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精确计算java中float和double的精度
[本文相关的代码放在github上，地址为：https://github.com/VigourJiang/StructuredFloat]
Java中double类型的格式是遵循IEEE 754标准的。尽管数学意义上的小数是连续的，但double仅仅能表示其中的一些离散点，把这些离散点组成的集合记为S，S的大小还是有限的。如果要保存的小数P刚好在集合S内，那么double类型就能精确的表示P；否则double类型只能从集合S中找一个与P最近的离散点P‘代替P。
以上表述对于float也成立。IEEE 754中float和double的表示策略完全相同，区别仅仅体现在各个字段（指数字段、小数字段）的bit数量不同。
也就是说，float和double都是不精确的，因此偶尔会有一些奇怪的事情发生：
double d = 1e16d;
double d2 = d +1.0d - d;
// 以下代码输出0.0，而不是1.0
System.out.println(d2);上述结果也许并不有趣，因为在学C语言的时候，你的老师就可能提醒过你。但有趣的是，float和double究竟有多不精确？给定一个double d = XXX，与d最接近的另外两个double的数值是多少？我用Java写了一个解析原始数据类型float和double的类StructuredFloat，给定一个float或者double数值P，它可以计算出与P的绝对值最近的、可以被float/double表示的浮点数。下面是用法：
double cur = 3.23d; // any valid double value
StructuredFloat sd = com.vigour.StructuredFloat.StructedFloatBuilder.buildDouble(cur);
StructuredFloat smaller = sd.absSmaller();
StructuredFloat bigger = sd.absBigger();
if(smaller != null){
double smaller_double = smaller.getBigDecimal().doubleValue();
// now you get the nearest double value whose absolute value is smaller
}
if(bigger!= null){
double bigger_double = bigger.getBigDecimal().doubleValue();
// now you get the nearest double value whose absolute value is bigger
}
下面是一些有趣的输出，可以看到，在1e16d附近double的精度就小于1了，在1e7f（一千万）附近，float的精度就等于1了，float果然难堪大用。
-------------Some Interesting Resule for Double-------------------- // 0.1d附近的double Nearest smaller double: 0.09999999999999999167332731531132594682276248931884765625 Current double: 0.1000000000000000055511151231257827021181583404541015625 Nearest bigger double : 0.10000000000000001942890293094023945741355419158935546875 // 1.0d附近的double Nearest smaller double: 0.99999999999999988897769753748434595763683319091796875 Current double: 1 Nearest bigger double : 1.0000000000000002220446049250313080847263336181640625 // 10.0d附近的double Nearest smaller double: 9.9999999999999982236431605997495353221893310546875000 Current double: 10.00 Nearest bigger double : 10.0000000000000017763568394002504646778106689453125000 // 1e14d附近的double Nearest smaller double: 99999999999999.9843750000000000000000000000000000000000000000000000 Current double: 100000000000000.00000000000000000000000000000000 Nearest bigger double : 100000000000000.0156250000000000000000000000000000000000000000000000 // 1e15d附近的double Nearest smaller double: 999999999999999.8750000000000000000000000000000000000000000000000000 Current double: 1000000000000000.0000000000000000000000000000000000 Nearest bigger double : 1000000000000000.1250000000000000000000000000000000000000000000000000 // 1e16d附近的double Nearest smaller double: 9999999999999998.0000000000000000000000000000000000000000000000000000 Current double: 10000000000000000.0000000000000000000000000000000000000 Nearest bigger double : 10000000000000002.0000000000000000000000000000000000000000000000000000 // 1e17d附近的double Nearest smaller double: 99999999999999984.0000000000000000000000000000000000000000000000000000 Current double: 100000000000000000.000000000000000000000000000000000000000 Nearest bigger double : 100000000000000016.0000000000000000000000000000000000000000000000000000 // 1e304d附近的double Nearest smaller double: 9999999999999998174371273630364736815867488735718786093662414371947263704524926751224722911637244940234972882804879769415602664816552507597839565690480126952738889402600333599657997758603312171995012866291845554976690497648524473448849371595248581587050582985041870802940253992811266476846330599148879872.0000000000000000000000000000000000000000000000000000 Current double: 9999999999999999392535525055364621860040287220117324953190771571323204563013233902843309257440507748436856118056162172578717193742636030530235798840866882774987301441682011041067710253162440905843719802548551599076639682550821832659549112269607949805346034918662572406407604380845959862074904348138143744.000000000000000000000000000000000000000000000000 Nearest bigger double : 10000000000000000610699776480364506904213085704515863812719128770699145421501541054461895603243770556638739353307444575741831722668719553462632031991253638597235713480763688482477422747721569639692426738805257643176588867453119191870248852943967318023641486852283274009874954768880653247303478097127407616.0000000000000000000000000000000000000000000000000000 -------------Some Interesting Resule for Float-------------------- // 0.1f附近的float Nearest smaller float: 0.0999999940395355224609375 Current float: 0.100000001490116119384765625 Nearest bigger float: 0.10000000894069671630859375 // 1.0f附近的float Nearest smaller float: 0.999999940395355224609375 Current float: 1 Nearest bigger float: 1.00000011920928955078125 // 10.0f附近的float Nearest smaller float: 9.99999904632568359375000 Current float: 10.00 Nearest bigger float: 10.00000095367431640625000 // 1e5f附近的float Nearest smaller float: 99999.99218750000000000000000 Current float: 100000.00000000000 Nearest bigger float: 100000.00781250000000000000000 // 1e6f附近的float Nearest smaller float: 999999.93750000000000000000000 Current float: 1000000.0000000000000 Nearest bigger float: 1000000.06250000000000000000000 // 1e7f附近的float Nearest smaller float: 9999999.00000000000000000000000 Current float: 10000000.0000000000000000 Nearest bigger float: 10000001.00000000000000000000000 // 1e8f附近的float Nearest smaller float: 99999992.00000000000000000000000 Current float: 100000000.000000000000000000 Nearest bigger float: 100000008.00000000000000000000000 // 1e38f附近的float Nearest smaller float: 99999986661652122824821048795547566080.00000000000000000000 Current float: 99999996802856924650656260769173209088.00000000000000000000000 Nearest bigger float: 100000006944061726476491472742798852096.0000000000000000000000
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