all: unify big.Int zero checks, use common/math in more places (#3716)

* common/math: optimize PaddedBigBytes, use it more

name              old time/op    new time/op    delta
PaddedBigBytes-8    71.1ns ± 5%    46.1ns ± 1%  -35.15%  (p=0.000 n=20+19)

name              old alloc/op   new alloc/op   delta
PaddedBigBytes-8     48.0B ± 0%     32.0B ± 0%  -33.33%  (p=0.000 n=20+20)

* all: unify big.Int zero checks

Various checks were in use. This commit replaces them all with Int.Sign,
which is cheaper and less code.

eg templates:

    func before(x *big.Int) bool { return x.BitLen() == 0 }
    func after(x *big.Int) bool  { return x.Sign() == 0 }

    func before(x *big.Int) bool { return x.BitLen() > 0 }
    func after(x *big.Int) bool  { return x.Sign() != 0 }

    func before(x *big.Int) int { return x.Cmp(common.Big0) }
    func after(x *big.Int) int  { return x.Sign() }

* common/math, crypto/secp256k1: make ReadBits public in package math

4 files changed, 6 insertions, 58 deletions

diff --git a/crypto/secp256k1/curve.go b/crypto/secp256k1/curve.go
index 61cad5463..ec6d266ce 100644
--- a/crypto/secp256k1/curve.go
+++ b/crypto/secp256k1/curve.go
@@ -36,6 +36,8 @@ import (
 	"math/big"
 	"sync"
 	"unsafe"
+
+	"github.com/ethereum/go-ethereum/common/math"
 )
 
 /*
@@ -230,8 +232,8 @@ func (BitCurve *BitCurve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int,
 
 	// Do the multiplication in C, updating point.
 	point := make([]byte, 64)
-	readBits(point[:32], Bx)
-	readBits(point[32:], By)
+	math.ReadBits(Bx, point[:32])
+	math.ReadBits(By, point[32:])
 	pointPtr := (*C.uchar)(unsafe.Pointer(&point[0]))
 	scalarPtr := (*C.uchar)(unsafe.Pointer(&scalar[0]))
 	res := C.secp256k1_pubkey_scalar_mul(context, pointPtr, scalarPtr)
diff --git a/crypto/secp256k1/curve_test.go b/crypto/secp256k1/curve_test.go
deleted file mode 100644
index d915ee852..000000000
--- a/crypto/secp256k1/curve_test.go
+++ /dev/null
@@ -1,39 +0,0 @@
-// Copyright 2015 The go-ethereum Authors
-// This file is part of the go-ethereum library.
-//
-// The go-ethereum library is free software: you can redistribute it and/or modify
-// it under the terms of the GNU Lesser General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// The go-ethereum library is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-// GNU Lesser General Public License for more details.
-//
-// You should have received a copy of the GNU Lesser General Public License
-// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
-
-package secp256k1
-
-import (
-	"bytes"
-	"encoding/hex"
-	"math/big"
-	"testing"
-)
-
-func TestReadBits(t *testing.T) {
-	check := func(input string) {
-		want, _ := hex.DecodeString(input)
-		int, _ := new(big.Int).SetString(input, 16)
-		buf := make([]byte, len(want))
-		readBits(buf, int)
-		if !bytes.Equal(buf, want) {
-			t.Errorf("have: %x\nwant: %x", buf, want)
-		}
-	}
-	check("000000000000000000000000000000000000000000000000000000FEFCF3F8F0")
-	check("0000000000012345000000000000000000000000000000000000FEFCF3F8F0")
-	check("18F8F8F1000111000110011100222004330052300000000000000000FEFCF3F8F0")
-}
diff --git a/crypto/secp256k1/secp256.go b/crypto/secp256k1/secp256.go
index 1a152a670..0ffa04fe0 100644
--- a/crypto/secp256k1/secp256.go
+++ b/crypto/secp256k1/secp256.go
@@ -38,7 +38,6 @@ import "C"
 
 import (
 	"errors"
-	"math/big"
 	"unsafe"
 )
 
@@ -129,16 +128,3 @@ func checkSignature(sig []byte) error {
 	}
 	return nil
 }
-
-// reads num into buf as big-endian bytes.
-func readBits(buf []byte, num *big.Int) {
-	const wordLen = int(unsafe.Sizeof(big.Word(0)))
-	i := len(buf)
-	for _, d := range num.Bits() {
-		for j := 0; j < wordLen && i > 0; j++ {
-			i--
-			buf[i] = byte(d)
-			d >>= 8
-		}
-	}
-}
diff --git a/crypto/secp256k1/secp256_test.go b/crypto/secp256k1/secp256_test.go
index 287ab512e..f6582ecd5 100644
--- a/crypto/secp256k1/secp256_test.go
+++ b/crypto/secp256k1/secp256_test.go
@@ -24,6 +24,7 @@ import (
 	"encoding/hex"
 	"testing"
 
+	"github.com/ethereum/go-ethereum/common/math"
 	"github.com/ethereum/go-ethereum/crypto/randentropy"
 )
 
@@ -35,9 +36,7 @@ func generateKeyPair() (pubkey, privkey []byte) {
 		panic(err)
 	}
 	pubkey = elliptic.Marshal(S256(), key.X, key.Y)
-	privkey = make([]byte, 32)
-	readBits(privkey, key.D)
-	return pubkey, privkey
+	return pubkey, math.PaddedBigBytes(key.D, 32)
 }
 
 func randSig() []byte {