A system for generating a continuous piece-wise linear approximating function that approximately corresponds to a predetermined function over a preselected domain, the approximating function having a selected number of linear segments, the approximating function at the endpoints of the domain falling on the predetermined function. The system first selects an initial error limit, then identifies the points which define the segments. In defining the segments, the system begins at a low endpoint, extends a test segment from the low point to a high endpoint on the predetermined function, and then tests the error between the test segment and the predetermined function at each point. If the error is less than the error limit, the system selects a new higher point on the predetermined function as the new high endpoint, and repeats the operation until the test segment error between it and the predetermined function by at most the error limit. The system then extends the test segment until the error is, at most, the error limit. After determining all but the last segment, the system tests the last segment to determine whether each point is within the selected error of the approximating function. The system then adjusts the error and repeats the procedure until a termination criterion is satisfied.
A circuit for preserving sign information in a computer system. The computer system is capable of comparing and operating on the absolute value of two operands utilizing a pipelined architecture. Sign information is preserved through the use of a first plurality of stages corresponding to stages of the pipeline for storing sign information of a first operand and a second plurality of stages corresponding to stages of the pipeline for storing sign information of a second operand. Sign information is piped through the first and second plurality of stages under common control with the control for the pipeline. Upon completion of the comparison operation, the sign information for the operands is available. Further, the sign information for the first and second operands are coupled as inputs to a multiplexor. The multiplexor is controlled to select either the sign information of the first operand or the sign information of the second operand for storage as the sign of the result depending on the result of the comparison operation.
The process applies to the approximate calculation of the exponential mean of a string of numbers u.sub.n coded in a floating-point format used to convey certain bit rate information in ATM networks, each number being defined with the aid of an exponent e.sub.n and a mantissa m.sub.n by a relation of the form u.sub.n =2.sup.e n.(1+m.sub.n /512). It consists in approximating the exponential mean by the code value associated with the exponential mean of the code words U.sub.n =512.e.sub.n +m.sub.n.
A method for approximating mathematical functions using polynomial expansions is implemented in a numeric processing system (10) which comprises a control and timing circuit (18), a microprogram store (20) and a multiplier circuit (34). The multiplier circuit (34) may comprise a rectangular aspect ratio multiplier circuit (40) having an additional ADDER INPUT to enable the repeated evaluation of first order polynomials to evaluate polynomial expansions associated with each mathematical function. A constant store (28) is used to store predetermined coefficients for the polynomial expansion associated with each mathematical functions. The microprogram store (20) is used to store argument transformation routines, polynomial expansions and result transformation routines associated with each mathematical function.
An apparatus (5) for generating an approximation function based on first pairs ((X.sub.1, Y.sub.1) to (X.sub.6, Y.sub.6)) of values associating a dependent variable (Y.sub.1 to Y.sub.6) with an independent variable (X.sub.1 to X.sub.6), and for determining second pairs (X.sub.A, Y'.sub.A) of values of said variables in accordance with said approximation function. The apparatus comprises: a) first means (10) for iteratively determining at least one current linear regression function, for selecting that one of the current linear functions which produces the approximation of all the pairs of said series with minimal errors, and for coding the selected linear regression function with the aid of specific codes (p, q), and b) second means (17) for determining said second pairs (X.sub.A, Y'.sub.A) with the aid of said specific codes. The apparatus can also be used for calculating approximated values of mathematical functions, for example a in a neural network, or for determining a regression function forming an approximation to experimental measurement results, for example distributed measurements resulting from monitoring an industrial process. The invention also relates to a method of generating an approximation function.
A temperature controller for a thermal system comprises a linearized feedback loop. A linearized thermistor and heating element are disclosed. A current source adjusts the bias current of the thermistor so that the thermistor voltage is equal to a given voltage when the thermistor is at the desired temperature. When the thermistor is biased in this way, the incremental gain from temperature errors to thermistor voltage errors becomes independent of set point. The heating element includes a power regulator and a power resistor. Because temperature is a linearly related to the power dissipated in the power resistor, square-law circuitry keeps the voltage output of the power regulator linearly related to the square root of the error in the controlled temperature. In other embodiments of the invention, a voltage source adjusts the bias voltage of the thermistor so that the incremental gain from temperature errors to thermistor current errors is independent of set point.
