# Fixed-Point Math Functions

MATLAB® functions that support fixed-point data types

Create and manipulate fixed-point matrices and arrays. Use arithmetic, linear algebra, trigonometric, statistics, and complex math functions that support fixed-point data types.

## Functions

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#### Array Creation

 `colon` Create vectors, array subscripting `eye` Create identity matrix with fixed-point properties `ones` Create array of all ones with fixed-point properties `zeros` Create array of all zeros with fixed-point properties

#### Array and Matrix Manipulation

 `horzcat` Concatenate multiple `fi` objects horizontally `sort` Sort elements of real-valued `fi` object in ascending or descending order `subsasgn` Subscripted assignment `subsref` Subscripted reference `vertcat` Vertically concatenate multiple `fi` objects

#### Basic Array and Matrix Information

 `isequivalent` Determine if two `numerictype` objects have equivalent properties `isfloat` Determine whether input is floating-point data type `max` Largest element in array of `fi` objects `min` Smallest element in array of `fi` objects `numel` Number of data elements in `fi` array

#### Array and Matrix Operators

 `ctranspose` Complex conjugate transpose of `fi` object `minus` Matrix difference between `fi` objects `mpower` Fixed-point matrix power (^) `mrdivide` Right-matrix division `mtimes` Matrix product of `fi` objects `plus` Matrix sum of `fi` objects `qr` Orthogonal-triangular decomposition `rdivide` Right-array division `shiftdata` Shift data to operate on specified dimension `sum` Sum of `fi` array elements `times` Element-by-element multiplication of `fi` objects `uminus` Negate elements of `fi` object array `unshiftdata` Inverse of `shiftdata`

#### Linear System Solvers and Matrix Factorizations

 `fixed.backwardSubstitute` Solve upper-triangular system of equations through backward substitution `fixed.forwardSubstitute` Solve lower-triangular system of equations through forward substitution `fixed.qlessQR` Q-less QR decomposition `fixed.qlessQRUpdate` Update QR factorization `fixed.qrAB` Compute C = Q'*B and upper-triangular factor R `fixed.qrMatrixSolve` Solve system of linear equations Ax = B for x using QR decomposition `fixed.qlessQRMatrixSolve` Solve system of linear equations (A'A)x = B for x using Q-less QR decomposition

#### Specialized Matrices

 `toeplitz` Create Toeplitz matrix
 `abs` Absolute value of `fi` object `complex` Construct complex `fi` object from real and imaginary parts `conj` Complex conjugate of `fi` object `sign` Perform sign function (signum function) on array
 `eps` Quantized relative accuracy for `fi` or `quantizer` objects `intmax` Largest positive stored integer value representable by `numerictype` of `fi` object `intmin` Smallest stored integer value representable by `numerictype` of `fi` object
 `nextpow2` Exponent of next higher power of 2 of `fi` object `pow2` Efficient fixed-point multiplication by 2K `power` Fixed-point element-wise power `sqrt` Square root of `fi` object
 `accumneg` Subtract two `fi` objects or values `accumpos` Add two `fi` objects or values `add` Add two `fi` objects using `fimath` object `atan2` Four-quadrant inverse tangent of fixed-point values `ceilDiv` Round the result of division toward positive infinity `conv` Convolution and polynomial multiplication of `fi` objects `cos` Cosine of `fi` object `divide` Divide two `fi` objects `fixDiv` Round the result of division toward zero `floorDiv` Round the result of division toward negative infinity `innerprodintbits` Number of integer bits needed for fixed-point inner product `mpy` Multiply two objects using `fimath` object `nearestDiv` Round the result of division toward the nearest integer `nnz` Number of nonzero elements in `fi` object `normalizedReciprocal` Compute normalized reciprocal `sin` Sine of fixed-point values `sqrt` Square root of `fi` object `sub` Subtract two `fi` objects using `fimath` object
 `bin` Unsigned binary representation of stored integer of `fi` object `bin2num` Convert two's complement binary string to number using `quantizer` object `dec` Unsigned decimal representation of stored integer of `fi` object `hex` Hexadecimal representation of stored integer of `fi` object `hex2num` Convert hexadecimal string to number using `quantizer` object `num2bin` Convert number to binary representation using `quantizer` object `num2hex` Convert number to hexadecimal equivalent using `quantizer` object `num2int` Convert number to signed integer using `quantizer` object `oct` Octal representation of stored integer of `fi` object `sdec` Signed decimal representation of stored integer of `fi` object
 `eq` Determine whether real-world values of two `fi` objects are equal `ge` Determine whether real-world value of one `fi` object is greater than or equal to another `gt` Determine whether real-world value of one `fi` object is greater than another `le` Determine whether real-world value of `fi` object is less than or equal to another `lt` Determine whether real-world value of one `fi` object is less than another `ne` Determine whether real-world values of two `fi` objects are not equal

#### Rounding Functions

 `ceil ` Rounds toward positive infinity `convergent` Round toward nearest integer with ties rounding to nearest even integer `fix` Round toward zero `floor` Round toward negative infinity `nearest` Round toward nearest integer with ties rounding toward positive infinity `round` Round `fi` object toward nearest integer or round input data using `quantizer` object

#### Modulus and Remainder Functions

 `mod` Modulus after division for `fi` objects `modByConstant` Modulus after division by a constant denominator
 `errmean` Mean of quantization error `errpdf` Probability density function of quantization error `errvar` Variance of quantization error `logreport` Quantization report `maxlog` Log maximums `minlog` Log minimums `noperations` Number of operations `noverflows` Number of overflows `nunderflows` Number of underflows `resetlog` Clear log for `fi` or `quantizer` object `mean` Average or mean value of fixed-point array `median` Median value of fixed-point array

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