[[!tag standards]]
+[[!toc levels=1]]
+
# Implementation Log
* ternlogi <https://bugs.libre-soc.org/show_bug.cgi?id=745>
* grev <https://bugs.libre-soc.org/show_bug.cgi?id=755>
-* remove Rc=1 from ternlog due to conflicts in encoding as well
- as saving space <https://bugs.libre-soc.org/show_bug.cgi?id=753#c5>
* GF2^M <https://bugs.libre-soc.org/show_bug.cgi?id=782>
+
# bitmanipulation
**DRAFT STATUS**
+pseudocode: [[openpower/isa/bitmanip]]
+
this extension amalgamates bitmanipulation primitives from many sources, including RISC-V bitmanip, Packed SIMD, AVX-512 and OpenPOWER VSX. Vectorisation and SIMD are removed: these are straight scalar (element) operations making them suitable for embedded applications.
Vectorisation Context is provided by [[openpower/sv]].
# summary
-minor opcode allocation
+two major opcodes are needed
+
+ternlog has its own major opcode
+
+| 29.30 |31| name |
+| ------ |--| --------- |
+| 0 0 |Rc| ternlogi |
+| 0 1 |sz| ternlogv |
+| 1 iv | | grevlogi |
+
+2nd major opcode for other bitmanip: minor opcode allocation
+
+| 28.30 |31| name |
+| ------ |--| --------- |
+| -00 |0 | xpermi |
+| -00 |1 | grevlog |
+| -01 | | crternlog |
+| 010 |Rc| bitmask |
+| 011 | | gf/cl madd* |
+| 110 |Rc| 1/2-op |
+| 111 | | bmrevi |
- | 28.30 |31| name |
- | ------ |--| --------- |
- | -00 |0 | ternlogi |
- | -00 |1 | grevlog |
- | -01 | | grevlogi |
- | 010 |Rc| bitmask |
- | 011 |Rc| gfmadd* |
- | 110 |Rc| 1/2-op |
- | 111 |1 | ternlogv |
- | 111 |0 | ternlogcr |
1-op and variants
| RT | RA | RB | shuf | shuffle |
| RT | RA | RB | unshuf| shuffle |
| RT | RA | RB | width | xperm |
-| RT | RA | RB | type | minmax |
+| RT | RA | RB | type | av minmax |
| RT | RA | RB | | av abs avgadd |
| RT | RA | RB | type | vmask ops |
| RT | RA | RB | | |
3 ops
* grevlog
-* ternlog bitops
* GF mul-add
* bitmask-reverse
TODO: convert all instructions to use RT and not RS
+| 0.5|6.8 | 9.11|12.14|15.17|18.20|21.28 | 29.30|31|name|
+| -- | -- | --- | --- | --- |-----|----- | -----|--|----|
+| NN | BT | BA | BB | BC |m0-2 | imm | 10 |m3|crternlog|
+
| 0.5|6.10|11.15|16.20 |21..25 | 26....30 |31| name |
| -- | -- | --- | --- | ----- | -------- |--| ------ |
-| NN | RT | RA | RB | im0-4 | im5-7 00 |0 | ternlogi |
+| NN | RT | RA |itype/| im0-4 | im5-7 00 |0 | xpermi |
| NN | RT | RA | RB | im0-4 | im5-7 00 |1 | grevlog |
-| NN | RT | RA | s0-4 | im0-4 | im5-7 01 |s5| grevlogi |
-| NN | RS | RA | RB | RC | 00 011 |Rc| gfmadd |
-| NN | RS | RA | RB | RC | 10 011 |Rc| gfmaddsub |
-| NN | RT | RA | RB | sh0-4 | sh5 1 011 |Rc| bmrevi |
-
-| 0.5|6.10|11.15| 16.23 |24.27 | 28.30 |31| name |
-| -- | -- | --- | ----- | ---- | ----- |--| ------ |
-| NN | RT | RA | imm | mask | 111 |1 | ternlogv |
-
-| 0.5|6.8 | 9.11|12.14|15|16.23|24.27 | 28.30|31| name |
-| -- | -- | --- | --- |- |-----|----- | -----|--| -------|
-| NN | BA | BB | BC |0 |imm | mask | 111 |0 | ternlogcr |
+| NN | | | | | ..... 01 |0 | crternlog |
+| NN | RT | RA | RB | RC | mode 010 |Rc| bitmask* |
+| NN | | | | | 00 011 | | rsvd |
+| NN | | | | | 01 011 | | rsvd |
+| NN | | | | | 10 011 | | rsvd |
+| NN | | | | | 11 011 |Rc| setvl |
+| NN | RT | RA | RB | sh0-4 | sh5 1 111 |Rc| bmrevi |
ops (note that av avg and abs as well as vec scalar mask
-are included here)
+are included here [[sv/vector_ops]], and
+the [[sv/av_opcodes]])
TODO: convert from RA, RB, and RC to correct field names of RT, RA, and RB, and
double check that instructions didn't need 3 inputs.
| 0.5|6.10|11.15|16.20| 21 | 22.23 | 24....30 |31| name |
| -- | -- | --- | --- | -- | ----- | -------- |--| ---- |
-| NN | RA | RB | | 0 | | 0000 110 |Rc| rsvd |
-| NN | RA | RB | RC | 1 | itype | 0000 110 |Rc| xperm |
-| NN | RA | RB | RC | 0 | itype | 0100 110 |Rc| minmax |
-| NN | RA | RB | RC | 1 | 00 | 0100 110 |Rc| av avgadd |
-| NN | RA | RB | RC | 1 | 01 | 0100 110 |Rc| av abs |
-| NN | RA | RB | | 1 | 10 | 0100 110 |Rc| rsvd |
-| NN | RA | RB | | 1 | 11 | 0100 110 |Rc| rsvd |
-| NN | RA | RB | sh | SH | itype | 1000 110 |Rc| bmopsi |
-| NN | RA | RB | | | | 1100 110 |Rc| rsvd |
-| NN | RT | RA | RB | 1 | 00 | 0001 110 |Rc| gfdiv |
-| NN | RT | RA | RB | 1 | 01 | 0001 110 |Rc| gfmod |
-| NN | RT | RA | RB | 1 | 10 | 0001 110 |Rc| gfmul |
-| NN | RA | RB | | 1 | 11 | 0001 110 |Rc| gfinf |
+| NN | RS | me | sh | SH | ME 0 | nn00 110 |Rc| bmopsi |
+| NN | RS | RB | sh | SH | 0 1 | nn00 110 |Rc| bmopsi |
+| NN | RT | RA | RB | 1 | 00 | 0001 110 |Rc| cldiv |
+| NN | RT | RA | RB | 1 | 01 | 0001 110 |Rc| clmod |
+| NN | RT | RA | RB | 1 | 10 | 0001 110 |Rc| |
+| NN | RT | RB | RB | 1 | 11 | 0001 110 |Rc| clinv |
| NN | RA | RB | RC | 0 | 00 | 0001 110 |Rc| vec sbfm |
| NN | RA | RB | RC | 0 | 01 | 0001 110 |Rc| vec sofm |
| NN | RA | RB | RC | 0 | 10 | 0001 110 |Rc| vec sifm |
| NN | RA | RB | RC | 0 | 11 | 0001 110 |Rc| vec cprop |
-| NN | RA | RB | | 0 | | 0101 110 |Rc| rsvd |
+| NN | RT | RA | RB | 0 | | 0101 110 |Rc| rsvd |
+| NN | RT | RA | RB | 1 | itype | 0101 110 |Rc| xperm |
+| NN | RA | RB | RC | 0 | itype | 1001 110 |Rc| av minmax |
+| NN | RA | RB | RC | 1 | 00 | 1001 110 |Rc| av abss |
+| NN | RA | RB | RC | 1 | 01 | 1001 110 |Rc| av absu|
+| NN | RA | RB | | 1 | 10 | 1001 110 |Rc| av avgadd |
+| NN | RA | RB | | 1 | 11 | 1001 110 |Rc| rsvd |
+| NN | RA | RB | | | | 1101 110 |Rc| rsvd |
| NN | RA | RB | RC | 0 | 00 | 0010 110 |Rc| gorc |
| NN | RA | RB | sh | SH | 00 | 1010 110 |Rc| gorci |
| NN | RA | RB | RC | 0 | 00 | 0110 110 |Rc| gorcw |
| NN | RA | RB | RC | 0 | 01 | 0110 110 |Rc| grevw |
| NN | RA | RB | sh | 0 | 01 | 1110 110 |Rc| grevwi |
| NN | RA | RB | RC | 1 | 01 | 1110 110 |Rc| bmatxor |
-| NN | RA | RB | RC | 0 | 10 | 0010 110 |Rc| shfl |
-| NN | RA | RB | sh | SH | 10 | 1010 110 |Rc| shfli |
-| NN | RA | RB | RC | 0 | 10 | 0110 110 |Rc| shflw |
-| NN | RA | RB | RC | | 10 | 1110 110 |Rc| rsvd |
+| NN | RA | RB | RC | | 10 | --10 110 |Rc| rsvd |
| NN | RA | RB | RC | 0 | 11 | 1110 110 |Rc| clmulr |
| NN | RA | RB | RC | 1 | 11 | 1110 110 |Rc| clmulh |
-| NN | | | | | | --11 110 |Rc| setvl |
-
-# bit to byte permute
-
-similar to matrix permute in RV bitmanip, which has XOR and OR variants
-
- do j = 0 to 7
- do k = 0 to 7
- b = VSR[VRB+32].dword[i].byte[k].bit[j]
- VSR[VRT+32].dword[i].byte[j].bit[k] = b
-
-# int min/max
-
-signed and unsigned min/max for integer. this is sort-of partly synthesiseable in [[sv/svp64]] with pred-result as long as the dest reg is one of the sources, but not both signed and unsigned. when the dest is also one of the srces and the mv fails due to the CR bittest failing this will only overwrite the dest where the src is greater (or less).
-
-signed/unsigned min/max gives more flexibility.
-
-```
-uint_xlen_t min(uint_xlen_t rs1, uint_xlen_t rs2)
-{ return (int_xlen_t)rs1 < (int_xlen_t)rs2 ? rs1 : rs2;
-}
-uint_xlen_t max(uint_xlen_t rs1, uint_xlen_t rs2)
-{ return (int_xlen_t)rs1 > (int_xlen_t)rs2 ? rs1 : rs2;
-}
-uint_xlen_t minu(uint_xlen_t rs1, uint_xlen_t rs2)
-{ return rs1 < rs2 ? rs1 : rs2;
-}
-uint_xlen_t maxu(uint_xlen_t rs1, uint_xlen_t rs2)
-{ return rs1 > rs2 ? rs1 : rs2;
-}
-```
-
+| NN | | | | | | --11 110 |Rc| rsvd |
# ternlog bitops
## ternlogi
-| 0.5|6.10|11.15|16.20| 21..25| 26..30 |31|
-| -- | -- | --- | --- | ----- | -------- |--|
-| NN | RT | RA | RB | im0-4 | im5-7 00 |0 |
+| 0.5|6.10|11.15|16.20| 21..28|29.30|31|
+| -- | -- | --- | --- | ----- | --- |--|
+| NN | RT | RA | RB | im0-7 | 00 |Rc|
lut3(imm, a, b, c):
idx = c << 2 | b << 1 | a
for i in range(64):
RT[i] = lut3(imm, RB[i], RA[i], RT[i])
-bits 21..22 may be used to specify a mode, such as treating the whole integer zero/nonzero and putting 1/0 in the result, rather than bitwise test.
-
-## ternlog
+## ternlogv
-a 4 operand variant which becomes more along the lines of an FPGA:
+also, another possible variant involving swizzle-like selection
+and masking, this only requires 3 64 bit registers (RA, RS, RB) and
+only 16 LUT3s.
+
+Note however that unless XLEN matches sz, this instruction
+is a Read-Modify-Write: RS must be read as a second operand
+and all unmodified bits preserved. SVP64 may provide limited
+alternative destination for RS from RS-as-source, but again
+all unmodified bits must still be copied.
+
+| 0.5|6.10|11.15|16.20|21.28 | 29.30 |31|
+| -- | -- | --- | --- | ---- | ----- |--|
+| NN | RS | RA | RB |idx0-3| 01 |sz|
+
+ SZ = (1+sz) * 8 # 8 or 16
+ raoff = MIN(XLEN, idx0 * SZ)
+ rboff = MIN(XLEN, idx1 * SZ)
+ rcoff = MIN(XLEN, idx2 * SZ)
+ rsoff = MIN(XLEN, idx3 * SZ)
+ imm = RB[0:8]
+ for i in range(MIN(XLEN, SZ)):
+ ra = RA[raoff:+i]
+ rb = RA[rboff+i]
+ rc = RA[rcoff+i]
+ res = lut3(imm, ra, rb, rc)
+ RS[rsoff+i] = res
-| 0.5|6.10|11.15|16.20|21.25| 26...30 |31|
-| -- | -- | --- | --- | --- | -------- |--|
-| NN | RT | RA | RB | RC | mode 100 |1 |
+## ternlogcr
- for i in range(64):
- idx = RT[i] << 2 | RA[i] << 1 | RB[i]
- RT[i] = (RC & (1<<idx)) != 0
+another mode selection would be CRs not Ints.
-mode (2 bit) may be used to do inversion of ordering, similar to carryless mul,
-3 modes.
+| 0.5|6.8 | 9.11|12.14|15.17|18.20|21.28 | 29.30|31|
+| -- | -- | --- | --- | --- |-----|----- | -----|--|
+| NN | BT | BA | BB | BC |m0-2 | imm | 10 |m3|
-## ternlogv
+ mask = m0-3,m4
+ for i in range(4):
+ if not mask[i] continue
+ crregs[BT][i] = lut3(imm,
+ crregs[BA][i],
+ crregs[BB][i],
+ crregs[BC][i])
-also, another possible variant involving swizzle and vec4:
-| 0.5|6.10|11.15| 16.23 |24.27 | 28.30 |31|
-| -- | -- | --- | ----- | ---- | ----- |--|
-| NN | RT | RA | imm | mask | 111 |1 |
+# int min/max
- for i in range(8):
- idx = RA.x[i] << 2 | RA.y[i] << 1 | RA.z[i]
- res = (imm & (1<<idx)) != 0
- for j in range(3):
- if mask[j]: RT[i+j*8] = res
+required for
+the [[sv/av_opcodes]]
-## ternlogcr
+signed and unsigned min/max for integer. this is sort-of partly synthesiseable in [[sv/svp64]] with pred-result as long as the dest reg is one of the sources, but not both signed and unsigned. when the dest is also one of the srces and the mv fails due to the CR bittest failing this will only overwrite the dest where the src is greater (or less).
-another mode selection would be CRs not Ints.
+signed/unsigned min/max gives more flexibility.
-| 0.5|6.8 | 9.11|12.14|15|16.23|24.27 | 28.30|31|
-| -- | -- | --- | --- |- |-----|----- | -----|--|
-| NN | BA | BB | BC |0 |imm | mask | 111 |0 |
+```
+uint_xlen_t min(uint_xlen_t rs1, uint_xlen_t rs2)
+{ return (int_xlen_t)rs1 < (int_xlen_t)rs2 ? rs1 : rs2;
+}
+uint_xlen_t max(uint_xlen_t rs1, uint_xlen_t rs2)
+{ return (int_xlen_t)rs1 > (int_xlen_t)rs2 ? rs1 : rs2;
+}
+uint_xlen_t minu(uint_xlen_t rs1, uint_xlen_t rs2)
+{ return rs1 < rs2 ? rs1 : rs2;
+}
+uint_xlen_t maxu(uint_xlen_t rs1, uint_xlen_t rs2)
+{ return rs1 > rs2 ? rs1 : rs2;
+}
+```
- for i in range(4):
- if not mask[i] continue
- idx = crregs[BA][i] << 2 |
- crregs[BB][i] << 1 |
- crregs[BC][i]
- crregs[BA][i] = (imm & (1<<idx)) != 0
## cmix
| 0.5|6.10|11.15|16.20|21.25| 26..30 |31| name |
| -- | -- | --- | --- | --- | ------- |--| ----- |
-| NN | RT | RA | RB | RC | mode 010 |Rc| bm* |
+| NN | RS | RA | RB | RC | mode 010 |Rc| bm* |
+
+Immediate-variant is an overwrite form:
+| 0.5|6.10|11.15|16.20| 21 | 22.23 | 24....30 |31| name |
+| -- | -- | --- | --- | -- | ----- | -------- |--| ---- |
+| NN | RS | RB | sh | SH | itype | 1000 110 |Rc| bm*i |
```
-uint_xlen_t bmset(RA, RB, sh)
+def MASK(x, y):
+ if x < y:
+ x = x+1
+ mask_a = ((1 << x) - 1) & ((1 << 64) - 1)
+ mask_b = ((1 << y) - 1) & ((1 << 64) - 1)
+ elif x == y:
+ return 1 << x
+ else:
+ x = x+1
+ mask_a = ((1 << x) - 1) & ((1 << 64) - 1)
+ mask_b = (~((1 << y) - 1)) & ((1 << 64) - 1)
+ return mask_a ^ mask_b
+
+
+uint_xlen_t bmset(RS, RB, sh)
{
int shamt = RB & (XLEN - 1);
mask = (2<<sh)-1;
- return RA | (mask << shamt);
+ return RS | (mask << shamt);
}
-uint_xlen_t bmclr(RA, RB, sh)
+uint_xlen_t bmclr(RS, RB, sh)
{
int shamt = RB & (XLEN - 1);
mask = (2<<sh)-1;
- return RA & ~(mask << shamt);
+ return RS & ~(mask << shamt);
}
-uint_xlen_t bminv(RA, RB, sh)
+uint_xlen_t bminv(RS, RB, sh)
{
int shamt = RB & (XLEN - 1);
mask = (2<<sh)-1;
- return RA ^ (mask << shamt);
+ return RS ^ (mask << shamt);
}
-uint_xlen_t bmext(RA, RB, sh)
+uint_xlen_t bmext(RS, RB, sh)
{
int shamt = RB & (XLEN - 1);
mask = (2<<sh)-1;
- return mask & (RA >> shamt);
+ return mask & (RS >> shamt);
}
```
-bitmask extract with reverse. can be done by bitinverting all of RA and getting bits of RA from the opposite end.
+bitmask extract with reverse. can be done by bit-order-inverting all of RB and getting bits of RB from the opposite end.
+
+when RA is zero, no shift occurs. this makes bmextrev useful for
+simply reversing all bits of a register.
```
-msb = rb[5:0];
-rev[0:msb] = ra[msb:0];
+msb = ra[5:0];
+rev[0:msb] = rb[msb:0];
rt = ZE(rev[msb:0]);
uint_xlen_t bmextrev(RA, RB, sh)
{
- int shamt = (RB & (XLEN - 1));
+ int shamt = XLEN-1;
+ if (RA != 0) shamt = (GPR(RA) & (XLEN - 1));
shamt = (XLEN-1)-shamt; # shift other end
- bra = bitreverse(RA) # swap LSB-MSB
+ bra = bitreverse(RB) # swap LSB-MSB
mask = (2<<sh)-1;
return mask & (bra >> shamt);
}
# grevlut
generalised reverse combined with a pair of LUT2s and allowing
-zero when RA=0 provides a wide range of instructions
+a constant `0b0101...0101` when RA=0, and an option to invert
+(including when RA=0, giving a constant 0b1010...1010 as the
+initial value) provides a wide range of instructions
and a means to set regular 64 bit patterns in one
32 bit instruction.
the two LUT2s are applied left-half (when not swapping)
and right-half (when swapping) so as to allow a wider
-range of options
+range of options.
<img src="/openpower/sv/grevlut2x2.jpg" width=700 />
+* A value of `0b11001010` for the immediate provides
+the functionality of a standard "grev".
+* `0b11101110` provides gorc
+
+grevlut should be arranged so as to produce the constants
+needed to put into bext (bitextract) so as in turn to
+be able to emulate x86 pmovmask instructions <https://www.felixcloutier.com/x86/pmovmskb>.
+This only requires 2 instructions (grevlut, bext).
+
+Note that if the mask is required to be placed
+directly into CR Fields (for use as CR Predicate
+masks rather than a integer mask) then sv.ori
+may be used instead, bearing in mind that sv.ori
+is a 64-bit instruction, and `VL` must have been
+set to the required length:
+
+ sv.ori./elwid=8 r10.v, r10.v, 0
+
+The following settings provide the required mask constants:
+
+| RA | RB | imm | iv | result |
+| ------- | ------- | ---------- | -- | ---------- |
+| 0x555.. | 0b10 | 0b01101100 | 0 | 0x111111... |
+| 0x555.. | 0b110 | 0b01101100 | 0 | 0x010101... |
+| 0x555.. | 0b1110 | 0b01101100 | 0 | 0x00010001... |
+| 0x555.. | 0b10 | 0b11000110 | 1 | 0x88888... |
+| 0x555.. | 0b110 | 0b11000110 | 1 | 0x808080... |
+| 0x555.. | 0b1110 | 0b11000110 | 1 | 0x80008000... |
+
+Better diagram showing the correct ordering of shamt (RB). A LUT2
+is applied to all locations marked in red using the first 4
+bits of the immediate, and a separate LUT2 applied to all
+locations in green using the upper 4 bits of the immediate.
+
+<img src="/openpower/sv/grevlut.png" width=700 />
+
+demo code [[openpower/sv/grevlut.py]]
+
```
lut2(imm, a, b):
idx = b << 1 | a
step_o[j] = lut2(imm, step_i[j], step_i[j ^ chunk_size])
return step_o
-uint64_t grevlut64(uint64_t RA, uint64_t RB, uint8 imm)
+uint64_t grevlut64(uint64_t RA, uint64_t RB, uint8 imm, bool iv)
{
- uint64_t x = RA;
+ uint64_t x = 0x5555_5555_5555_5555;
+ if (RA != 0) x = GPR(RA);
+ if (iv) x = ~x;
int shamt = RB & 63;
for i in 0 to 6
step = 1<<i
```
+| 0.5|6.10|11.15|16.20 |21..25 | 26....30 |31| name |
+| -- | -- | --- | --- | ----- | -------- |--| ------ |
+| NN | RT | RA | s0-4 | im0-4 | im5-7 1 iv |s5| grevlogi |
+| NN | RT | RA | RB | im0-4 | im5-7 00 |1 | grevlog |
+
+
# grev
based on RV bitmanip, this is also known as a butterfly network. however
```
-# shuffle / unshuffle
+# xperm
-based on RV bitmanip
+based on RV bitmanip.
-```
-uint32_t shfl32(uint32_t RA, uint32_t RB)
-{
- uint32_t x = RA;
- int shamt = RB & 15;
- if (shamt & 8) x = shuffle32_stage(x, 0x00ff0000, 0x0000ff00, 8);
- if (shamt & 4) x = shuffle32_stage(x, 0x0f000f00, 0x00f000f0, 4);
- if (shamt & 2) x = shuffle32_stage(x, 0x30303030, 0x0c0c0c0c, 2);
- if (shamt & 1) x = shuffle32_stage(x, 0x44444444, 0x22222222, 1);
- return x;
-}
-uint32_t unshfl32(uint32_t RA, uint32_t RB)
-{
- uint32_t x = RA;
- int shamt = RB & 15;
- if (shamt & 1) x = shuffle32_stage(x, 0x44444444, 0x22222222, 1);
- if (shamt & 2) x = shuffle32_stage(x, 0x30303030, 0x0c0c0c0c, 2);
- if (shamt & 4) x = shuffle32_stage(x, 0x0f000f00, 0x00f000f0, 4);
- if (shamt & 8) x = shuffle32_stage(x, 0x00ff0000, 0x0000ff00, 8);
- return x;
-}
+RA contains a vector of indices to select parts of RB to be
+copied to RT. The immediate-variant allows up to an 8 bit
+pattern (repeated) to be targetted at different parts of RT
-uint64_t shuffle64_stage(uint64_t src, uint64_t maskL, uint64_t maskR, int N)
-{
- uint64_t x = src & ~(maskL | maskR);
- x |= ((src << N) & maskL) | ((src >> N) & maskR);
- return x;
-}
-uint64_t shfl64(uint64_t RA, uint64_t RB)
-{
- uint64_t x = RA;
- int shamt = RB & 31;
- if (shamt & 16) x = shuffle64_stage(x, 0x0000ffff00000000LL,
- 0x00000000ffff0000LL, 16);
- if (shamt & 8) x = shuffle64_stage(x, 0x00ff000000ff0000LL,
- 0x0000ff000000ff00LL, 8);
- if (shamt & 4) x = shuffle64_stage(x, 0x0f000f000f000f00LL,
- 0x00f000f000f000f0LL, 4);
- if (shamt & 2) x = shuffle64_stage(x, 0x3030303030303030LL,
- 0x0c0c0c0c0c0c0c0cLL, 2);
- if (shamt & 1) x = shuffle64_stage(x, 0x4444444444444444LL,
- 0x2222222222222222LL, 1);
- return x;
-}
-uint64_t unshfl64(uint64_t RA, uint64_t RB)
+```
+uint_xlen_t xpermi(uint8_t imm8, uint_xlen_t RB, int sz_log2)
{
- uint64_t x = RA;
- int shamt = RB & 31;
- if (shamt & 1) x = shuffle64_stage(x, 0x4444444444444444LL,
- 0x2222222222222222LL, 1);
- if (shamt & 2) x = shuffle64_stage(x, 0x3030303030303030LL,
- 0x0c0c0c0c0c0c0c0cLL, 2);
- if (shamt & 4) x = shuffle64_stage(x, 0x0f000f000f000f00LL,
- 0x00f000f000f000f0LL, 4);
- if (shamt & 8) x = shuffle64_stage(x, 0x00ff000000ff0000LL,
- 0x0000ff000000ff00LL, 8);
- if (shamt & 16) x = shuffle64_stage(x, 0x0000ffff00000000LL,
- 0x00000000ffff0000LL, 16);
- return x;
+ uint_xlen_t r = 0;
+ uint_xlen_t sz = 1LL << sz_log2;
+ uint_xlen_t mask = (1LL << sz) - 1;
+ uint_xlen_t RA = imm8 | imm8<<8 | ... | imm8<<56;
+ for (int i = 0; i < XLEN; i += sz) {
+ uint_xlen_t pos = ((RA >> i) & mask) << sz_log2;
+ if (pos < XLEN)
+ r |= ((RB >> pos) & mask) << i;
+ }
+ return r;
}
-```
-
-# xperm
-
-based on RV bitmanip
-
-```
uint_xlen_t xperm(uint_xlen_t RA, uint_xlen_t RB, int sz_log2)
{
uint_xlen_t r = 0;
uint_xlen_t sz = 1LL << sz_log2;
uint_xlen_t mask = (1LL << sz) - 1;
for (int i = 0; i < XLEN; i += sz) {
- uint_xlen_t pos = ((RB >> i) & mask) << sz_log2;
+ uint_xlen_t pos = ((RA >> i) & mask) << sz_log2;
if (pos < XLEN)
- r |= ((RA >> pos) & mask) << i;
+ r |= ((RB >> pos) & mask) << i;
}
return r;
}
return x;
}
+```
+# Introduction to Carry-less and GF arithmetic
+
+* obligatory xkcd <https://xkcd.com/2595/>
+
+There are three completely separate types of Galois-Field-based
+arithmetic that we implement which are not well explained even in introductory literature. A slightly oversimplified explanation
+is followed by more accurate descriptions:
+
+* `GF(2)` carry-less binary arithmetic. this is not actually a Galois Field,
+ but is accidentally referred to as GF(2) - see below as to why.
+* `GF(p)` modulo arithmetic with a Prime number, these are "proper" Galois Fields
+* `GF(2^N)` carry-less binary arithmetic with two limits: modulo a power-of-2
+ (2^N) and a second "reducing" polynomial (similar to a prime number), these
+ are said to be GF(2^N) arithmetic.
+
+further detailed and more precise explanations are provided below
+
+* **Polynomials with coefficients in `GF(2)`**
+ (aka. Carry-less arithmetic -- the `cl*` instructions).
+ This isn't actually a Galois Field, but its coefficients are. This is
+ basically binary integer addition, subtraction, and multiplication like
+ usual, except that carries aren't propagated at all, effectively turning
+ both addition and subtraction into the bitwise xor operation. Division and
+ remainder are defined to match how addition and multiplication works.
+* **Galois Fields with a prime size**
+ (aka. `GF(p)` or Prime Galois Fields -- the `gfp*` instructions).
+ This is basically just the integers mod `p`.
+* **Galois Fields with a power-of-a-prime size**
+ (aka. `GF(p^n)` or `GF(q)` where `q == p^n` for prime `p` and
+ integer `n > 0`).
+ We only implement these for `p == 2`, called Binary Galois Fields
+ (`GF(2^n)` -- the `gfb*` instructions).
+ For any prime `p`, `GF(p^n)` is implemented as polynomials with
+ coefficients in `GF(p)` and degree `< n`, where the polynomials are the
+ remainders of dividing by a specificly chosen polynomial in `GF(p)` called
+ the Reducing Polynomial (we will denote that by `red_poly`). The Reducing
+ Polynomial must be an irreducable polynomial (like primes, but for
+ polynomials), as well as have degree `n`. All `GF(p^n)` for the same `p`
+ and `n` are isomorphic to each other -- the choice of `red_poly` doesn't
+ affect `GF(p^n)`'s mathematical shape, all that changes is the specific
+ polynomials used to implement `GF(p^n)`.
+
+Many implementations and much of the literature do not make a clear
+distinction between these three categories, which makes it confusing
+to understand what their purpose and value is.
+
+* carry-less multiply is extremely common and is used for the ubiquitous
+ CRC32 algorithm. [TODO add many others, helps justify to ISA WG]
+* GF(2^N) forms the basis of Rijndael (the current AES standard) and
+ has significant uses throughout cryptography
+* GF(p) is the basis again of a significant quantity of algorithms
+ (TODO, list them, jacob knows what they are), even though the
+ modulo is limited to be below 64-bit (size of a scalar int)
+
+# Instructions for Carry-less Operations
+
+aka. Polynomials with coefficients in `GF(2)`
+
+Carry-less addition/subtraction is simply XOR, so a `cladd`
+instruction is not provided since the `xor[i]` instruction can be used instead.
+
+These are operations on polynomials with coefficients in `GF(2)`, with the
+polynomial's coefficients packed into integers with the following algorithm:
+
+```python
+[[!inline pagenames="gf_reference/pack_poly.py" raw="yes"]]
+```
+
+## Carry-less Multiply Instructions
+
+based on RV bitmanip
+see <https://en.wikipedia.org/wiki/CLMUL_instruction_set> and
+<https://www.felixcloutier.com/x86/pclmulqdq> and
+<https://en.m.wikipedia.org/wiki/Carry-less_product>
+
+They are worth adding as their own non-overwrite operations
+(in the same pipeline).
+
+### `clmul` Carry-less Multiply
+
+```python
+[[!inline pagenames="gf_reference/clmul.py" raw="yes"]]
+```
+
+### `clmulh` Carry-less Multiply High
+
+```python
+[[!inline pagenames="gf_reference/clmulh.py" raw="yes"]]
+```
+
+### `clmulr` Carry-less Multiply (Reversed)
+
+Useful for CRCs. Equivalent to bit-reversing the result of `clmul` on
+bit-reversed inputs.
+
+```python
+[[!inline pagenames="gf_reference/clmulr.py" raw="yes"]]
+```
+
+## `clmadd` Carry-less Multiply-Add
+
+```
+clmadd RT, RA, RB, RC
+```
+
+```
+(RT) = clmul((RA), (RB)) ^ (RC)
+```
+
+## `cltmadd` Twin Carry-less Multiply-Add (for FFTs)
+
+Used in combination with SV FFT REMAP to perform a full Discrete Fourier
+Transform of Polynomials over GF(2) in-place. Possible by having 3-in 2-out,
+to avoid the need for a temp register. RS is written to as well as RT.
+
+Note: Polynomials over GF(2) are a Ring rather than a Field, so, because the
+definition of the Inverse Discrete Fourier Transform involves calculating a
+multiplicative inverse, which may not exist in every Ring, therefore the
+Inverse Discrete Fourier Transform may not exist. (AFAICT the number of inputs
+to the IDFT must be odd for the IDFT to be defined for Polynomials over GF(2).
+TODO: check with someone who knows for sure if that's correct.)
+
+```
+cltmadd RT, RA, RB, RC
+```
+
+TODO: add link to explanation for where `RS` comes from.
+
+```
+a = (RA)
+c = (RC)
+# read all inputs before writing to any outputs in case
+# an input overlaps with an output register.
+(RT) = clmul(a, (RB)) ^ c
+(RS) = a ^ c
+```
+
+## `cldivrem` Carry-less Division and Remainder
+
+`cldivrem` isn't an actual instruction, but is just used in the pseudo-code
+for other instructions.
+
+```python
+[[!inline pagenames="gf_reference/cldivrem.py" raw="yes"]]
```
-# Galois Field 2^M
+## `cldiv` Carry-less Division
+
+```
+cldiv RT, RA, RB
+```
+
+```
+n = (RA)
+d = (RB)
+q, r = cldivrem(n, d, width=XLEN)
+(RT) = q
+```
+
+## `clrem` Carry-less Remainder
+
+```
+clrem RT, RA, RB
+```
+
+```
+n = (RA)
+d = (RB)
+q, r = cldivrem(n, d, width=XLEN)
+(RT) = r
+```
+
+# Instructions for Binary Galois Fields `GF(2^m)`
see:
* <https://engineering.purdue.edu/kak/compsec/NewLectures/Lecture7.pdf>
* <https://foss.heptapod.net/math/libgf2/-/blob/branch/default/src/libgf2/gf2.py>
-## SPRs to set modulo and degree
+Binary Galois Field addition/subtraction is simply XOR, so a `gfbadd`
+instruction is not provided since the `xor[i]` instruction can be used instead.
-to save registers and make operations orthogonal with standard
-arithmetic the modulo is to be set in an SPR
+## `GFBREDPOLY` SPR -- Reducing Polynomial
-## Twin Butterfly (Tukey-Cooley) Mul-add-sub
+In order to save registers and to make operations orthogonal with standard
+arithmetic, the reducing polynomial is stored in a dedicated SPR `GFBREDPOLY`.
+This also allows hardware to pre-compute useful parameters (such as the
+degree, or look-up tables) based on the reducing polynomial, and store them
+alongside the SPR in hidden registers, only recomputing them whenever the SPR
+is written to, rather than having to recompute those values for every
+instruction.
-used in combination with SV FFT REMAP to perform
-a full NTT in-place. possible by having 3-in 2-out,
-to avoid the need for a temp register. RS is written
-to as well as RT.
+Because Galois Fields require the reducing polynomial to be an irreducible
+polynomial, that guarantees that any polynomial of `degree > 1` must have
+the LSB set, since otherwise it would be divisible by the polynomial `x`,
+making it reducible, making whatever we're working on no longer a Field.
+Therefore, we can reuse the LSB to indicate `degree == XLEN`.
- gffmadd RT,RA,RC,RB (Rc=0)
- gffmadd. RT,RA,RC,RB (Rc=1)
-
-Pseudo-code:
-
- RT <- GFADD(GFMUL(RA, RC), RB))
- RS <- GFADD(GFMUL(RA, RC), RB))
-
-
-## Multiply
-
-with the modulo and degree being in an SPR, multiply can be identical
-equivalent to standard integer add
-
- RS = GFMUL(RA, RB)
-
-| 0.5|6.10|11.15|16.20|21.25| 26..30 |31|
-| -- | -- | --- | --- | --- | ------ |--|
-| NN | RT | RA | RB |11000| 01110 |Rc|
-
-
-
-```
-from functools import reduce
-
-def gf_degree(a) :
- res = 0
- a >>= 1
- while (a != 0) :
- a >>= 1;
- res += 1;
- return res
-
-# constants used in the multGF2 function
-mask1 = mask2 = polyred = None
-
-def setGF2(irPoly):
- """Define parameters of binary finite field GF(2^m)/g(x)
- - irPoly: coefficients of irreducible polynomial g(x)
- """
- # degree: extension degree of binary field
- degree = gf_degree(irPoly)
-
- def i2P(sInt):
- """Convert an integer into a polynomial"""
- return [(sInt >> i) & 1
- for i in reversed(range(sInt.bit_length()))]
-
- global mask1, mask2, polyred
- mask1 = mask2 = 1 << degree
- mask2 -= 1
- polyred = reduce(lambda x, y: (x << 1) + y, i2P(irPoly)[1:])
-
-def multGF2(p1, p2):
- """Multiply two polynomials in GF(2^m)/g(x)"""
- p = 0
- while p2:
- # standard long-multiplication: check LSB and add
- if p2 & 1:
- p ^= p1
- p1 <<= 1
- # standard modulo: check MSB and add polynomial
- if p1 & mask1:
- p1 ^= polyred
- p2 >>= 1
- return p & mask2
-
-if __name__ == "__main__":
-
- # Define binary field GF(2^3)/x^3 + x + 1
- setGF2(0b1011) # degree 3
-
- # Evaluate the product (x^2 + x + 1)(x^2 + 1)
- print("{:02x}".format(multGF2(0b111, 0b101)))
-
- # Define binary field GF(2^8)/x^8 + x^4 + x^3 + x + 1
- # (used in the Advanced Encryption Standard-AES)
- setGF2(0b100011011) # degree 8
-
- # Evaluate the product (x^7)(x^7 + x + 1)
- print("{:02x}".format(multGF2(0b10000000, 0b10000011)))
-```
-## GF div and mod
-
-```
-def gf_degree(a) :
- res = 0
- a >>= 1
- while (a != 0) :
- a >>= 1;
- res += 1;
- return res
-
-def FullDivision(self, f, v):
- """
- Takes two arguments, f, v
- fDegree and vDegree are the degrees of the field elements
- f and v represented as a polynomials.
- This method returns the field elements a and b such that
-
- f(x) = a(x) * v(x) + b(x).
-
- That is, a is the divisor and b is the remainder, or in
- other words a is like floor(f/v) and b is like f modulo v.
- """
-
- fDegree, vDegree = gf_degree(f), gf_degree(v)
- res, rem = 0, f
- i = fDegree
- mask = 1 << i
- while (i >= vDegree):
- if (mask & rem): # check MSB
- res ^= (1 << (i - vDegree))
- rem ^= ( v << (i - vDegree)))
- i -= 1
- mask >>= 1
- return (res, rem)
+```python
+[[!inline pagenames="gf_reference/decode_reducing_polynomial.py" raw="yes"]]
```
-| 0.5|6.10|11.15|16.20|21.25| 26..30 |31| name |
-| -- | -- | --- | --- | --- | ------- |--| ----- |
-| NN | RS | RA | deg | RC | 0 1 011 |Rc| gfaddi |
-| NN | RS | RA | RB | RC | 1 1 111 |Rc| gfadd |
+## `gfbredpoly` -- Set the Reducing Polynomial SPR `GFBREDPOLY`
-GFMOD is a pseudo-op where RA=0
+unless this is an immediate op, `mtspr` is completely sufficient.
-## carryless mul
+```python
+[[!inline pagenames="gf_reference/gfbredpoly.py" raw="yes"]]
+```
-based on RV bitmanip
-see https://en.wikipedia.org/wiki/CLMUL_instruction_set
+## `gfbmul` -- Binary Galois Field `GF(2^m)` Multiplication
-these are GF2 operations with the modulo set to 2^degree.
-they are worth adding as their own non-overwrite operations
-(in the same pipeline).
+```
+gfbmul RT, RA, RB
+```
+```python
+[[!inline pagenames="gf_reference/gfbmul.py" raw="yes"]]
```
-uint_xlen_t clmul(uint_xlen_t RA, uint_xlen_t RB)
-{
- uint_xlen_t x = 0;
- for (int i = 0; i < XLEN; i++)
- if ((RB >> i) & 1)
- x ^= RA << i;
- return x;
-}
-uint_xlen_t clmulh(uint_xlen_t RA, uint_xlen_t RB)
-{
- uint_xlen_t x = 0;
- for (int i = 1; i < XLEN; i++)
- if ((RB >> i) & 1)
- x ^= RA >> (XLEN-i);
- return x;
-}
-uint_xlen_t clmulr(uint_xlen_t RA, uint_xlen_t RB)
-{
- uint_xlen_t x = 0;
- for (int i = 0; i < XLEN; i++)
- if ((RB >> i) & 1)
- x ^= RA >> (XLEN-i-1);
- return x;
-}
+
+## `gfbmadd` -- Binary Galois Field `GF(2^m)` Multiply-Add
+
+```
+gfbmadd RT, RA, RB, RC
+```
+
+```python
+[[!inline pagenames="gf_reference/gfbmadd.py" raw="yes"]]
+```
+
+## `gfbtmadd` -- Binary Galois Field `GF(2^m)` Twin Multiply-Add (for FFT)
+
+Used in combination with SV FFT REMAP to perform a full `GF(2^m)` Discrete
+Fourier Transform in-place. Possible by having 3-in 2-out, to avoid the need
+for a temp register. RS is written to as well as RT.
+
+```
+gfbtmadd RT, RA, RB, RC
+```
+
+TODO: add link to explanation for where `RS` comes from.
+
+```
+a = (RA)
+c = (RC)
+# read all inputs before writing to any outputs in case
+# an input overlaps with an output register.
+(RT) = gfbmadd(a, (RB), c)
+# use gfbmadd again since it reduces the result
+(RS) = gfbmadd(a, 1, c) # "a * 1 + c"
+```
+
+## `gfbinv` -- Binary Galois Field `GF(2^m)` Inverse
+
+```
+gfbinv RT, RA
+```
+
+```python
+[[!inline pagenames="gf_reference/gfbinv.py" raw="yes"]]
+```
+
+# Instructions for Prime Galois Fields `GF(p)`
+
+## `GFPRIME` SPR -- Prime Modulus For `gfp*` Instructions
+
+## `gfpadd` Prime Galois Field `GF(p)` Addition
+
+```
+gfpadd RT, RA, RB
+```
+
+```python
+[[!inline pagenames="gf_reference/gfpadd.py" raw="yes"]]
+```
+
+the addition happens on infinite-precision integers
+
+## `gfpsub` Prime Galois Field `GF(p)` Subtraction
+
+```
+gfpsub RT, RA, RB
+```
+
+```python
+[[!inline pagenames="gf_reference/gfpsub.py" raw="yes"]]
+```
+
+the subtraction happens on infinite-precision integers
+
+## `gfpmul` Prime Galois Field `GF(p)` Multiplication
+
+```
+gfpmul RT, RA, RB
+```
+
+```python
+[[!inline pagenames="gf_reference/gfpmul.py" raw="yes"]]
+```
+
+the multiplication happens on infinite-precision integers
+
+## `gfpinv` Prime Galois Field `GF(p)` Invert
+
+```
+gfpinv RT, RA
+```
+
+Some potential hardware implementations are found in:
+<https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.5233&rep=rep1&type=pdf>
+
+```python
+[[!inline pagenames="gf_reference/gfpinv.py" raw="yes"]]
+```
+
+## `gfpmadd` Prime Galois Field `GF(p)` Multiply-Add
+
+```
+gfpmadd RT, RA, RB, RC
+```
+
+```python
+[[!inline pagenames="gf_reference/gfpmadd.py" raw="yes"]]
+```
+
+the multiplication and addition happens on infinite-precision integers
+
+## `gfpmsub` Prime Galois Field `GF(p)` Multiply-Subtract
+
+```
+gfpmsub RT, RA, RB, RC
+```
+
+```python
+[[!inline pagenames="gf_reference/gfpmsub.py" raw="yes"]]
+```
+
+the multiplication and subtraction happens on infinite-precision integers
+
+## `gfpmsubr` Prime Galois Field `GF(p)` Multiply-Subtract-Reversed
+
+```
+gfpmsubr RT, RA, RB, RC
+```
+
+```python
+[[!inline pagenames="gf_reference/gfpmsubr.py" raw="yes"]]
+```
+
+the multiplication and subtraction happens on infinite-precision integers
+
+## `gfpmaddsubr` Prime Galois Field `GF(p)` Multiply-Add and Multiply-Sub-Reversed (for FFT)
+
+Used in combination with SV FFT REMAP to perform
+a full Number-Theoretic-Transform in-place. Possible by having 3-in 2-out,
+to avoid the need for a temp register. RS is written
+to as well as RT.
+
+```
+gfpmaddsubr RT, RA, RB, RC
+```
+
+TODO: add link to explanation for where `RS` comes from.
+
+```
+factor1 = (RA)
+factor2 = (RB)
+term = (RC)
+# read all inputs before writing to any outputs in case
+# an input overlaps with an output register.
+(RT) = gfpmadd(factor1, factor2, term)
+(RS) = gfpmsubr(factor1, factor2, term)
```
# bitmatrix
RA ← EXTZ64(count)
```
-## bit deposit
+## bit deposit
-vpdepd VRT,VRA,VRB, identical to RV bitmamip bdep, found already in v3.1 p106
+pdepd VRT,VRA,VRB, identical to RV bitmamip bdep, found already in v3.1 p106
do while(m < 64)
if VSR[VRB+32].dword[i].bit[63-m]=1 then do
```
-# bit extract
+## bit extract
-other way round: identical to RV bext, found in v3.1 p196
+other way round: identical to RV bext: pextd, found in v3.1 p196
```
uint_xlen_t bext(uint_xlen_t RA, uint_xlen_t RB)
}
```
-# centrifuge
+## centrifuge
found in v3.1 p106 so not to be added here
RA = result
```
+## bit to byte permute
+
+similar to matrix permute in RV bitmanip, which has XOR and OR variants,
+these perform a transpose. TODO this looks VSX is there a scalar variant
+in v3.0/1 already
+
+ do j = 0 to 7
+ do k = 0 to 7
+ b = VSR[VRB+32].dword[i].byte[k].bit[j]
+ VSR[VRT+32].dword[i].byte[j].bit[k] = b
+
+# Appendix
+
+see [[bitmanip/appendix]]
+
projects / libreriscv.git / blobdiff