Math Vector Library 1.1 Advanced Trigonometry Extension
Programming Reference Manual Fortran
Version 1.1 DD-00012-111
Math Vector Library 1.1 Advanced Trigonometry Extension
Reference Manual (Fortran)
DD-00012-111
Jan Adelsbach
March 14, 2025
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
Utility
3.1
mvecatrigver
- Version query
4
Standard Real Trigonometric Functions
4.1
vatsin
- Vector sine
4.2
vatcos
- Vector cosine
4.3
vattan
- Vector tangent
4.4
vatcsc
- Vector cosecant
4.5
vatsec
- Vector secant
4.6
vatcot
- Vector cotangent
4.7
vatasin
- Vector arcsine
4.8
vatacos
- Vector arccosine
4.9
vatatan
- Vector arctangent
4.10
vatacsc
- Vector arccosecant
4.11
vatasec
- Vector arcsecant
4.12
vatacot
- Vector arccotangent
5
Standard Real Trigonometric Functions (Half-Cycle)
5.1
vatsinpi
- Vector half-cycle sine
5.2
vatcospi
- Vector half-cycle cosine
5.3
vattanpi
- Vector half-cycle tangent
5.4
vatcscpi
- Vector half-cycle cosecant
5.5
vatsecpi
- Vector half-cycle secant
5.6
vatcotpi
- Vector half-cycle cotangent
5.7
vatasinpi
- Vector half-cycle arcsine
5.8
vatacospi
- Vector half-cycle arccosine
5.9
vatatanpi
- Vector half-cycle arctangent
5.10
vatacscpi
- Vector half-cycle arccosecant
5.11
vatasecpi
- Vector half-cycle arcsecant
5.12
vatacotpi
- Vector half-cycle arccotangent
6
Standard Real Trigonometric Functions (Degrees)
6.1
vatsind
- Vector sine
6.2
vatcosd
- Vector cosine
6.3
vattand
- Vector tangent
6.4
vatcscd
- Vector cosecant
6.5
vatsecd
- Vector secant
6.6
vatcotd
- Vector cotangent
6.7
vatasind
- Vector arcsine
6.8
vatacosd
- Vector arccosine
6.9
vatatand
- Vector arctangent
6.10
vatacscd
- Vector arccosecant
6.11
vatasecd
- Vector arcsecant
6.12
vatacotd
- Vector arccotangent
7
Standard Real Hyperbolic Trigonometric Functions
7.1
vatsinh
- Vector hyperbolic sine
7.2
vatcosh
- Vector hyperbolic cosine
7.3
vattanh
- Vector hyperbolic tangent
7.4
vatcsch
- Vector hyperbolic cosecant
7.5
vatsech
- Vector hyperbolic secant
7.6
vatcoth
- Vector hyperbolic cotangent
7.7
vatasinh
- Vector hyperbolic arcsine
7.8
vatacosh
- Vector hyperbolic arccosine
7.9
vatatanh
- Vector hyperbolic arctangent
7.10
vatacsch
- Vector hyperbolic arccosecant
7.11
vatasech
- Vector hyperbolic arcsecant
7.12
vatacoth
- Vector hyperbolic arccotangent
8
Versine Functions
8.1
vatver
- Vector versine
8.2
vatvcs
- Vector vercosine
8.3
vatcvs
- Vector coversine
8.4
vatcvc
- Vector covercosine
8.5
vathav
- Vector haversine
8.6
vathac
- Vector havercosine
8.7
vathcv
- Vector hacoversine
8.8
vathcc
- Vector hacoversine
8.9
vataver
- Vector arcversine
8.10
vatavcs
- Vector arcvercosine
8.11
vatacvs
- Vector arccoversine
8.12
vatacvc
- Vector arccovercosine
8.13
vatahav
- Vector archaversine
8.14
vatahac
- Vector archavercosine
8.15
vatahcv
- Vector archacoversine
8.16
vatahcc
- Vector archacovercosine
9
Versine Functions (Half-Cycle)
9.1
vatverpi
- Vector half-cycle versine
9.2
vatvcspi
- Vector half-cycle vercosine
9.3
vatcvspi
- Vector half-cycle coversine
9.4
vatcvcpi
- Vector half-cycle covercosine
9.5
vathavpi
- Vector half-cycle haversine
9.6
vathacpi
- Vector half-cycle havercosine
9.7
vathcvpi
- Vector half-cycle hacoversine
9.8
vathccpi
- Vector half-cycle hacovercosine
9.9
vataverpi
- Vector half-cycle arcversine
9.10
vatavcspi
- Vector half-cycle arcvercosine
9.11
vatacvspi
- Vector hald-cycle arccoversine
9.12
vatacvcpi
- Vector half-cycle arccovercosine
9.13
vatahavpi
- Vector half-cycle archaversine
9.14
vatahacpi
- Vector half-cycle archacovercosine
9.15
vatahcvpi
- Vector half-cycle archacoversine
9.16
vatahccpi
- Vector half-cycle archacovercosine
10
Versine Functions (Degrees)
10.1
vatverd
- Vector versine
10.2
vatvcsd
- Vector vercosine
10.3
vatcvsd
- Vector coversine
10.4
vatcvcd
- Vector covercosine
10.5
vathavd
- Vector haversine
10.6
vathacd
- Vector havercosine
10.7
vathcvd
- Vector hacoversine
10.8
vathccd
- Vector hacovercosine
10.9
vataverd
- Vector arcversine
10.10
vatavcsd
- Vector arcvercosine
10.11
vatacvsd
- Vector arccoversine
10.12
vatacvcd
- Vector arcovercosine
10.13
vatahavd
- Vector archaversine
10.14
vatahacd
- Vector archavercosine
10.15
vatahcvd
- Vector archacoversine
10.16
vatahccd
- Vector archacovercosine
11
Cardinal Trigonometric Functions
11.1
vatsinc
- Vector cardinal sine
11.2
vatcosc
- Vector cardinal cosine
11.3
vattanc
- Vector cardinal tangent
12
Cardinal Normalized Trigonometric Functions
12.1
vatsincpi
- Vector cardinal sine
12.2
vatcoscpi
- Vector cardinal cosine
12.3
vattancpi
- Vector cardinal tangent
13
Cardinal Hyperbolic Trigonometric Functions
13.1
vatsinhc
- Vector cardinal hyperbolic sine
13.2
vatcoshc
- Vector cardinal hyperbolic cosine
13.3
vattanhc
- Vector cardinal hyperbolic tangent
14
Hyperbolic Trigonometric Functions Minus X
14.1
vatsinhmx
- Vector hyperbolic sine minus x
14.2
vatcoshmx
- Vector hyperbolic cosine minus x
14.3
vattanhmx
- Vector hyperbolic tangent minus x
15
Exsecant and Excosecant
15.1
vatexs
- Vector exsecant
15.2
vatexc
- Vector excosecant
15.3
vataexs
- Vector arcexsecant
15.4
vataexc
- Vector arcexcosecant
16
Exsecant and Excosecant (Half-Cycle)
16.1
vatexspi
- Vector half-cycle exsecant
16.2
vatexcpi
- Vector half-cycle excosecant
16.3
vataexspi
- Vector half-cycle arcexsecant
16.4
vataexcpi
- Vector half-cycle arcexcosecant
17
Exsecant and Excosecant (Degree)
17.1
vatexsd
- Vector exsecant
17.2
vatexcd
- Vector excosecant
17.3
vataexsd
- Vector arcexsecant
17.4
vataexcd
- Vector arcexcosecant
18
Chord
18.1
vatcrd
- Vector chord
18.2
vatacrd
- Vector arcchord
19
Gudermannian
19.1
vatgd
- Vector Gudermannian function
19.2
vatagd
- Vector inverse Gudremannian function
20
Standard Complex Trigonometric Functions
20.1
vatcsin
- Vector complex sine
20.2
vatccos
- Vector complex cosine
20.3
vatctan
- Vector complex tangent
20.4
vatccsc
- Vector complex cosecant
20.5
vatcsec
- Vector complex secant
20.6
vatccot
- Vector complex cotangent
20.7
vatcasin
- Vector complex arcsine
20.8
vatcacos
- Vector complex arccosine
20.9
vatcatan
- Vector complex arctangent
20.10
vatcacsc
- Vector complex arccosecant
20.11
vatcasec
- Vector complex arcsecant
20.12
vatcacot
- Vector complex arccotangent
21
Standard Complex Hyperbolic Trigonometric Functions
21.1
vatcsinh
- Vector complex hyperbolic sine
21.2
vatccosh
- Vector complex hyperbolic cosine
21.3
vatctanh
- Vector complex hyperbolic tangent
21.4
vatccsch
- Vector complex hyperbolic cosecant
21.5
vatcsech
- Vector complex hyperbolic secant
21.6
vatccoth
- Vector complex hyperbolic cotangent
21.7
vatcasinh
- Vector complex hyperbolic arcsine
21.8
vatcacosh
- Vector complex hyperbolic arccosine
21.9
vatcatanh
- Vector complex hyperbolic arctangent
21.10
vatcacsch
- Vector complex hyperbolic arccosecant
21.11
vatcasech
- Vector complex hyperbolic arcsecant
21.12
vatcacoth
- Vector complex hyperbolic arccotangent
22
Complex Versine Functions
22.1
vatcver
- Vector complex versine
22.2
vatcvcs
- Vector complex vercosine
22.3
vatccvs
- Vector complex coversine
22.4
vatccvc
- Vector complex covercosine
22.5
vatchav
- Vector complex haversine
22.6
vatchac
- Vector complex havercosine
22.7
vatchcv
- Vector complex hacoversine
22.8
vatchcc
- Vector complex hacovercosine
22.9
vatcaver
- Vector complex arcversine
22.10
vatcavcs
- Vector complex arcvercosine
22.11
vatcacvs
- Vector complex arccoversine
22.12
vatcacvc
- Vector complex arccovercosine
22.13
vatcahav
- Vector complex archaversine
22.14
vatcahac
- Vector complex archavercosine
22.15
vatcahcv
- Vector complex archacoversine
22.16
vatcahcc
- Vector complex archacovercosine
23
Complex Cardinal Trigonometric Functions
23.1
vatcsinc
- Vector complex cardinal sine
23.2
vatccosc
- Vector complex caridnal cosine
23.3
vatctanc
- Vector complex cardinal tangent
24
Complex Cardinal Hyperbolic Trigonometric Functions
24.1
vatcsinhc
- Vector complex cardinal hyperbolic sine
24.2
vatccoshc
- Vector complex caridnal hyperbolic cosine
24.3
vatctanhc
- Vector complex cardinal hyperbolic tangent
25
Complex Hyperbolic Trigonometric Minus X Functions
25.1
vatcsinhmx
- Vector complex hyperbolic sine minus x
25.2
vatccoshmx
- Vector complex hyperbolic cosine minus x
25.3
vatctanhmx
- Vector complex hyperbolic tangent minus x
26
Complex Gudermannian
26.1
vatcgd
- Vector complex Gudermannian
26.2
vatcagd
- Vector complex inverse Gudermannian
27
Acknowledgements
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