Arithmetic circuit
An arithmetic circuit includes an LUT generation circuit ( 1 ) that, when coefficients c[n] (n=1, . . . , N) are paired two by two, outputs a value calculated for each of the pairs, and a distributed arithmetic circuit ( 2 -m) that calculates values y[m] of product-sum arithmetic, by which data x[m, n] of a data set X[m] containing M pairs of data x[m, n] is multiplied by the coefficients c[n] and the products are summed up, in parallel for each of the M pairs. The distributed arithmetic circuit ( 2 -m) includes a plurality of binomial distributed arithmetic circuits that calculate the value of binomial product-sum arithmetic in parallel for each of the pairs, based on a value obtained by pairing N data x[m, n] corresponding to the circuit two by two, a value obtained by pairing the coefficients c[n] two by two, and the value calculated by the LUT generation circuit ( 1 ), and a binomial distributed arithmetic result summing circuit that sums up the values calculated by the binomial distributed arithmetic circuits and outputs the sum as y[m].
1. An arithmetic circuit that receives M (M is an integer of not less than 2) complex numbers X[m] (m=1, . . . , M) each of which is divided into a real part value x_real[m] and an imaginary part value x_imag[m] (m=1, . . . , M), and a complex number coefficient C divided into a real part value c_real and an imaginary part value c_imag, and calculates and outputs M complex number values Y[m] containing a result of real part product-sum arithmetic and a result of imaginary part product-sum arithmetic, the arithmetic circuit comprising:
an LUT generation circuit configured to calculate a value d_sub of a difference between the real part value c_real and the imaginary part value c_imag of the complex number coefficient C, and a value d_add of a sum of the real part value c_real and the imaginary part value c_imag; and
M distributed arithmetic circuits configured to calculate and output, in parallel for each of M, the complex number values Y[m] as a result of multiplying each of data, which correspond to the circuit, of the complex numbers X[m] by the complex number coefficient C and summing up the products,
wherein each of the distributed arithmetic circuits receives the complex number X[m], the real part value c_real and the imaginary part value c_imag of the complex number coefficient C, and the values d_sub and d_add calculated by the LUT generation circuit, and calculates and outputs, in parallel for each of M, y_real[m] as a result of product-sum arithmetic c_real×x_real[m]−c_imag×x_imag[m] of the real part, and y_imag[m] as a result of product-sum arithmetic c_imag×x_real[m]+c_real×x_imag[m] of the imaginary part.
2. The arithmetic circuit according to claim 1 , further comprising an LUT latch circuit formed between the LUT generation circuit and the M distributed arithmetic circuits, and configured to hold the real part value c_real and the imaginary part value c_imag of the complex number coefficient C and the values d_sub and d_add calculated by the LUT generation circuit in synchronism with a clock, and output the held values to the M distributed arithmetic circuits.
3. The arithmetic circuit according to claim 1 , wherein the distributed arithmetic circuit includes:
a plurality of first indexing circuits formed for each bit position of the real part value x_real[m] and the imaginary part value x_imag[m] of the complex number X[m], and configured to obtain, for each bit position, one element value corresponding to two values, in a bit position corresponding to the circuit, of the real part value x_real[m] and the imaginary part value x_imag[m], from element values including 0, c_real, −c_imag, and d_sub;
a plurality of first multiple calculation circuits configured to multiply, for each bit position, each of the element values obtained by the plurality of first indexing circuits by 2 (l-1) (l is an ordinal number of a bit position);
a first summing circuit configured to output a result of summing up the values calculated by the plurality of first multiple calculation circuits, as the value y_real[m] of the real part product-sum arithmetic;
a plurality of second indexing circuits formed for each bit position of the real part value x_real[m] and the imaginary part value x_imag[m] of the complex number X[m], and configured to obtain, for each bit position, one element value corresponding to two values, in a bit position corresponding to the circuit, of the real part value x_real[m] and the imaginary part value x_imag[m], from element values including 0, c_real, −c_imag, and d_add;
a plurality of second multiple calculation circuits configured to multiply, for each bit position, each of the element values obtained by the plurality of second indexing circuits by 2 (l-1) ; and
a second summing circuit configured to output a result of summing up the values calculated by the plurality of second multiple calculation circuits, as the value y_imag[m] of the imaginary part product-sum arithmetic.