-
Notifications
You must be signed in to change notification settings - Fork 0
/
FLOAT256.py
240 lines (206 loc) · 5.76 KB
/
FLOAT256.py
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
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
import taichi as ti
from decimal import Decimal, getcontext
"""
设置外部精度
2**-192 = 1.6e-58
"""
getcontext().prec = 100
F256 = ti.types.vector(4, ti.int64)
_INT2 = ti.types.vector(2, ti.int64)
F256_ALL = F256(-1)
INT64_MIN = -0x8000000000000000
INT64_MAX = 0x7fffffffffffffff
UINT64_MAX = 0xffffffffffffffff
def cvt_int_bin(n, bit=64):
assert INT64_MIN <= n <= INT64_MAX
if n < 0:
n = n + 2 ** bit
bin_str = bin(n).replace("0b", "")
if len(bin_str) < bit:
bin_str = "0" * (bit - len(bin_str)) + bin_str
return bin_str
def cvt_int_hex(n, bit=64):
if n < 0:
n = n + 2 ** bit
hex_str = hex(n).replace("0x", "")
byte = bit % 8
if len(hex_str) < byte:
hex_str = "f" * (byte - len(hex_str)) + hex_str
return hex_str
def cvt_int_uint(n, bit=64):
assert INT64_MIN <= n <= INT64_MAX
if n < 0:
n = n + 2 ** bit
return n
def cvt_uint_int(n, bit=64):
assert 0 <= n <= UINT64_MAX
if n > INT64_MAX:
n = n - 2 ** bit
return n
def F256_print(f):
print("==============")
print(f)
print("DEC:", f[0], f[1], f[2], f[3])
print("BIN:", cvt_int_bin(f[0]), cvt_int_bin(f[1]), cvt_int_bin(f[2]), cvt_int_bin(f[3]))
print("HEX:", cvt_int_hex(f[0]), cvt_int_hex(f[1]), cvt_int_hex(f[2]), cvt_int_hex(f[3]))
print("==============")
# 字符串转F256，不支持科学计数法，不要有前缀加号，不要有前缀0
# 补码形式存储，保证二进制正确
def str2F256(s: str, bit=64):
lim = bit * 3
res = F256(0)
neg = False
if s[0] == '-':
neg = True
if s.find(".") == -1:
r = s
d = "0"
else:
r, d = s.split(".")
res[0] = int(r)
assert INT64_MIN <= res[0] <= INT64_MAX
d = Decimal("0." + d)
if neg:
d = 1 - d
res[0] -= 1
bit_list = []
while True:
d = d * 2
if d < 1:
bit_list.append("0")
elif d > 1:
bit_list.append("1")
d = d - 1
elif d == 1:
bit_list.append("1")
break
if len(bit_list) == lim:
break
if len(bit_list) != lim:
bit_list = bit_list + ["0" for i in range(lim - len(bit_list))]
res[1] = cvt_uint_int(int("".join(bit_list[0:bit]), 2))
res[2] = cvt_uint_int(int("".join(bit_list[bit:bit * 2]), 2))
res[3] = cvt_uint_int(int("".join(bit_list[bit * 2:bit * 3]), 2))
return res
# F256转字符串
def F2562str(f):
d = Decimal(f[0])
bit_str = cvt_int_bin(f[1]) + cvt_int_bin(f[2]) + cvt_int_bin(f[3])
base = Decimal(0.5)
mul = Decimal(0.5)
for c in bit_str:
if c == '1':
d = d + base
base = base * mul
return d
@ti.func
# F256,增加1最小单位
def inc256(u) -> F256:
h = u == F256_ALL
c = F256(h[1] & h[2] & h[3] & 1, h[2] & h[3] & 1, h[3] & 1, 1)
return u + c
@ti.func
# 取相反数
def neg256(u) -> F256:
u = u ^ F256_ALL
return inc256(u)
@ti.func
# return u<v
def uint64_less(u, v):
u0: ti.uint64 = u[0]
u1: ti.uint64 = u[1]
u2: ti.uint64 = u[2]
u3: ti.uint64 = u[3]
v0: ti.uint64 = v[0]
v1: ti.uint64 = v[1]
v2: ti.uint64 = v[2]
v3: ti.uint64 = v[3]
return F256(u0 < v0, u1 < v1, u2 < v2, u3 < v3)
@ti.func
# F256+F256
def add256(u, v) -> F256:
s = u + v
# h = s < u
h = uint64_less(s, u)
c1 = F256(h[1], h[2], h[3], h[0]) & F256(1, 1, 1, 0)
h = s == F256_ALL
c2 = F256((c1[1] | (c1[2] & h[2])) & h[1], c1[2] & h[2], 0, 0)
return s + c1 + c2
@ti.func
# u<<1
def shl256(u):
h = ti.bit_shr(u, 63) & F256(0, 1, 1, 1)
return u << 1 | F256(h[1], h[2], h[3], h[0])
@ti.func
# 计算两个int64位乘法，返回高64位与低64位
def mul_hi_lo(op1: ti.int64, op2: ti.int64) -> _INT2:
u1 = op1 & ti.i64(0xffffffff)
v1 = op2 & ti.i64(0xffffffff)
t = u1 * v1
w3 = t & ti.i64(0xffffffff)
k = ti.bit_shr(t, 32)
op1 = ti.bit_shr(op1, 32)
t = op1 * v1 + k
k = t & ti.i64(0xffffffff)
w1 = ti.bit_shr(t, 32)
op2 = ti.bit_shr(op2, 32)
t = (u1 * op2) + k
k = ti.bit_shr(t, 32)
hi = op1 * op2 + w1 + k
lo = (t << 32) + w3
return _INT2(hi, lo)
@ti.func
# return U*V
def mulfpu(u, v):
neg = 0
usign = ti.bit_shr(u[0], 63)
vsign = ti.bit_shr(v[0], 63)
if usign == 1:
u = neg256(u)
neg += 1
if vsign == 1:
v = neg256(v)
neg += 1
_t = mul_hi_lo(u[1], v[1])
s = F256(u[0] * v[0], _t[0], _t[1], mul_hi_lo(u[2], v[2])[0])
_t = mul_hi_lo(u[0], v[1])
_t1 = mul_hi_lo(u[0], v[3])
t1 = F256(_t[0], _t[1], _t1[0], _t1[1])
_t = mul_hi_lo(v[0], u[1])
_t1 = mul_hi_lo(v[0], u[3])
t2 = F256(_t[0], _t[1], _t1[0], _t1[1])
s = add256(s, add256(t1, t2))
_t = mul_hi_lo(u[0], v[2])
t1 = F256(0, _t[0], _t[1], mul_hi_lo(u[1], v[3])[0])
_t = mul_hi_lo(v[0], u[2])
t2 = F256(0, _t[0], _t[1], mul_hi_lo(v[1], u[3])[0])
s = add256(s, add256(t1, t2))
_t = mul_hi_lo(u[1], v[2])
t1 = F256(0, 0, _t[0], _t[1])
_t = mul_hi_lo(v[1], u[2])
t2 = F256(0, 0, _t[0], _t[1])
s = add256(s, add256(t1, t2))
res = add256(s, F256(0, 0, 0, 3))
if neg == 1:
res = neg256(res)
return res
@ti.func
# return U^2
def sqrfpu(u):
usign = ti.bit_shr(u[0], 63)
if usign == 1:
u = neg256(u)
_t = mul_hi_lo(u[1], u[1])
s = F256(u[0] * u[0], _t[0], _t[1], mul_hi_lo(u[2], u[2])[0])
_t = mul_hi_lo(u[0], u[1])
_t1 = mul_hi_lo(u[0], u[3])
t = F256(_t[0], _t[1], _t1[0], _t1[1])
s = add256(s, shl256(t))
_t = mul_hi_lo(u[0], u[2])
t = F256(0, _t[0], _t[1], mul_hi_lo(u[1], u[3])[0])
s = add256(s, shl256(t))
_t = mul_hi_lo(u[1], u[2])
t = F256(0, 0, _t[0], _t[1])
s = add256(s, shl256(t))
res = add256(s, F256(0, 0, 0, 3))
return res