|
1 ------------------------------------------------------------------------ |
|
2 -- minmag.decTest -- decimal minimum by magnitude -- |
|
3 -- Copyright (c) IBM Corporation, 1981, 2008. All rights reserved. -- |
|
4 ------------------------------------------------------------------------ |
|
5 -- Please see the document "General Decimal Arithmetic Testcases" -- |
|
6 -- at http://www2.hursley.ibm.com/decimal for the description of -- |
|
7 -- these testcases. -- |
|
8 -- -- |
|
9 -- These testcases are experimental ('beta' versions), and they -- |
|
10 -- may contain errors. They are offered on an as-is basis. In -- |
|
11 -- particular, achieving the same results as the tests here is not -- |
|
12 -- a guarantee that an implementation complies with any Standard -- |
|
13 -- or specification. The tests are not exhaustive. -- |
|
14 -- -- |
|
15 -- Please send comments, suggestions, and corrections to the author: -- |
|
16 -- Mike Cowlishaw, IBM Fellow -- |
|
17 -- IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK -- |
|
18 -- mfc@uk.ibm.com -- |
|
19 ------------------------------------------------------------------------ |
|
20 version: 2.58 |
|
21 |
|
22 -- we assume that base comparison is tested in compare.decTest, so |
|
23 -- these mainly cover special cases and rounding |
|
24 |
|
25 extended: 1 |
|
26 precision: 9 |
|
27 rounding: half_up |
|
28 maxExponent: 384 |
|
29 minexponent: -383 |
|
30 |
|
31 -- sanity checks |
|
32 mngx001 minmag -2 -2 -> -2 |
|
33 mngx002 minmag -2 -1 -> -1 |
|
34 mngx003 minmag -2 0 -> 0 |
|
35 mngx004 minmag -2 1 -> 1 |
|
36 mngx005 minmag -2 2 -> -2 |
|
37 mngx006 minmag -1 -2 -> -1 |
|
38 mngx007 minmag -1 -1 -> -1 |
|
39 mngx008 minmag -1 0 -> 0 |
|
40 mngx009 minmag -1 1 -> -1 |
|
41 mngx010 minmag -1 2 -> -1 |
|
42 mngx011 minmag 0 -2 -> 0 |
|
43 mngx012 minmag 0 -1 -> 0 |
|
44 mngx013 minmag 0 0 -> 0 |
|
45 mngx014 minmag 0 1 -> 0 |
|
46 mngx015 minmag 0 2 -> 0 |
|
47 mngx016 minmag 1 -2 -> 1 |
|
48 mngx017 minmag 1 -1 -> -1 |
|
49 mngx018 minmag 1 0 -> 0 |
|
50 mngx019 minmag 1 1 -> 1 |
|
51 mngx020 minmag 1 2 -> 1 |
|
52 mngx021 minmag 2 -2 -> -2 |
|
53 mngx022 minmag 2 -1 -> -1 |
|
54 mngx023 minmag 2 0 -> 0 |
|
55 mngx025 minmag 2 1 -> 1 |
|
56 mngx026 minmag 2 2 -> 2 |
|
57 |
|
58 -- extended zeros |
|
59 mngx030 minmag 0 0 -> 0 |
|
60 mngx031 minmag 0 -0 -> -0 |
|
61 mngx032 minmag 0 -0.0 -> -0.0 |
|
62 mngx033 minmag 0 0.0 -> 0.0 |
|
63 mngx034 minmag -0 0 -> -0 |
|
64 mngx035 minmag -0 -0 -> -0 |
|
65 mngx036 minmag -0 -0.0 -> -0 |
|
66 mngx037 minmag -0 0.0 -> -0 |
|
67 mngx038 minmag 0.0 0 -> 0.0 |
|
68 mngx039 minmag 0.0 -0 -> -0 |
|
69 mngx040 minmag 0.0 -0.0 -> -0.0 |
|
70 mngx041 minmag 0.0 0.0 -> 0.0 |
|
71 mngx042 minmag -0.0 0 -> -0.0 |
|
72 mngx043 minmag -0.0 -0 -> -0 |
|
73 mngx044 minmag -0.0 -0.0 -> -0.0 |
|
74 mngx045 minmag -0.0 0.0 -> -0.0 |
|
75 |
|
76 mngx046 minmag 0E1 -0E1 -> -0E+1 |
|
77 mngx047 minmag -0E1 0E2 -> -0E+1 |
|
78 mngx048 minmag 0E2 0E1 -> 0E+1 |
|
79 mngx049 minmag 0E1 0E2 -> 0E+1 |
|
80 mngx050 minmag -0E3 -0E2 -> -0E+3 |
|
81 mngx051 minmag -0E2 -0E3 -> -0E+3 |
|
82 |
|
83 -- Specials |
|
84 precision: 9 |
|
85 mngx090 minmag Inf -Inf -> -Infinity |
|
86 mngx091 minmag Inf -1000 -> -1000 |
|
87 mngx092 minmag Inf -1 -> -1 |
|
88 mngx093 minmag Inf -0 -> -0 |
|
89 mngx094 minmag Inf 0 -> 0 |
|
90 mngx095 minmag Inf 1 -> 1 |
|
91 mngx096 minmag Inf 1000 -> 1000 |
|
92 mngx097 minmag Inf Inf -> Infinity |
|
93 mngx098 minmag -1000 Inf -> -1000 |
|
94 mngx099 minmag -Inf Inf -> -Infinity |
|
95 mngx100 minmag -1 Inf -> -1 |
|
96 mngx101 minmag -0 Inf -> -0 |
|
97 mngx102 minmag 0 Inf -> 0 |
|
98 mngx103 minmag 1 Inf -> 1 |
|
99 mngx104 minmag 1000 Inf -> 1000 |
|
100 mngx105 minmag Inf Inf -> Infinity |
|
101 |
|
102 mngx120 minmag -Inf -Inf -> -Infinity |
|
103 mngx121 minmag -Inf -1000 -> -1000 |
|
104 mngx122 minmag -Inf -1 -> -1 |
|
105 mngx123 minmag -Inf -0 -> -0 |
|
106 mngx124 minmag -Inf 0 -> 0 |
|
107 mngx125 minmag -Inf 1 -> 1 |
|
108 mngx126 minmag -Inf 1000 -> 1000 |
|
109 mngx127 minmag -Inf Inf -> -Infinity |
|
110 mngx128 minmag -Inf -Inf -> -Infinity |
|
111 mngx129 minmag -1000 -Inf -> -1000 |
|
112 mngx130 minmag -1 -Inf -> -1 |
|
113 mngx131 minmag -0 -Inf -> -0 |
|
114 mngx132 minmag 0 -Inf -> 0 |
|
115 mngx133 minmag 1 -Inf -> 1 |
|
116 mngx134 minmag 1000 -Inf -> 1000 |
|
117 mngx135 minmag Inf -Inf -> -Infinity |
|
118 |
|
119 -- 2004.08.02 754r chooses number over NaN in mixed cases |
|
120 mngx141 minmag NaN -Inf -> -Infinity |
|
121 mngx142 minmag NaN -1000 -> -1000 |
|
122 mngx143 minmag NaN -1 -> -1 |
|
123 mngx144 minmag NaN -0 -> -0 |
|
124 mngx145 minmag NaN 0 -> 0 |
|
125 mngx146 minmag NaN 1 -> 1 |
|
126 mngx147 minmag NaN 1000 -> 1000 |
|
127 mngx148 minmag NaN Inf -> Infinity |
|
128 mngx149 minmag NaN NaN -> NaN |
|
129 mngx150 minmag -Inf NaN -> -Infinity |
|
130 mngx151 minmag -1000 NaN -> -1000 |
|
131 mngx152 minmag -1 -NaN -> -1 |
|
132 mngx153 minmag -0 NaN -> -0 |
|
133 mngx154 minmag 0 -NaN -> 0 |
|
134 mngx155 minmag 1 NaN -> 1 |
|
135 mngx156 minmag 1000 NaN -> 1000 |
|
136 mngx157 minmag Inf NaN -> Infinity |
|
137 |
|
138 mngx161 minmag sNaN -Inf -> NaN Invalid_operation |
|
139 mngx162 minmag sNaN -1000 -> NaN Invalid_operation |
|
140 mngx163 minmag sNaN -1 -> NaN Invalid_operation |
|
141 mngx164 minmag sNaN -0 -> NaN Invalid_operation |
|
142 mngx165 minmag -sNaN 0 -> -NaN Invalid_operation |
|
143 mngx166 minmag -sNaN 1 -> -NaN Invalid_operation |
|
144 mngx167 minmag sNaN 1000 -> NaN Invalid_operation |
|
145 mngx168 minmag sNaN NaN -> NaN Invalid_operation |
|
146 mngx169 minmag sNaN sNaN -> NaN Invalid_operation |
|
147 mngx170 minmag NaN sNaN -> NaN Invalid_operation |
|
148 mngx171 minmag -Inf sNaN -> NaN Invalid_operation |
|
149 mngx172 minmag -1000 sNaN -> NaN Invalid_operation |
|
150 mngx173 minmag -1 sNaN -> NaN Invalid_operation |
|
151 mngx174 minmag -0 sNaN -> NaN Invalid_operation |
|
152 mngx175 minmag 0 sNaN -> NaN Invalid_operation |
|
153 mngx176 minmag 1 sNaN -> NaN Invalid_operation |
|
154 mngx177 minmag 1000 sNaN -> NaN Invalid_operation |
|
155 mngx178 minmag Inf sNaN -> NaN Invalid_operation |
|
156 mngx179 minmag NaN sNaN -> NaN Invalid_operation |
|
157 |
|
158 -- propagating NaNs |
|
159 mngx181 minmag NaN9 -Inf -> -Infinity |
|
160 mngx182 minmag -NaN8 9990 -> 9990 |
|
161 mngx183 minmag NaN71 Inf -> Infinity |
|
162 |
|
163 mngx184 minmag NaN1 NaN54 -> NaN1 |
|
164 mngx185 minmag NaN22 -NaN53 -> NaN22 |
|
165 mngx186 minmag -NaN3 NaN6 -> -NaN3 |
|
166 mngx187 minmag -NaN44 NaN7 -> -NaN44 |
|
167 |
|
168 mngx188 minmag -Inf NaN41 -> -Infinity |
|
169 mngx189 minmag -9999 -NaN33 -> -9999 |
|
170 mngx190 minmag Inf NaN2 -> Infinity |
|
171 |
|
172 mngx191 minmag sNaN99 -Inf -> NaN99 Invalid_operation |
|
173 mngx192 minmag sNaN98 -11 -> NaN98 Invalid_operation |
|
174 mngx193 minmag -sNaN97 NaN8 -> -NaN97 Invalid_operation |
|
175 mngx194 minmag sNaN69 sNaN94 -> NaN69 Invalid_operation |
|
176 mngx195 minmag NaN95 sNaN93 -> NaN93 Invalid_operation |
|
177 mngx196 minmag -Inf sNaN92 -> NaN92 Invalid_operation |
|
178 mngx197 minmag 088 sNaN91 -> NaN91 Invalid_operation |
|
179 mngx198 minmag Inf -sNaN90 -> -NaN90 Invalid_operation |
|
180 mngx199 minmag NaN sNaN86 -> NaN86 Invalid_operation |
|
181 |
|
182 -- rounding checks -- chosen is rounded, or not |
|
183 maxExponent: 999 |
|
184 minexponent: -999 |
|
185 precision: 9 |
|
186 mngx201 minmag -12345678000 1 -> 1 |
|
187 mngx202 minmag 1 -12345678000 -> 1 |
|
188 mngx203 minmag -1234567800 1 -> 1 |
|
189 mngx204 minmag 1 -1234567800 -> 1 |
|
190 mngx205 minmag -1234567890 1 -> 1 |
|
191 mngx206 minmag 1 -1234567890 -> 1 |
|
192 mngx207 minmag -1234567891 1 -> 1 |
|
193 mngx208 minmag 1 -1234567891 -> 1 |
|
194 mngx209 minmag -12345678901 1 -> 1 |
|
195 mngx210 minmag 1 -12345678901 -> 1 |
|
196 mngx211 minmag -1234567896 1 -> 1 |
|
197 mngx212 minmag 1 -1234567896 -> 1 |
|
198 mngx213 minmag 1234567891 1 -> 1 |
|
199 mngx214 minmag 1 1234567891 -> 1 |
|
200 mngx215 minmag 12345678901 1 -> 1 |
|
201 mngx216 minmag 1 12345678901 -> 1 |
|
202 mngx217 minmag 1234567896 1 -> 1 |
|
203 mngx218 minmag 1 1234567896 -> 1 |
|
204 |
|
205 precision: 15 |
|
206 mngx221 minmag -12345678000 1 -> 1 |
|
207 mngx222 minmag 1 -12345678000 -> 1 |
|
208 mngx223 minmag -1234567800 1 -> 1 |
|
209 mngx224 minmag 1 -1234567800 -> 1 |
|
210 mngx225 minmag -1234567890 1 -> 1 |
|
211 mngx226 minmag 1 -1234567890 -> 1 |
|
212 mngx227 minmag -1234567891 1 -> 1 |
|
213 mngx228 minmag 1 -1234567891 -> 1 |
|
214 mngx229 minmag -12345678901 1 -> 1 |
|
215 mngx230 minmag 1 -12345678901 -> 1 |
|
216 mngx231 minmag -1234567896 1 -> 1 |
|
217 mngx232 minmag 1 -1234567896 -> 1 |
|
218 mngx233 minmag 1234567891 1 -> 1 |
|
219 mngx234 minmag 1 1234567891 -> 1 |
|
220 mngx235 minmag 12345678901 1 -> 1 |
|
221 mngx236 minmag 1 12345678901 -> 1 |
|
222 mngx237 minmag 1234567896 1 -> 1 |
|
223 mngx238 minmag 1 1234567896 -> 1 |
|
224 |
|
225 -- from examples |
|
226 mngx280 minmag '3' '2' -> '2' |
|
227 mngx281 minmag '-10' '3' -> '3' |
|
228 mngx282 minmag '1.0' '1' -> '1.0' |
|
229 mngx283 minmag '1' '1.0' -> '1.0' |
|
230 mngx284 minmag '7' 'NaN' -> '7' |
|
231 |
|
232 -- overflow and underflow tests .. subnormal results [inputs] now allowed |
|
233 maxExponent: 999999999 |
|
234 minexponent: -999999999 |
|
235 mngx330 minmag -1.23456789012345E-0 -9E+999999999 -> -1.23456789012345 |
|
236 mngx331 minmag -9E+999999999 -1.23456789012345E-0 -> -1.23456789012345 |
|
237 mngx332 minmag -0.100 -9E-999999999 -> -9E-999999999 |
|
238 mngx333 minmag -9E-999999999 -0.100 -> -9E-999999999 |
|
239 mngx335 minmag +1.23456789012345E-0 -9E+999999999 -> 1.23456789012345 |
|
240 mngx336 minmag -9E+999999999 1.23456789012345E-0 -> 1.23456789012345 |
|
241 mngx337 minmag +0.100 -9E-999999999 -> -9E-999999999 |
|
242 mngx338 minmag -9E-999999999 0.100 -> -9E-999999999 |
|
243 |
|
244 mngx339 minmag -1e-599999999 -1e-400000001 -> -1E-599999999 |
|
245 mngx340 minmag -1e-599999999 -1e-400000000 -> -1E-599999999 |
|
246 mngx341 minmag -1e-600000000 -1e-400000000 -> -1E-600000000 |
|
247 mngx342 minmag -9e-999999998 -0.01 -> -9E-999999998 |
|
248 mngx343 minmag -9e-999999998 -0.1 -> -9E-999999998 |
|
249 mngx344 minmag -0.01 -9e-999999998 -> -9E-999999998 |
|
250 mngx345 minmag -1e599999999 -1e400000001 -> -1E+400000001 |
|
251 mngx346 minmag -1e599999999 -1e400000000 -> -1E+400000000 |
|
252 mngx347 minmag -1e600000000 -1e400000000 -> -1E+400000000 |
|
253 mngx348 minmag -9e999999998 -100 -> -100 |
|
254 mngx349 minmag -9e999999998 -10 -> -10 |
|
255 mngx350 minmag -100 -9e999999998 -> -100 |
|
256 -- signs |
|
257 mngx351 minmag -1e+777777777 -1e+411111111 -> -1E+411111111 |
|
258 mngx352 minmag -1e+777777777 +1e+411111111 -> 1E+411111111 |
|
259 mngx353 minmag +1e+777777777 -1e+411111111 -> -1E+411111111 |
|
260 mngx354 minmag +1e+777777777 +1e+411111111 -> 1E+411111111 |
|
261 mngx355 minmag -1e-777777777 -1e-411111111 -> -1E-777777777 |
|
262 mngx356 minmag -1e-777777777 +1e-411111111 -> -1E-777777777 |
|
263 mngx357 minmag +1e-777777777 -1e-411111111 -> 1E-777777777 |
|
264 mngx358 minmag +1e-777777777 +1e-411111111 -> 1E-777777777 |
|
265 |
|
266 -- expanded list from min/max 754r purple prose |
|
267 -- [explicit tests for exponent ordering] |
|
268 mngx401 minmag Inf 1.1 -> 1.1 |
|
269 mngx402 minmag 1.1 1 -> 1 |
|
270 mngx403 minmag 1 1.0 -> 1.0 |
|
271 mngx404 minmag 1.0 0.1 -> 0.1 |
|
272 mngx405 minmag 0.1 0.10 -> 0.10 |
|
273 mngx406 minmag 0.10 0.100 -> 0.100 |
|
274 mngx407 minmag 0.10 0 -> 0 |
|
275 mngx408 minmag 0 0.0 -> 0.0 |
|
276 mngx409 minmag 0.0 -0 -> -0 |
|
277 mngx410 minmag 0.0 -0.0 -> -0.0 |
|
278 mngx411 minmag 0.00 -0.0 -> -0.0 |
|
279 mngx412 minmag 0.0 -0.00 -> -0.00 |
|
280 mngx413 minmag 0 -0.0 -> -0.0 |
|
281 mngx414 minmag 0 -0 -> -0 |
|
282 mngx415 minmag -0.0 -0 -> -0 |
|
283 mngx416 minmag -0 -0.100 -> -0 |
|
284 mngx417 minmag -0.100 -0.10 -> -0.10 |
|
285 mngx418 minmag -0.10 -0.1 -> -0.1 |
|
286 mngx419 minmag -0.1 -1.0 -> -0.1 |
|
287 mngx420 minmag -1.0 -1 -> -1 |
|
288 mngx421 minmag -1 -1.1 -> -1 |
|
289 mngx423 minmag -1.1 -Inf -> -1.1 |
|
290 -- same with operands reversed |
|
291 mngx431 minmag 1.1 Inf -> 1.1 |
|
292 mngx432 minmag 1 1.1 -> 1 |
|
293 mngx433 minmag 1.0 1 -> 1.0 |
|
294 mngx434 minmag 0.1 1.0 -> 0.1 |
|
295 mngx435 minmag 0.10 0.1 -> 0.10 |
|
296 mngx436 minmag 0.100 0.10 -> 0.100 |
|
297 mngx437 minmag 0 0.10 -> 0 |
|
298 mngx438 minmag 0.0 0 -> 0.0 |
|
299 mngx439 minmag -0 0.0 -> -0 |
|
300 mngx440 minmag -0.0 0.0 -> -0.0 |
|
301 mngx441 minmag -0.0 0.00 -> -0.0 |
|
302 mngx442 minmag -0.00 0.0 -> -0.00 |
|
303 mngx443 minmag -0.0 0 -> -0.0 |
|
304 mngx444 minmag -0 0 -> -0 |
|
305 mngx445 minmag -0 -0.0 -> -0 |
|
306 mngx446 minmag -0.100 -0 -> -0 |
|
307 mngx447 minmag -0.10 -0.100 -> -0.10 |
|
308 mngx448 minmag -0.1 -0.10 -> -0.1 |
|
309 mngx449 minmag -1.0 -0.1 -> -0.1 |
|
310 mngx450 minmag -1 -1.0 -> -1 |
|
311 mngx451 minmag -1.1 -1 -> -1 |
|
312 mngx453 minmag -Inf -1.1 -> -1.1 |
|
313 -- largies |
|
314 mngx460 minmag 1000 1E+3 -> 1000 |
|
315 mngx461 minmag 1E+3 1000 -> 1000 |
|
316 mngx462 minmag 1000 -1E+3 -> -1E+3 |
|
317 mngx463 minmag 1E+3 -1000 -> -1000 |
|
318 mngx464 minmag -1000 1E+3 -> -1000 |
|
319 mngx465 minmag -1E+3 1000 -> -1E+3 |
|
320 mngx466 minmag -1000 -1E+3 -> -1E+3 |
|
321 mngx467 minmag -1E+3 -1000 -> -1E+3 |
|
322 |
|
323 -- rounding (results treated as though plus) |
|
324 maxexponent: 999999999 |
|
325 minexponent: -999999999 |
|
326 precision: 3 |
|
327 |
|
328 mngx470 minmag 1 5 -> 1 |
|
329 mngx471 minmag 10 50 -> 10 |
|
330 mngx472 minmag 100 500 -> 100 |
|
331 mngx473 minmag 1000 5000 -> 1.00E+3 Rounded |
|
332 mngx474 minmag 10000 50000 -> 1.00E+4 Rounded |
|
333 mngx475 minmag 6 50 -> 6 |
|
334 mngx476 minmag 66 500 -> 66 |
|
335 mngx477 minmag 666 5000 -> 666 |
|
336 mngx478 minmag 6666 50000 -> 6.67E+3 Rounded Inexact |
|
337 mngx479 minmag 66666 500000 -> 6.67E+4 Rounded Inexact |
|
338 mngx480 minmag 33333 500000 -> 3.33E+4 Rounded Inexact |
|
339 mngx481 minmag 75401 1 -> 1 |
|
340 mngx482 minmag 75402 10 -> 10 |
|
341 mngx483 minmag 75403 100 -> 100 |
|
342 mngx484 minmag 75404 1000 -> 1.00E+3 Rounded |
|
343 mngx485 minmag 75405 10000 -> 1.00E+4 Rounded |
|
344 mngx486 minmag 75406 6 -> 6 |
|
345 mngx487 minmag 75407 66 -> 66 |
|
346 mngx488 minmag 75408 666 -> 666 |
|
347 mngx489 minmag 75409 6666 -> 6.67E+3 Rounded Inexact |
|
348 mngx490 minmag 75410 66666 -> 6.67E+4 Rounded Inexact |
|
349 mngx491 minmag 75411 33333 -> 3.33E+4 Rounded Inexact |
|
350 |
|
351 |
|
352 -- overflow tests |
|
353 maxexponent: 999999999 |
|
354 minexponent: -999999999 |
|
355 precision: 3 |
|
356 mngx500 minmag 9.999E+999999999 0 -> 0 |
|
357 mngx501 minmag -9.999E+999999999 0 -> 0 |
|
358 |
|
359 -- subnormals and underflow |
|
360 precision: 3 |
|
361 maxexponent: 999 |
|
362 minexponent: -999 |
|
363 mngx510 minmag 1.00E-999 0 -> 0 |
|
364 mngx511 minmag 0.1E-999 0 -> 0 |
|
365 mngx512 minmag 0.10E-999 0 -> 0 |
|
366 mngx513 minmag 0.100E-999 0 -> 0 |
|
367 mngx514 minmag 0.01E-999 0 -> 0 |
|
368 mngx515 minmag 0.999E-999 0 -> 0 |
|
369 mngx516 minmag 0.099E-999 0 -> 0 |
|
370 mngx517 minmag 0.009E-999 0 -> 0 |
|
371 mngx518 minmag 0.001E-999 0 -> 0 |
|
372 mngx519 minmag 0.0009E-999 0 -> 0 |
|
373 mngx520 minmag 0.0001E-999 0 -> 0 |
|
374 |
|
375 mngx530 minmag -1.00E-999 0 -> 0 |
|
376 mngx531 minmag -0.1E-999 0 -> 0 |
|
377 mngx532 minmag -0.10E-999 0 -> 0 |
|
378 mngx533 minmag -0.100E-999 0 -> 0 |
|
379 mngx534 minmag -0.01E-999 0 -> 0 |
|
380 mngx535 minmag -0.999E-999 0 -> 0 |
|
381 mngx536 minmag -0.099E-999 0 -> 0 |
|
382 mngx537 minmag -0.009E-999 0 -> 0 |
|
383 mngx538 minmag -0.001E-999 0 -> 0 |
|
384 mngx539 minmag -0.0009E-999 0 -> 0 |
|
385 mngx540 minmag -0.0001E-999 0 -> 0 |
|
386 |
|
387 |
|
388 -- Null tests |
|
389 mng900 minmag 10 # -> NaN Invalid_operation |
|
390 mng901 minmag # 10 -> NaN Invalid_operation |