MySQL trig数学计算距离结果为null

Question

我在计算lat lng距离时遇到了一个奇怪的问题。 如果我将此查询输入mysql

SELECT (3959 * acos(cos(radians(30.50492800)) * cos(radians(30.50492800)) * cos(radians(-90.49670600) - radians(-90.496706)) + sin(radians(30.50492800)) * sin(radians(30.50492800))))

它导致null。但是，输入

SELECT (3959 * acos(cos(radians(30.50492800)) * cos(radians(30.50492800)) * cos(radians(-90.49670600) - radians(-90.496706)) + sin(radians(30.50492800)) * sin(radians(30.50492700))))

或

SELECT (3959 * acos(cos(radians(30.50492800)) * cos(radians(30.50492800)) * cos(radians(-90.49670600) - radians(-90.49670)) + sin(radians(30.50492800)) * sin(radians(30.50492800))))

给出结果。

导致这种情况的原因是什么？

Answer 1

这根本不奇怪，

3个表达式中没有一个计算相同的东西。

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差异

SELECT (3959 * acos(cos(radians(30.50492800)) * cos(radians(30.50492800)) * cos(radians(-90.49670600) - radians(-90.496706)) + sin(radians(30.50492800)) * sin(radians(30.50492800))))

SELECT (3959 * acos(cos(radians(30.50492800)) * cos(radians(30.50492800)) * cos(radians(-90.49670600) - radians(-90.496706)) + sin(radians(30.50492800)) * sin(radians( 30.50492700 ))))

SELECT (3959 * acos(cos(radians(30.50492800)) * cos(radians(30.50492800)) * cos(radians(-90.49670600) - radians(的 -90.49670 )) + sin(radians(30.50492800)) * sin(radians(30.50492800))))

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<强>评价

• 第一个表达
  1. cos(radians(30.50492800))等于0.861585503968495
  2. cos(radians(30.50492800))等于0.861585503968495
  3. cos(radians(-90.49670600) - radians(-90.496706))等于1
  4. sin(radians(30.50492800)) * sin(radians(30.50492800))等于0.257670419351355
  5. 所以我们评估了0.861585503968495 * 0.861585503968495 * 1 + 0.257670419351355
  的1.000000000000000513393952565025
  6. acos(1.000000000000000513393952565025)返回null。
• 第二个表达
  1. cos(radians(30.50492800))等于0.861585503968495
  2. cos(radians(30.50492800))等于0.861585503968495
  3. cos(radians(-90.49670600) - radians(-90.496706))等于1
  4. sin(radians(30.50492800)) * sin(radians(30.50492700))等于0.257670411718131
  5. 所以我们评估0.861585503968495 * 0.861585503968495 * 1 + 0.257670411718131等于0.999999992366776513393952565025
  6. acos(0.999999992366776513393952565025) = 0.000123557464423953
  7. 3959 * 0.000123557464423953 = 0.489164001654431
• 第三个表达
  1. cos(radians(30.50492800))等于0.861585503968495
  2. cos(radians(30.50492800))等于0.861585503968495
  3. cos(radians(-90.49670600) - radians(-90.49670))等于0.999999999999995
  4. sin(radians(30.50492800)) * sin(radians(30.50492800))等于0.257670419351355
  5. 因此，我们评估等于0.861585503968495 * 0.861585503968495 * 0.999999999999995 + 0.257670419351355
  的0.999999999999996801746049321797
  6. acos(0.999999999999996801746049321797)等于8.16170211889098e-08
  7. 乘以3959，我们得到0.000323121786886894

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为什么acos（1.000000000000000513393952565025）会返回null？

来自documentation，

  

返回X的反余弦值，即余弦为X的值。   如果X不在-1到1的范围内，则返回NULL。

如您所见，1.000000000000000513393952565025高于1。

对于不给出null的其他两个表达式，acos的给定参数是

• 0.999999992366776513393952565025
• 0.000323121786886894

两者都在[-1, 1]范围内，所以我们得不到空。