Math Vector Library 1.1 Reference Manual (C/C++) DD-00002-011

Math Vector Library 1.1
Reference Manual (C/C++)
DD-00002-011

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 Thread Safety
2.3 SIMD/SPMD Unit Usage
2.4 Performance Characteristics
2.5 Extended Vector Sizes (_64 suffix functions)
3 Utility
3.1 mvecver - Version query
4 Rounding
4.1 vfloor - Vector round down
4.2 vceil - Vector round up
4.3 vtrunc - Vector truncate
4.4 vround - Vector rounding
5 Roots
5.1 vsqrt - Vector square root $⎷ -- x$
5.2 vrsqrt - Vector reciprocal square root $⎷ -- 1/ x$
5.3 vcbrt - Vector cube root $⎷3-- x$
5.4 vrcbrt - Vector reciprocal cube root $⎷3-- 1/ x$
6 Trigonometric Functions
6.1 vsin - Vector sine $sin(x)$
6.2 vcos - Vector cosine $cos(x)$
6.3 vtan - Vector tangent $tan(x)$
6.4 vasin - Vector arcsine $-1 sin (x)$
6.5 vacos - Vector arccosine $-1 cos (x)$
6.6 vatan - Vector arctangent $-1 tan (x)$
6.7 vatan2 - Vector arctangent $-1 tan (x/y)$
6.8 vsind - Vector sine $sin(x)$ (degrees)
6.9 vcosd - Vector cosine $cos(x)$ (degrees)
6.10 vtand - Vector tangent $tan(x)$ (degrees)
6.11 vasind - Vector arcsine $-1 sin (x)$ (degrees)
6.12 vacosd - Vector arccosine $-1 cos (x)$ (degrees)
6.13 vatand - Vector arctangent $-1 tan (x)$ (degrees)
6.14 vsinpi - Vector half-cycle sine $sin(πx)$
6.15 vcospi - Vector half-cycle cosine $cos(πx)$
6.16 vtanpi - Vector half-cycle tangent $tan(πx)$
6.17 vasinpi - Vector half-cycle arcsine $-1 sin (x)/π$
6.18 vacospi - Vector half-cycle arccosine $-1 cos (x)/π$
6.19 vatanpi - Vector half-cycle arctangent $-1 tan (x)/π$
7 Hypergeometric Functions
7.1 vsinh - Vector hypergeometric sine $sinh(x)$
7.2 vcosh - Vector hypergeometric cosine $cosh(x)$
7.3 vtanh - Vector hypergeometric tangent $tanh(x)$
7.4 vasinh - Vector hypergeometric arcsine $-1 sinh (x)$
7.5 vacosh - Vector hypergeometric arccosine $-1 cosh (x)$
7.6 vatanh - Vector hypergeometric arctangent $-1 tanh (x)$
8 Exponentials and Logarithms
8.1 vexp - Vector exponential $x e$
8.2 vexpm1 - Vector exponential $x e -1$
8.3 vexp2 - Vector binary exponential $x 2$
8.4 vexp2m1 - Vector binary exponential minus one $x 2 -1$
8.5 vexp10 - Vector natural exponential $x 10$
8.6 vexp10m1 - Vector natural exponential minus one $x 10 -1$
8.7 vlog - Vector logarithm $log(x)$
8.8 vlog2 - Vector binary logarithm $log2(x)$
8.9 vlog10 - Vector base-10 logarithm $log10(x)$
8.10 vlog1p - Vector logarithm $log(x+ 1)$
8.11 vpow - Vector power $y x$
8.12 vpows - Vector power scalar exponent $y x$
8.13 vmod - Vector modulus $mod(x,y)$
9 Error Functions
9.1 verf - Vector error function $erf(x)$
9.2 verfinv - Vector inverse error function $-1 erf (x)$
9.3 verfc - Vector complementary error function $erfc(x)$
9.4 verfcinv - Vector inverse complementary error function $-1 erfc (x)$
10 Bessel Functions
10.1 vbesj0 - Vector Bessel Function $J0(x)$
10.2 vbesy0 - Vector Bessel Function $Y0(x)$
10.3 vbesj1 - Vector Bessel Function $J1(x)$
10.4 vbesy1 - Vector Bessel Function $Y1(x)$
10.5 vbesjn - Vector Bessel Function $Jn(x)$
10.6 vbesyn - Vector Bessel Function $Yn(x)$
11 Gamma Function Related
11.1 vlgamma - Vector Log-Gamma $logΓ (x)$
12 Einstein Functions
12.1 veinst1 - Vector Einstein function $E1(x)$
12.2 veinst2 - Vector Einstein function $E2(x)$
12.3 veinst3 - Vector Einstein function $E3(x)$
12.4 veinst4 - Vector Einstein function $E4(x)$
13 Integrals
13.1 vsi - Vector Sine Integral $Si(x)$
13.2 vci - Vector Cosine Integral $Ci(x)$
13.3 vti2 - Vector Inverse Tangent Integral $Ti2(x)$
14 Other Functions
14.1 vabs - Vector absolute value $|x|$
14.2 vhypot - Vector euclidean distance $√︁ -2--2- x +y$
14.3 vrem - Vector remainder
15 Arithmetic Functions
15.1 vadd - Vector addition $x+y$
15.2 vsadd - Vector scalar addition $x+ α$
15.3 vsub - Vector subtraction $x-y$
15.4 vssub - Vector scalar subtraction $x-α$
15.5 vmul - Vector multiplication $xy$
15.6 vsmul - Vector scalar multiplication $αx$
15.7 vdiv - Vector division $x/y$
15.8 vsdiv - Vector scalar division $x/α$
15.9 vrecp - Vector reciprocal $1/x$
16 Complex Numbers
16.1 vcreal - Vector complex real compoment $Re(x)$
16.2 vcimag - Vector complex imaginary compoment $Im(x)$
16.3 vcabs - Vector complex absolute value $|x|$
16.4 vcarg - Vector complex argument $arg(x)$
16.5 vconj - Vector complex conjugate $-- x$
16.6 vcproj - Vector complex Riemann sphere projection $proj(x)$
17 Complex Exponentials and Logarithms
17.1 vcexp - Vector complex exponentiation $exp(x)$
17.2 vclog - Vector complex logarithm $log(x)$
17.3 vcpow - Vector complex power $y x$
17.4 vcpows - Vector complex power scalar exponent $y x$
17.5 vccis - Vector complex Euler’s Formula $exp(ix)$
18 Complex Roots
18.1 vcsqrt - Vector complex square root $⎷ -- x$
19 Complex Trigonometric Functions
19.1 vcsin - Vector complex sine $sin(x)$
19.2 vccos - Vector complex cosine $cos(x)$
19.3 vctan - Vector complex tangent $tan(x)$
19.4 vcasin - Vector complex arcsine $-1 sin (x)$
19.5 vcacos - Vector complex arccosine $-1 cos (x)$
19.6 vcatan - Vector complex arctangent $-1 tan (x)$
20 Complex Hypergeometric Functions
20.1 vcsinh - Vector complex hyperbolic sine $sinh(x)$
20.2 vccosh - Vector complex hyperbolic cosine $cosh(x)$
20.3 vctanh - Vector complex hyperbolic tangent $tanh(x)$
20.4 vcasinh - Vector complex hyperbolic arcsine $-1 sinh (x)$
20.5 vcacosh - Vector complex hyperbolic arccosine $-1 cosh (x)$
20.6 vcatanh - Vector complex hyperbolic arctangent $-1 tanh (x)$
21 Complex Arithmetic
21.1 vcadd - Vector complex addition $x+ y$
21.2 vcsadd - Vector complex scalar subtraction $x+ α$
21.3 vcsub - Vector complex subtraction $x -y$
21.4 vcssub - Vector complex scalar subtraction $x- α$
21.5 vcmul - Vector complex multiplication $xy$
21.6 vcsmul - Vector complex scalar multiplication $αx$
21.7 vcmulc - Vector complex conjugate multiplication $-- xy$
21.8 vcdiv - Vector complex division $x/y$
21.9 vcsdiv - Vector complex scalar division $x/α$
22 Acknowledgements