Calculating square root of binary numbers with fixed-point microprocessor

#This application relates generally to numerical calculators and more particularly to calculating square roots of binary numbers using a fixed-point processor.

#In the field of numerical calculating using systems such as calculators, computers, and software, calculating square roots of numbers is a time consuming task, often requiring a great deal of memory. Calculating square roots is often required in systems in which relatively fast response times and compact size are demanded. For example, in a disc drive, in order to determine the velocity profile during a seek, the square root of a function of disc drive parameters is calculated. Traditional disc drives employ lookup tables having a relatively large set of values used during disc drive operation in order to implement traditional square root algorithms. The look-up tables consume a large amount of valuable non-volatile memory. In the disc drive industry, a continuing push exists to read and write data more quickly from and to the data storage disc. Additionally, as non-volatile memory may greatly increase the cost of a given system, square root calculators employing look-up tables are unsuitable in smaller applications where reduced circuit size and low cost is desirable or necessary.

#Many traditional systems utilize fixed-point processors for numerical calculations. A fixed-point processor, or fixed-point microprocessor, is generally an integrated circuit that performs numerical calculations in which the decimal point is always in the same location; that is, there is no variation in precision. Stated another way, the number of bits allocated for the mantissa never changes. Systems that utilize a fixed-point processor are ill-suited for conventional iterative algorithms for calculating a square root.

#FIG. 1 is a plan view of a disc drive incorporating an embodiment of the present invention showing the primary internal components.

#FIG. 2 is a functional block diagram of the disc drive of FIG. 1 in accordance with a preferred embodiment of the present invention.

#FIG. 3 is a flow chart of the square root calculation subroutine in accordance with a preferred embodiment of the present invention.

#The invention is described in detail below with reference to the drawing figures. When referring to the figures, like structures and elements shown throughout are indicated with like reference numerals.

#A disc drive 100 constructed in accordance with a preferred embodiment of the present invention is shown in FIG. 1. The disc drive 100 includes a base 102 to which various components of the disc drive 100 are mounted. A top cover 104, shown partially cut away, cooperates with the base 102 to form an internal, sealed environment for the disc drive in a conventional manner. The components include a spindle motor 106 which rotates one or more discs 108 at a constant high speed. Information is written to and read from tracks on the discs 108 through the use of an actuator assembly 110, which rotates during a seek operation about a bearing shaft assembly 112 positioned adjacent the discs 108. The actuator assembly 110 includes a plurality of actuator arms 114 which extend towards the discs 108, with one or more flexures 116 extending from each of the actuator arms 114. Mounted at the distal end of each of the flexures 116 is a head 118 which includes an air bearing slider enabling the head 118 to fly in close proximity above the corresponding surface of the associated disc 108.

#During a seek operation, the track position of the heads 118 is controlled through the use of a voice coil motor (VCM) 124, which typically includes a coil 126 attached to the actuator assembly 110, as well as one or more permanent magnets 128 which establish a magnetic field in which the coil 126 is immersed. The controlled application of current to the coil 126 causes magnetic interaction between the permanent magnets 128 and the coil 126 so that the coil 126 moves in accordance with the well known Lorentz relationship. As the coil 126 moves, the actuator assembly 110 pivots about the bearing shaft assembly 112, and the heads 118 are caused to move across the surfaces of the discs 108.