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Efficient fixed-point multiplication by 2^{K}
b = pow2(a,K)
b = pow2(a,K) returns the value of a shifted by K bits where K is an integer and a and b are fi objects. The output b always has the same word length and fraction length as the input a.
Note: In fixed-point arithmetic, shifting by K bits is equivalent to, and more efficient than, computing b = a*2^{k}. |
If K is a non-integer, the pow2 function will round it to floor before performing the calculation.
The scaling of a must be equivalent to binary point-only scaling; in other words, it must have a power of 2 slope and a bias of 0.
a can be real or complex. If a is complex, pow2 operates on both the real and complex portions of a.
The pow2 function obeys the OverflowAction and RoundingMethod properties associated with a. If obeying the RoundingMethod property associated with a is not important, try using the bitshift function.
The pow2 function does not support fi objects of data type Boolean.
The function also does not support the syntax b = pow2(a) when a is a fi object.
Example 1
In the following example, a is a real-valued fi object, and K is a positive integer.
The pow2 function shifts the bits of a 3 places to the left, effectively multiplying a by 2^{3}.
a = fi(pi,1,16,8) b = pow2(a,3) binary_a = bin(a) binary_b = bin(b)
MATLAB^{®} returns:
a = 3.1406 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 8 b = 25.1250 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 8 binary_a = 0000001100100100 binary_b = 0001100100100000
Example 2
In the following example, a is a real-valued fi object, and K is a negative integer.
The pow2 function shifts the bits of a 4 places to the right, effectively multiplying a by 2^{–4}.
a = fi(pi,1,16,8) b = pow2(a,-4) binary_a = bin(a) binary_b = bin(b)
MATLAB returns:
a = 3.1406 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 8 b = 0.1953 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 8 binary_a = 0000001100100100 binary_b = 0000000000110010
Example 3
The following example shows the use of pow2 with a complex fi object:
format long g P = fipref('NumericTypeDisplay', 'short'); a = fi(57 - 2i, 1, 16, 8) a = 57 - 2i s16,8 pow2(a, 2) ans = 127.99609375 - 8i s16,8