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71 lines
1.6 KiB
Go
71 lines
1.6 KiB
Go
package bigfft
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import (
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"math/big"
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)
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// FromDecimalString converts the base 10 string
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// representation of a natural (non-negative) number
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// into a *big.Int.
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// Its asymptotic complexity is less than quadratic.
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func FromDecimalString(s string) *big.Int {
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var sc scanner
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z := new(big.Int)
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sc.scan(z, s)
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return z
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}
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type scanner struct {
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// powers[i] is 10^(2^i * quadraticScanThreshold).
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powers []*big.Int
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}
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func (s *scanner) chunkSize(size int) (int, *big.Int) {
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if size <= quadraticScanThreshold {
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panic("size < quadraticScanThreshold")
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}
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pow := uint(0)
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for n := size; n > quadraticScanThreshold; n /= 2 {
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pow++
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}
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// threshold * 2^(pow-1) <= size < threshold * 2^pow
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return quadraticScanThreshold << (pow - 1), s.power(pow - 1)
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}
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func (s *scanner) power(k uint) *big.Int {
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for i := len(s.powers); i <= int(k); i++ {
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z := new(big.Int)
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if i == 0 {
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if quadraticScanThreshold%14 != 0 {
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panic("quadraticScanThreshold % 14 != 0")
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}
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z.Exp(big.NewInt(1e14), big.NewInt(quadraticScanThreshold/14), nil)
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} else {
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z.Mul(s.powers[i-1], s.powers[i-1])
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}
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s.powers = append(s.powers, z)
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}
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return s.powers[k]
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}
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func (s *scanner) scan(z *big.Int, str string) {
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if len(str) <= quadraticScanThreshold {
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z.SetString(str, 10)
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return
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}
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sz, pow := s.chunkSize(len(str))
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// Scan the left half.
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s.scan(z, str[:len(str)-sz])
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// FIXME: reuse temporaries.
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left := Mul(z, pow)
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// Scan the right half
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s.scan(z, str[len(str)-sz:])
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z.Add(z, left)
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}
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// quadraticScanThreshold is the number of digits
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// below which big.Int.SetString is more efficient
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// than subquadratic algorithms.
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// 1232 digits fit in 4096 bits.
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const quadraticScanThreshold = 1232
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