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blas: imported blas as a subtree
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Brendan Tracey
226
blas/native/internal/math32/math_test.go
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226
blas/native/internal/math32/math_test.go
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// Copyright ©2015 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package math32
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import (
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"math"
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"testing"
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"testing/quick"
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"github.com/gonum/floats"
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)
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const tol = 1e-7
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func TestAbs(t *testing.T) {
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f := func(x float32) bool {
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y := Abs(x)
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return y == float32(math.Abs(float64(x)))
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}
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if err := quick.Check(f, nil); err != nil {
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t.Error(err)
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}
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}
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func TestCopySign(t *testing.T) {
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f := func(x struct{ X, Y float32 }) bool {
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y := Copysign(x.X, x.Y)
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return y == float32(math.Copysign(float64(x.X), float64(x.Y)))
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}
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if err := quick.Check(f, nil); err != nil {
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t.Error(err)
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}
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}
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func TestHypot(t *testing.T) {
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f := func(x struct{ X, Y float32 }) bool {
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y := Hypot(x.X, x.Y)
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if math.Hypot(float64(x.X), float64(x.Y)) > math.MaxFloat32 {
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return true
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}
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return floats.EqualWithinRel(float64(y), math.Hypot(float64(x.X), float64(x.Y)), tol)
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}
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if err := quick.Check(f, nil); err != nil {
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t.Error(err)
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}
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}
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func TestInf(t *testing.T) {
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if float64(Inf(1)) != math.Inf(1) || float64(Inf(-1)) != math.Inf(-1) {
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t.Error("float32(inf) not infinite")
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}
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}
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func TestIsInf(t *testing.T) {
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posInf := float32(math.Inf(1))
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negInf := float32(math.Inf(-1))
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if !IsInf(posInf, 0) || !IsInf(negInf, 0) || !IsInf(posInf, 1) || !IsInf(negInf, -1) || IsInf(posInf, -1) || IsInf(negInf, 1) {
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t.Error("unexpected isInf value")
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}
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f := func(x struct {
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F float32
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Sign int
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}) bool {
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y := IsInf(x.F, x.Sign)
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return y == math.IsInf(float64(x.F), x.Sign)
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}
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if err := quick.Check(f, nil); err != nil {
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t.Error(err)
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}
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}
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func TestIsNaN(t *testing.T) {
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f := func(x float32) bool {
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y := IsNaN(x)
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return y == math.IsNaN(float64(x))
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}
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if err := quick.Check(f, nil); err != nil {
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t.Error(err)
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}
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}
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func TestNaN(t *testing.T) {
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if !math.IsNaN(float64(NaN())) {
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t.Errorf("float32(nan) is a number: %f", NaN())
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}
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}
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func TestSqrt(t *testing.T) {
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f := func(x float32) bool {
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y := Sqrt(x)
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if IsNaN(y) && IsNaN(sqrt(x)) {
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return true
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}
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return floats.EqualWithinRel(float64(y), float64(sqrt(x)), tol)
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}
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if err := quick.Check(f, nil); err != nil {
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t.Error(err)
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}
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}
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// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// The original C code and the long comment below are
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// from FreeBSD's /usr/src/lib/msun/src/e_sqrt.c and
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// came with this notice. The go code is a simplified
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// version of the original C.
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//
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// ====================================================
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// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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//
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// Developed at SunPro, a Sun Microsystems, Inc. business.
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// Permission to use, copy, modify, and distribute this
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// software is freely granted, provided that this notice
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// is preserved.
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// ====================================================
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//
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// __ieee754_sqrt(x)
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// Return correctly rounded sqrt.
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// -----------------------------------------
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// | Use the hardware sqrt if you have one |
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// -----------------------------------------
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// Method:
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// Bit by bit method using integer arithmetic. (Slow, but portable)
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// 1. Normalization
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// Scale x to y in [1,4) with even powers of 2:
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// find an integer k such that 1 <= (y=x*2**(2k)) < 4, then
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// sqrt(x) = 2**k * sqrt(y)
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// 2. Bit by bit computation
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// Let q = sqrt(y) truncated to i bit after binary point (q = 1),
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// i 0
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// i+1 2
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// s = 2*q , and y = 2 * ( y - q ). (1)
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// i i i i
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//
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// To compute q from q , one checks whether
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// i+1 i
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//
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// -(i+1) 2
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// (q + 2 ) <= y. (2)
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// i
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// -(i+1)
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// If (2) is false, then q = q ; otherwise q = q + 2 .
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// i+1 i i+1 i
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//
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// With some algebraic manipulation, it is not difficult to see
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// that (2) is equivalent to
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// -(i+1)
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// s + 2 <= y (3)
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// i i
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//
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// The advantage of (3) is that s and y can be computed by
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// i i
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// the following recurrence formula:
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// if (3) is false
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//
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// s = s , y = y ; (4)
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// i+1 i i+1 i
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//
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// otherwise,
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// -i -(i+1)
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// s = s + 2 , y = y - s - 2 (5)
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// i+1 i i+1 i i
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//
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// One may easily use induction to prove (4) and (5).
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// Note. Since the left hand side of (3) contain only i+2 bits,
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// it does not necessary to do a full (53-bit) comparison
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// in (3).
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// 3. Final rounding
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// After generating the 53 bits result, we compute one more bit.
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// Together with the remainder, we can decide whether the
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// result is exact, bigger than 1/2ulp, or less than 1/2ulp
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// (it will never equal to 1/2ulp).
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// The rounding mode can be detected by checking whether
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// huge + tiny is equal to huge, and whether huge - tiny is
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// equal to huge for some floating point number "huge" and "tiny".
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//
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func sqrt(x float32) float32 {
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// special cases
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switch {
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case x == 0 || IsNaN(x) || IsInf(x, 1):
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return x
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case x < 0:
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return NaN()
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}
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ix := math.Float32bits(x)
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// normalize x
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exp := int((ix >> shift) & mask)
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if exp == 0 { // subnormal x
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for ix&1<<shift == 0 {
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ix <<= 1
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exp--
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}
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exp++
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}
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exp -= bias // unbias exponent
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ix &^= mask << shift
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ix |= 1 << shift
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if exp&1 == 1 { // odd exp, double x to make it even
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ix <<= 1
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}
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exp >>= 1 // exp = exp/2, exponent of square root
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// generate sqrt(x) bit by bit
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ix <<= 1
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var q, s uint32 // q = sqrt(x)
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r := uint32(1 << (shift + 1)) // r = moving bit from MSB to LSB
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for r != 0 {
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t := s + r
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if t <= ix {
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s = t + r
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ix -= t
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q += r
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}
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ix <<= 1
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r >>= 1
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}
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// final rounding
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if ix != 0 { // remainder, result not exact
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q += q & 1 // round according to extra bit
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}
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ix = q>>1 + uint32(exp-1+bias)<<shift // significand + biased exponent
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return math.Float32frombits(ix)
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}
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