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math: fix inaccurate result of Exp(1)

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The existing implementation is translated from C, which uses a
polynomial coefficient very close to 1/6. If the function uses
1/6 as this coeffient, the result of Exp(1) will be more accurate.
And this change doesn't introduce more error to Exp function.

Fixes #20319

Change-Id: I94c236a18cf95570ebb69f7fb99884b0d7cf5f6e
Reviewed-on: https://go-review.googlesource.com/49294
Reviewed-by: Robert Griesemer <gri@golang.org>
This commit is contained in:
crvv 2017-07-18 14:37:01 +08:00 committed by Robert Griesemer
parent 3366f51544
commit d46953c9f6
2 changed files with 4 additions and 2 deletions
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2
src/math/all_test.go
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@ -953,6 +953,7 @@ var vfexpSC = []float64{
// Issue 18912
1.48852223e+09,
1.4885222e+09,
1,
}
var expSC = []float64{
0,
@ -963,6 +964,7 @@ var expSC = []float64{
Inf(1),
Inf(1),
Inf(1),
2.718281828459045,
}
var vfexp2SC = []float64{

4
src/math/exp.go
View File

@ -44,7 +44,7 @@ func Exp(x float64) float64
// the interval [0,0.34658]:
// Write
// R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
// We use a special Remes algorithm on [0,0.34658] to generate
// We use a special Remez algorithm on [0,0.34658] to generate
// a polynomial of degree 5 to approximate R. The maximum error
// of this polynomial approximation is bounded by 2**-59. In
// other words,
@ -175,7 +175,7 @@ func exp2(x float64) float64 {
// exp1 returns e**r × 2**k where r = hi - lo and |r| ≤ ln(2)/2.
func expmulti(hi, lo float64, k int) float64 {
const (
P1 = 1.66666666666666019037e-01 /* 0x3FC55555; 0x5555553E */
P1 = 1.66666666666666657415e-01 /* 0x3FC55555; 0x55555555 */
P2 = -2.77777777770155933842e-03 /* 0xBF66C16C; 0x16BEBD93 */
P3 = 6.61375632143793436117e-05 /* 0x3F11566A; 0xAF25DE2C */
P4 = -1.65339022054652515390e-06 /* 0xBEBBBD41; 0xC5D26BF1 */