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remove FpM::init
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@herumi
herumi committed Jun 28, 2024
1 parent 7ab194f commit 4e172b0
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Showing 5 changed files with 91 additions and 72 deletions.
1 change: 0 additions & 1 deletion include/mcl/bn.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -2283,7 +2283,6 @@ inline void init(bool *pb, const mcl::CurveParam& cp = mcl::BN254, fp::Mode mode
mcl::msm::Func func;
func.fp = &Fp::getOp();
func.fr = &Fr::getOp();
func.rw = local::GLV1::rw.getUnit();
func.invVecFp = mcl::msm::invVecFpFunc(mcl::invVec<mcl::bn::Fp>);
func.normalizeVecG1 = mcl::msm::normalizeVecG1Func(mcl::ec::normalizeVec<mcl::bn::G1>);
#if defined(__GNUC__) && !defined(__EMSCRIPTEN__) && !defined(__clang__)
Expand Down
1 change: 0 additions & 1 deletion include/mcl/op.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -445,7 +445,6 @@ typedef void (*clearG1Func)(G1A& z);
struct Func {
const mcl::fp::Op *fp;
const mcl::fp::Op *fr;
const Unit *rw;
invVecFpFunc invVecFp;
normalizeVecG1Func normalizeVecG1;
addG1Func addG1;
Expand Down
29 changes: 19 additions & 10 deletions src/gen_msm_para.py
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Original file line number Diff line number Diff line change
Expand Up @@ -78,21 +78,30 @@ def expandN(name, v):
def putCode(curve, mont):
print('// generated by src/gen_msm_para.py')
print(f'static const uint64_t g_mask = {hex(mont.mask)};')
expand("g_vmask_", mont.mask)
expand("g_vrp_", mont.rp)
expandN('g_vpN_', toArray(curve.p))
expandN('g_vR_', toArray(mont.R)) # Fp:M::one()
expandN('g_vR2_', toArray(mont.R2)) # Fp:M::R2()
expand("g_mask_", mont.mask)
expand("g_rp_", mont.rp)
expandN('g_ap_', toArray(curve.p)) # array of p
expandN('g_R_', toArray(mont.R)) # FpM::one()
expandN('g_R2_', toArray(mont.R2)) # FpM::R2()
expandN('g_m64to52_', toArray(mont.toMont(2**32)))
expandN('g_m52to64_', toArray(mont.toMont(pow(2**32, -1, curve.p))))
expandN('g_vrawOne_', toArray(1)) # Fp:M::rawOne()
expand("g_offset_", [0, 1, 2, 3, 4, 5, 6, 7, 8])
expandN('g_zero_', toArray(0)) # FpM::zero()
expandN('g_rawOne_', toArray(1)) # FpM::rawOne()
expand('g_offset_', [0, 1, 2, 3, 4, 5, 6, 7, 8])
p = curve.p
rw = pow(-3, (p+1)//4, p)
rw = p-(rw+1)//2
if (rw*rw+rw+1)%p != 0:
print(f'ERR rw {rw=}')
return
print(f'// rw={hex(rw)}')
expandN('g_rw_', toArray(mont.toMont(rw)))

print(f'''
struct G {{
static const Vec& vmask() {{ return *(const Vec*)g_vmask_; }}
static const Vec& vrp() {{ return *(const Vec*)g_vrp_; }}
static const Vec* vpN() {{ return (const Vec*)g_vpN_; }}
static const Vec& mask() {{ return *(const Vec*)g_mask_; }}
static const Vec& rp() {{ return *(const Vec*)g_rp_; }}
static const Vec* ap() {{ return (const Vec*)g_ap_; }}
static const Vec& offset() {{ return *(const Vec*)g_offset_; }}
}};
''')
Expand Down
93 changes: 42 additions & 51 deletions src/msm_avx.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -137,7 +137,7 @@ inline void vrawAdd(Vec *z, const Vec *x, const Vec *y)
{
Vec t = vpaddq(x[0], y[0]);
Vec c = vpsrlq(t, W);
z[0] = vpandq(t, G::vmask());
z[0] = vpandq(t, G::mask());

for (size_t i = 1; i < n; i++) {
t = vpaddq(x[i], y[i]);
Expand All @@ -147,7 +147,7 @@ inline void vrawAdd(Vec *z, const Vec *x, const Vec *y)
return;
}
c = vpsrlq(t, W);
z[i] = vpandq(t, G::vmask());
z[i] = vpandq(t, G::mask());
}
}

Expand All @@ -156,12 +156,12 @@ inline Vmask vrawSub(Vec *z, const Vec *x, const Vec *y)
{
Vec t = vpsubq(x[0], y[0]);
Vec c = vpsrlq(t, S);
z[0] = vpandq(t, G::vmask());
z[0] = vpandq(t, G::mask());
for (size_t i = 1; i < n; i++) {
t = vpsubq(x[i], y[i]);
t = vpsubq(t, c);
c = vpsrlq(t, S);
z[i] = vpandq(t, G::vmask());
z[i] = vpandq(t, G::mask());
}
return vcmpneqq(c, vzero());
}
Expand All @@ -177,16 +177,16 @@ inline void uvadd(Vec *z, const Vec *x, const Vec *y)
{
Vec sN[N], tN[N];
vrawAdd(sN, x, y);
Vmask c = vrawSub(tN, sN, G::vpN());
Vmask c = vrawSub(tN, sN, G::ap());
uvselect(z, c, sN, tN);
}

inline void uvsub(Vec *z, const Vec *x, const Vec *y)
{
Vec sN[N], tN[N];
Vmask c = vrawSub(sN, x, y);
vrawAdd(tN, sN, G::vpN());
tN[N-1] = vpandq(tN[N-1], G::vmask());
vrawAdd(tN, sN, G::ap());
tN[N-1] = vpandq(tN[N-1], G::mask());
uvselect(z, c, tN, sN);
}

Expand Down Expand Up @@ -293,15 +293,15 @@ inline void vset(Vec *t, const Vmask& c, const Vec a[n])
inline void uvmont(Vec z[N], Vec xy[N*2])
{
for (size_t i = 0; i < N; i++) {
Vec q = vmulL(xy[i], G::vrp());
xy[N+i] = vpaddq(xy[N+i], vrawMulUnitAdd(xy+i, G::vpN(), q));
Vec q = vmulL(xy[i], G::rp());
xy[N+i] = vpaddq(xy[N+i], vrawMulUnitAdd(xy+i, G::ap(), q));
xy[i+1] = vpaddq(xy[i+1], vpsrlq(xy[i], W));
}
for (size_t i = N; i < N*2-1; i++) {
xy[i+1] = vpaddq(xy[i+1], vpsrlq(xy[i], W));
xy[i] = vpandq(xy[i], G::vmask());
xy[i] = vpandq(xy[i], G::mask());
}
Vmask c = vrawSub(z, xy+N, G::vpN());
Vmask c = vrawSub(z, xy+N, G::ap());
uvselect(z, c, xy+N, z);
}

Expand All @@ -314,19 +314,19 @@ inline void uvmul(Vec *z, const Vec *x, const Vec *y)
#else
Vec t[N*2], q;
vrawMulUnit(t, x, y[0]);
q = vmulL(t[0], G::vrp());
t[N] = vpaddq(t[N], vrawMulUnitAdd(t, G::vpN(), q));
q = vmulL(t[0], G::rp());
t[N] = vpaddq(t[N], vrawMulUnitAdd(t, G::ap(), q));
for (size_t i = 1; i < N; i++) {
t[N+i] = vrawMulUnitAdd(t+i, x, y[i]);
t[i] = vpaddq(t[i], vpsrlq(t[i-1], W));
q = vmulL(t[i], G::vrp());
t[N+i] = vpaddq(t[N+i], vrawMulUnitAdd(t+i, G::vpN(), q));
q = vmulL(t[i], G::rp());
t[N+i] = vpaddq(t[N+i], vrawMulUnitAdd(t+i, G::ap(), q));
}
for (size_t i = N; i < N*2; i++) {
t[i] = vpaddq(t[i], vpsrlq(t[i-1], W));
t[i-1] = vpandq(t[i-1], G::vmask());
t[i-1] = vpandq(t[i-1], G::mask());
}
Vmask c = vrawSub(z, t+N, G::vpN());
Vmask c = vrawSub(z, t+N, G::ap());
uvselect(z, c, t+N, z);
#endif
}
Expand Down Expand Up @@ -427,13 +427,13 @@ class Montgomery {
inline void split52bit(Vec y[8], const Vec x[6])
{
assert(&y != &x);
y[0] = vpandq(x[0], G::vmask());
y[1] = vpandq(vporq(vpsrlq(x[0], 52), vpsllq(x[1], 12)), G::vmask());
y[2] = vpandq(vporq(vpsrlq(x[1], 40), vpsllq(x[2], 24)), G::vmask());
y[3] = vpandq(vporq(vpsrlq(x[2], 28), vpsllq(x[3], 36)), G::vmask());
y[4] = vpandq(vporq(vpsrlq(x[3], 16), vpsllq(x[4], 48)), G::vmask());
y[5] = vpandq(vpsrlq(x[4], 4), G::vmask());
y[6] = vpandq(vporq(vpsrlq(x[4], 56), vpsllq(x[5], 8)), G::vmask());
y[0] = vpandq(x[0], G::mask());
y[1] = vpandq(vporq(vpsrlq(x[0], 52), vpsllq(x[1], 12)), G::mask());
y[2] = vpandq(vporq(vpsrlq(x[1], 40), vpsllq(x[2], 24)), G::mask());
y[3] = vpandq(vporq(vpsrlq(x[2], 28), vpsllq(x[3], 36)), G::mask());
y[4] = vpandq(vporq(vpsrlq(x[3], 16), vpsllq(x[4], 48)), G::mask());
y[5] = vpandq(vpsrlq(x[4], 4), G::mask());
y[6] = vpandq(vporq(vpsrlq(x[4], 56), vpsllq(x[5], 8)), G::mask());
y[7] = vpsrlq(x[5], 44);
}

Expand Down Expand Up @@ -527,16 +527,14 @@ inline void cvt6Ux8to8Ux8(Vec y[8], const Unit x[6*8])

struct FpM {
Vec v[N];
static FpM zero_;
static FpM rawOne_;
static FpM rw_;
static Montgomery g_mont;
static const FpM& zero() { return zero_; }
static const FpM& one() { return *(const FpM*)g_vR_; }
static const FpM& R2() { return *(const FpM*)g_vR2_; }
static const FpM& rawOne() { return *(const FpM*)g_vrawOne_; }
static const FpM& zero() { return *(const FpM*)g_zero_; }
static const FpM& one() { return *(const FpM*)g_R_; }
static const FpM& R2() { return *(const FpM*)g_R2_; }
static const FpM& rawOne() { return *(const FpM*)g_rawOne_; }
static const FpM& m64to52() { return *(const FpM*)g_m64to52_; }
static const FpM& m52to64() { return *(const FpM*)g_m52to64_; }
static const FpM& rw() { return *(const FpM*)g_rw_; }
static void add(FpM& z, const FpM& x, const FpM& y)
{
uvadd(z.v, x.v, y.v);
Expand Down Expand Up @@ -639,12 +637,12 @@ struct FpM {
const size_t bitLen = sizeof(Unit)*8;
const size_t jn = bitLen / w;
z = tbl[0];
const Vec vmask4 = vpbroadcastq(getMask(4));
const Vec mask4 = vpbroadcastq(getMask(4));
for (size_t i = 0; i < yn; i++) {
const Vec& v = y[yn-1-i];
for (size_t j = 0; j < jn; j++) {
for (int k = 0; k < w; k++) FpM::sqr(z, z);
Vec idx = vpandq(vpsrlq(v, bitLen-w-j*w), vmask4);
Vec idx = vpandq(vpsrlq(v, bitLen-w-j*w), mask4);
idx = vpsllq(idx, 6); // 512 B = 64 Unit
idx = vpaddq(idx, G::offset());
FpM t;
Expand Down Expand Up @@ -704,17 +702,11 @@ struct FpM {
}
return d;
}
static void init(const mpz_class& mp)
{
g_mont.init(mp);
}
#ifdef MCL_MSM_TEST
void dump(size_t pos, const char *msg = nullptr) const;
#endif
};

FpM FpM::zero_;
FpM FpM::rw_;
Montgomery FpM::g_mont;

template<class E, size_t n>
Expand Down Expand Up @@ -974,7 +966,7 @@ struct EcM {
}
static void mulLambda(EcM& Q, const EcM& P)
{
FpM::mul(Q.x, P.x, FpM::rw_);
FpM::mul(Q.x, P.x, FpM::rw());
Q.y = P.y;
Q.z = P.z;
}
Expand Down Expand Up @@ -1011,13 +1003,13 @@ struct EcM {
pb[i+M*0] = bb[0]; pb[i+M*1] = bb[1];
}
const size_t bitLen = 128;
Vec vmask = vpbroadcastq((1<<w)-1);
Vec mask = vpbroadcastq((1<<w)-1);
bool first = true;
size_t pos = bitLen;
for (size_t i = 0; i < (bitLen + w-1)/w; i++) {
size_t dblN = w;
if (pos < w) {
vmask = vpbroadcastq((1<<pos)-1);
mask = vpbroadcastq((1<<pos)-1);
dblN = pos;
pos = 0;
} else {
Expand All @@ -1026,15 +1018,15 @@ struct EcM {
if (!first) for (size_t k = 0; k < dblN; k++) EcM::dbl<isProj>(Q, Q);
EcM T;
Vec idx;
idx = vpandq(getUnitAt(b, 2, pos), vmask);
idx = vpandq(getUnitAt(b, 2, pos), mask);
if (first) {
Q.gather(tbl2, idx);
first = false;
} else {
T.gather(tbl2, idx);
add<isProj, mixed>(Q, Q, T);
}
idx = vpandq(getUnitAt(a, 2, pos), vmask);
idx = vpandq(getUnitAt(a, 2, pos), mask);
T.gather(tbl1, idx);
add<isProj, mixed>(Q, Q, T);
}
Expand All @@ -1044,7 +1036,7 @@ struct EcM {
template<size_t bitLen, size_t w>
static void makeNAFtbl(Vec *idxTbl, Vmask *negTbl, const Vec a[2])
{
const Vec vmask = vpbroadcastq((1<<w)-1);
const Vec mask = vpbroadcastq((1<<w)-1);
#ifdef SIGNED_TABLE
(void)negTbl;
#else
Expand All @@ -1057,16 +1049,16 @@ struct EcM {
const size_t n = (bitLen+w-1)/w;
for (size_t i = 0; i < n; i++) {
Vec idx = getUnitAt(a, 2, pos);
idx = vpandq(idx, vmask);
idx = vpandq(idx, mask);
idx = vpaddq(idx, CF);
#ifdef SIGNED_TABLE
Vec masked = vpandq(idx, vmask);
Vec masked = vpandq(idx, mask);
Vmask v = vcmpgtq(masked, H);
idxTbl[i] = masked; //vselect(negTbl[i], vpsubq(F, masked), masked); // idx >= H ? F - idx : idx;
CF = vpsrlq(idx, w);
CF = vpaddq(v, CF, one);
#else
Vec masked = vpandq(idx, vmask);
Vec masked = vpandq(idx, mask);
negTbl[i] = vcmpgtq(masked, H);
idxTbl[i] = vselect(negTbl[i], vpsubq(F, masked), masked); // idx >= H ? F - idx : idx;
CF = vpsrlq(idx, w);
Expand Down Expand Up @@ -1325,10 +1317,9 @@ bool initMsm(const mcl::CurveParam& cp, const mcl::msm::Func *func)
g_func = *func;

const mpz_class& mp = g_func.fp->mp;
FpM::init(mp);
FpM::g_mont.init(mp);
// FpM::init(mp);
Montgomery& mont = FpM::g_mont;
FpM::zero_.clear();
FpM::rw_.setFp(g_func.rw);
EcM::init(mont);
return true;
}
Expand Down
39 changes: 30 additions & 9 deletions src/msm_avx_bls12_381.h
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Original file line number Diff line number Diff line change
Expand Up @@ -9,9 +9,9 @@ rp=0x3fffcfffcfffd
#endif
// generated by src/gen_msm_para.py
static const uint64_t g_mask = 0xfffffffffffff;
static const CYBOZU_ALIGN(64) uint64_t g_vmask_[] = { 0xfffffffffffff, 0xfffffffffffff, 0xfffffffffffff, 0xfffffffffffff, 0xfffffffffffff, 0xfffffffffffff, 0xfffffffffffff, 0xfffffffffffff, };
static const CYBOZU_ALIGN(64) uint64_t g_vrp_[] = { 0x3fffcfffcfffd, 0x3fffcfffcfffd, 0x3fffcfffcfffd, 0x3fffcfffcfffd, 0x3fffcfffcfffd, 0x3fffcfffcfffd, 0x3fffcfffcfffd, 0x3fffcfffcfffd, };
static const CYBOZU_ALIGN(64) uint64_t g_vpN_[] = {
static const CYBOZU_ALIGN(64) uint64_t g_mask_[] = { 0xfffffffffffff, 0xfffffffffffff, 0xfffffffffffff, 0xfffffffffffff, 0xfffffffffffff, 0xfffffffffffff, 0xfffffffffffff, 0xfffffffffffff, };
static const CYBOZU_ALIGN(64) uint64_t g_rp_[] = { 0x3fffcfffcfffd, 0x3fffcfffcfffd, 0x3fffcfffcfffd, 0x3fffcfffcfffd, 0x3fffcfffcfffd, 0x3fffcfffcfffd, 0x3fffcfffcfffd, 0x3fffcfffcfffd, };
static const CYBOZU_ALIGN(64) uint64_t g_ap_[] = {
0xeffffffffaaab, 0xeffffffffaaab, 0xeffffffffaaab, 0xeffffffffaaab, 0xeffffffffaaab, 0xeffffffffaaab, 0xeffffffffaaab, 0xeffffffffaaab,
0xfeb153ffffb9f, 0xfeb153ffffb9f, 0xfeb153ffffb9f, 0xfeb153ffffb9f, 0xfeb153ffffb9f, 0xfeb153ffffb9f, 0xfeb153ffffb9f, 0xfeb153ffffb9f,
0x6b0f6241eabff, 0x6b0f6241eabff, 0x6b0f6241eabff, 0x6b0f6241eabff, 0x6b0f6241eabff, 0x6b0f6241eabff, 0x6b0f6241eabff, 0x6b0f6241eabff,
Expand All @@ -21,7 +21,7 @@ static const CYBOZU_ALIGN(64) uint64_t g_vpN_[] = {
0x1ea397fe69a4b, 0x1ea397fe69a4b, 0x1ea397fe69a4b, 0x1ea397fe69a4b, 0x1ea397fe69a4b, 0x1ea397fe69a4b, 0x1ea397fe69a4b, 0x1ea397fe69a4b,
0x1a011, 0x1a011, 0x1a011, 0x1a011, 0x1a011, 0x1a011, 0x1a011, 0x1a011,
};
static const CYBOZU_ALIGN(64) uint64_t g_vR_[] = {
static const CYBOZU_ALIGN(64) uint64_t g_R_[] = {
0x6480ea8e9b9af, 0x6480ea8e9b9af, 0x6480ea8e9b9af, 0x6480ea8e9b9af, 0x6480ea8e9b9af, 0x6480ea8e9b9af, 0x6480ea8e9b9af, 0x6480ea8e9b9af,
0x65766c8fe444f, 0x65766c8fe444f, 0x65766c8fe444f, 0x65766c8fe444f, 0x65766c8fe444f, 0x65766c8fe444f, 0x65766c8fe444f, 0x65766c8fe444f,
0x8b540fea96f7d, 0x8b540fea96f7d, 0x8b540fea96f7d, 0x8b540fea96f7d, 0x8b540fea96f7d, 0x8b540fea96f7d, 0x8b540fea96f7d, 0x8b540fea96f7d,
Expand All @@ -31,7 +31,7 @@ static const CYBOZU_ALIGN(64) uint64_t g_vR_[] = {
0xe06ef23c24a25, 0xe06ef23c24a25, 0xe06ef23c24a25, 0xe06ef23c24a25, 0xe06ef23c24a25, 0xe06ef23c24a25, 0xe06ef23c24a25, 0xe06ef23c24a25,
0x14c8e, 0x14c8e, 0x14c8e, 0x14c8e, 0x14c8e, 0x14c8e, 0x14c8e, 0x14c8e,
};
static const CYBOZU_ALIGN(64) uint64_t g_vR2_[] = {
static const CYBOZU_ALIGN(64) uint64_t g_R2_[] = {
0xa5bf4cb89af51, 0xa5bf4cb89af51, 0xa5bf4cb89af51, 0xa5bf4cb89af51, 0xa5bf4cb89af51, 0xa5bf4cb89af51, 0xa5bf4cb89af51, 0xa5bf4cb89af51,
0x3afbba7ca31a2, 0x3afbba7ca31a2, 0x3afbba7ca31a2, 0x3afbba7ca31a2, 0x3afbba7ca31a2, 0x3afbba7ca31a2, 0x3afbba7ca31a2, 0x3afbba7ca31a2,
0x2646160ec71f1, 0x2646160ec71f1, 0x2646160ec71f1, 0x2646160ec71f1, 0x2646160ec71f1, 0x2646160ec71f1, 0x2646160ec71f1, 0x2646160ec71f1,
Expand Down Expand Up @@ -61,7 +61,17 @@ static const CYBOZU_ALIGN(64) uint64_t g_m52to64_[] = {
0xec3fa80e4935c, 0xec3fa80e4935c, 0xec3fa80e4935c, 0xec3fa80e4935c, 0xec3fa80e4935c, 0xec3fa80e4935c, 0xec3fa80e4935c, 0xec3fa80e4935c,
0x15f65, 0x15f65, 0x15f65, 0x15f65, 0x15f65, 0x15f65, 0x15f65, 0x15f65,
};
static const CYBOZU_ALIGN(64) uint64_t g_vrawOne_[] = {
static const CYBOZU_ALIGN(64) uint64_t g_zero_[] = {
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
};
static const CYBOZU_ALIGN(64) uint64_t g_rawOne_[] = {
0x1, 0x1, 0x1, 0x1, 0x1, 0x1, 0x1, 0x1,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
Expand All @@ -72,11 +82,22 @@ static const CYBOZU_ALIGN(64) uint64_t g_vrawOne_[] = {
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
};
static const CYBOZU_ALIGN(64) uint64_t g_offset_[] = { 0x0, 0x1, 0x2, 0x3, 0x4, 0x5, 0x6, 0x7, 0x8 };
// rw=0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac
static const CYBOZU_ALIGN(64) uint64_t g_rw_[] = {
0xa424657e25648, 0xa424657e25648, 0xa424657e25648, 0xa424657e25648, 0xa424657e25648, 0xa424657e25648, 0xa424657e25648, 0xa424657e25648,
0xc75706049e739, 0xc75706049e739, 0xc75706049e739, 0xc75706049e739, 0xc75706049e739, 0xc75706049e739, 0xc75706049e739, 0xc75706049e739,
0xb59085299e0e2, 0xb59085299e0e2, 0xb59085299e0e2, 0xb59085299e0e2, 0xb59085299e0e2, 0xb59085299e0e2, 0xb59085299e0e2, 0xb59085299e0e2,
0xd9cf17286a964, 0xd9cf17286a964, 0xd9cf17286a964, 0xd9cf17286a964, 0xd9cf17286a964, 0xd9cf17286a964, 0xd9cf17286a964, 0xd9cf17286a964,
0x69ec7cb33aa8, 0x69ec7cb33aa8, 0x69ec7cb33aa8, 0x69ec7cb33aa8, 0x69ec7cb33aa8, 0x69ec7cb33aa8, 0x69ec7cb33aa8, 0x69ec7cb33aa8,
0x35e995b239c7e, 0x35e995b239c7e, 0x35e995b239c7e, 0x35e995b239c7e, 0x35e995b239c7e, 0x35e995b239c7e, 0x35e995b239c7e, 0x35e995b239c7e,
0x82faa0ff3c329, 0x82faa0ff3c329, 0x82faa0ff3c329, 0x82faa0ff3c329, 0x82faa0ff3c329, 0x82faa0ff3c329, 0x82faa0ff3c329, 0x82faa0ff3c329,
0x17601, 0x17601, 0x17601, 0x17601, 0x17601, 0x17601, 0x17601, 0x17601,
};

struct G {
static const Vec& vmask() { return *(const Vec*)g_vmask_; }
static const Vec& vrp() { return *(const Vec*)g_vrp_; }
static const Vec* vpN() { return (const Vec*)g_vpN_; }
static const Vec& mask() { return *(const Vec*)g_mask_; }
static const Vec& rp() { return *(const Vec*)g_rp_; }
static const Vec* ap() { return (const Vec*)g_ap_; }
static const Vec& offset() { return *(const Vec*)g_offset_; }
};

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