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bits.go
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bits.go
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package fork
import "math/big"
// CompactToBig converts a compact representation of a whole number N to an unsigned 32-bit number. The representation is similar to IEEE754 floating point numbers.
// Like IEEE754 floating point, there are three basic components: the sign, the exponent, and the mantissa. They are broken out as follows:
// * the most significant 8 bits represent the unsigned base 256 exponent
// * bit 23 (the 24th bit) represents the sign bit
// * the least significant 23 bits represent the mantissa
// -------------------------------------------------
// | Exponent | Sign | Mantissa |
// -------------------------------------------------
// | 8 bits [31-24] | 1 bit [23] | 23 bits [22-00] |
// -------------------------------------------------
// The formula to calculate N is:
// N = (-1^sign) * mantissa * 256^(exponent-3)
// This compact form is only used in bitcoin to encode unsigned 256-bit numbers which represent difficulty targets, thus there really is not a need for a sign bit, but it is implemented here to stay consistent with bitcoind.
func CompactToBig(compact uint32) *big.Int {
// Extract the mantissa, sign bit, and exponent.
mantissa := compact & 0x007fffff
isNegative := compact&0x00800000 != 0
exponent := uint(compact >> 24)
// Since the base for the exponent is 256, the exponent can be treated as the number of bytes to represent the full 256-bit number. So, treat the exponent as the number of bytes and shift the mantissa right or left accordingly. This is equivalent to N = mantissa * 256^(exponent-3)
var bn *big.Int
if exponent <= 3 {
mantissa >>= 8 * (3 - exponent)
bn = big.NewInt(int64(mantissa))
} else {
bn = big.NewInt(int64(mantissa))
bn.Lsh(bn, 8*(exponent-3))
}
// Make it negative if the sign bit is set.
if isNegative {
bn = bn.Neg(bn)
}
return bn
}
// BigToCompact converts a whole number N to a compact representation using an unsigned 32-bit number. The compact representation only provides 23 bits of precision, so values larger than (2^23 - 1) only encode the most significant digits of the number. See CompactToBig for details.
func BigToCompact(n *big.Int) uint32 {
// No need to do any work if it's zero.
if n.Sign() == 0 {
return 0
}
// Since the base for the exponent is 256, the exponent can be treated as the number of bytes. So, shift the number right or left accordingly. This is equivalent to: mantissa = mantissa / 256^(exponent-3)
var mantissa uint32
exponent := uint(len(n.Bytes()))
if exponent <= 3 {
mantissa = uint32(n.Bits()[0])
mantissa <<= 8 * (3 - exponent)
} else {
// Use a copy to avoid modifying the caller's original number.
tn := new(big.Int).Set(n)
mantissa = uint32(tn.Rsh(tn, 8*(exponent-3)).Bits()[0])
}
// When the mantissa already has the sign bit set, the number is too large to fit into the available 23-bits, so divide the number by 256 and increment the exponent accordingly.
if mantissa&0x00800000 != 0 {
mantissa >>= 8
exponent++
}
// Pack the exponent, sign bit, and mantissa into an unsigned 32-bit int and return it.
compact := uint32(exponent<<24) | mantissa
if n.Sign() < 0 {
compact |= 0x00800000
}
return compact
}