math: speed up bessel functions on AMD64

J0-4            71.9ns ± 1%  54.6ns ± 0%  -24.08%  (p=0.000 n=20+18)
J1-4            71.6ns ± 0%  55.4ns ± 0%  -22.60%  (p=0.000 n=19+20)
Jn-4             153ns ± 0%   118ns ± 1%  -22.71%  (p=0.000 n=20+20)
Y0-4            70.8ns ± 0%  53.9ns ± 0%  -23.87%  (p=0.000 n=19+19)
Y1-4            70.8ns ± 0%  54.1ns ± 0%  -23.54%  (p=0.000 n=20+20)
Yn-4             149ns ± 0%   116ns ± 0%  -22.15%  (p=0.000 n=19+20)

Fixes #16889

Change-Id: Ie88496407b42f6acb918ffae1226b1b4c0500cb9
Reviewed-on: https://go-review.googlesource.com/28086
Run-TryBot: Ilya Tocar <ilya.tocar@intel.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>

diff --git a/src/math/j0.go b/src/math/j0.go
index cbef7aa7d6e0021608a0aa40333c2840b53cb333..fe26791175117a048096a123445c54d7b7c0f296 100644 (file)
--- a/src/math/j0.go
+++ b/src/math/j0.go
@@ -305,20 +305,20 @@ var p0S2 = [5]float64{
 }
 
 func pzero(x float64) float64 {
-       var p [6]float64
-       var q [5]float64
+       var p *[6]float64
+       var q *[5]float64
        if x >= 8 {
-               p = p0R8
-               q = p0S8
+               p = &p0R8
+               q = &p0S8
        } else if x >= 4.5454 {
-               p = p0R5
-               q = p0S5
+               p = &p0R5
+               q = &p0S5
        } else if x >= 2.8571 {
-               p = p0R3
-               q = p0S3
+               p = &p0R3
+               q = &p0S3
        } else if x >= 2 {
-               p = p0R2
-               q = p0S2
+               p = &p0R2
+               q = &p0S2
        }
        z := 1 / (x * x)
        r := p[0] + z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))))
@@ -408,19 +408,19 @@ var q0S2 = [6]float64{
 }
 
 func qzero(x float64) float64 {
-       var p, q [6]float64
+       var p, q *[6]float64
        if x >= 8 {
-               p = q0R8
-               q = q0S8
+               p = &q0R8
+               q = &q0S8
        } else if x >= 4.5454 {
-               p = q0R5
-               q = q0S5
+               p = &q0R5
+               q = &q0S5
        } else if x >= 2.8571 {
-               p = q0R3
-               q = q0S3
+               p = &q0R3
+               q = &q0S3
        } else if x >= 2 {
-               p = q0R2
-               q = q0S2
+               p = &q0R2
+               q = &q0S2
        }
        z := 1 / (x * x)
        r := p[0] + z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))))

diff --git a/src/math/j1.go b/src/math/j1.go
index d359d9072e340fd78f823fd483b056a3f17366f7..f1adcb6f41670f627572007fc24fd8b882d460ce 100644 (file)
--- a/src/math/j1.go
+++ b/src/math/j1.go
@@ -298,20 +298,20 @@ var p1S2 = [5]float64{
 }
 
 func pone(x float64) float64 {
-       var p [6]float64
-       var q [5]float64
+       var p *[6]float64
+       var q *[5]float64
        if x >= 8 {
-               p = p1R8
-               q = p1S8
+               p = &p1R8
+               q = &p1S8
        } else if x >= 4.5454 {
-               p = p1R5
-               q = p1S5
+               p = &p1R5
+               q = &p1S5
        } else if x >= 2.8571 {
-               p = p1R3
-               q = p1S3
+               p = &p1R3
+               q = &p1S3
        } else if x >= 2 {
-               p = p1R2
-               q = p1S2
+               p = &p1R2
+               q = &p1S2
        }
        z := 1 / (x * x)
        r := p[0] + z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))))
@@ -401,19 +401,19 @@ var q1S2 = [6]float64{
 }
 
 func qone(x float64) float64 {
-       var p, q [6]float64
+       var p, q *[6]float64
        if x >= 8 {
-               p = q1R8
-               q = q1S8
+               p = &q1R8
+               q = &q1S8
        } else if x >= 4.5454 {
-               p = q1R5
-               q = q1S5
+               p = &q1R5
+               q = &q1S5
        } else if x >= 2.8571 {
-               p = q1R3
-               q = q1S3
+               p = &q1R3
+               q = &q1S3
        } else if x >= 2 {
-               p = q1R2
-               q = q1S2
+               p = &q1R2
+               q = &q1S2
        }
        z := 1 / (x * x)
        r := p[0] + z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))))