package/gonum
1
0
Fork 0
mirror of https://github.com/gonum/gonum.git synced 2025-10-18 21:15:23 +08:00
Code Issues Actions Packages Projects Releases Wiki Activity

all: run gofmt and generate all packages

Browse Source 
Changes made in dsp/fourier/internal/fftpack break the formatting used
there, so these are reverted. There will be complaints in CI.

[git-generate]
gofmt -w .
go generate gonum.org/v1/gonum/blas
go generate gonum.org/v1/gonum/blas/gonum
go generate gonum.org/v1/gonum/unit
go generate gonum.org/v1/gonum/unit/constant
go generate gonum.org/v1/gonum/graph/formats/dot
go generate gonum.org/v1/gonum/graph/formats/rdf
go generate gonum.org/v1/gonum/stat/card

git checkout -- dsp/fourier/internal/fftpack
This commit is contained in:
Dan Kortschak
2022-08-05 20:57:59 +09:30
parent fee5019b48
commit 5f0141ca4c
308 changed files with 5004 additions and 3064 deletions
Download Patch File Download Diff File Expand all files Collapse all files

100
internal/math32/math_test.go
View File

@@ -178,64 +178,66 @@ func TestSqrt(t *testing.T) {
//
// __ieee754_sqrt(x)
// Return correctly rounded sqrt.
// -----------------------------------------
// | Use the hardware sqrt if you have one |
// -----------------------------------------
//
// -----------------------------------------
// | Use the hardware sqrt if you have one |
// -----------------------------------------
//
// Method:
// Bit by bit method using integer arithmetic. (Slow, but portable)
// 1. Normalization
// Scale x to y in [1,4) with even powers of 2:
// find an integer k such that 1 <= (y=x*2**(2k)) < 4, then
// sqrt(x) = 2**k * sqrt(y)
// 2. Bit by bit computation
// Let q = sqrt(y) truncated to i bit after binary point (q = 1),
// i 0
// i+1 2
// s = 2*q , and y = 2 * ( y - q ). (1)
// i i i i
//
// To compute q from q , one checks whether
// i+1 i
// Bit by bit method using integer arithmetic. (Slow, but portable)
// 1. Normalization
// Scale x to y in [1,4) with even powers of 2:
// find an integer k such that 1 <= (y=x*2**(2k)) < 4, then
// sqrt(x) = 2**k * sqrt(y)
// 2. Bit by bit computation
// Let q = sqrt(y) truncated to i bit after binary point (q = 1),
// i 0
// i+1 2
// s = 2*q , and y = 2 * ( y - q ). (1)
// i i i i
//
// -(i+1) 2
// (q + 2 ) <= y. (2)
// i
// -(i+1)
// If (2) is false, then q = q ; otherwise q = q + 2 .
// i+1 i i+1 i
// To compute q from q , one checks whether
// i+1 i
//
// With some algebraic manipulation, it is not difficult to see
// that (2) is equivalent to
// -(i+1)
// s + 2 <= y (3)
// i i
// -(i+1) 2
// (q + 2 ) <= y. (2)
// i
// -(i+1)
// If (2) is false, then q = q ; otherwise q = q + 2 .
// i+1 i i+1 i
//
// The advantage of (3) is that s and y can be computed by
// i i
// the following recurrence formula:
// if (3) is false
// With some algebraic manipulation, it is not difficult to see
// that (2) is equivalent to
// -(i+1)
// s + 2 <= y (3)
// i i
//
// s = s , y = y ; (4)
// i+1 i i+1 i
// The advantage of (3) is that s and y can be computed by
// i i
// the following recurrence formula:
// if (3) is false
//
// otherwise,
// -i -(i+1)
// s = s + 2 , y = y - s - 2 (5)
// i+1 i i+1 i i
// s = s , y = y ; (4)
// i+1 i i+1 i
//
// One may easily use induction to prove (4) and (5).
// Note. Since the left hand side of (3) contain only i+2 bits,
// it does not necessary to do a full (53-bit) comparison
// in (3).
// 3. Final rounding
// After generating the 53 bits result, we compute one more bit.
// Together with the remainder, we can decide whether the
// result is exact, bigger than 1/2ulp, or less than 1/2ulp
// (it will never equal to 1/2ulp).
// The rounding mode can be detected by checking whether
// huge + tiny is equal to huge, and whether huge - tiny is
// equal to huge for some floating point number "huge" and "tiny".
// otherwise,
// -i -(i+1)
// s = s + 2 , y = y - s - 2 (5)
// i+1 i i+1 i i
//
// One may easily use induction to prove (4) and (5).
// Note. Since the left hand side of (3) contain only i+2 bits,
// it does not necessary to do a full (53-bit) comparison
// in (3).
// 3. Final rounding
// After generating the 53 bits result, we compute one more bit.
// Together with the remainder, we can decide whether the
// result is exact, bigger than 1/2ulp, or less than 1/2ulp
// (it will never equal to 1/2ulp).
// The rounding mode can be detected by checking whether
// huge + tiny is equal to huge, and whether huge - tiny is
// equal to huge for some floating point number "huge" and "tiny".
func sqrt(x float32) float32 {
// special cases
switch {