US 5,926,406 A · System and method for calculating floating point exponential values in a geometry accelerator

Abstract

A novel system and method computes a floating point value of an exponential expression in the form of "a.sup.x " in a geometry accelerator. In accordance with one aspect of the invention, the method includes the steps of receiving the values "a" and x of the exponential expression, where both "a" and x are represented in floating point format. As will be appreciated by those skilled in the art, the values will by supplied by software through an appropriate graphics application program interface (API). The method utilizes a mantissa value of the floating point representation of "a" to index a first value in a first look-up table, the value being an approximation for log2(a). Then, the method multiplies the looked-up value by the value of x to obtain an intermediate result. This intermediate result is then partitioned into a fractional component and an integer component, wherein the fractional component is normalized/converted to floating point format. The method then utilizes a mantissa value of the floating point representation of the fractional component of the intermediate result to index a first value in a second look-up table, the value being an approximation for 2.sup.fract, where fract is the fractional component. Thereafter, the method computing 2.sup.integer, where integer is the integer component. This step may be directly computed by the math core of the geometry accelerator, since it is an integer exponent. Finally, the method multiplies the results of steps that compute the 2.sup.fract and 2.sup.integer values to obtain a final value. This final value is a close approximation of the exponential expression a.sup.x.

Claims25

Dependent claims

A method for computing a floating point value of an exponential expression in the form of a.sup.x in a geometry accelerator, comprising the steps of:

(a) receiving the values a and x of the exponential expression, where both a and x are represented in floating point format;
(b) utilizing a mantissa value of the floating point representation of a to index a first value in a first look-up table, the value being an approximation for log2(a);
(c) multiplying the looked-up value by x to obtain a result;
(d) breaking the result into a fractional component and an integer component, wherein the fractional component is stored in floating point format;
(e) utilizing a mantissa value of the floating point format of the fractional component of the result to index a first value in a second look-up table, the value being an approximation for 2.sup.fract, where fract is the fractional component;
(f) computing 2.sup.integer, where integer is the integer component;
(g) multiplying the results of steps (e) and (f) to obtain a final value, the final value being a close approximation of the exponential expression a.sup.x ;
and
(h) using the calculated result of a.sup.x to compute a lighting equation in a geometry accelerator.

6 more elements

A system for computing a floating point value of an exponential expression in the form of a.sup.x in a geometry accelerator, comprising the steps of:

receiving means for receiving the values a and x of the exponential expression, where both a and x are represented in floating point format;
first indexing means for indexing a first value in a first look-up table based upon the mantissa value of the floating point representation of a, the looked-up value being a predefined approximation for log2(a);
first multiplying means for multiplying the looked-up value by x to obtain an intermediate result;
separating means for splitting the intermediate result into a fractional component and an integer component, wherein the fractional component is stored in floating point format;
second indexing means for indexing a first value in a second look-up table based upon the mantissa value of the floating point representation of the fractional component, the looked-up value being a predefined approximation for 2.sup.fract, where fract is the fractional component;
computing means for computing 2.sup.integer, where integer is the integer component;
and
second multiplying means for multiplying the value obtained from the second indexing means and the computed 2.sup.integer value to obtain a final value, the final value being a close approximation of the exponential expression a.sup.x.

5 more elements

Dependencies are inferred from the claim text.

System and method for calculating floating point exponential values in a geometry accelerator

Life of this patent

System and method for calculating floating point exponential values in a geometry accelerator

Life of this patent

Abstract

Claims25