86 lines
1.8 KiB
Nim
86 lines
1.8 KiB
Nim
# Stint
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# Copyright 2018 Status Research & Development GmbH
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# Licensed under either of
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#
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# * Apache License, version 2.0, ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)
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# * MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)
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#
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# at your option. This file may not be copied, modified, or distributed except according to those terms.
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import ./uintops, private/datatypes
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{.push raises: [], gcsafe.}
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func addmod_internal(a, b, m: StUint): StUint {.inline.}=
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## Modular addition
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## ⚠⚠ Assume a < m and b < m
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doAssert a < m
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doAssert b < m
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# We don't do a_m + b_m directly to avoid overflows
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let b_from_m = m - b
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if a >= b_from_m:
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a - b_from_m
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else:
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m - b_from_m + a
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func submod_internal(a, b, m: StUint): StUint {.inline.}=
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## Modular substraction
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## ⚠⚠ Assume a < m and b < m
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doAssert a < m
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doAssert b < m
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# We don't do a_m - b_m directly to avoid underflows
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if a >= b:
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a - b
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else:
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m - b + a
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func addmod*(a, b, m: StUint): StUint =
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## Modular addition
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let a_m = if a < m: a
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else: a mod m
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let b_m = if b < m: b
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else: b mod m
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addmod_internal(a_m, b_m, m)
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func submod*(a, b, m: StUint): StUint =
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## Modular substraction
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let a_m = if a < m: a
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else: a mod m
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let b_m = if b < m: b
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else: b mod m
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submod_internal(a_m, b_m, m)
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func mulmod*(a, b, m: StUint): StUint =
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## Modular multiplication
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let
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ax = a.stuint(a.bits * 2)
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bx = b.stuint(b.bits * 2)
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mx = m.stuint(m.bits * 2)
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px = ax * bx
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divmod(px, mx).rem.stuint(a.bits)
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func powmod*(a, b, m: StUint): StUint =
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## Modular exponentiation
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var (a, b) = (a, b)
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result = one(type a)
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while not b.isZero:
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if b.isOdd:
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result = result.mulmod(a, m)
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b = b shr 1
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a = mulmod(a, a, m)
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{.pop.}
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