[New Hints] uint256_improvements.json

[pefontana]

Implement the remaining hints in uint256_improvements.json

NewHint#42

Assigned: @MegaRedHand
Status: #1013

                "a = (ids.a.high << 128) + ids.a.low",
                "div = (ids.div.b23 << 128) + ids.div.b01",
                "quotient, remainder = divmod(a, div)",
                "",
                "ids.quotient.low = quotient & ((1 << 128) - 1)",
                "ids.quotient.high = quotient >> 128",
                "ids.remainder.low = remainder & ((1 << 128) - 1)",
                "ids.remainder.high = remainder >> 128"

NewHint#43

Assigned: @MegaRedHand
Status: #1016

"def split(num: int, num_bits_shift: int = 128, length: int = 2):",
                "    a = []",
                "    for _ in range(length):",
                "        a.append( num & ((1 << num_bits_shift) - 1) )",
                "        num = num >> num_bits_shift",
                "    return tuple(a)",
                "",
                "def pack(z, num_bits_shift: int = 128) -> int:",
                "    limbs = (z.low, z.high)",
                "    return sum(limb << (num_bits_shift * i) for i, limb in enumerate(limbs))",
                "",
                "a = pack(ids.a)",
                "b = pack(ids.b)",
                "res = (a - b)%2**256",
                "res_split = split(res)",
                "ids.res.low = res_split[0]",
                "ids.res.high = res_split[1]"

NewHint#44

Assigned: @MegaRedHand
Status: #1025

                "from starkware.python.math_utils import isqrt",
                "n = (ids.n.high << 128) + ids.n.low",
                "root = isqrt(n)",
                "assert 0 <= root < 2 ** 128",
                "ids.root = root"

NewHint#45

Assigned: @MegaRedHand
Status: #1024

          "res = ids.a + ids.b",
          "ids.carry = 1 if res >= ids.SHIFT else 0"