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    • 25. 发明授权
    • Method and apparatus for finding arctangents
    • 发现反正切的方法和装置
    • US5648924A
    • 1997-07-15
    • US424033
    • 1995-04-18
    • Roger A. Smith
    • Roger A. Smith
    • G06F7/548
    • G06F7/548
    • Arctangents (tan.sup.-1) are calculated utilizing binary floating point numbers through much of the function's range by extracting into an Integer Register (54) as an index ("i") the exponent and a specified number of fraction bits from a Floating Point Register(s) (60). The index is utilized by an Integer Unit (52) to index into tables of polynomial coefficients and reference values. The floating point difference between the absolute value of the argument(s) and the reference value selected by the index is a polynomial linear term. The coefficients in the table entry selected by the index are multiplied in a Floating Point Unit (58) by integral powers of the linear term. The Floating Point Unit (58) then sums the high order polynomial terms. The zero.sup.th level term added to the product of the first level term multiplied by the linear term forms a "big" term. The rounding error resulting from the computation of the "Big" Term is calculated as a "Small" Term, which is added to the high order polynomial terms before the Big Term is added.
    • 通过将整数寄存器(54)提取为指数(“i”)和浮点寄存器的指定数量的分数比特,通过大部分功能范围的二进制浮点数来计算Arctangents(tan-1) (s)(60)。 索引由整数单元(52)用于索引到多项式系数和参考值的表中。 参数的绝对值与由索引选择的参考值之间的浮点差是多项式线性项。 由索引选择的表条目中的系数在浮点单元(58)中乘以线性项的积分功率。 浮点单元(58)然后对高阶多项式项求和。 添加到第一级项的乘积中的第零级项被乘以线性项形成“大”项。 计算“大”项时产生的舍入误差被计算为“小”项,它被添加到加入大期限之前的高阶多项式项。
    • 26. 发明授权
    • Method and data processor for finding a logarithm of a number
    • 用于查找数字对数的方法和数据处理器
    • US5570310A
    • 1996-10-29
    • US349571
    • 1994-12-05
    • Roger A. Smith
    • Roger A. Smith
    • G06F7/556G06F1/02
    • G06F7/556
    • A data processor and method are used to find log.sub.p (x) wherein p is a numerical base and x is a floating point value. The method begins by deriving a number y from the quantity x wherein the number y has a predetermined sign portion, a predetermined exponent portion, and the fraction portion f. The predetermined fraction portion f being a truncated portion of x. A logarithm to the predetermined base p of the number y is found by calculating:log.sub.p (y)=-log.sub.p (a)+log.sub.p (1+(ay-1))where the constant a is read from a memory table of constants indexed by an index i. Index i is calculated from y where the fraction portion f of y lies in the range of 1.ltoreq.y
    • 使用数据处理器和方法来查找logp(x),其中p是数字库,x是浮点值。 该方法通过从数量x导出数量y开始,其中数量y具有预定符号部分,预定指数部分和分数部分f。 预定分数部分f是x的截断部分。 通过计算:logp(y)= - logp(a)+ logp(1+(ay-1))找出数目y的预定基数p的对数,其中常数a是从索引的常数的存储表中读取的 通过索引我 索引i由y计算,其中y的分数部分f位于1