(tonumber('+1.23E18') == 1.23*10.0^18)
528+-- testing order operators
529+assert(not(1<1) and (1<2) and not(2<1))
530+assert(not('a'<'a') and ('a'<'b') and not('b'<'a'))
531+assert((1<=1) and (1<=2) and not(2<=1))
532+assert(('a'<='a') and ('a'<='b') and not('b'<='a'))
533+assert(not(1>1) and not(1>2) and (2>1))
534+assert(not('a'>'a') and not('a'>'b') and ('b'>'a'))
535+assert((1>=1) and not(1>=2) and (2>=1))
536+assert(('a'>='a') and not('a'>='b') and ('b'>='a'))
537+assert(1.3 < 1.4 and 1.3 <= 1.4 and not (1.3 < 1.3) and 1.3 <= 1.3)
539+-- testing mod operator
540+assert(eqT(-4 % 3, 2))
541+assert(eqT(4 % -3, -2))
542+assert(eqT(-4.0 % 3, 2.0))
543+assert(eqT(4 % -3.0, -2.0))
544+assert(eqT(4 % -5, -1))
545+assert(eqT(4 % -5.0, -1.0))
546+assert(eqT(4 % 5, 4))
547+assert(eqT(4 % 5.0, 4.0))
548+assert(eqT(-4 % -5, -4))
549+assert(eqT(-4 % -5.0, -4.0))
550+assert(eqT(-4 % 5, 1))
551+assert(eqT(-4 % 5.0, 1.0))
552+assert(eqT(4.25 % 4, 0.25))
553+assert(eqT(10.0 % 2, 0.0))
554+assert(eqT(-10.0 % 2, 0.0))
555+assert(eqT(-10.0 % -2, 0.0))
556+assert(math.pi - math.pi % 1 == 3)
557+assert(math.pi - math.pi % 0.001 == 3.141)
559+do -- very small numbers
560+ local i, j = 0, 20000
562+ local m = (i + j) // 2
569+ -- 'i' is the smallest possible ten-exponent
570+ local b = 10^-(i - (i // 10)) -- a very small number
571+ assert(b > 0 and b * b == 0)
572+ local delta = b / 1000
573+ assert(eq((2.1 * b) % (2 * b), (0.1 * b), delta))
574+ assert(eq((-2.1 * b) % (2 * b), (2 * b) - (0.1 * b), delta))
575+ assert(eq((2.1 * b) % (-2 * b), (0.1 * b) - (2 * b), delta))
576+ assert(eq((-2.1 * b) % (-2 * b), (-0.1 * b), delta))
580+-- basic consistency between integer modulo and float modulo
584+ assert((i + 0.0) % j == i % j)
592+ assert((2^i) % j == (1 << i) % j)
597+do -- precision of module for large numbers
599+ while (1 << i) > 0 do
600+ assert((1 << i) % 3 == i % 2 + 1)
605+ while 2^i < math.huge do
606+ assert(2^i % 3 == i % 2 + 1)
611+assert(eqT(minint % minint, 0))
612+assert(eqT(maxint % maxint, 0))
613+assert((minint + 1) % minint == minint + 1)
614+assert((maxint - 1) % maxint == maxint - 1)
615+assert(minint % maxint == maxint - 1)
617+assert(minint % -1 == 0)
618+assert(minint % -2 == 0)
619+assert(maxint % -2 == -1)
621+-- non-portable tests because Windows C library cannot compute
622+-- fmod(1, huge) correctly
624+ local function anan (x) assert(isNaN(x)) end -- assert Not a Number
628+ anan(math.huge % 1e30)
629+ anan(-math.huge % 1e30)
630+ anan(-math.huge % -1e30)
631+ assert(1 % math.huge == 1)
632+ assert(1e30 % math.huge == 1e30)
633+ assert(1e30 % -math.huge == -math.huge)
634+ assert(-1 % math.huge == math.huge)
635+ assert(-1 % -math.huge == -1)
639+-- testing unsigned comparisons
640+assert(math.ult(3, 4))
641+assert(not math.ult(4, 4))
642+assert(math.ult(-2, -1))
643+assert(math.ult(2, -1))
644+assert(not math.ult(-2, -2))
645+assert(math.ult(maxint, minint))
646+assert(not math.ult(minint, maxint))
649+assert(eq(math.sin(-9.8)^2 + math.cos(-9.8)^2, 1))
650+assert(eq(math.tan(math.pi/4), 1))
651+assert(eq(math.sin(math.pi/2), 1) and eq(math.cos(math.pi/2), 0))
652+assert(eq(math.atan(1), math.pi/4) and eq(math.acos(0), math.pi/2) and
653+ eq(math.asin(1), math.pi/2))
654+assert(eq(math.deg(math.pi/2), 90) and eq(math.rad(90), math.pi/2))
655+assert(math.abs(-10.43) == 10.43)
656+assert(eqT(math.abs(minint), minint))
657+assert(eqT(math.abs(maxint), maxint))
658+assert(eqT(math.abs(-maxint), maxint))
659+assert(eq(math.atan(1,0), math.pi/2))
660+assert(math.fmod(10,3) == 1)
661+assert(eq(math.sqrt(10)^2, 10))
662+assert(eq(math.log(2, 10), math.log(2)/math.log(10)))
663+assert(eq(math.log(2, 2), 1))
664+assert(eq(math.log(9, 3), 2))
665+assert(eq(math.exp(0), 1))
666+assert(eq(math.sin(10), math.sin(10%(2*math.pi))))
669+assert(tonumber(' 1.3e-2 ') == 1.3e-2)
670+assert(tonumber(' -1.00000000000001 ') == -1.00000000000001)
672+-- testing constant limits
674+assert(8388609 + -8388609 == 0)
675+assert(8388608 + -8388608 == 0)
676+assert(8388607 + -8388607 == 0)
680+do -- testing floor & ceil
681+ assert(eqT(math.floor(3.4), 3))
682+ assert(eqT(math.ceil(3.4), 4))
683+ assert(eqT(math.floor(-3.4), -4))
684+ assert(eqT(math.ceil(-3.4), -3))
685+ assert(eqT(math.floor(maxint), maxint))
686+ assert(eqT(math.ceil(maxint), maxint))
687+ assert(eqT(math.floor(minint), minint))
688+ assert(eqT(math.floor(minint + 0.0), minint))
689+ assert(eqT(math.ceil(minint), minint))
690+ assert(eqT(math.ceil(minint + 0.0), minint))
691+ assert(math.floor(1e50) == 1e50)
692+ assert(math.ceil(1e50) == 1e50)
693+ assert(math.floor(-1e50) == -1e50)
694+ assert(math.ceil(-1e50) == -1e50)
695+ for _, p in pairs{31,32,63,64} do
696+ assert(math.floor(2^p) == 2^p)
697+ assert(math.floor(2^p + 0.5) == 2^p)
698+ assert(math.ceil(2^p) == 2^p)
699+ assert(math.ceil(2^p - 0.5) == 2^p)
701+ checkerror("number expected", math.floor, {})
702+ checkerror("number expected", math.ceil, print)
703+ assert(eqT(math.tointeger(minint), minint))
704+ assert(eqT(math.tointeger(minint .. ""), minint))
705+ assert(eqT(math.tointeger(maxint), maxint))
706+ assert(eqT(math.tointeger(maxint .. ""), maxint))
707+ assert(eqT(math.tointeger(minint + 0.0), minint))
708+ assert(not math.tointeger(0.0 - minint))
709+ assert(not math.tointeger(math.pi))
710+ assert(not math.tointeger(-math.pi))
711+ assert(math.floor(math.huge) == math.huge)
712+ assert(math.ceil(math.huge) == math.huge)
713+ assert(not math.tointeger(math.huge))
714+ assert(math.floor(-math.huge) == -math.huge)
715+ assert(math.ceil(-math.huge) == -math.huge)
716+ assert(not math.tointeger(-math.huge))
717+ assert(math.tointeger("34.0") == 34)
718+ assert(not math.tointeger("34.3"))
719+ assert(not math.tointeger({}))
720+ assert(not math.tointeger(0/0)) -- NaN
724+-- testing fmod for integers
728+ local mi = math.fmod(i, j)
729+ local mf = math.fmod(i + 0.0, j)
731+ assert(math.type(mi) == 'integer' and math.type(mf) == 'float')
732+ if (i >= 0 and j >= 0) or (i <= 0 and j <= 0) or mi == 0 then
733+ assert(eqT(mi, i % j))
738+assert(eqT(math.fmod(minint, minint), 0))
739+assert(eqT(math.fmod(maxint, maxint), 0))
740+assert(eqT(math.fmod(minint + 1, minint), minint + 1))
741+assert(eqT(math.fmod(maxint - 1, maxint), maxint - 1))
743+checkerror("zero", math.fmod, 3, 0)
746+do -- testing max/min
747+ checkerror("value expected", math.max)
748+ checkerror("value expected", math.min)
749+ assert(eqT(math.max(3), 3))
750+ assert(eqT(math.max(3, 5, 9, 1), 9))
751+ assert(math.max(maxint, 10e60) == 10e60)
752+ assert(eqT(math.max(minint, minint + 1), minint + 1))
753+ assert(eqT(math.min(3), 3))
754+ assert(eqT(math.min(3, 5, 9, 1), 1))
755+ assert(math.min(3.2, 5.9, -9.2, 1.1) == -9.2)
756+ assert(math.min(1.9, 1.7, 1.72) == 1.7)
757+ assert(math.min(-10e60, minint) == -10e60)
758+ assert(eqT(math.min(maxint, maxint - 1), maxint - 1))
759+ assert(eqT(math.min(maxint - 2, maxint, maxint - 1), maxint - 2))
761+-- testing implicit conversions
763+local a,b = '10', '20'
764+assert(a*b == 200 and a+b == 30 and a-b == -10 and a/b == 0.5 and -b == -20)
765+assert(a == '10' and b == '20')
769+ print("testing -0 and NaN")
770+ local mz <const> = -0.0
771+ local z <const> = 0.0
773+ assert(1/mz < 0 and 0 < 1/z)
774+ local a = {[mz] = 1}
775+ assert(a[z] == 1 and a[mz] == 1)
777+ assert(a[z] == 2 and a[mz] == 2)
778+ local inf = math.huge * 2 + 1
779+ local mz <const> = -1/inf
780+ local z <const> = 1/inf
782+ assert(1/mz < 0 and 0 < 1/z)
783+ local NaN <const> = inf - inf
785+ assert(not (NaN < NaN))
786+ assert(not (NaN <= NaN))
787+ assert(not (NaN > NaN))
788+ assert(not (NaN >= NaN))
789+ assert(not (0 < NaN) and not (NaN < 0))
790+ local NaN1 <const> = 0/0
791+ assert(NaN ~= NaN1 and not (NaN <= NaN1) and not (NaN1 <= NaN))
793+ assert(not pcall(rawset, a, NaN, 1))
794+ assert(a[NaN] == undef)
796+ assert(not pcall(rawset, a, NaN, 1))
797+ assert(a[NaN] == undef)
798+ -- strings with same binary representation as 0.0 (might create problems
799+ -- for constant manipulation in the pre-compiler)
800+ 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"
801+ assert(a1 == a2 and a2 == a4 and a1 ~= a3)
806+print("testing 'math.random'")
808+local random, max, min = math.random, math.max, math.min
810+local function testnear (val, ref, tol)
811+ return (math.abs(val - ref) < ref * tol)
815+-- low-level!! For the current implementation of random in Lua,
816+-- the first call after seed 1007 should return 0x7a7040a5a323c9d6
818+ -- all computations should work with 32-bit integers
819+ local h <const> = 0x7a7040a5 -- higher half
820+ local l <const> = 0xa323c9d6 -- lower half
822+ math.randomseed(1007)
823+ -- get the low 'intbits' of the 64-bit expected result
824+ local res = (h << 32 | l) & ~(~0 << intbits)
825+ assert(random(0) == res)
827+ math.randomseed(1007, 0)
828+ -- using higher bits to generate random floats; (the '% 2^32' converts
829+ -- 32-bit integers to floats as unsigned)
831+ if floatbits <= 32 then
832+ -- get all bits from the higher half
833+ res = (h >> (32 - floatbits)) % 2^32
835+ -- get 32 bits from the higher half and the rest from the lower half
836+ res = (h % 2^32) * 2^(floatbits - 32) + ((l >> (64 - floatbits)) % 2^32)
838+ local rand = random()
839+ assert(eq(rand, 0x0.7a7040a5a323c9d6, 2^-floatbits))
840+ assert(rand * 2^floatbits == res)
844+ -- testing return of 'randomseed'
845+ local x, y = math.randomseed()
846+ local res = math.random(0)
847+ x, y = math.randomseed(x, y) -- should repeat the state
848+ assert(math.random(0) == res)
849+ math.randomseed(x, y) -- again should repeat the state
850+ assert(math.random(0) == res)
851+ -- keep the random seed for following tests
852+ print(string.format("random seeds: %d, %d", x, y))
855+do -- test random for floats
856+ local randbits = math.min(floatbits, 64) -- at most 64 random bits
857+ local mult = 2^randbits -- to make random float into an integral
858+ local counts = {} -- counts for bits
859+ for i = 1, randbits do counts[i] = 0 end
860+ local up = -math.huge
861+ local low = math.huge
862+ local rounds = 100 * randbits -- 100 times for each bit
863+ local totalrounds = 0
864+ ::doagain:: -- will repeat test until we get good statistics
865+ for i = 0, rounds do
867+ assert(0 <= t and t < 1)
870+ assert(t * mult % 1 == 0) -- no extra bits
871+ local bit = i % randbits -- bit to be tested
872+ if (t * 2^bit) % 1 >= 0.5 then -- is bit set?
873+ counts[bit + 1] = counts[bit + 1] + 1 -- increment its count
876+ totalrounds = totalrounds + rounds
877+ if not (eq(up, 1, 0.001) and eq(low, 0, 0.001)) then
880+ -- all bit counts should be near 50%
881+ local expected = (totalrounds / randbits / 2)
882+ for i = 1, randbits do
883+ if not testnear(counts[i], expected, 0.10) then
887+ print(string.format("float random range in %d calls: [%f, %f]",
888+ totalrounds, low, up))
892+do -- test random for full integers
895+ local counts = {} -- counts for bits
896+ for i = 1, intbits do counts[i] = 0 end
897+ local rounds = 100 * intbits -- 100 times for each bit
898+ local totalrounds = 0
899+ ::doagain:: -- will repeat test until we get good statistics
900+ for i = 0, rounds do
904+ local bit = i % intbits -- bit to be tested
905+ -- increment its count if it is set
906+ counts[bit + 1] = counts[bit + 1] + ((t >> bit) & 1)
908+ totalrounds = totalrounds + rounds
909+ local lim = maxint >> 10
910+ if not (maxint - up < lim and low - minint < lim) then
913+ -- all bit counts should be near 50%
914+ local expected = (totalrounds / intbits / 2)
915+ for i = 1, intbits do
916+ if not testnear(counts[i], expected, 0.10) then
920+ print(string.format(
921+ "integer random range in %d calls: [minint + %.0fppm, maxint - %.0fppm]",
922+ totalrounds, (minint - low) / minint * 1e6,
923+ (maxint - up) / maxint * 1e6))
927+ -- test distribution for a dice
928+ local count = {0, 0, 0, 0, 0, 0}
932+ for i = 1, rep * 6 do
934+ count[r] = count[r] + 1
936+ totalrep = totalrep + rep
938+ if not testnear(count[i], totalrep, 0.05) then
945+ local function aux (x1, x2) -- test random for small intervals
946+ local mark = {}; local count = 0 -- to check that all values appeared
948+ local t = random(x1, x2)
949+ assert(x1 <= t and t <= x2)
950+ if not mark[t] then -- new value
953+ if count == x2 - x1 + 1 then -- all values appeared; OK
969+ aux(-10,-10) -- unit set
970+ aux(minint, minint) -- unit set
971+ aux(maxint, maxint) -- unit set
972+ aux(minint, minint + 9)
973+ aux(maxint - 3, maxint)
977+ local function aux(p1, p2) -- test random for large intervals
981+ local mark = {}; local count = 0 -- to count how many different values
984+ local t = random(p1, p2)
985+ if not mark[t] then -- new value
986+ assert(p1 <= t and t <= p2)
987+ max = math.max(max, t)
988+ min = math.min(min, t)
993+ -- at least 80% of values are different
994+ if not (count >= n * 0.8) then
997+ -- min and max not too far from formal min and max
998+ local diff = (p2 - p1) >> 4
999+ if not (min < p1 + diff and max > p2 - diff) then
1005+ aux(3, maxint // 3)
1007+ aux(minint // 2, maxint // 2)
1008+ aux(minint, maxint)
1009+ aux(minint + 1, maxint)
1010+ aux(minint, maxint - 1)
1011+ aux(0, 1 << (intbits - 5))
1015+assert(not pcall(random, 1, 2, 3)) -- too many arguments
1018+assert(not pcall(random, minint + 1, minint))
1019+assert(not pcall(random, maxint, maxint - 1))
1020+assert(not pcall(random, maxint, minint))