From c02423707d6d9bf409ebc4f3f8e3314a4bd27e0d Mon Sep 17 00:00:00 2001 From: guide Date: Mon, 13 Dec 2021 10:29:23 +0800 Subject: [PATCH] =?UTF-8?q?[docs=20add]=20BigDecimal=E8=A7=A3=E5=86=B3?= =?UTF-8?q?=E6=B5=AE=E7=82=B9=E6=95=B0=E8=BF=90=E7=AE=97=E7=B2=BE=E5=BA=A6?= =?UTF-8?q?=E4=B8=A2=E5=A4=B1=E9=97=AE=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- docs/.vuepress/config.js | 5 +- ...解决浮点数运算精度丢失问题.md | 69 ---- docs/java/basis/bigdecimal.md | 340 ++++++++++++++++++ .../basis/images/image-20211213102222601.png | Bin 0 -> 35427 bytes .../basis/images/java-value-passing-03.png | Bin 114234 -> 114194 bytes 5 files changed, 344 insertions(+), 70 deletions(-) delete mode 100644 docs/java/basis/BigDecimal解决浮点数运算精度丢失问题.md create mode 100644 docs/java/basis/bigdecimal.md create mode 100644 docs/java/basis/images/image-20211213102222601.png diff --git a/docs/.vuepress/config.js b/docs/.vuepress/config.js index 9ac8baf2..f5ad8820 100644 --- a/docs/.vuepress/config.js +++ b/docs/.vuepress/config.js @@ -157,7 +157,10 @@ module.exports = config({ "java基础知识总结", { title: "重要知识点", - children: ["why-there-only-value-passing-in-java", "反射机制详解", "代理模式详解", "io模型详解"], + children: [ + "why-there-only-value-passing-in-java", "反射机制详解", "代理模式详解", "io模型详解", + "bigdecimal" + ], },], }, { diff --git a/docs/java/basis/BigDecimal解决浮点数运算精度丢失问题.md b/docs/java/basis/BigDecimal解决浮点数运算精度丢失问题.md deleted file mode 100644 index 5f788f08..00000000 --- a/docs/java/basis/BigDecimal解决浮点数运算精度丢失问题.md +++ /dev/null @@ -1,69 +0,0 @@ -## BigDecimal 介绍 - -`BigDecimal` 可以实现对浮点数的运算,不会造成精度丢失。 - -那为什么浮点数 `float` 或 `double` 运算的时候会有精度丢失的风险呢? - -这是因为计算机是二进制的,浮点数没有办法用二进制精确表示。 - -## BigDecimal 的用处 - -《阿里巴巴Java开发手册》中提到:**浮点数之间的等值判断,基本数据类型不能用==来比较,包装数据类型不能用 equals 来判断。** 具体原理和浮点数的编码方式有关,这里就不多提了,我们下面直接上实例: - -```java -float a = 1.0f - 0.9f; -float b = 0.9f - 0.8f; -System.out.println(a);// 0.100000024 -System.out.println(b);// 0.099999964 -System.out.println(a == b);// false -``` -具有基本数学知识的我们很清楚的知道输出并不是我们想要的结果(**精度丢失**),我们如何解决这个问题呢?一种很常用的方法是:**使用 BigDecimal 来定义浮点数的值,再进行浮点数的运算操作。** - -```java -BigDecimal a = new BigDecimal("1.0"); -BigDecimal b = new BigDecimal("0.9"); -BigDecimal c = new BigDecimal("0.8"); - -BigDecimal x = a.subtract(b); -BigDecimal y = b.subtract(c); - -System.out.println(x); /* 0.1 */ -System.out.println(y); /* 0.1 */ -System.out.println(Objects.equals(x, y)); /* true */ -``` - -## BigDecimal 常见方法 - -## 大小比较 - -`a.compareTo(b)` : 返回 -1 表示 `a` 小于 `b`,0 表示 `a` 等于 `b` , 1表示 `a` 大于 `b`。 - -```java -BigDecimal a = new BigDecimal("1.0"); -BigDecimal b = new BigDecimal("0.9"); -System.out.println(a.compareTo(b));// 1 -``` -### 保留几位小数 - -通过 `setScale`方法设置保留几位小数以及保留规则。保留规则有挺多种,不需要记,IDEA会提示。 - -```java -BigDecimal m = new BigDecimal("1.255433"); -BigDecimal n = m.setScale(3,BigDecimal.ROUND_HALF_DOWN); -System.out.println(n);// 1.255 -``` - -## BigDecimal 的使用注意事项 - -注意:我们在使用BigDecimal时,为了防止精度丢失,推荐使用它的 **BigDecimal(String)** 构造方法来创建对象。《阿里巴巴Java开发手册》对这部分内容也有提到如下图所示。 - -![《阿里巴巴Java开发手册》对这部分BigDecimal的描述](https://my-blog-to-use.oss-cn-beijing.aliyuncs.com/2019/7/BigDecimal.png) - -## 总结 - -BigDecimal 主要用来操作(大)浮点数,BigInteger 主要用来操作大整数(超过 long 类型)。 - -BigDecimal 的实现利用到了 BigInteger, 所不同的是 BigDecimal 加入了小数位的概念 - - - diff --git a/docs/java/basis/bigdecimal.md b/docs/java/basis/bigdecimal.md new file mode 100644 index 00000000..4c106cde --- /dev/null +++ b/docs/java/basis/bigdecimal.md @@ -0,0 +1,340 @@ +--- +title: BigDecimal解决浮点数运算精度丢失问题 +category: Java +tag: + - Java基础 +--- + +## BigDecimal 介绍 + +`BigDecimal` 可以实现对浮点数的运算,不会造成精度丢失。通常情况下,大部分需要浮点数精确运算结果的业务场景(比如涉及到钱的场景)都是通过 `BigDecimal` 来做的。 + +纳尼,浮点数的运算竟然还会有精度丢失的风险吗?确实会! + +示例代码: + +```java +float a = 2.0f - 1.9f; +float b = 1.8f - 1.7f; +System.out.println(a);// 0.100000024 +System.out.println(b);// 0.099999905 +System.out.println(a == b);// false +``` + +**为什么浮点数 `float` 或 `double` 运算的时候会有精度丢失的风险呢?** + +这个和计算机保存浮点数的机制有很大关系。我们知道计算机是二进制的,而且计算机在表示一个数字时,宽度是有限的,无限循环的小数存储在计算机时,只能被截断,所以就会导致小数精度发生损失的情况。这也就是解释了为什么浮点数没有办法用二进制精确表示。 + +就比如说十进制下的 0.2 就没办法精确转换成二进制小数: + +```java +// 0.2 转换为二进制数的过程为,不断乘以 2,直到不存在小数为止, +// 在这个计算过程中,得到的整数部分从上到下排列就是二进制的结果。 +0.2 * 2 = 0.4 -> 0 +0.4 * 2 = 0.8 -> 0 +0.8 * 2 = 1.6 -> 1 +0.6 * 2 = 1.2 -> 1 +0.2 * 2 = 0.4 -> 0(发生循环) +... +``` + +关于浮点数的更多内容,建议看一下[计算机系统基础(四)浮点数](http://kaito-kidd.com/2018/08/08/computer-system-float-point/)这篇文章。 + +## BigDecimal 的用处 + +《阿里巴巴 Java 开发手册》中提到:**浮点数之间的等值判断,基本数据类型不能用==来比较,包装数据类型不能用 equals 来判断。** + +![](https://guide-blog-images.oss-cn-shenzhen.aliyuncs.com/javaguide/image-20211213101646884.png) + +具体原因我们在上面已经详细介绍了,这里就不多提了,我们下面直接上实例: + +```java +float a = 1.0f - 0.9f; +float b = 0.9f - 0.8f; +System.out.println(a);// 0.100000024 +System.out.println(b);// 0.099999964 +System.out.println(a == b);// false +``` + +从输出结果就可以看出发生精度丢失的问题。 + +想要解决这个问题也很简单,直接使用 `BigDecimal` 来定义浮点数的值,再进行浮点数的运算操作即可。 + +```java +BigDecimal a = new BigDecimal("1.0"); +BigDecimal b = new BigDecimal("0.9"); +BigDecimal c = new BigDecimal("0.8"); + +BigDecimal x = a.subtract(b); +BigDecimal y = b.subtract(c); + +System.out.println(x); /* 0.1 */ +System.out.println(y); /* 0.1 */ +System.out.println(Objects.equals(x, y)); /* true */ +``` + +## BigDecimal 常见方法 + +### 加减乘除 + +`add` 方法用于将两个 `BigDecimal` 对象相加,`subtract` 方法用于将两个 `BigDecimal` 对象相减。`multiply` 方法用于将两个 `BigDecimal` 对象相乘,`divide` 方法用于将两个 `BigDecimal` 对象相除。 + +```java +BigDecimal a = new BigDecimal("1.0"); +BigDecimal b = new BigDecimal("0.9"); +System.out.println(a.add(b));// 1.9 +System.out.println(a.subtract(b));// 0.1 +System.out.println(a.multiply(b));// 0.90 +System.out.println(a.divide(b));// 无法除尽,抛出 ArithmeticException 异常 +System.out.println(a.divide(b, 2, RoundingMode.HALF_UP));// 1.11 +``` + +这里需要注意的是,在我们使用 `divide` 方法的时候尽量使用 3 个参数版本,并且`RoundingMode` 不要选择 `UNNECESSARY`,否则很可能会遇到 `ArithmeticException`(无法除尽出现无限循环小数的时候),其中 `scale` 表示要保留几位小数,`roundingMode` 代表保留规则。 + +```java +public BigDecimal divide(BigDecimal divisor, int scale, RoundingMode roundingMode) { + return divide(divisor, scale, roundingMode.oldMode); +} +``` + +保留规则非常多,这里列举几种: + +```java +public enum RoundingMode { + // 2.5 -> 3 , 1.6 -> 2 + // -1.6 -> -2 , -2.5 -> -3 + UP(BigDecimal.ROUND_UP), + // 2.5 -> 2 , 1.6 -> 1 + // -1.6 -> -1 , -2.5 -> -2 + DOWN(BigDecimal.ROUND_DOWN), + // 2.5 -> 3 , 1.6 -> 2 + // -1.6 -> -1 , -2.5 -> -2 + CEILING(BigDecimal.ROUND_CEILING), + // 2.5 -> 2 , 1.6 -> 1 + // -1.6 -> -2 , -2.5 -> -3 + FLOOR(BigDecimal.ROUND_FLOOR), + // 2.5 -> 3 , 1.6 -> 2 + // -1.6 -> -2 , -2.5 -> -3 + HALF_UP(BigDecimal.ROUND_HALF_UP), + //...... +} +``` + +### 大小比较 + +`a.compareTo(b)` : 返回 -1 表示 `a` 小于 `b`,0 表示 `a` 等于 `b` , 1 表示 `a` 大于 `b`。 + +```java +BigDecimal a = new BigDecimal("1.0"); +BigDecimal b = new BigDecimal("0.9"); +System.out.println(a.compareTo(b));// 1 +``` + +### 保留几位小数 + +通过 `setScale`方法设置保留几位小数以及保留规则。保留规则有挺多种,不需要记,IDEA 会提示。 + +```java +BigDecimal m = new BigDecimal("1.255433"); +BigDecimal n = m.setScale(3,RoundingMode.HALF_DOWN); +System.out.println(n);// 1.255 +``` + +## BigDecimal 的使用注意事项 + +注意:我们在使用 `BigDecimal` 时,为了防止精度丢失,推荐使用它的`BigDecimal(String val)`构造方法或者 `BigDecimal.valueOf(double val)` 静态方法来创建对象。 + +《阿里巴巴 Java 开发手册》对这部分内容也有提到,如下图所示。 + +![](https://guide-blog-images.oss-cn-shenzhen.aliyuncs.com/javaguide/image-20211213102222601.png) + +## BigDecimal 工具类分享 + +网上有一个使用人数比较多的 `BigDecimal` 工具类,提供了多个静态方法来简化 `BigDecimal` 的操作。 + +我对其进行了简单改进,分享一下源码: + +```java +import java.math.BigDecimal; +import java.math.RoundingMode; + +/** + * 简化BigDecimal计算的小工具类 + */ +public class BigDecimalUtil { + + /** + * 默认除法运算精度 + */ + private static final int DEF_DIV_SCALE = 10; + + private BigDecimalUtil() { + } + + /** + * 提供精确的加法运算。 + * + * @param v1 被加数 + * @param v2 加数 + * @return 两个参数的和 + */ + public static double add(double v1, double v2) { + BigDecimal b1 = BigDecimal.valueOf(v1); + BigDecimal b2 = BigDecimal.valueOf(v2); + return b1.add(b2).doubleValue(); + } + + /** + * 提供精确的减法运算。 + * + * @param v1 被减数 + * @param v2 减数 + * @return 两个参数的差 + */ + public static double subtract(double v1, double v2) { + BigDecimal b1 = BigDecimal.valueOf(v1); + BigDecimal b2 = BigDecimal.valueOf(v2); + return b1.subtract(b2).doubleValue(); + } + + /** + * 提供精确的乘法运算。 + * + * @param v1 被乘数 + * @param v2 乘数 + * @return 两个参数的积 + */ + public static double multiply(double v1, double v2) { + BigDecimal b1 = BigDecimal.valueOf(v1); + BigDecimal b2 = BigDecimal.valueOf(v2); + return b1.multiply(b2).doubleValue(); + } + + /** + * 提供(相对)精确的除法运算,当发生除不尽的情况时,精确到 + * 小数点以后10位,以后的数字四舍五入。 + * + * @param v1 被除数 + * @param v2 除数 + * @return 两个参数的商 + */ + public static double divide(double v1, double v2) { + return divide(v1, v2, DEF_DIV_SCALE); + } + + /** + * 提供(相对)精确的除法运算。当发生除不尽的情况时,由scale参数指 + * 定精度,以后的数字四舍五入。 + * + * @param v1 被除数 + * @param v2 除数 + * @param scale 表示表示需要精确到小数点以后几位。 + * @return 两个参数的商 + */ + public static double divide(double v1, double v2, int scale) { + if (scale < 0) { + throw new IllegalArgumentException( + "The scale must be a positive integer or zero"); + } + BigDecimal b1 = BigDecimal.valueOf(v1); + BigDecimal b2 = BigDecimal.valueOf(v2); + return b1.divide(b2, scale, RoundingMode.HALF_UP).doubleValue(); + } + + /** + * 提供精确的小数位四舍五入处理。 + * + * @param v 需要四舍五入的数字 + * @param scale 小数点后保留几位 + * @return 四舍五入后的结果 + */ + public static double round(double v, int scale) { + if (scale < 0) { + throw new IllegalArgumentException( + "The scale must be a positive integer or zero"); + } + BigDecimal b = BigDecimal.valueOf(v); + BigDecimal one = new BigDecimal("1"); + return b.divide(one, scale, RoundingMode.HALF_UP).doubleValue(); + } + + /** + * 提供精确的类型转换(Float) + * + * @param v 需要被转换的数字 + * @return 返回转换结果 + */ + public static float convertToFloat(double v) { + BigDecimal b = new BigDecimal(v); + return b.floatValue(); + } + + /** + * 提供精确的类型转换(Int)不进行四舍五入 + * + * @param v 需要被转换的数字 + * @return 返回转换结果 + */ + public static int convertsToInt(double v) { + BigDecimal b = new BigDecimal(v); + return b.intValue(); + } + + /** + * 提供精确的类型转换(Long) + * + * @param v 需要被转换的数字 + * @return 返回转换结果 + */ + public static long convertsToLong(double v) { + BigDecimal b = new BigDecimal(v); + return b.longValue(); + } + + /** + * 返回两个数中大的一个值 + * + * @param v1 需要被对比的第一个数 + * @param v2 需要被对比的第二个数 + * @return 返回两个数中大的一个值 + */ + public static double returnMax(double v1, double v2) { + BigDecimal b1 = new BigDecimal(v1); + BigDecimal b2 = new BigDecimal(v2); + return b1.max(b2).doubleValue(); + } + + /** + * 返回两个数中小的一个值 + * + * @param v1 需要被对比的第一个数 + * @param v2 需要被对比的第二个数 + * @return 返回两个数中小的一个值 + */ + public static double returnMin(double v1, double v2) { + BigDecimal b1 = new BigDecimal(v1); + BigDecimal b2 = new BigDecimal(v2); + return b1.min(b2).doubleValue(); + } + + /** + * 精确对比两个数字 + * + * @param v1 需要被对比的第一个数 + * @param v2 需要被对比的第二个数 + * @return 如果两个数一样则返回0,如果第一个数比第二个数大则返回1,反之返回-1 + */ + public static int compareTo(double v1, double v2) { + BigDecimal b1 = BigDecimal.valueOf(v1); + BigDecimal b2 = BigDecimal.valueOf(v2); + return b1.compareTo(b2); + } + +} +``` + +## 总结 + +`BigDecimal` 主要用来操作(大)浮点数,`BigInteger` 主要用来操作大整数(超过 `long` 类型)。 + +`BigDecimal` 的实现利用到了 `BigInteger`, 所不同的是 `BigDecimal` 加入了小数位的概念 diff --git a/docs/java/basis/images/image-20211213102222601.png b/docs/java/basis/images/image-20211213102222601.png new file mode 100644 index 0000000000000000000000000000000000000000..e05ded5116afedbd0b5eff84b2689d0e09babf56 GIT binary patch literal 35427 zcmbSyWl$VW@Ffm`5ZoOSAq z&4-zus{Sz5J@tC3=e=+x1u1k?VpJFy7<3tFaTORCc<_JrJqrAPvn{vL&;J$#GZCN& z3`|`t+N%NLe|uO*6)91e>Pgb0|GZ(8S||a7cx1ux4+-j-7BM@^7!~TI5c!|aWOkT9}*VMCoHxMUFji) zkylb19vS_mtsfm5|BdN;R!%M}2e*s6r-6z2`}2#alx%HXy_b()YDQ*db@g`u-}=9Q z!otE4(XsBHJ_*UG@bK_LV$!tCKLUb7#>OWCL&EDDo03!0Ev)VQ0)k&&UNW+>^$bn= z2L@Gt{pJx65fGIOkBqT%bm8I?yuQBf?dxAySp569%gM!^ok!rep25cECN(uR$kxHw 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