17  *	   for x in (0,2)
34  *		j0(0) = 1
35  *		j0(inf) = 0
54  *	3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
62 static const volatile double vone = 1, vzero = 0;
67 invsqrtpi=  5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
68 tpi      =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
69 /* R0/S0 on [0, 2.00] */
70 R02  =  1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */
71 R03  = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */
72 R04  =  1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */
73 R05  = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */
74 S01  =  1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */
75 S02  =  1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */
76 S03  =  5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */
77 S04  =  1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */
79 static const double zero = 0, qrtr = 0.25;
88 	ix = hx&0x7fffffff;  in j0()
89 	if(ix>=0x7ff00000) return one/(x*x);  in j0()
91 	if(ix >= 0x40000000) {	/* |x| >= 2.0 */  in j0()
95 		if(ix<0x7fe00000) {  /* Make sure x+x does not overflow. */  in j0()
101 	 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)  in j0()
102 	 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)  in j0()
104 		if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(x);  in j0()
111 	if(ix<0x3f200000) {	/* |x| < 2**-13 */  in j0()
112 	    if(huge+x>one) {	/* raise inexact if x != 0 */  in j0()
113 	        if(ix<0x3e400000) return one;	/* |x|<2**-27 */  in j0()
120 	if(ix < 0x3FF00000) {	/* |x| < 1.00 */  in j0()
129 u00  = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */
130 u01  =  1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */
131 u02  = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */
132 u03  =  3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */
133 u04  = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */
134 u05  =  1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */
135 u06  = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */
136 v01  =  1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
137 v02  =  7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */
138 v03  =  2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */
139 v04  =  4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */
148         ix = 0x7fffffff&hx;  in y0()
151 	 * y0(Inf) = 0.  in y0()
154 	if(ix>=0x7ff00000) return vone/(x+x*x);  in y0()
155 	/* y0(+-0) = -inf and raise divide-by-zero exception. */  in y0()
156 	if((ix|lx)==0) return -one/vzero;  in y0()
157 	/* y0(x<0) = NaN and raise invalid exception. */  in y0()
158 	if(hx<0) return vzero/vzero;  in y0()
159         if(ix >= 0x40000000) {  /* |x| >= 2.0 */  in y0()
175 	 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)  in y0()
176 	 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)  in y0()
178                 if(ix<0x7fe00000) {  /* make sure x+x not overflow */  in y0()
183                 if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);  in y0()
190 	if(ix<=0x3e400000) {	/* x < 2**-27 */  in y0()
208 static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
209   0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
210  -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
211  -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
212  -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */
213  -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
214  -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
217   1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
218   3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
219   4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
220   1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */
221   4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
225  -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
226  -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
227  -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
228  -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */
229  -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
230  -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
233   6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
234   1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
235   5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
236   9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */
237   2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
241  -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
242  -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
243  -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
244  -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */
245  -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
246  -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
249   3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
250   3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
251   1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
252   1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */
253   1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
257  -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
258  -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
259  -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
260  -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */
261  -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
262  -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
265   2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
266   1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
267   2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
268   1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */
269   1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
279 	ix &= 0x7fffffff;  in pzero()
280 	if(ix>=0x40200000)     {p = pR8; q= pS8;}  in pzero()
281 	else if(ix>=0x40122E8B){p = pR5; q= pS5;}  in pzero()
282 	else if(ix>=0x4006DB6D){p = pR3; q= pS3;}  in pzero()
283 	else                   {p = pR2; q= pS2;}	/* ix>=0x40000000 */  in pzero()
285 	r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));  in pzero()
286 	s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));  in pzero()
300 static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
301   0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
302   7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
303   1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
304   5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */
305   8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
306   3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
309   1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */
310   8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */
311   1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */
312   8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */
313   8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */
314  -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
318   1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
319   7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
320   5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
321   1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */
322   1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
323   1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
326   8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */
327   2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */
328   1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */
329   5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */
330   3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */
331  -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
335   4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
336   7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
337   3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
338   4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */
339   1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
340   1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
343   4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */
344   7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */
345   3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */
346   6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */
347   2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */
348  -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
352   1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
353   7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
354   1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
355   1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */
356   3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
357   1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
360   3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */
361   2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */
362   8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */
363   8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */
364   2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */
365  -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
376 	ix &= 0x7fffffff;  in qzero()
377 	if(ix>=0x40200000)     {p = qR8; q= qS8;}  in qzero()
378 	else if(ix>=0x40122E8B){p = qR5; q= qS5;}  in qzero()
379 	else if(ix>=0x4006DB6D){p = qR3; q= qS3;}  in qzero()
380 	else                   {p = qR2; q= qS2;}	/* ix>=0x40000000 */  in qzero()
382 	r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));  in qzero()
383 	s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));  in qzero()