Initial support for live code checker / lint.
JavaLintService parses the code as you type and displays all errors
and other problems. This is done by running compiler in check mode
in background. This also removes the necessity for JavaCompilerProblemRegistry.
/* @(#)e_j0.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_j0(x), __ieee754_y0(x)
* Bessel function of the first and second kinds of order zero.
* Method -- j0(x):
* 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ...
* 2. Reduce x to |x| since j0(x)=j0(-x), and
* for x in (0,2)
* j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x;
* (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 )
* for x in (2,inf)
* j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
* where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
* as follow:
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
* = 1/sqrt(2) * (cos(x) + sin(x))
* sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* (To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.)
*
* 3 Special cases
* j0(nan)= nan
* j0(0) = 1
* j0(inf) = 0
*
* Method -- y0(x):
* 1. For x<2.
* Since
* y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
* therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
* We use the following function to approximate y0,
* y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
* where
* U(z) = u00 + u01*z + ... + u06*z^6
* V(z) = 1 + v01*z + ... + v04*z^4
* with absolute approximation error bounded by 2**-72.
* Note: For tiny x, U/V = u0 and j0(x)~1, hence
* y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
* 2. For x>=2.
* y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
* where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
* by the method mentioned above.
* 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
*/
#include "fdlibm.h"
#ifdef __STDC__
static double pzero(double), qzero(double);
#else
static double pzero(), qzero();
#endif
#ifdef __STDC__
static const double
#else
static double
#endif
huge = 1e300,
one = 1.0,
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
/* R0/S0 on [0, 2.00] */
R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */
R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */
R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */
R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */
S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */
S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */
S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */
S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */
static double zero = 0.0;
#ifdef __STDC__
double __ieee754_j0(double x)
#else
double __ieee754_j0(x)
double x;
#endif
{
double z, s,c,ss,cc,r,u,v;
int hx,ix;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return one/(x*x);
x = fabs(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = sin(x);
c = cos(x);
ss = s-c;
cc = s+c;
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = -cos(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(x);
else {
u = pzero(x); v = qzero(x);
z = invsqrtpi*(u*cc-v*ss)/sqrt(x);
}
return z;
}
if(ix<0x3f200000) { /* |x| < 2**-13 */
if(huge+x>one) { /* raise inexact if x != 0 */
if(ix<0x3e400000) return one; /* |x|<2**-27 */
else return one - 0.25*x*x;
}
}
z = x*x;
r = z*(R02+z*(R03+z*(R04+z*R05)));
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
if(ix < 0x3FF00000) { /* |x| < 1.00 */
return one + z*(-0.25+(r/s));
} else {
u = 0.5*x;
return((one+u)*(one-u)+z*(r/s));
}
}
#ifdef __STDC__
static const double
#else
static double
#endif
u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */
u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */
u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */
u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */
u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */
u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */
u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */
v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */
v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */
v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */
#ifdef __STDC__
double __ieee754_y0(double x)
#else
double __ieee754_y0(x)
double x;
#endif
{
double z, s,c,ss,cc,u,v;
int hx,ix,lx;
hx = __HI(x);
ix = 0x7fffffff&hx;
lx = __LO(x);
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
if(ix>=0x7ff00000) return one/(x+x*x);
if((ix|lx)==0) return -one/zero;
if(hx<0) return zero/zero;
if(ix >= 0x40000000) { /* |x| >= 2.0 */
/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
* where x0 = x-pi/4
* Better formula:
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
* = 1/sqrt(2) * (sin(x) + cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
s = sin(x);
c = cos(x);
ss = s-c;
cc = s+c;
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = -cos(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);
else {
u = pzero(x); v = qzero(x);
z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
}
return z;
}
if(ix<=0x3e400000) { /* x < 2**-27 */
return(u00 + tpi*__ieee754_log(x));
}
z = x*x;
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x)));
}
/* The asymptotic expansions of pzero is
* 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
* For x >= 2, We approximate pzero by
* pzero(x) = 1 + (R/S)
* where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
* S = 1 + pS0*s^2 + ... + pS4*s^10
* and
* | pzero(x)-1-R/S | <= 2 ** ( -60.26)
*/
#ifdef __STDC__
static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#else
static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#endif
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
-7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
-8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
-2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */
-2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
-5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
};
#ifdef __STDC__
static const double pS8[5] = {
#else
static double pS8[5] = {
#endif
1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */
4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
};
#ifdef __STDC__
static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#else
static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#endif
-1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
-7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
-4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
-6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */
-3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
-3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
};
#ifdef __STDC__
static const double pS5[5] = {
#else
static double pS5[5] = {
#endif
6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */
2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
};
#ifdef __STDC__
static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#else
static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#endif
-2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
-7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
-2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
-2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */
-5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
-3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
};
#ifdef __STDC__
static const double pS3[5] = {
#else
static double pS3[5] = {
#endif
3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */
1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
};
#ifdef __STDC__
static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#else
static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#endif
-8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
-7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
-1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
-7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */
-1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
-3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
};
#ifdef __STDC__
static const double pS2[5] = {
#else
static double pS2[5] = {
#endif
2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */
1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
};
#ifdef __STDC__
static double pzero(double x)
#else
static double pzero(x)
double x;
#endif
{
#ifdef __STDC__
const double *p,*q;
#else
double *p,*q;
#endif
double z,r,s;
int ix;
ix = 0x7fffffff&__HI(x);
if(ix>=0x40200000) {p = pR8; q= pS8;}
else if(ix>=0x40122E8B){p = pR5; q= pS5;}
else if(ix>=0x4006DB6D){p = pR3; q= pS3;}
else if(ix>=0x40000000){p = pR2; q= pS2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return one+ r/s;
}
/* For x >= 8, the asymptotic expansions of qzero is
* -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
* We approximate pzero by
* qzero(x) = s*(-1.25 + (R/S))
* where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
* S = 1 + qS0*s^2 + ... + qS5*s^12
* and
* | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
*/
#ifdef __STDC__
static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#else
static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
#endif
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */
8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
};
#ifdef __STDC__
static const double qS8[6] = {
#else
static double qS8[6] = {
#endif
1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */
8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */
1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */
8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */
8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */
-3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
};
#ifdef __STDC__
static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#else
static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
#endif
1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */
1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
};
#ifdef __STDC__
static const double qS5[6] = {
#else
static double qS5[6] = {
#endif
8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */
2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */
1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */
5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */
3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */
-5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
};
#ifdef __STDC__
static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#else
static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
#endif
4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */
1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
};
#ifdef __STDC__
static const double qS3[6] = {
#else
static double qS3[6] = {
#endif
4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */
7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */
3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */
6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */
2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */
-1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
};
#ifdef __STDC__
static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#else
static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
#endif
1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */
3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
};
#ifdef __STDC__
static const double qS2[6] = {
#else
static double qS2[6] = {
#endif
3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */
2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */
8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */
8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */
2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */
-5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
};
#ifdef __STDC__
static double qzero(double x)
#else
static double qzero(x)
double x;
#endif
{
#ifdef __STDC__
const double *p,*q;
#else
double *p,*q;
#endif
double s,r,z;
int ix;
ix = 0x7fffffff&__HI(x);
if(ix>=0x40200000) {p = qR8; q= qS8;}
else if(ix>=0x40122E8B){p = qR5; q= qS5;}
else if(ix>=0x4006DB6D){p = qR3; q= qS3;}
else if(ix>=0x40000000){p = qR2; q= qS2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
return (-.125 + r/s)/x;
}