    const std = @import("std");
    const common = @import("../common.zig");
    const crypto = std.crypto;
    const debug = std.debug;
    const math = std.math;
    const mem = std.mem;

    const Field = common.Field;

    const NonCanonicalError = std.crypto.errors.NonCanonicalError;
    const NotSquareError = std.crypto.errors.NotSquareError;

    /// Number of bytes required to encode a scalar.
    pub const encoded_length = 32;

    /// A compressed scalar, in canonical form.
    pub const CompressedScalar = [encoded_length]u8;

    const Fe = Field(.{
        .fiat = @import("p256_scalar_64.zig"),
        .field_order = 115792089210356248762697446949407573529996955224135760342422259061068512044369,
        .field_bits = 256,
        .saturated_bits = 256,
        .encoded_length = encoded_length,
    });

    /// The scalar field order.
    pub const field_order = Fe.field_order;

    /// Reject a scalar whose encoding is not canonical.
    pub fn rejectNonCanonical(s: CompressedScalar, endian: std.builtin.Endian) NonCanonicalError!void {
        return Fe.rejectNonCanonical(s, endian);
    }

    /// Reduce a 48-bytes scalar to the field size.
    pub fn reduce48(s: [48]u8, endian: std.builtin.Endian) CompressedScalar {
        return Scalar.fromBytes48(s, endian).toBytes(endian);
    }

    /// Reduce a 64-bytes scalar to the field size.
    pub fn reduce64(s: [64]u8, endian: std.builtin.Endian) CompressedScalar {
        return ScalarDouble.fromBytes64(s, endian).toBytes(endian);
    }

    /// Return a*b (mod L)
    pub fn mul(a: CompressedScalar, b: CompressedScalar, endian: std.builtin.Endian) NonCanonicalError!CompressedScalar {
        return (try Scalar.fromBytes(a, endian)).mul(try Scalar.fromBytes(b, endian)).toBytes(endian);
    }

    /// Return a*b+c (mod L)
    pub fn mulAdd(a: CompressedScalar, b: CompressedScalar, c: CompressedScalar, endian: std.builtin.Endian) NonCanonicalError!CompressedScalar {
        return (try Scalar.fromBytes(a, endian)).mul(try Scalar.fromBytes(b, endian)).add(try Scalar.fromBytes(c, endian)).toBytes(endian);
    }

    /// Return a+b (mod L)
    pub fn add(a: CompressedScalar, b: CompressedScalar, endian: std.builtin.Endian) NonCanonicalError!CompressedScalar {
        return (try Scalar.fromBytes(a, endian)).add(try Scalar.fromBytes(b, endian)).toBytes(endian);
    }

    /// Return -s (mod L)
    pub fn neg(s: CompressedScalar, endian: std.builtin.Endian) NonCanonicalError!CompressedScalar {
        return (try Scalar.fromBytes(s, endian)).neg().toBytes(endian);
    }

    /// Return (a-b) (mod L)
    pub fn sub(a: CompressedScalar, b: CompressedScalar, endian: std.builtin.Endian) NonCanonicalError!CompressedScalar {
        return (try Scalar.fromBytes(a, endian)).sub(try Scalar.fromBytes(b, endian)).toBytes(endian);
    }

    /// Return a random scalar
    pub fn random(endian: std.builtin.Endian) CompressedScalar {
        return Scalar.random().toBytes(endian);
    }

    /// A scalar in unpacked representation.
    pub const Scalar = struct {
        fe: Fe,

        /// Zero.
        pub const zero = Scalar{ .fe = Fe.zero };

        /// One.
        pub const one = Scalar{ .fe = Fe.one };

        /// Unpack a serialized representation of a scalar.
        pub fn fromBytes(s: CompressedScalar, endian: std.builtin.Endian) NonCanonicalError!Scalar {
            return Scalar{ .fe = try Fe.fromBytes(s, endian) };
        }

        /// Reduce a 384 bit input to the field size.
        pub fn fromBytes48(s: [48]u8, endian: std.builtin.Endian) Scalar {
            const t = ScalarDouble.fromBytes(384, s, endian);
            return t.reduce(384);
        }

        /// Reduce a 512 bit input to the field size.
        pub fn fromBytes64(s: [64]u8, endian: std.builtin.Endian) Scalar {
            const t = ScalarDouble.fromBytes(512, s, endian);
            return t.reduce(512);
        }

        /// Pack a scalar into bytes.
        pub fn toBytes(n: Scalar, endian: std.builtin.Endian) CompressedScalar {
            return n.fe.toBytes(endian);
        }

        /// Return true if the scalar is zero..
        pub fn isZero(n: Scalar) bool {
            return n.fe.isZero();
        }

        /// Return true if the scalar is odd.
        pub fn isOdd(n: Scalar) bool {
            return n.fe.isOdd();
        }

        /// Return true if a and b are equivalent.
        pub fn equivalent(a: Scalar, b: Scalar) bool {
            return a.fe.equivalent(b.fe);
        }

        /// Compute x+y (mod L)
        pub fn add(x: Scalar, y: Scalar) Scalar {
            return Scalar{ .fe = x.fe.add(y.fe) };
        }

        /// Compute x-y (mod L)
        pub fn sub(x: Scalar, y: Scalar) Scalar {
            return Scalar{ .fe = x.fe.sub(y.fe) };
        }

        /// Compute 2n (mod L)
        pub fn dbl(n: Scalar) Scalar {
            return Scalar{ .fe = n.fe.dbl() };
        }

        /// Compute x*y (mod L)
        pub fn mul(x: Scalar, y: Scalar) Scalar {
            return Scalar{ .fe = x.fe.mul(y.fe) };
        }

        /// Compute x^2 (mod L)
        pub fn sq(n: Scalar) Scalar {
            return Scalar{ .fe = n.fe.sq() };
        }

        /// Compute x^n (mod L)
        pub fn pow(a: Scalar, comptime T: type, comptime n: T) Scalar {
            return Scalar{ .fe = a.fe.pow(n) };
        }

        /// Compute -x (mod L)
        pub fn neg(n: Scalar) Scalar {
            return Scalar{ .fe = n.fe.neg() };
        }

        /// Compute x^-1 (mod L)
        pub fn invert(n: Scalar) Scalar {
            return Scalar{ .fe = n.fe.invert() };
        }

        /// Return true if n is a quadratic residue mod L.
        pub fn isSquare(n: Scalar) Scalar {
            return n.fe.isSquare();
        }

        /// Return the square root of L, or NotSquare if there isn't any solutions.
        pub fn sqrt(n: Scalar) NotSquareError!Scalar {
            return Scalar{ .fe = try n.fe.sqrt() };
        }

        /// Return a random scalar < L.
        pub fn random() Scalar {
            var s: [48]u8 = undefined;
            while (true) {
                crypto.random.bytes(&s);
                const n = Scalar.fromBytes48(s, .Little);
                if (!n.isZero()) {
                    return n;
                }
            }
        }
    };

    const ScalarDouble = struct {
        x1: Fe,
        x2: Fe,
        x3: Fe,

        fn fromBytes(comptime bits: usize, s_: [bits / 8]u8, endian: std.builtin.Endian) ScalarDouble {
            debug.assert(bits > 0 and bits <= 512 and bits >= Fe.saturated_bits and bits <= Fe.saturated_bits * 3);

            var s = s_;
            if (endian == .Big) {
                for (s_, 0..) |x, i| s[s.len - 1 - i] = x;
            }
            var t = ScalarDouble{ .x1 = undefined, .x2 = Fe.zero, .x3 = Fe.zero };
            {
                var b = [_]u8{0} ** encoded_length;
                const len = @min(s.len, 24);
                b[0..len].* = s[0..len].*;
                t.x1 = Fe.fromBytes(b, .Little) catch unreachable;
            }
            if (s_.len >= 24) {
                var b = [_]u8{0} ** encoded_length;
                const len = @min(s.len - 24, 24);
                b[0..len].* = s[24..][0..len].*;
                t.x2 = Fe.fromBytes(b, .Little) catch unreachable;
            }
            if (s_.len >= 48) {
                var b = [_]u8{0} ** encoded_length;
                const len = s.len - 48;
                b[0..len].* = s[48..][0..len].*;
                t.x3 = Fe.fromBytes(b, .Little) catch unreachable;
            }
            return t;
        }

        fn reduce(expanded: ScalarDouble, comptime bits: usize) Scalar {
            debug.assert(bits > 0 and bits <= Fe.saturated_bits * 3 and bits <= 512);
            var fe = expanded.x1;
            if (bits >= 192) {
                const st1 = Fe.fromInt(1 << 192) catch unreachable;
                fe = fe.add(expanded.x2.mul(st1));
                if (bits >= 384) {
                    const st2 = st1.sq();
                    fe = fe.add(expanded.x3.mul(st2));
                }
            }
            return Scalar{ .fe = fe };
        }
    };