| 1 | """
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| 2 | Math operations, e.g. for arbitrary precision integers
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| 3 |
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| 4 | They are currently int64_t, rather than C int, but we want to upgrade to
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| 5 | heap-allocated integers.
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| 6 |
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| 7 | Regular int ops can use the normal operators + - * /, or maybe i_add() if we
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| 8 | really want. Does that make code gen harder or worse?
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| 9 |
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| 10 | Float ops could be + - * / too, but it feels nicer to develop a formal
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| 11 | interface?
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| 12 | """
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| 13 | from __future__ import print_function
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| 14 |
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| 15 | from typing import Tuple
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| 16 |
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| 17 |
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| 18 | class BigInt(object):
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| 19 |
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| 20 | def __init__(self, i):
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| 21 | # type: (int) -> None
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| 22 | self.i = i
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| 23 |
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| 24 | def __eq__(self, other):
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| 25 | # type: (object) -> bool
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| 26 |
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| 27 | # Disabled check
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| 28 | # Prevent possible mistakes. Could do this with other operators
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| 29 | # raise AssertionError('Use mops.Equal()')
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| 30 |
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| 31 | if not isinstance(other, BigInt):
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| 32 | raise AssertionError()
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| 33 |
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| 34 | # Used for hashing
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| 35 | return self.i == other.i
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| 36 |
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| 37 | def __gt__(self, other):
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| 38 | # type: (object) -> bool
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| 39 | raise AssertionError('Use functions in mops.py')
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| 40 |
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| 41 | def __ge__(self, other):
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| 42 | # type: (object) -> bool
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| 43 | raise AssertionError('Use functions in mops.py')
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| 44 |
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| 45 | def __hash__(self):
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| 46 | # type: () -> int
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| 47 | """For dict lookups."""
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| 48 | return hash(self.i)
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| 49 |
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| 50 |
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| 51 | ZERO = BigInt(0)
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| 52 | ONE = BigInt(1)
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| 53 | MINUS_ONE = BigInt(-1)
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| 54 | MINUS_TWO = BigInt(-2) # for printf
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| 55 |
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| 56 |
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| 57 | def ToStr(b):
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| 58 | # type: (BigInt) -> str
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| 59 | return str(b.i)
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| 60 |
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| 61 |
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| 62 | def ToOctal(b):
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| 63 | # type: (BigInt) -> str
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| 64 | return '%o' % b.i
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| 65 |
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| 66 |
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| 67 | def ToHexUpper(b):
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| 68 | # type: (BigInt) -> str
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| 69 | return '%X' % b.i
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| 70 |
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| 71 |
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| 72 | def ToHexLower(b):
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| 73 | # type: (BigInt) -> str
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| 74 | return '%x' % b.i
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| 75 |
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| 76 |
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| 77 | # Notes on FromStr() and recognizing integers
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| 78 | #
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| 79 | # 3 similar but DIFFERENT cases:
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| 80 | #
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| 81 | # 1. trap ' 42 ' x - unsigned, including 09, but not -1
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| 82 | # 2. echo $(( x )) - 0123 is octal, but no -0123 because that's separate I think
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| 83 | # 3. int(), j8 - 077 is decimal
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| 84 | #
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| 85 | # - mops.FromStr should not use exceptions? That is consistent with mops.FromFloat
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| 86 | # - under the hood it uses StringToInt64, which uses strtoll
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| 87 | # - problem: we DO NOT want to rely on strtoll() to define a language, to
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| 88 | # reject user-facing strings - we want to use something like
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| 89 | # match.LooksLikeInteger() usually. This is part of our spec-driven
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| 90 | # philosophy.
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| 91 | #
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| 92 | # - a problem though is if we support 00, because sometimes that is OCTAL
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| 93 | # - int("00") is zero
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| 94 | # - match.LooksLikeInteger returns it
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| 95 |
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| 96 | # uses LooksLikeInteger and then FromStr()
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| 97 | # - YSH int()
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| 98 | # - printf builtin
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| 99 | # - YSH expression conversion
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| 100 |
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| 101 | # Uses only FromStr()
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| 102 | # - j8 - uses its own regex though
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| 103 | # - ulimit
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| 104 | # - trap - NON-NEGATIVE only
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| 105 | # - arg parser
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| 106 |
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| 107 |
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| 108 | def FromStr(s, base=10):
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| 109 | # type: (str, int) -> BigInt
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| 110 | return BigInt(int(s, base))
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| 111 |
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| 112 |
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| 113 | MAX_POS_INT = 2**63 - 1
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| 114 | MAX_NEG_INT = 2**63
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| 115 |
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| 116 |
|
| 117 | def FromStr2(s, base=10):
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| 118 | # type: (str, int) -> Tuple[bool, BigInt]
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| 119 | """
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| 120 | Simulate C++
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| 121 | """
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| 122 | try:
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| 123 | big_int = BigInt(int(s, base))
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| 124 | except ValueError:
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| 125 | # Simulate C++ overflow
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| 126 | if big_int.i > MAX_POS_INT:
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| 127 | return (False, MINUS_ONE)
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| 128 | if big_int.i < MAX_NEG_INT:
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| 129 | return (False, MINUS_ONE)
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| 130 |
|
| 131 | return (True, big_int)
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| 132 | else:
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| 133 | return (False, MINUS_ONE)
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| 134 |
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| 135 |
|
| 136 | def BigTruncate(b):
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| 137 | # type: (BigInt) -> int
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| 138 | """Only truncates in C++"""
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| 139 | return b.i
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| 140 |
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| 141 |
|
| 142 | def IntWiden(i):
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| 143 | # type: (int) -> BigInt
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| 144 | """Only widens in C++"""
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| 145 | return BigInt(i)
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| 146 |
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| 147 |
|
| 148 | def FromC(i):
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| 149 | # type: (int) -> BigInt
|
| 150 | """A no-op in C, for RLIM_INFINITY"""
|
| 151 | return BigInt(i)
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| 152 |
|
| 153 |
|
| 154 | def FromBool(b):
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| 155 | # type: (bool) -> BigInt
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| 156 | """Only widens in C++"""
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| 157 | return BigInt(1) if b else BigInt(0)
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| 158 |
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| 159 |
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| 160 | def ToFloat(b):
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| 161 | # type: (BigInt) -> float
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| 162 | """Used by float(42) in Oils"""
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| 163 | return float(b.i)
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| 164 |
|
| 165 |
|
| 166 | def FromFloat(f):
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| 167 | # type: (float) -> Tuple[bool, BigInt]
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| 168 | """Used by int(3.14) in Oils"""
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| 169 | try:
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| 170 | big = int(f)
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| 171 | except ValueError: # NAN
|
| 172 | return False, MINUS_ONE
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| 173 | except OverflowError: # INFINITY
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| 174 | return False, MINUS_ONE
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| 175 | return True, BigInt(big)
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| 176 |
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| 177 |
|
| 178 | # Can't use operator overloading
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| 179 |
|
| 180 |
|
| 181 | def Negate(b):
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| 182 | # type: (BigInt) -> BigInt
|
| 183 | return BigInt(-b.i)
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| 184 |
|
| 185 |
|
| 186 | def Add(a, b):
|
| 187 | # type: (BigInt, BigInt) -> BigInt
|
| 188 | return BigInt(a.i + b.i)
|
| 189 |
|
| 190 |
|
| 191 | def Sub(a, b):
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| 192 | # type: (BigInt, BigInt) -> BigInt
|
| 193 | return BigInt(a.i - b.i)
|
| 194 |
|
| 195 |
|
| 196 | def Mul(a, b):
|
| 197 | # type: (BigInt, BigInt) -> BigInt
|
| 198 | return BigInt(a.i * b.i)
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| 199 |
|
| 200 |
|
| 201 | def Div(a, b):
|
| 202 | # type: (BigInt, BigInt) -> BigInt
|
| 203 | """Integer division.
|
| 204 |
|
| 205 | Oils rounds toward zero.
|
| 206 |
|
| 207 | Python rounds toward negative infinity, while C++ rounds toward zero. We
|
| 208 | have to work around Python a bit.
|
| 209 | """
|
| 210 | assert b.i != 0, b.i # divisor can't be zero -- caller checks
|
| 211 |
|
| 212 | # Only use Python // on non-negative numbers. Apply sign afterward.
|
| 213 | sign = 1
|
| 214 |
|
| 215 | if a.i < 0:
|
| 216 | pa = -a.i
|
| 217 | sign = -1
|
| 218 | else:
|
| 219 | pa = a.i
|
| 220 |
|
| 221 | if b.i < 0:
|
| 222 | pb = -b.i
|
| 223 | sign = -sign
|
| 224 | else:
|
| 225 | pb = b.i
|
| 226 |
|
| 227 | return BigInt(sign * (pa // pb))
|
| 228 |
|
| 229 |
|
| 230 | def Rem(a, b):
|
| 231 | # type: (BigInt, BigInt) -> BigInt
|
| 232 | """Integer remainder."""
|
| 233 | assert b.i != 0, b.i # YSH divisor must be positive, but OSH can be negative
|
| 234 |
|
| 235 | # Only use Python % on non-negative numbers. Apply sign afterward.
|
| 236 | if a.i < 0:
|
| 237 | pa = -a.i
|
| 238 | sign = -1
|
| 239 | else:
|
| 240 | pa = a.i
|
| 241 | sign = 1
|
| 242 |
|
| 243 | if b.i < 0:
|
| 244 | pb = -b.i
|
| 245 | else:
|
| 246 | pb = b.i
|
| 247 |
|
| 248 | return BigInt(sign * (pa % pb))
|
| 249 |
|
| 250 |
|
| 251 | def Equal(a, b):
|
| 252 | # type: (BigInt, BigInt) -> bool
|
| 253 | return a.i == b.i
|
| 254 |
|
| 255 |
|
| 256 | def Greater(a, b):
|
| 257 | # type: (BigInt, BigInt) -> bool
|
| 258 | return a.i > b.i
|
| 259 |
|
| 260 |
|
| 261 | # GreaterEq, Less, LessEq can all be expressed as the 2 ops above
|
| 262 |
|
| 263 |
|
| 264 | def LShift(a, b):
|
| 265 | # type: (BigInt, BigInt) -> BigInt
|
| 266 | assert b.i >= 0, b.i # Must be checked by caller
|
| 267 | return BigInt(a.i << b.i)
|
| 268 |
|
| 269 |
|
| 270 | def RShift(a, b):
|
| 271 | # type: (BigInt, BigInt) -> BigInt
|
| 272 | assert b.i >= 0, b.i # Must be checked by caller
|
| 273 | return BigInt(a.i >> b.i)
|
| 274 |
|
| 275 |
|
| 276 | def BitAnd(a, b):
|
| 277 | # type: (BigInt, BigInt) -> BigInt
|
| 278 | return BigInt(a.i & b.i)
|
| 279 |
|
| 280 |
|
| 281 | def BitOr(a, b):
|
| 282 | # type: (BigInt, BigInt) -> BigInt
|
| 283 | return BigInt(a.i | b.i)
|
| 284 |
|
| 285 |
|
| 286 | def BitXor(a, b):
|
| 287 | # type: (BigInt, BigInt) -> BigInt
|
| 288 | return BigInt(a.i ^ b.i)
|
| 289 |
|
| 290 |
|
| 291 | def BitNot(a):
|
| 292 | # type: (BigInt) -> BigInt
|
| 293 | return BigInt(~a.i)
|