As each variable has a different number of bits lengths, we represent m, p and q as vectors, of n positions, representing the integer-width, the fractional width and 'quantizers', respectively, for each variable.
As discussed in Section 3.1, based on the range information, we are able to determine the integer bit width of fixed-point, and partly determine the exponent bit width of floating-point numbers (as exponent bit width does not only relate to the range but also to the accuracy).
Based on their values, the integer bit width of fixed-point numbers can be determined.
We therefore define the cell that includes the front as the front cell (i=FC t), where FC t) is an integer), and the width of the region that the current occupies in the front cell as Δ x FC (t)(0≤Δ x FC (t)<Δ x; see Fig. 4).
(2) A single-width integer multiplication that returns the n least-significant product bits and an overflow signal.
This approach not only allows to compute the transform in reduced bit-width integer arithmetic (e.g. 16 bits) but also exclusively using integer multiplications and additions.
The spline interpolation algorithm maintains the shape of the argument triangle while (1) scaling its longest side to an integer number of pixel widths, (2) following with either bilinear or biquadratic interpolation through lattice points surrounding the third vertex, and finally (3) completing the estimate with a quadratic Newton forward-difference interpolation in the triangle scale size.
where K is a positive integer called the window half-width.
where is a constant integer,, and, ( and are the image width and height, resp).
Integer and fixed-point numbers with widths that are not exponents of 2. Strings.
