BigDecimal, precision 和scale概念

╰半夏微凉° 2021-09-27 10:58 909阅读 0赞

A `BigDecimal` is defined by two values: an arbitrary precision integer and a 32-bit integer *scale*.

The value of the `BigDecimal` is defined to be ![unscaledValue\*10^\{-scale\}][unscaledValue_10_-scale].

**Precision:**

> The [precision][] is the number of digits in the unscaled value. For instance, for the number 123.45, the precision returned is 5.

So, *precision* indicates the length of the arbitrary precision integer. Here are a few examples of numbers with the same scale, but different precision:

*  12345 / 100000 = 0.12345 // scale = 5, precision = 5
 *  12340 / 100000 = 0.1234 // scale = 5, precision = 4
 *  1 / 100000 = 0.00001 // scale = 5, precision = 1

In the special case that the number is equal to zero (i.e. 0.000), the precision is always 1.

**Scale:**

> If zero or positive, the [scale][] is the number of digits to the right of the decimal point. If negative, the unscaled value of the number is multiplied by ten to the power of the negation of the scale. For example, a scale of -3 means the unscaled value is multiplied by 1000.

This means that the integer value of the ‘BigDecimal’ is multiplied by ![10^\{-scale\}][10_-scale].

Here are a few examples of the same precision, with different scales:

*  12345 with scale 5 = 0.12345
 *  12345 with scale 4 = 1.2345
 *  …
 *  12345 with scale 0 = 12345
 *  12345 with scale -1 = 123450 *†*

**BigDecimal.toString:**

The `toString` method for a `BigDecimal` behaves differently based on the scale and `precision`. (Thanks to @RudyVelthuis for pointing this out.)

*  If `scale == 0`, the integer is just printed out, as-is.
 *  If `scale < 0`, E-Notation is always used (e.g. 5 scale -1 produces "5E+1")
 *  If `scale >= 0` and `precision - scale -1 >= -6` a plain decimal number is produced (e.g. 10000000 scale 1 produces "1000000.0")
 *  Otherwise, E-notation is used, e.g. 10 scale 8 produces "1.0E-7" since `precision - scale -1`equals ![unscaledValue\*10^\{-scale\}][unscaledValue_10_-scale 1] is less than -6.

**More examples:**

*  19/100 = 0.19 // integer=19, scale=2, precision=2
 *  1/1000 = 0.0001 // integer=1, scale = 4, precision = 1

summary:

**Precision:** Total number of significant digits

**Scale:** Number of digits to the right of the decimal point

参考：[BigDecimal, precision and scale][BigDecimal_ precision and scale]

[unscaledValue_10_-scale]: https://chart.googleapis.com/chart?cht=tx&chl=unscaledValue%5Ctimes10%5E%7B-scale%7D
[precision]: https://docs.oracle.com/javase/7/docs/api/java/math/BigDecimal.html#precision%28%29
[scale]: https://docs.oracle.com/javase/7/docs/api/java/math/BigDecimal.html#scale%28%29
[10_-scale]: https://chart.googleapis.com/chart?cht=tx&chl=10%5E%7B-scale%7D
[unscaledValue_10_-scale 1]: https://chart.googleapis.com/chart?cht=tx&chl=2-8-1=-7
[BigDecimal_ precision and scale]: https://stackoverflow.com/questions/35435691/bigdecimal-precision-and-scale#