+[[!tag standards]]
+
+# bitmanipulation
+
+**DRAFT STATUS**
+
+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]].
+
+When combined with SV, scalar variants of bitmanip operations found in VSX are added so that VSX may be retired as "legacy" in the far future (10 to 20 years). Also, VSX is hundreds of opcodes, requires 128 bit pathways, and is wholly unsuited to low power or embedded scenarios.
+
+ternlogv 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 ternlog 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 similar objectives.
+
+general-purpose Galois Field operations are added so as to avoid huge custom 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.
+
+note that there are brownfield spaces below that could incorporate some of the set-before-first and other scalar operations listed in [[sv/vector_ops]], and
+the [[sv/av_opcodes]] as well as [[sv/setvl]]
+
+Useful resource:
+
+* <https://en.wikiversity.org/wiki/Reed%E2%80%93Solomon_codes_for_coders>
+* <https://maths-people.anu.edu.au/~brent/pd/rpb232tr.pdf>
+
+# summary
+
+minor opcode allocation
+
+ | 28.30 |31| name |
+ | ------ |--| --------- |
+ | 00 |Rc| ternlogi |
+ | 001 |Rc| ternlog |
+ | 010 |Rc| bitmask |
+ | 011 |Rc| gf* |
+ | 101 |1 | ternlogv |
+ | 101 |0 | ternlogcr |
+ | 110 |Rc| 1/2-op |
+ | 111 |Rc| 3-op |
+
+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 | | 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 | | av abs avgadd |
+| RT | RA | RB | type | vmask ops |
+| RT | RA | RB | | |
+
+3 ops
+
+* bitmask set/extract
+* ternlog bitops
+* GF
+
+| 0.5|6.10|11.15|16.20|21..25 | 26....30 |31| name |
+| -- | -- | --- | --- | ----- | -------- |--| ------ |
+| NN | RT | RA | RB | RC | mode 001 |Rc| ternlog |
+| NN | RT | RA | RB | im0-4 | im5-7 00 |Rc| ternlogi |
+| NN | RS | RA | RB | RC | 00 011 |Rc| gfmul |
+| NN | RS | RA | RB | RC | 01 011 |Rc| gfadd |
+| NN | RT | RA | RB | deg | 10 011 |Rc| gfinv |
+| NN | RS | RA | RB | deg | 11 011 |Rc| gfmuli |
+| NN | RS | RA | RB | deg | 11 111 |Rc| gfaddi |
+
+| 0.5|6.10|11.15| 16.23 |24.27 | 28.30 |31| name |
+| -- | -- | --- | ----- | ---- | ----- |--| ------ |
+| NN | RT | RA | imm | mask | 101 |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 | 101 |0 | ternlogcr |
+
+ops (note that av avg and abs as well as vec scalar mask
+are included here)
+
+| 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 | RC | 00 | 1 | 0100 110 |Rc| av avgadd |
+| NN | RA | RB | RC | 01 | 1 | 0100 110 |Rc| av abs |
+| NN | RA | RB | | 10 | 1 | 0100 110 |Rc| rsvd |
+| NN | RA | RB | | 11 | 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 | | | 1 | 0001 110 |Rc| rsvd |
+| NN | RA | RB | RC | 00 | 0 | 0001 110 |Rc| vec sbfm |
+| NN | RA | RB | RC | 01 | 0 | 0001 110 |Rc| vec sofm |
+| NN | RA | RB | RC | 10 | 0 | 0001 110 |Rc| vec sifm |
+| NN | RA | RB | RC | 11 | 0 | 0001 110 |Rc| vec cprop |
+| 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 | | 1110 110 |Rc| rsvd |
+| NN | RA | RB | RC | 11 | 0 | 1110 110 |Rc| clmulr |
+| NN | RA | RB | RC | 11 | 1 | 1110 110 |Rc| clmulh |
+| NN | | | | | | --11 110 |Rc| setvl |
+
+# count leading/trailing zeros with mask
+
+in v3.1 p105
+
+```
+count = 0
+do i = 0 to 63 if((RB)i=1) then do
+if((RS)i=1) then break end end count ← count + 1
+RA ← EXTZ64(count)
+```
+
# 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
-# vector bit deposit
+# bit deposit
-vpdepd VRT,VRA,VRB
+vpdepd 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
k = k + 1
m = m + 1
-# vector bit extract
+```
+
+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;
+}
-other way round
+```
-# single bit set
+# bit extract
+
+other way round: identical to RV bext, found in v3.1 p196
```
-uint_xlen_t sbset(uint_xlen_t rs1, uint_xlen_t rs2) { int shamt = rs2 & (XLEN - 1);
+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;
}
-return rs1 | (uint_xlen_t(1) << shamt);
-uint_xlen_t sbclr(uint_xlen_t rs1, uint_xlen_t rs2) { int shamt = rs2 & (XLEN - 1);
+```
+
+# centrifuge
+
+found in v3.1 p106 so not to be added here
+
+```
+ptr0 = 0
+ptr1 = 0
+do i = 0 to 63
+ if((RB)i=0) then do
+ resultptr0 = (RS)i
+ end
+ ptr0 = ptr0 + 1
+ if((RB)63-i==1) then do
+ result63-ptr1 = (RS)63-i
+ end
+ ptr1 = ptr1 + 1
+RA = result
+```
+
+# 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;
+}
+```
+
+
+# ternlog bitops
+
+Similar to FPGA LUTs: for every bit perform a lookup into a table using an 8bit immediate, or in another register.
+
+Like the x86 AVX512F [vpternlogd/vpternlogq](https://www.felixcloutier.com/x86/vpternlogd:vpternlogq) instructions.
+
+| 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]
+ RT[i] = (imm & (1<<idx)) != 0
+
+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|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[BA][i] = (imm & (1<<idx)) != 0
+
+# 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.
+
+bmset (register for mask amount) is particularly useful for creating
+predicate masks where the length is a dynamic runtime quantity.
+bmset(RA=0, RB=0, RC=mask) will produce a run of ones of length "mask" in a single instruction without needing to initialise or depend on any other registers.
+
+| 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 |
+
+
+```
+uint_xlen_t bmset(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 bmclr(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 sbext(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);
+}
+
+uint_xlen_t bmext(RA, RB, sh)
+{
+ int shamt = RB & (XLEN - 1);
+ mask = (2<<sh)-1;
+ return mask & (RA >> shamt);
}
-return 1 & (rs1 >> shamt);
+```
+
+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);
+}
+```
+
+| 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 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);
+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;
}
-x |= ((src << N) & maskL) | ((src >> N) & maskR); return x;
-uint64_t shfl64(uint64_t rs1, uint64_t rs2) { uint64_t x = rs1;
+
+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;
}
-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;
+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;
}
-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);
```
# 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;
+ if (pos < XLEN)
+ r |= ((RA >> pos) & mask) << i;
+ }
+ return r;
+}
+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 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;
+}
+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;
+}
+
+```
+
+# cmix
+
+based on RV bitmanip, covered by ternlog bitops
+
+```
+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 xperm(uint_xlen_t rs1, uint_xlen_t rs2, int sz_log2) { uint_xlen_t r = 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;
}
-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 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;
+}
+```
+# 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 = GFADDI(RS, RA|0, gfdegree, modulo=RB)
+ RS = GFADD(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 | deg | 0 1 011 |Rc| gfaddi |
+| NN | RS | RA | RB | RC | 1 1 111 |Rc| gfadd |
+
+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