constantine/tests/test_bigints.nim

# Constantine
# Copyright (c) 2018-2019    Status Research & Development GmbH
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
# Licensed and distributed under either of
#   * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
#   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.

import  unittest, random, strutils,
        ../constantine/io/io_bigints,
        ../constantine/arithmetic/bigints_checked,
        ../constantine/config/common,
        ../constantine/primitives/constant_time

proc main() =
  suite "isZero":
    test "isZero for zero":
      var x: BigInt[128]
      check: x.isZero().bool
    test "isZero for non-zero":
      block:
        var x = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000001")
        check: not x.isZero().bool
      block:
        var x = fromHex(BigInt[128], "0x00000000_00000001_00000000_00000000")
        check: not x.isZero().bool
      block:
        var x = fromHex(BigInt[128], "0xFFFFFFFF_FFFFFFFF_FFFFFFFF_FFFFFFFF")
        check: not x.isZero().bool

  suite "Arithmetic operations - Addition":
    test "Adding 2 zeros":
      var a = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000000")
      let b = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000000")
      let carry = a.add(b, ctrue(Word))
      check: a.isZero().bool

    test "Adding 1 zero - real addition":
      block:
        var a = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000000")
        let b = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000001")
        let carry = a.add(b, ctrue(Word))

        let c = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000001")
        check:
          bool(a == c)
      block:
        var a = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000001")
        let b = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000000")
        let carry = a.add(b, ctrue(Word))

        let c = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000001")
        check:
          bool(a == c)

    test "Adding 1 zero - fake addition":
      block:
        var a = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000000")
        let b = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000001")
        let carry = a.add(b, cfalse(Word))

        let c = a
        check:
          bool(a == c)
      block:
        var a = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000001")
        let b = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000000")
        let carry = a.add(b, cfalse(Word))

        let c = a
        check:
          bool(a == c)

    test "Adding non-zeros - real addition":
      block:
        var a = fromHex(BigInt[128], "0x00000000_00000001_00000000_00000000")
        let b = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000001")
        let carry = a.add(b, ctrue(Word))

        let c = fromHex(BigInt[128], "0x00000000_00000001_00000000_00000001")
        check:
          bool(a == c)
      block:
        var a = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000001")
        let b = fromHex(BigInt[128], "0x00000000_00000001_00000000_00000000")
        let carry = a.add(b, ctrue(Word))

        let c = fromHex(BigInt[128], "0x00000000_00000001_00000000_00000001")
        check:
          bool(a == c)

    test "Adding non-zeros - fake addition":
      block:
        var a = fromHex(BigInt[128], "0x00000000_00000001_00000000_00000000")
        let b = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000001")
        let carry = a.add(b, cfalse(Word))

        let c = a
        check:
          bool(a == c)
      block:
        var a = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000001")
        let b = fromHex(BigInt[128], "0x00000000_00000001_00000000_00000000")
        let carry = a.add(b, cfalse(Word))

        let c = a
        check:
          bool(a == c)

    test "Addition limbs carry":
      block:
        var a = fromHex(BigInt[128], "0x00000000_FFFFFFFF_FFFFFFFF_FFFFFFFE")
        let b = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000001")
        let carry = a.add(b, ctrue(Word))

        let c = fromHex(BigInt[128], "0x00000000_FFFFFFFF_FFFFFFFF_FFFFFFFF")
        check:
          bool(a == c)
          not bool(carry)

      block:
        var a = fromHex(BigInt[128], "0x00000000_FFFFFFFF_FFFFFFFF_FFFFFFFF")
        let b = fromHex(BigInt[128], "0x00000000_00000000_00000000_00000001")
        let carry = a.add(b, ctrue(Word))

        let c = fromHex(BigInt[128], "0x00000001_00000000_00000000_00000000")
        check:
          bool(a == c)
          not bool(carry)

  suite "Modular operations - small modulus":
    # Vectors taken from Stint - https://github.com/status-im/nim-stint
    test "100 mod 13":
      # Test 1 word and more than 1 word
      block:
        let a = BigInt[7].fromUint(100'u32)
        let m = BigInt[4].fromUint(13'u8)

        var r: BigInt[4]
        r.reduce(a, m)
        check:
          bool(r == BigInt[4].fromUint(100'u8 mod 13))

      block: #
        let a = BigInt[32].fromUint(100'u32)
        let m = BigInt[4].fromUint(13'u8)

        var r: BigInt[4]
        r.reduce(a, m)
        check:
          bool(r == BigInt[4].fromUint(100'u8 mod 13))

      block: #
        let a = BigInt[64].fromUint(100'u32)
        let m = BigInt[4].fromUint(13'u8)

        var r: BigInt[4]
        r.reduce(a, m)
        check:
          bool(r == BigInt[4].fromUint(100'u8 mod 13))

    test "2^64 mod 3":
      let a = BigInt[65].fromHex("0x1_00000000_00000000")
      let m = BigInt[8].fromUint(3'u8)

      var r: BigInt[8]
      r.reduce(a, m)
      check:
        bool(r == BigInt[8].fromUint(1'u8))

    test "1234567891234567890 mod 10":
      let a = BigInt[64].fromUint(1234567891234567890'u64)
      let m = BigInt[8].fromUint(10'u8)

      var r: BigInt[8]
      r.reduce(a, m)
      check:
        bool(r == BigInt[8].fromUint(0'u8))

  suite "Modular operations - small modulus - Stint specific failures highlighted by property-based testing":
    # Vectors taken from Stint - https://github.com/status-im/nim-stint
    test "Modulo: 65696211516342324 mod 174261910798982":
      let u = 65696211516342324'u64
      let v = 174261910798982'u64

      let a = BigInt[56].fromUint(u)
      let m = BigInt[48].fromUint(v)

      var r: BigInt[48]
      r.reduce(a, m)

      check:
        bool(r == BigInt[48].fromUint(u mod v))

    test "Modulo: 15080397990160655 mod 600432699691":
      let u = 15080397990160655'u64
      let v = 600432699691'u64

      let a = BigInt[54].fromUint(u)
      let m = BigInt[40].fromUint(v)

      var r: BigInt[40]
      r.reduce(a, m)

      check:
        bool(r == BigInt[40].fromUint(u mod v))

main()