}

// Power-series constructors return channels on which power
// series flow.  They start an encapsulated generator that
// puts the terms of the series on the channel.

// Make a pair of power series identical to a given power series

func Split(U PS) *dch2 {
	UU := mkdch2()
	go split(U, UU)
	return UU
}

// Add two power series
func Add(U, V PS) PS {
	Z := mkPS()

}

// Power-series constructors return channels on which power
// series flow.  They start an encapsulated generator that
// puts the terms of the series on the channel.

// Make a pair of power series identical to a given power series

func Split(U PS) *dch2 {
	UU := mkdch2()
	go split(U, UU)
	return UU
}

// Add two power series
func Add(U, V PS) PS {
	Z := mkPS()

powens.png...

				mantissa += uint64(c - '0')
				ndMant++
			} else if c != '0' {
				trunc = true
			}
			continue

		case base == 16 && 'a' <= lower(c) && lower(c) <= 'f':
			sawdigits = true
			nd++
			if ndMant < maxMantDigits {
				mantissa *= 16
				mantissa += uint64(lower(c) - 'a' + 10)
				ndMant++
			} else {
				trunc = true
			}
			continue
		}
		break
	}
	if !sawdigits {
		return

	zzp := getNat(w)
	zz := *zzp

	const n = 4
	// powers[i] contains x^i.
	var powers [1 << n]*nat
	for i := range powers {
		powers[i] = getNat(w)
	}
	*powers[0] = powers[0].set(natOne)
	*powers[1] = powers[1].trunc(x, logM)
	for i := 2; i < 1<<n; i += 2 {
		p2, p, p1 := powers[i/2], powers[i], powers[i+1]
		*p = p.sqr(*p2)
		*p = p.trunc(*p, logM)
		*p1 = p1.mul(*p, x)

func computeBounds(mant uint64, exp int, flt *floatInfo) (lower, central, upper uint64, e2 int) {
	if mant != 1<<flt.mantbits || exp == flt.bias+1-int(flt.mantbits) {
		// regular case (or denormals)
		lower, central, upper = 2*mant-1, 2*mant, 2*mant+1
		e2 = exp - 1
		return
	} else {
		// border of an exponent
		lower, central, upper = 4*mant-1, 4*mant, 4*mant+2
		e2 = exp - 2
		return
	}
}

  /**
   * Returns the smallest power of two greater than or equal to {@code x}. This is equivalent to
   * {@code checkedPow(2, log2(x, CEILING))}.
   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @throws ArithmeticException of the next-higher power of two is not representable as an {@code
   *     int}, i.e. when {@code x > 2^30}
   * @since 20.0
   */

  /**
   * Returns the smallest power of two greater than or equal to {@code x}. This is equivalent to
   * {@code checkedPow(2, log2(x, CEILING))}.
   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @throws ArithmeticException of the next-higher power of two is not representable as an {@code
   *     int}, i.e. when {@code x > 2^30}
   * @since 20.0
   */

  /**
   * Returns the smallest power of two greater than or equal to {@code x}. This is equivalent to
   * {@code checkedPow(2, log2(x, CEILING))}.
   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @throws ArithmeticException of the next-higher power of two is not representable as a {@code
   *     long}, i.e. when {@code x > 2^62}
   * @since 20.0
   */

	// base**fcount. An exponent means multiplication by ebase**exp.
	// Multiplications are commutative, so we can apply them in any
	// order. We only have powers of 2 and 10, and we split powers
	// of 10 into the product of the same powers of 2 and 5. This
	// may reduce the size of shift/multiplication factors or
	// divisors required to create the final fraction, depending
	// on the actual floating-point value.