// len(x) > 0

	// allocate buffer for conversion
	i := int(float64(x.bitLen())/math.Log2(float64(base))) + 1 // off by 1 at most
	if neg {
		i++
	}
	s := make([]byte, i)

	// convert power of two and non power of two bases separately
	if b := Word(base); b == b&-b {
		// shift is base b digit size in bits
		shift := uint(bits.TrailingZeros(uint(b))) // shift > 0 because b >= 2
		mask := Word(1<<shift - 1)

	// a correcting multiplication by 2**(-shiftcount). Multiplications
	// are commutative, so we can apply them in any order as long as there
	// is no loss of precision. 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 reduces the size of the multiplication factor
	// needed for base-10 exponents.

	// normalize mantissa and determine initial exponent contributions

// license that can be found in the LICENSE file.

//go:build ppc64 || ppc64le

#include "textflag.h"

TEXT ·publicationBarrier(SB),NOSPLIT|NOFRAME,$0-0
	// LWSYNC is the "export" barrier recommended by Power ISA
	// v2.07 book II, appendix B.2.2.2.
	// LWSYNC is a load/load, load/store, and store/store barrier.
	LWSYNC

 *
 * @author Louis Wasserman
 * @since 11.0
 */
@GwtCompatible(emulated = true)
@ElementTypesAreNonnullByDefault
public final class BigIntegerMath {
  /**
   * Returns the smallest power of two greater than or equal to {@code x}. This is equivalent to
   * {@code BigInteger.valueOf(2).pow(log2(x, CEILING))}.
   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @since 20.0
   */

// source listings for the gamma function and the incomplete beta
// integral.
//
//   Stephen L. Moshier
//   ******@****.***

// Complex power function
//
// DESCRIPTION:
//
// Raises complex A to the complex Zth power.
// Definition is per AMS55 # 4.2.8,
// analytically equivalent to cpow(a,z) = cexp(z clog(a)).
//
// ACCURACY:
//
//                      Relative error:

	// prefix and at least one digit.
	if len(s) < 4 {
		return 0, false
	}
	power := 0
	switch s[len(s)-3] {
	case 'K':
		power = 1
	case 'M':
		power = 2
	case 'G':
		power = 3
	case 'T':
		power = 4
	default:
		// Invalid suffix.
		return 0, false
	}
	m := uint64(1)
	for i := 0; i < power; i++ {
		m *= 1024
	}
	n, ok := atoi64(s[:len(s)-3])
	if !ok || n < 0 {

func Log2(x float64) float64 {
	if haveArchLog2 {
		return archLog2(x)
	}
	return log2(x)
}

func log2(x float64) float64 {
	frac, exp := Frexp(x)
	// Make sure exact powers of two give an exact answer.
	// Don't depend on Log(0.5)*(1/Ln2)+exp being exactly exp-1.
	if frac == 0.5 {
		return float64(exp - 1)
	}
	return Log(frac)*(1/Ln2) + float64(exp)

#include "mlir/Support/LogicalResult.h"  // from @llvm-project

namespace mlir::quant::stablehlo {

// Decomposes a given floating point value num into a normalized and quantized
// fraction and an integral power of two.
LogicalResult QuantizeMultiplier(double double_multiplier,
                                 int32_t& quantized_fraction, int32_t& shift);

}  // namespace mlir::quant::stablehlo

   * can hold setSize elements with the desired load factor.
   */
  @VisibleForTesting
  static int chooseTableSize(int setSize) {
    if (setSize == 1) {
      return 2;
    }
    // Correct the size for open addressing to match desired load factor.
    // Round up to the next highest power of 2.
    int tableSize = Integer.highestOneBit(setSize - 1) << 1;

// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package math

// Frexp breaks f into a normalized fraction
// and an integral power of two.
// It returns frac and exp satisfying f == frac × 2**exp,
// with the absolute value of frac in the interval [½, 1).
//
// Special cases are:
//
//	Frexp(±0) = ±0, 0
//	Frexp(±Inf) = ±Inf, 0