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-digraph TrigonometricsFunctions {
- node [shape=circle];
-
-//
-// -*- Basic Call -*-
-//
-F77_Call [label="Fortan Call", shape=doublecircle, color=green];
-C_Call [label="C Call", shape=doublecircle, color=blue];
-LAPACK_Call [label="LAPACK Call", shape=doublecircle, color=red];
-
-//
-// -*- Specific LAPACK Call -*-
-//
-Dlamch_E_Call [label="dlamch('E')", comment="Précision Machine - LAPACK", shape=doublecircle, color=red];
-Dlamch_U_Call [label="dlamch('U')", comment="Borne Inférieure - LAPACK", shape=doublecircle, color=red];
-Dlamch_O_Call [label="dlamch('O')", comment="Borne Supérieure - LAPACK", shape=doublecircle, color=red];
-
-//
-// -*- Functions definition -*-
-//
-
-// Cosinus
-subgraph clusterCosinus {
- label="Cosine";
- color=yellow;
- style=filled;
- Cos_Real [label="cos(R)"];
- Cos_Complex [label="cos(C)"];
-}
-subgraph clusterHyperbolicCosinus {
- label="Hyperbolic Cosine";
- color="wheat";
- style=filled;
- Cos_Hyperbolic_Real [label="ch(R)"];
- Cos_Hyperbolic_Complex [label="ch(C)"];
-}
-
-// ArcCosinus
-subgraph clusterArcCosinus {
- label="Inverse Cosine";
- color=springgreen;
- style=filled;
- ACos_Real [label="acos(R)"];
- ACos_Complex [label="acos(C)"];
-}
-subgraph clusterArcHyperbolicCosinus {
- label="Inverse Hyperbolic Cosine";
- color=slategray;
- style=filled;
- ACos_Hyperbolic_Real [label="ach(R)"];
- ACos_Hyperbolic_Complex [label="ach(C)"];
-}
-
-// Sinus
-subgraph clusterSinus {
- label="Sine";
- color="violetred";
- style=filled;
- Sin_Real [label="sin(R)"];
- Sin_Complex [label="sin(C)"];
-}
-subgraph clusterHyperbolicSinus {
- label="Hyperbolic Sine";
- color=skyblue;
- style=filled;
- Sin_Hyperbolic_Real [label="sh(R)"];
- Sin_Hyperbolic_Complex [label="sh(C)"];
-}
-
-
-// ArcSinus
-subgraph clusterArcSinus {
- label="Inverse Sine";
- color=slateblue;
- style=filled;
- ASin_Real [label="asin(R)"];
- ASin_Complex [label="asin(C)"];
-}
-subgraph clusterArcHyperbolicSinus {
- label="Inverse Hyperbolic Sine";
- color=violet;
- style=filled;
- ASin_Hyperbolic_Real [label="ash(R)"];
- ASin_Hyperbolic_Complex [label="ash(C)"];
-}
-
-
-// Tangeante
-subgraph clusterTan {
- label="Tan";
- color=turquoise;
- style=filled;
- Tan_Real [label="tan(R)"];
- Tan_Complex [label="tan(C)", comment="wtan"];
-}
-subgraph clusterHyperbolicTan {
- label="Hyperbolic Tan";
- color=tomato;
- style=filled;
- Tan_Hyperbolic_Real [label="tanh(R)"];
- Tan_Hyperbolic_Complex [label="tanh(C)"];
-}
-
-
-// ArcTangeante
-subgraph clusterArcTan {
- label="Inverse Tan";
- color=limegreen;
- style=filled;
- ATan_Real [label="atan(R)"];
- ATan_Complex [label="atan(C)", comment="watan"];
-}
-subgraph clusterArcHyperbolicTan {
- label="Inverse Hyperbolic Tan";
- color=mediumorchid;
- style=filled;
- ATan_Hyperbolic_Real [label="atanh(R)"];
- ATan_Hyperbolic_Complex [label="atanh(C)"];
-}
-
-
-// ArcTaneante2
-ATan2_Real [label="atan2(R)"];
-
-// Exponentielle
-subgraph clusterExponential {
- label="Exponential";
- color=thistle;
- style=filled;
- Exp_Real [label="exp(R)"];
- Exp_Complex [label="exp(C)"];
-}
-
-// Log
-subgraph clusterLog {
- label="Log";
- color=tan;
- style=filled;
- Log_Real [label="log(R)"];
- Log_Positive_Real [label="log(R+)"];
- Log_Negative_Real [label="log(R-)"];
- Log_Complex [label="log(C)"];
-}
-
-// Log1p
-Log1p_Real [label="log1p(R)"];
-
-// Racine Carrée
-subgraph clusterSquare {
- label="Square Root";
- color=steelblue;
- style=filled;
- Sqrt_Real [label="sqrt(R)"];
- Sqrt_Positive_Real [label="sqrt(R+)"];
- Sqrt_Negative_Real [label="sqrt(R-)"];
- Sqrt_Complex [label="sqrt(C)", comment="wsqrt"];
-}
-
-// Partie Imaginaire
-Imag_Complex [label="imag(C)"];
-
-// Valeur Absolue
-Abs_Real [label="abs(R)", comment="|R|"];
-
-// Signe
-Sign_Real [label="sign(R)"];
-
-// Pythagore
-Pythag_Real [label="pythag(R)"];
-
-
-//
-// -*- Functions call links -*-
-//
-subgraph clusterLAPACK {
- style=filled;
- color=lightsteelblue;
- label="LAPACK";
- // -*- DLAMCH -*-
- Dlamch_E_Call -> LAPACK_Call;
- Dlamch_U_Call -> LAPACK_Call;
- Dlamch_O_Call -> LAPACK_Call;
-}
-
-
-// -*- COS -*-
-//
-// cos(a+ib) = cos(a).ch(b) - i.sin(a).sh(b)
-Cos_Complex -> {
- Cos_Real
- Sin_Real
- Cos_Hyperbolic_Real
- Sin_Hyperbolic_Real
- };
-
-// Call a cosinus function in F77 math lib
-Cos_Real -> F77_Call;
-
-
-// -*- ACOS -*-
-//
-// acos(a+ib) = see $SCIHOME/modules/elementaries_functions/src/fortran/wacos.f
-ACos_Complex -> {
- Dlamch_O_Call
- Dlamch_E_Call
- Dlamch_U_Call
- Sqrt_Real
- Abs_Real
- ACos_Real
- ATan_Real
- Log1p_Real
- Log_Real
- Sign_Real
- };
-
-// Call an inverse cosine function in F77 math lib
-ACos_Real -> F77_Call;
-
-
-// -*- COSH -*-
-//
-// ch(z) = cos(i.z)
-Cos_Hyperbolic_Complex -> {
- Cos_Complex
- };
-
-// ch(x) = 1/2 . exp(|x|) + exp(-|x|)
-Cos_Hyperbolic_Real -> {
- Exp_Real
- Abs_Real
- };
-
-
-// -*- ACOSH -*-
-//
-// acosh(z) = sign(-imag(acos(z)) i acos(z)
-ACos_Hyperbolic_Complex -> {
- Imag_Complex
- ACos_Complex
-};
-// acosh(z) = sign(-imag(acos(z)) i acos(
-ACos_Hyperbolic_Real -> {
- Imag_Complex
- ACos_Complex
- Min_Real
-};
-
-
-// -*- SIN -*-
-//
-// sin(a+ib) = sin(a).ch(b) + i.cos(a).sh(b)
-Sin_Complex -> {
- Cos_Real
- Sin_Real
- Cos_Hyperbolic_Real
- Sin_Hyperbolic_Real
- };
-
-// Call a sinus function in F77 math lib
-Sin_Real -> F77_Call;
-
-
-// -*- ASIN -*-
-//
-// asin(a+ib) = see $SCIHOME/modules/elementaries_functions/src/fortran/wasin.f
-ASin_Complex -> {
- Dlamch_O_Call
- Dlamch_U_Call
- Dlamch_E_Call
- Abs_Real
- Sqrt_Real
- ASin_Real
- ATan_Real
- Log1p_Real
- Log_Real
- Sign_Real
-};
-
-// Call an inverse sine function in F77 math lib
-ASin_Real -> F77_Call;
-
-
-// -*- SINH -*-
-//
-// sh(z) = -i.sin(i.z)
-Sin_Hyperbolic_Complex -> {
- Sin_Complex
- };
-
-// sh(x) = imag(sin(i.x))
-Sin_Hyperbolic_Real -> {
- Sin_Complex
- Imag_Complex
- };
-
-
-// -*- ASINH -*-
-//
-// asinh(z) = -i asin(i z)
-ASin_Hyperbolic_Complex -> {
- ASin_Complex
-};
-
-// asinh(z) = -i asin(i z)
-ASin_Hyperbolic_Real -> {
- ASin_Complex
- Imag_Complex
-};
-
-
-// -*- TAN -*-
-//
-// tan(a+ib) = x_r + i.x_i
-//
-// x_r= 1/2 sin(2.a) / d
-//
-// x_i = | sh(2.b) / 2.d si |b| <= L
-// | sign(a)
-//
-// d = cos(a)^2 + sh(b)^2
-//
-// L = 1 + log(2 / sqrt(dlamch('e')))
-Tan_Complex -> {
- Cos_Real
- Sin_Hyperbolic_Real
- Log_Real
- Sqrt_Real
- Dlamch_E_Call
- Abs_Real
- Sign_Real
- };
-
-// Call a tangeante function in F77 math lib
-Tan_Real -> F77_Call;
-
-
-//
-// -*- ATAN -*-
-//
-ATan_Complex -> {
- Dlamch_O_Call
- ATan_Real
- Abs_Real
- Sign_Real
- Log_Real
- ATan2_Real
-};
-
-// Call an inverse tangeant function in F77 math lib
-ATan_Real -> F77_Call;
-
-
-// -*- TANH -*-
-//
-// tanh(z) = -i.tan(i.z)
-Tan_Hyperbolic_Complex -> {
- Tan_Complex
- };
-
-// tanh(x) = imag(tan(i.x))
-Tan_Hyperbolic_Real -> {
- Tan_Complex
- Imag_Complex
- };
-
-// -*- ATANH -*-
-//
-// atanh(z) = i atan(-i z)
-ATan_Hyperbolic_Complex -> {
- ATan_Complex
- };
-
-// atanh(x) = -imag(atan(i.x)) | i.atan(-i.x)
-ATan_Hyperbolic_Real -> {
- ATan_Complex
- Imag_Complex
- };
-
-
-// -*- LOG -*-
-//
-// log(a+ib) = x_r + i.x_i
-//
-// Constantes :
-// L_inf = sqrt(dlamch('U'))
-// L_sup = sqrt(R_max / 2)
-// R_max = dlamch('O')
-// t = pythag(|a|,|b|)
-// r = |b|/|a|
-//
-// x_i = atan2(b, a)
-//
-// x_r = | 1/2 logp1((|a|-1)(|a|+1) + |b|^2) si 1/2 <= |a| <= sqrt(2)
-// | 1/2 log(|a|^2 + |b|^2) si L_inf < |b| && |a| < L_sup
-// | |a| si |a| > R_max
-// | log(t) si t <= R_max
-// | log(|a|) + 1/2 logp1(r^2) sinon
-Log_Complex -> {
- Sqrt_Real
- Dlamch_U_Call
- Dlamch_O_Call
- Pythag_Real
- Log1p_Real
- Log_Real
- Abs_Real
- Pythag_Real
- ATan2_Real
- };
-
-// Separate positive and negative case
-Log_Real -> {
- Log_Positive_Real
- Log_Negative_Real
- };
-
-// Call another log function, treat it as complex
-Log_Negative_Real -> Log_Complex;
-
-// Call a log function in F77 math lib
-Log_Positive_Real -> F77_Call;
-
-// Call a log1p function in F77 math lib
-Log1p_Real -> F77_Call;
-
-
-// -*- SQRT -*-
-//
-// sqrt(a+ib) = x_r + i.x_i
-//
-// Constantes :
-// Rmax = dlamch('O')
-// BRmin = 2.dlamch('U')
-// t = sqrt(2.|a| + pythag(a,b))
-//
-// (1) a = 0
-//~~~~~~~~~~~~
-// x_r = | sqrt(|b| / 2) si |b| <= BRmin
-// | sqrt(|b|).sqrt(1/2)
-//
-// x_i = sign(b).x_r
-//
-// (2) |a| >= BRmax && |b| >= BRmax
-//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-// - Si t > Rmax
-// a = a / 16
-// b = b / 16
-// t = sqrt(2.|a| + pythag(a,b))
-// x_r = | 2.t si a >= 0
-// | 4.|b| / t
-// x_i = | 4.b / t si a >= 0
-// | 2.sign(b).t
-//
-// - Sinon
-//
-// x_r = | t / 2 si a >= 0
-// | |b| / t
-//
-// x_i = | b / t si a >= 0
-// | sign(b) / 2.t
-//
-// (3) Tous les cas pourris
-//~~~~~~~~~~~~~~~~~~~~~~~~~~
-//
-// x_r = | a + b si a is NaN && b is NaN
-// | |b| si |b| > Rmax
-// | 0 si a < -Rmax
-// | a
-//
-// x_i = | a + b si a is NaN && b is NaN
-// | b si |b| > Rmax
-// | sign(b).|a| si a < -Rmax
-// | 0
-//
-Sqrt_Complex -> {
- Abs_Real
- Sqrt_Real
- Sign_Real
- Pythag_Real
- Dlamch_U_Call
- Dlamch_O_Call
- };
-
-// Separate positive and negative case
-Sqrt_Real -> {
- Sqrt_Positive_Real
- Sqrt_Negative_Real
- };
-
-// Call another sqrt function, treat it as complex
-Sqrt_Negative_Real -> Sqrt_Complex;
-
-// Call a sqrt function in F77 math lib
-Sqrt_Positive_Real -> F77_Call;
-
-// -*- PYTHAG -*-
-//
-// pythag(a,b) = sqrt(a^2 + b^2)
-//
-//
-Pythag_Real -> {
- Sqrt_Real
- Dlamch_O_Call
- };
-
-
-
-// -*- SIGN -*-
-//
-// Call a sign function in F77 math lib
-Sign_Real -> F77_Call;
-
-
-// -*- ABS -*-
-//
-// Call a abs function in F77 math lib
-Abs_Real -> F77_Call;
-
-
-// -*- EXP -*-
-//
-// exp(a+i.b) = exp(a).cos(b) + i.exp(a)sin(b)
-Exp_Complex -> {
- Exp_Real
- Cos_Real
- Sin_Real
- };
-
-// Call a exp function in F77 math lib
-Exp_Real -> F77_Call;
-
-
-// -*- ATAN2 -*-
-//
-// Call atan2 function in C math lib
-ATan2_Real -> C_Call;
-
-
-// -*- IMAG -*-
-//
-// Call a imag function in F77 math lib
-Imag_Complex -> F77_Call;
-
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-03-13 15:18:00 +0000