Method and apparatus for providing high numerical accuracy with packed multiply-add or multiply-subtract operations

In a computer system, a improving the accuracy of multiply-accumulating operations comprising the computer-implemented steps of:

• reading a first packed data and a second packed data, said first packed data having representations of values A.sub.0 and A.sub.1 and said second packed data having representation of N least significant bits of values B.sub.0 (B.sub.0,LSB) and B.sub.1 (B.sub.1,LSB), wherein each of B.sub.0,LSB and B.sub.1,LSB are represented as signed integers;
• generating a first result having a representation of value A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB ;
• reading said first packed data and a third packed data, said third packed data having representation of most significant bits of values B.sub.0 (B.sub.0,MSB) and B.sub.1 (B.sub.1,MSB);
• generating a second result having a representation of value A.sub.0 B.sub.0,MSB +A.sub.1 B.sub.1,MSB ;
• generating a third result by right shifting said value A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB in said first packed data result by less than N bits;
• reading said second result and said third result;
• and
• generating a final result having a representation of value A.sub.0 B.sub.0 +A.sub.1 B.sub.1.

A machine readable medium having stored thereon data representing a sequence of instructions, said sequence of instructions which, when executed by a processor, cause said processor to perform a method comprising the computer-implemented steps of:

• reading a first packed data and a second packed data, said first packed data having representations of values A.sub.0 and A.sub.1 and said second packed data having representation of N least significant bits of values B.sub.0 (B.sub.0,LSB) and B.sub.1 (B.sub.1,LSB), wherein B.sub.0,LSB and B.sub.1,LSB are represented as unsigned integers;
• generating a first result having a representation of value A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB ;
• reading said first packed data and a third packed data, said third packed data having representation of most significant bits of values B.sub.0 (B.sub.0,MSB) and B.sub.1 (B.sub.1,MSB);
• generating a second result having a representation of value A.sub.0 B.sub.0,MSB +A.sub.1 B.sub.1,MSB ;
• generating a third result by right shifting the value A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB in said first result by N bits;
• reading said second result and said third result;
• and
• generating a final result having a representation of value A.sub.0 B.sub.0 +A.sub.1 B.sub.1.

A machine-readable medium having stored thereon data representing a sequence of instructions, said sequence of instructions which, when executed by a processor, cause said processor to perform a method comprising the computer-implemented steps of:

• reading first packed data and a second packed data, said first packed data having representations of values A.sub.0 and A.sub.1 said second packed data having representation of N least significant bits of values B.sub.0 (B.sub.0,LSB) and B.sub.1 (B.sub.1,LSB), wherein each of B.sub.0,LSB and B.sub.1,LSB are represented as signed integers;
• generating a first result having a representation of value A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB ;
• reading said first packed data an third packed data, said third packed data having representations of first significant bits of values B.sub.0 (B.sub.0,MSB) and B.sub.1 (B.sub.1,MSB);
• generating a second result having a representation of value A.sub.0 B.sub.0,MSB +A.sub.1 B.sub.1,MSB ;
• generating a third result by right shifting said value A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB in said first packed data result by less than N bits;
• reading said second result and said third result;
• and
• generating a final result having a representation of value A.sub.0 B.sub.0 +A.sub.1 B.sub.1.

In a computer system, a method of improving the accuracy of a multiply-accumulating operations comprising the computer-implemented steps of:

• in response to a first instruction, performing the steps of:
• reading a first packed data and a second packed data, said first packed data having representations of values A.sub.0 and A.sub.1 and said second packed data having representation of N least significant bits of values B.sub.0 (B.sub.0,LSB) and B.sub.1 (B.sub.1,LSB), wherein each of said B.sub.0,LSB value and said B.sub.1,LSB value are represented unsigned integers;
• and
• generating a first result having a representation of value A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB ;
• in response to a second instruction, performing the steps of:
• reading said first packed data and a third packed data, said third packed data having representation of most significant bits of values B.sub.0 (B.sub.0,MSB) and B.sub.1 (B.sub.1,MSB);
• and
• generating a second result having a representation of value A.sub.0 B.sub.0,MSB +A.sub.1 B.sub.1,MSB ;
• in response to a third instruction, performing the steps of:
• generating a third result by right shifting the value A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB in said first result by N bits;
• and
• in response to a fourth instruction, performing the steps of:
• reading said second result and said third result;
• and
• generating a final result having a representation of value A.sub.0 B.sub.0 +A.sub.1 B.sub.1.

In a computer system, a method of improving the accuracy of multiply-accumulating operations comprising the compute-implemented steps of:

• in response to a first instruction, performing the steps of:
• reading a first packed data and a second packed data, said first packed data having representations of values A.sub.0 and A.sub.1 and said second packed data having representation of N least significant bits of values B.sub.0 (B.sub.0,LSB) and B.sub.1 (B.sub.1,LSB), wherein each of said B.sub.0,LSB value and said B.sub.1,LSB value are represented as signed integers comprising N bits;
• and
• generating a first result having a presentation of value A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB ;
• in response to a second instruction, performing the steps of:
• reading said first packed data and a third packed data, said third packed data having representation of most significant bits of values B.sub.0 (B.sub.0,MSB) and B.sub.1 (B.sub.1,MSB);
• and
• generating a second result having a representation of value A.sub.0 B.sub.0,MSB +A.sub.1 B.sub.1,MSB ;
• in response to a third instruction, performing the steps of:
• generating a third packed data result by right shifting the said value A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB in said first packed data result by less than N bits;
• and
• in responce to a fourth instruction, performing the steps of:
• reading said second result and said third result;
• and
• generating a final result having a representation of value A.sub.0 B.sub.0 +A.sub.1 B.sub.1.

A machine readable medium having stored thereon data representing a sequence of instructions, said sequence of instructions which, when executed by a processor, cause said processor to perform a method comprising the computer-implemented steps of;

• in response to a first instruction, performing the steps of:
• reading a first packed data and a second packed data, said first packed data having representations of values A.sub.0 and A.sub.1 and said second packed data having representation of N least significant bits of values B.sub.0 (B.sub.0,LSB) and B.sub.1 (B.sub.1,LSB), wherein each of said B.sub.0,LSB value and said B.sub.1,LSB value are represented as unsigned integers;
• and
• generating a first result having a representation of value A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB ;
• in response to a second instruction, performing the steps of:
• reading said first packed data and a third packed data, said third packed data having representation of most significant bits of values B.sub.0 (B.sub.0,MSB) and B.sub.1 (B.sub.1,MSB);
• and
• generating a second result having a representation of value A.sub.0 B.sub.0,MSB +A.sub.1 B.sub.1,MSB ;
• in response to a third instruction, performing the steps of:
• generating a third result by right shifting the value A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB in said first result by N bits;
• and
• in response to a fourth instruction, performing the steps of:
• reading said second result and said third result;
• and
• generating a final result having a representation of value A.sub.0 B.sub.0 +A.sub.1 B.sub.1.

A machine-readable medium having stored thereon data representing a sequence of instructions, said sequence of instructions which, when executed by a processor, cause said processor to perform a method comprising the computer-implemented steps of:

• in response to a first instruction, performing the steps of:
• reading first packed data and a second packed data, said first packed data having representation of values A.sub.0 and A.sub.1 and said second packed data having representation of N least significant bits of values B.sub.0 (B.sub.0,LSB) and B.sub.1 (B.sub.1,LSB), wherein each of said B.sub.0,LSB value and said B.sub.1,LSB value are represented as signed integers comprising N bits;
• and
• generating a first result having a representation of value A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB ;
• in response to a second instruction, performing the steps of:
• reading said first packed data and a third packed data, said third packed data having representation of most significant bits of values B.sub.0 (B.sub.0,MSB) and B.sub.1 (B.sub.1,MSB);
• and
• generating a second result having a representation of value A.sub.0 B.sub.0,MSB +A.sub.1 B.sub.1,MSB ;
• in response to a third instruction, performing the steps of:
• generating a third packed data result by right shifting the said value A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB in said first packed data result by less than N bits;
• and
• in response to a fourth instruction, performing the steps of:
• reading said second result and said third result;
• and
• generating a final result having a representation of value A.sub.0 B.sub.0 +A.sub.1 B.sub.1.

In a computer system, a method of improving the accuracy of multiply-accumulating operations comprising the computer-implemented steps of:

• in response to a first instruction, performing the steps of:
• reading a first packed data and a second packed data, said first packed data having representations of values A.sub.0, A.sub.1, A.sub.2, and A.sub.3 and said second packed data having representation of N least significant bits of values B.sub.0 (B.sub.0,LSB), B.sub.1 (B.sub.1,LSB), B.sub.2 (B.sub.2,LSB), and B.sub.3 (B.sub.3,LSB), wherein each of said least significant bit values B.sub.0,LSB, B.sub.1,LSB, B.sub.2,LSB and B.sub.3,LSB are represented as unsigned integers;
• and
• generating a first packed data result having representations, of values A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB and A.sub.2 B.sub.2,LSB +A.sub.3 B.sub.3,LSB ;
• in response to a second instruction, performing the steps of:
• reading said first packed data and a third packed data, said third packed data having representation of most significant bit values B.sub.0 (B.sub.0,MSB), B.sub.1 (B.sub.1,MSB), B.sub.2 (B.sub.2,MSB), and B.sub.3 (B.sub.3,MSB);
• and
• generating a second packed data result having representations of values A.sub.0 B.sub.0,MSB +A.sub.1 B.sub.1,MSB and A.sub.2 B.sub.2,MSB +A.sub.3 B.sub.3,MSB ;
• in response to a third instruction generating a third packed data result by right shifting each value in said first packed data result by N bits;
• and
• in response to a fourth instruction:
• reading said second packed data result and said third packed data result;
• and
• generating a final packed data result having representations of values A.sub.0 B.sub.0 +A.sub.1 B.sub.1 and A.sub.2 B.sub.2 +A.sub.3 B.sub.3.

In a computer system, a method of improving the accuracy of multiply-accumulating operations comprising the computer-implemented steps of:

• in response to a first instruction, performing the steps of:
• reading a first packed data and a second packed data, said first packed data having representations of values A.sub.0, A.sub.1, A.sub.2, and A.sub.3 said second packed data having representation of N least significant bits of values B.sub.0 (B.sub.0,LSB), B.sub.1 (B.sub.1,LSB), B.sub.2 (B.sub.2,LSB), and B.sub.3 (B.sub.3,LSB), wherein each of said least significant bit values B.sub.0,LSB, B.sub.1,LSB, B.sub.2,LSB, and B.sub.3,LSB are represented as signed integers;
• and
• generating a first packed data result having representations of values A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB and A.sub.2 B.sub.2,LSB +A.sub.3 B.sub.3,LSB ;
• in response to a second instruction, performing the steps of:
• reading said first packed data and a third packed data, said third packed data having representation of most significant bit values B.sub.0 (B.sub.0,MSB), B.sub.1 (B.sub.1,MSB), B.sub.2 (B.sub.2,MSB), and B.sub.3 (B.sub.3,MSB);
• and
• generating a second packed data result having representations of values A.sub.0 B.sub.0,MSB +A.sub.1 B.sub.1,MSB and A.sub.2 B.sub.2,MSB +A.sub.3 B.sub.3,MSB ;
• in response to a third instruction generating a third packed data result by right shifting each value in said first packed data result by less than N bits;
• and
• in response to a fourth instruction:
• reading said second packed data result and said third packed data result;
• and
• generating a final packed data result having representations of values A.sub.0 B.sub.0 +A.sub.1 B.sub.1 and A.sub.2 B.sub.2 +A.sub.3 B.sub.3.

A machine readable medium having stored thereon data representing a sequence of instructions, said sequence of instructions which, when executed by a processor, cause said processor to perform a method comprising the computer-implemented steps of:

• in response to a first instruction, performing the steps of:
• reading a first packed data and a second packed data, said first packed data having representations of values A.sub.0, A.sub.1, A.sub.2, and A.sub.3 and said second packed data having representation of N least significant bits of values B.sub.0 (B.sub.0,LSB), B.sub.1 (B.sub.1,LSB), B.sub.2 (B.sub.2,LSB), and B.sub.3 (B.sub.3,LSB), wherein each of said least significant bit values B.sub.0,LSB, B.sub.1,LSB, B.sub.2,LSB and B.sub.3,LSB are represented as unsigned integers;
• and
• generating a first packed data result having representations of values A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB and A.sub.2 B.sub.2,LSB +A.sub.3 B.sub.3,LSB ;
• in response to a second instruction, performing the steps of;
• reading said first packed data and a third packed data, said third packed data having representation of most significant bit values B.sub.0 (B.sub.0, MSB), B.sub.1 (B.sub.1,MSB), B.sub.2 (B.sub.2,MSB), and B.sub.3 (B.sub.3,MSB);
• and
• generating a second packed data result having representations of values A.sub.0 B.sub.0,MSB +A.sub.1 B.sub.1,MSB and A.sub.2 B.sub.2,MSB +A.sub.3 B.sub.3,MSB ;
• in response to a third instruction generating a third packed data result by right shifting each value in said first packed data result by N bits;
• and
• in response to a fourth instruction:
• reading said second packed data result and said third packed data result;
• and
• generating a final packed data result having representations of values A.sub.0 B.sub.0 +A.sub.1 B.sub.1 and A.sub.2 B.sub.2 +A.sub.3 B.sub.3.

A machine readable medium having stored thereon data representing a sequence of instructions, said sequence of instructions which, when executed by a processor, cause said processor to perform a method comprising the computer-implemented steps of:

• in response to a first instruction, performing the steps of:
• reading a first packed data and a second packed data, said first packed data having representations of values A.sub.0, A.sub.1, A.sub.2, and A.sub.3 and said second packed data having representation of N least significant bits of value B.sub.0 (B.sub.0,LSB), B.sub.1 (B.sub.1,LSB), B.sub.2 (B.sub.2,LSB), and B.sub.3 (B.sub.3,LSB), wherein each of said least significant bit values B.sub.0,LSB, B.sub.1,LSB, B.sub.2,LSB, and B.sub.3,LSB are represented as signed integers;
• and
• generating first packed data result having representations of values A.sub.0 B.sub.0,LSB +A.sub.1 B.sub.1,LSB and A.sub.2 B.sub.2,LSB +A.sub.3 B.sub.3,LSB ;
• in response to a second instruction, performing the steps of:
• reading said first packed data and a third packed data, said third packed data having representation of most significant bit values B.sub.0 (B.sub.0,MSB), B.sub.1 (B.sub.1,MSB), B.sub.2 (B.sub.2,MSB), and B.sub.3 (B.sub.3,MSB);
• and
• generating a second packed data result having representations of values A.sub.0 B.sub.0,MSB +A.sub.1 B.sub.1,MSB and A.sub.2 B.sub.2,MSB +A.sub.3 B.sub.3,MSB ;
• in response to a third instruction generating a third packed data result by right shifting each value in said first packed data result by less than N bits;
• and
• in response to a fourth instruction:
• reading said second packed data result and said third packed data result;
• and
• generating a final packed data result having representations of values A.sub.0 B.sub.0 +A.sub.1 B.sub.1 and A.sub.2 B.sub.2 +A.sub.3 B.sub.3.

In a computer system, a method of improving the accuracy of multiply-accumulating operation comprising the computer-implemented steps of:

• reading a first packed data and a second packed data, said first packed data having representations of values A.sub.0 and A.sub.1 and said second packed, data having representations of N least significant bits of values B.sub.0 (B.sub.0,LSB) and B.sub.1 (B.sub.1,LSB), wherein each of said least significant bits are represented as unsigned integers;
• and
• generating a first result having a representation of value A.sub.0 B.sub.0,LSB -A.sub.1 B.sub.1,LSB ;
• reading said first packed data and a third packed data, said third packed data having representation of most significant bits of values B.sub.0 (B.sub.0,MSB) and B.sub.1 (B.sub.1,MSB);
• generating a second result having a representation of value A.sub.0 B.sub.0,MSB -A.sub.1 B.sub.1,MSB ;
• generating a third result by right shifting said value A.sub.0 B.sub.0,LSB -A.sub.1 B.sub.1,LSB in said first result by N bits;
• reading said second result and said third result;
• and
• generating a final result having a representation of value A.sub.0 B.sub.0 -A.sub.1 B.sub.1.

In a computer system a method of improving the accuracy of multiply-accumulating operations comprising the computer-implemented steps of:

• reading a first packed data and a second packed data, said first packed data having representations of values A.sub.0 and A.sub.1 and said second packed data having representations of N least significant bits of values B.sub.0 (B.sub.0,LSB) and B.sub.1 (B.sub.1,LSB), wherein each of said values B.sub.0,LSB and B.sub.1,LSB are represented a signed integers;
• and
• generating a first result having a representation of value A.sub.0 B.sub.0,LSB -A.sub.1 B.sub.1,LSB ;
• reading said first packed data and a third packed data, said third packed data having representation of most significant bits of values B.sub.0 (B.sub.0,MSB) and B.sub.1 (B.sub.1,MSB);
• generating a second result having a representation of value A.sub.0 B.sub.0,MSB -A.sub.1 B.sub.1,MSB ;
• generating a third result by right shifting the value A.sub.0 B.sub.0,LSB -A.sub.1 B.sub.1,LSB in said first result by less than N bits;
• reading said second result and said third result;
• and
• generating a final result having a representation of value A.sub.0 B.sub.0 -A.sub.1 B.sub.1.