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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 | |||
4 | print("testing numbers and math lib") | ||
5 | |||
6 | local minint = math.mininteger | ||
7 | local maxint = math.maxinteger | ||
8 | |||
9 | local intbits = math.floor(math.log(maxint, 2) + 0.5) + 1 | ||
10 | assert((1 << intbits) == 0) | ||
11 | |||
12 | assert(minint == 1 << (intbits - 1)) | ||
13 | assert(maxint == minint - 1) | ||
14 | |||
15 | -- number of bits in the mantissa of a floating-point number | ||
16 | local floatbits = 24 | ||
17 | do | ||
18 | local p = 2.0^floatbits | ||
19 | while p < p + 1.0 do | ||
20 | p = p * 2.0 | ||
21 | floatbits = floatbits + 1 | ||
22 | end | ||
23 | end | ||
24 | |||
25 | local function isNaN (x) | ||
26 | return (x ~= x) | ||
27 | end | ||
28 | |||
29 | assert(isNaN(0/0)) | ||
30 | assert(not isNaN(1/0)) | ||
31 | |||
32 | |||
33 | do | ||
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)) | ||
39 | end | ||
40 | |||
41 | assert(math.type(0) == "integer" and math.type(0.0) == "float" | ||
42 | and math.type("10") == nil) | ||
43 | |||
44 | |||
45 | local function checkerror (msg, f, ...) | ||
46 | local s, err = pcall(f, ...) | ||
47 | assert(not s and string.find(err, msg)) | ||
48 | end | ||
49 | |||
50 | local msgf2i = "number.* has no integer representation" | ||
51 | |||
52 | -- float equality | ||
53 | function 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 | ||
61 | end | ||
62 | |||
63 | |||
64 | -- equality with types | ||
65 | function eqT (a,b) | ||
66 | return a == b and math.type(a) == math.type(b) | ||
67 | end | ||
68 | |||
69 | |||
70 | -- basic float notation | ||
71 | assert(0e12 == 0 and .0 == 0 and 0. == 0 and .2e2 == 20 and 2.E-1 == 0.2) | ||
72 | |||
73 | do | ||
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) | ||
81 | end | ||
82 | |||
83 | do | ||
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]) | ||
88 | end | ||
89 | |||
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)) | ||
109 | end | ||
110 | |||
111 | assert(math.huge > 10e30) | ||
112 | assert(-math.huge < -10e30) | ||
113 | |||
114 | |||
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) | ||
121 | |||
122 | |||
123 | -- testing floor division and conversions | ||
124 | |||
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 | ||
129 | local x = i + ti | ||
130 | local y = j + tj | ||
131 | assert(i//j == math.floor(i/j)) | ||
132 | end | ||
133 | end | ||
134 | end | ||
135 | end | ||
136 | |||
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)) | ||
141 | |||
142 | assert(maxint // maxint == 1) | ||
143 | assert(maxint // 1 == maxint) | ||
144 | assert((maxint - 1) // maxint == 0) | ||
145 | assert(maxint // (maxint - 1) == 1) | ||
146 | assert(minint // minint == 1) | ||
147 | assert(minint // minint == 1) | ||
148 | assert((minint + 1) // minint == 0) | ||
149 | assert(minint // (minint + 1) == 1) | ||
150 | assert(minint // 1 == minint) | ||
151 | |||
152 | assert(minint // -1 == -minint) | ||
153 | assert(minint // -2 == 2^(intbits - 2)) | ||
154 | assert(maxint // -1 == -maxint) | ||
155 | |||
156 | |||
157 | -- negative exponents | ||
158 | do | ||
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 | ||
169 | end | ||
170 | |||
171 | -- comparison between floats and integers (border cases) | ||
172 | if 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) | ||
178 | else -- 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) | ||
183 | end | ||
184 | assert(maxint + 0.0 == 2.0^(intbits - 1) - 1.0) | ||
185 | assert(minint + 0.0 == minint) | ||
186 | assert(minint + 0.0 == -2.0^(intbits - 1)) | ||
187 | |||
188 | |||
189 | -- order between floats and integers | ||
190 | assert(1 < 1.1); assert(not (1 < 0.9)) | ||
191 | assert(1 <= 1.1); assert(not (1 <= 0.9)) | ||
192 | assert(-1 < -0.9); assert(not (-1 < -1.1)) | ||
193 | assert(1 <= 1.1); assert(not (-1 <= -1.1)) | ||
194 | assert(-1 < -0.9); assert(not (-1 < -1.1)) | ||
195 | assert(-1 <= -0.9); assert(not (-1 <= -1.1)) | ||
196 | assert(minint <= minint + 0.0) | ||
197 | assert(minint + 0.0 <= minint) | ||
198 | assert(not (minint < minint + 0.0)) | ||
199 | assert(not (minint + 0.0 < minint)) | ||
200 | assert(maxint < minint * -1.0) | ||
201 | assert(maxint <= minint * -1.0) | ||
202 | |||
203 | do | ||
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) | ||
210 | end | ||
211 | |||
212 | if 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) | ||
230 | else | ||
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)) | ||
259 | end | ||
260 | |||
261 | do | ||
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)) | ||
270 | end | ||
271 | |||
272 | |||
273 | -- avoiding errors at compile time | ||
274 | local function checkcompt (msg, code) | ||
275 | checkerror(msg, assert(load(code))) | ||
276 | end | ||
277 | checkcompt("divide by zero", "return 2 // 0") | ||
278 | checkcompt(msgf2i, "return 2.3 >> 0") | ||
279 | checkcompt(msgf2i, ("return 2.0^%d & 1"):format(intbits - 1)) | ||
280 | checkcompt("field 'huge'", "return math.huge << 1") | ||
281 | checkcompt(msgf2i, ("return 1 | 2.0^%d"):format(intbits - 1)) | ||
282 | checkcompt(msgf2i, "return 2.3 ~ '0.0'") | ||
283 | |||
284 | |||
285 | -- testing overflow errors when converting from float to integer (runtime) | ||
286 | local function f2i (x) return x | x end | ||
287 | checkerror(msgf2i, f2i, math.huge) -- +inf | ||
288 | checkerror(msgf2i, f2i, -math.huge) -- -inf | ||
289 | checkerror(msgf2i, f2i, 0/0) -- NaN | ||
290 | |||
291 | if 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 | ||
304 | else | ||
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) | ||
311 | end | ||
312 | |||
313 | -- 'minint' should be representable as a float no matter the precision | ||
314 | assert(f2i(minint + 0.0) == minint) | ||
315 | |||
316 | |||
317 | -- testing numeric strings | ||
318 | |||
319 | assert("2" + 1 == 3) | ||
320 | assert("2 " + 1 == 3) | ||
321 | assert(" -2 " + 1 == -1) | ||
322 | assert(" -0xa " + 1 == -9) | ||
323 | |||
324 | |||
325 | -- Literal integer Overflows (new behavior in 5.3.3) | ||
326 | do | ||
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)) | ||
358 | end | ||
359 | |||
360 | |||
361 | -- testing 'tonumber' | ||
362 | |||
363 | -- 'tonumber' with numbers | ||
364 | assert(tonumber(3.4) == 3.4) | ||
365 | assert(eqT(tonumber(3), 3)) | ||
366 | assert(eqT(tonumber(maxint), maxint) and eqT(tonumber(minint), minint)) | ||
367 | assert(tonumber(1/0) == 1/0) | ||
368 | |||
369 | -- 'tonumber' with strings | ||
370 | assert(tonumber("0") == 0) | ||
371 | assert(tonumber("") == nil) | ||
372 | assert(tonumber(" ") == nil) | ||
373 | assert(tonumber("-") == nil) | ||
374 | assert(tonumber(" -0x ") == nil) | ||
375 | assert(tonumber{} == nil) | ||
376 | assert(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) | ||
379 | assert(tonumber'+ 0.01' == nil and tonumber'+.e1' == nil and | ||
380 | tonumber'1e' == nil and tonumber'1.0e+' == nil and | ||
381 | tonumber'.' == nil) | ||
382 | assert(tonumber('-012') == -010-2) | ||
383 | assert(tonumber('-1.2e2') == - - -120) | ||
384 | |||
385 | assert(tonumber("0xffffffffffff") == (1 << (4*12)) - 1) | ||
386 | assert(tonumber("0x"..string.rep("f", (intbits//4))) == -1) | ||
387 | assert(tonumber("-0x"..string.rep("f", (intbits//4))) == 1) | ||
388 | |||
389 | -- testing 'tonumber' with base | ||
390 | assert(tonumber(' 001010 ', 2) == 10) | ||
391 | assert(tonumber(' 001010 ', 10) == 001010) | ||
392 | assert(tonumber(' -1010 ', 2) == -10) | ||
393 | assert(tonumber('10', 36) == 36) | ||
394 | assert(tonumber(' -10 ', 36) == -36) | ||
395 | assert(tonumber(' +1Z ', 36) == 36 + 35) | ||
396 | assert(tonumber(' -1z ', 36) == -36 + -35) | ||
397 | assert(tonumber('-fFfa', 16) == -(10+(16*(15+(16*(15+(16*15))))))) | ||
398 | assert(tonumber(string.rep('1', (intbits - 2)), 2) + 1 == 2^(intbits - 2)) | ||
399 | assert(tonumber('ffffFFFF', 16)+1 == (1 << 32)) | ||
400 | assert(tonumber('0ffffFFFF', 16)+1 == (1 << 32)) | ||
401 | assert(tonumber('-0ffffffFFFF', 16) - 1 == -(1 << 40)) | ||
402 | for 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) | ||
406 | end | ||
407 | |||
408 | if 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) | ||
423 | end | ||
424 | |||
425 | -- testing 'tonumber' for invalid formats | ||
426 | |||
427 | local function f (...) | ||
428 | if select('#', ...) == 1 then | ||
429 | return (...) | ||
430 | else | ||
431 | return "***" | ||
432 | end | ||
433 | end | ||
434 | |||
435 | assert(f(tonumber('fFfa', 15)) == nil) | ||
436 | assert(f(tonumber('099', 8)) == nil) | ||
437 | assert(f(tonumber('1\0', 2)) == nil) | ||
438 | assert(f(tonumber('', 8)) == nil) | ||
439 | assert(f(tonumber(' ', 9)) == nil) | ||
440 | assert(f(tonumber(' ', 9)) == nil) | ||
441 | assert(f(tonumber('0xf', 10)) == nil) | ||
442 | |||
443 | assert(f(tonumber('inf')) == nil) | ||
444 | assert(f(tonumber(' INF ')) == nil) | ||
445 | assert(f(tonumber('Nan')) == nil) | ||
446 | assert(f(tonumber('nan')) == nil) | ||
447 | |||
448 | assert(f(tonumber(' ')) == nil) | ||
449 | assert(f(tonumber('')) == nil) | ||
450 | assert(f(tonumber('1 a')) == nil) | ||
451 | assert(f(tonumber('1 a', 2)) == nil) | ||
452 | assert(f(tonumber('1\0')) == nil) | ||
453 | assert(f(tonumber('1 \0')) == nil) | ||
454 | assert(f(tonumber('1\0 ')) == nil) | ||
455 | assert(f(tonumber('e1')) == nil) | ||
456 | assert(f(tonumber('e 1')) == nil) | ||
457 | assert(f(tonumber(' 3.4.5 ')) == nil) | ||
458 | |||
459 | |||
460 | -- testing 'tonumber' for invalid hexadecimal formats | ||
461 | |||
462 | assert(tonumber('0x') == nil) | ||
463 | assert(tonumber('x') == nil) | ||
464 | assert(tonumber('x3') == nil) | ||
465 | assert(tonumber('0x3.3.3') == nil) -- two decimal points | ||
466 | assert(tonumber('00x2') == nil) | ||
467 | assert(tonumber('0x 2') == nil) | ||
468 | assert(tonumber('0 x2') == nil) | ||
469 | assert(tonumber('23x') == nil) | ||
470 | assert(tonumber('- 0xaa') == nil) | ||
471 | assert(tonumber('-0xaaP ') == nil) -- no exponent | ||
472 | assert(tonumber('0x0.51p') == nil) | ||
473 | assert(tonumber('0x5p+-2') == nil) | ||
474 | |||
475 | |||
476 | -- testing hexadecimal numerals | ||
477 | |||
478 | assert(0x10 == 16 and 0xfff == 2^12 - 1 and 0XFB == 251) | ||
479 | assert(0x0p12 == 0 and 0x.0p-3 == 0) | ||
480 | assert(0xFFFFFFFF == (1 << 32) - 1) | ||
481 | assert(tonumber('+0x2') == 2) | ||
482 | assert(tonumber('-0xaA') == -170) | ||
483 | assert(tonumber('-0xffFFFfff') == -(1 << 32) + 1) | ||
484 | |||
485 | -- possible confusion with decimal exponent | ||
486 | assert(0E+1 == 0 and 0xE+1 == 15 and 0xe-1 == 13) | ||
487 | |||
488 | |||
489 | -- floating hexas | ||
490 | |||
491 | assert(tonumber(' 0x2.5 ') == 0x25/16) | ||
492 | assert(tonumber(' -0x2.5 ') == -0x25/16) | ||
493 | assert(tonumber(' +0x0.51p+8 ') == 0x51) | ||
494 | assert(0x.FfffFFFF == 1 - '0x.00000001') | ||
495 | assert('0xA.a' + 0 == 10 + 10/16) | ||
496 | assert(0xa.aP4 == 0XAA) | ||
497 | assert(0x4P-2 == 1) | ||
498 | assert(0x1.1 == '0x1.' + '+0x.1') | ||
499 | assert(0Xabcdef.0 == 0x.ABCDEFp+24) | ||
500 | |||
501 | |||
502 | assert(1.1 == 1.+.1) | ||
503 | assert(100.0 == 1E2 and .01 == 1e-2) | ||
504 | assert(1111111111 - 1111111110 == 1000.00e-03) | ||
505 | assert(1.1 == '1.'+'.1') | ||
506 | assert(tonumber'1111111111' - tonumber'1111111110' == | ||
507 | tonumber" +0.001e+3 \n\t") | ||
508 | |||
509 | assert(0.1e-30 > 0.9E-31 and 0.9E30 < 0.1e31) | ||
510 | |||
511 | assert(0.123456 > 0.123455) | ||
512 | |||
513 | assert(tonumber('+1.23E18') == 1.23*10.0^18) | ||
514 | |||
515 | -- testing order operators | ||
516 | assert(not(1<1) and (1<2) and not(2<1)) | ||
517 | assert(not('a'<'a') and ('a'<'b') and not('b'<'a')) | ||
518 | assert((1<=1) and (1<=2) and not(2<=1)) | ||
519 | assert(('a'<='a') and ('a'<='b') and not('b'<='a')) | ||
520 | assert(not(1>1) and not(1>2) and (2>1)) | ||
521 | assert(not('a'>'a') and not('a'>'b') and ('b'>'a')) | ||
522 | assert((1>=1) and not(1>=2) and (2>=1)) | ||
523 | assert(('a'>='a') and not('a'>='b') and ('b'>='a')) | ||
524 | assert(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 | ||
527 | assert(eqT(-4 % 3, 2)) | ||
528 | assert(eqT(4 % -3, -2)) | ||
529 | assert(eqT(-4.0 % 3, 2.0)) | ||
530 | assert(eqT(4 % -3.0, -2.0)) | ||
531 | assert(math.pi - math.pi % 1 == 3) | ||
532 | assert(math.pi - math.pi % 0.001 == 3.141) | ||
533 | |||
534 | assert(eqT(minint % minint, 0)) | ||
535 | assert(eqT(maxint % maxint, 0)) | ||
536 | assert((minint + 1) % minint == minint + 1) | ||
537 | assert((maxint - 1) % maxint == maxint - 1) | ||
538 | assert(minint % maxint == maxint - 1) | ||
539 | |||
540 | assert(minint % -1 == 0) | ||
541 | assert(minint % -2 == 0) | ||
542 | assert(maxint % -2 == -1) | ||
543 | |||
544 | -- non-portable tests because Windows C library cannot compute | ||
545 | -- fmod(1, huge) correctly | ||
546 | if 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) | ||
559 | end | ||
560 | |||
561 | |||
562 | -- testing unsigned comparisons | ||
563 | assert(math.ult(3, 4)) | ||
564 | assert(not math.ult(4, 4)) | ||
565 | assert(math.ult(-2, -1)) | ||
566 | assert(math.ult(2, -1)) | ||
567 | assert(not math.ult(-2, -2)) | ||
568 | assert(math.ult(maxint, minint)) | ||
569 | assert(not math.ult(minint, maxint)) | ||
570 | |||
571 | |||
572 | assert(eq(math.sin(-9.8)^2 + math.cos(-9.8)^2, 1)) | ||
573 | assert(eq(math.tan(math.pi/4), 1)) | ||
574 | assert(eq(math.sin(math.pi/2), 1) and eq(math.cos(math.pi/2), 0)) | ||
575 | assert(eq(math.atan(1), math.pi/4) and eq(math.acos(0), math.pi/2) and | ||
576 | eq(math.asin(1), math.pi/2)) | ||
577 | assert(eq(math.deg(math.pi/2), 90) and eq(math.rad(90), math.pi/2)) | ||
578 | assert(math.abs(-10.43) == 10.43) | ||
579 | assert(eqT(math.abs(minint), minint)) | ||
580 | assert(eqT(math.abs(maxint), maxint)) | ||
581 | assert(eqT(math.abs(-maxint), maxint)) | ||
582 | assert(eq(math.atan(1,0), math.pi/2)) | ||
583 | assert(math.fmod(10,3) == 1) | ||
584 | assert(eq(math.sqrt(10)^2, 10)) | ||
585 | assert(eq(math.log(2, 10), math.log(2)/math.log(10))) | ||
586 | assert(eq(math.log(2, 2), 1)) | ||
587 | assert(eq(math.log(9, 3), 2)) | ||
588 | assert(eq(math.exp(0), 1)) | ||
589 | assert(eq(math.sin(10), math.sin(10%(2*math.pi)))) | ||
590 | |||
591 | |||
592 | assert(tonumber(' 1.3e-2 ') == 1.3e-2) | ||
593 | assert(tonumber(' -1.00000000000001 ') == -1.00000000000001) | ||
594 | |||
595 | -- testing constant limits | ||
596 | -- 2^23 = 8388608 | ||
597 | assert(8388609 + -8388609 == 0) | ||
598 | assert(8388608 + -8388608 == 0) | ||
599 | assert(8388607 + -8388607 == 0) | ||
600 | |||
601 | |||
602 | |||
603 | do -- 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 | ||
644 | end | ||
645 | |||
646 | |||
647 | -- testing fmod for integers | ||
648 | for 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 | ||
660 | end | ||
661 | assert(eqT(math.fmod(minint, minint), 0)) | ||
662 | assert(eqT(math.fmod(maxint, maxint), 0)) | ||
663 | assert(eqT(math.fmod(minint + 1, minint), minint + 1)) | ||
664 | assert(eqT(math.fmod(maxint - 1, maxint), maxint - 1)) | ||
665 | |||
666 | checkerror("zero", math.fmod, 3, 0) | ||
667 | |||
668 | |||
669 | do -- 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)) | ||
683 | end | ||
684 | -- testing implicit convertions | ||
685 | |||
686 | local a,b = '10', '20' | ||
687 | assert(a*b == 200 and a+b == 30 and a-b == -10 and a/b == 0.5 and -b == -20) | ||
688 | assert(a == '10' and b == '20') | ||
689 | |||
690 | |||
691 | do | ||
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) | ||
724 | end | ||
725 | |||
726 | |||
727 | print("testing 'math.random'") | ||
728 | math.randomseed(0) | ||
729 | |||
730 | do -- 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:: | ||
745 | end | ||
746 | |||
747 | do | ||
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}) | ||
777 | end | ||
778 | |||
779 | do | ||
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) | ||
804 | end | ||
805 | |||
806 | for i=1,100 do | ||
807 | assert(math.random(maxint) > 0) | ||
808 | assert(math.random(minint, -1) < 0) | ||
809 | end | ||
810 | |||
811 | assert(not pcall(math.random, 1, 2, 3)) -- too many arguments | ||
812 | |||
813 | -- empty interval | ||
814 | assert(not pcall(math.random, minint + 1, minint)) | ||
815 | assert(not pcall(math.random, maxint, maxint - 1)) | ||
816 | assert(not pcall(math.random, maxint, minint)) | ||
817 | |||
818 | -- interval too large | ||
819 | assert(not pcall(math.random, minint, 0)) | ||
820 | assert(not pcall(math.random, -1, maxint)) | ||
821 | assert(not pcall(math.random, minint // 2, maxint // 2 + 1)) | ||
822 | |||
823 | |||
824 | print('OK') | ||