Matlab：如何在不扩展基础数据类型的情况下执行定点算术？

debugcn 发表于 Dev

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Google在此问题上保持沉默。我目前在Matlab中仅在16位有符号固定点上实现数字计算器。但是对16位定点进行算术运算会导致将数据类型扩展到以下类型

>> a = int16(1.5 * 4)
a = 6
>> T = numerictype(1, 16, 2)

T = DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 16
        FractionLength: 2
>> dis = reinterpretcast(a, T)

dis = 1.5000

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 16
        FractionLength: 2
>> c = dis * dis

c = 2.2500

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 32
        FractionLength: 4

我希望变量c保持在WordLength 16，FractionLength 2中。是否有可能在不扩展基础数据类型的情况下完成16位固定点的算术运算？我要冒任何上溢和下溢的风险。任何帮助都是极好的。

编辑：键入fimath命令窗口导致错误。为什么会发生此错误？

>> F = fimath('OverflowAction','Wrap', 'RoundingMethod', 'Floor', ...
           'ProductWordLength', 16, 'ProductFractionLength', 2);
No public field OverflowAction exists for class embedded.fimath.

Error in fimath (line 72)
  this.(varargin{k}) = varargin{k+1};

Mohsen Nosratinia

本地解决方案：您可以使用一个fimath对象来指定乘积结果的精度：

F = fimath('OverflowMode','Wrap', 'RoundMode', 'Floor', ...
           'ProductMode', 'SpecifyPrecision', ...
           'ProductWordLength', 16, 'ProductFractionLength', 2);
dis.fimath = F;

那么结果将是：

>> dis*dis
ans =
         2.25

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 16
        FractionLength: 2

             RoundMode: floor
          OverflowMode: wrap
           ProductMode: SpecifyPrecision
     ProductWordLength: 16
 ProductFractionLength: 2
               SumMode: FullPrecision
      MaxSumWordLength: 128

全局解决方案：或者，如果您希望将此方法应用于所有定点变量，则可以使用

globalfimath('OverflowMode','Wrap', 'RoundMode', 'Floor', ...
             'ProductMode', 'SpecifyPrecision', ...
             'ProductWordLength', 16, 'ProductFractionLength', 2);

请注意，要限制为16位，您还需要指定sum的精度（的使用SumMode和SumWordLength属性fimath），否则sum的字长为17：

>> dis+dis
ans =
     3

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 17
        FractionLength: 2

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