func Fconv(fvp *Mpflt, flag int) string {
if flag&obj.FmtSharp == 0 {
return fvp.Val.Text('b', 0)
}
// use decimal format for error messages
// determine sign
f := &fvp.Val
var sign string
if f.Sign() < 0 {
sign = "-"
f = new(big.Float).Abs(f)
} else if flag&obj.FmtSign != 0 {
sign = "+"
}
// Don't try to convert infinities (will not terminate).
if f.IsInf() {
return sign + "Inf"
}
// Use exact fmt formatting if in float64 range (common case):
// proceed if f doesn't underflow to 0 or overflow to inf.
if x, _ := f.Float64(); f.Sign() == 0 == (x == 0) && !math.IsInf(x, 0) {
return fmt.Sprintf("%s%.6g", sign, x)
}
// Out of float64 range. Do approximate manual to decimal
// conversion to avoid precise but possibly slow Float
// formatting.
// f = mant * 2**exp
var mant big.Float
exp := f.MantExp(&mant) // 0.5 <= mant < 1.0
// approximate float64 mantissa m and decimal exponent d
// f ~ m * 10**d
m, _ := mant.Float64() // 0.5 <= m < 1.0
d := float64(exp) * (math.Ln2 / math.Ln10) // log_10(2)
// adjust m for truncated (integer) decimal exponent e
e := int64(d)
m *= math.Pow(10, d-float64(e))
// ensure 1 <= m < 10
switch {
case m < 1-0.5e-6:
// The %.6g format below rounds m to 5 digits after the
// decimal point. Make sure that m*10 < 10 even after
// rounding up: m*10 + 0.5e-5 < 10 => m < 1 - 0.5e6.
m *= 10
e--
case m >= 10:
m /= 10
e++
}
return fmt.Sprintf("%s%.6ge%+d", sign, m, e)
}
func Fconv(fvp *Mpflt, flag int) string {
if flag&obj.FmtSharp == 0 {
return fvp.Val.Text('b', 0)
}
// use decimal format for error messages
// determine sign
f := &fvp.Val
var sign string
if f.Sign() < 0 {
sign = "-"
f = new(big.Float).Abs(f)
} else if flag&obj.FmtSign != 0 {
sign = "+"
}
// Don't try to convert infinities (will not terminate).
if f.IsInf() {
return sign + "Inf"
}
// Use fmt formatting if in float64 range (common case).
if x, _ := f.Float64(); !math.IsInf(x, 0) {
return fmt.Sprintf("%s%.6g", sign, x)
}
// Out of float64 range. Do approximate manual to decimal
// conversion to avoid precise but possibly slow Float
// formatting. The exponent is > 0 since a negative out-
// of-range exponent would have underflowed and led to 0.
// f = mant * 2**exp
var mant big.Float
exp := float64(f.MantExp(&mant)) // 0.5 <= mant < 1.0, exp > 0
// approximate float64 mantissa m and decimal exponent d
// f ~ m * 10**d
m, _ := mant.Float64() // 0.5 <= m < 1.0
d := exp * (math.Ln2 / math.Ln10) // log_10(2)
// adjust m for truncated (integer) decimal exponent e
e := int64(d)
m *= math.Pow(10, d-float64(e))
for m >= 10 {
m /= 10
e++
}
return fmt.Sprintf("%s%.5fe+%d", sign, m, e)
}
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("internal error")
}
p.int(sign)
p.int(exp)
p.string(string(mant.Bytes()))
}
func mpmovefltfix(a *Mpint, b *Mpflt) int {
// avoid converting huge floating-point numbers to integers
// (2*Mpprec is large enough to permit all tests to pass)
if b.Val.MantExp(nil) > 2*Mpprec {
return -1
}
if _, acc := b.Val.Int(&a.Val); acc == big.Exact {
return 0
}
const delta = 16 // a reasonably small number of bits > 0
var t big.Float
t.SetPrec(Mpprec - delta)
// try rounding down a little
t.SetMode(big.ToZero)
t.Set(&b.Val)
if _, acc := t.Int(&a.Val); acc == big.Exact {
return 0
}
// try rounding up a little
t.SetMode(big.AwayFromZero)
t.Set(&b.Val)
if _, acc := t.Int(&a.Val); acc == big.Exact {
return 0
}
return -1
}
func mpmovefltfix(a *Mpint, b *Mpflt) int {
if _, acc := b.Val.Int(&a.Val); acc == big.Exact {
return 0
}
const delta = 16 // a reasonably small number of bits > 0
var t big.Float
t.SetPrec(Mpprec - delta)
// try rounding down a little
t.SetMode(big.ToZero)
t.Set(&b.Val)
if _, acc := t.Int(&a.Val); acc == big.Exact {
return 0
}
// try rounding up a little
t.SetMode(big.AwayFromZero)
t.Set(&b.Val)
if _, acc := t.Int(&a.Val); acc == big.Exact {
return 0
}
return -1
}
func ExampleFloat_Add() {
// Operating on numbers of different precision.
var x, y, z big.Float
x.SetInt64(1000) // x is automatically set to 64bit precision
y.SetFloat64(2.718281828) // y is automatically set to 53bit precision
z.SetPrec(32)
z.Add(&x, &y)
fmt.Printf("x = %.10g (%s, prec = %d, acc = %s)\n", &x, x.Text('p', 0), x.Prec(), x.Acc())
fmt.Printf("y = %.10g (%s, prec = %d, acc = %s)\n", &y, y.Text('p', 0), y.Prec(), y.Acc())
fmt.Printf("z = %.10g (%s, prec = %d, acc = %s)\n", &z, z.Text('p', 0), z.Prec(), z.Acc())
// Output:
// x = 1000 (0x.fap+10, prec = 64, acc = Exact)
// y = 2.718281828 (0x.adf85458248cd8p+2, prec = 53, acc = Exact)
// z = 1002.718282 (0x.faadf854p+10, prec = 32, acc = Below)
}
// This example shows how to use big.Float to compute the square root of 2 with
// a precision of 200 bits, and how to print the result as a decimal number.
func Example_sqrt2() {
// We'll do computations with 200 bits of precision in the mantissa.
const prec = 200
// Compute the square root of 2 using Newton's Method. We start with
// an initial estimate for sqrt(2), and then iterate:
// x_{n+1} = 1/2 * ( x_n + (2.0 / x_n) )
// Since Newton's Method doubles the number of correct digits at each
// iteration, we need at least log_2(prec) steps.
steps := int(math.Log2(prec))
// Initialize values we need for the computation.
two := new(big.Float).SetPrec(prec).SetInt64(2)
half := new(big.Float).SetPrec(prec).SetFloat64(0.5)
// Use 1 as the initial estimate.
x := new(big.Float).SetPrec(prec).SetInt64(1)
// We use t as a temporary variable. There's no need to set its precision
// since big.Float values with unset (== 0) precision automatically assume
// the largest precision of the arguments when used as the result (receiver)
// of a big.Float operation.
t := new(big.Float)
// Iterate.
for i := 0; i <= steps; i++ {
t.Quo(two, x) // t = 2.0 / x_n
t.Add(x, t) // t = x_n + (2.0 / x_n)
x.Mul(half, t) // x_{n+1} = 0.5 * t
}
// We can use the usual fmt.Printf verbs since big.Float implements fmt.Formatter
fmt.Printf("sqrt(2) = %.50f\n", x)
// Print the error between 2 and x*x.
t.Mul(x, x) // t = x*x
fmt.Printf("error = %e\n", t.Sub(two, t))
// Output:
// sqrt(2) = 1.41421356237309504880168872420969807856967187537695
// error = 0.000000e+00
}