+[[!tag standards]]
+
+# bitmanipulation
+
+**DRAFT STATUS**
+
+this extension amalgamates bitnanipulation 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. Vectorisation Context is provided by [[openpower/sv]].
+
+ternaryv is experimental and is the only operation that may be considered a "Packed SIMD". It is added as a variant of the already well-justified ternary operation (done in AVX512 as an immediate only) "because it looks fun". As it is based on the LUT4 concept it will allow accelerated emulation of FPGAs. Other vendors of ISAs are buying FPGA companies to achieve a similar objective.
+
+general-purpose Galois Field operations are added so as to avoid huge opcode proliferation across many areas of Computer Science. however for convenience and also to avoid setup costs, some of the more common operations (clmul, crc32) are also added. The expectation is that these operations would all be covered by the same pipeline.
+
+# summary
+
+minor opcode allocation
+
+ | 28.30 |31| name |
+ | ------ |--| --------- |
+ | 00 |Rc| ternaryi |
+ | 001 |Rc| ternary |
+ | 010 |Rc| bitmask |
+ | 011 |Rc| gf* |
+ | 101 |1 | ternaryv |
+ | 101 |0 | ternarycr |
+ | 110 |Rc| 1/2-op |
+ | 111 |Rc| bitmaski |
+
+1-op and variants
+
+| dest | src1 | subop | op |
+| ---- | ---- | ----- | -------- |
+| RT | RA | .. | bmatflip |
+
+2-op and variants
+
+| dest | src1 | src2 | subop | op |
+| ---- | ---- | ---- | ----- | -------- |
+| RT | RA | RB | or | bmatflip |
+| RT | RA | RB | xor | bmatflip |
+| RT | RA | RB | bdep | dep/ext |
+| RT | RA | RB | bext | dep/ext |
+| RT | RA | RB | | grev |
+| RT | RA | RB | | clmul* |
+| RT | RA | RB | | gorc |
+| RT | RA | RB | shuf | shuffle |
+| RT | RA | RB | unshuf| shuffle |
+| RT | RA | RB | width | xperm |
+| RT | RA | RB | type | minmax |
+| RT | RA | RB | | |
+| RT | RA | RB | | |
+| RT | RA | RB | | |
+
+3 ops
+
+* bitmask set/extract
+* ternary bitops
+* GF
+
+| 0.5|6.10|11.15|16.20|21..25 | 26....30 |31| name |
+| -- | -- | --- | --- | ----- | -------- |--| ------ |
+| NN | RT | RA | RB | RC | mode 001 |Rc| ternary |
+| NN | RT | RA | RB | im0-4 | im5-7 00 |Rc| ternaryi |
+| NN | RS | RA | RB | RC | 00 011 |Rc| gfmul |
+| NN | RS | RA | RB | deg | 01 011 |Rc| gfadd |
+| NN | RT | RA | RB | deg | 10 011 |Rc| gfinv |
+| NN | RS | RA | RB | deg | 11 011 |Rc| gfmuli |
+
+| 0.5|6.10|11.15| 16.23 |24.27 | 28.30 |31| name |
+| -- | -- | --- | ----- | ---- | ----- |--| ------ |
+| NN | RT | RA | imm | mask | 101 |1 | ternaryv |
+
+| 0.5|6.8 | 9.11|12.14|15|16.23|24.27 | 28.30|31| name |
+| -- | -- | --- | --- |- |-----|----- | -----|--| -------|
+| NN | BA | BB | BC |0 |imm | mask | 101 |0 | ternarycr |
+
+ops
+
+| 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 | itype | 1 | 0000 110 |Rc| xperm |
+| NN | RA | RB | RC | itype | 0 | 0100 110 |Rc| minmax |
+| NN | RA | RB | | | 1 | 0100 110 |Rc| rsvd |
+| NN | RA | RB | sh | itype | SH | 1000 110 |Rc| bmopsi |
+| NN | RA | RB | | | | 1100 110 |Rc| rsvd |
+| NN | RA | RB | | | | 1100 110 |Rc| rsvd |
+| NN | RA | RB | | | | 1100 110 |Rc| rsvd |
+| NN | RA | RB | | | | 1100 110 |Rc| rsvd |
+| NN | RA | RB | | | 0 | 0001 110 |Rc| rsvd |
+| NN | RA | RB | | | 0 | 0101 110 |Rc| rsvd |
+| NN | RA | RB | RC | 00 | 0 | 0010 110 |Rc| gorc |
+| NN | RA | RB | sh | 00 | SH | 1010 110 |Rc| gorci |
+| NN | RA | RB | RC | 00 | 0 | 0110 110 |Rc| gorcw |
+| NN | RA | RB | sh | 00 | 0 | 1110 110 |Rc| gorcwi |
+| NN | RA | RB | RC | 00 | 1 | 1110 110 |Rc| bmator |
+| NN | RA | RB | RC | 01 | 0 | 0010 110 |Rc| grev |
+| NN | RA | RB | RC | 01 | 1 | 0010 110 |Rc| clmul |
+| NN | RA | RB | sh | 01 | SH | 1010 110 |Rc| grevi |
+| NN | RA | RB | RC | 01 | 0 | 0110 110 |Rc| grevw |
+| NN | RA | RB | sh | 01 | 0 | 1110 110 |Rc| grevwi |
+| NN | RA | RB | RC | 01 | 1 | 1110 110 |Rc| bmatxor |
+| NN | RA | RB | RC | 10 | 0 | 0010 110 |Rc| shfl |
+| NN | RA | RB | sh | 10 | SH | 1010 110 |Rc| shfli |
+| NN | RA | RB | RC | 10 | 0 | 0110 110 |Rc| shflw |
+| NN | RA | RB | RC | 10 | 0 | 1110 110 |Rc| bdep |
+| NN | RA | RB | RC | 10 | 1 | 1110 110 |Rc| bext |
+| NN | RA | RB | RC | 11 | 0 | 1110 110 |Rc| clmulr |
+| NN | RA | RB | RC | 11 | 1 | 1110 110 |Rc| clmulh |
+| NN | RA | RB | | | | NN11 110 |Rc| rsvd |
+
# 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]
# vector bit deposit
-vpdepd VRT,VRA,VRB
+vpdepd VRT,VRA,VRB, identical to RV bitmamip bdep
do while(m < 64)
if VSR[VRB+32].dword[i].bit[63-m]=1 then do
k = k + 1
m = m + 1
+```
+
+uint_xlen_t bdep(uint_xlen_t RA, uint_xlen_t RB)
+{
+ uint_xlen_t r = 0;
+ for (int i = 0, j = 0; i < XLEN; i++)
+ if ((RB >> i) & 1) {
+ if ((RA >> j) & 1)
+ r |= uint_xlen_t(1) << i;
+ j++;
+ }
+ return r;
+}
+
+```
+
# vector bit extract
-other way round
+other way round: identical to RV bext
+
+```
+uint_xlen_t bext(uint_xlen_t RA, uint_xlen_t RB)
+{
+ uint_xlen_t r = 0;
+ for (int i = 0, j = 0; i < XLEN; i++)
+ if ((RB >> i) & 1) {
+ if ((RA >> i) & 1)
+ r |= uint_xlen_t(1) << j;
+ j++;
+ }
+ return r;
+}
+```
+
+# 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;
+}
+```
+
# ternary bitops
-for every bit perform a lookup into a table using an 8bit immediate
+Similar to FPGA LUTs: for every bit perform a lookup into a table using an 8bit immediate, or in another register
-| 0.5|6.10|11.15|16.20| 21..22 | 23...30 |31| name |
-| -- | -- | --- | --- | ------ | ------- |--| ------- |
-| NN | RT | RA | RB | M 0 | im[0:7] |Rc| XL-Form |
+| 0.5|6.10|11.15|16.20| 21..25| 26..30 |31|
+| -- | -- | --- | --- | ----- | -------- |--|
+| NN | RT | RA | RB | im0-4 | im5-7 00 |Rc|
for i in range(64):
idx = RT[i] << 2 | RA[i] << 1 | RB[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.
+a 4 operand variant which becomes more along the lines of an FPGA:
+
+| 0.5|6.10|11.15|16.20|21.25| 26...30 |31|
+| -- | -- | --- | --- | --- | -------- |--|
+| NN | RT | RA | RB | RC | mode 001 |Rc|
+
+ for i in range(64):
+ idx = RT[i] << 2 | RA[i] << 1 | RB[i]
+ RT[i] = (RC & (1<<idx)) != 0
+
+mode (2 bit) may be used to do inversion of ordering, similar to carryless mul,
+3 modes.
+
+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 | 101 |1 |
+
+ 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
+
another mode selection would be CRs not Ints.
-| 0.5|6.8 | 9.11|12.14|15.17|18.21|22 | 23...30 |31| name |
-| -- | -- | --- | --- | --- |-----| - | ------- |--| ------- |
-| NN | BT | BA | BB | BC |mask | 1 | im[0:7] |Rc| XL-Form |
+| 0.5|6.8 | 9.11|12.14|15|16.23|24.27 | 28.30|31|
+| -- | -- | --- | --- |- |-----|----- | -----|--|
+| NN | BA | BB | BC |0 |imm | mask | 101 |0 |
for i in range(4):
if not mask[i] continue
idx = crregs[BA][i] << 2 |
crregs[BB][i] << 1 |
crregs[BC][i]
- crregs[BT][i] = (imm & (1<<idx)) != 0
+ crregs[BA][i] = (imm & (1<<idx)) != 0
-# single bit set
+# bitmask set
+
+based on RV bitmanip singlebit set, instruction format similar to shift
+[[isa/fixedshift]]. bmext is actually covered already (shift-with-mask rldicl but only immediate version).
+however bitmask-invert is not, and set/clr are not covered, although they can use the same Shift ALU.
+
+bmext (RB) version is not the same as rldicl because bmext is a right shift by RC, where rldicl is a left rotate. for the immediate version this does not matter, so a bmexti is not required.
+bmrev however there is no direct equivalent and consequently a bmrevi is required.
+
+| 0.5|6.10|11.15|16.20|21.25| 26..30 |31| name |
+| -- | -- | --- | --- | --- | ------- |--| ----- |
+| NN | RT | RA | RB | RC | mode 010 |Rc| bm* |
+| NN | RT | RA | RB | RC | 0 1 111 |Rc| bmrev |
-based on RV bitmanip
```
-uint_xlen_t sbset(uint_xlen_t rs1, uint_xlen_t rs2) {
- int shamt = rs2 & (XLEN - 1);
- return rs1 | (uint_xlen_t(1) << shamt);
+uint_xlen_t bmset(RA, RB, sh)
+{
+ int shamt = RB & (XLEN - 1);
+ mask = (2<<sh)-1;
+ return RA | (mask << shamt);
+}
+
+uint_xlen_t bmclr(RA, RB, sh)
+{
+ int shamt = RB & (XLEN - 1);
+ mask = (2<<sh)-1;
+ return RA & ~(mask << shamt);
}
-uint_xlen_t sbclr(uint_xlen_t rs1, uint_xlen_t rs2) {
- int shamt = rs2 & (XLEN - 1);
+
+uint_xlen_t bminv(RA, RB, sh)
+{
+ int shamt = RB & (XLEN - 1);
+ mask = (2<<sh)-1;
+ return RA ^ (mask << shamt);
}
-return rs1 & ~(uint_xlen_t(1) << shamt);
-uint_xlen_t sbinv(uint_xlen_t rs1, uint_xlen_t rs2) {
- int shamt = rs2 & (XLEN - 1);
+
+uint_xlen_t bmext(RA, RB, sh)
+{
+ int shamt = RB & (XLEN - 1);
+ mask = (2<<sh)-1;
+ return mask & (RA >> shamt);
}
-return rs1 ^ (uint_xlen_t(1) << shamt);
-uint_xlen_t sbext(uint_xlen_t rs1, uint_xlen_t rs2) {
- int shamt = rs2 & (XLEN - 1);
+```
+
+bitmask extract with reverse. can be done by bitinverting all of RA and getting bits of RA from the opposite end.
+
+```
+msb = rb[5:0];
+rev[0:msb] = ra[msb:0];
+rt = ZE(rev[msb:0]);
+
+uint_xlen_t bmextrev(RA, RB, sh)
+{
+ int shamt = (RB & (XLEN - 1));
+ shamt = (XLEN-1)-shamt; # shift other end
+ bra = bitreverse(RA) # swap LSB-MSB
+ mask = (2<<sh)-1;
+ return mask & (bra >> shamt);
}
-return 1 & (rs1 >> shamt);
```
+| 0.5|6.10|11.15|16.20|21.26| 27..30 |31| name |
+| -- | -- | --- | --- | --- | ------- |--| ------ |
+| NN | RT | RA | RB | sh | 0 111 |Rc| bmrevi |
+
+
+
# grev
based on RV bitmanip
```
-uint64_t grev64(uint64_t rs1, uint64_t rs2) { uint64_t x = rs1;
-}
-int shamt = rs2 & 63;
-if (shamt & 1) x = ((x & 0x5555555555555555LL) << 1) |
-((x & 0xAAAAAAAAAAAAAAAALL) >> 1);
-if (shamt & 2) x = ((x & 0x3333333333333333LL) << 2) |
-((x & 0xCCCCCCCCCCCCCCCCLL) >> 2);
-if (shamt & 4) x = ((x & 0x0F0F0F0F0F0F0F0FLL) << 4) |
-((x & 0xF0F0F0F0F0F0F0F0LL) >> 4);
-if (shamt & 8) x = ((x & 0x00FF00FF00FF00FFLL) << 8) |
-((x & 0xFF00FF00FF00FF00LL) >> 8);
-if (shamt & 16) x = ((x & 0x0000FFFF0000FFFFLL) << 16) |
-((x & 0xFFFF0000FFFF0000LL) >> 16);
-if (shamt & 32) x = ((x & 0x00000000FFFFFFFFLL) << 32) |
-return x;
-((x & 0xFFFFFFFF00000000LL) >> 32);
-grev stage 4 (shamt[4])
-grev stage 3 (shamt[3])
-grev stage 2 (shamt[2])
-grev stage 1 (shamt[1])
-grev stage 0 (shamt[0])
+uint64_t grev64(uint64_t RA, uint64_t RB)
+{
+ uint64_t x = RA;
+ int shamt = RB & 63;
+ if (shamt & 1) x = ((x & 0x5555555555555555LL) << 1) |
+ ((x & 0xAAAAAAAAAAAAAAAALL) >> 1);
+ if (shamt & 2) x = ((x & 0x3333333333333333LL) << 2) |
+ ((x & 0xCCCCCCCCCCCCCCCCLL) >> 2);
+ if (shamt & 4) x = ((x & 0x0F0F0F0F0F0F0F0FLL) << 4) |
+ ((x & 0xF0F0F0F0F0F0F0F0LL) >> 4);
+ if (shamt & 8) x = ((x & 0x00FF00FF00FF00FFLL) << 8) |
+ ((x & 0xFF00FF00FF00FF00LL) >> 8);
+ if (shamt & 16) x = ((x & 0x0000FFFF0000FFFFLL) << 16) |
+ ((x & 0xFFFF0000FFFF0000LL) >> 16);
+ if (shamt & 32) x = ((x & 0x00000000FFFFFFFFLL) << 32) |
+ ((x & 0xFFFFFFFF00000000LL) >> 32);
+ return x;
+}
+
```
# shuffle / unshuffle
based on RV bitmanip
```
-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 rs1, uint64_t rs2) { uint64_t x = rs1;
-}
-int shamt = rs2 & 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,
-return x;
-0x2222222222222222LL, 1);
-uint64_t unshfl64(uint64_t rs1, uint64_t rs2) {
-uint64_t x = rs1;
-}
-int shamt = rs2 & 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,
-return x;
-0x00000000ffff0000LL, 16);
+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;
+}
+
+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)
+{
+ 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;
+}
```
# xperm
based on RV bitmanip
```
-uint_xlen_t xperm(uint_xlen_t rs1, uint_xlen_t rs2, int sz_log2) {
-uint_xlen_t r = 0;
+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;
+ if (pos < XLEN)
+ r |= ((RA >> pos) & mask) << i;
+ }
+ return r;
}
-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 = ((rs2 >> i) & mask) << sz_log2;
-if (pos < XLEN)
-r |= ((rs1 >> pos) & mask) << i; }
-return r;
-uint_xlen_t xperm_n (uint_xlen_t rs1, uint_xlen_t rs2) {
-return xperm(rs1, rs2, 2); }
-uint_xlen_t xperm_b (uint_xlen_t rs1, uint_xlen_t rs2) {
-return xperm(rs1, rs2, 3); }
-uint_xlen_t xperm_h (uint_xlen_t rs1, uint_xlen_t rs2) {
-return xperm(rs1, rs2, 4); }
-uint_xlen_t xperm_w (uint_xlen_t rs1, uint_xlen_t rs2) {
-return xperm(rs1, rs2, 5); }
+uint_xlen_t xperm_n (uint_xlen_t RA, uint_xlen_t RB)
+{ return xperm(RA, RB, 2); }
+uint_xlen_t xperm_b (uint_xlen_t RA, uint_xlen_t RB)
+{ return xperm(RA, RB, 3); }
+uint_xlen_t xperm_h (uint_xlen_t RA, uint_xlen_t RB)
+{ return xperm(RA, RB, 4); }
+uint_xlen_t xperm_w (uint_xlen_t RA, uint_xlen_t RB)
+{ return xperm(RA, RB, 5); }
```
# gorc
based on RV bitmanip
```
-uint32_t gorc32(uint32_t rs1, uint32_t rs2) {
-
-uint32_t x = rs1;
+uint32_t gorc32(uint32_t RA, uint32_t RB)
+{
+ uint32_t x = RA;
+ int shamt = RB & 31;
+ if (shamt & 1) x |= ((x & 0x55555555) << 1) | ((x & 0xAAAAAAAA) >> 1);
+ if (shamt & 2) x |= ((x & 0x33333333) << 2) | ((x & 0xCCCCCCCC) >> 2);
+ if (shamt & 4) x |= ((x & 0x0F0F0F0F) << 4) | ((x & 0xF0F0F0F0) >> 4);
+ if (shamt & 8) x |= ((x & 0x00FF00FF) << 8) | ((x & 0xFF00FF00) >> 8);
+ if (shamt & 16) x |= ((x & 0x0000FFFF) << 16) | ((x & 0xFFFF0000) >> 16);
+ return x;
}
-int shamt = rs2 & 31;
-if (shamt & 1) x |= ((x & 0x55555555) << 1) | ((x & 0xAAAAAAAA) >> 1);
-if (shamt & 2) x |= ((x & 0x33333333) << 2) | ((x & 0xCCCCCCCC) >> 2);
-if (shamt & 4) x |= ((x & 0x0F0F0F0F) << 4) | ((x & 0xF0F0F0F0) >> 4);
-if (shamt & 8) x |= ((x & 0x00FF00FF) << 8) | ((x & 0xFF00FF00) >> 8);
-if (shamt & 16) x |= ((x & 0x0000FFFF) << 16) | ((x & 0xFFFF0000) >> 16); return x;
-uint64_t gorc64(uint64_t rs1, uint64_t rs2) {
-uint64_t x = rs1;
+uint64_t gorc64(uint64_t RA, uint64_t RB)
+{
+ uint64_t x = RA;
+ int shamt = RB & 63;
+ if (shamt & 1) x |= ((x & 0x5555555555555555LL) << 1) |
+ ((x & 0xAAAAAAAAAAAAAAAALL) >> 1);
+ if (shamt & 2) x |= ((x & 0x3333333333333333LL) << 2) |
+ ((x & 0xCCCCCCCCCCCCCCCCLL) >> 2);
+ if (shamt & 4) x |= ((x & 0x0F0F0F0F0F0F0F0FLL) << 4) |
+ ((x & 0xF0F0F0F0F0F0F0F0LL) >> 4);
+ if (shamt & 8) x |= ((x & 0x00FF00FF00FF00FFLL) << 8) |
+ ((x & 0xFF00FF00FF00FF00LL) >> 8);
+ if (shamt & 16) x |= ((x & 0x0000FFFF0000FFFFLL) << 16) |
+ ((x & 0xFFFF0000FFFF0000LL) >> 16);
+ if (shamt & 32) x |= ((x & 0x00000000FFFFFFFFLL) << 32) |
+ ((x & 0xFFFFFFFF00000000LL) >> 32);
+ return x;
}
-int shamt = rs2 & 63;
-if (shamt & 1) x |= ((x & 0x5555555555555555LL) << 1) |
-((x & 0xAAAAAAAAAAAAAAAALL) >> 1);
-if (shamt & 2) x |= ((x & 0x3333333333333333LL) << 2) |
-((x & 0xCCCCCCCCCCCCCCCCLL) >> 2);
-if (shamt & 4) x |= ((x & 0x0F0F0F0F0F0F0F0FLL) << 4) |
-((x & 0xF0F0F0F0F0F0F0F0LL) >> 4);
-if (shamt & 8) x |= ((x & 0x00FF00FF00FF00FFLL) << 8) |
-((x & 0xFF00FF00FF00FF00LL) >> 8);
-if (shamt & 16) x |= ((x & 0x0000FFFF0000FFFFLL) << 16) |
-((x & 0xFFFF0000FFFF0000LL) >> 16);
-if (shamt & 32) x |= ((x & 0x00000000FFFFFFFFLL) << 32) |
-return x;
-((x & 0xFFFFFFFF00000000LL) >> 32);
+
```
# cmix
-based on RV bitmanip
+based on RV bitmanip, covered by ternary bitops
```
-uint_xlen_t cmix(uint_xlen_t rs1, uint_xlen_t rs2, uint_xlen_t rs3) {
- return (rs1 & rs2) | (rs3 & ~rs2);
+uint_xlen_t cmix(uint_xlen_t RA, uint_xlen_t RB, uint_xlen_t RC) {
+ return (RA & RB) | (RC & ~RB);
}
```
# carryless mul
based on RV bitmanip
+see https://en.wikipedia.org/wiki/CLMUL_instruction_set
```
-uint_xlen_t clmul(uint_xlen_t rs1, uint_xlen_t rs2)
-{ uint_xlen_t x = 0;
+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;
}
-for (int i = 0; i < XLEN; i++)
-if ((rs2 >> i) & 1)
-x ^= rs1 << i; return x;
-uint_xlen_t clmulh(uint_xlen_t rs1, uint_xlen_t rs2) {
-uint_xlen_t x = 0;
+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;
}
-for (int i = 1; i < XLEN; i++)
- if ((rs2 >> i) & 1)
-x ^= rs1 >> (XLEN-i); return x;
-uint_xlen_t clmulr(uint_xlen_t rs1, uint_xlen_t rs2) {
-uint_xlen_t x = 0;
+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;
}
-for (int i = 0; i < XLEN; i++)
-if ((rs2 >> i) & 1)
-x ^= rs1 >> (XLEN-i-1); return x;
+```
+# Galois Field
+
+see <https://courses.csail.mit.edu/6.857/2016/files/ffield.py>
+
+## Multiply
+
+this requires 3 parameters and a "degree"
+
+ RT = GFMUL(RA, RB, gfdegree, modulo=RC)
+
+realistically with the degree also needing to be an immediate it should be brought down to an overwrite version:
+
+ RS = GFMUL(RS, RA, gfdegree, modulo=RB)
+ RS = GFMUL(RS, RA, gfdegree=RC, modulo=RB)
+
+| 0.5|6.10|11.15|16.20|21.25| 26..30 |31|
+| -- | -- | --- | --- | --- | ------- |--|
+| NN | RS | RA | RB | deg | 00 011 |Rc|
+| NN | RS | RA | RB | RC | 11 011 |Rc|
+
+where the SimpleV variant may override RS-as-src differently from RS-as-dest
+
+
+
+```
+from functools import reduce
+
+# constants used in the multGF2 function
+mask1 = mask2 = polyred = None
+
+def setGF2(degree, irPoly):
+ """Define parameters of binary finite field GF(2^m)/g(x)
+ - degree: extension degree of binary field
+ - irPoly: coefficients of irreducible polynomial g(x)
+ """
+ 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:
+ if p2 & 1:
+ p ^= p1
+ p1 <<= 1
+ if p1 & mask1:
+ p1 ^= polyred
+ p2 >>= 1
+ return p & mask2
+
+if __name__ == "__main__":
+
+ # Define binary field GF(2^3)/x^3 + x + 1
+ setGF2(3, 0b1011)
+
+ # 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(8, 0b100011011)
+
+ # Evaluate the product (x^7)(x^7 + x + 1)
+ print("{:02x}".format(multGF2(0b10000000, 0b10000011)))
+```
+## GF add
+
+ RS = GFADD(RS, RA|0, gfdegree, modulo=RB)
+ RS = GFADDI(RS, RA|0, gfdegree=RC, modulo=RB)
+
+| 0.5|6.10|11.15|16.20|21.25| 26..30 |31| name |
+| -- | -- | --- | --- | --- | ------- |--| ----- |
+| NN | RS | RA | RB | RC | 0 1 011 |Rc| gfadd |
+| NN | RS | RA | RB | RC | 1 1 111 |Rc| gfaddi |
+
+GFMOD is a pseudo-op where RA=0
+
+## gf invert
+
+```
+def gf_degree(a) :
+ res = 0
+ a >>= 1
+ while (a != 0) :
+ a >>= 1;
+ res += 1;
+ return res
+
+def gf_invert(a, mod=0x1B) :
+ v = mod
+ g1 = 1
+ g2 = 0
+ j = gf_degree(a) - 8
+
+ while (a != 1) :
+ if (j < 0) :
+ a, v = v, a
+ g1, g2 = g2, g1
+ j = -j
+
+ a ^= v << j
+ g1 ^= g2 << j
+
+ a %= 256 # Emulating 8-bit overflow
+ g1 %= 256 # Emulating 8-bit overflow
+
+ j = gf_degree(a) - gf_degree(v)
+
+ return g1
+```
+
+# bitmatrix
+
+```
+uint64_t bmatflip(uint64_t RA)
+{
+ uint64_t x = RA;
+ x = shfl64(x, 31);
+ x = shfl64(x, 31);
+ x = shfl64(x, 31);
+ return x;
+}
+uint64_t bmatxor(uint64_t RA, uint64_t RB)
+{
+ // transpose of RB
+ uint64_t RBt = bmatflip(RB);
+ uint8_t u[8]; // rows of RA
+ uint8_t v[8]; // cols of RB
+ for (int i = 0; i < 8; i++) {
+ u[i] = RA >> (i*8);
+ v[i] = RBt >> (i*8);
+ }
+ uint64_t x = 0;
+ for (int i = 0; i < 64; i++) {
+ if (pcnt(u[i / 8] & v[i % 8]) & 1)
+ x |= 1LL << i;
+ }
+ return x;
+}
+uint64_t bmator(uint64_t RA, uint64_t RB)
+{
+ // transpose of RB
+ uint64_t RBt = bmatflip(RB);
+ uint8_t u[8]; // rows of RA
+ uint8_t v[8]; // cols of RB
+ for (int i = 0; i < 8; i++) {
+ u[i] = RA >> (i*8);
+ v[i] = RBt >> (i*8);
+ }
+ uint64_t x = 0;
+ for (int i = 0; i < 64; i++) {
+ if ((u[i / 8] & v[i % 8]) != 0)
+ x |= 1LL << i;
+ }
+ return x;
+}
+
```
projects / libreriscv.git / blobdiff