// Copyright (c) 2013-2016 The btcsuite developers
// Copyright (c) 2015-2024 The Decred developers
// Copyright (c) 2013-2024 Dave Collins
// Use of this source code is governed by an ISC
// license that can be found in the LICENSE file.

package secp256k1

import (
	"bytes"
	"encoding/hex"
	"fmt"
	"math/big"
	"math/rand"
	"reflect"
	"testing"
	"time"
)

// SetHex decodes the passed big-endian hex string into the internal field value
// representation.  Only the first 32-bytes are used.
//
// This is NOT constant time.
//
// The field value is returned to support chaining.  This enables syntax like:
// f := new(FieldVal).SetHex("0abc").Add(1) so that f = 0x0abc + 1
func (f *FieldVal) SetHex(hexString string) *FieldVal {
	if len(hexString)%2 != 0 {
		hexString = "0" + hexString
	}
	bytes, _ := hex.DecodeString(hexString)
	f.SetByteSlice(bytes)
	return f
}

// randFieldVal returns a field value created from a random value generated by
// the passed rng.
func randFieldVal(t *testing.T, rng *rand.Rand) *FieldVal {
	t.Helper()

	var buf [32]byte
	if _, err := rng.Read(buf[:]); err != nil {
		t.Fatalf("failed to read random: %v", err)
	}

	// Create and return a field value.
	var fv FieldVal
	fv.SetBytes(&buf)
	fv.Normalize()
	return &fv
}

// randIntAndFieldVal returns a big integer and a field value both created from
// the same random value generated by the passed rng.
func randIntAndFieldVal(t *testing.T, rng *rand.Rand) (*big.Int, *FieldVal) {
	t.Helper()

	var buf [32]byte
	if _, err := rng.Read(buf[:]); err != nil {
		t.Fatalf("failed to read random: %v", err)
	}

	// Create and return both a big integer and a field value.
	bigIntVal := new(big.Int).SetBytes(buf[:])
	bigIntVal.Mod(bigIntVal, curveParams.N)
	var fv FieldVal
	fv.SetBytes(&buf)
	return bigIntVal, &fv
}

// TestFieldSetInt ensures that setting a field value to various native
// integers works as expected.
func TestFieldSetInt(t *testing.T) {
	tests := []struct {
		name     string     // test description
		in       uint16     // test value
		expected [10]uint32 // expected raw ints
	}{{
		name:     "one",
		in:       1,
		expected: [10]uint32{1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
	}, {
		name:     "five",
		in:       5,
		expected: [10]uint32{5, 0, 0, 0, 0, 0, 0, 0, 0, 0},
	}, {
		name:     "2^16 - 1",
		in:       65535,
		expected: [10]uint32{65535, 0, 0, 0, 0, 0, 0, 0, 0, 0},
	}}

	for _, test := range tests {
		f := new(FieldVal).SetInt(test.in)
		if !reflect.DeepEqual(f.n, test.expected) {
			t.Errorf("%s: wrong result\ngot: %v\nwant: %v", test.name, f.n,
				test.expected)
			continue
		}
	}
}

// TestFieldSetBytes ensures that setting a field value to a 256-bit big-endian
// unsigned integer via both the slice and array methods works as expected for
// edge cases.  Random cases are tested via the various other tests.
func TestFieldSetBytes(t *testing.T) {
	tests := []struct {
		name     string     // test description
		in       string     // hex encoded test value
		expected [10]uint32 // expected raw ints
		overflow bool       // expected overflow result
	}{{
		name:     "zero",
		in:       "00",
		expected: [10]uint32{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
		overflow: false,
	}, {
		name: "field prime",
		in:   "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		expected: [10]uint32{
			0x03fffc2f, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff,
			0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff,
		},
		overflow: true,
	}, {
		name: "field prime - 1",
		in:   "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
		expected: [10]uint32{
			0x03fffc2e, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff,
			0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff,
		},
		overflow: false,
	}, {
		name: "field prime + 1 (overflow in word zero)",
		in:   "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30",
		expected: [10]uint32{
			0x03fffc30, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff,
			0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff,
		},
		overflow: true,
	}, {
		name: "field prime first 32 bits",
		in:   "fffffc2f",
		expected: [10]uint32{
			0x03fffc2f, 0x00000003f, 0x00000000, 0x00000000, 0x00000000,
			0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
		},
		overflow: false,
	}, {
		name: "field prime word zero",
		in:   "03fffc2f",
		expected: [10]uint32{
			0x03fffc2f, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
			0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
		},
		overflow: false,
	}, {
		name: "field prime first 64 bits",
		in:   "fffffffefffffc2f",
		expected: [10]uint32{
			0x03fffc2f, 0x03ffffbf, 0x00000fff, 0x00000000, 0x00000000,
			0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
		},
		overflow: false,
	}, {
		name: "field prime word zero and one",
		in:   "0ffffefffffc2f",
		expected: [10]uint32{
			0x03fffc2f, 0x03ffffbf, 0x00000000, 0x00000000, 0x00000000,
			0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
		},
		overflow: false,
	}, {
		name: "field prime first 96 bits",
		in:   "fffffffffffffffefffffc2f",
		expected: [10]uint32{
			0x03fffc2f, 0x03ffffbf, 0x03ffffff, 0x0003ffff, 0x00000000,
			0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
		},
		overflow: false,
	}, {
		name: "field prime word zero, one, and two",
		in:   "3ffffffffffefffffc2f",
		expected: [10]uint32{
			0x03fffc2f, 0x03ffffbf, 0x03ffffff, 0x00000000, 0x00000000,
			0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
		},
		overflow: false,
	}, {
		name: "overflow in word one (prime + 1<<26)",
		in:   "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff03fffc2f",
		expected: [10]uint32{
			0x03fffc2f, 0x03ffffc0, 0x03ffffff, 0x03ffffff, 0x03ffffff,
			0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff,
		},
		overflow: true,
	}, {
		name: "(field prime - 1) * 2 NOT mod P, truncated >32 bytes",
		in:   "01fffffffffffffffffffffffffffffffffffffffffffffffffffffffdfffff85c",
		expected: [10]uint32{
			0x01fffff8, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff,
			0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x00007fff,
		},
		overflow: false,
	}, {
		name: "2^256 - 1",
		in:   "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
		expected: [10]uint32{
			0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff,
			0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff,
		},
		overflow: true,
	}, {
		name: "alternating bits",
		in:   "a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5",
		expected: [10]uint32{
			0x01a5a5a5, 0x01696969, 0x025a5a5a, 0x02969696, 0x01a5a5a5,
			0x01696969, 0x025a5a5a, 0x02969696, 0x01a5a5a5, 0x00296969,
		},
		overflow: false,
	}, {
		name: "alternating bits 2",
		in:   "5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a",
		expected: [10]uint32{
			0x025a5a5a, 0x02969696, 0x01a5a5a5, 0x01696969, 0x025a5a5a,
			0x02969696, 0x01a5a5a5, 0x01696969, 0x025a5a5a, 0x00169696,
		},
		overflow: false,
	}}

	for _, test := range tests {
		inBytes := hexToBytes(test.in)

		// Ensure setting the bytes via the slice method works as expected.
		var f FieldVal
		overflow := f.SetByteSlice(inBytes)
		if !reflect.DeepEqual(f.n, test.expected) {
			t.Errorf("%s: unexpected result\ngot: %x\nwant: %x", test.name, f.n,
				test.expected)
			continue
		}

		// Ensure the setting the bytes via the slice method produces the
		// expected overflow result.
		if overflow != test.overflow {
			t.Errorf("%s: unexpected overflow -- got: %v, want: %v", test.name,
				overflow, test.overflow)
			continue
		}

		// Ensure setting the bytes via the array method works as expected.
		var f2 FieldVal
		var b32 [32]byte
		truncatedInBytes := inBytes
		if len(truncatedInBytes) > 32 {
			truncatedInBytes = truncatedInBytes[:32]
		}
		copy(b32[32-len(truncatedInBytes):], truncatedInBytes)
		overflow = f2.SetBytes(&b32) != 0
		if !reflect.DeepEqual(f2.n, test.expected) {
			t.Errorf("%s: unexpected result\ngot: %x\nwant: %x", test.name,
				f2.n, test.expected)
			continue
		}

		// Ensure the setting the bytes via the array method produces the
		// expected overflow result.
		if overflow != test.overflow {
			t.Errorf("%s: unexpected overflow -- got: %v, want: %v", test.name,
				overflow, test.overflow)
			continue
		}
	}
}

// TestFieldBytes ensures that retrieving the bytes for a 256-bit big-endian
// unsigned integer via the various methods works as expected for edge cases.
// Random cases are tested via the various other tests.
func TestFieldBytes(t *testing.T) {
	tests := []struct {
		name     string // test description
		in       string // hex encoded test value
		expected string // expected hex encoded bytes
	}{{
		name:     "zero",
		in:       "0",
		expected: "0000000000000000000000000000000000000000000000000000000000000000",
	}, {
		name:     "field prime (aka 0)",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		expected: "0000000000000000000000000000000000000000000000000000000000000000",
	}, {
		name:     "field prime - 1",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
		expected: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
	}, {
		name:     "field prime + 1 (aka 1, overflow in word zero)",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30",
		expected: "0000000000000000000000000000000000000000000000000000000000000001",
	}, {
		name:     "field prime first 32 bits",
		in:       "fffffc2f",
		expected: "00000000000000000000000000000000000000000000000000000000fffffc2f",
	}, {
		name:     "field prime word zero",
		in:       "03fffc2f",
		expected: "0000000000000000000000000000000000000000000000000000000003fffc2f",
	}, {
		name:     "field prime first 64 bits",
		in:       "fffffffefffffc2f",
		expected: "000000000000000000000000000000000000000000000000fffffffefffffc2f",
	}, {
		name:     "field prime word zero and one",
		in:       "0ffffefffffc2f",
		expected: "000000000000000000000000000000000000000000000000000ffffefffffc2f",
	}, {
		name:     "field prime first 96 bits",
		in:       "fffffffffffffffefffffc2f",
		expected: "0000000000000000000000000000000000000000fffffffffffffffefffffc2f",
	}, {
		name:     "field prime word zero, one, and two",
		in:       "3ffffffffffefffffc2f",
		expected: "000000000000000000000000000000000000000000003ffffffffffefffffc2f",
	}, {
		name:     "overflow in word one (prime + 1<<26)",
		in:       "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff03fffc2f",
		expected: "0000000000000000000000000000000000000000000000000000000004000000",
	}, {
		name:     "2^256 - 1",
		in:       "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
		expected: "00000000000000000000000000000000000000000000000000000001000003d0",
	}, {
		name:     "alternating bits",
		in:       "a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5",
		expected: "a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5",
	}, {
		name:     "alternating bits 2",
		in:       "5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a",
		expected: "5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a",
	}}

	for _, test := range tests {
		f := new(FieldVal).SetHex(test.in).Normalize()
		expected := hexToBytes(test.expected)

		// Ensure getting the bytes works as expected.
		gotBytes := f.Bytes()
		if !bytes.Equal(gotBytes[:], expected) {
			t.Errorf("%s: unexpected result\ngot: %x\nwant: %x", test.name,
				*gotBytes, expected)
			continue
		}

		// Ensure getting the bytes directly into an array works as expected.
		var b32 [32]byte
		f.PutBytes(&b32)
		if !bytes.Equal(b32[:], expected) {
			t.Errorf("%s: unexpected result\ngot: %x\nwant: %x", test.name,
				b32, expected)
			continue
		}

		// Ensure getting the bytes directly into a slice works as expected.
		var buffer [64]byte
		f.PutBytesUnchecked(buffer[:])
		if !bytes.Equal(buffer[:32], expected) {
			t.Errorf("%s: unexpected result\ngot: %x\nwant: %x", test.name,
				buffer[:32], expected)
			continue
		}
	}
}

// TestFieldZero ensures that zeroing a field value works as expected.
func TestFieldZero(t *testing.T) {
	var f FieldVal
	f.SetHex("a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5")
	f.Zero()
	for idx, rawInt := range f.n {
		if rawInt != 0 {
			t.Errorf("internal integer at index #%d is not zero - got %d", idx,
				rawInt)
		}
	}
}

// TestFieldIsZero ensures that checking if a field is zero via IsZero and
// IsZeroBit works as expected.
func TestFieldIsZero(t *testing.T) {
	f := new(FieldVal)
	if !f.IsZero() {
		t.Errorf("new field value is not zero - got %v (rawints %x)", f, f.n)
	}
	if f.IsZeroBit() != 1 {
		t.Errorf("new field value is not zero - got %v (rawints %x)", f, f.n)
	}

	f.SetInt(1)
	if f.IsZero() {
		t.Errorf("claims zero for nonzero field - got %v (rawints %x)", f, f.n)
	}
	if f.IsZeroBit() == 1 {
		t.Errorf("claims zero for nonzero field - got %v (rawints %x)", f, f.n)
	}

	f.Zero()
	if !f.IsZero() {
		t.Errorf("claims nonzero for zero field - got %v (rawints %x)", f, f.n)
	}
	if f.IsZeroBit() != 1 {
		t.Errorf("claims nonzero for zero field - got %v (rawints %x)", f, f.n)
	}

	f.SetInt(1)
	f.Zero()
	if !f.IsZero() {
		t.Errorf("claims zero for nonzero field - got %v (rawints %x)", f, f.n)
	}
	if f.IsZeroBit() != 1 {
		t.Errorf("claims zero for nonzero field - got %v (rawints %x)", f, f.n)
	}
}

// TestFieldIsOne ensures that checking if a field is one via IsOne and IsOneBit
// works as expected.
func TestFieldIsOne(t *testing.T) {
	tests := []struct {
		name      string // test description
		in        string // hex encoded test value
		normalize bool   // whether or not to normalize the test value
		expected  bool   // expected result
	}{{
		name:      "zero",
		in:        "0",
		normalize: true,
		expected:  false,
	}, {
		name:      "one",
		in:        "1",
		normalize: true,
		expected:  true,
	}, {
		name:      "secp256k1 prime NOT normalized (would be 0)",
		in:        "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		normalize: false,
		expected:  false,
	}, {
		name:      "secp256k1 prime normalized (aka 0)",
		in:        "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		normalize: true,
		expected:  false,
	}, {
		name:      "secp256k1 prime + 1 normalized (aka 1)",
		in:        "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30",
		normalize: true,
		expected:  true,
	}, {
		name:      "secp256k1 prime + 1 NOT normalized (would be 1)",
		in:        "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30",
		normalize: false,
		expected:  false,
	}, {
		name:      "2^26 (one bit in second internal field word",
		in:        "4000000",
		normalize: false,
		expected:  false,
	}, {
		name:      "2^52 (one bit in third internal field word",
		in:        "10000000000000",
		normalize: false,
		expected:  false,
	}, {
		name:      "2^78 (one bit in fourth internal field word",
		in:        "40000000000000000000",
		normalize: false,
		expected:  false,
	}, {
		name:      "2^104 (one bit in fifth internal field word",
		in:        "100000000000000000000000000",
		normalize: false,
		expected:  false,
	}, {
		name:      "2^130 (one bit in sixth internal field word",
		in:        "400000000000000000000000000000000",
		normalize: false,
		expected:  false,
	}, {
		name:      "2^156 (one bit in seventh internal field word",
		in:        "1000000000000000000000000000000000000000",
		normalize: false,
		expected:  false,
	}, {
		name:      "2^182 (one bit in eighth internal field word",
		in:        "4000000000000000000000000000000000000000000000",
		normalize: false,
		expected:  false,
	}, {
		name:      "2^208 (one bit in ninth internal field word",
		in:        "10000000000000000000000000000000000000000000000000000",
		normalize: false,
		expected:  false,
	}, {
		name:      "2^234 (one bit in tenth internal field word",
		in:        "40000000000000000000000000000000000000000000000000000000000",
		normalize: false,
		expected:  false,
	}}

	for _, test := range tests {
		f := new(FieldVal).SetHex(test.in)
		if test.normalize {
			f.Normalize()
		}
		result := f.IsOne()
		if result != test.expected {
			t.Errorf("%s: wrong result -- got: %v, want: %v", test.name, result,
				test.expected)
			continue
		}

		result2 := f.IsOneBit() == 1
		if result2 != test.expected {
			t.Errorf("%s: wrong result -- got: %v, want: %v", test.name,
				result2, test.expected)
			continue
		}
	}
}

// TestFieldStringer ensures the stringer returns the appropriate hex string.
func TestFieldStringer(t *testing.T) {
	tests := []struct {
		name     string // test description
		in       string // hex encoded test value
		expected string // expected result
	}{{
		name:     "zero",
		in:       "0",
		expected: "0000000000000000000000000000000000000000000000000000000000000000",
	}, {
		name:     "one",
		in:       "1",
		expected: "0000000000000000000000000000000000000000000000000000000000000001",
	}, {
		name:     "ten",
		in:       "a",
		expected: "000000000000000000000000000000000000000000000000000000000000000a",
	}, {
		name:     "eleven",
		in:       "b",
		expected: "000000000000000000000000000000000000000000000000000000000000000b",
	}, {
		name:     "twelve",
		in:       "c",
		expected: "000000000000000000000000000000000000000000000000000000000000000c",
	}, {
		name:     "thirteen",
		in:       "d",
		expected: "000000000000000000000000000000000000000000000000000000000000000d",
	}, {
		name:     "fourteen",
		in:       "e",
		expected: "000000000000000000000000000000000000000000000000000000000000000e",
	}, {
		name:     "fifteen",
		in:       "f",
		expected: "000000000000000000000000000000000000000000000000000000000000000f",
	}, {
		name:     "240",
		in:       "f0",
		expected: "00000000000000000000000000000000000000000000000000000000000000f0",
	}, {
		name:     "2^26 - 1",
		in:       "3ffffff",
		expected: "0000000000000000000000000000000000000000000000000000000003ffffff",
	}, {
		name:     "2^32 - 1",
		in:       "ffffffff",
		expected: "00000000000000000000000000000000000000000000000000000000ffffffff",
	}, {
		name:     "2^64 - 1",
		in:       "ffffffffffffffff",
		expected: "000000000000000000000000000000000000000000000000ffffffffffffffff",
	}, {
		name:     "2^96 - 1",
		in:       "ffffffffffffffffffffffff",
		expected: "0000000000000000000000000000000000000000ffffffffffffffffffffffff",
	}, {
		name:     "2^128 - 1",
		in:       "ffffffffffffffffffffffffffffffff",
		expected: "00000000000000000000000000000000ffffffffffffffffffffffffffffffff",
	}, {
		name:     "2^160 - 1",
		in:       "ffffffffffffffffffffffffffffffffffffffff",
		expected: "000000000000000000000000ffffffffffffffffffffffffffffffffffffffff",
	}, {
		name:     "2^192 - 1",
		in:       "ffffffffffffffffffffffffffffffffffffffffffffffff",
		expected: "0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffff",
	}, {
		name:     "2^224 - 1",
		in:       "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
		expected: "00000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
	}, {
		name:     "2^256-4294968273 (the secp256k1 prime, so should result in 0)",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		expected: "0000000000000000000000000000000000000000000000000000000000000000",
	}, {
		name:     "2^256-4294968274 (the secp256k1 prime+1, so should result in 1)",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30",
		expected: "0000000000000000000000000000000000000000000000000000000000000001",
	}, {
		name:     "invalid hex g",
		in:       "g",
		expected: "0000000000000000000000000000000000000000000000000000000000000000",
	}, {
		name:     "invalid hex 1h",
		in:       "1h",
		expected: "0000000000000000000000000000000000000000000000000000000000000000",
	}, {
		name:     "invalid hex i1",
		in:       "i1",
		expected: "0000000000000000000000000000000000000000000000000000000000000000",
	}}

	for _, test := range tests {
		f := new(FieldVal).SetHex(test.in)
		result := f.String()
		if result != test.expected {
			t.Errorf("%s: wrong result\ngot: %v\nwant: %v", test.name, result,
				test.expected)
			continue
		}
	}
}

// TestFieldNormalize ensures that normalizing the internal field words works as
// expected.
func TestFieldNormalize(t *testing.T) {
	tests := []struct {
		name       string     // test description
		raw        [10]uint32 // Intentionally denormalized value
		normalized [10]uint32 // Normalized form of the raw value
	}{{
		name:       "5",
		raw:        [10]uint32{0x00000005, 0, 0, 0, 0, 0, 0, 0, 0, 0},
		normalized: [10]uint32{0x00000005, 0, 0, 0, 0, 0, 0, 0, 0, 0},
	}, {
		name:       "2^26",
		raw:        [10]uint32{0x04000000, 0x0, 0, 0, 0, 0, 0, 0, 0, 0},
		normalized: [10]uint32{0x00000000, 0x1, 0, 0, 0, 0, 0, 0, 0, 0},
	}, {
		name:       "2^26 + 1",
		raw:        [10]uint32{0x04000001, 0x0, 0, 0, 0, 0, 0, 0, 0, 0},
		normalized: [10]uint32{0x00000001, 0x1, 0, 0, 0, 0, 0, 0, 0, 0},
	}, {
		name:       "2^32 - 1",
		raw:        [10]uint32{0xffffffff, 0x00, 0, 0, 0, 0, 0, 0, 0, 0},
		normalized: [10]uint32{0x03ffffff, 0x3f, 0, 0, 0, 0, 0, 0, 0, 0},
	}, {
		name:       "2^32",
		raw:        [10]uint32{0x04000000, 0x3f, 0, 0, 0, 0, 0, 0, 0, 0},
		normalized: [10]uint32{0x00000000, 0x40, 0, 0, 0, 0, 0, 0, 0, 0},
	}, {
		name:       "2^32 + 1",
		raw:        [10]uint32{0x04000001, 0x3f, 0, 0, 0, 0, 0, 0, 0, 0},
		normalized: [10]uint32{0x00000001, 0x40, 0, 0, 0, 0, 0, 0, 0, 0},
	}, {
		name:       "2^64 - 1",
		raw:        [10]uint32{0xffffffff, 0xffffffc0, 0xfc0, 0, 0, 0, 0, 0, 0, 0},
		normalized: [10]uint32{0x03ffffff, 0x03ffffff, 0xfff, 0, 0, 0, 0, 0, 0, 0},
	}, {
		name:       "2^64",
		raw:        [10]uint32{0x04000000, 0x03ffffff, 0x0fff, 0, 0, 0, 0, 0, 0, 0},
		normalized: [10]uint32{0x00000000, 0x00000000, 0x1000, 0, 0, 0, 0, 0, 0, 0},
	}, {
		name:       "2^64 + 1",
		raw:        [10]uint32{0x04000001, 0x03ffffff, 0x0fff, 0, 0, 0, 0, 0, 0, 0},
		normalized: [10]uint32{0x00000001, 0x00000000, 0x1000, 0, 0, 0, 0, 0, 0, 0},
	}, {
		name:       "2^96 - 1",
		raw:        [10]uint32{0xffffffff, 0xffffffc0, 0xffffffc0, 0x3ffc0, 0, 0, 0, 0, 0, 0},
		normalized: [10]uint32{0x03ffffff, 0x03ffffff, 0x03ffffff, 0x3ffff, 0, 0, 0, 0, 0, 0},
	}, {
		name:       "2^96",
		raw:        [10]uint32{0x04000000, 0x03ffffff, 0x03ffffff, 0x3ffff, 0, 0, 0, 0, 0, 0},
		normalized: [10]uint32{0x00000000, 0x00000000, 0x00000000, 0x40000, 0, 0, 0, 0, 0, 0},
	}, {
		name:       "2^128 - 1",
		raw:        [10]uint32{0xffffffff, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffc0, 0, 0, 0, 0, 0},
		normalized: [10]uint32{0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0xffffff, 0, 0, 0, 0, 0},
	}, {
		name:       "2^128",
		raw:        [10]uint32{0x04000000, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x0ffffff, 0, 0, 0, 0, 0},
		normalized: [10]uint32{0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x1000000, 0, 0, 0, 0, 0},
	}, {
		name:       "2^256 - 4294968273 (secp256k1 prime)",
		raw:        [10]uint32{0xfffffc2f, 0xffffff80, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
		normalized: [10]uint32{0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
	}, {
		// Value larger than P where both first and second words are larger than
		// P's first and second words
		name:       "Value > P with 1st and 2nd words > P's 1st and 2nd words",
		raw:        [10]uint32{0xfffffc30, 0xffffff86, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
		normalized: [10]uint32{0x00000001, 0x00000006, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
	}, {
		// Value larger than P where only the second word is larger than P's
		// second word.
		name:       "Value > P with 2nd word > P's 2nd word",
		raw:        [10]uint32{0xfffffc2a, 0xffffff87, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
		normalized: [10]uint32{0x03fffffb, 0x00000006, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
	}, {
		name:       "2^256 - 1",
		raw:        [10]uint32{0xffffffff, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
		normalized: [10]uint32{0x000003d0, 0x00000040, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
	}, {
		// Prime with field representation such that the initial reduction does
		// not result in a carry to bit 256.
		//
		// 2^256 - 4294968273 (secp256k1 prime)
		name:       "2^256 - 4294968273 (secp256k1 prime)",
		raw:        [10]uint32{0x03fffc2f, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff},
		normalized: [10]uint32{0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000},
	}, {
		// Value larger than P that reduces to a value which is still larger
		// than P when it has a magnitude of 1 due to its first word and does
		// not result in a carry to bit 256.
		//
		// 2^256 - 4294968272 (secp256k1 prime + 1)
		name:       "2^256 - 4294968272 (secp256k1 prime + 1)",
		raw:        [10]uint32{0x03fffc30, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff},
		normalized: [10]uint32{0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000},
	}, {
		// Value larger than P that reduces to a value which is still larger
		// than P when it has a magnitude of 1 due to its second word and does
		// not result in a carry to bit 256.
		//
		// 2^256 - 4227859409 (secp256k1 prime + 0x4000000)
		name:       "2^256 - 4227859409 (secp256k1 prime + 0x4000000)",
		raw:        [10]uint32{0x03fffc2f, 0x03ffffc0, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff},
		normalized: [10]uint32{0x00000000, 0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000},
	}, {
		// Value larger than P that reduces to a value which is still larger
		// than P when it has a magnitude of 1 due to a carry to bit 256, but
		// would not be without the carry.  These values come from the fact that
		// P is 2^256 - 4294968273 and 977 is the low order word in the internal
		// field representation.
		//
		// 2^256 * 5 - ((4294968273 - (977+1)) * 4)
		name:       "2^256 * 5 - ((4294968273 - (977+1)) * 4)",
		raw:        [10]uint32{0x03ffffff, 0x03fffeff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x0013fffff},
		normalized: [10]uint32{0x00001314, 0x00000040, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000000},
	}, {
		// Value larger than P that reduces to a value which is still larger
		// than P when it has a magnitude of 1 due to both a carry to bit 256
		// and the first word.
		name:       "Value > P with redux > P at mag 1 due to 1st word and carry to bit 256",
		raw:        [10]uint32{0x03fffc30, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x07ffffff, 0x003fffff},
		normalized: [10]uint32{0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000001},
	}, {
		// Value larger than P that reduces to a value which is still larger
		// than P when it has a magnitude of 1 due to both a carry to bit 256
		// and the second word.
		name:       "Value > P with redux > P at mag 1 due to 2nd word and carry to bit 256",
		raw:        [10]uint32{0x03fffc2f, 0x03ffffc0, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x3ffffff, 0x07ffffff, 0x003fffff},
		normalized: [10]uint32{0x00000000, 0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x0000000, 0x00000000, 0x00000001},
	}, {
		// Value larger than P that reduces to a value which is still larger
		// than P when it has a magnitude of 1 due to a carry to bit 256 and the
		// first and second words.
		name:       "Value > P with redux > P at mag 1 due to 1st and 2nd words and carry to bit 256",
		raw:        [10]uint32{0x03fffc30, 0x03ffffc0, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x07ffffff, 0x003fffff},
		normalized: [10]uint32{0x00000001, 0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000001},
	}, {
		// ---------------------------------------------------------------------
		// There are 3 main conditions that must be true if the final reduction
		// is needed after the initial reduction to magnitude 1 when there was
		// NOT a carry to bit 256 (in other words when the original value was <
		// 2^256):
		// 1) The final word of the reduced value is equal to the one of P
		// 2) The 3rd through 9th words are equal to those of P
		// 3) Either:
		//    - The 2nd word is greater than the one of P; or
		//    - The 2nd word is equal to that of P AND the 1st word is greater
		//
		// Therefore the eight possible combinations of those 3 main conditions
		// can be thought of in binary where each bit starting from the left
		// corresponds to the aforementioned conditions as such:
		// 000, 001, 010, 011, 100, 101, 110, 111
		//
		// For example, combination 6 is when both conditons 1 and 2 are true,
		// but condition 3 is NOT true.
		//
		// The following tests hit each of these combinations and refer to each
		// by its decimal equivalent for ease of reference.
		//
		// NOTE: The final combination (7) is already tested above since it only
		// happens when the original value is already the normalized
		// representation of P.
		// ---------------------------------------------------------------------

		name:       "Value < 2^256 final reduction combination 0",
		raw:        [10]uint32{0x03fff85e, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03fffffe, 0x003ffffe},
		normalized: [10]uint32{0x03fff85e, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03fffffe, 0x003ffffe},
	}, {
		name:       "Value < 2^256 final reduction combination 1 via 2nd word",
		raw:        [10]uint32{0x03fff85e, 0x03ffffc0, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03fffffe, 0x003ffffe},
		normalized: [10]uint32{0x03fff85e, 0x03ffffc0, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03fffffe, 0x003ffffe},
	}, {
		name:       "Value < 2^256 final reduction combination 1 via 1st word",
		raw:        [10]uint32{0x03fffc2f, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03fffffe, 0x003ffffe},
		normalized: [10]uint32{0x03fffc2f, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03fffffe, 0x003ffffe},
	}, {
		name:       "Value < 2^256 final reduction combination 2",
		raw:        [10]uint32{0x03fff85e, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003ffffe},
		normalized: [10]uint32{0x03fff85e, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003ffffe},
	}, {
		name:       "Value < 2^256 final reduction combination 3 via 2nd word",
		raw:        [10]uint32{0x03fff85e, 0x03ffffc0, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003ffffe},
		normalized: [10]uint32{0x03fff85e, 0x03ffffc0, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003ffffe},
	}, {
		name:       "Value < 2^256 final reduction combination 3 via 1st word",
		raw:        [10]uint32{0x03fffc2f, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003ffffe},
		normalized: [10]uint32{0x03fffc2f, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003ffffe},
	}, {
		name:       "Value < 2^256 final reduction combination 4",
		raw:        [10]uint32{0x03fff85e, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03fffffe, 0x003fffff},
		normalized: [10]uint32{0x03fff85e, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03fffffe, 0x003fffff},
	}, {
		name:       "Value < 2^256 final reduction combination 5 via 2nd word",
		raw:        [10]uint32{0x03fff85e, 0x03ffffc0, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03fffffe, 0x003fffff},
		normalized: [10]uint32{0x03fff85e, 0x03ffffc0, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03fffffe, 0x003fffff},
	}, {
		name:       "Value < 2^256 final reduction combination 5 via 1st word",
		raw:        [10]uint32{0x03fffc2f, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03fffffe, 0x003fffff},
		normalized: [10]uint32{0x03fffc2f, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03fffffe, 0x003fffff},
	}, {
		name:       "Value < 2^256 final reduction combination 6",
		raw:        [10]uint32{0x03fff85e, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff},
		normalized: [10]uint32{0x03fff85e, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff},
	}}

	for _, test := range tests {
		f := new(FieldVal)
		f.n = test.raw
		f.Normalize()
		if !reflect.DeepEqual(f.n, test.normalized) {
			t.Errorf("%s: wrong normalized result\ngot: %x\nwant: %x",
				test.name, f.n, test.normalized)
			continue
		}
	}
}

// TestFieldIsOdd ensures that checking if a field value is odd via IsOdd and
// IsOddBit works as expected.
func TestFieldIsOdd(t *testing.T) {
	tests := []struct {
		name     string // test description
		in       string // hex encoded value
		expected bool   // expected oddness
	}{{
		name:     "zero",
		in:       "0",
		expected: false,
	}, {
		name:     "one",
		in:       "1",
		expected: true,
	}, {
		name:     "two",
		in:       "2",
		expected: false,
	}, {
		name:     "2^32 - 1",
		in:       "ffffffff",
		expected: true,
	}, {
		name:     "2^64 - 2",
		in:       "fffffffffffffffe",
		expected: false,
	}, {
		name:     "secp256k1 prime (not normalized so should be incorrect result)",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		expected: true,
	}, {
		name:     "secp256k1 prime + 1 (not normalized so should be incorrect result)",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30",
		expected: false,
	}}

	for _, test := range tests {
		f := new(FieldVal).SetHex(test.in)
		result := f.IsOdd()
		if result != test.expected {
			t.Errorf("%s: wrong result -- got: %v, want: %v", test.name,
				result, test.expected)
			continue
		}

		result2 := f.IsOddBit() == 1
		if result2 != test.expected {
			t.Errorf("%s: wrong result -- got: %v, want: %v", test.name,
				result2, test.expected)
			continue
		}
	}
}

// TestFieldEquals ensures that checking two field values for equality via
// Equals works as expected.
func TestFieldEquals(t *testing.T) {
	tests := []struct {
		name     string // test description
		in1      string // hex encoded value
		in2      string // hex encoded value
		expected bool   // expected equality
	}{{
		name:     "0 == 0?",
		in1:      "0",
		in2:      "0",
		expected: true,
	}, {
		name:     "0 == 1?",
		in1:      "0",
		in2:      "1",
		expected: false,
	}, {
		name:     "1 == 0?",
		in1:      "1",
		in2:      "0",
		expected: false,
	}, {
		name:     "2^32 - 1 == 2^32 - 1?",
		in1:      "ffffffff",
		in2:      "ffffffff",
		expected: true,
	}, {
		name:     "2^64 - 1 == 2^64 - 2?",
		in1:      "ffffffffffffffff",
		in2:      "fffffffffffffffe",
		expected: false,
	}, {
		name:     "0 == prime (mod prime)?",
		in1:      "0",
		in2:      "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		expected: true,
	}, {
		name:     "1 == prime + 1 (mod prime)?",
		in1:      "1",
		in2:      "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30",
		expected: true,
	}}

	for _, test := range tests {
		f := new(FieldVal).SetHex(test.in1).Normalize()
		f2 := new(FieldVal).SetHex(test.in2).Normalize()
		result := f.Equals(f2)
		if result != test.expected {
			t.Errorf("%s: wrong result -- got: %v, want: %v", test.name, result,
				test.expected)
			continue
		}
	}
}

// TestFieldNegate ensures that negating field values via Negate works as
// expected.
func TestFieldNegate(t *testing.T) {
	tests := []struct {
		name     string // test description
		in       string // hex encoded test value
		expected string // hex encoded expected result
	}{{
		name:     "zero",
		in:       "0",
		expected: "0",
	}, {
		name:     "secp256k1 prime (direct val in with 0 out)",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		expected: "0",
	}, {
		name:     "secp256k1 prime (0 in with direct val out)",
		in:       "0",
		expected: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
	}, {
		name:     "1 -> secp256k1 prime - 1",
		in:       "1",
		expected: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
	}, {
		name:     "secp256k1 prime - 1 -> 1",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
		expected: "1",
	}, {
		name:     "2 -> secp256k1 prime - 2",
		in:       "2",
		expected: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
	}, {
		name:     "secp256k1 prime - 2 -> 2",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
		expected: "2",
	}, {
		name:     "random sampling #1",
		in:       "b3d9aac9c5e43910b4385b53c7e78c21d4cd5f8e683c633aed04c233efc2e120",
		expected: "4c2655363a1bc6ef4bc7a4ac381873de2b32a07197c39cc512fb3dcb103d1b0f",
	}, {
		name:     "random sampling #2",
		in:       "f8a85984fee5a12a7c8dd08830d83423c937d77c379e4a958e447a25f407733f",
		expected: "757a67b011a5ed583722f77cf27cbdc36c82883c861b56a71bb85d90bf888f0",
	}, {
		name:     "random sampling #3",
		in:       "45ee6142a7fda884211e93352ed6cb2807800e419533be723a9548823ece8312",
		expected: "ba119ebd5802577bdee16ccad12934d7f87ff1be6acc418dc56ab77cc131791d",
	}, {
		name:     "random sampling #4",
		in:       "53c2a668f07e411a2e473e1c3b6dcb495dec1227af27673761d44afe5b43d22b",
		expected: "ac3d59970f81bee5d1b8c1e3c49234b6a213edd850d898c89e2bb500a4bc2a04",
	}}

	for _, test := range tests {
		f := new(FieldVal).SetHex(test.in).Normalize()
		expected := new(FieldVal).SetHex(test.expected).Normalize()

		// Ensure negating another value produces the expected result.
		result := new(FieldVal).NegateVal(f, 1).Normalize()
		if !result.Equals(expected) {
			t.Errorf("%s: unexpected result -- got: %v, want: %v", test.name,
				result, expected)
			continue
		}

		// Ensure self negating also produces the expected result.
		result2 := f.Negate(1).Normalize()
		if !result2.Equals(expected) {
			t.Errorf("%s: unexpected result -- got: %v, want: %v", test.name,
				result2, expected)
			continue
		}
	}
}

// TestFieldAddInt ensures that adding an integer to field values via AddInt
// works as expected.
func TestFieldAddInt(t *testing.T) {
	tests := []struct {
		name     string // test description
		in1      string // hex encoded value
		in2      uint16 // unsigned integer to add to the value above
		expected string // expected hex encoded value
	}{{
		name:     "zero + one",
		in1:      "0",
		in2:      1,
		expected: "1",
	}, {
		name:     "one + zero",
		in1:      "1",
		in2:      0,
		expected: "1",
	}, {
		name:     "one + one",
		in1:      "1",
		in2:      1,
		expected: "2",
	}, {
		name:     "secp256k1 prime-1 + 1",
		in1:      "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
		in2:      1,
		expected: "0",
	}, {
		name:     "secp256k1 prime + 1",
		in1:      "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		in2:      1,
		expected: "1",
	}, {
		name:     "random sampling #1",
		in1:      "ff95ad9315aff04ab4af0ce673620c7145dc85d03bab5ba4b09ca2c4dec2d6c1",
		in2:      0x10f,
		expected: "ff95ad9315aff04ab4af0ce673620c7145dc85d03bab5ba4b09ca2c4dec2d7d0",
	}, {
		name:     "random sampling #2",
		in1:      "44bdae6b772e7987941f1ba314e6a5b7804a4c12c00961b57d20f41deea9cecf",
		in2:      0x3196,
		expected: "44bdae6b772e7987941f1ba314e6a5b7804a4c12c00961b57d20f41deeaa0065",
	}, {
		name:     "random sampling #3",
		in1:      "88c3ecae67b591935fb1f6a9499c35315ffad766adca665c50b55f7105122c9c",
		in2:      0x966f,
		expected: "88c3ecae67b591935fb1f6a9499c35315ffad766adca665c50b55f710512c30b",
	}, {
		name:     "random sampling #4",
		in1:      "8523e9edf360ca32a95aae4e57fcde5a542b471d08a974d94ea0ee09a015e2a6",
		in2:      0xc54,
		expected: "8523e9edf360ca32a95aae4e57fcde5a542b471d08a974d94ea0ee09a015eefa",
	}}

	for _, test := range tests {
		f := new(FieldVal).SetHex(test.in1).Normalize()
		expected := new(FieldVal).SetHex(test.expected).Normalize()
		result := f.AddInt(test.in2).Normalize()
		if !result.Equals(expected) {
			t.Errorf("%s: wrong result -- got: %v -- want: %v", test.name,
				result, expected)
			continue
		}
	}
}

// TestFieldAdd ensures that adding two field values together via Add and Add2
// works as expected.
func TestFieldAdd(t *testing.T) {
	tests := []struct {
		name     string // test description
		in1      string // first hex encoded value
		in2      string // second hex encoded value to add
		expected string // expected hex encoded value
	}{{
		name:     "zero + one",
		in1:      "0",
		in2:      "1",
		expected: "1",
	}, {
		name:     "one + zero",
		in1:      "1",
		in2:      "0",
		expected: "1",
	}, {
		name:     "secp256k1 prime-1 + 1",
		in1:      "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
		in2:      "1",
		expected: "0",
	}, {
		name:     "secp256k1 prime + 1",
		in1:      "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		in2:      "1",
		expected: "1",
	}, {
		name:     "random sampling #1",
		in1:      "2b2012f975404e5065b4292fb8bed0a5d315eacf24c74d8b27e73bcc5430edcc",
		in2:      "2c3cefa4e4753e8aeec6ac4c12d99da4d78accefda3b7885d4c6bab46c86db92",
		expected: "575d029e59b58cdb547ad57bcb986e4aaaa0b7beff02c610fcadf680c0b7c95e",
	}, {
		name:     "random sampling #2",
		in1:      "8131e8722fe59bb189692b96c9f38de92885730f1dd39ab025daffb94c97f79c",
		in2:      "ff5454b765f0aab5f0977dcc629becc84cabeb9def48e79c6aadb2622c490fa9",
		expected: "80863d2995d646677a00a9632c8f7ab175315ead0d1c824c9088b21c78e10b16",
	}, {
		name:     "random sampling #3",
		in1:      "c7c95e93d0892b2b2cdd77e80eb646ea61be7a30ac7e097e9f843af73fad5c22",
		in2:      "3afe6f91a74dfc1c7f15c34907ee981656c37236d946767dd53ccad9190e437c",
		expected: "2c7ce2577d72747abf33b3116a4df00b881ec6785c47ffc74c105d158bba36f",
	}, {
		name:     "random sampling #4",
		in1:      "fd1c26f6a23381e5d785ba889494ec059369b888ad8431cd67d8c934b580dbe1",
		in2:      "a475aa5a31dcca90ef5b53c097d9133d6b7117474b41e7877bb199590fc0489c",
		expected: "a191d150d4104c76c6e10e492c6dff42fedacfcff8c61954e38a628ec541284e",
	}, {
		name:     "random sampling #5",
		in1:      "ad82b8d1cc136e23e9fd77fe2c7db1fe5a2ecbfcbde59ab3529758334f862d28",
		in2:      "4d6a4e95d6d61f4f46b528bebe152d408fd741157a28f415639347a84f6f574b",
		expected: "faed0767a2e98d7330b2a0bcea92df3eea060d12380e8ec8b62a9fdb9ef58473",
	}, {
		name:     "random sampling #6",
		in1:      "f3f43a2540054a86e1df98547ec1c0e157b193e5350fb4a3c3ea214b228ac5e7",
		in2:      "25706572592690ea3ddc951a1b48b504a4c83dc253756e1b96d56fdfb3199522",
		expected: "19649f97992bdb711fbc2d6e9a0a75e5fc79d1a7888522bf5abf912bd5a45eda",
	}, {
		name:     "random sampling #7",
		in1:      "6915bb94eef13ff1bb9b2633d997e13b9b1157c713363cc0e891416d6734f5b8",
		in2:      "11f90d6ac6fe1c4e8900b1c85fb575c251ec31b9bc34b35ada0aea1c21eded22",
		expected: "7b0ec8ffb5ef5c40449bd7fc394d56fdecfd8980cf6af01bc29c2b898922e2da",
	}, {
		name:     "random sampling #8",
		in1:      "48b0c9eae622eed9335b747968544eb3e75cb2dc8128388f948aa30f88cabde4",
		in2:      "0989882b52f85f9d524a3a3061a0e01f46d597839d2ba637320f4b9510c8d2d5",
		expected: "523a5216391b4e7685a5aea9c9f52ed32e324a601e53dec6c699eea4999390b9",
	}}

	for _, test := range tests {
		// Parse test hex.
		f1 := new(FieldVal).SetHex(test.in1).Normalize()
		f2 := new(FieldVal).SetHex(test.in2).Normalize()
		expected := new(FieldVal).SetHex(test.expected).Normalize()

		// Ensure adding the two values with the result going to another
		// variable produces the expected result.
		result := new(FieldVal).Add2(f1, f2).Normalize()
		if !result.Equals(expected) {
			t.Errorf("%s: unexpected result\ngot: %v\nwant: %v", test.name,
				result, expected)
			continue
		}

		// Ensure adding the value to an existing field value produces the
		// expected result.
		f1.Add(f2).Normalize()
		if !f1.Equals(expected) {
			t.Errorf("%s: unexpected result\ngot: %v\nwant: %v", test.name,
				f1, expected)
			continue
		}
	}
}

// TestFieldMulInt ensures that multiplying an integer to field values via
// MulInt works as expected.
func TestFieldMulInt(t *testing.T) {
	tests := []struct {
		name     string // test description
		in1      string // hex encoded value
		in2      uint8  // unsigned integer to multiply with value above
		expected string // expected hex encoded value
	}{{
		name:     "zero * zero",
		in1:      "0",
		in2:      0,
		expected: "0",
	}, {
		name:     "one * zero",
		in1:      "1",
		in2:      0,
		expected: "0",
	}, {
		name:     "zero * one",
		in1:      "0",
		in2:      1,
		expected: "0",
	}, {
		name:     "one * one",
		in1:      "1",
		in2:      1,
		expected: "1",
	}, {
		name:     "secp256k1 prime-1 * 2",
		in1:      "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
		in2:      2,
		expected: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
	}, {
		name:     "secp256k1 prime * 3",
		in1:      "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		in2:      3,
		expected: "0",
	}, {
		name:     "secp256k1 prime-1 * 8",
		in1:      "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
		in2:      8,
		expected: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc27",
	}, {
		// Random samples for first value.  The second value is limited
		// to 8 since that is the maximum int used in the elliptic curve
		// calculations.
		name:     "random sampling #1",
		in1:      "b75674dc9180d306c692163ac5e089f7cef166af99645c0c23568ab6d967288a",
		in2:      6,
		expected: "4c06bd2b6904f228a76c8560a3433bced9a8681d985a2848d407404d186b0280",
	}, {
		name:     "random sampling #2",
		in1:      "54873298ac2b5ba8591c125ae54931f5ea72040aee07b208d6135476fb5b9c0e",
		in2:      3,
		expected: "fd9597ca048212f90b543710afdb95e1bf560c20ca17161a8239fd64f212d42a",
	}, {
		name:     "random sampling #3",
		in1:      "7c30fbd363a74c17e1198f56b090b59bbb6c8755a74927a6cba7a54843506401",
		in2:      5,
		expected: "6cf4eb20f2447c77657fccb172d38c0aa91ea4ac446dc641fa463a6b5091fba7",
	}, {
		name:     "random sampling #3",
		in1:      "fb4529be3e027a3d1587d8a500b72f2d312e3577340ef5175f96d113be4c2ceb",
		in2:      8,
		expected: "da294df1f013d1e8ac3ec52805b979698971abb9a077a8bafcb688a4f261820f",
	}}

	for _, test := range tests {
		f := new(FieldVal).SetHex(test.in1).Normalize()
		expected := new(FieldVal).SetHex(test.expected).Normalize()
		result := f.MulInt(test.in2).Normalize()
		if !result.Equals(expected) {
			t.Errorf("%s: wrong result -- got: %v -- want: %v", test.name,
				result, expected)
			continue
		}
	}
}

// TestFieldMul ensures that multiplying two field values via Mul and Mul2 works
// as expected.
func TestFieldMul(t *testing.T) {
	tests := []struct {
		name     string // test description
		in1      string // first hex encoded value
		in2      string // second hex encoded value to multiply with
		expected string // expected hex encoded value
	}{{
		name:     "zero * zero",
		in1:      "0",
		in2:      "0",
		expected: "0",
	}, {
		name:     "one * zero",
		in1:      "1",
		in2:      "0",
		expected: "0",
	}, {
		name:     "zero * one",
		in1:      "0",
		in2:      "1",
		expected: "0",
	}, {
		name:     "one * one",
		in1:      "1",
		in2:      "1",
		expected: "1",
	}, {
		name:     "slightly over prime",
		in1:      "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff1ffff",
		in2:      "1000",
		expected: "1ffff3d1",
	}, {
		name:     "secp256k1 prime-1 * 2",
		in1:      "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
		in2:      "2",
		expected: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
	}, {
		name:     "secp256k1 prime * 3",
		in1:      "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		in2:      "3",
		expected: "0",
	}, {
		name:     "secp256k1 prime * 3",
		in1:      "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
		in2:      "8",
		expected: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc27",
	}, {
		name:     "random sampling #1",
		in1:      "cfb81753d5ef499a98ecc04c62cb7768c2e4f1740032946db1c12e405248137e",
		in2:      "58f355ad27b4d75fb7db0442452e732c436c1f7c5a7c4e214fa9cc031426a7d3",
		expected: "1018cd2d7c2535235b71e18db9cd98027386328d2fa6a14b36ec663c4c87282b",
	}, {
		name:     "random sampling #2",
		in1:      "26e9d61d1cdf3920e9928e85fa3df3e7556ef9ab1d14ec56d8b4fc8ed37235bf",
		in2:      "2dfc4bbe537afee979c644f8c97b31e58be5296d6dbc460091eae630c98511cf",
		expected: "da85f48da2dc371e223a1ae63bd30b7e7ee45ae9b189ac43ff357e9ef8cf107a",
	}, {
		name:     "random sampling #3",
		in1:      "5db64ed5afb71646c8b231585d5b2bf7e628590154e0854c4c29920b999ff351",
		in2:      "279cfae5eea5d09ade8e6a7409182f9de40981bc31c84c3d3dfe1d933f152e9a",
		expected: "2c78fbae91792dd0b157abe3054920049b1879a7cc9d98cfda927d83be411b37",
	}, {
		name:     "random sampling #4",
		in1:      "b66dfc1f96820b07d2bdbd559c19319a3a73c97ceb7b3d662f4fe75ecb6819e6",
		in2:      "bf774aba43e3e49eb63a6e18037d1118152568f1a3ac4ec8b89aeb6ff8008ae1",
		expected: "c4f016558ca8e950c21c3f7fc15f640293a979c7b01754ee7f8b3340d4902ebb",
	}}

	for _, test := range tests {
		f1 := new(FieldVal).SetHex(test.in1).Normalize()
		f2 := new(FieldVal).SetHex(test.in2).Normalize()
		expected := new(FieldVal).SetHex(test.expected).Normalize()

		// Ensure multiplying the two values with the result going to another
		// variable produces the expected result.
		result := new(FieldVal).Mul2(f1, f2).Normalize()
		if !result.Equals(expected) {
			t.Errorf("%s: unexpected result\ngot: %v\nwant: %v", test.name,
				result, expected)
			continue
		}

		// Ensure multiplying the value to an existing field value produces the
		// expected result.
		f1.Mul(f2).Normalize()
		if !f1.Equals(expected) {
			t.Errorf("%s: unexpected result\ngot: %v\nwant: %v", test.name,
				f1, expected)
			continue
		}
	}
}

// TestFieldSquare ensures that squaring field values via Square and SqualVal
// works as expected.
func TestFieldSquare(t *testing.T) {
	tests := []struct {
		name     string // test description
		in       string // hex encoded value
		expected string // expected hex encoded value
	}{{
		name:     "zero",
		in:       "0",
		expected: "0",
	}, {
		name:     "secp256k1 prime (direct val in with 0 out)",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		expected: "0",
	}, {
		name:     "secp256k1 prime (0 in with direct val out)",
		in:       "0",
		expected: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
	}, {
		name:     "secp256k1 prime - 1",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
		expected: "1",
	}, {
		name:     "secp256k1 prime - 2",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
		expected: "4",
	}, {
		name:     "random sampling #1",
		in:       "b0ba920360ea8436a216128047aab9766d8faf468895eb5090fc8241ec758896",
		expected: "133896b0b69fda8ce9f648b9a3af38f345290c9eea3cbd35bafcadf7c34653d3",
	}, {
		name:     "random sampling #2",
		in:       "c55d0d730b1d0285a1599995938b042a756e6e8857d390165ffab480af61cbd5",
		expected: "cd81758b3f5877cbe7e5b0a10cebfa73bcbf0957ca6453e63ee8954ab7780bee",
	}, {
		name:     "random sampling #3",
		in:       "e89c1f9a70d93651a1ba4bca5b78658f00de65a66014a25544d3365b0ab82324",
		expected: "39ffc7a43e5dbef78fd5d0354fb82c6d34f5a08735e34df29da14665b43aa1f",
	}, {
		name:     "random sampling #4",
		in:       "7dc26186079d22bcbe1614aa20ae627e62d72f9be7ad1e99cac0feb438956f05",
		expected: "bf86bcfc4edb3d81f916853adfda80c07c57745b008b60f560b1912f95bce8ae",
	}}

	for _, test := range tests {
		f := new(FieldVal).SetHex(test.in).Normalize()
		expected := new(FieldVal).SetHex(test.expected).Normalize()

		// Ensure squaring the value with the result going to another variable
		// produces the expected result.
		result := new(FieldVal).SquareVal(f).Normalize()
		if !result.Equals(expected) {
			t.Errorf("%s: unexpected result\ngot: %v\nwant: %v", test.name,
				result, expected)
			continue
		}

		// Ensure self squaring an existing field value produces the expected
		// result.
		f.Square().Normalize()
		if !f.Equals(expected) {
			t.Errorf("%s: unexpected result\ngot: %v\nwant: %v", test.name,
				f, expected)
			continue
		}
	}
}

// TestFieldSquareRoot ensures that calculating the square root of field values
// via SquareRootVal works as expected for edge cases.
func TestFieldSquareRoot(t *testing.T) {
	tests := []struct {
		name  string // test description
		in    string // hex encoded value
		valid bool   // whether or not the value has a square root
		want  string // expected hex encoded value
	}{{
		name:  "secp256k1 prime (as 0 in and out)",
		in:    "0",
		valid: true,
		want:  "0",
	}, {
		name:  "secp256k1 prime (direct val with 0 out)",
		in:    "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		valid: true,
		want:  "0",
	}, {
		name:  "secp256k1 prime (as 0 in direct val out)",
		in:    "0",
		valid: true,
		want:  "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
	}, {
		name:  "secp256k1 prime-1",
		in:    "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
		valid: false,
		want:  "0000000000000000000000000000000000000000000000000000000000000001",
	}, {
		name:  "secp256k1 prime-2",
		in:    "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
		valid: false,
		want:  "210c790573632359b1edb4302c117d8a132654692c3feeb7de3a86ac3f3b53f7",
	}, {
		name:  "(secp256k1 prime-2)^2",
		in:    "0000000000000000000000000000000000000000000000000000000000000004",
		valid: true,
		want:  "0000000000000000000000000000000000000000000000000000000000000002",
	}, {
		name:  "value 1",
		in:    "0000000000000000000000000000000000000000000000000000000000000001",
		valid: true,
		want:  "0000000000000000000000000000000000000000000000000000000000000001",
	}, {
		name:  "value 2",
		in:    "0000000000000000000000000000000000000000000000000000000000000002",
		valid: true,
		want:  "210c790573632359b1edb4302c117d8a132654692c3feeb7de3a86ac3f3b53f7",
	}, {
		name:  "random sampling 1",
		in:    "16fb970147a9acc73654d4be233cc48b875ce20a2122d24f073d29bd28805aca",
		valid: false,
		want:  "6a27dcfca440cf7930a967be533b9620e397f122787c53958aaa7da7ad3d89a4",
	}, {
		name:  "square of random sampling 1",
		in:    "f4a8c3738ace0a1c3abf77737ae737f07687b5e24c07a643398298bd96893a18",
		valid: true,
		want:  "e90468feb8565338c9ab2b41dcc33b7478a31df5dedd2db0f8c2d641d77fa165",
	}, {
		name:  "random sampling 2",
		in:    "69d1323ce9f1f7b3bd3c7320b0d6311408e30281e273e39a0d8c7ee1c8257919",
		valid: true,
		want:  "61f4a7348274a52d75dfe176b8e3aaff61c1c833b6678260ba73def0fb2ad148",
	}, {
		name:  "random sampling 3",
		in:    "e0debf988ae098ecda07d0b57713e97c6d213db19753e8c95aa12a2fc1cc5272",
		valid: false,
		want:  "6e1cc9c311d33d901670135244f994b1ea39501f38002269b34ce231750cfbac",
	}, {
		name:  "random sampling 4",
		in:    "dcd394f91f74c2ba16aad74a22bb0ed47fe857774b8f2d6c09e28bfb14642878",
		valid: true,
		want:  "72b22fe6f173f8bcb21898806142ed4c05428601256eafce5d36c1b08fb82bab",
	}}

	for _, test := range tests {
		input := new(FieldVal).SetHex(test.in).Normalize()
		want := new(FieldVal).SetHex(test.want).Normalize()

		// Calculate the square root and enusre the validity flag matches the
		// expected value.
		var result FieldVal
		isValid := result.SquareRootVal(input)
		if isValid != test.valid {
			t.Errorf("%s: mismatched validity -- got %v, want %v", test.name,
				isValid, test.valid)
			continue
		}

		// Ensure the calculated result matches the expected value.
		result.Normalize()
		if !result.Equals(want) {
			t.Errorf("%s: d wrong result\ngot: %v\nwant: %v", test.name, result,
				want)
			continue
		}
	}
}

// TestFieldSquareRootRandom ensures that calculating the square root for random
// field values works as expected by also performing the same operation with big
// ints and comparing the results.
func TestFieldSquareRootRandom(t *testing.T) {
	// Use a unique random seed each test instance and log it if the tests fail.
	seed := time.Now().Unix()
	rng := rand.New(rand.NewSource(seed))
	defer func(t *testing.T, seed int64) {
		if t.Failed() {
			t.Logf("random seed: %d", seed)
		}
	}(t, seed)

	for i := 0; i < 100; i++ {
		// Generate big integer and field value with the same random value.
		bigIntVal, fVal := randIntAndFieldVal(t, rng)

		// Calculate the square root of the value using big ints.
		bigIntResult := new(big.Int).ModSqrt(bigIntVal, curveParams.P)
		bigIntHasSqrt := bigIntResult != nil

		// Calculate the square root of the value using a field value.
		var fValResult FieldVal
		fValHasSqrt := fValResult.SquareRootVal(fVal)

		// Ensure they match.
		if bigIntHasSqrt != fValHasSqrt {
			t.Fatalf("mismatched square root existence\nbig int in: %x\nfield "+
				"in: %v\nbig int result: %v\nfield result %v", bigIntVal, fVal,
				bigIntHasSqrt, fValHasSqrt)
		}
		if !fValHasSqrt {
			continue
		}
		bigIntResultHex := fmt.Sprintf("%064x", bigIntResult)
		fieldValResultHex := fmt.Sprintf("%v", fValResult)
		if bigIntResultHex != fieldValResultHex {
			t.Fatalf("mismatched square root\nbig int in: %x\nfield in: %v\n"+
				"big int result: %x\nfield result %v", bigIntVal, fVal,
				bigIntResult, fValResult)
		}
	}
}

// TestFieldInverse ensures that finding the multiplicative inverse via Inverse
// works as expected.
func TestFieldInverse(t *testing.T) {
	tests := []struct {
		name     string // test description
		in       string // hex encoded value
		expected string // expected hex encoded value
	}{{
		name:     "zero",
		in:       "0",
		expected: "0",
	}, {
		name:     "secp256k1 prime (direct val in with 0 out)",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
		expected: "0",
	}, {
		name:     "secp256k1 prime (0 in with direct val out)",
		in:       "0",
		expected: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
	}, {
		name:     "secp256k1 prime - 1",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
		expected: "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
	}, {
		name:     "secp256k1 prime - 2",
		in:       "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
		expected: "7fffffffffffffffffffffffffffffffffffffffffffffffffffffff7ffffe17",
	}, {
		name:     "random sampling #1",
		in:       "16fb970147a9acc73654d4be233cc48b875ce20a2122d24f073d29bd28805aca",
		expected: "987aeb257b063df0c6d1334051c47092b6d8766c4bf10c463786d93f5bc54354",
	}, {
		name:     "random sampling #2",
		in:       "69d1323ce9f1f7b3bd3c7320b0d6311408e30281e273e39a0d8c7ee1c8257919",
		expected: "49340981fa9b8d3dad72de470b34f547ed9179c3953797d0943af67806f4bb6",
	}, {
		name:     "random sampling #3",
		in:       "e0debf988ae098ecda07d0b57713e97c6d213db19753e8c95aa12a2fc1cc5272",
		expected: "64f58077b68af5b656b413ea366863f7b2819f8d27375d9c4d9804135ca220c2",
	}, {
		name:     "random sampling #4",
		in:       "dcd394f91f74c2ba16aad74a22bb0ed47fe857774b8f2d6c09e28bfb14642878",
		expected: "fb848ec64d0be572a63c38fe83df5e7f3d032f60bf8c969ef67d36bf4ada22a9",
	}}

	for _, test := range tests {
		f := new(FieldVal).SetHex(test.in).Normalize()
		expected := new(FieldVal).SetHex(test.expected).Normalize()
		result := f.Inverse().Normalize()
		if !result.Equals(expected) {
			t.Errorf("%s: d wrong result\ngot: %v\nwant: %v", test.name, result,
				expected)
			continue
		}
	}
}

// TestFieldIsGtOrEqPrimeMinusOrder ensures that field values report whether or
// not they are greater than or equal to the field prime minus the group order
// as expected for edge cases.
func TestFieldIsGtOrEqPrimeMinusOrder(t *testing.T) {
	tests := []struct {
		name     string // test description
		in       string // hex encoded test value
		expected bool   // expected result
	}{{
		name:     "zero",
		in:       "0",
		expected: false,
	}, {
		name:     "one",
		in:       "1",
		expected: false,
	}, {
		name:     "p - n - 1",
		in:       "14551231950b75fc4402da1722fc9baed",
		expected: false,
	}, {
		name:     "p - n",
		in:       "14551231950b75fc4402da1722fc9baee",
		expected: true,
	}, {
		name:     "p - n + 1",
		in:       "14551231950b75fc4402da1722fc9baef",
		expected: true,
	}, {
		name:     "over p - n word one",
		in:       "14551231950b75fc4402da17233c9baee",
		expected: true,
	}, {
		name:     "over p - n word two",
		in:       "14551231950b75fc4403da1722fc9baee",
		expected: true,
	}, {
		name:     "over p - n word three",
		in:       "14551231950b79fc4402da1722fc9baee",
		expected: true,
	}, {
		name:     "over p - n word four",
		in:       "14551241950b75fc4402da1722fc9baee",
		expected: true,
	}, {
		name:     "over p - n word five",
		in:       "54551231950b75fc4402da1722fc9baee",
		expected: true,
	}, {
		name:     "over p - n word six",
		in:       "100000014551231950b75fc4402da1722fc9baee",
		expected: true,
	}, {
		name:     "over p - n word seven",
		in:       "000000000000000000400000000000014551231950b75fc4402da1722fc9baee",
		expected: true,
	}, {
		name:     "over p - n word eight",
		in:       "000000000001000000000000000000014551231950b75fc4402da1722fc9baee",
		expected: true,
	}, {
		name:     "over p - n word nine",
		in:       "000004000000000000000000000000014551231950b75fc4402da1722fc9baee",
		expected: true,
	}}

	for _, test := range tests {
		result := new(FieldVal).SetHex(test.in).IsGtOrEqPrimeMinusOrder()
		if result != test.expected {
			t.Errorf("%s: unexpected result -- got: %v, want: %v", test.name,
				result, test.expected)
			continue
		}
	}
}

// TestFieldIsGtOrEqPrimeMinusOrderRandom ensures that field values report
// whether or not they are greater than or equal to the field prime minus the
// group order as expected by also performing the same operation with big ints
// and comparing the results.
func TestFieldIsGtOrEqPrimeMinusOrderRandom(t *testing.T) {
	// Use a unique random seed each test instance and log it if the tests fail.
	seed := time.Now().Unix()
	rng := rand.New(rand.NewSource(seed))
	defer func(t *testing.T, seed int64) {
		if t.Failed() {
			t.Logf("random seed: %d", seed)
		}
	}(t, seed)

	bigPMinusN := new(big.Int).Sub(curveParams.P, curveParams.N)
	for i := 0; i < 100; i++ {
		// Generate big integer and field value with the same random value.
		bigIntVal, fVal := randIntAndFieldVal(t, rng)

		// Determine the value is greater than or equal to the prime minus the
		// order using big ints.
		bigIntResult := bigIntVal.Cmp(bigPMinusN) >= 0

		// Determine the value is greater than or equal to the prime minus the
		// order using a field value.
		fValResult := fVal.IsGtOrEqPrimeMinusOrder()

		// Ensure they match.
		if bigIntResult != fValResult {
			t.Fatalf("mismatched is gt or eq prime minus order\nbig int in: "+
				"%x\nscalar in: %v\nbig int result: %v\nscalar result %v",
				bigIntVal, fVal, bigIntResult, fValResult)
		}
	}
}