Geometry pipeline implemented on a SIMD machine

• US 5,973,705 A
• Filed: 04/24/1997
• Issued: 10/26/1999
• Est. Priority Date: 04/24/1997
• Status: Expired due to Fees

• Current Assignee: International Business Machines Corporation
• Original Assignee: International Business Machines Corporation
• Inventors: Narayanaswami, Chandrasekhar
• Primary Examiner(s): CHAUHAN, ULKA J
• Application Number:
  US08/840,058
• Time in Patent Office: 915 Days
• Field of Search: 345/418, 345/419, 345/425-439, 345/501-506, 345/522-524, 345/507, 364/130-134, 364/136, 364/748.01, 364/748.08, 364/748.13, 364/752, 364/753, 364/765, 395/800.1, 395/800.16, 395/800.17-800.23, 395/562, 395/563
• US Class Current: 345/505
• CPC Class Codes: G06F 2207/3884 Pipelining
• CPC Class Codes: G06F 2207/5355 Using iterative approximation not using digit recurrence, e.g. Newton Raphson or Goldschmidt
• CPC Class Codes: G06F 2207/5521 Inverse root of a number or a function, e.g. the reciprocal of a Pythagorean sum
• CPC Class Codes: G06F 7/483 Computations with numbers represented by a non-linear combination of denominational numbers, e.g. rational numbers, logarithmic number system or floating-point numbers G06F7/4806, G06F7/4824, G06F7/49, G06F7/491, G06F7/544 take precedence
• CPC Class Codes: G06F 7/535 Dividing only
• CPC Class Codes: G06F 7/5525 Roots or inverse roots of single operands
• CPC Class Codes: G06F 9/30014 with variable precision

Abstract

Instructions in an execution pipeline of a SIMD machine are monitored, preferably in the instruction decode phase. Upon detecting a 1/x or 1/sqrt(x) reciprocal operation, portions of the data are forwarded to logic that implements the given instruction. The portions of the instruction that are forwarded include the data value of x and the target address (or register) to which to write the result. The logic generates an n-bit seed for iterative processing by an arithmetic unit, and eliminates a requirement to provide lookup tables in each SIMD processor.

Claims

1. A data processor, comprising:

a memory for storing graphics data, wherein portions of the graphics data are expressed in floating point format having a sign field, an exponent field, and a mantissa field; and

a graphics processor coupled to said memory for preparing the graphics data for display, said graphics processor comprising a plurality of processors organized in a SIMD architecture, each of said processors comprising circuitry for extracting an exponent for its associated portions of the graphics data and for performing reciprocal operations on those portions of the graphics data expressed in floating point format, each of said processors comprising a combinatorial logic circuit having inputs coupled to the memory for inputting the portions of the graphics data, said logic circuit having outputs providing a seed value based upon the inputted portions of the graphics data.

2. A data processor as in claim 1, wherein each of said processors comprises an exponent reverser that implements a (127-e) operation, where e is the exponent field of an input floating point formatted graphics data value of a reciprocal operation of the form 1/x.

3. A data processor as in claim 1, wherein each of said processors comprises an exponent reverser that implements a (379-e)/2 operation, where e is the exponent field of an input floating point formatted graphics data value of a reciprocal operation of the form 1/sqrt(x).

4. A data processor as in claim 1, wherein said reciprocal operation is of the form 1/x.

5. A data processor as in claim 1, wherein said reciprocal operation is of the form 1/sqrt(x).

6. A data processor, comprising:

a memory for storing graphics data, wherein portions of the graphics data are expressed in floating point format having a sign field, an exponent field, and a mantissa field; and

a graphics processor coupled to said memory for preparing the graphics data for display, said graphics processor comprising a plurality of processors organized in a SIMD architecture, each of the said processors performing reciprocal operations on those portions of the graphics data expressed in floating point format, each of said processors comprising a combinatorial logic circuit having inputs coupled to the memory for inputting the portions of the graphics data, said logic circuit having outputs providing a seed value based upon the inputted portions of the graphics data;

wherein said logic circuits comprise a seed logic block having n inputs coupled to n MSBs of an input mantissa field (f) portion of graphics data, and n outputs coupled to n MSBs of an output mantissa field (g).

7. A data processor as in claim 6, wherein n is equal to or greater than three.

8. A data processor as in claim 6, wherein in each of said processors at least said output mantissa field is coupled to an input of an arithmetic unit for providing the seed value thereto, and wherein said arithmetic unit operates under the central of microcode to iteratively refine a result of the reciprocal operation starting with the seed value.

9. A data processor as in claim 8, wherein each of said arithmetic units operates in accordance with a Goldshmidt iterative technique.

10. A data processor as in claim 6, wherein n=4.

11. A data processor as in claim 6, wherein n=3, wherein said reciprocal operation is of the form 1/x, wherein said three MSBs of the input mantissa field are designated X2, X1 and X0, where X2 is the MSB, wherein said three outputs are designated Y2, Y1 and Y0, and wherein said logic circuit is constructed to implement:

space="preserve" listing-type="equation">Y.sub.0 =X.sub.2 X.sub.1 +X.sub.2 X.sub.1 X.sub.0

space="preserve" listing-type="equation">Y.sub.1 =X.sub.2 X.sub.1 +X.sub.2 X.sub.0

space="preserve" listing-type="equation">Y.sub.2 =X.sub.2 X.sub.1 .

12. A data processor as in claim 6, wherein n=3, wherein said reciprocal operation is of the form 1/sqrt(x), wherein said three MSBs of the input mantissa field are designated X2, X1 and X0, where X2 is the MSB, wherein said three outputs are designated Y2, Y1 and Y0, and wherein said logic circuit is constructed to implement:

space="preserve" listing-type="equation">Y.sub.0 =X.sub.1 +X.sub.2 X.sub.0

space="preserve" listing-type="equation">Y.sub.1 =X.sub.2 X.sub.1 +X.sub.2 X.sub.1

space="preserve" listing-type="equation">Y.sub.2 =X.sub.2 +X.sub.1 .

13.

13. A data processor as in claim 6, wherein n=4, wherein said reciprocal operation is of the form 1/x, wherein said four MSBs of the input mantissa field are designated X3, X2, X1 and X0, where X3 is the MSB, wherein said four outputs are designated Y3, Y2, Y1 and Y0, and wherein said logic circuit is constructed to implement:

space="preserve" listing-type="equation">Y.sub.0 =X.sub.3 X.sub.1 X.sub.0 +X.sub.2 X.sub.1 X.sub.0 +X.sub.3 X.sub.1 X.sub.0 +X.sub.3 X.sub.2 X.sub.1

space="preserve" listing-type="equation">Y.sub.1 =X.sub.3 X.sub.2 X.sub.1 X.sub.0 +X.sub.3 X.sub.2 X.sub.0 +X.sub.3 X.sub.1 X.sub.0 +X.sub.3 X.sub.2 X.sub.0 +X.sub.3 X.sub.2 X.sub.1

space="preserve" listing-type="equation">Y.sub.2 =X.sub.2 X.sub.1 X.sub.0 +X.sub.3 X.sub.1 X.sub.0 +X.sub.3 X.sub.2 X.sub.1

space="preserve" listing-type="equation">Y.sub.3 =X.sub.3 X.sub.2 +X.sub.3 X.sub.1 X.sub.0 .

14. A data processor as in claim 6, wherein n=4, wherein said reciprocal operation is of the form 1/sqrt(x), wherein said four MSBs of the input mantissa field are designated X3, X2, X1 and X0, where X3 is the MSB, wherein said four outputs are designated Y3, Y2, Y1 and Y0, and wherein said logic circuit is constructed to implement:

space="preserve" listing-type="equation">Y.sub.0 =X.sub.3 X.sub.2 X.sub.0 +X.sub.2 X.sub.1 +X.sub.3 X.sub.1

space="preserve" listing-type="equation">Y.sub.1 =X.sub.3 X.sub.1 +X.sub.2

space="preserve" listing-type="equation">Y.sub.2 =X.sub.3 X.sub.2 +X.sub.3 X.sub.2

space="preserve" listing-type="equation">Y.sub.3 =X.sub.3 +X.sub.2 .

15.

15. A method for performing graphics data calculations, comprising the steps of:

executing a reciprocal mathematical operation in parallel on a plurality of data processors, each of said data processors operating or different graphical data expressed in floating point format;

generating, in each data processor, a seed value for the reciprocal mathematical operation with a combinatorial logic circuit having n inputs coupled to n MSB mantissa bits of the graphical data, the logic circuit having n outputs coupled to an input of an arithmetic unit; and

iteratively refining the seed value with the arithmetic unit to provide a result.

16. A method as in claim 15, wherein each data processor comprises an exponent reverser that implements one of a 127-e operation or a (379-e)/2 operation, where e is the exponent field of an input floating point formatted graphics data value.

17. A method as in claim 15, wherein n is equal to or greater than three.

18. A method as in claim 15, wherein the reciprocal mathematical operation is of the form 1/x.

19. A method as in claim 15, wherein the reciprocal mathematical operation is of the form 1/sqrt(x).

20. A method as in claim 15, wherein n=4.

21. A method as in claim 15, wherein each of the arithmetic units performs an exponent reversal step having the form 127-e or (379-e)/2, where e is the exponent field of an input floating point formatted graphics data value.

22. A method as in claim 15, wherein n=3, wherein said reciprocal mathematical operation is of the form 1/x, wherein the three MSBs of the input mantissa field are designated X2, X1 and X0, where X2 is the MSB, wherein the three outputs are designated Y2, Y1 and Y0, and wherein the logic circuit is constructed to implement:

space="preserve" listing-type="equation">Y.sub.0 =X.sub.2 X.sub.1 +X.sub.2 X.sub.1 X.sub.0

space="preserve" listing-type="equation">Y.sub.1 =X.sub.2 X.sub.1 +X.sub.2 X.sub.0

space="preserve" listing-type="equation">Y.sub.2 =X.sub.2 X.sub.1 .

23.

23. A method as in claim 15, wherein n=3, wherein the reciprocal mathematical operation is of the form 1/sqrt(x), wherein the three MSBs of the input mantissa field are designated X2, X1 and X0, where X2 is the MSB, wherein the three outputs are designated Y2, Y1 and Y0, and wherein the logic circuit is constructed to implement:

space="preserve" listing-type="equation">Y.sub.0 =X.sub.1 +X.sub.2 X.sub.0

space="preserve" listing-type="equation">Y.sub.1 =X.sub.2 X.sub.1 +X.sub.2 X.sub.1

space="preserve" listing-type="equation">Y.sub.2 =X.sub.2 +X.sub.1 .

24.

24. A method as in claim 15, wherein n=4, wherein the reciprocal mathematical operation is of the form 1/x, wherein the four MSBs of the input mantissa field are designated X3, X2, X1 and X0, where X3 is the MSB, wherein the four outputs are designated Y3, Y2, Y1 and Y0, and wherein the logic circuit is constructed to implement:

space="preserve" listing-type="equation">Y.sub.0 =X.sub.3 X.sub.1 X.sub.0 +X.sub.2 X.sub.1 X.sub.0 +X.sub.3 X.sub.1 X.sub.0 +X.sub.3 X.sub.2 X.sub.1

space="preserve" listing-type="equation">Y.sub.1 =X.sub.3 X.sub.2 X.sub.1 X.sub.0 +X.sub.3 X.sub.2 X.sub.0 +X.sub.3 X.sub.1 X.sub.0 +X.sub.3 X.sub.2 X.sub.0 +X.sub.3 X.sub.2 X.sub.1

space="preserve" listing-type="equation">Y.sub.2 =X.sub.2 X.sub.1 X.sub.0 +X.sub.3 X.sub.1 X.sub.0 +X.sub.3 X.sub.2 X.sub.1

space="preserve" listing-type="equation">Y.sub.3 =X.sub.3 X.sub.2 +X.sub.3 X.sub.1 X.sub.0 .

25.

25. A method as in claim 15, wherein n=4, wherein the reciprocal mathematical operation is of the form 1/sqrt (x), wherein the four MSBs of the input mantissa field are designated X3, X2, X1 and X0, where X3 is the MSB, wherein the four outputs are designated Y3, Y2, Y1 and Y0, and wherein the logic circuit is constructed to implement:

space="preserve" listing-type="equation">Y.sub.0 =X.sub.3 X.sub.2 X.sub.0 +X.sub.2 X.sub.1 +X.sub.3 X.sub.1

space="preserve" listing-type="equation">Y.sub.1 =X.sub.3 X.sub.1 +X.sub.2

space="preserve" listing-type="equation">Y.sub.2 =X.sub.3 X.sub.2 +X.sub.3 X.sub.2

space="preserve" listing-type="equation">Y.sub.3 =X.sub.3 +X.sub.2 .