C++ RGB颜色值为双精度-精度太大

我目前正在重新编写一个名为RGBConverter的Arduino库，用于将RGB颜色空间中的颜色值转换为其他颜色。我还想添加一些使用gtest的测试，因为当涉及到以浮点数表示的颜色时，准确性确实很重要。这不仅适用于人眼的颜色感知，也适用于处理光的各种传感器

在创建一个基本测试用例时，我循环了一个RGB颜色值组件，例如红色；从0到10作为整数，并将其转换为它的双精度表示，我非常失望这个过程是多么不准确

以下是我的测试用例的代码：

TEST(UnitCoversion, IntToDouble_single) {
  double x = 0.00000, x_res;
  int color = 0;
  for(; color < 10; color++) {
    printf("%d -> (expected: %.5f | actual: %.5f", color, x, x_res);
    RGBConverter::rgbIntToDouble_single(color, &x_res);
    EXPECT_NEAR(x, x_res, 0.0001);
    x+=0.004;
  }
}

不用说测试失败了：

The difference between x and x_res is 0.00015686274509803949, which exceeds 0.0001, where
x evaluates to 0.0080000000000000002,
x_res evaluates to 0.0078431372549019607, and
0.0001 evaluates to 0.0001.
3 -> (expected: 0.01200 | actual: 0.00784/RGBConverter/main.cpp:15: Failure
The difference between x and x_res is 0.00023529411764705924, which exceeds 0.0001, where
x evaluates to 0.012,
x_res evaluates to 0.011764705882352941, and
0.0001 evaluates to 0.0001.
4 -> (expected: 0.01600 | actual: 0.01176/RGBConverter/main.cpp:15: Failure
The difference between x and x_res is 0.00031372549019607898, which exceeds 0.0001, where
x evaluates to 0.016,
x_res evaluates to 0.015686274509803921, and
0.0001 evaluates to 0.0001.
5 -> (expected: 0.02000 | actual: 0.01569/RGBConverter/main.cpp:15: Failure
The difference between x and x_res is 0.00039215686274509873, which exceeds 0.0001, where
x evaluates to 0.02,
x_res evaluates to 0.019607843137254902, and
0.0001 evaluates to 0.0001.
6 -> (expected: 0.02400 | actual: 0.01961/RGBConverter/main.cpp:15: Failure
The difference between x and x_res is 0.00047058823529411847, which exceeds 0.0001, where
x evaluates to 0.024,
x_res evaluates to 0.023529411764705882, and
0.0001 evaluates to 0.0001.
7 -> (expected: 0.02800 | actual: 0.02353/RGBConverter/main.cpp:15: Failure
The difference between x and x_res is 0.00054901960784313822, which exceeds 0.0001, where
x evaluates to 0.028000000000000001,
x_res evaluates to 0.027450980392156862, and
0.0001 evaluates to 0.0001.
8 -> (expected: 0.03200 | actual: 0.02745/RGBConverter/main.cpp:15: Failure
The difference between x and x_res is 0.00062745098039215796, which exceeds 0.0001, where
x evaluates to 0.032000000000000001,
x_res evaluates to 0.031372549019607843, and
0.0001 evaluates to 0.0001.
9 -> (expected: 0.03600 | actual: 0.03137/RGBConverter/main.cpp:15: Failure
The difference between x and x_res is 0.00070588235294118118, which exceeds 0.0001, where
x evaluates to 0.036000000000000004,
x_res evaluates to 0.035294117647058823, and
0.0001 evaluates to 0.0001.
[  FAILED  ] UnitCoversion.IntToDouble_single (1 ms)
[----------] 1 test from UnitCoversion (1 ms total)

[----------] Global test environment tear-down
[==========] 1 test from 1 test case ran. (1 ms total)
[  PASSED  ] 0 tests.
[  FAILED  ] 1 test, listed below:
[  FAILED  ] UnitCoversion.IntToDouble_single

 1 FAILED TEST

正如你所看到的，在浮点后的2-3位小数后，我得到的结果非常糟糕。我觉得这种行为太接近浮子了。不过我用的是双打

---

我的问题是：我是不是做错了什么？我确实意识到，对浮点数求和会在时间上累积舍入误差，但在这里它从一开始就开始了！使用0.1或0.01作为EXPECT_NEAR的绝对误差参数值几乎不是任何测试。。。这种程度的误差确实会影响用一堆LED测试的色觉。如果可能，我该如何改进？如果是这样的话，我还不如换成浮点数。至少在内存方面，它会更有效。

您计算了一些奇怪的东西，对于步骤1而不是步骤0，您有x==0.004和xres=1255。，这当然不等于0.004=1/250，在那之后误差就增大了。你的意思是1/255。是的，我忽略了这张脸。你能把答案贴出来吗？这样我就可以接受了。

The difference between x and x_res is 0.00015686274509803949, which exceeds 0.0001, where
x evaluates to 0.0080000000000000002,
x_res evaluates to 0.0078431372549019607, and
0.0001 evaluates to 0.0001.
3 -> (expected: 0.01200 | actual: 0.00784/RGBConverter/main.cpp:15: Failure
The difference between x and x_res is 0.00023529411764705924, which exceeds 0.0001, where
x evaluates to 0.012,
x_res evaluates to 0.011764705882352941, and
0.0001 evaluates to 0.0001.
4 -> (expected: 0.01600 | actual: 0.01176/RGBConverter/main.cpp:15: Failure
The difference between x and x_res is 0.00031372549019607898, which exceeds 0.0001, where
x evaluates to 0.016,
x_res evaluates to 0.015686274509803921, and
0.0001 evaluates to 0.0001.
5 -> (expected: 0.02000 | actual: 0.01569/RGBConverter/main.cpp:15: Failure
The difference between x and x_res is 0.00039215686274509873, which exceeds 0.0001, where
x evaluates to 0.02,
x_res evaluates to 0.019607843137254902, and
0.0001 evaluates to 0.0001.
6 -> (expected: 0.02400 | actual: 0.01961/RGBConverter/main.cpp:15: Failure
The difference between x and x_res is 0.00047058823529411847, which exceeds 0.0001, where
x evaluates to 0.024,
x_res evaluates to 0.023529411764705882, and
0.0001 evaluates to 0.0001.
7 -> (expected: 0.02800 | actual: 0.02353/RGBConverter/main.cpp:15: Failure
The difference between x and x_res is 0.00054901960784313822, which exceeds 0.0001, where
x evaluates to 0.028000000000000001,
x_res evaluates to 0.027450980392156862, and
0.0001 evaluates to 0.0001.
8 -> (expected: 0.03200 | actual: 0.02745/RGBConverter/main.cpp:15: Failure
The difference between x and x_res is 0.00062745098039215796, which exceeds 0.0001, where
x evaluates to 0.032000000000000001,
x_res evaluates to 0.031372549019607843, and
0.0001 evaluates to 0.0001.
9 -> (expected: 0.03600 | actual: 0.03137/RGBConverter/main.cpp:15: Failure
The difference between x and x_res is 0.00070588235294118118, which exceeds 0.0001, where
x evaluates to 0.036000000000000004,
x_res evaluates to 0.035294117647058823, and
0.0001 evaluates to 0.0001.
[  FAILED  ] UnitCoversion.IntToDouble_single (1 ms)
[----------] 1 test from UnitCoversion (1 ms total)

[----------] Global test environment tear-down
[==========] 1 test from 1 test case ran. (1 ms total)
[  PASSED  ] 0 tests.
[  FAILED  ] 1 test, listed below:
[  FAILED  ] UnitCoversion.IntToDouble_single

 1 FAILED TEST