/* specfunc/airy_zero.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/* Author: G. Jungman */
#include <config.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_sf_airy.h>
#include "error.h"
static const double zero_Ai[] = {
0,
-2.3381074104597670385,
-4.087949444130970617,
-5.520559828095551059,
-6.786708090071758999,
-7.944133587120853123,
-9.022650853340980380,
-10.04017434155808593,
-11.00852430373326289,
-11.93601556323626252,
-12.82877675286575720,
-13.69148903521071793,
-14.52782995177533498,
-15.34075513597799686,
-16.13268515694577144,
-16.90563399742994263,
-17.661300105697057509,
-18.401132599207115416,
-19.126380474246952144,
-19.838129891721499701,
-20.537332907677566360,
-21.224829943642096955,
-21.901367595585130707,
-22.567612917496502831,
-23.224165001121681061,
-23.871564455535918567,
-24.510301236589677490,
-25.140821166148963748,
-25.763531400982756459,
-26.378805052137232374,
-26.986985111606367686,
-27.588387809882444812,
-28.183305502632644923,
-28.772009165237435382,
-29.354750558766287963,
-29.931764119086555913,
-30.503268611418505287,
-31.069468585183755604,
-31.63055565801265934,
-32.18670965295205069,
-32.73809960900026913,
-33.28488468190140188,
-33.82721494950865194,
-34.36523213386365906,
-34.89907025034531210,
-35.42885619274788846,
-35.95471026189862926,
-36.47674664437480896,
-36.99507384699450161,
-37.50979509200501613,
-38.02100867725525443,
-38.52880830509424882,
-39.03328338327251391,
-39.53451930072301805,
-40.03259768075417603,
-40.52759661388971821,
-41.01959087233248966,
-41.50865210780525018,
-41.99484903432643004,
-42.47824759730839188,
-42.95891113021656009,
-43.43690049989685412,
-43.91227424156370168,
-44.38508868433939023,
-44.85539806814583243,
-45.32325465267043011,
-45.78870881905730086,
-46.25180916491254629,
-46.71260259315651633,
-47.17113439520631705,
-47.62744832892739292,
-48.08158669175325711,
-48.53359038933679845,
-48.98349900006458366,
-49.43135083573678341,
-49.87718299868941729,
-50.32103143561221860,
-50.76293098829428522,
-51.20291544151056412,
-51.64101756824489758,
-52.07726917242964943,
-52.51170112936766183,
-52.94434342398931824,
-53.37522518708567514,
-53.80437472964785717,
-54.23181957543308298,
-54.65758649186871111,
-55.08170151939748312,
-55.50418999935962251,
-55.92507660050055598,
-56.34438534418670066,
-56.76213962840595327,
-57.17836225062417808,
-57.59307542956407782,
-58.00630082596830627,
-58.41805956240450934,
-58.82837224216613231,
-59.23725896731927534,
-59.64473935594259360,
-60.05083255860419805,
-60.45555727411669871
};
static const size_t size_zero_Ai = sizeof(zero_Ai)/sizeof(double);
static const double zero_Bi[] = {
0,
-1.173713222709127925,
-3.271093302836352716,
-4.830737841662015933,
-6.169852128310251260,
-7.376762079367763714,
-8.491948846509388013,
-9.538194379346238887,
-10.52991350670535792,
-11.47695355127877944,
-12.38641713858273875,
-13.26363952294180555,
-14.11275680906865779,
-14.93705741215416404,
-15.739210351190482771,
-16.521419550634379054,
-17.285531624581242533,
-18.033113287225001572,
-18.765508284480081041,
-19.483880132989234014,
-20.189244785396202420,
-20.882495994193175768,
-21.564425284712977653,
-22.235737881803385167,
-22.897065554219793474,
-23.548977079642448269,
-24.191986850649000086,
-24.826562012152892172,
-25.453128427085131994,
-26.072075698466804494,
-26.683761425120990449,
-27.288514830076298204,
-27.886639871735962459,
-28.478417925678661737,
-29.064110107777650305,
-29.643959295918396591,
-30.218191897047274645,
-30.787019397921766297,
-31.350639731255585371,
-31.90923848358456965,
-32.46298996683685318,
-33.01205817205683814,
-33.55659762084006113,
-34.09675412765602851,
-34.63266548426775468,
-35.16446207582101720,
-35.69226743681080479,
-36.21619875398748222,
-36.73636732230120657,
-37.25287895916828697,
-37.76583438165180116,
-38.27532955056003997,
-38.78145598496327279,
-39.28430105019802461,
-39.78394822205711298,
-40.28047732954369150,
-40.77396477829068148,
-41.26448375650675678,
-41.75210442510106287,
-42.23689409345656643,
-42.71891738216253539,
-43.19823637387693118,
-43.67491075336673948,
-44.14899793766617113,
-44.62055319719727274,
-45.08962976861312825,
-45.55627896004907928,
-46.02055024940102076,
-46.48249137619078661,
-46.94214842752602207,
-47.39956591861496210,
-47.85478686825452176,
-48.30785286967246692,
-48.75880415707066192,
-49.20767966818603897,
-49.65451710315861501,
-50.09935297997125482,
-50.54222268670364757,
-50.98316053082286586,
-51.42219978571468262,
-51.85937273464332870,
-52.29471071231240525,
-52.72824414418606069,
-53.16000258371716397,
-53.59001474761792882,
-54.01830854929815828,
-54.44491113058688729,
-54.86984889184461534,
-55.29314752056546491,
-55.71483201856140365,
-56.13492672781406761,
-56.55345535507366411,
-56.97044099527886475,
-57.38590615386647834,
-57.79987276803497897,
-58.21236222702161974,
-58.62339539144885603,
-59.03299261179210306,
-59.44117374601743460,
-59.84795817643466996,
-60.25336482580837088
};
static const size_t size_zero_Bi = sizeof(zero_Bi)/sizeof(double);
static const double zero_Aip[] = {
0,
-1.018792971647471089,
-3.248197582179836738,
-4.820099211178735639,
-6.163307355639486822,
-7.372177255047770177,
-8.488486734019722133,
-9.535449052433547471,
-10.52766039695740728,
-11.47505663348024529,
-12.384788371845747325,
-13.262218961665210382,
-14.111501970462995282,
-14.935937196720517467,
-15.738201373692538303,
-16.520503825433793542,
-17.284695050216437357,
-18.032344622504393395,
-18.764798437665954740,
-19.483221656567231178,
-20.188631509463373154,
-20.881922755516737701,
-21.563887723198974958,
-22.235232285348913331,
-22.896588738874619001,
-23.548526295928801574,
-24.191559709526353841,
-24.826156425921155001,
-25.452742561777649948,
-26.071707935173912515,
-26.683410328322449767,
-27.288179121523985029,
-27.886318408768461192,
-28.478109683102278108,
-29.063814162638199090,
-29.643674814632015921,
-30.217918124468574603,
-30.786755648012502519,
-31.350385379083034671,
-31.90899295843046320,
-32.46275274623847982,
-33.01182877663428709,
-33.55637560978942190,
-34.09653909480913771,
-34.63245705463586589,
-35.16425990255340758,
-35.69207119851046870,
-36.21600815233519918,
-36.73618207994680321,
-37.25269881785414827,
-37.76565910053887108,
-38.27515890473087933,
-38.78128976408036876,
-39.28413905729859644,
-39.78379027246823278,
-40.28032324990371935,
-40.77381440566486637,
-41.26433693758643383,
-41.75196101547722703,
-42.23675395695976012,
-42.71878039026198233,
-43.19810240513270670,
-43.67477969292950869,
-44.14886967681966886,
-44.62042763293925724,
-45.08950680327102630,
-45.55615850092696446,
-46.02043220845493728,
-46.48237566972975615,
-46.94203497593635633,
-47.39945464610575493,
-47.85467770262241617,
-48.30774574208398774,
-48.75869900186057804,
-49.20757642267037247,
-49.65441570746105074,
-50.09925337686182515,
-50.54212482144867502,
-50.98306435104524282,
-51.42210524126365311,
-51.85927977747301469,
-52.29461929636838876,
-52.72815422529939506,
-53.15991411950524351,
-53.58992769739169611,
-54.01822287397517367,
-54.44482679260982599,
-54.86976585510479430,
-55.29306575033103518,
-55.71475148140987392,
-56.13484739156885235,
-56.55337718874437424,
-56.97036396900508167,
-57.38583023886477265,
-57.79979793654895377,
-58.21228845227477578,
-58.62332264760009139,
-59.03292087389367419,
-59.44110298997521892,
-59.84788837897058171,
-60.25329596442479317
};
static const size_t size_zero_Aip = sizeof(zero_Aip)/sizeof(double);
static const double zero_Bip[] = {
0,
-2.294439682614123247,
-4.073155089071828216,
-5.512395729663599496,
-6.781294445990305390,
-7.940178689168578927,
-9.019583358794239067,
-10.037696334908545802,
-11.006462667712289940,
-11.934261645014844663,
-12.827258309177217640,
-13.690155826835049101,
-14.526645763485711410,
-15.339693082242404109,
-16.131724782385900578,
-16.904759411889649958,
-17.660498743114976102,
-18.400394367181703280,
-19.125697156412638066,
-19.837494718415910503,
-20.536740241453273980,
-21.224275044889266569,
-21.900846445139208281,
-22.567122080497200470,
-23.223701521208962116,
-23.871125771677973595,
-24.509885117016242729,
-25.140425655367878908,
-25.763154776913454319,
-26.378445791146615697,
-26.986641859775034987,
-27.588059359225600573,
-28.182990771292975456,
-28.771707180886056250,
-29.354460444612957224,
-29.931485082026055160,
-30.502999931936645516,
-31.069209608721234058,
-31.63030578754333679,
-32.18646834257807369,
-32.73786635840274752,
-33.28465903151424981,
-33.82699647630635587,
-34.36502044767239631,
-34.89886499060196419,
-35.42865702564380962,
-35.95451687785511190,
-36.47655875580547918,
-36.99489118631672770,
-37.50961740986809593,
-38.02083574095788210
};
static const size_t size_zero_Bip = sizeof(zero_Bip)/sizeof(double);
/* [Abramowitz+Stegun, 10.4.105] */
static double
zero_f(double z)
{
const double pre = pow(z, 2.0/3.0);
const double zi2 = 1.0/(z*z);
const double zi4 = zi2 * zi2;
const double t1 = 5.0/48.0 * zi2;
const double t2 = -5.0/36.0 * zi4;
const double t3 = 77125.0/82944.0 * zi4 * zi2;
const double t4 = -108056875.0/6967296.0 * zi4 * zi4;
return pre * (1.0 + t1 + t2 + t3 + t4);
}
static double
zero_g(double z)
{
const double pre = pow(z, 2.0/3.0);
const double zi2 = 1.0/(z*z);
const double zi4 = zi2 * zi2;
const double t1 = -7.0/48.0 * zi2;
const double t2 = 35.0/288.0 * zi4;
const double t3 = -181223.0/207360.0 * zi4 * zi2;
const double t4 = 18683371.0/1244160.0 * zi4 * zi4;
return pre * (1.0 + t1 + t2 + t3 + t4);
}
int
gsl_sf_airy_zero_Ai_e(unsigned int s, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(s < 1) {
DOMAIN_ERROR_MSG("s is less than 1", result);
}
else if(s < size_zero_Ai) {
result->val = zero_Ai[s];
result->err = GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
const double z = 3.0*M_PI/8.0 * (4.0*s - 1.0);
const double f = zero_f(z);
result->val = -f;
result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
}
int
gsl_sf_airy_zero_Bi_e(unsigned int s, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(s < 1) {
DOMAIN_ERROR_MSG("s is less than 1", result);
}
else if(s < size_zero_Bi) {
result->val = zero_Bi[s];
result->err = GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
const double z = 3.0*M_PI/8.0 * (4.0*s - 3.0);
const double f = zero_f(z);
result->val = -f;
result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
}
int
gsl_sf_airy_zero_Ai_deriv_e(unsigned int s, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(s < 1) {
DOMAIN_ERROR_MSG("s is less than 1", result);
}
else if(s < size_zero_Aip) {
result->val = zero_Aip[s];
result->err = GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
const double z = 3.0*M_PI/8.0 * (4.0*s - 3.0);
const double g = zero_g(z);
result->val = -g;
result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
}
int
gsl_sf_airy_zero_Bi_deriv_e(unsigned int s, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(s < 1) {
DOMAIN_ERROR_MSG("s is less than 1", result);
}
else if(s < size_zero_Bip) {
result->val = zero_Bip[s];
result->err = GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
else {
const double z = 3.0*M_PI/8.0 * (4.0*s - 1.0);
const double g = zero_g(z);
result->val = -g;
result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
}
/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
#include "eval.h"
double gsl_sf_airy_zero_Ai(unsigned int s)
{
EVAL_RESULT(gsl_sf_airy_zero_Ai_e(s, &result));
}
double gsl_sf_airy_zero_Bi(unsigned int s)
{
EVAL_RESULT(gsl_sf_airy_zero_Bi_e(s, &result));
}
double gsl_sf_airy_zero_Ai_deriv(unsigned int s)
{
EVAL_RESULT(gsl_sf_airy_zero_Ai_deriv_e(s, &result));
}
double gsl_sf_airy_zero_Bi_deriv(unsigned int s)
{
EVAL_RESULT(gsl_sf_airy_zero_Bi_deriv_e(s, &result));
}