// license that can be found in the LICENSE file.
// Copy of math/sqrt.go, here for use by ARM softfloat.
+// Modified to not use any floating point arithmetic so
+// that we don't clobber any floating-point registers
+// while emulating the sqrt instruction.
package runtime
-import "unsafe"
-
// The original C code and the long comment below are
// from FreeBSD's /usr/src/lib/msun/src/e_sqrt.c and
// came with this notice. The go code is a simplified
float64Mask = 0x7FF
float64Shift = 64 - 11 - 1
float64Bias = 1023
+ float64NaN = 0x7FF8000000000001
+ float64Inf = 0x7FF0000000000000
maxFloat64 = 1.797693134862315708145274237317043567981e+308 // 2**1023 * (2**53 - 1) / 2**52
)
-func float64bits(f float64) uint64 { return *(*uint64)(unsafe.Pointer(&f)) }
-func float64frombits(b uint64) float64 { return *(*float64)(unsafe.Pointer(&b)) }
+// isnanu returns whether ix represents a NaN floating point number.
+func isnanu(ix uint64) bool {
+ exp := (ix >> float64Shift) & float64Mask
+ sig := ix << (64 - float64Shift) >> (64 - float64Shift)
+ return exp == float64Mask && sig != 0
+}
-func sqrt(x float64) float64 {
+func sqrt(ix uint64) uint64 {
// special cases
switch {
- case x == 0 || x != x || x > maxFloat64:
- return x
- case x < 0:
- return nan()
+ case ix == 0 || ix == 1<<63: // x == 0
+ return ix
+ case isnanu(ix): // x != x
+ return ix
+ case ix&(1<<63) != 0: // x < 0
+ return float64NaN
+ case ix == float64Inf: // x > MaxFloat
+ return ix
}
- ix := float64bits(x)
// normalize x
exp := int((ix >> float64Shift) & float64Mask)
if exp == 0 { // subnormal x
q += q & 1 // round according to extra bit
}
ix = q>>1 + uint64(exp-1+float64Bias)<<float64Shift // significand + biased exponent
- return float64frombits(ix)
+ return ix
}
--- /dev/null
+// Copyright 2015 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// A copy of Sqrt tests from the math package to test the
+// purely integer arithmetic implementaiton in sqrt.go.
+
+package runtime_test
+
+import (
+ "math"
+ "runtime"
+ "testing"
+)
+
+func SqrtRT(x float64) float64 {
+ return math.Float64frombits(runtime.Sqrt(math.Float64bits(x)))
+}
+
+func TestSqrt(t *testing.T) {
+ for i := 0; i < len(vf); i++ {
+ a := math.Abs(vf[i])
+ if f := SqrtRT(a); sqrt[i] != f {
+ t.Errorf("Sqrt(%g) = %g, want %g", a, f, sqrt[i])
+ }
+ }
+ for i := 0; i < len(vfsqrtSC); i++ {
+ if f := SqrtRT(vfsqrtSC[i]); !alike(sqrtSC[i], f) {
+ t.Errorf("Sqrt(%g) = %g, want %g", vfsqrtSC[i], f, sqrtSC[i])
+ }
+ }
+}
+
+func alike(a, b float64) bool {
+ switch {
+ case math.IsNaN(a) && math.IsNaN(b):
+ return true
+ case a == b:
+ return math.Signbit(a) == math.Signbit(b)
+ }
+ return false
+}
+
+var vf = []float64{
+ 4.9790119248836735e+00,
+ 7.7388724745781045e+00,
+ -2.7688005719200159e-01,
+ -5.0106036182710749e+00,
+ 9.6362937071984173e+00,
+ 2.9263772392439646e+00,
+ 5.2290834314593066e+00,
+ 2.7279399104360102e+00,
+ 1.8253080916808550e+00,
+ -8.6859247685756013e+00,
+}
+
+var sqrt = []float64{
+ 2.2313699659365484748756904e+00,
+ 2.7818829009464263511285458e+00,
+ 5.2619393496314796848143251e-01,
+ 2.2384377628763938724244104e+00,
+ 3.1042380236055381099288487e+00,
+ 1.7106657298385224403917771e+00,
+ 2.286718922705479046148059e+00,
+ 1.6516476350711159636222979e+00,
+ 1.3510396336454586262419247e+00,
+ 2.9471892997524949215723329e+00,
+}
+
+var vfsqrtSC = []float64{
+ math.Inf(-1),
+ -math.Pi,
+ math.Copysign(0, -1),
+ 0,
+ math.Inf(1),
+ math.NaN(),
+}
+var sqrtSC = []float64{
+ math.NaN(),
+ math.NaN(),
+ math.Copysign(0, -1),
+ 0,
+ math.Inf(1),
+ math.NaN(),
+}