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1-- $Id: math.lua,v 1.78 2016/11/07 13:11:28 roberto Exp $
2-- See Copyright Notice in file all.lua
3
4print("testing numbers and math lib")
5
6local minint = math.mininteger
7local maxint = math.maxinteger
8
9local intbits = math.floor(math.log(maxint, 2) + 0.5) + 1
10assert((1 << intbits) == 0)
11
12assert(minint == 1 << (intbits - 1))
13assert(maxint == minint - 1)
14
15-- number of bits in the mantissa of a floating-point number
16local floatbits = 24
17do
18 local p = 2.0^floatbits
19 while p < p + 1.0 do
20 p = p * 2.0
21 floatbits = floatbits + 1
22 end
23end
24
25local function isNaN (x)
26 return (x ~= x)
27end
28
29assert(isNaN(0/0))
30assert(not isNaN(1/0))
31
32
33do
34 local x = 2.0^floatbits
35 assert(x > x - 1.0 and x == x + 1.0)
36
37 print(string.format("%d-bit integers, %d-bit (mantissa) floats",
38 intbits, floatbits))
39end
40
41assert(math.type(0) == "integer" and math.type(0.0) == "float"
42 and math.type("10") == nil)
43
44
45local function checkerror (msg, f, ...)
46 local s, err = pcall(f, ...)
47 assert(not s and string.find(err, msg))
48end
49
50local msgf2i = "number.* has no integer representation"
51
52-- float equality
53function eq (a,b,limit)
54 if not limit then
55 if floatbits >= 50 then limit = 1E-11
56 else limit = 1E-5
57 end
58 end
59 -- a == b needed for +inf/-inf
60 return a == b or math.abs(a-b) <= limit
61end
62
63
64-- equality with types
65function eqT (a,b)
66 return a == b and math.type(a) == math.type(b)
67end
68
69
70-- basic float notation
71assert(0e12 == 0 and .0 == 0 and 0. == 0 and .2e2 == 20 and 2.E-1 == 0.2)
72
73do
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)
79 a = 0
80 assert(a == -a and 0 == -0)
81end
82
83do
84 local x = -1
85 local mz = 0/x -- minus zero
86 t = {[0] = 10, 20, 30, 40, 50}
87 assert(t[mz] == t[0] and t[-0] == t[0])
88end
89
90do -- 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))
109end
110
111assert(math.huge > 10e30)
112assert(-math.huge < -10e30)
113
114
115-- integer arithmetic
116assert(minint < minint + 1)
117assert(maxint - 1 < maxint)
118assert(0 - minint == minint)
119assert(minint * minint == 0)
120assert(maxint * maxint * maxint == maxint)
121
122
123-- testing floor division and conversions
124
125for _, 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
129 local x = i + ti
130 local y = j + tj
131 assert(i//j == math.floor(i/j))
132 end
133 end
134 end
135end
136
137assert(1//0.0 == 1/0)
138assert(-1 // 0.0 == -1/0)
139assert(eqT(3.5 // 1.5, 2.0))
140assert(eqT(3.5 // -1.5, -3.0))
141
142assert(maxint // maxint == 1)
143assert(maxint // 1 == maxint)
144assert((maxint - 1) // maxint == 0)
145assert(maxint // (maxint - 1) == 1)
146assert(minint // minint == 1)
147assert(minint // minint == 1)
148assert((minint + 1) // minint == 0)
149assert(minint // (minint + 1) == 1)
150assert(minint // 1 == minint)
151
152assert(minint // -1 == -minint)
153assert(minint // -2 == 2^(intbits - 2))
154assert(maxint // -1 == -maxint)
155
156
157-- negative exponents
158do
159 assert(2^-3 == 1 / 2^3)
160 assert(eq((-3)^-3, 1 / (-3)^3))
161 for i = -3, 3 do -- variables avoid constant folding
162 for j = -3, 3 do
163 -- domain errors (0^(-n)) are not portable
164 if not _port or i ~= 0 or j > 0 then
165 assert(eq(i^j, 1 / i^(-j)))
166 end
167 end
168 end
169end
170
171-- comparison between floats and integers (border cases)
172if floatbits < intbits then
173 assert(2.0^floatbits == (1 << floatbits))
174 assert(2.0^floatbits - 1.0 == (1 << floatbits) - 1.0)
175 assert(2.0^floatbits - 1.0 ~= (1 << floatbits))
176 -- float is rounded, int is not
177 assert(2.0^floatbits + 1.0 ~= (1 << floatbits) + 1)
178else -- floats can express all integers with full accuracy
179 assert(maxint == maxint + 0.0)
180 assert(maxint - 1 == maxint - 1.0)
181 assert(minint + 1 == minint + 1.0)
182 assert(maxint ~= maxint - 1.0)
183end
184assert(maxint + 0.0 == 2.0^(intbits - 1) - 1.0)
185assert(minint + 0.0 == minint)
186assert(minint + 0.0 == -2.0^(intbits - 1))
187
188
189-- order between floats and integers
190assert(1 < 1.1); assert(not (1 < 0.9))
191assert(1 <= 1.1); assert(not (1 <= 0.9))
192assert(-1 < -0.9); assert(not (-1 < -1.1))
193assert(1 <= 1.1); assert(not (-1 <= -1.1))
194assert(-1 < -0.9); assert(not (-1 < -1.1))
195assert(-1 <= -0.9); assert(not (-1 <= -1.1))
196assert(minint <= minint + 0.0)
197assert(minint + 0.0 <= minint)
198assert(not (minint < minint + 0.0))
199assert(not (minint + 0.0 < minint))
200assert(maxint < minint * -1.0)
201assert(maxint <= minint * -1.0)
202
203do
204 local fmaxi1 = 2^(intbits - 1)
205 assert(maxint < fmaxi1)
206 assert(maxint <= fmaxi1)
207 assert(not (fmaxi1 <= maxint))
208 assert(minint <= -2^(intbits - 1))
209 assert(-2^(intbits - 1) <= minint)
210end
211
212if floatbits < intbits then
213 print("testing order (floats cannot represent all integers)")
214 local fmax = 2^floatbits
215 local ifmax = fmax | 0
216 assert(fmax < ifmax + 1)
217 assert(fmax - 1 < ifmax)
218 assert(-(fmax - 1) > -ifmax)
219 assert(not (fmax <= ifmax - 1))
220 assert(-fmax > -(ifmax + 1))
221 assert(not (-fmax >= -(ifmax - 1)))
222
223 assert(fmax/2 - 0.5 < ifmax//2)
224 assert(-(fmax/2 - 0.5) > -ifmax//2)
225
226 assert(maxint < 2^intbits)
227 assert(minint > -2^intbits)
228 assert(maxint <= 2^intbits)
229 assert(minint >= -2^intbits)
230else
231 print("testing order (floats can represent all integers)")
232 assert(maxint < maxint + 1.0)
233 assert(maxint < maxint + 0.5)
234 assert(maxint - 1.0 < maxint)
235 assert(maxint - 0.5 < maxint)
236 assert(not (maxint + 0.0 < maxint))
237 assert(maxint + 0.0 <= maxint)
238 assert(not (maxint < maxint + 0.0))
239 assert(maxint + 0.0 <= maxint)
240 assert(maxint <= maxint + 0.0)
241 assert(not (maxint + 1.0 <= maxint))
242 assert(not (maxint + 0.5 <= maxint))
243 assert(not (maxint <= maxint - 1.0))
244 assert(not (maxint <= maxint - 0.5))
245
246 assert(minint < minint + 1.0)
247 assert(minint < minint + 0.5)
248 assert(minint <= minint + 0.5)
249 assert(minint - 1.0 < minint)
250 assert(minint - 1.0 <= minint)
251 assert(not (minint + 0.0 < minint))
252 assert(not (minint + 0.5 < minint))
253 assert(not (minint < minint + 0.0))
254 assert(minint + 0.0 <= minint)
255 assert(minint <= minint + 0.0)
256 assert(not (minint + 1.0 <= minint))
257 assert(not (minint + 0.5 <= minint))
258 assert(not (minint <= minint - 1.0))
259end
260
261do
262 local NaN = 0/0
263 assert(not (NaN < 0))
264 assert(not (NaN > minint))
265 assert(not (NaN <= -9))
266 assert(not (NaN <= maxint))
267 assert(not (NaN < maxint))
268 assert(not (minint <= NaN))
269 assert(not (minint < NaN))
270end
271
272
273-- avoiding errors at compile time
274local function checkcompt (msg, code)
275 checkerror(msg, assert(load(code)))
276end
277checkcompt("divide by zero", "return 2 // 0")
278checkcompt(msgf2i, "return 2.3 >> 0")
279checkcompt(msgf2i, ("return 2.0^%d & 1"):format(intbits - 1))
280checkcompt("field 'huge'", "return math.huge << 1")
281checkcompt(msgf2i, ("return 1 | 2.0^%d"):format(intbits - 1))
282checkcompt(msgf2i, "return 2.3 ~ '0.0'")
283
284
285-- testing overflow errors when converting from float to integer (runtime)
286local function f2i (x) return x | x end
287checkerror(msgf2i, f2i, math.huge) -- +inf
288checkerror(msgf2i, f2i, -math.huge) -- -inf
289checkerror(msgf2i, f2i, 0/0) -- NaN
290
291if floatbits < intbits then
292 -- conversion tests when float cannot represent all integers
293 assert(maxint + 1.0 == maxint + 0.0)
294 assert(minint - 1.0 == minint + 0.0)
295 checkerror(msgf2i, f2i, maxint + 0.0)
296 assert(f2i(2.0^(intbits - 2)) == 1 << (intbits - 2))
297 assert(f2i(-2.0^(intbits - 2)) == -(1 << (intbits - 2)))
298 assert((2.0^(floatbits - 1) + 1.0) // 1 == (1 << (floatbits - 1)) + 1)
299 -- maximum integer representable as a float
300 local mf = maxint - (1 << (floatbits - intbits)) + 1
301 assert(f2i(mf + 0.0) == mf) -- OK up to here
302 mf = mf + 1
303 assert(f2i(mf + 0.0) ~= mf) -- no more representable
304else
305 -- conversion tests when float can represent all integers
306 assert(maxint + 1.0 > maxint)
307 assert(minint - 1.0 < minint)
308 assert(f2i(maxint + 0.0) == maxint)
309 checkerror("no integer rep", f2i, maxint + 1.0)
310 checkerror("no integer rep", f2i, minint - 1.0)
311end
312
313-- 'minint' should be representable as a float no matter the precision
314assert(f2i(minint + 0.0) == minint)
315
316
317-- testing numeric strings
318
319assert("2" + 1 == 3)
320assert("2 " + 1 == 3)
321assert(" -2 " + 1 == -1)
322assert(" -0xa " + 1 == -9)
323
324
325-- Literal integer Overflows (new behavior in 5.3.3)
326do
327 -- no overflows
328 assert(eqT(tonumber(tostring(maxint)), maxint))
329 assert(eqT(tonumber(tostring(minint)), minint))
330
331 -- add 1 to last digit as a string (it cannot be 9...)
332 local function incd (n)
333 local s = string.format("%d", n)
334 s = string.gsub(s, "%d$", function (d)
335 assert(d ~= '9')
336 return string.char(string.byte(d) + 1)
337 end)
338 return s
339 end
340
341 -- 'tonumber' with overflow by 1
342 assert(eqT(tonumber(incd(maxint)), maxint + 1.0))
343 assert(eqT(tonumber(incd(minint)), minint - 1.0))
344
345 -- large numbers
346 assert(eqT(tonumber("1"..string.rep("0", 30)), 1e30))
347 assert(eqT(tonumber("-1"..string.rep("0", 30)), -1e30))
348
349 -- hexa format still wraps around
350 assert(eqT(tonumber("0x1"..string.rep("0", 30)), 0))
351
352 -- lexer in the limits
353 assert(minint == load("return " .. minint)())
354 assert(eqT(maxint, load("return " .. maxint)()))
355
356 assert(eqT(10000000000000000000000.0, 10000000000000000000000))
357 assert(eqT(-10000000000000000000000.0, -10000000000000000000000))
358end
359
360
361-- testing 'tonumber'
362
363-- 'tonumber' with numbers
364assert(tonumber(3.4) == 3.4)
365assert(eqT(tonumber(3), 3))
366assert(eqT(tonumber(maxint), maxint) and eqT(tonumber(minint), minint))
367assert(tonumber(1/0) == 1/0)
368
369-- 'tonumber' with strings
370assert(tonumber("0") == 0)
371assert(tonumber("") == nil)
372assert(tonumber(" ") == nil)
373assert(tonumber("-") == nil)
374assert(tonumber(" -0x ") == nil)
375assert(tonumber{} == nil)
376assert(tonumber'+0.01' == 1/100 and tonumber'+.01' == 0.01 and
377 tonumber'.01' == 0.01 and tonumber'-1.' == -1 and
378 tonumber'+1.' == 1)
379assert(tonumber'+ 0.01' == nil and tonumber'+.e1' == nil and
380 tonumber'1e' == nil and tonumber'1.0e+' == nil and
381 tonumber'.' == nil)
382assert(tonumber('-012') == -010-2)
383assert(tonumber('-1.2e2') == - - -120)
384
385assert(tonumber("0xffffffffffff") == (1 << (4*12)) - 1)
386assert(tonumber("0x"..string.rep("f", (intbits//4))) == -1)
387assert(tonumber("-0x"..string.rep("f", (intbits//4))) == 1)
388
389-- testing 'tonumber' with base
390assert(tonumber(' 001010 ', 2) == 10)
391assert(tonumber(' 001010 ', 10) == 001010)
392assert(tonumber(' -1010 ', 2) == -10)
393assert(tonumber('10', 36) == 36)
394assert(tonumber(' -10 ', 36) == -36)
395assert(tonumber(' +1Z ', 36) == 36 + 35)
396assert(tonumber(' -1z ', 36) == -36 + -35)
397assert(tonumber('-fFfa', 16) == -(10+(16*(15+(16*(15+(16*15)))))))
398assert(tonumber(string.rep('1', (intbits - 2)), 2) + 1 == 2^(intbits - 2))
399assert(tonumber('ffffFFFF', 16)+1 == (1 << 32))
400assert(tonumber('0ffffFFFF', 16)+1 == (1 << 32))
401assert(tonumber('-0ffffffFFFF', 16) - 1 == -(1 << 40))
402for i = 2,36 do
403 local i2 = i * i
404 local i10 = i2 * i2 * i2 * i2 * i2 -- i^10
405 assert(tonumber('\t10000000000\t', i) == i10)
406end
407
408if not _soft then
409 -- tests with very long numerals
410 assert(tonumber("0x"..string.rep("f", 13)..".0") == 2.0^(4*13) - 1)
411 assert(tonumber("0x"..string.rep("f", 150)..".0") == 2.0^(4*150) - 1)
412 assert(tonumber("0x"..string.rep("f", 300)..".0") == 2.0^(4*300) - 1)
413 assert(tonumber("0x"..string.rep("f", 500)..".0") == 2.0^(4*500) - 1)
414 assert(tonumber('0x3.' .. string.rep('0', 1000)) == 3)
415 assert(tonumber('0x' .. string.rep('0', 1000) .. 'a') == 10)
416 assert(tonumber('0x0.' .. string.rep('0', 13).."1") == 2.0^(-4*14))
417 assert(tonumber('0x0.' .. string.rep('0', 150).."1") == 2.0^(-4*151))
418 assert(tonumber('0x0.' .. string.rep('0', 300).."1") == 2.0^(-4*301))
419 assert(tonumber('0x0.' .. string.rep('0', 500).."1") == 2.0^(-4*501))
420
421 assert(tonumber('0xe03' .. string.rep('0', 1000) .. 'p-4000') == 3587.0)
422 assert(tonumber('0x.' .. string.rep('0', 1000) .. '74p4004') == 0x7.4)
423end
424
425-- testing 'tonumber' for invalid formats
426
427local function f (...)
428 if select('#', ...) == 1 then
429 return (...)
430 else
431 return "***"
432 end
433end
434
435assert(f(tonumber('fFfa', 15)) == nil)
436assert(f(tonumber('099', 8)) == nil)
437assert(f(tonumber('1\0', 2)) == nil)
438assert(f(tonumber('', 8)) == nil)
439assert(f(tonumber(' ', 9)) == nil)
440assert(f(tonumber(' ', 9)) == nil)
441assert(f(tonumber('0xf', 10)) == nil)
442
443assert(f(tonumber('inf')) == nil)
444assert(f(tonumber(' INF ')) == nil)
445assert(f(tonumber('Nan')) == nil)
446assert(f(tonumber('nan')) == nil)
447
448assert(f(tonumber(' ')) == nil)
449assert(f(tonumber('')) == nil)
450assert(f(tonumber('1 a')) == nil)
451assert(f(tonumber('1 a', 2)) == nil)
452assert(f(tonumber('1\0')) == nil)
453assert(f(tonumber('1 \0')) == nil)
454assert(f(tonumber('1\0 ')) == nil)
455assert(f(tonumber('e1')) == nil)
456assert(f(tonumber('e 1')) == nil)
457assert(f(tonumber(' 3.4.5 ')) == nil)
458
459
460-- testing 'tonumber' for invalid hexadecimal formats
461
462assert(tonumber('0x') == nil)
463assert(tonumber('x') == nil)
464assert(tonumber('x3') == nil)
465assert(tonumber('0x3.3.3') == nil) -- two decimal points
466assert(tonumber('00x2') == nil)
467assert(tonumber('0x 2') == nil)
468assert(tonumber('0 x2') == nil)
469assert(tonumber('23x') == nil)
470assert(tonumber('- 0xaa') == nil)
471assert(tonumber('-0xaaP ') == nil) -- no exponent
472assert(tonumber('0x0.51p') == nil)
473assert(tonumber('0x5p+-2') == nil)
474
475
476-- testing hexadecimal numerals
477
478assert(0x10 == 16 and 0xfff == 2^12 - 1 and 0XFB == 251)
479assert(0x0p12 == 0 and 0x.0p-3 == 0)
480assert(0xFFFFFFFF == (1 << 32) - 1)
481assert(tonumber('+0x2') == 2)
482assert(tonumber('-0xaA') == -170)
483assert(tonumber('-0xffFFFfff') == -(1 << 32) + 1)
484
485-- possible confusion with decimal exponent
486assert(0E+1 == 0 and 0xE+1 == 15 and 0xe-1 == 13)
487
488
489-- floating hexas
490
491assert(tonumber(' 0x2.5 ') == 0x25/16)
492assert(tonumber(' -0x2.5 ') == -0x25/16)
493assert(tonumber(' +0x0.51p+8 ') == 0x51)
494assert(0x.FfffFFFF == 1 - '0x.00000001')
495assert('0xA.a' + 0 == 10 + 10/16)
496assert(0xa.aP4 == 0XAA)
497assert(0x4P-2 == 1)
498assert(0x1.1 == '0x1.' + '+0x.1')
499assert(0Xabcdef.0 == 0x.ABCDEFp+24)
500
501
502assert(1.1 == 1.+.1)
503assert(100.0 == 1E2 and .01 == 1e-2)
504assert(1111111111 - 1111111110 == 1000.00e-03)
505assert(1.1 == '1.'+'.1')
506assert(tonumber'1111111111' - tonumber'1111111110' ==
507 tonumber" +0.001e+3 \n\t")
508
509assert(0.1e-30 > 0.9E-31 and 0.9E30 < 0.1e31)
510
511assert(0.123456 > 0.123455)
512
513assert(tonumber('+1.23E18') == 1.23*10.0^18)
514
515-- testing order operators
516assert(not(1<1) and (1<2) and not(2<1))
517assert(not('a'<'a') and ('a'<'b') and not('b'<'a'))
518assert((1<=1) and (1<=2) and not(2<=1))
519assert(('a'<='a') and ('a'<='b') and not('b'<='a'))
520assert(not(1>1) and not(1>2) and (2>1))
521assert(not('a'>'a') and not('a'>'b') and ('b'>'a'))
522assert((1>=1) and not(1>=2) and (2>=1))
523assert(('a'>='a') and not('a'>='b') and ('b'>='a'))
524assert(1.3 < 1.4 and 1.3 <= 1.4 and not (1.3 < 1.3) and 1.3 <= 1.3)
525
526-- testing mod operator
527assert(eqT(-4 % 3, 2))
528assert(eqT(4 % -3, -2))
529assert(eqT(-4.0 % 3, 2.0))
530assert(eqT(4 % -3.0, -2.0))
531assert(math.pi - math.pi % 1 == 3)
532assert(math.pi - math.pi % 0.001 == 3.141)
533
534assert(eqT(minint % minint, 0))
535assert(eqT(maxint % maxint, 0))
536assert((minint + 1) % minint == minint + 1)
537assert((maxint - 1) % maxint == maxint - 1)
538assert(minint % maxint == maxint - 1)
539
540assert(minint % -1 == 0)
541assert(minint % -2 == 0)
542assert(maxint % -2 == -1)
543
544-- non-portable tests because Windows C library cannot compute
545-- fmod(1, huge) correctly
546if not _port then
547 local function anan (x) assert(isNaN(x)) end -- assert Not a Number
548 anan(0.0 % 0)
549 anan(1.3 % 0)
550 anan(math.huge % 1)
551 anan(math.huge % 1e30)
552 anan(-math.huge % 1e30)
553 anan(-math.huge % -1e30)
554 assert(1 % math.huge == 1)
555 assert(1e30 % math.huge == 1e30)
556 assert(1e30 % -math.huge == -math.huge)
557 assert(-1 % math.huge == math.huge)
558 assert(-1 % -math.huge == -1)
559end
560
561
562-- testing unsigned comparisons
563assert(math.ult(3, 4))
564assert(not math.ult(4, 4))
565assert(math.ult(-2, -1))
566assert(math.ult(2, -1))
567assert(not math.ult(-2, -2))
568assert(math.ult(maxint, minint))
569assert(not math.ult(minint, maxint))
570
571
572assert(eq(math.sin(-9.8)^2 + math.cos(-9.8)^2, 1))
573assert(eq(math.tan(math.pi/4), 1))
574assert(eq(math.sin(math.pi/2), 1) and eq(math.cos(math.pi/2), 0))
575assert(eq(math.atan(1), math.pi/4) and eq(math.acos(0), math.pi/2) and
576 eq(math.asin(1), math.pi/2))
577assert(eq(math.deg(math.pi/2), 90) and eq(math.rad(90), math.pi/2))
578assert(math.abs(-10.43) == 10.43)
579assert(eqT(math.abs(minint), minint))
580assert(eqT(math.abs(maxint), maxint))
581assert(eqT(math.abs(-maxint), maxint))
582assert(eq(math.atan(1,0), math.pi/2))
583assert(math.fmod(10,3) == 1)
584assert(eq(math.sqrt(10)^2, 10))
585assert(eq(math.log(2, 10), math.log(2)/math.log(10)))
586assert(eq(math.log(2, 2), 1))
587assert(eq(math.log(9, 3), 2))
588assert(eq(math.exp(0), 1))
589assert(eq(math.sin(10), math.sin(10%(2*math.pi))))
590
591
592assert(tonumber(' 1.3e-2 ') == 1.3e-2)
593assert(tonumber(' -1.00000000000001 ') == -1.00000000000001)
594
595-- testing constant limits
596-- 2^23 = 8388608
597assert(8388609 + -8388609 == 0)
598assert(8388608 + -8388608 == 0)
599assert(8388607 + -8388607 == 0)
600
601
602
603do -- testing floor & ceil
604 assert(eqT(math.floor(3.4), 3))
605 assert(eqT(math.ceil(3.4), 4))
606 assert(eqT(math.floor(-3.4), -4))
607 assert(eqT(math.ceil(-3.4), -3))
608 assert(eqT(math.floor(maxint), maxint))
609 assert(eqT(math.ceil(maxint), maxint))
610 assert(eqT(math.floor(minint), minint))
611 assert(eqT(math.floor(minint + 0.0), minint))
612 assert(eqT(math.ceil(minint), minint))
613 assert(eqT(math.ceil(minint + 0.0), minint))
614 assert(math.floor(1e50) == 1e50)
615 assert(math.ceil(1e50) == 1e50)
616 assert(math.floor(-1e50) == -1e50)
617 assert(math.ceil(-1e50) == -1e50)
618 for _, p in pairs{31,32,63,64} do
619 assert(math.floor(2^p) == 2^p)
620 assert(math.floor(2^p + 0.5) == 2^p)
621 assert(math.ceil(2^p) == 2^p)
622 assert(math.ceil(2^p - 0.5) == 2^p)
623 end
624 checkerror("number expected", math.floor, {})
625 checkerror("number expected", math.ceil, print)
626 assert(eqT(math.tointeger(minint), minint))
627 assert(eqT(math.tointeger(minint .. ""), minint))
628 assert(eqT(math.tointeger(maxint), maxint))
629 assert(eqT(math.tointeger(maxint .. ""), maxint))
630 assert(eqT(math.tointeger(minint + 0.0), minint))
631 assert(math.tointeger(0.0 - minint) == nil)
632 assert(math.tointeger(math.pi) == nil)
633 assert(math.tointeger(-math.pi) == nil)
634 assert(math.floor(math.huge) == math.huge)
635 assert(math.ceil(math.huge) == math.huge)
636 assert(math.tointeger(math.huge) == nil)
637 assert(math.floor(-math.huge) == -math.huge)
638 assert(math.ceil(-math.huge) == -math.huge)
639 assert(math.tointeger(-math.huge) == nil)
640 assert(math.tointeger("34.0") == 34)
641 assert(math.tointeger("34.3") == nil)
642 assert(math.tointeger({}) == nil)
643 assert(math.tointeger(0/0) == nil) -- NaN
644end
645
646
647-- testing fmod for integers
648for i = -6, 6 do
649 for j = -6, 6 do
650 if j ~= 0 then
651 local mi = math.fmod(i, j)
652 local mf = math.fmod(i + 0.0, j)
653 assert(mi == mf)
654 assert(math.type(mi) == 'integer' and math.type(mf) == 'float')
655 if (i >= 0 and j >= 0) or (i <= 0 and j <= 0) or mi == 0 then
656 assert(eqT(mi, i % j))
657 end
658 end
659 end
660end
661assert(eqT(math.fmod(minint, minint), 0))
662assert(eqT(math.fmod(maxint, maxint), 0))
663assert(eqT(math.fmod(minint + 1, minint), minint + 1))
664assert(eqT(math.fmod(maxint - 1, maxint), maxint - 1))
665
666checkerror("zero", math.fmod, 3, 0)
667
668
669do -- testing max/min
670 checkerror("value expected", math.max)
671 checkerror("value expected", math.min)
672 assert(eqT(math.max(3), 3))
673 assert(eqT(math.max(3, 5, 9, 1), 9))
674 assert(math.max(maxint, 10e60) == 10e60)
675 assert(eqT(math.max(minint, minint + 1), minint + 1))
676 assert(eqT(math.min(3), 3))
677 assert(eqT(math.min(3, 5, 9, 1), 1))
678 assert(math.min(3.2, 5.9, -9.2, 1.1) == -9.2)
679 assert(math.min(1.9, 1.7, 1.72) == 1.7)
680 assert(math.min(-10e60, minint) == -10e60)
681 assert(eqT(math.min(maxint, maxint - 1), maxint - 1))
682 assert(eqT(math.min(maxint - 2, maxint, maxint - 1), maxint - 2))
683end
684-- testing implicit convertions
685
686local a,b = '10', '20'
687assert(a*b == 200 and a+b == 30 and a-b == -10 and a/b == 0.5 and -b == -20)
688assert(a == '10' and b == '20')
689
690
691do
692 print("testing -0 and NaN")
693 local mz, z = -0.0, 0.0
694 assert(mz == z)
695 assert(1/mz < 0 and 0 < 1/z)
696 local a = {[mz] = 1}
697 assert(a[z] == 1 and a[mz] == 1)
698 a[z] = 2
699 assert(a[z] == 2 and a[mz] == 2)
700 local inf = math.huge * 2 + 1
701 mz, z = -1/inf, 1/inf
702 assert(mz == z)
703 assert(1/mz < 0 and 0 < 1/z)
704 local NaN = inf - inf
705 assert(NaN ~= NaN)
706 assert(not (NaN < NaN))
707 assert(not (NaN <= NaN))
708 assert(not (NaN > NaN))
709 assert(not (NaN >= NaN))
710 assert(not (0 < NaN) and not (NaN < 0))
711 local NaN1 = 0/0
712 assert(NaN ~= NaN1 and not (NaN <= NaN1) and not (NaN1 <= NaN))
713 local a = {}
714 assert(not pcall(rawset, a, NaN, 1))
715 assert(a[NaN] == nil)
716 a[1] = 1
717 assert(not pcall(rawset, a, NaN, 1))
718 assert(a[NaN] == nil)
719 -- strings with same binary representation as 0.0 (might create problems
720 -- for constant manipulation in the pre-compiler)
721 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"
722 assert(a1 == a2 and a2 == a4 and a1 ~= a3)
723 assert(a3 == a5)
724end
725
726
727print("testing 'math.random'")
728math.randomseed(0)
729
730do -- test random for floats
731 local max = -math.huge
732 local min = math.huge
733 for i = 0, 20000 do
734 local t = math.random()
735 assert(0 <= t and t < 1)
736 max = math.max(max, t)
737 min = math.min(min, t)
738 if eq(max, 1, 0.001) and eq(min, 0, 0.001) then
739 goto ok
740 end
741 end
742 -- loop ended without satisfing condition
743 assert(false)
744 ::ok::
745end
746
747do
748 local function aux (p, lim) -- test random for small intervals
749 local x1, x2
750 if #p == 1 then x1 = 1; x2 = p[1]
751 else x1 = p[1]; x2 = p[2]
752 end
753 local mark = {}; local count = 0 -- to check that all values appeared
754 for i = 0, lim or 2000 do
755 local t = math.random(table.unpack(p))
756 assert(x1 <= t and t <= x2)
757 if not mark[t] then -- new value
758 mark[t] = true
759 count = count + 1
760 end
761 if count == x2 - x1 + 1 then -- all values appeared; OK
762 goto ok
763 end
764 end
765 -- loop ended without satisfing condition
766 assert(false)
767 ::ok::
768 end
769
770 aux({-10,0})
771 aux({6})
772 aux({-10, 10})
773 aux({minint, minint})
774 aux({maxint, maxint})
775 aux({minint, minint + 9})
776 aux({maxint - 3, maxint})
777end
778
779do
780 local function aux(p1, p2) -- test random for large intervals
781 local max = minint
782 local min = maxint
783 local n = 200
784 local mark = {}; local count = 0 -- to count how many different values
785 for _ = 1, n do
786 local t = math.random(p1, p2)
787 max = math.max(max, t)
788 min = math.min(min, t)
789 if not mark[t] then -- new value
790 mark[t] = true
791 count = count + 1
792 end
793 end
794 -- at least 80% of values are different
795 assert(count >= n * 0.8)
796 -- min and max not too far from formal min and max
797 local diff = (p2 - p1) // 8
798 assert(min < p1 + diff and max > p2 - diff)
799 end
800 aux(0, maxint)
801 aux(1, maxint)
802 aux(minint, -1)
803 aux(minint // 2, maxint // 2)
804end
805
806for i=1,100 do
807 assert(math.random(maxint) > 0)
808 assert(math.random(minint, -1) < 0)
809end
810
811assert(not pcall(math.random, 1, 2, 3)) -- too many arguments
812
813-- empty interval
814assert(not pcall(math.random, minint + 1, minint))
815assert(not pcall(math.random, maxint, maxint - 1))
816assert(not pcall(math.random, maxint, minint))
817
818-- interval too large
819assert(not pcall(math.random, minint, 0))
820assert(not pcall(math.random, -1, maxint))
821assert(not pcall(math.random, minint // 2, maxint // 2 + 1))
822
823
824print('OK')