File size: 5,385 Bytes
4fc906a | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 | from __future__ import annotations
import random
import numpy as np
import torch
PAD_HEAD = 3
def _rand_bits_int(rng: random.Random, l: int) -> int:
if l == 1:
return 1
return (1 << (l - 1)) | rng.getrandbits(l - 1)
def sample_modulus(rng: random.Random, n: int) -> int:
lmax = n - PAD_HEAD
r = rng.random()
if r < 0.50:
l = lmax
elif r < 0.80:
l = rng.randint(2, lmax)
else:
l = min(lmax, 1 + int(2 ** (rng.random() * 4)))
l = max(2, l)
if l <= 3 and rng.random() < 0.7:
return rng.choice([2, 3, 5, 7][: 2 if l == 2 else 4])
if l >= 5 and rng.random() < 0.15:
c = rng.choice([1, 3, 5, 7, 9, 15, 17, 31, 33, 63, rng.randint(1, 99)])
if rng.random() < 0.7:
m = (1 << l) - c
else:
m = (1 << (l - 1)) + c
if rng.random() < 0.9:
m |= 1
if 2 <= m and m.bit_length() <= l:
return m
m = _rand_bits_int(rng, l)
if rng.random() < 0.75:
m |= 1
return max(2, m)
def _carry_stress(rng: random.Random, hi: int) -> int:
nbits = max(2, hi.bit_length())
j = rng.randint(1, nbits)
i = rng.randint(0, j - 1)
v = (1 << j) - (1 << i)
if rng.random() < 0.5:
v |= rng.getrandbits(max(1, i))
return v % hi
def _sample_x(rng: random.Random, m: int, hi_mult: int, w: int) -> int:
hi = hi_mult * m
r = rng.random()
if r < 0.40:
for _ in range(8):
q = rng.randint(0, hi_mult)
lo_s = max(q * m, w)
hi_s = min((q + 1) * m, hi + w)
if lo_s < hi_s:
x = rng.randrange(lo_s, hi_s) - w
if 0 <= x < hi:
return x
return rng.randrange(hi)
if r < 0.50:
return rng.randrange(hi)
if r < 0.58:
u = rng.randrange(m)
d = rng.randrange(hi_mult)
return min(hi - 1, hi_mult * u + d)
if r < 0.64:
return rng.randrange(m)
if r < 0.78:
k = rng.randint(1, hi_mult)
delta = rng.choice([0, 1, 2, 3, rng.randint(0, 8)])
s_t = k * m + (delta if rng.random() < 0.5 else -delta)
x = s_t - w
return x if 0 <= x < hi else rng.randrange(hi)
if r < 0.96:
if rng.random() < 0.5:
x = _carry_stress(rng, hi)
else:
k = rng.randint(1, hi_mult)
x = k * m - w + (1 << rng.randint(0, max(1, hi.bit_length() - 2))) \
- rng.randint(0, 3)
if not (0 <= x < hi):
x = _carry_stress(rng, hi)
return x
return rng.choice([0, 1, 2, 3])
def sample_reduce(rng: random.Random, n: int) -> tuple[int, int]:
m = sample_modulus(rng, n)
return m, _sample_x(rng, m, 4, 0)
def _pack_bits(vals: list[int], n: int) -> np.ndarray:
out = np.empty((len(vals), n), dtype=np.uint8)
for i, v in enumerate(vals):
s = np.frombuffer(format(v, f"0{n}b").encode(), dtype=np.uint8)
out[i] = s - 48
return out
def _T(vals, n):
return torch.from_numpy(_pack_bits(vals, n)).float()
def make_reduce_batch(rng, n, bsz, instances=None):
mask = (1 << n) - 1
ms, xs, zs, qs, p3s = [], [], [], [], []
borrows = [[], [], []]
for j in range(bsz):
if instances is not None:
m, x = instances[j % len(instances)]
else:
m, x = sample_reduce(rng, n)
q = x // m
zs.append(x - q * m)
qs.append(q)
for k in (1, 2, 3):
km = k * m
diff = (x - km) & mask
borrows[k - 1].append((x ^ km ^ diff) & mask)
ms.append(m); xs.append(x); p3s.append(3 * m)
batch = {
"x": _T(xs, n), "p": _T(ms, n), "p3": _T(p3s, n),
"z": _T(zs, n),
"borrow": torch.stack([_T(borrows[k], n) for k in range(3)], dim=-1),
"q": torch.tensor(qs, dtype=torch.long),
"raw": list(zip(ms, xs)),
}
return batch
def sample_add(rng: random.Random, n: int) -> tuple[int, int, int]:
r = rng.random()
if r < 0.45:
x = rng.getrandbits(rng.randint(1, n - 2)) if rng.random() < 0.5 \
else rng.randrange(1 << (n - 2))
elif r < 0.85:
x = _carry_stress(rng, 1 << (n - 2))
elif r < 0.95:
x = rng.choice([0, 1, 2, 3])
else:
x = (1 << (n - 2)) - rng.randint(1, 4)
if rng.random() < 0.7:
x &= ~1
r = rng.random()
if r < 0.5:
y = rng.getrandbits(rng.randint(1, n - 3)) if rng.random() < 0.5 \
else rng.randrange(1 << (n - 3))
elif r < 0.9:
y = _carry_stress(rng, 1 << (n - 3))
else:
y = rng.choice([0, 1, (1 << (n - 3)) - 1])
g = rng.randint(0, 1)
return x, y, g
def make_add_batch(rng, n, bsz, instances=None):
mask = (1 << n) - 1
xs, ys, gs, ss, cs = [], [], [], [], []
for j in range(bsz):
if instances is not None:
x, y, g = instances[j % len(instances)]
else:
x, y, g = sample_add(rng, n)
w = g * y
s = x + w
ss.append(s & mask)
cs.append((x ^ w ^ s) & mask)
xs.append(x); ys.append(y); gs.append(g)
batch = {
"x": _T(xs, n), "y": _T(ys, n),
"g": torch.tensor(gs, dtype=torch.float32),
"z": _T(ss, n), "carry": _T(cs, n),
"raw": list(zip(xs, ys, gs)),
}
return batch
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