Contents

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Contents

1 About this Guide
1.1 Legal Information
1.2 Feedback and Contact
1.3 Introduction
1.4 Audience for This Guide
1.5 How to Use This Guide
1.6 Conventions Used in This Guide
2 Overview
2.1 Introduction
2.2 Thread Safety
2.3 SIMD/SPMD Unit Usage
2.4 Performance Characteristics
2.5 Extended Vector Sizes (_64 suffix functions)
3 Standard Real Trigonometric Functions
3.1 vatsin - Vector sine $sin(x)$
3.1.1 Parameters
3.1.2 Function Graphs
3.2 vatcos - Vector cosine $cos(x)$
3.2.1 Parameters
3.2.2 Function Graphs
3.3 vattan - Vector tangent $tan(x)$
3.3.1 Parameters
3.3.2 Function Graphs
3.4 vatcsc - Vector cosecant $csc(x)$
3.4.1 Parameters
3.4.2 Function Graphs
3.5 vatsec - Vector secant $sec(x)$
3.5.1 Parameters
3.5.2 Function Graphs
3.6 vatcot - Vector cotangent $cot(x)$
3.6.1 Parameters
3.6.2 Function Graphs
3.7 vatasin - Vector arcsine $-1 sin (x)$
3.7.1 Parameters
3.7.2 Function Graphs
3.8 vatacos - Vector arccosine $-1 cos (x)$
3.8.1 Parameters
3.8.2 Function Graphs
3.9 vatatan - Vector arctangent $-1 tan (x)$
3.9.1 Parameters
3.9.2 Function Graphs
3.10 vatacsc - Vector arccosecant $-1 csc (x)$
3.10.1 Parameters
3.10.2 Function Graphs
3.11 vatasec - Vector arcsecant $-1 sec (x)$
3.11.1 Parameters
3.11.2 Function Graphs
3.12 vatacot - Vector arccotangent $-1 cot (x)$
3.12.1 Parameters
3.12.2 Function Graphs
4 Standard Real Trigonometric Functions (Half-Cycle)
4.1 vatsinpi - Vector half-cycle sine $sin(πx)$
4.1.1 Parameters
4.1.2 Function Graphs
4.2 vatcospi - Vector half-cycle cosine $cos(πx)$
4.2.1 Parameters
4.2.2 Function Graphs
4.3 vattanpi - Vector half-cycle tangent $tan(πx)$
4.3.1 Parameters
4.3.2 Function Graphs
4.4 vatcscpi - Vector half-cycle cosecant $csc(πx)$
4.4.1 Parameters
4.4.2 Function Graphs
4.5 vatsecpi - Vector half-cycle secant $sec(πx)$
4.5.1 Parameters
4.5.2 Function Graphs
4.6 vatcotpi - Vector half-cycle cotangent $cot(πx)$
4.6.1 Parameters
4.6.2 Function Graphs
4.7 vatasinpi - Vector half-cycle arcsine $-1 sin (x)/π$
4.7.1 Parameters
4.7.2 Function Graphs
4.8 vatacospi - Vector half-cycle arccosine $-1 cos (x)/π$
4.8.1 Parameters
4.8.2 Function Graphs
4.9 vatatanpi - Vector half-cycle arctangent $-1 tan (x)/π$
4.9.1 Parameters
4.9.2 Function Graphs
4.10 vatacscpi - Vector half-cycle arccosecant $-1 csc (x)/π$
4.10.1 Parameters
4.10.2 Function Graphs
4.11 vatasecpi - Vector half-cycle arcsecant $-1 sec (x)/π$
4.11.1 Parameters
4.11.2 Function Graphs
4.12 vatacotpi - Vector half-cycle arccotangent $-1 cot (x)/π$
4.12.1 Parameters
4.12.2 Function Graphs
5 Standard Real Trigonometric Functions (Degrees)
5.1 vatsind - Vector sine $sin(x)$
5.1.1 Parameters
5.1.2 Function Graphs
5.2 vatcosd - Vector cosine $cos(x)$
5.2.1 Parameters
5.2.2 Function Graphs
5.3 vattand - Vector tangent $tan(x)$
5.3.1 Parameters
5.3.2 Function Graphs
5.4 vatcscd - Vector cosecant $csc(x)$
5.4.1 Parameters
5.4.2 Function Graphs
5.5 vatsecd - Vector secant $sec(x)$
5.5.1 Parameters
5.5.2 Function Graphs
5.6 vatcotd - Vector cotangent $cot(x)$
5.6.1 Parameters
5.6.2 Function Graphs
5.7 vatasind - Vector arcsine $-1 sin (x)$
5.7.1 Parameters
5.7.2 Function Graphs
5.8 vatacosd - Vector arccosine $-1 cos (x)$
5.8.1 Parameters
5.8.2 Function Graphs
5.9 vatatand - Vector arctangent $-1 tan (x)$
5.9.1 Parameters
5.9.2 Function Graphs
5.10 vatacscd - Vector arccosecant $-1 csc (x)$
5.10.1 Parameters
5.10.2 Function Graphs
5.11 vatasecd - Vector arcsecant $-1 sec (x)$
5.11.1 Parameters
5.11.2 Function Graphs
5.12 vatacotd - Vector arccotangent $-1 cot (x)$
5.12.1 Parameters
5.12.2 Function Graphs
6 Standard Real Hyperbolic Trigonometric Functions
6.1 vatsinh - Vector hyperbolic sine $sinh(x)$
6.1.1 Parameters
6.1.2 Function Graphs
6.2 vatcosh - Vector hyperbolic cosine $cosh(x)$
6.2.1 Parameters
6.2.2 Function Graphs
6.3 vattanh - Vector hyperbolic tangent $tanh(x)$
6.3.1 Parameters
6.3.2 Function Graphs
6.4 vatcsch - Vector hyperbolic cosecant $csch(x)$
6.4.1 Parameters
6.4.2 Function Graphs
6.5 vatsech - Vector hyperbolic secant $sech(x)$
6.5.1 Parameters
6.5.2 Function Graphs
6.6 vatcoth - Vector hyperbolic cotangent $coth(x)$
6.6.1 Parameters
6.6.2 Function Graphs
6.7 vatasinh - Vector hyperbolic arcsine $-1 sinh (x)$
6.7.1 Parameters
6.7.2 Function Graphs
6.8 vatacosh - Vector hyperbolic arccosine $-1 cosh (x)$
6.8.1 Parameters
6.8.2 Function Graphs
6.9 vatatanh - Vector hyperbolic arctangent $-1 tanh (x)$
6.9.1 Parameters
6.9.2 Function Graphs
6.10 vatacsch - Vector hyperbolic arccosecant $-1 csch (x)$
6.10.1 Parameters
6.10.2 Function Graphs
6.11 vatasech - Vector hyperbolic arcsecant $-1 sech (x)$
6.11.1 Parameters
6.11.2 Function Graphs
6.12 vatacoth - Vector hyperbolic arccotangent $-1 coth (x)$
6.12.1 Parameters
6.12.2 Function Graphs
7 Versine Functions
7.1 vatver - Vector versine $ver(x)$
7.1.1 Parameters
7.1.2 Function Graphs
7.2 vatvcs - Vector vercosine $vcs(x)$
7.2.1 Parameters
7.2.2 Function Graphs
7.3 vatcvs - Vector coversine $cvs(x)$
7.3.1 Parameters
7.3.2 Function Graphs
7.4 vatcvc - Vector covercosine $cvc(x)$
7.4.1 Parameters
7.4.2 Function Graphs
7.5 vathav - Vector haversine $hav(x)$
7.5.1 Parameters
7.5.2 Function Graphs
7.6 vathac - Vector havercosine $hac(x)$
7.6.1 Parameters
7.6.2 Function Graphs
7.7 vathcv - Vector hacoversine $hcv(x)$
7.7.1 Parameters
7.7.2 Function Graphs
7.8 vathcc - Vector hacoversine $hcc(x)$
7.8.1 Parameters
7.8.2 Function Graphs
7.9 vataver - Vector arcversine $-1 ver (x)$
7.9.1 Parameters
7.9.2 Function Graphs
7.10 vatavcs - Vector arcvercosine $-1 vcs (x)$
7.10.1 Parameters
7.10.2 Function Graphs
7.11 vatacvs - Vector arccoversine $-1 cvs (x)$
7.11.1 Parameters
7.11.2 Function Graphs
7.12 vatacvc - Vector arccovercosine $-1 cvc (x)$
7.12.1 Parameters
7.12.2 Function Graphs
7.13 vatahav - Vector archaversine $-1 hav (x)$
7.13.1 Parameters
7.13.2 Function Graphs
7.14 vatahac - Vector archavercosine $-1 hac (x)$
7.14.1 Parameters
7.14.2 Function Graphs
7.15 vatahcv - Vector archacoversine $-1 hcv (x)$
7.15.1 Parameters
7.15.2 Function Graphs
7.16 vatahcc - Vector archacovercosine $-1 hcc (x)$
7.16.1 Parameters
7.16.2 Function Graphs
8 Versine Functions (Half-Cycle)
8.1 vatverpi - Vector half-cycle versine $ver(πx)$
8.1.1 Parameters
8.1.2 Function Graphs
8.2 vatvcspi - Vector half-cycle vercosine $vcs(πx)$
8.2.1 Parameters
8.2.2 Function Graphs
8.3 vatcvspi - Vector half-cycle coversine $cvs(πx)$
8.3.1 Parameters
8.3.2 Function Graphs
8.4 vatcvcpi - Vector half-cycle covercosine $cvc(πx)$
8.4.1 Parameters
8.4.2 Function Graphs
8.5 vathavpi - Vector half-cycle haversine $hav(πx)$
8.5.1 Parameters
8.5.2 Function Graphs
8.6 vathacpi - Vector half-cycle havercosine $hac(πx)$
8.6.1 Parameters
8.6.2 Function Graphs
8.7 vathcvpi - Vector half-cycle hacoversine $hcv(πx)$
8.7.1 Parameters
8.7.2 Function Graphs
8.8 vathccpi - Vector half-cycle hacovercosine $hcc(πx)$
8.8.1 Parameters
8.8.2 Function Graphs
8.9 vataverpi - Vector half-cycle arcversine $-1 ver (x)/π$
8.9.1 Parameters
8.9.2 Function Graphs
8.10 vatavcspi - Vector half-cycle arcvercosine $-1 vcs (x)/π$
8.10.1 Parameters
8.10.2 Function Graphs
8.11 vatacvspi - Vector hald-cycle arccoversine $-1 cvs (x)/π$
8.11.1 Parameters
8.11.2 Function Graphs
8.12 vatacvcpi - Vector half-cycle arccovercosine $-1 cvc (x)/π$
8.12.1 Parameters
8.12.2 Function Graphs
8.13 vatahavpi - Vector half-cycle archaversine $-1 hav (x)/π$
8.13.1 Parameters
8.13.2 Function Graphs
8.14 vatahacpi - Vector half-cycle archacovercosine $-1 hac (x)/π$
8.14.1 Parameters
8.14.2 Function Graphs
8.15 vatahcvpi - Vector half-cycle archacoversine $-1 hcv (x)/π$
8.15.1 Parameters
8.15.2 Function Graphs
8.16 vatahccpi - Vector half-cycle archacovercosine $-1 hcc (x)/π$
8.16.1 Parameters
8.16.2 Function Graphs
9 Versine Functions (Degrees)
9.1 vatverd - Vector versine $ver(x)$
9.1.1 Parameters
9.1.2 Function Graphs
9.2 vatvcsd - Vector vercosine $vcs(x)$
9.2.1 Parameters
9.2.2 Function Graphs
9.3 vatcvsd - Vector coversine $cvs(x)$
9.3.1 Parameters
9.3.2 Function Graphs
9.4 vatcvcd - Vector covercosine $cvc(x)$
9.4.1 Parameters
9.4.2 Function Graphs
9.5 vathavd - Vector haversine $hav(x)$
9.5.1 Parameters
9.5.2 Function Graphs
9.6 vathacd - Vector havercosine $hac(x)$
9.6.1 Parameters
9.6.2 Function Graphs
9.7 vathcvd - Vector hacoversine $hcv(x)$
9.7.1 Parameters
9.7.2 Function Graphs
9.8 vathccd - Vector hacovercosine $hcc(x)$
9.8.1 Parameters
9.8.2 Function Graphs
9.9 vataverd - Vector arcversine $-1 ver (x)$
9.9.1 Parameters
9.9.2 Function Graphs
9.10 vatavcsd - Vector arcvercosine $-1 vcs (x)$
9.10.1 Parameters
9.10.2 Function Graphs
9.11 vatacvsd - Vector arccoversine $-1 cvs (x)$
9.11.1 Parameters
9.11.2 Function Graphs
9.12 vatacvcd - Vector arcovercosine $-1 cvc (x)$
9.12.1 Parameters
9.12.2 Function Graphs
9.13 vatahavd - Vector archaversine $-1 hav (x)$
9.13.1 Parameters
9.13.2 Function Graphs
9.14 vatahacd - Vector archavercosine $-1 hac (x)$
9.14.1 Parameters
9.14.2 Function Graphs
9.15 vatahcvd - Vector archacoversine $-1 hcv (x)$
9.15.1 Parameters
9.15.2 Function Graphs
9.16 vatahccd - Vector archacovercosine $-1 hcc (x)$
9.16.1 Parameters
9.16.2 Function Graphs
10 Cardinal Trigonometric Functions
10.1 vatsinc - Vector cardinal sine $sinc(x)$
10.1.1 Parameters
10.1.2 Function Graphs
10.2 vatcosc - Vector cardinal cosine $cosc(x)$
10.2.1 Parameters
10.2.2 Function Graphs
10.3 vattanc - Vector cardinal tangent $tanc(x)$
10.3.1 Parameters
10.3.2 Function Graphs
11 Cardinal Normalized Trigonometric Functions
11.1 vatsincpi - Vector cardinal sine $sincπ(x)$
11.1.1 Parameters
11.1.2 Function Graphs
11.2 vatcoscpi - Vector cardinal cosine $coscπ(x)$
11.2.1 Parameters
11.2.2 Function Graphs
11.3 vattancpi - Vector cardinal tangent $tancπ(x)$
11.3.1 Parameters
11.3.2 Function Graphs
12 Cardinal Hyperbolic Trigonometric Functions
12.1 vatsinhc - Vector cardinal hyperbolic sine $sinhc(x)$
12.1.1 Parameters
12.1.2 Function Graphs
12.2 vatcoshc - Vector cardinal hyperbolic cosine $coshc(x)$
12.2.1 Parameters
12.2.2 Function Graphs
12.3 vattanhc - Vector cardinal hyperbolic tangent $tanhc(x)$
12.3.1 Parameters
12.3.2 Function Graphs
13 Hyperbolic Trigonometric Functions Minus X
13.1 vatsinhmx - Vector hyperbolic sine minus x $sinh(x)-x$
13.1.1 Parameters
13.1.2 Function Graphs
13.2 vatcoshmx - Vector hyperbolic cosine minus x $cosh(x)-x$
13.2.1 Parameters
13.2.2 Function Graphs
13.3 vattanhmx - Vector hyperbolic tangent minus x $tanh(x)-x$
13.3.1 Parameters
13.3.2 Function Graphs
14 Exsecant and Excosecant
14.1 vatexs - Vector exsecant $exs(x)$
14.1.1 Parameters
14.1.2 Function Graphs
14.2 vatexc - Vector excosecant $exc(x)$
14.2.1 Parameters
14.2.2 Function Graphs
14.3 vataexs - Vector arcexsecant $-1 exs (x)$
14.3.1 Parameters
14.3.2 Function Graphs
14.4 vataexc - Vector arcexcosecant $-1 exc (x)$
14.4.1 Parameters
14.4.2 Function Graphs
15 Exsecant and Excosecant (Half-Cycle)
15.1 vatexspi - Vector half-cycle exsecant $exs(πx)$
15.1.1 Parameters
15.1.2 Function Graphs
15.2 vatexcpi - Vector half-cycle excosecant $exc(πx)$
15.2.1 Parameters
15.2.2 Function Graphs
15.3 vataexspi - Vector half-cycle arcexsecant $-1 exs (x)/π$
15.3.1 Parameters
15.3.2 Function Graphs
15.4 vataexcpi - Vector half-cycle arcexcosecant $-1 exc (x)/π$
15.4.1 Parameters
15.4.2 Function Graphs
16 Exsecant and Excosecant (Degree)
16.1 vatexsd - Vector exsecant $exs(x)$
16.1.1 Parameters
16.1.2 Function Graphs
16.2 vatexcd - Vector excosecant $exc(x)$
16.2.1 Parameters
16.2.2 Function Graphs
16.3 vataexsd - Vector arcexsecant $-1 exs (x)$
16.3.1 Parameters
16.3.2 Function Graphs
16.4 vataexcd - Vector arcexcosecant $-1 exc (x)$
16.4.1 Parameters
16.4.2 Function Graphs
17 Chord
17.1 vatcrd - Vector chord $crd(x)$
17.1.1 Parameters
17.1.2 Function Graphs
17.2 vatacrd - Vector arcchord $-1 crd (x)$
17.2.1 Parameters
17.2.2 Function Graphs
18 Gudermannian
18.1 vatgd - Vector Gudermannian function $gd(x)$
18.1.1 Parameters
18.1.2 Function Graphs
18.2 vatagd - Vector inverse Gudremannian function $-1 gd (x)$
18.2.1 Parameters
18.2.2 Function Graphs
19 Standard Complex Trigonometric Functions
19.1 vatcsin - Vector complex sine $sin(x)$
19.1.1 Parameters
19.1.2 Function Graphs
19.2 vatccos - Vector complex cosine $cos(x)$
19.2.1 Parameters
19.2.2 Function Graphs
19.3 vatctan - Vector complex tangent $tan(x)$
19.3.1 Parameters
19.3.2 Function Graphs
19.4 vatccsc - Vector complex cosecant $csc(x)$
19.4.1 Parameters
19.4.2 Function Graphs
19.5 vatcsec - Vector complex secant $sec(x)$
19.5.1 Parameters
19.5.2 Function Graphs
19.6 vatccot - Vector complex cotangent $cot(x)$
19.6.1 Parameters
19.6.2 Function Graphs
19.7 vatcasin - Vector complex arcsine $-1 sin (x)$
19.7.1 Parameters
19.7.2 Function Graphs
19.8 vatcacos - Vector complex arccosine $-1 cos (x)$
19.8.1 Parameters
19.8.2 Function Graphs
19.9 vatcatan - Vector complex arctangent $-1 tan (x)$
19.9.1 Parameters
19.9.2 Function Graphs
19.10 vatcacsc - Vector complex arccosecant $-1 csc (x)$
19.10.1 Parameters
19.10.2 Function Graphs
19.11 vatcasec - Vector complex arcsecant $-1 sec (x)$
19.11.1 Parameters
19.11.2 Function Graphs
19.12 vatcacot - Vector complex arccotangent $-1 cot (x)$
19.12.1 Parameters
19.12.2 Function Graphs
20 Standard Complex Hyperbolic Trigonometric Functions
20.1 vatcsinh - Vector complex hyperbolic sine $sinh(x)$
20.1.1 Parameters
20.1.2 Function Graphs
20.2 vatccosh - Vector complex hyperbolic cosine $cosh(x)$
20.2.1 Parameters
20.2.2 Function Graphs
20.3 vatctanh - Vector complex hyperbolic tangent $tanh(x)$
20.3.1 Parameters
20.3.2 Function Graphs
20.4 vatccsch - Vector complex hyperbolic cosecant $csch(x)$
20.4.1 Parameters
20.4.2 Function Graphs
20.5 vatcsech - Vector complex hyperbolic secant $sech(x)$
20.5.1 Parameters
20.5.2 Function Graphs
20.6 vatccoth - Vector complex hyperbolic cotangent $coth(x)$
20.6.1 Parameters
20.6.2 Function Graphs
20.7 vatcasinh - Vector complex hyperbolic arcsine $-1 sinh (x)$
20.7.1 Parameters
20.7.2 Function Graphs
20.8 vatcacosh - Vector complex hyperbolic arccosine $-1 cosh (x)$
20.8.1 Parameters
20.8.2 Function Graphs
20.9 vatcatanh - Vector complex hyperbolic arctangent $-1 tanh (x)$
20.9.1 Parameters
20.9.2 Function Graphs
20.10 vatcacsch - Vector complex hyperbolic arccosecant $-1 csch (x)$
20.10.1 Parameters
20.10.2 Function Graphs
20.11 vatcasech - Vector complex hyperbolic arcsecant $-1 sech (x)$
20.11.1 Parameters
20.11.2 Function Graphs
20.12 vatcacoth - Vector complex hyperbolic arccotangent $-1 coth (x)$
20.12.1 Parameters
20.12.2 Function Graphs
21 Complex Versine Functions
21.1 vatcver - Vector complex versine $ver(x)$
21.1.1 Parameters
21.1.2 Function Graphs
21.2 vatcvcs - Vector complex vercosine $vcs(x)$
21.2.1 Parameters
21.2.2 Function Graphs
21.3 vatccvs - Vector complex coversine $cvs(x)$
21.3.1 Parameters
21.3.2 Function Graphs
21.4 vatccvc - Vector complex covercosine $cvc(x)$
21.4.1 Parameters
21.4.2 Function Graphs
21.5 vatchav - Vector complex haversine $hav(x)$
21.5.1 Parameters
21.5.2 Function Graphs
21.6 vatchac - Vector complex havercosine $hac(x)$
21.6.1 Parameters
21.6.2 Function Graphs
21.7 vatchcv - Vector complex hacoversine $hcv(x)$
21.7.1 Parameters
21.7.2 Function Graphs
21.8 vatchcc - Vector complex hacovercosine $hcc(x)$
21.8.1 Parameters
21.8.2 Function Graphs
21.9 vatcaver - Vector complex arcversine $-1 ver (x)$
21.9.1 Parameters
21.9.2 Function Graphs
21.10 vatcavcs - Vector complex arcvercosine $-1 vcs (x)$
21.10.1 Parameters
21.10.2 Function Graphs
21.11 vatcacvs - Vector complex arccoversine $-1 cvs (x)$
21.11.1 Parameters
21.11.2 Function Graphs
21.12 vatcacvc - Vector complex arccovercosine $-1 cvc (x)$
21.12.1 Parameters
21.12.2 Function Graphs
21.13 vatcahav - Vector complex archaversine $-1 hav (x)$
21.13.1 Parameters
21.13.2 Function Graphs
21.14 vatcahac - Vector complex archavercosine $-1 hac (x)$
21.14.1 Parameters
21.14.2 Function Graphs
21.15 vatcahcv - Vector complex archacoversine $-1 hcv (x)$
21.15.1 Parameters
21.15.2 Function Graphs
21.16 vatcahcc - Vector complex archacovercosine $-1 hcc (x)$
21.16.1 Parameters
21.16.2 Function Graphs
22 Complex Cardinal Trigonometric Functions
22.1 vatcsinc - Vector complex cardinal sine $sinc(x)$
22.1.1 Parameters
22.1.2 Function Graphs
22.2 vatccosc - Vector complex caridnal cosine $cosc(x)$
22.2.1 Parameters
22.2.2 Function Graphs
22.3 vatctanc - Vector complex cardinal tangent $tanc(x)$
22.3.1 Parameters
22.3.2 Function Graphs
23 Complex Cardinal Hyperbolic Trigonometric Functions
23.1 vatcsinhc - Vector complex cardinal hyperbolic sine $sinhc(x)$
23.1.1 Parameters
23.1.2 Function Graphs
23.2 vatccoshc - Vector complex caridnal hyperbolic cosine $coshc(x)$
23.2.1 Parameters
23.2.2 Function Graphs
23.3 vatctanhc - Vector complex cardinal hyperbolic tangent $tanhc(x)$
23.3.1 Parameters
23.3.2 Function Graphs
24 Complex Hyperbolic Trigonometric Minus X Functions
24.1 vatcsinhmx - Vector complex hyperbolic sine minus x $sinh(x)-x$
24.1.1 Parameters
24.1.2 Function Graphs
24.2 vatccoshmx - Vector complex hyperbolic cosine minus x $cosh(x)-x$
24.2.1 Parameters
24.2.2 Function Graphs
24.3 vatctanhmx - Vector complex hyperbolic tangent minus x $tanh(x)-x$
24.3.1 Parameters
24.3.2 Function Graphs
25 Complex Gudermannian
25.1 vatcgd - Vector complex Gudermannian $gd(x)$
25.1.1 Parameters
25.1.2 Function Graphs
25.2 vatcagd - Vector complex inverse Gudermannian $-1 gd (x)$
25.2.1 Parameters
25.2.2 Function Graphs
26 Acknowledgements

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