diff options
Diffstat (limited to 'Doc/Elementary Functions/TrigonometricsFunctionsDependeces.dot')
| -rw-r--r-- | Doc/Elementary Functions/TrigonometricsFunctionsDependeces.dot | 464 |
1 files changed, 0 insertions, 464 deletions
diff --git a/Doc/Elementary Functions/TrigonometricsFunctionsDependeces.dot b/Doc/Elementary Functions/TrigonometricsFunctionsDependeces.dot deleted file mode 100644 index 43efa900..00000000 --- a/Doc/Elementary Functions/TrigonometricsFunctionsDependeces.dot +++ /dev/null @@ -1,464 +0,0 @@ -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 -Cos_Real [label="cos(R)"]; -Cos_Complex [label="cos(C)"]; -Cos_Hyperbolic_Real [label="ch(R)"]; -Cos_Hyperbolic_Complex [label="ch(C)"]; - -// ArcCosinus -ACos_Real [label="acos(R)"]; -ACos_Complex [label="acos(C)"]; -ACos_Hyperbolic_Real [label="ach(R)"]; -ACos_Hyperbolic_Complex [label="ach(C)"]; - -// Sinus -Sin_Real [label="sin(R)"]; -Sin_Complex [label="sin(C)"]; -Sin_Hyperbolic_Real [label="sh(R)"]; -Sin_Hyperbolic_Complex [label="sh(C)"]; - -// ArcSinus -ASin_Real [label="asin(R)"]; -ASin_Complex [label="asin(C)"]; -ASin_Hyperbolic_Real [label="ash(R)"]; -ASin_Hyperbolic_Complex [label="ash(C)"]; - -// Tangeante -Tan_Real [label="tan(R)"]; -Tan_Complex [label="tan(C)", comment="wtan"]; -Tan_Hyperbolic_Real [label="tanh(R)"]; -Tan_Hyperbolic_Complex [label="tanh(C)"]; - -// ArcTangeante -ATan_Real [label="atan(R)"]; -ATan_Complex [label="atan(C)", comment="watan"]; -ATan_Hyperbolic_Real [label="atanh(R)"]; -ATan_Hyperbolic_Complex [label="atanh(C)"]; - -// ArcTaneante2 -ATan2_Real [label="atan2(R)"]; - -// Exponentielle -Exp_Real [label="exp(R)"]; -Exp_Complex [label="exp(C)"]; - -// Log -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 -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 |