Golang Float.SetMantExp方法代码示例

func (p *exporter) float(x *Mpflt) {
	// extract sign (there is no -0)
	f := &x.Val
	sign := f.Sign()
	if sign == 0 {
		// x == 0
		p.int(0)
		return
	}
	// x != 0

	// extract exponent such that 0.5 <= m < 1.0
	var m big.Float
	exp := f.MantExp(&m)

	// extract mantissa as *big.Int
	// - set exponent large enough so mant satisfies mant.IsInt()
	// - get *big.Int from mant
	m.SetMantExp(&m, int(m.MinPrec()))
	mant, acc := m.Int(nil)
	if acc != big.Exact {
		Fatalf("exporter: internal error")
	}

	p.int(sign)
	p.int(exp)
	p.string(string(mant.Bytes()))
}

func (bed BinaryVarintEncoderDecoder) Decode(r io.Reader, n *big.Float) error {
	var isInteger int8
	var f float64
	var exponent int32
	n.SetUint64(0)

	if err := binary.Read(r, binary.BigEndian, &isInteger); err != nil {
		return err
	}

	if isInteger <= 0 {
		var x int64
		var err error
		if x, err = binary.ReadVarint(miniByteReader{r}); err != nil {
			return err
		}
		n.SetInt64(x)
		n.SetPrec(ENCODER_DECODER_PREC)
		return nil
	} else {
		if err := binary.Read(r, binary.BigEndian, &f); err != nil {
			return err
		}
		if err := binary.Read(r, binary.BigEndian, &exponent); err != nil {
			return err
		}
		bed.tmp.SetFloat64(f)
		bed.tmp.SetPrec(ENCODER_DECODER_PREC)
		n.SetMantExp(bed.tmp, int(exponent))
		return nil
	}
}

// Sqrt returns a big.Float representation of the square root of
// z. Precision is the same as the one of the argument. The function
// panics if z is negative, returns ±0 when z = ±0, and +Inf when z =
// +Inf.
func Sqrt(z *big.Float) *big.Float {

	// panic on negative z
	if z.Sign() == -1 {
		panic("Sqrt: argument is negative")
	}

	// √±0 = ±0
	if z.Sign() == 0 {
		return big.NewFloat(float64(z.Sign()))
	}

	// √+Inf  = +Inf
	if z.IsInf() {
		return big.NewFloat(math.Inf(+1))
	}

	// Compute √(a·2**b) as
	//   √(a)·2**b/2       if b is even
	//   √(2a)·2**b/2      if b > 0 is odd
	//   √(0.5a)·2**b/2    if b < 0 is odd
	//
	// The difference in the odd exponent case is due to the fact that
	// exp/2 is rounded in different directions when exp is negative.
	mant := new(big.Float)
	exp := z.MantExp(mant)
	switch exp % 2 {
	case 1:
		mant.Mul(big.NewFloat(2), mant)
	case -1:
		mant.Mul(big.NewFloat(0.5), mant)
	}

	// Solving x² - z = 0 directly requires a Quo call, but it's
	// faster for small precisions.
	//
	// Solving 1/x² - z = 0 avoids the Quo call and is much faster for
	// high precisions.
	//
	// Use sqrtDirect for prec <= 128 and sqrtInverse for prec > 128.
	var x *big.Float
	if z.Prec() <= 128 {
		x = sqrtDirect(mant)
	} else {
		x = sqrtInverse(mant)
	}

	// re-attach the exponent and return
	return x.SetMantExp(x, exp/2)

}

func (bed BinaryEncoderDecoder) Decode(r io.Reader, n *big.Float) error {
	var f float64
	var exponent int32
	n.SetUint64(0)
	if err := binary.Read(r, binary.BigEndian, &f); err != nil {
		return err
	}
	if err := binary.Read(r, binary.BigEndian, &exponent); err != nil {
		return err
	}
	bed.tmp.SetFloat64(f)
	bed.tmp.SetPrec(ENCODER_DECODER_PREC)
	n.SetMantExp(bed.tmp, int(exponent))
	return nil
}

func (p *exporter) float(x constant.Value) {
	if x.Kind() != constant.Float {
		log.Fatalf("gcimporter: unexpected constant %v, want float", x)
	}
	// extract sign (there is no -0)
	sign := constant.Sign(x)
	if sign == 0 {
		// x == 0
		p.int(0)
		return
	}
	// x != 0

	var f big.Float
	if v, exact := constant.Float64Val(x); exact {
		// float64
		f.SetFloat64(v)
	} else if num, denom := constant.Num(x), constant.Denom(x); num.Kind() == constant.Int {
		// TODO(gri): add big.Rat accessor to constant.Value.
		r := valueToRat(num)
		f.SetRat(r.Quo(r, valueToRat(denom)))
	} else {
		// Value too large to represent as a fraction => inaccessible.
		// TODO(gri): add big.Float accessor to constant.Value.
		f.SetFloat64(math.MaxFloat64) // FIXME
	}

	// extract exponent such that 0.5 <= m < 1.0
	var m big.Float
	exp := f.MantExp(&m)

	// extract mantissa as *big.Int
	// - set exponent large enough so mant satisfies mant.IsInt()
	// - get *big.Int from mant
	m.SetMantExp(&m, int(m.MinPrec()))
	mant, acc := m.Int(nil)
	if acc != big.Exact {
		log.Fatalf("gcimporter: internal error")
	}

	p.int(sign)
	p.int(exp)
	p.string(string(mant.Bytes()))
}

// Log returns a big.Float representation of the natural logarithm of
// z. Precision is the same as the one of the argument. The function
// panics if z is negative, returns -Inf when z = 0, and +Inf when z =
// +Inf
func Log(z *big.Float) *big.Float {

	// panic on negative z
	if z.Sign() == -1 {
		panic("Log: argument is negative")
	}

	// Log(0) = -Inf
	if z.Sign() == 0 {
		return big.NewFloat(math.Inf(-1)).SetPrec(z.Prec())
	}

	prec := z.Prec() + 64 // guard digits

	one := big.NewFloat(1).SetPrec(prec)
	two := big.NewFloat(2).SetPrec(prec)
	four := big.NewFloat(4).SetPrec(prec)

	// Log(1) = 0
	if z.Cmp(one) == 0 {
		return big.NewFloat(0).SetPrec(z.Prec())
	}

	// Log(+Inf) = +Inf
	if z.IsInf() {
		return big.NewFloat(math.Inf(+1)).SetPrec(z.Prec())
	}

	x := new(big.Float).SetPrec(prec)

	// if 0 < z < 1 we compute log(z) as -log(1/z)
	var neg bool
	if z.Cmp(one) < 0 {
		x.Quo(one, z)
		neg = true
	} else {
		x.Set(z)
	}

	// We scale up x until x >= 2**(prec/2), and then we'll be allowed
	// to use the AGM formula for Log(x).
	//
	// Double x until the condition is met, and keep track of the
	// number of doubling we did (needed to scale back later).

	lim := new(big.Float)
	lim.SetMantExp(two, int(prec/2))

	k := 0
	for x.Cmp(lim) < 0 {
		x.Mul(x, x)
		k++
	}

	// Compute the natural log of x using the fact that
	//     log(x) = π / (2 * AGM(1, 4/x))
	// if
	//     x >= 2**(prec/2),
	// where prec is the desired precision (in bits)
	pi := pi(prec)
	agm := agm(one, x.Quo(four, x)) // agm = AGM(1, 4/x)

	x.Quo(pi, x.Mul(two, agm)) // reuse x, we don't need it

	if neg {
		x.Neg(x)
	}

	// scale the result back multiplying by 2**-k
	// reuse lim to reduce allocations.
	x.Mul(x, lim.SetMantExp(one, -k))

	return x.SetPrec(z.Prec())
}