High accuracy estimates of elementary functions

• Main Authors: SCHMOOKLER, MARTIN STANLEY, SENZIG, DONALD NORMAN
• Format: Patent
• Language: English; French; German
• Published: 25.08.1999
• Edition: 6
• Subjects: CALCULATING; COMPUTING; COUNTING; ELECTRIC DIGITAL DATA PROCESSING; PHYSICS

An improved method of estimating the square root, reciprocal square root, and reciprocal of an input value in a computer system. The input value, after being normalized, is used to select a pair of constants from a table. The constants are based on a linear approximation of the function for each interval of the input value, offset to reduce a maximum error value for a given interval. The estimated function is calculated by adding or subtracting the product of a part of the normalized input value and the first constant from the second constant. In one implementation, the input value is normalized within the range 1 ≤ x < 2, and one lookup table is used, having an interval size of 1/32. In a further preferred embodiment, only a lower order part of the mantissa is used in the multiply-add operation, to reduce the number of bits required (the high order part of the mantissa is used to select the constants from the table). In another implementation, the input value is normalized within the range 0.5 ≤ x < 2, and two lookup tables are used, a first table having an interval size of 1/32 for the range 0.5 ≤ x < 1, and a second table having an interval size of 1/16 for the range 1 ≤ x < 2.