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-rw-r--r--src/pkg/math/cmplx/abs.go12
-rw-r--r--src/pkg/math/cmplx/asin.go170
-rw-r--r--src/pkg/math/cmplx/cmath_test.go866
-rw-r--r--src/pkg/math/cmplx/conj.go8
-rw-r--r--src/pkg/math/cmplx/exp.go55
-rw-r--r--src/pkg/math/cmplx/isinf.go21
-rw-r--r--src/pkg/math/cmplx/isnan.go25
-rw-r--r--src/pkg/math/cmplx/log.go64
-rw-r--r--src/pkg/math/cmplx/phase.go11
-rw-r--r--src/pkg/math/cmplx/polar.go12
-rw-r--r--src/pkg/math/cmplx/pow.go78
-rw-r--r--src/pkg/math/cmplx/rect.go13
-rw-r--r--src/pkg/math/cmplx/sin.go132
-rw-r--r--src/pkg/math/cmplx/sqrt.go104
-rw-r--r--src/pkg/math/cmplx/tan.go184
15 files changed, 0 insertions, 1755 deletions
diff --git a/src/pkg/math/cmplx/abs.go b/src/pkg/math/cmplx/abs.go
deleted file mode 100644
index f3cd1073e..000000000
--- a/src/pkg/math/cmplx/abs.go
+++ /dev/null
@@ -1,12 +0,0 @@
-// Copyright 2010 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.
-
-// Package cmplx provides basic constants and mathematical functions for
-// complex numbers.
-package cmplx
-
-import "math"
-
-// Abs returns the absolute value (also called the modulus) of x.
-func Abs(x complex128) float64 { return math.Hypot(real(x), imag(x)) }
diff --git a/src/pkg/math/cmplx/asin.go b/src/pkg/math/cmplx/asin.go
deleted file mode 100644
index 61880a257..000000000
--- a/src/pkg/math/cmplx/asin.go
+++ /dev/null
@@ -1,170 +0,0 @@
-// Copyright 2010 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.
-
-package cmplx
-
-import "math"
-
-// The original C code, the long comment, and the constants
-// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
-// The go code is a simplified version of the original C.
-//
-// Cephes Math Library Release 2.8: June, 2000
-// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
-//
-// The readme file at http://netlib.sandia.gov/cephes/ says:
-// Some software in this archive may be from the book _Methods and
-// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
-// International, 1989) or from the Cephes Mathematical Library, a
-// commercial product. In either event, it is copyrighted by the author.
-// What you see here may be used freely but it comes with no support or
-// guarantee.
-//
-// The two known misprints in the book are repaired here in the
-// source listings for the gamma function and the incomplete beta
-// integral.
-//
-// Stephen L. Moshier
-// moshier@na-net.ornl.gov
-
-// Complex circular arc sine
-//
-// DESCRIPTION:
-//
-// Inverse complex sine:
-// 2
-// w = -i clog( iz + csqrt( 1 - z ) ).
-//
-// casin(z) = -i casinh(iz)
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// DEC -10,+10 10100 2.1e-15 3.4e-16
-// IEEE -10,+10 30000 2.2e-14 2.7e-15
-// Larger relative error can be observed for z near zero.
-// Also tested by csin(casin(z)) = z.
-
-// Asin returns the inverse sine of x.
-func Asin(x complex128) complex128 {
- if imag(x) == 0 {
- if math.Abs(real(x)) > 1 {
- return complex(math.Pi/2, 0) // DOMAIN error
- }
- return complex(math.Asin(real(x)), 0)
- }
- ct := complex(-imag(x), real(x)) // i * x
- xx := x * x
- x1 := complex(1-real(xx), -imag(xx)) // 1 - x*x
- x2 := Sqrt(x1) // x2 = sqrt(1 - x*x)
- w := Log(ct + x2)
- return complex(imag(w), -real(w)) // -i * w
-}
-
-// Asinh returns the inverse hyperbolic sine of x.
-func Asinh(x complex128) complex128 {
- // TODO check range
- if imag(x) == 0 {
- if math.Abs(real(x)) > 1 {
- return complex(math.Pi/2, 0) // DOMAIN error
- }
- return complex(math.Asinh(real(x)), 0)
- }
- xx := x * x
- x1 := complex(1+real(xx), imag(xx)) // 1 + x*x
- return Log(x + Sqrt(x1)) // log(x + sqrt(1 + x*x))
-}
-
-// Complex circular arc cosine
-//
-// DESCRIPTION:
-//
-// w = arccos z = PI/2 - arcsin z.
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// DEC -10,+10 5200 1.6e-15 2.8e-16
-// IEEE -10,+10 30000 1.8e-14 2.2e-15
-
-// Acos returns the inverse cosine of x.
-func Acos(x complex128) complex128 {
- w := Asin(x)
- return complex(math.Pi/2-real(w), -imag(w))
-}
-
-// Acosh returns the inverse hyperbolic cosine of x.
-func Acosh(x complex128) complex128 {
- w := Acos(x)
- if imag(w) <= 0 {
- return complex(-imag(w), real(w)) // i * w
- }
- return complex(imag(w), -real(w)) // -i * w
-}
-
-// Complex circular arc tangent
-//
-// DESCRIPTION:
-//
-// If
-// z = x + iy,
-//
-// then
-// 1 ( 2x )
-// Re w = - arctan(-----------) + k PI
-// 2 ( 2 2)
-// (1 - x - y )
-//
-// ( 2 2)
-// 1 (x + (y+1) )
-// Im w = - log(------------)
-// 4 ( 2 2)
-// (x + (y-1) )
-//
-// Where k is an arbitrary integer.
-//
-// catan(z) = -i catanh(iz).
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// DEC -10,+10 5900 1.3e-16 7.8e-18
-// IEEE -10,+10 30000 2.3e-15 8.5e-17
-// The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
-// had peak relative error 1.5e-16, rms relative error
-// 2.9e-17. See also clog().
-
-// Atan returns the inverse tangent of x.
-func Atan(x complex128) complex128 {
- if real(x) == 0 && imag(x) > 1 {
- return NaN()
- }
-
- x2 := real(x) * real(x)
- a := 1 - x2 - imag(x)*imag(x)
- if a == 0 {
- return NaN()
- }
- t := 0.5 * math.Atan2(2*real(x), a)
- w := reducePi(t)
-
- t = imag(x) - 1
- b := x2 + t*t
- if b == 0 {
- return NaN()
- }
- t = imag(x) + 1
- c := (x2 + t*t) / b
- return complex(w, 0.25*math.Log(c))
-}
-
-// Atanh returns the inverse hyperbolic tangent of x.
-func Atanh(x complex128) complex128 {
- z := complex(-imag(x), real(x)) // z = i * x
- z = Atan(z)
- return complex(imag(z), -real(z)) // z = -i * z
-}
diff --git a/src/pkg/math/cmplx/cmath_test.go b/src/pkg/math/cmplx/cmath_test.go
deleted file mode 100644
index f285646af..000000000
--- a/src/pkg/math/cmplx/cmath_test.go
+++ /dev/null
@@ -1,866 +0,0 @@
-// Copyright 2010 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.
-
-package cmplx
-
-import (
- "math"
- "testing"
-)
-
-var vc26 = []complex128{
- (4.97901192488367350108546816 + 7.73887247457810456552351752i),
- (7.73887247457810456552351752 - 0.27688005719200159404635997i),
- (-0.27688005719200159404635997 - 5.01060361827107492160848778i),
- (-5.01060361827107492160848778 + 9.63629370719841737980004837i),
- (9.63629370719841737980004837 + 2.92637723924396464525443662i),
- (2.92637723924396464525443662 + 5.22908343145930665230025625i),
- (5.22908343145930665230025625 + 2.72793991043601025126008608i),
- (2.72793991043601025126008608 + 1.82530809168085506044576505i),
- (1.82530809168085506044576505 - 8.68592476857560136238589621i),
- (-8.68592476857560136238589621 + 4.97901192488367350108546816i),
-}
-var vc = []complex128{
- (4.9790119248836735e+00 + 7.7388724745781045e+00i),
- (7.7388724745781045e+00 - 2.7688005719200159e-01i),
- (-2.7688005719200159e-01 - 5.0106036182710749e+00i),
- (-5.0106036182710749e+00 + 9.6362937071984173e+00i),
- (9.6362937071984173e+00 + 2.9263772392439646e+00i),
- (2.9263772392439646e+00 + 5.2290834314593066e+00i),
- (5.2290834314593066e+00 + 2.7279399104360102e+00i),
- (2.7279399104360102e+00 + 1.8253080916808550e+00i),
- (1.8253080916808550e+00 - 8.6859247685756013e+00i),
- (-8.6859247685756013e+00 + 4.9790119248836735e+00i),
-}
-
-// The expected results below were computed by the high precision calculators
-// at http://keisan.casio.com/. More exact input values (array vc[], above)
-// were obtained by printing them with "%.26f". The answers were calculated
-// to 26 digits (by using the "Digit number" drop-down control of each
-// calculator).
-
-var abs = []float64{
- 9.2022120669932650313380972e+00,
- 7.7438239742296106616261394e+00,
- 5.0182478202557746902556648e+00,
- 1.0861137372799545160704002e+01,
- 1.0070841084922199607011905e+01,
- 5.9922447613166942183705192e+00,
- 5.8978784056736762299945176e+00,
- 3.2822866700678709020367184e+00,
- 8.8756430028990417290744307e+00,
- 1.0011785496777731986390856e+01,
-}
-
-var acos = []complex128{
- (1.0017679804707456328694569 - 2.9138232718554953784519807i),
- (0.03606427612041407369636057 + 2.7358584434576260925091256i),
- (1.6249365462333796703711823 + 2.3159537454335901187730929i),
- (2.0485650849650740120660391 - 3.0795576791204117911123886i),
- (0.29621132089073067282488147 - 3.0007392508200622519398814i),
- (1.0664555914934156601503632 - 2.4872865024796011364747111i),
- (0.48681307452231387690013905 - 2.463655912283054555225301i),
- (0.6116977071277574248407752 - 1.8734458851737055262693056i),
- (1.3649311280370181331184214 + 2.8793528632328795424123832i),
- (2.6189310485682988308904501 - 2.9956543302898767795858704i),
-}
-var acosh = []complex128{
- (2.9138232718554953784519807 + 1.0017679804707456328694569i),
- (2.7358584434576260925091256 - 0.03606427612041407369636057i),
- (2.3159537454335901187730929 - 1.6249365462333796703711823i),
- (3.0795576791204117911123886 + 2.0485650849650740120660391i),
- (3.0007392508200622519398814 + 0.29621132089073067282488147i),
- (2.4872865024796011364747111 + 1.0664555914934156601503632i),
- (2.463655912283054555225301 + 0.48681307452231387690013905i),
- (1.8734458851737055262693056 + 0.6116977071277574248407752i),
- (2.8793528632328795424123832 - 1.3649311280370181331184214i),
- (2.9956543302898767795858704 + 2.6189310485682988308904501i),
-}
-var asin = []complex128{
- (0.56902834632415098636186476 + 2.9138232718554953784519807i),
- (1.5347320506744825455349611 - 2.7358584434576260925091256i),
- (-0.054140219438483051139860579 - 2.3159537454335901187730929i),
- (-0.47776875817017739283471738 + 3.0795576791204117911123886i),
- (1.2745850059041659464064402 + 3.0007392508200622519398814i),
- (0.50434073530148095908095852 + 2.4872865024796011364747111i),
- (1.0839832522725827423311826 + 2.463655912283054555225301i),
- (0.9590986196671391943905465 + 1.8734458851737055262693056i),
- (0.20586519875787848611290031 - 2.8793528632328795424123832i),
- (-1.0481347217734022116591284 + 2.9956543302898767795858704i),
-}
-var asinh = []complex128{
- (2.9113760469415295679342185 + 0.99639459545704326759805893i),
- (2.7441755423994259061579029 - 0.035468308789000500601119392i),
- (-2.2962136462520690506126678 - 1.5144663565690151885726707i),
- (-3.0771233459295725965402455 + 1.0895577967194013849422294i),
- (3.0048366100923647417557027 + 0.29346979169819220036454168i),
- (2.4800059370795363157364643 + 1.0545868606049165710424232i),
- (2.4718773838309585611141821 + 0.47502344364250803363708842i),
- (1.8910743588080159144378396 + 0.56882925572563602341139174i),
- (2.8735426423367341878069406 - 1.362376149648891420997548i),
- (-2.9981750586172477217567878 + 0.5183571985225367505624207i),
-}
-var atan = []complex128{
- (1.5115747079332741358607654 + 0.091324403603954494382276776i),
- (1.4424504323482602560806727 - 0.0045416132642803911503770933i),
- (-1.5593488703630532674484026 - 0.20163295409248362456446431i),
- (-1.5280619472445889867794105 + 0.081721556230672003746956324i),
- (1.4759909163240799678221039 + 0.028602969320691644358773586i),
- (1.4877353772046548932715555 + 0.14566877153207281663773599i),
- (1.4206983927779191889826 + 0.076830486127880702249439993i),
- (1.3162236060498933364869556 + 0.16031313000467530644933363i),
- (1.5473450684303703578810093 - 0.11064907507939082484935782i),
- (-1.4841462340185253987375812 + 0.049341850305024399493142411i),
-}
-var atanh = []complex128{
- (0.058375027938968509064640438 + 1.4793488495105334458167782i),
- (0.12977343497790381229915667 - 1.5661009410463561327262499i),
- (-0.010576456067347252072200088 - 1.3743698658402284549750563i),
- (-0.042218595678688358882784918 + 1.4891433968166405606692604i),
- (0.095218997991316722061828397 + 1.5416884098777110330499698i),
- (0.079965459366890323857556487 + 1.4252510353873192700350435i),
- (0.15051245471980726221708301 + 1.4907432533016303804884461i),
- (0.25082072933993987714470373 + 1.392057665392187516442986i),
- (0.022896108815797135846276662 - 1.4609224989282864208963021i),
- (-0.08665624101841876130537396 + 1.5207902036935093480142159i),
-}
-var conj = []complex128{
- (4.9790119248836735e+00 - 7.7388724745781045e+00i),
- (7.7388724745781045e+00 + 2.7688005719200159e-01i),
- (-2.7688005719200159e-01 + 5.0106036182710749e+00i),
- (-5.0106036182710749e+00 - 9.6362937071984173e+00i),
- (9.6362937071984173e+00 - 2.9263772392439646e+00i),
- (2.9263772392439646e+00 - 5.2290834314593066e+00i),
- (5.2290834314593066e+00 - 2.7279399104360102e+00i),
- (2.7279399104360102e+00 - 1.8253080916808550e+00i),
- (1.8253080916808550e+00 + 8.6859247685756013e+00i),
- (-8.6859247685756013e+00 - 4.9790119248836735e+00i),
-}
-var cos = []complex128{
- (3.024540920601483938336569e+02 + 1.1073797572517071650045357e+03i),
- (1.192858682649064973252758e-01 + 2.7857554122333065540970207e-01i),
- (7.2144394304528306603857962e+01 - 2.0500129667076044169954205e+01i),
- (2.24921952538403984190541e+03 - 7.317363745602773587049329e+03i),
- (-9.148222970032421760015498e+00 + 1.953124661113563541862227e+00i),
- (-9.116081175857732248227078e+01 - 1.992669213569952232487371e+01i),
- (3.795639179042704640002918e+00 + 6.623513350981458399309662e+00i),
- (-2.9144840732498869560679084e+00 - 1.214620271628002917638748e+00i),
- (-7.45123482501299743872481e+02 + 2.8641692314488080814066734e+03i),
- (-5.371977967039319076416747e+01 + 4.893348341339375830564624e+01i),
-}
-var cosh = []complex128{
- (8.34638383523018249366948e+00 + 7.2181057886425846415112064e+01i),
- (1.10421967379919366952251e+03 - 3.1379638689277575379469861e+02i),
- (3.051485206773701584738512e-01 - 2.6805384730105297848044485e-01i),
- (-7.33294728684187933370938e+01 + 1.574445942284918251038144e+01i),
- (-7.478643293945957535757355e+03 + 1.6348382209913353929473321e+03i),
- (4.622316522966235701630926e+00 - 8.088695185566375256093098e+00i),
- (-8.544333183278877406197712e+01 + 3.7505836120128166455231717e+01i),
- (-1.934457815021493925115198e+00 + 7.3725859611767228178358673e+00i),
- (-2.352958770061749348353548e+00 - 2.034982010440878358915409e+00i),
- (7.79756457532134748165069e+02 + 2.8549350716819176560377717e+03i),
-}
-var exp = []complex128{
- (1.669197736864670815125146e+01 + 1.4436895109507663689174096e+02i),
- (2.2084389286252583447276212e+03 - 6.2759289284909211238261917e+02i),
- (2.227538273122775173434327e-01 + 7.2468284028334191250470034e-01i),
- (-6.5182985958153548997881627e-03 - 1.39965837915193860879044e-03i),
- (-1.4957286524084015746110777e+04 + 3.269676455931135688988042e+03i),
- (9.218158701983105935659273e+00 - 1.6223985291084956009304582e+01i),
- (-1.7088175716853040841444505e+02 + 7.501382609870410713795546e+01i),
- (-3.852461315830959613132505e+00 + 1.4808420423156073221970892e+01i),
- (-4.586775503301407379786695e+00 - 4.178501081246873415144744e+00i),
- (4.451337963005453491095747e-05 - 1.62977574205442915935263e-04i),
-}
-var log = []complex128{
- (2.2194438972179194425697051e+00 + 9.9909115046919291062461269e-01i),
- (2.0468956191154167256337289e+00 - 3.5762575021856971295156489e-02i),
- (1.6130808329853860438751244e+00 - 1.6259990074019058442232221e+00i),
- (2.3851910394823008710032651e+00 + 2.0502936359659111755031062e+00i),
- (2.3096442270679923004800651e+00 + 2.9483213155446756211881774e-01i),
- (1.7904660933974656106951860e+00 + 1.0605860367252556281902109e+00i),
- (1.7745926939841751666177512e+00 + 4.8084556083358307819310911e-01i),
- (1.1885403350045342425648780e+00 + 5.8969634164776659423195222e-01i),
- (2.1833107837679082586772505e+00 - 1.3636647724582455028314573e+00i),
- (2.3037629487273259170991671e+00 + 2.6210913895386013290915234e+00i),
-}
-var log10 = []complex128{
- (9.6389223745559042474184943e-01 + 4.338997735671419492599631e-01i),
- (8.8895547241376579493490892e-01 - 1.5531488990643548254864806e-02i),
- (7.0055210462945412305244578e-01 - 7.0616239649481243222248404e-01i),
- (1.0358753067322445311676952e+00 + 8.9043121238134980156490909e-01i),
- (1.003065742975330237172029e+00 + 1.2804396782187887479857811e-01i),
- (7.7758954439739162532085157e-01 + 4.6060666333341810869055108e-01i),
- (7.7069581462315327037689152e-01 + 2.0882857371769952195512475e-01i),
- (5.1617650901191156135137239e-01 + 2.5610186717615977620363299e-01i),
- (9.4819982567026639742663212e-01 - 5.9223208584446952284914289e-01i),
- (1.0005115362454417135973429e+00 + 1.1383255270407412817250921e+00i),
-}
-
-type ff struct {
- r, theta float64
-}
-
-var polar = []ff{
- {9.2022120669932650313380972e+00, 9.9909115046919291062461269e-01},
- {7.7438239742296106616261394e+00, -3.5762575021856971295156489e-02},
- {5.0182478202557746902556648e+00, -1.6259990074019058442232221e+00},
- {1.0861137372799545160704002e+01, 2.0502936359659111755031062e+00},
- {1.0070841084922199607011905e+01, 2.9483213155446756211881774e-01},
- {5.9922447613166942183705192e+00, 1.0605860367252556281902109e+00},
- {5.8978784056736762299945176e+00, 4.8084556083358307819310911e-01},
- {3.2822866700678709020367184e+00, 5.8969634164776659423195222e-01},
- {8.8756430028990417290744307e+00, -1.3636647724582455028314573e+00},
- {1.0011785496777731986390856e+01, 2.6210913895386013290915234e+00},
-}
-var pow = []complex128{
- (-2.499956739197529585028819e+00 + 1.759751724335650228957144e+00i),
- (7.357094338218116311191939e+04 - 5.089973412479151648145882e+04i),
- (1.320777296067768517259592e+01 - 3.165621914333901498921986e+01i),
- (-3.123287828297300934072149e-07 - 1.9849567521490553032502223E-7i),
- (8.0622651468477229614813e+04 - 7.80028727944573092944363e+04i),
- (-1.0268824572103165858577141e+00 - 4.716844738244989776610672e-01i),
- (-4.35953819012244175753187e+01 + 2.2036445974645306917648585e+02i),
- (8.3556092283250594950239e-01 - 1.2261571947167240272593282e+01i),
- (1.582292972120769306069625e+03 + 1.273564263524278244782512e+04i),
- (6.592208301642122149025369e-08 + 2.584887236651661903526389e-08i),
-}
-var sin = []complex128{
- (-1.1073801774240233539648544e+03 + 3.024539773002502192425231e+02i),
- (1.0317037521400759359744682e+00 - 3.2208979799929570242818e-02i),
- (-2.0501952097271429804261058e+01 - 7.2137981348240798841800967e+01i),
- (7.3173638080346338642193078e+03 + 2.249219506193664342566248e+03i),
- (-1.964375633631808177565226e+00 - 9.0958264713870404464159683e+00i),
- (1.992783647158514838337674e+01 - 9.11555769410191350416942e+01i),
- (-6.680335650741921444300349e+00 + 3.763353833142432513086117e+00i),
- (1.2794028166657459148245993e+00 - 2.7669092099795781155109602e+00i),
- (2.8641693949535259594188879e+03 + 7.451234399649871202841615e+02i),
- (-4.893811726244659135553033e+01 - 5.371469305562194635957655e+01i),
-}
-var sinh = []complex128{
- (8.34559353341652565758198e+00 + 7.2187893208650790476628899e+01i),
- (1.1042192548260646752051112e+03 - 3.1379650595631635858792056e+02i),
- (-8.239469336509264113041849e-02 + 9.9273668758439489098514519e-01i),
- (7.332295456982297798219401e+01 - 1.574585908122833444899023e+01i),
- (-7.4786432301380582103534216e+03 + 1.63483823493980029604071e+03i),
- (4.595842179016870234028347e+00 - 8.135290105518580753211484e+00i),
- (-8.543842533574163435246793e+01 + 3.750798997857594068272375e+01i),
- (-1.918003500809465688017307e+00 + 7.4358344619793504041350251e+00i),
- (-2.233816733239658031433147e+00 - 2.143519070805995056229335e+00i),
- (-7.797564130187551181105341e+02 - 2.8549352346594918614806877e+03i),
-}
-var sqrt = []complex128{
- (2.6628203086086130543813948e+00 + 1.4531345674282185229796902e+00i),
- (2.7823278427251986247149295e+00 - 4.9756907317005224529115567e-02i),
- (1.5397025302089642757361015e+00 - 1.6271336573016637535695727e+00i),
- (1.7103411581506875260277898e+00 + 2.8170677122737589676157029e+00i),
- (3.1390392472953103383607947e+00 + 4.6612625849858653248980849e-01i),
- (2.1117080764822417640789287e+00 + 1.2381170223514273234967850e+00i),
- (2.3587032281672256703926939e+00 + 5.7827111903257349935720172e-01i),
- (1.7335262588873410476661577e+00 + 5.2647258220721269141550382e-01i),
- (2.3131094974708716531499282e+00 - 1.8775429304303785570775490e+00i),
- (8.1420535745048086240947359e-01 + 3.0575897587277248522656113e+00i),
-}
-var tan = []complex128{
- (-1.928757919086441129134525e-07 + 1.0000003267499169073251826e+00i),
- (1.242412685364183792138948e+00 - 3.17149693883133370106696e+00i),
- (-4.6745126251587795225571826e-05 - 9.9992439225263959286114298e-01i),
- (4.792363401193648192887116e-09 + 1.0000000070589333451557723e+00i),
- (2.345740824080089140287315e-03 + 9.947733046570988661022763e-01i),
- (-2.396030789494815566088809e-05 + 9.9994781345418591429826779e-01i),
- (-7.370204836644931340905303e-03 + 1.0043553413417138987717748e+00i),
- (-3.691803847992048527007457e-02 + 9.6475071993469548066328894e-01i),
- (-2.781955256713729368401878e-08 - 1.000000049848910609006646e+00i),
- (9.4281590064030478879791249e-05 + 9.9999119340863718183758545e-01i),
-}
-var tanh = []complex128{
- (1.0000921981225144748819918e+00 + 2.160986245871518020231507e-05i),
- (9.9999967727531993209562591e-01 - 1.9953763222959658873657676e-07i),
- (-1.765485739548037260789686e+00 + 1.7024216325552852445168471e+00i),
- (-9.999189442732736452807108e-01 + 3.64906070494473701938098e-05i),
- (9.9999999224622333738729767e-01 - 3.560088949517914774813046e-09i),
- (1.0029324933367326862499343e+00 - 4.948790309797102353137528e-03i),
- (9.9996113064788012488693567e-01 - 4.226995742097032481451259e-05i),
- (1.0074784189316340029873945e+00 - 4.194050814891697808029407e-03i),
- (9.9385534229718327109131502e-01 + 5.144217985914355502713437e-02i),
- (-1.0000000491604982429364892e+00 - 2.901873195374433112227349e-08i),
-}
-
-// special cases
-var vcAbsSC = []complex128{
- NaN(),
-}
-var absSC = []float64{
- math.NaN(),
-}
-var vcAcosSC = []complex128{
- NaN(),
-}
-var acosSC = []complex128{
- NaN(),
-}
-var vcAcoshSC = []complex128{
- NaN(),
-}
-var acoshSC = []complex128{
- NaN(),
-}
-var vcAsinSC = []complex128{
- NaN(),
-}
-var asinSC = []complex128{
- NaN(),
-}
-var vcAsinhSC = []complex128{
- NaN(),
-}
-var asinhSC = []complex128{
- NaN(),
-}
-var vcAtanSC = []complex128{
- NaN(),
-}
-var atanSC = []complex128{
- NaN(),
-}
-var vcAtanhSC = []complex128{
- NaN(),
-}
-var atanhSC = []complex128{
- NaN(),
-}
-var vcConjSC = []complex128{
- NaN(),
-}
-var conjSC = []complex128{
- NaN(),
-}
-var vcCosSC = []complex128{
- NaN(),
-}
-var cosSC = []complex128{
- NaN(),
-}
-var vcCoshSC = []complex128{
- NaN(),
-}
-var coshSC = []complex128{
- NaN(),
-}
-var vcExpSC = []complex128{
- NaN(),
-}
-var expSC = []complex128{
- NaN(),
-}
-var vcIsNaNSC = []complex128{
- complex(math.Inf(-1), math.Inf(-1)),
- complex(math.Inf(-1), math.NaN()),
- complex(math.NaN(), math.Inf(-1)),
- complex(0, math.NaN()),
- complex(math.NaN(), 0),
- complex(math.Inf(1), math.Inf(1)),
- complex(math.Inf(1), math.NaN()),
- complex(math.NaN(), math.Inf(1)),
- complex(math.NaN(), math.NaN()),
-}
-var isNaNSC = []bool{
- false,
- false,
- false,
- true,
- true,
- false,
- false,
- false,
- true,
-}
-var vcLogSC = []complex128{
- NaN(),
-}
-var logSC = []complex128{
- NaN(),
-}
-var vcLog10SC = []complex128{
- NaN(),
-}
-var log10SC = []complex128{
- NaN(),
-}
-var vcPolarSC = []complex128{
- NaN(),
-}
-var polarSC = []ff{
- {math.NaN(), math.NaN()},
-}
-var vcPowSC = [][2]complex128{
- {NaN(), NaN()},
-}
-var powSC = []complex128{
- NaN(),
-}
-var vcSinSC = []complex128{
- NaN(),
-}
-var sinSC = []complex128{
- NaN(),
-}
-var vcSinhSC = []complex128{
- NaN(),
-}
-var sinhSC = []complex128{
- NaN(),
-}
-var vcSqrtSC = []complex128{
- NaN(),
-}
-var sqrtSC = []complex128{
- NaN(),
-}
-var vcTanSC = []complex128{
- NaN(),
-}
-var tanSC = []complex128{
- NaN(),
-}
-var vcTanhSC = []complex128{
- NaN(),
-}
-var tanhSC = []complex128{
- NaN(),
-}
-
-// functions borrowed from pkg/math/all_test.go
-func tolerance(a, b, e float64) bool {
- d := a - b
- if d < 0 {
- d = -d
- }
-
- if a != 0 {
- e = e * a
- if e < 0 {
- e = -e
- }
- }
- return d < e
-}
-func soclose(a, b, e float64) bool { return tolerance(a, b, e) }
-func veryclose(a, b float64) bool { return tolerance(a, b, 4e-16) }
-func alike(a, b float64) bool {
- switch {
- case a != a && b != b: // math.IsNaN(a) && math.IsNaN(b):
- return true
- case a == b:
- return math.Signbit(a) == math.Signbit(b)
- }
- return false
-}
-
-func cTolerance(a, b complex128, e float64) bool {
- d := Abs(a - b)
- if a != 0 {
- e = e * Abs(a)
- if e < 0 {
- e = -e
- }
- }
- return d < e
-}
-func cSoclose(a, b complex128, e float64) bool { return cTolerance(a, b, e) }
-func cVeryclose(a, b complex128) bool { return cTolerance(a, b, 4e-16) }
-func cAlike(a, b complex128) bool {
- switch {
- case IsNaN(a) && IsNaN(b):
- return true
- case a == b:
- return math.Signbit(real(a)) == math.Signbit(real(b)) && math.Signbit(imag(a)) == math.Signbit(imag(b))
- }
- return false
-}
-
-func TestAbs(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Abs(vc[i]); !veryclose(abs[i], f) {
- t.Errorf("Abs(%g) = %g, want %g", vc[i], f, abs[i])
- }
- }
- for i := 0; i < len(vcAbsSC); i++ {
- if f := Abs(vcAbsSC[i]); !alike(absSC[i], f) {
- t.Errorf("Abs(%g) = %g, want %g", vcAbsSC[i], f, absSC[i])
- }
- }
-}
-func TestAcos(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Acos(vc[i]); !cSoclose(acos[i], f, 1e-14) {
- t.Errorf("Acos(%g) = %g, want %g", vc[i], f, acos[i])
- }
- }
- for i := 0; i < len(vcAcosSC); i++ {
- if f := Acos(vcAcosSC[i]); !cAlike(acosSC[i], f) {
- t.Errorf("Acos(%g) = %g, want %g", vcAcosSC[i], f, acosSC[i])
- }
- }
-}
-func TestAcosh(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Acosh(vc[i]); !cSoclose(acosh[i], f, 1e-14) {
- t.Errorf("Acosh(%g) = %g, want %g", vc[i], f, acosh[i])
- }
- }
- for i := 0; i < len(vcAcoshSC); i++ {
- if f := Acosh(vcAcoshSC[i]); !cAlike(acoshSC[i], f) {
- t.Errorf("Acosh(%g) = %g, want %g", vcAcoshSC[i], f, acoshSC[i])
- }
- }
-}
-func TestAsin(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Asin(vc[i]); !cSoclose(asin[i], f, 1e-14) {
- t.Errorf("Asin(%g) = %g, want %g", vc[i], f, asin[i])
- }
- }
- for i := 0; i < len(vcAsinSC); i++ {
- if f := Asin(vcAsinSC[i]); !cAlike(asinSC[i], f) {
- t.Errorf("Asin(%g) = %g, want %g", vcAsinSC[i], f, asinSC[i])
- }
- }
-}
-func TestAsinh(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Asinh(vc[i]); !cSoclose(asinh[i], f, 4e-15) {
- t.Errorf("Asinh(%g) = %g, want %g", vc[i], f, asinh[i])
- }
- }
- for i := 0; i < len(vcAsinhSC); i++ {
- if f := Asinh(vcAsinhSC[i]); !cAlike(asinhSC[i], f) {
- t.Errorf("Asinh(%g) = %g, want %g", vcAsinhSC[i], f, asinhSC[i])
- }
- }
-}
-func TestAtan(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Atan(vc[i]); !cVeryclose(atan[i], f) {
- t.Errorf("Atan(%g) = %g, want %g", vc[i], f, atan[i])
- }
- }
- for i := 0; i < len(vcAtanSC); i++ {
- if f := Atan(vcAtanSC[i]); !cAlike(atanSC[i], f) {
- t.Errorf("Atan(%g) = %g, want %g", vcAtanSC[i], f, atanSC[i])
- }
- }
-}
-func TestAtanh(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Atanh(vc[i]); !cVeryclose(atanh[i], f) {
- t.Errorf("Atanh(%g) = %g, want %g", vc[i], f, atanh[i])
- }
- }
- for i := 0; i < len(vcAtanhSC); i++ {
- if f := Atanh(vcAtanhSC[i]); !cAlike(atanhSC[i], f) {
- t.Errorf("Atanh(%g) = %g, want %g", vcAtanhSC[i], f, atanhSC[i])
- }
- }
-}
-func TestConj(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Conj(vc[i]); !cVeryclose(conj[i], f) {
- t.Errorf("Conj(%g) = %g, want %g", vc[i], f, conj[i])
- }
- }
- for i := 0; i < len(vcConjSC); i++ {
- if f := Conj(vcConjSC[i]); !cAlike(conjSC[i], f) {
- t.Errorf("Conj(%g) = %g, want %g", vcConjSC[i], f, conjSC[i])
- }
- }
-}
-func TestCos(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Cos(vc[i]); !cSoclose(cos[i], f, 3e-15) {
- t.Errorf("Cos(%g) = %g, want %g", vc[i], f, cos[i])
- }
- }
- for i := 0; i < len(vcCosSC); i++ {
- if f := Cos(vcCosSC[i]); !cAlike(cosSC[i], f) {
- t.Errorf("Cos(%g) = %g, want %g", vcCosSC[i], f, cosSC[i])
- }
- }
-}
-func TestCosh(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Cosh(vc[i]); !cSoclose(cosh[i], f, 2e-15) {
- t.Errorf("Cosh(%g) = %g, want %g", vc[i], f, cosh[i])
- }
- }
- for i := 0; i < len(vcCoshSC); i++ {
- if f := Cosh(vcCoshSC[i]); !cAlike(coshSC[i], f) {
- t.Errorf("Cosh(%g) = %g, want %g", vcCoshSC[i], f, coshSC[i])
- }
- }
-}
-func TestExp(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Exp(vc[i]); !cSoclose(exp[i], f, 1e-15) {
- t.Errorf("Exp(%g) = %g, want %g", vc[i], f, exp[i])
- }
- }
- for i := 0; i < len(vcExpSC); i++ {
- if f := Exp(vcExpSC[i]); !cAlike(expSC[i], f) {
- t.Errorf("Exp(%g) = %g, want %g", vcExpSC[i], f, expSC[i])
- }
- }
-}
-func TestIsNaN(t *testing.T) {
- for i := 0; i < len(vcIsNaNSC); i++ {
- if f := IsNaN(vcIsNaNSC[i]); isNaNSC[i] != f {
- t.Errorf("IsNaN(%v) = %v, want %v", vcIsNaNSC[i], f, isNaNSC[i])
- }
- }
-}
-func TestLog(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Log(vc[i]); !cVeryclose(log[i], f) {
- t.Errorf("Log(%g) = %g, want %g", vc[i], f, log[i])
- }
- }
- for i := 0; i < len(vcLogSC); i++ {
- if f := Log(vcLogSC[i]); !cAlike(logSC[i], f) {
- t.Errorf("Log(%g) = %g, want %g", vcLogSC[i], f, logSC[i])
- }
- }
-}
-func TestLog10(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Log10(vc[i]); !cVeryclose(log10[i], f) {
- t.Errorf("Log10(%g) = %g, want %g", vc[i], f, log10[i])
- }
- }
- for i := 0; i < len(vcLog10SC); i++ {
- if f := Log10(vcLog10SC[i]); !cAlike(log10SC[i], f) {
- t.Errorf("Log10(%g) = %g, want %g", vcLog10SC[i], f, log10SC[i])
- }
- }
-}
-func TestPolar(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if r, theta := Polar(vc[i]); !veryclose(polar[i].r, r) && !veryclose(polar[i].theta, theta) {
- t.Errorf("Polar(%g) = %g, %g want %g, %g", vc[i], r, theta, polar[i].r, polar[i].theta)
- }
- }
- for i := 0; i < len(vcPolarSC); i++ {
- if r, theta := Polar(vcPolarSC[i]); !alike(polarSC[i].r, r) && !alike(polarSC[i].theta, theta) {
- t.Errorf("Polar(%g) = %g, %g, want %g, %g", vcPolarSC[i], r, theta, polarSC[i].r, polarSC[i].theta)
- }
- }
-}
-func TestPow(t *testing.T) {
- // Special cases for Pow(0, c).
- var zero = complex(0, 0)
- zeroPowers := [][2]complex128{
- {0, 1 + 0i},
- {1.5, 0 + 0i},
- {-1.5, complex(math.Inf(0), 0)},
- {-1.5 + 1.5i, Inf()},
- }
- for _, zp := range zeroPowers {
- if f := Pow(zero, zp[0]); f != zp[1] {
- t.Errorf("Pow(%g, %g) = %g, want %g", zero, zp[0], f, zp[1])
- }
- }
- var a = complex(3.0, 3.0)
- for i := 0; i < len(vc); i++ {
- if f := Pow(a, vc[i]); !cSoclose(pow[i], f, 4e-15) {
- t.Errorf("Pow(%g, %g) = %g, want %g", a, vc[i], f, pow[i])
- }
- }
- for i := 0; i < len(vcPowSC); i++ {
- if f := Pow(vcPowSC[i][0], vcPowSC[i][0]); !cAlike(powSC[i], f) {
- t.Errorf("Pow(%g, %g) = %g, want %g", vcPowSC[i][0], vcPowSC[i][0], f, powSC[i])
- }
- }
-}
-func TestRect(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Rect(polar[i].r, polar[i].theta); !cVeryclose(vc[i], f) {
- t.Errorf("Rect(%g, %g) = %g want %g", polar[i].r, polar[i].theta, f, vc[i])
- }
- }
- for i := 0; i < len(vcPolarSC); i++ {
- if f := Rect(polarSC[i].r, polarSC[i].theta); !cAlike(vcPolarSC[i], f) {
- t.Errorf("Rect(%g, %g) = %g, want %g", polarSC[i].r, polarSC[i].theta, f, vcPolarSC[i])
- }
- }
-}
-func TestSin(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Sin(vc[i]); !cSoclose(sin[i], f, 2e-15) {
- t.Errorf("Sin(%g) = %g, want %g", vc[i], f, sin[i])
- }
- }
- for i := 0; i < len(vcSinSC); i++ {
- if f := Sin(vcSinSC[i]); !cAlike(sinSC[i], f) {
- t.Errorf("Sin(%g) = %g, want %g", vcSinSC[i], f, sinSC[i])
- }
- }
-}
-func TestSinh(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Sinh(vc[i]); !cSoclose(sinh[i], f, 2e-15) {
- t.Errorf("Sinh(%g) = %g, want %g", vc[i], f, sinh[i])
- }
- }
- for i := 0; i < len(vcSinhSC); i++ {
- if f := Sinh(vcSinhSC[i]); !cAlike(sinhSC[i], f) {
- t.Errorf("Sinh(%g) = %g, want %g", vcSinhSC[i], f, sinhSC[i])
- }
- }
-}
-func TestSqrt(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Sqrt(vc[i]); !cVeryclose(sqrt[i], f) {
- t.Errorf("Sqrt(%g) = %g, want %g", vc[i], f, sqrt[i])
- }
- }
- for i := 0; i < len(vcSqrtSC); i++ {
- if f := Sqrt(vcSqrtSC[i]); !cAlike(sqrtSC[i], f) {
- t.Errorf("Sqrt(%g) = %g, want %g", vcSqrtSC[i], f, sqrtSC[i])
- }
- }
-}
-func TestTan(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Tan(vc[i]); !cSoclose(tan[i], f, 3e-15) {
- t.Errorf("Tan(%g) = %g, want %g", vc[i], f, tan[i])
- }
- }
- for i := 0; i < len(vcTanSC); i++ {
- if f := Tan(vcTanSC[i]); !cAlike(tanSC[i], f) {
- t.Errorf("Tan(%g) = %g, want %g", vcTanSC[i], f, tanSC[i])
- }
- }
-}
-func TestTanh(t *testing.T) {
- for i := 0; i < len(vc); i++ {
- if f := Tanh(vc[i]); !cSoclose(tanh[i], f, 2e-15) {
- t.Errorf("Tanh(%g) = %g, want %g", vc[i], f, tanh[i])
- }
- }
- for i := 0; i < len(vcTanhSC); i++ {
- if f := Tanh(vcTanhSC[i]); !cAlike(tanhSC[i], f) {
- t.Errorf("Tanh(%g) = %g, want %g", vcTanhSC[i], f, tanhSC[i])
- }
- }
-}
-
-func BenchmarkAbs(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Abs(complex(2.5, 3.5))
- }
-}
-func BenchmarkAcos(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Acos(complex(2.5, 3.5))
- }
-}
-func BenchmarkAcosh(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Acosh(complex(2.5, 3.5))
- }
-}
-func BenchmarkAsin(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Asin(complex(2.5, 3.5))
- }
-}
-func BenchmarkAsinh(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Asinh(complex(2.5, 3.5))
- }
-}
-func BenchmarkAtan(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Atan(complex(2.5, 3.5))
- }
-}
-func BenchmarkAtanh(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Atanh(complex(2.5, 3.5))
- }
-}
-func BenchmarkConj(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Conj(complex(2.5, 3.5))
- }
-}
-func BenchmarkCos(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Cos(complex(2.5, 3.5))
- }
-}
-func BenchmarkCosh(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Cosh(complex(2.5, 3.5))
- }
-}
-func BenchmarkExp(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Exp(complex(2.5, 3.5))
- }
-}
-func BenchmarkLog(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Log(complex(2.5, 3.5))
- }
-}
-func BenchmarkLog10(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Log10(complex(2.5, 3.5))
- }
-}
-func BenchmarkPhase(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Phase(complex(2.5, 3.5))
- }
-}
-func BenchmarkPolar(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Polar(complex(2.5, 3.5))
- }
-}
-func BenchmarkPow(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Pow(complex(2.5, 3.5), complex(2.5, 3.5))
- }
-}
-func BenchmarkRect(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Rect(2.5, 1.5)
- }
-}
-func BenchmarkSin(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Sin(complex(2.5, 3.5))
- }
-}
-func BenchmarkSinh(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Sinh(complex(2.5, 3.5))
- }
-}
-func BenchmarkSqrt(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Sqrt(complex(2.5, 3.5))
- }
-}
-func BenchmarkTan(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Tan(complex(2.5, 3.5))
- }
-}
-func BenchmarkTanh(b *testing.B) {
- for i := 0; i < b.N; i++ {
- Tanh(complex(2.5, 3.5))
- }
-}
diff --git a/src/pkg/math/cmplx/conj.go b/src/pkg/math/cmplx/conj.go
deleted file mode 100644
index 34a4277c1..000000000
--- a/src/pkg/math/cmplx/conj.go
+++ /dev/null
@@ -1,8 +0,0 @@
-// Copyright 2010 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.
-
-package cmplx
-
-// Conj returns the complex conjugate of x.
-func Conj(x complex128) complex128 { return complex(real(x), -imag(x)) }
diff --git a/src/pkg/math/cmplx/exp.go b/src/pkg/math/cmplx/exp.go
deleted file mode 100644
index 485ed2c78..000000000
--- a/src/pkg/math/cmplx/exp.go
+++ /dev/null
@@ -1,55 +0,0 @@
-// Copyright 2010 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.
-
-package cmplx
-
-import "math"
-
-// The original C code, the long comment, and the constants
-// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
-// The go code is a simplified version of the original C.
-//
-// Cephes Math Library Release 2.8: June, 2000
-// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
-//
-// The readme file at http://netlib.sandia.gov/cephes/ says:
-// Some software in this archive may be from the book _Methods and
-// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
-// International, 1989) or from the Cephes Mathematical Library, a
-// commercial product. In either event, it is copyrighted by the author.
-// What you see here may be used freely but it comes with no support or
-// guarantee.
-//
-// The two known misprints in the book are repaired here in the
-// source listings for the gamma function and the incomplete beta
-// integral.
-//
-// Stephen L. Moshier
-// moshier@na-net.ornl.gov
-
-// Complex exponential function
-//
-// DESCRIPTION:
-//
-// Returns the complex exponential of the complex argument z.
-//
-// If
-// z = x + iy,
-// r = exp(x),
-// then
-// w = r cos y + i r sin y.
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// DEC -10,+10 8700 3.7e-17 1.1e-17
-// IEEE -10,+10 30000 3.0e-16 8.7e-17
-
-// Exp returns e**x, the base-e exponential of x.
-func Exp(x complex128) complex128 {
- r := math.Exp(real(x))
- s, c := math.Sincos(imag(x))
- return complex(r*c, r*s)
-}
diff --git a/src/pkg/math/cmplx/isinf.go b/src/pkg/math/cmplx/isinf.go
deleted file mode 100644
index d5a65b44b..000000000
--- a/src/pkg/math/cmplx/isinf.go
+++ /dev/null
@@ -1,21 +0,0 @@
-// Copyright 2010 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.
-
-package cmplx
-
-import "math"
-
-// IsInf returns true if either real(x) or imag(x) is an infinity.
-func IsInf(x complex128) bool {
- if math.IsInf(real(x), 0) || math.IsInf(imag(x), 0) {
- return true
- }
- return false
-}
-
-// Inf returns a complex infinity, complex(+Inf, +Inf).
-func Inf() complex128 {
- inf := math.Inf(1)
- return complex(inf, inf)
-}
diff --git a/src/pkg/math/cmplx/isnan.go b/src/pkg/math/cmplx/isnan.go
deleted file mode 100644
index 05d0cce63..000000000
--- a/src/pkg/math/cmplx/isnan.go
+++ /dev/null
@@ -1,25 +0,0 @@
-// Copyright 2010 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.
-
-package cmplx
-
-import "math"
-
-// IsNaN returns true if either real(x) or imag(x) is NaN
-// and neither is an infinity.
-func IsNaN(x complex128) bool {
- switch {
- case math.IsInf(real(x), 0) || math.IsInf(imag(x), 0):
- return false
- case math.IsNaN(real(x)) || math.IsNaN(imag(x)):
- return true
- }
- return false
-}
-
-// NaN returns a complex ``not-a-number'' value.
-func NaN() complex128 {
- nan := math.NaN()
- return complex(nan, nan)
-}
diff --git a/src/pkg/math/cmplx/log.go b/src/pkg/math/cmplx/log.go
deleted file mode 100644
index 881a064d8..000000000
--- a/src/pkg/math/cmplx/log.go
+++ /dev/null
@@ -1,64 +0,0 @@
-// Copyright 2010 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.
-
-package cmplx
-
-import "math"
-
-// The original C code, the long comment, and the constants
-// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
-// The go code is a simplified version of the original C.
-//
-// Cephes Math Library Release 2.8: June, 2000
-// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
-//
-// The readme file at http://netlib.sandia.gov/cephes/ says:
-// Some software in this archive may be from the book _Methods and
-// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
-// International, 1989) or from the Cephes Mathematical Library, a
-// commercial product. In either event, it is copyrighted by the author.
-// What you see here may be used freely but it comes with no support or
-// guarantee.
-//
-// The two known misprints in the book are repaired here in the
-// source listings for the gamma function and the incomplete beta
-// integral.
-//
-// Stephen L. Moshier
-// moshier@na-net.ornl.gov
-
-// Complex natural logarithm
-//
-// DESCRIPTION:
-//
-// Returns complex logarithm to the base e (2.718...) of
-// the complex argument z.
-//
-// If
-// z = x + iy, r = sqrt( x**2 + y**2 ),
-// then
-// w = log(r) + i arctan(y/x).
-//
-// The arctangent ranges from -PI to +PI.
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// DEC -10,+10 7000 8.5e-17 1.9e-17
-// IEEE -10,+10 30000 5.0e-15 1.1e-16
-//
-// Larger relative error can be observed for z near 1 +i0.
-// In IEEE arithmetic the peak absolute error is 5.2e-16, rms
-// absolute error 1.0e-16.
-
-// Log returns the natural logarithm of x.
-func Log(x complex128) complex128 {
- return complex(math.Log(Abs(x)), Phase(x))
-}
-
-// Log10 returns the decimal logarithm of x.
-func Log10(x complex128) complex128 {
- return math.Log10E * Log(x)
-}
diff --git a/src/pkg/math/cmplx/phase.go b/src/pkg/math/cmplx/phase.go
deleted file mode 100644
index 03cece8a5..000000000
--- a/src/pkg/math/cmplx/phase.go
+++ /dev/null
@@ -1,11 +0,0 @@
-// Copyright 2010 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.
-
-package cmplx
-
-import "math"
-
-// Phase returns the phase (also called the argument) of x.
-// The returned value is in the range [-Pi, Pi].
-func Phase(x complex128) float64 { return math.Atan2(imag(x), real(x)) }
diff --git a/src/pkg/math/cmplx/polar.go b/src/pkg/math/cmplx/polar.go
deleted file mode 100644
index 9b192bc62..000000000
--- a/src/pkg/math/cmplx/polar.go
+++ /dev/null
@@ -1,12 +0,0 @@
-// Copyright 2010 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.
-
-package cmplx
-
-// Polar returns the absolute value r and phase θ of x,
-// such that x = r * e**θi.
-// The phase is in the range [-Pi, Pi].
-func Polar(x complex128) (r, θ float64) {
- return Abs(x), Phase(x)
-}
diff --git a/src/pkg/math/cmplx/pow.go b/src/pkg/math/cmplx/pow.go
deleted file mode 100644
index 1630b879b..000000000
--- a/src/pkg/math/cmplx/pow.go
+++ /dev/null
@@ -1,78 +0,0 @@
-// Copyright 2010 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.
-
-package cmplx
-
-import "math"
-
-// The original C code, the long comment, and the constants
-// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
-// The go code is a simplified version of the original C.
-//
-// Cephes Math Library Release 2.8: June, 2000
-// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
-//
-// The readme file at http://netlib.sandia.gov/cephes/ says:
-// Some software in this archive may be from the book _Methods and
-// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
-// International, 1989) or from the Cephes Mathematical Library, a
-// commercial product. In either event, it is copyrighted by the author.
-// What you see here may be used freely but it comes with no support or
-// guarantee.
-//
-// The two known misprints in the book are repaired here in the
-// source listings for the gamma function and the incomplete beta
-// integral.
-//
-// Stephen L. Moshier
-// moshier@na-net.ornl.gov
-
-// Complex power function
-//
-// DESCRIPTION:
-//
-// Raises complex A to the complex Zth power.
-// Definition is per AMS55 # 4.2.8,
-// analytically equivalent to cpow(a,z) = cexp(z clog(a)).
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// IEEE -10,+10 30000 9.4e-15 1.5e-15
-
-// Pow returns x**y, the base-x exponential of y.
-// For generalized compatibility with math.Pow:
-// Pow(0, ±0) returns 1+0i
-// Pow(0, c) for real(c)<0 returns Inf+0i if imag(c) is zero, otherwise Inf+Inf i.
-func Pow(x, y complex128) complex128 {
- if x == 0 { // Guaranteed also true for x == -0.
- r, i := real(y), imag(y)
- switch {
- case r == 0:
- return 1
- case r < 0:
- if i == 0 {
- return complex(math.Inf(1), 0)
- }
- return Inf()
- case r > 0:
- return 0
- }
- panic("not reached")
- }
- modulus := Abs(x)
- if modulus == 0 {
- return complex(0, 0)
- }
- r := math.Pow(modulus, real(y))
- arg := Phase(x)
- theta := real(y) * arg
- if imag(y) != 0 {
- r *= math.Exp(-imag(y) * arg)
- theta += imag(y) * math.Log(modulus)
- }
- s, c := math.Sincos(theta)
- return complex(r*c, r*s)
-}
diff --git a/src/pkg/math/cmplx/rect.go b/src/pkg/math/cmplx/rect.go
deleted file mode 100644
index bf94d787e..000000000
--- a/src/pkg/math/cmplx/rect.go
+++ /dev/null
@@ -1,13 +0,0 @@
-// Copyright 2010 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.
-
-package cmplx
-
-import "math"
-
-// Rect returns the complex number x with polar coordinates r, θ.
-func Rect(r, θ float64) complex128 {
- s, c := math.Sincos(θ)
- return complex(r*c, r*s)
-}
diff --git a/src/pkg/math/cmplx/sin.go b/src/pkg/math/cmplx/sin.go
deleted file mode 100644
index 2c57536ed..000000000
--- a/src/pkg/math/cmplx/sin.go
+++ /dev/null
@@ -1,132 +0,0 @@
-// Copyright 2010 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.
-
-package cmplx
-
-import "math"
-
-// The original C code, the long comment, and the constants
-// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
-// The go code is a simplified version of the original C.
-//
-// Cephes Math Library Release 2.8: June, 2000
-// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
-//
-// The readme file at http://netlib.sandia.gov/cephes/ says:
-// Some software in this archive may be from the book _Methods and
-// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
-// International, 1989) or from the Cephes Mathematical Library, a
-// commercial product. In either event, it is copyrighted by the author.
-// What you see here may be used freely but it comes with no support or
-// guarantee.
-//
-// The two known misprints in the book are repaired here in the
-// source listings for the gamma function and the incomplete beta
-// integral.
-//
-// Stephen L. Moshier
-// moshier@na-net.ornl.gov
-
-// Complex circular sine
-//
-// DESCRIPTION:
-//
-// If
-// z = x + iy,
-//
-// then
-//
-// w = sin x cosh y + i cos x sinh y.
-//
-// csin(z) = -i csinh(iz).
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// DEC -10,+10 8400 5.3e-17 1.3e-17
-// IEEE -10,+10 30000 3.8e-16 1.0e-16
-// Also tested by csin(casin(z)) = z.
-
-// Sin returns the sine of x.
-func Sin(x complex128) complex128 {
- s, c := math.Sincos(real(x))
- sh, ch := sinhcosh(imag(x))
- return complex(s*ch, c*sh)
-}
-
-// Complex hyperbolic sine
-//
-// DESCRIPTION:
-//
-// csinh z = (cexp(z) - cexp(-z))/2
-// = sinh x * cos y + i cosh x * sin y .
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// IEEE -10,+10 30000 3.1e-16 8.2e-17
-
-// Sinh returns the hyperbolic sine of x.
-func Sinh(x complex128) complex128 {
- s, c := math.Sincos(imag(x))
- sh, ch := sinhcosh(real(x))
- return complex(c*sh, s*ch)
-}
-
-// Complex circular cosine
-//
-// DESCRIPTION:
-//
-// If
-// z = x + iy,
-//
-// then
-//
-// w = cos x cosh y - i sin x sinh y.
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// DEC -10,+10 8400 4.5e-17 1.3e-17
-// IEEE -10,+10 30000 3.8e-16 1.0e-16
-
-// Cos returns the cosine of x.
-func Cos(x complex128) complex128 {
- s, c := math.Sincos(real(x))
- sh, ch := sinhcosh(imag(x))
- return complex(c*ch, -s*sh)
-}
-
-// Complex hyperbolic cosine
-//
-// DESCRIPTION:
-//
-// ccosh(z) = cosh x cos y + i sinh x sin y .
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// IEEE -10,+10 30000 2.9e-16 8.1e-17
-
-// Cosh returns the hyperbolic cosine of x.
-func Cosh(x complex128) complex128 {
- s, c := math.Sincos(imag(x))
- sh, ch := sinhcosh(real(x))
- return complex(c*ch, s*sh)
-}
-
-// calculate sinh and cosh
-func sinhcosh(x float64) (sh, ch float64) {
- if math.Abs(x) <= 0.5 {
- return math.Sinh(x), math.Cosh(x)
- }
- e := math.Exp(x)
- ei := 0.5 / e
- e *= 0.5
- return e - ei, e + ei
-}
diff --git a/src/pkg/math/cmplx/sqrt.go b/src/pkg/math/cmplx/sqrt.go
deleted file mode 100644
index 4ef6807ad..000000000
--- a/src/pkg/math/cmplx/sqrt.go
+++ /dev/null
@@ -1,104 +0,0 @@
-// Copyright 2010 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.
-
-package cmplx
-
-import "math"
-
-// The original C code, the long comment, and the constants
-// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
-// The go code is a simplified version of the original C.
-//
-// Cephes Math Library Release 2.8: June, 2000
-// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
-//
-// The readme file at http://netlib.sandia.gov/cephes/ says:
-// Some software in this archive may be from the book _Methods and
-// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
-// International, 1989) or from the Cephes Mathematical Library, a
-// commercial product. In either event, it is copyrighted by the author.
-// What you see here may be used freely but it comes with no support or
-// guarantee.
-//
-// The two known misprints in the book are repaired here in the
-// source listings for the gamma function and the incomplete beta
-// integral.
-//
-// Stephen L. Moshier
-// moshier@na-net.ornl.gov
-
-// Complex square root
-//
-// DESCRIPTION:
-//
-// If z = x + iy, r = |z|, then
-//
-// 1/2
-// Re w = [ (r + x)/2 ] ,
-//
-// 1/2
-// Im w = [ (r - x)/2 ] .
-//
-// Cancellation error in r-x or r+x is avoided by using the
-// identity 2 Re w Im w = y.
-//
-// Note that -w is also a square root of z. The root chosen
-// is always in the right half plane and Im w has the same sign as y.
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// DEC -10,+10 25000 3.2e-17 9.6e-18
-// IEEE -10,+10 1,000,000 2.9e-16 6.1e-17
-
-// Sqrt returns the square root of x.
-// The result r is chosen so that real(r) ≥ 0 and imag(r) has the same sign as imag(x).
-func Sqrt(x complex128) complex128 {
- if imag(x) == 0 {
- if real(x) == 0 {
- return complex(0, 0)
- }
- if real(x) < 0 {
- return complex(0, math.Sqrt(-real(x)))
- }
- return complex(math.Sqrt(real(x)), 0)
- }
- if real(x) == 0 {
- if imag(x) < 0 {
- r := math.Sqrt(-0.5 * imag(x))
- return complex(r, -r)
- }
- r := math.Sqrt(0.5 * imag(x))
- return complex(r, r)
- }
- a := real(x)
- b := imag(x)
- var scale float64
- // Rescale to avoid internal overflow or underflow.
- if math.Abs(a) > 4 || math.Abs(b) > 4 {
- a *= 0.25
- b *= 0.25
- scale = 2
- } else {
- a *= 1.8014398509481984e16 // 2**54
- b *= 1.8014398509481984e16
- scale = 7.450580596923828125e-9 // 2**-27
- }
- r := math.Hypot(a, b)
- var t float64
- if a > 0 {
- t = math.Sqrt(0.5*r + 0.5*a)
- r = scale * math.Abs((0.5*b)/t)
- t *= scale
- } else {
- r = math.Sqrt(0.5*r - 0.5*a)
- t = scale * math.Abs((0.5*b)/r)
- r *= scale
- }
- if b < 0 {
- return complex(t, -r)
- }
- return complex(t, r)
-}
diff --git a/src/pkg/math/cmplx/tan.go b/src/pkg/math/cmplx/tan.go
deleted file mode 100644
index 9485315d8..000000000
--- a/src/pkg/math/cmplx/tan.go
+++ /dev/null
@@ -1,184 +0,0 @@
-// Copyright 2010 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.
-
-package cmplx
-
-import "math"
-
-// The original C code, the long comment, and the constants
-// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
-// The go code is a simplified version of the original C.
-//
-// Cephes Math Library Release 2.8: June, 2000
-// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
-//
-// The readme file at http://netlib.sandia.gov/cephes/ says:
-// Some software in this archive may be from the book _Methods and
-// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
-// International, 1989) or from the Cephes Mathematical Library, a
-// commercial product. In either event, it is copyrighted by the author.
-// What you see here may be used freely but it comes with no support or
-// guarantee.
-//
-// The two known misprints in the book are repaired here in the
-// source listings for the gamma function and the incomplete beta
-// integral.
-//
-// Stephen L. Moshier
-// moshier@na-net.ornl.gov
-
-// Complex circular tangent
-//
-// DESCRIPTION:
-//
-// If
-// z = x + iy,
-//
-// then
-//
-// sin 2x + i sinh 2y
-// w = --------------------.
-// cos 2x + cosh 2y
-//
-// On the real axis the denominator is zero at odd multiples
-// of PI/2. The denominator is evaluated by its Taylor
-// series near these points.
-//
-// ctan(z) = -i ctanh(iz).
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// DEC -10,+10 5200 7.1e-17 1.6e-17
-// IEEE -10,+10 30000 7.2e-16 1.2e-16
-// Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
-
-// Tan returns the tangent of x.
-func Tan(x complex128) complex128 {
- d := math.Cos(2*real(x)) + math.Cosh(2*imag(x))
- if math.Abs(d) < 0.25 {
- d = tanSeries(x)
- }
- if d == 0 {
- return Inf()
- }
- return complex(math.Sin(2*real(x))/d, math.Sinh(2*imag(x))/d)
-}
-
-// Complex hyperbolic tangent
-//
-// DESCRIPTION:
-//
-// tanh z = (sinh 2x + i sin 2y) / (cosh 2x + cos 2y) .
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// IEEE -10,+10 30000 1.7e-14 2.4e-16
-
-// Tanh returns the hyperbolic tangent of x.
-func Tanh(x complex128) complex128 {
- d := math.Cosh(2*real(x)) + math.Cos(2*imag(x))
- if d == 0 {
- return Inf()
- }
- return complex(math.Sinh(2*real(x))/d, math.Sin(2*imag(x))/d)
-}
-
-// Program to subtract nearest integer multiple of PI
-func reducePi(x float64) float64 {
- const (
- // extended precision value of PI:
- DP1 = 3.14159265160560607910E0 // ?? 0x400921fb54000000
- DP2 = 1.98418714791870343106E-9 // ?? 0x3e210b4610000000
- DP3 = 1.14423774522196636802E-17 // ?? 0x3c6a62633145c06e
- )
- t := x / math.Pi
- if t >= 0 {
- t += 0.5
- } else {
- t -= 0.5
- }
- t = float64(int64(t)) // int64(t) = the multiple
- return ((x - t*DP1) - t*DP2) - t*DP3
-}
-
-// Taylor series expansion for cosh(2y) - cos(2x)
-func tanSeries(z complex128) float64 {
- const MACHEP = 1.0 / (1 << 53)
- x := math.Abs(2 * real(z))
- y := math.Abs(2 * imag(z))
- x = reducePi(x)
- x = x * x
- y = y * y
- x2 := 1.0
- y2 := 1.0
- f := 1.0
- rn := 0.0
- d := 0.0
- for {
- rn += 1
- f *= rn
- rn += 1
- f *= rn
- x2 *= x
- y2 *= y
- t := y2 + x2
- t /= f
- d += t
-
- rn += 1
- f *= rn
- rn += 1
- f *= rn
- x2 *= x
- y2 *= y
- t = y2 - x2
- t /= f
- d += t
- if math.Abs(t/d) <= MACHEP {
- break
- }
- }
- return d
-}
-
-// Complex circular cotangent
-//
-// DESCRIPTION:
-//
-// If
-// z = x + iy,
-//
-// then
-//
-// sin 2x - i sinh 2y
-// w = --------------------.
-// cosh 2y - cos 2x
-//
-// On the real axis, the denominator has zeros at even
-// multiples of PI/2. Near these points it is evaluated
-// by a Taylor series.
-//
-// ACCURACY:
-//
-// Relative error:
-// arithmetic domain # trials peak rms
-// DEC -10,+10 3000 6.5e-17 1.6e-17
-// IEEE -10,+10 30000 9.2e-16 1.2e-16
-// Also tested by ctan * ccot = 1 + i0.
-
-// Cot returns the cotangent of x.
-func Cot(x complex128) complex128 {
- d := math.Cosh(2*imag(x)) - math.Cos(2*real(x))
- if math.Abs(d) < 0.25 {
- d = tanSeries(x)
- }
- if d == 0 {
- return Inf()
- }
- return complex(math.Sin(2*real(x))/d, -math.Sinh(2*imag(x))/d)
-}
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