diff options
| -rw-r--r-- | src/elementaryFunctions/atan/catans.c | 67 | ||||
| -rw-r--r-- | src/elementaryFunctions/atan/zatans.c | 69 |
2 files changed, 5 insertions, 131 deletions
diff --git a/src/elementaryFunctions/atan/catans.c b/src/elementaryFunctions/atan/catans.c index ba448d96..d3a232fb 100644 --- a/src/elementaryFunctions/atan/catans.c +++ b/src/elementaryFunctions/atan/catans.c @@ -148,74 +148,11 @@ #include <math.h> #include "atan.h" #include "abs.h" +#include "lnp1m1.h" #include "lapack.h" #define _sign(a, b) b >=0 ? a : -a -/* - PURPOSE : Compute v = log ( (1 + s)/(1 - s) ) - for small s, this is for |s| < SLIM = 0.20 - - ALGORITHM : - 1/ if |s| is "very small" we use a truncated - taylor dvp (by keeping 3 terms) from : - 2 4 6 - t = 2 * s * ( 1 + 1/3 s + 1/5 s + [ 1/7 s + ....] ) - 2 4 - t = 2 * s * ( 1 + 1/3 s + 1/5 s + er) - - The limit E until we use this formula may be simply - gotten so that the negliged part er is such that : - 2 4 - (#) er <= epsm * ( 1 + 1/3 s + 1/5 s ) for all |s|<= E - - As er = 1/7 s^6 + 1/9 s^8 + ... - er <= 1/7 * s^6 ( 1 + s^2 + s^4 + ...) = 1/7 s^6/(1-s^2) - - the inequality (#) is forced if : - - 1/7 s^6 / (1-s^2) <= epsm * ( 1 + 1/3 s^2 + 1/5 s^4 ) - - s^6 <= 7 epsm * (1 - 2/3 s^2 - 3/15 s^4 - 1/5 s^6) - - So that E is very near (7 epsm)^(1/6) (approximately 3.032d-3): - - 2/ For larger |s| we used a minimax polynome : - - yi = s * (2 + d3 s^3 + d5 s^5 .... + d13 s^13 + d15 s^15) - - This polynome was computed (by some remes algorithm) following - (*) the sin(x) example (p 39) of the book : - - "ELEMENTARY FUNCTIONS" - "Algorithms and implementation" - J.M. Muller (Birkhauser) - - (*) without the additionnal raffinement to get the first coefs - very near floating point numbers) -*/ -static float lnp1m1(float _dblVar) -{ - static float sdblD3 = 0.66666666666672679472f; - static float sdblD5 = 0.39999999996176889299f; - static float sdblD7 = 0.28571429392829380980f; - static float sdblD9 = 0.22222138684562683797f; - static float sdblD11 = 0.18186349187499222459f; - static float sdblD13 = 0.15250315884469364710f; - static float sdblD15 = 0.15367270224757008114f; - static float sdblE = 3.032E-3f; - static float sdblC3 = 2.0f/3.0f; - static float sdblC5 = 2.0f/5.0f; - - float dblS2 = _dblVar * _dblVar; - if( dabss(_dblVar) <= sdblE) - return _dblVar * (2 + dblS2 * (sdblC3 + sdblC5 * dblS2)); - else - return _dblVar * (2 + dblS2 * (sdblD3 + dblS2 * (sdblD5 + dblS2 * (sdblD7 + dblS2 * (sdblD9 + dblS2 * (sdblD11 + dblS2 * (sdblD13 + dblS2 * sdblD15))))))); -} - - - floatComplex catans(floatComplex z) { static float sSlim = 0.2f; /* . @@ -268,7 +205,7 @@ floatComplex catans(floatComplex z) { D- = D(center = [0; -1/slim], radius = sqrt(1/slim**2 - 1)) if b < 0 use the special evaluation of log((1+s)/(1-s)) (5) */ - _outImg = lnp1m1(S) * 0.25f; + _outImg = slnp1m1s(S) * 0.25f; } else { diff --git a/src/elementaryFunctions/atan/zatans.c b/src/elementaryFunctions/atan/zatans.c index 0c8ed72e..c511d790 100644 --- a/src/elementaryFunctions/atan/zatans.c +++ b/src/elementaryFunctions/atan/zatans.c @@ -146,76 +146,13 @@ */ #include <math.h> +#include "lapack.h" #include "atan.h" #include "abs.h" -#include "lapack.h" +#include "lnp1m1.h" #define _sign(a, b) b >=0 ? a : -a -/* - PURPOSE : Compute v = log ( (1 + s)/(1 - s) ) - for small s, this is for |s| < SLIM = 0.20 - - ALGORITHM : - 1/ if |s| is "very small" we use a truncated - taylor dvp (by keeping 3 terms) from : - 2 4 6 - t = 2 * s * ( 1 + 1/3 s + 1/5 s + [ 1/7 s + ....] ) - 2 4 - t = 2 * s * ( 1 + 1/3 s + 1/5 s + er) - - The limit E until we use this formula may be simply - gotten so that the negliged part er is such that : - 2 4 - (#) er <= epsm * ( 1 + 1/3 s + 1/5 s ) for all |s|<= E - - As er = 1/7 s^6 + 1/9 s^8 + ... - er <= 1/7 * s^6 ( 1 + s^2 + s^4 + ...) = 1/7 s^6/(1-s^2) - - the inequality (#) is forced if : - - 1/7 s^6 / (1-s^2) <= epsm * ( 1 + 1/3 s^2 + 1/5 s^4 ) - - s^6 <= 7 epsm * (1 - 2/3 s^2 - 3/15 s^4 - 1/5 s^6) - - So that E is very near (7 epsm)^(1/6) (approximately 3.032d-3): - - 2/ For larger |s| we used a minimax polynome : - - yi = s * (2 + d3 s^3 + d5 s^5 .... + d13 s^13 + d15 s^15) - - This polynome was computed (by some remes algorithm) following - (*) the sin(x) example (p 39) of the book : - - "ELEMENTARY FUNCTIONS" - "Algorithms and implementation" - J.M. Muller (Birkhauser) - - (*) without the additionnal raffinement to get the first coefs - very near floating point numbers) -*/ -static double lnp1m1(double _dblVar) -{ - static double sdblD3 = 0.66666666666672679472; - static double sdblD5 = 0.39999999996176889299; - static double sdblD7 = 0.28571429392829380980; - static double sdblD9 = 0.22222138684562683797; - static double sdblD11 = 0.18186349187499222459; - static double sdblD13 = 0.15250315884469364710; - static double sdblD15 = 0.15367270224757008114; - static double sdblE = 3.032E-3; - static double sdblC3 = 2.0/3.0; - static double sdblC5 = 2.0/5.0; - - double dblS2 = _dblVar * _dblVar; - if( dabss(_dblVar) <= sdblE) - return _dblVar * (2 + dblS2 * (sdblC3 + sdblC5 * dblS2)); - else - return _dblVar * (2 + dblS2 * (sdblD3 + dblS2 * (sdblD5 + dblS2 * (sdblD7 + dblS2 * (sdblD9 + dblS2 * (sdblD11 + dblS2 * (sdblD13 + dblS2 * sdblD15))))))); -} - - - doubleComplex zatans(doubleComplex z) { static double sSlim = 0.2; static double sAlim = 1E-150; @@ -261,7 +198,7 @@ doubleComplex zatans(doubleComplex z) { D- = D(center = [0; -1/slim], radius = sqrt(1/slim**2 - 1)) if b < 0 use the special evaluation of log((1+s)/(1-s)) (5) */ - _outImg = lnp1m1(S) * 0.25; + _outImg = dlnp1m1s(S) * 0.25; } else { |