Math Scalar Library 1.1 Reference Manual (Fortran) DD-00003-111

Math Scalar Library 1.1
Reference Manual (Fortran)
DD-00003-111

Jan Adelsbach

February 17, 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 Function Naming Scheme
2.3 Thread Safety
2.4 FPU Signaling
3 Utility
3.1 mscaver - Version query
4 Rounding
4.1 sfloor - Round down to nearest integral part
4.2 sceil - Round up to nearest integral part
4.3 strunc - Truncate to nearest integral part
4.4 sround - Round to nearest integral part
5 Roots
5.1 ssqrt - Square root $⎷- x$
5.2 srsqrt - Inverse square root $⎷- 1/ x$
5.3 scbrt - Cube root $⎷3- x$
5.4 srcbrt - Inverse cube root $3⎷- 1/ x$
6 Trigonometric Functions
6.1 ssin - Sine $sin(x)$
6.2 scos - Cosine $cos(x)$
6.3 stan - Tangent $tan(x)$
6.4 scsc - Cosecant $csc(x)$
6.5 ssec - Secant $sec(x)$
6.6 scot - Cotangent $cot(x)$
6.7 sasin - Arcsine $-1 sin (x)$
6.8 sacos - Arccosine $-1 cos (x)$
6.9 satan - Arctangent $-1 tan (x)$
6.10 sacsc - Arccosecant $-1 csc (x)$
6.11 sasec - Arcsecant $-1 sec (x)$
6.12 sacot - Arcotangent $-1 cot (x)$
7 Trigonometric Functions (Half-Cycle)
7.1 ssinpi - Half-Cycle Sine $sin(πx)$
7.2 scospi - Half-Cycle Cosine $cos(πx)$
7.3 stanpi - Half-Cycle Tangent $tan(πx)$
7.4 scscpi - Half-Cycle Cosecant $csc(πx)$
7.5 ssecpi - Half-Cycle Secant $sec(πx)$
7.6 scotpi - Half-Cycle Cotangent $cot(πx)$
7.7 sasinpi - Half-Cycle Arcsine $-1 sin (x)/π$
7.8 sacospi - Half-Cycle Arccosine $-1 cos (x)/π$
7.9 satanpi - Half-Cycle Arctangent $-1 tan (x)/π$
7.10 sacscpi - Half-Cycle Arccosecant $-1 csc (x)/π$
7.11 sasecpi - Half-Cycle Arcsecant $-1 sec (x)/π$
7.12 sacotpi - Half-Cycle Arcotangent $-1 cot (x)/π$
8 Trigonometric Functions (Degrees)
8.1 ssind - Degree Sine $sin(x)$
8.2 scosd - Degree Cosine $cos(x)$
8.3 stand - Degree Tangent $tan(x)$
8.4 scscd - Degree Cosecant $csc(x)$
8.5 ssecd - Degree Secant $sec(x)$
8.6 scotd - Degree Cotangent $cot(x)$
8.7 sasind - Degree Arcsine $-1 sin (x)$
8.8 sacosd - Degree Arccosine $-1 cos (x)$
8.9 satand - Degree Arctangent $-1 tan (x)$
8.10 sacscd - Degree Arccosecant $-1 csc (x)$
8.11 sasecd - Degree Arcsecant $-1 sec (x)$
8.12 sacotd - Degree Arcotangent $-1 cot (x)$
9 Hypergeometric Functions
9.1 ssinh - Hypergeometric sine $sinh(x)$
9.2 scosh - Hypergeometric cosine $cosh(x)$
9.3 stanh - Hypergeometric tangent $tanh(x)$
9.4 scsch - Hypergeometric Cosecant $csch(x)$
9.5 scsch - Hypergeometric Secant $csech(x)$
9.6 scsch - Hypergeometric Cotangent $ccoth(x)$
9.7 sasinh - Hypergeometric arcsine $-1 sinh (x)$
9.8 sacosh - Hypergeometric arccosine $-1 cosh (x)$
9.9 satanh - Hypergeometric arctangent $-1 tanh (x)$
9.10 sacsch - Hypergeometric arccosecant $-1 csch (x)$
9.11 sasech - Hypergeometric arcsecant $-1 sech (x)$
9.12 sacoth - Hypergeometric arccotangent $-1 coth (x)$
10 Hypergeometric Functions Minus X
10.1 ssinhmx - Hypergeometric sine minus x $sinh(x)-x$
10.2 scoshmx - Hypergeometric cosine minux x $cosh(x)-x$
10.3 stanhmx - Hypergeometric tangent minus x $tanh(x)-x$
11 Versine Functions
11.1 sver - Versine $ver(x)$
11.2 svcs - Vercosine $vcs(x)$
11.3 scvs - Coversine $cvs(x)$
11.4 scvc - Covercone $cvc(x)$
11.5 shav - Haversine $hav(x)$
11.6 shac - Havercosine $hac(x)$
11.7 shcv - Hacoversine $hcv(x)$
11.8 shcc - Hacovercosine $hcc(x)$
11.9 saver - Arcversine $-1 ver (x)$
11.10 savcs - Arcvercosine $-1 vcs (x)$
11.11 sacvs - Arccoversine $-1 cvs (x)$
11.12 sacvc - Arccovercone $-1 cvc (x)$
11.13 sahav - Archaversine $-1 hav (x)$
11.14 sahac - Archavercosine $-1 hac (x)$
11.15 sahcv - Archacoversine $-1 hcv (x)$
11.16 sahcc - Archacovercosine $-1 hcc (x)$
12 Versines (Half-Cycle)
12.1 sverpi - Half-Cycle Versine $ver(πx)$
12.2 svcspi - Half-Cycle Vercosine $vcs(πx)$
12.3 scvspi - Half-Cycle Coversine $cvs(πx)$
12.4 scvcpi - Half-Cycle Covercosine $cvc(πx)$
12.5 shavpi - Half-Cycle Haversine $hav(πx)$
12.6 shacpi - Half-Cycle Havercosine $hac(πx)$
12.7 shcvpi - Half-Cycle Hacoversine $hcv(πx)$
12.8 shccpi - Half-Cycle Hacovercosine $hcc(πx)$
12.9 saverpi - Half-Cycle Arcversine $-1 ver (x)/π$
12.10 savcspi - Half-Cycle Arcvercosine $-1 vcs (x)/π$
12.11 sacvspi - Half-Cycle Arccoversine $-1 cvs (x)/π$
12.12 sacvcpi - Half-Cycle Arccovercone $-1 cvc (x)/π$
12.13 sahavpi - Half-Cycle Archaversine $-1 hav (x)/π$
12.14 sahacpi - Half-Cycle Archavercosine $-1 hac (x)/π$
12.15 sahcvpi - Half-Cycle Archacoversine $-1 hcv (x)/π$
12.16 sahccpi - Half-Cycle Archacovercosine $-1 hcc (x)/π$
13 Versines (Degree)
13.1 sverd - Versine $ver(x)$
13.2 svcsd - Vercosine $vcs(x)$
13.3 scvsd - Coversine $cvs(x)$
13.4 scvcd - Covercosine $cvc(x)$
13.5 shavd - Haversine $hav(x)$
13.6 shacd - Havercosine $hac(x)$
13.7 shcvd - Hacoversine $hcv(x)$
13.8 shccd - Hacovercosine $hcc(x)$
13.9 saverd - Arcversine $-1 ver (x)$
13.10 savcsd - Arcvercosine $-1 vcs (x)$
13.11 sacvsd - Arccoversine $-1 cvs (x)$
13.12 sacvcd - Arccovercone $-1 cvc (x)$
13.13 sahavd - Archaversine $-1 hav (x)$
13.14 sahacd - Archavercosine $-1 hac (x)$
13.15 sahcvd - Archacoversine $-1 hcv (x)$
13.16 sahccd - Archacovercosine $-1 hcc (x)$
14 Exsecant and Excosecant
14.1 sexs - Exsecant $exs(x)$
14.2 sexc - Excosecant $exc(x)$
14.3 saexs - Arcexsecant $-1 exs (x)$
14.4 saexc - Arcexcosecant $-1 exc (x)$
15 Exsecant and Excosecant (Half-Cycle)
15.1 sexspi - Half-Cycle Exsecant $exs(πx)$
15.2 sexcpi - Half-Cycle Excosecant $exc(πx)$
15.3 saexspi - Half-Cycle Arcexsecant $-1 exs (x)/π$
15.4 saexcpi - Half-Cycle Arcexcosecant $-1 exc (x)/π$
16 Exsecant and Excosecant (Degrees)
16.1 sexsd - Exsecant $exs(x)$
16.2 sexcd - Excosecant $exc(x)$
16.3 saexsd - Arcexsecant $-1 exs (x)$
16.4 saexcd - Arcexcosecant $-1 exc (x)$
17 Other Trigonometric functions
17.1 sgd - Gudermannian function $gd(x)$
17.2 sagd - Inverse Gudermannian function $-1 gd (x)$
17.3 scrd - Chord $crd(x)$
17.4 sacrd - Inverse Chord $-1 crd (x)$
18 Cardinal Trigonometric Functions
18.1 ssinc - Cardinal Sine $sinc(x)$
18.2 scosc - Cardinal Cosine $cosc(x)$
18.3 stanc - Cardinal Tangent $tanc(x)$
19 Cardinal Normalized Trigonometric Functions
19.1 ssincpi - Cardinal Normalized Sine $sincπ(x)$
19.2 scoscpi - Cardinal Normalized Cosine $coscπ(x)$
19.3 stancpi - Cardinal Normalized Tangent $tancπ(x)$
20 Cardinal Hyperbolic Trigonometric Functions
20.1 ssinhc - Cardinal Hyperbolic Sine $sinhc(x)$
20.2 scoshc - Cardinal Hyperbolic Cosine $coshc(x)$
20.3 stanhc - Cardinal Hyperbolic Tangent $tanhc(x)$
21 Expoentials and Logarithms
21.1 sexp - Exponentiation $x e$
21.2 sexpm1 - Exponentiation $x e -1$
21.3 sexp2 - Binary exponentiation $x 2$
21.4 sexp2m1 - Binary exponentiation minus one $x 2 -1$
21.5 sexp10 - Natural exponentiation $x 10$
21.6 sexp10m1 - Natural exponentiation minus one $x 10 -1$
21.7 slog - Natural logarithm $log(x)$
21.8 slog2 - Base-2 logarithm $log2(x)$
21.9 slog10 - Base-10 logarithm $log10(x)$
21.10 slog1p - Natural logarithm plus one $log(x+1)$
21.11 spow - Raise $y x$
21.12 sfmod - Remainder $mod(x,y)$
22 Special Functions
22.1 serf - Error function $erf(x)$
22.2 serfinv - Inverse Error function $-1 erf (x)$
22.3 serfc - Complementary error function $erfc(x)$
22.4 serfcinv - Inverse Complementary error function $-1 erfc (x)$
22.5 sj0 - Bessel function $J0(x)$
22.6 sy0 - Bessel function $Y0(x)$
22.7 sj1 - Bessel function $J1(x)$
22.8 sy1 - Bessel function $Y1(x)$
22.9 sjn - Bessel function $Jn(x)$
22.10 syn - Bessel function $Yn(x)$
22.11 slgamma - Log-Gamma function $logΓ (x)$
22.12 seinst1 - Einstein function $E1(x)$
22.13 seinst2 - Einstein function $E2(x)$
22.14 seinst3 - Einstein function $E3(x)$
22.15 seinst4 - Einstein function $E4(x)$
22.16 ssi - Sine Integral $Si(x)$
22.17 sci - Cosine Integral $Ci(x)$
22.18 sti2 - Inverse Tangent Integral $Ti2(x)$
23 Other Functions
23.1 sfabs - Absolute value $|x|$
23.2 scopysign - Copy sign
23.3 shypot - Euclidean distance $√︁-2---2 x + y$
23.4 sremainder - Remainder
24 Complex Numbers
24.1 screal - Complex real component $Re(x)$
24.2 scimag - Complex imaginary component $Im(x)$
24.3 scabs - Complex absolute value $|x|$
24.4 scarg - Complex argument $arg(x)$
24.5 sconj - Complex conjugate $- x$
24.6 scproj - Complex Riemann sphere projection $proj(x)$
24.7 scexp - Complex exponentiation $exp(x)$
24.8 sclog - Complex logarithm $log(x)$
24.9 scsqrt - Complex square root $⎷- x$
24.10 scpow - Complex power $y x$
24.11 sccis - Complex Euler’s Formula $exp(ix)$
25 Complex Trigonometry
25.1 scsin - Complex sine $sin(x)$
25.2 sccos - Complex cosine $cos(x)$
25.3 sctan - Complex tangent $tan(x)$
25.4 scasin - Complex arcsine $-1 sin (x)$
25.5 scacos - Complex arccosine $-1 cos (x)$
25.6 scatan - Complex arctangent $-1 tan (x)$
25.7 scsinh - Complex hyperbolic sine $sinh(x)$
25.8 sccosh - Complex hyperbolic cosine $cosh(x)$
25.9 sctanh - Complex hyperbolic tangent $tanh(x)$
25.10 sccsch - Complex hyperbolic cosecant $csch(x)$
25.11 scsech - Complex hyperbolic secant $sech(x)$
25.12 sccoth - Complex hyperbolic cotangent $coth(x)$
25.13 scasinh - Complex hyperbolic arcsine $-1 sinh (x)$
25.14 scacosh - Complex hyperbolic arccosine $-1 cosh (x)$
25.15 scatanh - Complex hyperbolic arctangent $-1 tanh (x)$
25.16 scacsch - Complex hyperbolic arccosecant $-1 csch (x)$
25.17 scasech - Complex hyperbolic arcsecant $-1 sech (x)$
25.18 scacoth - Complex hyperbolic arccotangent $-1 coth (x)$
25.19 scgd - Complex Gudermannian $gd(x)$
25.20 scagd - Complex inverse Gudermannian $-1 gd (x)$
26 Complex Versines
26.1 scver - Complex Versine $ver(x)$
26.2 scvcs - Complex Vercosine $vcs(x)$
26.3 sccvs - Complex Coversine $cvs(x)$
26.4 sccvc - Complex Covercone $cvc(x)$
26.5 schav - Complex Haversine $hav(x)$
26.6 schac - Complex Havercosine $hac(x)$
26.7 schcv - Complex Hacoversine $hcv(x)$
26.8 schcc - Complex Hacovercosine $hcc(x)$
26.9 scaver - Complex Arcversine $-1 ver (x)$
26.10 scavcs - Complex Arcvercosine $-1 vcs (x)$
26.11 scacvs - Complex Arccoversine $-1 cvs (x)$
26.12 scacvc - Complex Arccovercone $-1 cvc (x)$
26.13 scahav - Complex Archaversine $-1 hav (x)$
26.14 scahac - Complex Archavercosine $-1 hac (x)$
26.15 scahcv - Complex Archacoversine $-1 hcv (x)$
26.16 scahcc - Complex Archacovercosine $-1 hcc (x)$
27 Complex Cardinal Trigonometric Functions
27.1 scsinc - Complex Cardinal Sine $sinc(x)$
27.2 sccosc - Complex Cardinal Cosine $cosc(x)$
27.3 sctanc - Complex Cardinal Tangent $tanc(x)$
28 Complex Cardinal Hyperbolic Trigonometric Functions
28.1 scsinhc - Complex Cardinal Hyperbolic Sine $sinhc(x)$
28.2 sccoshc - Complex Cardinal Hyperbolic Cosine $coshc(x)$
28.3 sctanhc - Complex Cardinal Hyperbolic Tangent $tanhc(x)$
29 Acknowledgements