A trigonometric function arithmetic processor comprises a first arithmetic unit for executing, in m steps, a pseudo-division operation for obtaining from an initial value .theta. a sequence of numbers {ak} and a pseudoremainder .epsilon. which fulfill the following equation ##EQU1## where a.sub.k =+1 or -1, and the trigonometric function arithmetic processor also comprises a second arithmetic unit for executing the following pseudo-multiplication operation in m steps from initial values Xm=P and Ym=.epsilon..times.P (where P=constant) and the sequence of numbers {a.sub.k }, for k=m-1, m-2, . . . 1 and 0, so that X.sub.o =Q.times.cos .theta. nd Yo=Q.times.sin .theta. (Q=constant) are simultaneously obtained.
A method and device are provided for processing an input value to provide an output inverse trigonometric function value of the input value. It substantially comprises a method and device for modifying the input value to obtain an approximation value, determining at least one correction factor, generating at least one intermediate function value, being substantially an inverse trigonometric function value of the approximation value, and combining the intermediate function value with at least one correction factor to determine an output inverse trigonometric function value.
A 64-bit precision digital circuit for computing the exponential function and a related 64-bit precision digital circuit for computing sine and cosine, each circuit comprising a master circuit and a slave circuit. The master circuit computes the remainders x.sub.i for every "logical" iteration i using fast, low-precision circuit, thereby accumulating temporary errors. Only at the end of every 8 i's, which marks the end of a "physical" iteration, is a complete and fast correction to the accumulated errors performed. The slave circuit computes quantities called the y.sub.i 's, which will eventually converge to the desired output.
A 64-bit precision digital circuit for computing the exponential function and a related 64-bit precision digital circuit for computing sine and cosine, each circuit comprising a master circuit and a slave circuit. The master circuit computes the remainders x.sub.i for every "logical" iteration i using fast, low-precision circuit, thereby accumulating temporary errors. Only at the end of every 8 i's, which marks the end of a "physical" iteration, is a complete and fast correction to the accumulated errors performed. The slave circuit computes quantities called the y.sub.i 's, which will eventually converge to the desired output.
A method and device are provided for processing an input value to provide an output trigonometric function value of the input value. It comprises a method and device for modifying the input value to obtain an approximation value, determining an error value with respect to the approximation value, generating first and second function values with respect to the approximation value, the first and second function values typically being trigonometric function values and typically being obtained from a memory device, determining at least one correction value utilizing a predetermined number of terms of at least one power series, and combining the at least one correction value with the first and second function values to determine the output trigonometric function value.
A method for approximating mathematical functions using polynomial expansions is implemented in a numeric processing system. A partial remainder operation is set forth for high accuracy reduction of polynomials whose arguments are greater than pi/4. The method may be practiced in a processor having a bus of approximately half the width of the precision of the desired result. Temporary registers are utilized for the storage of intermediate results. Full bus width accuracy is obtained through successive half bus width operations.
