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Additional Features

This section describes several additional features available in this mode over and above basic memory-reference operations applied to vectors.

It describes extra instructions that perform functions such as setting mask bits based on the individual elements of a vector, other extra instructions that assist with performing the Fast Fourier Transform, and a class of instructions that allows different operations to be performed in parallel on the individual elements of a vector.

Additional Operations

Instructions for setting mask bits corresponding to the values in a vector were present among the short vector instructions. These instructions were special instructions, not standard memory-reference instructions, but had four-bit opcodes patterned after those of the standard memory-reference instructions, along with a separate three-bit byte indication, as part of the second word of the instruction.

Instructions having this function are also provided for use with those long vector addressing modes that have a long vector register as their destination. These instructions, however, are standard memory-reference instructions.

No opcodes exist corresponding to the opcodes used for this purpose with short vectors for the floating types, however. As this is a function requiring only one operand, this is dealt with by performing the integer operation when the destination register is zero, and the corresponding floating-point operation when the destination register is four.

The opcodes so used are the ones corresponding to the unsigned compare, multiply extensibly, and divide extensibly instructions, which are not usable with long vectors.

The same opcodes apply to these instructions as to those pictured above. However, the unsigned compare, multiply extensibly, and divide extensibly operations are not applicable for long vector operations, and thus their opcodes are instead used for instructions used to set up mask registers. Since these are integer operations, and they are single-operand instructions, the floating-point versions of the operations are indicated by a destination register value of four:

Normal         Simple
-------------  -------------
002x11 001110  12x110 001110  SMBLVZB   Set Mask Bit Long Vector if Zero Byte
002x11 001610  12x110 001610  SMBLVPB   Set Mask Bit Long Vector if Positive Byte
002x11 001710  12x110 001710  SMBLVNB   Set Mask Bit Long Vector if Negative Byte

002x11 001114  12x110 001114  SMBLVZM   Set Mask Bit Long Vector if Zero Medium
002x11 001614  12x110 001614  SMBLVPM   Set Mask Bit Long Vector if Positive Medium
002x11 001714  12x110 001714  SMBLVPM   Set Mask Bit Long Vector if Negative Medium

002x11 003110  12x110 003110  SMBLVZH   Set Mask Bit Long Vector if Zero Halfword
002x11 003610  12x110 003610  SMBLVPH   Set Mask Bit Long Vector if Positive Halfword
002x11 003710  12x110 003710  SMBLVNH   Set Mask Bit Long Vector if Negative Halfword

002x11 003114  12x110 003114  SMBLVZF   Set Mask Bit Long Vector if Zero Floating
002x11 003614  12x110 003614  SMBLVPF   Set Mask Bit Long Vector if Positive Floating
002x11 003714  12x110 003714  SMBLVPF   Set Mask Bit Long Vector if Negative Floating

002x11 005110  12x110 005110  SMBLVZ    Set Mask Bit Long Vector if Zero
002x11 005610  12x110 005610  SMBLVP    Set Mask Bit Long Vector if Positive
002x11 005710  12x110 005710  SMBLVN    Set Mask Bit Long Vector if Negative

002x11 005114  12x110 005114  SMBLVZD   Set Mask Bit Long Vector if Zero Double
002x11 005614  12x110 005614  SMBLVPD   Set Mask Bit Long Vector if Positive Double
002x11 005714  12x110 005714  SMBLVND   Set Mask Bit Long Vector if Negative Double

002x11 007110  12x110 007110  SMBLVZL   Set Mask Bit Long Vector if Zero Long
002x11 007610  12x110 007610  SMBLVPL   Set Mask Bit Long Vector if Positive Long
002x11 007710  12x110 007710  SMBLVNL   Set Mask Bit Long Vector if Negative Long

002x11 007114  12x110 007114  SMBLVZQ   Set Mask Bit Long Vector if Zero Quad
002x11 007614  12x110 007614  SMBLVPQ   Set Mask Bit Long Vector if Medium Quad
002x11 007714  12x110 007714  SMBLVPQ   Set Mask Bit Long Vector if Negative Quad

These opcodes, that is, the ones for the unsigned compare, multiply extensibly, and divide extensibly instructions, can also be used for setting mask bits based on the contents of a vector register, or a vector scratchpad element, by using them within the vector register address format, or the vector scratchpad to vector register address format, respectively.

With long vectors, the medium and quad types are allowed, unlike the case of short vectors. This is true both of the long vector registers and the register scratchpad. And the mask bits are only used to control operations involving those registers as well.

In the memory to memory vector instructions of constant and reversed constant type, the S bit, which replaces the I bit for the constant register operand, indicates if 0 that it is found in one of the regular registers, and is indicated by the oR or sR field, and if 1 that it is found in one of the supplementary registers, and is indicated by the oS or sS field of the instruction.

As the identities of the low and high scratchpad registers define the length, the vector-to-scratchpad instructions need no length field; they are similar to multiple-register instructions. None of the vector instruction formats allows the multiply extensibly or divide extensibly instructions, as they have operands of unequal length.

In the vector register constant and vector scratchpad constant modes, the R bit in the instruction allows the destination vector to be subtracted from the source scalar, or the source scalar to be divided by the destination vector, in forming the result to be placed in the destination vector.

The seven-bit opcode 0110000, which would correspond to an "insert long" instruction, is used for those addressing modes in which the destination is the supplementary registers, for the LTL (Load Transposed Long) instruction. This instruction loads the 64 supplementary arithmetic-index registers with the bit matrix transpose of the operand consisting of 64 values each 64 bits long. Using this instruction twice, combined with rearranging the individual 64-bit values in the supplementary arithmetic/index registers, and moving them out, allows sixty-four bit transpositions on 64-bit words to be carried out in parallel.

As with vector mode, the opcodes that would be used for compare instructions instead specify multiply and accumulate instructions when used in conjunction with long vector instruction formats, giving the following opcodes for these operations:

Normal         Simple
-------------  -------------
002x11 002110  12x110 002110  MAH  Multiply and Accumulate Halfword
002x11 004110  12x110 004110  MA   Multiply and Accumulate
002x11 006110  12x110 006110  MAL  Multiply and Accumulate Long
002x11 010110  12x110 010110  MAM  Multiply and Accumulate Medium
002x11 012110  12x110 012110  MAF  Multiply and Accumulate Floating
002x11 014110  12x110 014110  MAD  Multiply and Accumulate Double
002x11 016110  12x110 016110  MAQ  Multiply and Accumulate Quad

And one of the additional bits provided with a ten-bit opcode field is used to specify the Bit Reversed Load and Shuffle operations which are used to assist with Fourier transforms:

002x11 4001xx  BRL16B    002x11 4201xx  BRL16H    002x11 4401xx  BRL16     002x11 4601xx  BRL16L

002x11 4021xx  BRL32B    002x11 4221xx  BRL32H    002x11 4421xx  BRL32     002x11 4621xx  BRL32L
002x11 4031xx  SH32B     002x11 4231xx  SH32H     002x11 4431xx  SH32      002x11 4631xx  SH32L
002x11 4041xx  BRL64B    002x11 4241xx  BRL64H    002x11 4441xx  BRL64     002x11 4641xx  BRL64L
002x11 4051xx  SH64B     002x11 4251xx  SH64H     002x11 4451xx  SH64      002x11 4651xx  SH64L
002x11 4061xx  US128B    002x11 4261xx  US128H    002x11 4461xx  US128     002x11 4661xx  US128L
002x11 4071xx  SH128B    002x11 4271xx  SH128H    002x11 4471xx  SH128     002x11 4671xx  SH128L

002x11 5001xx  BRL16M    002x11 5201xx  BRL16F    002x11 5401xx  BRL16D    002x11 5501xx  BRL16Q

002x11 5021xx  BRL32M    002x11 5221xx  BRL32F    002x11 5421xx  BRL32D    002x11 5521xx  BRL32Q
002x11 5031xx  SH32M     002x11 5231xx  SH32M     002x11 5431xx  SH32D     002x11 5531xx  SH32Q
002x11 5041xx  BRL64M    002x11 5241xx  BRL64F    002x11 5441xx  BRL64D    002x11 5541xx  BRL64Q
002x11 5051xx  SH64M     002x11 5251xx  SH64F     002x11 5451xx  SH64D     002x11 5551xx  SH64Q
002x11 5061xx  US128M    002x11 5261xx  US128F    002x11 5461xx  US128D    002x11 5561xx  US128Q
002x11 5071xx  SH128M    002x11 5271xx  SH128F    002x11 5471xx  SH128D    002x11 5571xx  SH128Q

These are the various Bit-Reversed Load instructions and the various Shuffle instructions.

Again, in Simple Mode, the first halfword of these instructions, 002x11, becomes 12x110, following the general rule given above.

For the BRL64 instructions, the range must be the range of locations within a vector:


and the instruction loads register abcdef (in binary) of the destination from register fedcba of the source. This operation has some use with the Fast Fourier Transform algorithm, as we will see below.

For the BRL32 instructions, the range must be one or both of the ranges:


and within each range, register xabcde of the destination is loaded from register xedcba of the source.

For the BRL16 instructions, the range must be any contiguous combination of the following subranges:


and within each range, register xxabcd of the destination is loaded from register xxdcba of the source.

Thus, a BRL16 instruction takes elements 0 through 16 of the source, and places them in the destination in the order:

 0  8  4 12  2 10  6 14  1  9  5 13  3 11  7 15

The SH32 and SH64 instructions have the same ranges as the BRL32 and BRL64 instructions. A Shuffle instruction combines elements from the first and second halves of each subrange in the source by taking one element from each half in turn alternately.

Thus, an SH32 instruction takes the elements 0 through 31 of the source, and places them in the destination in the order:

 0 16  1 17  2 18  3 19  4 20  5 21  6 22  7 23
 8 24  9 25 10 26 11 27 12 28 13 29 14 30 15 31

The range given for an SH128 instruction must also be from 0 to 63, but its operands must be even-numbered long vector registers or long vector scratchpad locations, as the source and destination are considered to be the entire addressed register and the entire register following.

The shuffle instructions are also intended for use in performing Fast Fourier Transform calculations. One long vector register would normally contain the real parts of the numbers involved, and another one the complex parts: the diagram below, showing the classic Cooley-Tukey Fast Fourier Transform algorithm in its original form, followed by the reversed, or Sande-Tukey form of the algorithm, shows why the shuffle operation is highly useful to an efficient fast Fourier transform using vector arithmetic.

All three formulations are equivalent, but the third performs all its operations with vectors of the maximum length. Since the operations, in this eight point FFT, use vectors of four items, it is also clear why, given the ability to perform vector operations on vectors with 64 elements, the SH128 instruction needed to be defined.

Note that while the operation in the last column of the FFT using a shuffle after each stage appears the same as that for the classic Cooley-Tukey algorithm, the elements of the transformed vector are not in natural order, but are in bit-reversed order within each half, which makes bit-reversed operations having half the length of the shuffle used still relevant. Thus, the algorithm illustrated in the third part of the diagram is the Pease framework for the Fast Fourier Transform.

It is intended that a 128-point FFT would make use of the SH128 and BRL64 instructions, where the real parts of the first 64 points, the imaginary parts of the first 64 points, the real parts of the second 64 points, and the imaginary parts of the second 64 points would each occupy a vector.

The US128 instructions perform the inverse operation of the SH128 instructions, and are used in converting arrays of complex numbers into separate vectors of their real and imaginary parts.

It should be noted that a more modern form of the Fast Fourier Transform, the Stockham framework, is currently more popular than the Pease framework:

This form of the FFT corrects the flaw of the Pease framework, and presents its result with elements in order. However, a different transposition of vector elements is required at each stage of the algorithm, first a shuffle of individual elements, then a shuffle of pairs of elements, then a shuffle of groups of four elements, and so on. For hardware acceleration with 64-element vectors, therefore, the Stockham framework requires that five special operations be defined, while the Pease framework requires only two: SH128 and LBR64. In the case of short vector operations, where the length of the vector, rather than the number of its elements, is fixed, it is the Stockham framework rather than the Pease framework which is simpler to implement, and thus it is the framework for which hardware assist instructions are provided there.

When the op2 field equals 2, another set of useful operations involving rearranging the items within a vector of 64 elements is provided.

Once again, the first four bits of the main opcode indicate the type of the operands:

0000 byte
0010 halfword
0100 integer
0110 long
1000 medium
1001 floating
1010 double
1011 quad

and this time the last three bits indicate displacements:

      X    Y
000  -1   -1
001   0   -1
010  +1   -1
011  -1    0
100  +1    0
101  -1   +1
110   0   +1
111  +1   +1

where the 64 elements of a long vector are considered to be arranged in a square array in the following order:

 56 57 58 59 60 61 62 63
 48 49 50 51 52 53 54 55
 40 41 42 43 44 45 46 47
 32 33 34 35 36 37 38 39
 24 25 26 27 28 29 30 31
 16 17 18 19 20 21 22 23
  8  9 10 11 12 13 14 15
  0  1  2  3  4  5  6  7

and a displacement of (+1,0) means that element 18 is loaded from element 19, increased by one in the X direction; a displacement of (0,+1) means that element 18 is loaded from element 26, an increase of one in the Y direction.

The instruction is maskable, and the rows and columns are both considered to wrap around, so that if 7 comes after 6, 0 comes after 7. These instructions allow values in a long vector to interact with their nearest neighbors where a long vector is considered to be acting as part of a two-dimensional array of numbers.

Multi-Way Vector Operations

In order to keep the 64 arithmetic-logic units of the long vector unit as busy as possible, while stopping short of having 64 separate instruction streams, instruction modes are defined in which one to three mask registers can be designated in an instruction.

This type of operation is available under the same terms as the three-address long vector instructions: from Normal Mode, Scratchpad Mode, Condensed Mode, Compact Mode and Local Mode and with modified opcodes from Simple Mode as well, since it is indicated by a prefix consisting of a register-to-register instruction invalidated by having the same register as source and destination.

If one mask register is designated, instead of merely indicating whether or not an operation is performed, it indicates which of two operations are performed.

Similarly, two mask registers indicate, by means of their corresponding bits, which of four operations are performed on each of the 64 values accessed in parallel in the supplementary registers, the long vector registers, or the long vector scratchpad.

And three mask registers indicate one of eight possible operations.

The type field in the instruction has the usual interpretation, and can indicate fixed-point as well as floating types.

The possible operations are:

000 no operation
001 subtract reversed
010 load
011 divide reversed
100 add
101 subtract
110 multiply
111 divide

There is a load instruction, causing the destination to be replaced by the source, but no store instruction, since that cannot easily be executed in parallel with the other operations.

Subtract reversed replaces the destination with the source minus the destination, and divide reversed replaces the destination with the source divided by the destination.

The bottom portion of the diagram shows the last part of the instruction, having the same form for two-way, four-way, and eight-way instructions, which gives the two operands to the instruction.

The instructions used for this feature have the following form:

The possible operations specified by each of the three-bit operation fields are:

000 no operation
001 subtract reversed
010 load
011 divide reversed
100 add
101 subtract
110 multiply
111 divide

Each instruction begins with the 16-bit prefix for operate instructions, and then includes a beginning part, in the format shown.

The prefix becomes 100000 instead of 010000 in Simple Mode.

The two-way vector operation instructions, if acting on fixed-point vectors, occupy the opcode space left over from standard register to register instructions; if acting on floating-point vectors,they occupy the opcode space continuing from standard memory-reference instructions. In both case, the opcode space left over by the fact that a standard seven-bit opcode does not begin with the first two bits equal to 11 is used.

The opcode space left over by the load and store instructions with standard indexing when the base register is zero, as this is not needed to indicate an alternate way of expressing register to register forms of these instructions is what is used by both the four-way and eight-way vector operation instructions.

Each instruction also includes an end part, in the format shown in the diagram. Note that the end part of the instruction always begins with a 1.

When a halfword beginning with a 0 is found immediately after the end of the beginning part of the instruction, that means this halfword is the middle part of the instruction, and that the instruction is ranged; the low and high destination scratchpad fields of the instruction specify the start and end of the contiguous group of elements, from among the possible 64 elements of a vector, that are operated upon by the instruction.

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