rem函数和mod函数很相似，二者认真看一个，另一个看一下区别即可。

mod函数介绍：【 MATLAB 】mod 函数介绍

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rem

Remainder after division

Syntax

r = rem(a,b)

Description

r = rem(a,b) returns the remainder after division of a by b, where a is the dividend and b is the divisor. This function is often called the remainder operation, which can be expressed asr = a - b.*fix(a./b). The rem function follows the convention that rem(a,0) is NaN.

a/b之后的余数便是r。如果除数为0，则rem(a,0)为NaN，这和我们的认知也很符合。

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Remainder After Division of Scalar

Compute the remainder after dividing 5 into 23.

a = 23; b = 5; r = rem(a,b) r = 3

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Remainder After Division of Vector

Find the remainder after division for a vector of integers and the divisor 3.

a = 1:5; b = 3; r = rem(a,b) r = 1×5 1 2 0 1 2

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Remainder After Division for Positive and Negative Values

Find the remainder after division for a set of integers including both positive and negative values. Note that nonzero results have the same sign as the dividend.

a = [-4 -1 7 9]; b = 3; r = rem(a,b) r = 1×4 -1 -1 1 0

注：从这个例子开始，就和mod函数不一样了，这里余数符号与被除数一致。

a = [-4 -1 7 9]; b = 3; r1 = rem(a,b) r2 = mod(a,b)

r1 =

    -1    -1     1     0

r2 =

     2     2     1     0

二者结果是不一样的，我们想想这个rem是怎么计算的。

它是先将被输出a中的符号去掉，当成正数来算，结果符号在和a一致即可。

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Remainder After Division for Floating-Point Values

Find the remainder after division for several angles using a divisor of 2*pi. When possible, rem attempts to produce exact integer results by compensating for floating-point round-off effects.

theta = [0.0 3.5 5.9 6.2 9.0 4*pi]; b = 2*pi; r = rem(theta,b) r = 1×6 0 3.5000 5.9000 6.2000 2.7168 0

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Differences Between mod and rem

The concept of remainder after division is not uniquely defined, and the two functions mod and rem each compute a different variation. The mod function produces a result that is either zero or has the same sign as the divisor. The rem function produces a result that is either zero or has the same sign as the dividend.

Another difference is the convention when the divisor is zero. The mod function follows the convention that mod(a,0) returns a, whereas the rem function follows the convention that rem(a,0)returns NaN.

Both variants have their uses. For example, in signal processing, the mod function is useful in the context of periodic signals because its output is periodic (with period equal to the divisor).