27 static const volatile long double tiny = 0x1p-10000L;
34  * In the domain [0, 2**-34], only the first term in the power series
36  * terms is less than 2**-102.
39 efxu  = LD80C(0x8375d410a6db446c, -3,  1.28379167095512573902e-1L),
40 efx8u = LD80C(0x8375d410a6db446c,  0,  1.02703333676410059122e+0L),
42  * Domain [0, 0.84375], range ~[-1.423e-22, 1.423e-22]:
43  * |(erf(x) - x)/x - pp(x)/qq(x)| < 2**-72.573
45 pp0u  = LD80C(0x8375d410a6db446c, -3,   1.28379167095512573902e-1L),
46 pp1u  = LD80C(0xa46c7d09ec3d0cec, -2,  -3.21140201054840180596e-1L),
47 pp2u  = LD80C(0x9b31e66325576f86, -5,  -3.78893851760347812082e-2L),
48 pp3u  = LD80C(0x804ac72c9a0b97dd, -7,  -7.83032847030604679616e-3L),
49 pp4u  = LD80C(0x9f42bcbc3d5a601d, -12, -3.03765663857082048459e-4L),
50 pp5u  = LD80C(0x9ec4ad6193470693, -16, -1.89266527398167917502e-5L),
51 qq1u  = LD80C(0xdb4b8eb713188d6b, -2,   4.28310832832310510579e-1L),
52 qq2u  = LD80C(0xa5750835b2459bd1, -4,   8.07896272074540216658e-2L),
53 qq3u  = LD80C(0x8b85d6bd6a90b51c, -7,   8.51579638189385354266e-3L),
54 qq4u  = LD80C(0x87332f82cff4ff96, -11,  5.15746855583604912827e-4L),
55 qq5u  = LD80C(0x83466cb6bf9dca00, -16,  1.56492109706256700009e-5L),
56 qq6u  = LD80C(0xf5bf98c2f996bf63, -24,  1.14435527803073879724e-7L);
57 #define	efx	(efxu.e)
58 #define	efx8	(efx8u.e)
59 #define	pp0	(pp0u.e)
60 #define	pp1	(pp1u.e)
61 #define	pp2	(pp2u.e)
62 #define	pp3	(pp3u.e)
63 #define	pp4	(pp4u.e)
64 #define	pp5	(pp5u.e)
65 #define	qq1	(qq1u.e)
66 #define	qq2	(qq2u.e)
67 #define	qq3	(qq3u.e)
68 #define	qq4	(qq4u.e)
69 #define	qq5	(qq5u.e)
70 #define	qq6	(qq6u.e)
72 erxu  = LD80C(0xd7bb3d0000000000, -1,  8.42700779438018798828e-1L),
74  * Domain [0.84375, 1.25], range ~[-8.132e-22, 8.113e-22]:
75  * |(erf(x) - erx) - pa(x)/qa(x)| < 2**-71.762
77 pa0u  = LD80C(0xe8211158da02c692, -27,  1.35116960705131296711e-8L),
78 pa1u  = LD80C(0xd488f89f36988618, -2,   4.15107507167065612570e-1L),
79 pa2u  = LD80C(0xece74f8c63fa3942, -4,  -1.15675565215949226989e-1L),
80 pa3u  = LD80C(0xc8d31e020727c006, -4,   9.80589241379624665791e-2L),
81 pa4u  = LD80C(0x985d5d5fafb0551f, -5,   3.71984145558422368847e-2L),
82 pa5u  = LD80C(0xa5b6c4854d2f5452, -8,  -5.05718799340957673661e-3L),
83 pa6u  = LD80C(0x85c8d58fe3993a47, -8,   4.08277919612202243721e-3L),
84 pa7u  = LD80C(0xddbfbc23677b35cf, -13,  2.11476292145347530794e-4L),
85 qa1u  = LD80C(0xb8a977896f5eff3f, -1,   7.21335860303380361298e-1L),
86 qa2u  = LD80C(0x9fcd662c3d4eac86, -1,   6.24227891731886593333e-1L),
87 qa3u  = LD80C(0x9d0b618eac67ba07, -2,   3.06727455774491855801e-1L),
88 qa4u  = LD80C(0x881a4293f6d6c92d, -3,   1.32912674218195890535e-1L),
89 qa5u  = LD80C(0xbab144f07dea45bf, -5,   4.55792134233613027584e-2L),
90 qa6u  = LD80C(0xa6c34ba438bdc900, -7,   1.01783980070527682680e-2L),
91 qa7u  = LD80C(0x8fa866dc20717a91, -9,   2.19204436518951438183e-3L);
92 #define erx	(erxu.e)
93 #define pa0	(pa0u.e)
94 #define pa1	(pa1u.e)
95 #define pa2	(pa2u.e)
96 #define pa3	(pa3u.e)
97 #define pa4	(pa4u.e)
98 #define pa5	(pa5u.e)
99 #define pa6	(pa6u.e)
100 #define pa7	(pa7u.e)
101 #define qa1	(qa1u.e)
102 #define qa2	(qa2u.e)
103 #define qa3	(qa3u.e)
104 #define qa4	(qa4u.e)
105 #define qa5	(qa5u.e)
106 #define qa6	(qa6u.e)
107 #define qa7	(qa7u.e)
110  * Domain [1.25,2.85715], range ~[-2.334e-22,2.334e-22]:
111  * |log(x*erfc(x)) + x**2 + 0.5625 - ra(x)/sa(x)| < 2**-71.860
113 ra0u  = LD80C(0xa1a091e0fb4f335a, -7, -9.86494298915814308249e-3L),
114 ra1u  = LD80C(0xc2b0d045ae37df6b, -1, -7.60510460864878271275e-1L),
115 ra2u  = LD80C(0xf2cec3ee7da636c5, 3,  -1.51754798236892278250e+1L),
116 ra3u  = LD80C(0x813cc205395adc7d, 7,  -1.29237335516455333420e+2L),
117 ra4u  = LD80C(0x8737c8b7b4062c2f, 9,  -5.40871625829510494776e+2L),
118 ra5u  = LD80C(0x8ffe5383c08d4943, 10, -1.15194769466026108551e+3L),
119 ra6u  = LD80C(0x983573e64d5015a9, 10, -1.21767039790249025544e+3L),
120 ra7u  = LD80C(0x92a794e763a6d4db, 9,  -5.86618463370624636688e+2L),
121 ra8u  = LD80C(0xd5ad1fae77c3d9a3, 6,  -1.06838132335777049840e+2L),
122 ra9u  = LD80C(0x934c1a247807bb9c, 2,  -4.60303980944467334806e+0L),
123 sa1u  = LD80C(0xd342f90012bb1189, 4,   2.64077014928547064865e+1L),
124 sa2u  = LD80C(0x839be13d9d5da883, 8,   2.63217811300123973067e+2L),
125 sa3u  = LD80C(0x9f8cba6d1ae1b24b, 10,  1.27639775710344617587e+3L),
126 sa4u  = LD80C(0xcaa83f403713e33e, 11,  3.24251544209971162003e+3L),
127 sa5u  = LD80C(0x8796aff2f3c47968, 12,  4.33883591261332837874e+3L),
128 sa6u  = LD80C(0xb6ef97f9c753157b, 11,  2.92697460344182158454e+3L),
129 sa7u  = LD80C(0xe02aee5f83773d1c, 9,   8.96670799139389559818e+2L),
130 sa8u  = LD80C(0xc82b83855b88e07e, 6,   1.00084987800048510018e+2L),
131 sa9u  = LD80C(0x92f030aefadf28ad, 1,   2.29591004455459083843e+0L);
132 #define ra0	(ra0u.e)
133 #define ra1	(ra1u.e)
134 #define ra2	(ra2u.e)
135 #define ra3	(ra3u.e)
136 #define ra4	(ra4u.e)
137 #define ra5	(ra5u.e)
138 #define ra6	(ra6u.e)
139 #define ra7	(ra7u.e)
140 #define ra8	(ra8u.e)
141 #define ra9	(ra9u.e)
142 #define sa1	(sa1u.e)
143 #define sa2	(sa2u.e)
144 #define sa3	(sa3u.e)
145 #define sa4	(sa4u.e)
146 #define sa5	(sa5u.e)
147 #define sa6	(sa6u.e)
148 #define sa7	(sa7u.e)
149 #define sa8	(sa8u.e)
150 #define sa9	(sa9u.e)
152  * Domain [2.85715,7], range ~[-8.323e-22,8.390e-22]:
153  * |log(x*erfc(x)) + x**2 + 0.5625 - rb(x)/sb(x)| < 2**-70.326
156 rb0u = LD80C(0xa1a091cf43abcd26, -7, -9.86494292470284646962e-3L),
157 rb1u = LD80C(0xd19d2df1cbb8da0a, -1, -8.18804618389296662837e-1L),
158 rb2u = LD80C(0x9a4dd1383e5daf5b, 4,  -1.92879967111618594779e+1L),
159 rb3u = LD80C(0xbff0ae9fc0751de6, 7,  -1.91940164551245394969e+2L),
160 rb4u = LD80C(0xdde08465310b472b, 9,  -8.87508080766577324539e+2L),
161 rb5u = LD80C(0xe796e1d38c8c70a9, 10, -1.85271506669474503781e+3L),
162 rb6u = LD80C(0xbaf655a76e0ab3b5, 10, -1.49569795581333675349e+3L),
163 rb7u = LD80C(0x95d21e3e75503c21, 8,  -2.99641547972948019157e+2L),
164 sb1u = LD80C(0x814487ed823c8cbd, 5,   3.23169247732868256569e+1L),
165 sb2u = LD80C(0xbe4bfbb1301304be, 8,   3.80593618534539961773e+2L),
166 sb3u = LD80C(0x809c4ade46b927c7, 11,  2.05776827838541292848e+3L),
167 sb4u = LD80C(0xa55284359f3395a8, 12,  5.29031455540062116327e+3L),
168 sb5u = LD80C(0xbcfa72da9b820874, 12,  6.04730608102312640462e+3L),
169 sb6u = LD80C(0x9d09a35988934631, 11,  2.51260238030767176221e+3L),
170 sb7u = LD80C(0xd675bbe542c159fa, 7,   2.14459898308561015684e+2L);
171 #define rb0	(rb0u.e)
172 #define rb1	(rb1u.e)
173 #define rb2	(rb2u.e)
174 #define rb3	(rb3u.e)
175 #define rb4	(rb4u.e)
176 #define rb5	(rb5u.e)
177 #define rb6	(rb6u.e)
178 #define rb7	(rb7u.e)
179 #define sb1	(sb1u.e)
180 #define sb2	(sb2u.e)
181 #define sb3	(sb3u.e)
182 #define sb4	(sb4u.e)
183 #define sb5	(sb5u.e)
184 #define sb6	(sb6u.e)
185 #define sb7	(sb7u.e)
187  * Domain [7,108], range ~[-4.422e-22,4.422e-22]:
188  * |log(x*erfc(x)) + x**2 + 0.5625 - rc(x)/sc(x)| < 2**-70.938
191 /* err = -4.422092275318925082e-22 -70.937689 */
192 rc0u = LD80C(0xa1a091cf437a17ad, -7, -9.86494292470008707260e-3L),
193 rc1u = LD80C(0xbe79c5a978122b00, -1, -7.44045595049165939261e-1L),
194 rc2u = LD80C(0xdb26f9bbe31a2794, 3,  -1.36970155085888424425e+1L),
195 rc3u = LD80C(0xb5f69a38f5747ac8, 6,  -9.09816453742625888546e+1L),
196 rc4u = LD80C(0xd79676d970d0a21a, 7,  -2.15587750997584074147e+2L),
197 rc5u = LD80C(0xfe528153c45ec97c, 6,  -1.27161142938347796666e+2L),
198 sc1u = LD80C(0xc5e8cd46d5604a96, 4,   2.47386727842204312937e+1L),
199 sc2u = LD80C(0xc5f0f5a5484520eb, 7,   1.97941248254913378865e+2L),
200 sc3u = LD80C(0x964e3c7b34db9170, 9,   6.01222441484087787522e+2L),
201 sc4u = LD80C(0x99be1b89faa0596a, 9,   6.14970430845978077827e+2L),
202 sc5u = LD80C(0xf80dfcbf37ffc5ea, 6,   1.24027318931184605891e+2L);
203 #define rc0	(rc0u.e)
204 #define rc1	(rc1u.e)
205 #define rc2	(rc2u.e)
206 #define rc3	(rc3u.e)
207 #define rc4	(rc4u.e)
208 #define rc5	(rc5u.e)
209 #define sc1	(sc1u.e)
210 #define sc2	(sc2u.e)
211 #define sc3	(sc3u.e)
212 #define sc4	(sc4u.e)
213 #define sc5	(sc5u.e)
227 		return (1-i)+one/x;	/* erfl(+-inf)=+-1 */  in erfl()
234 	    if(ax < 0x1p-34L) {  in erfl()
235 	        if(ax < 0x1p-16373L)	  in erfl()
246 	    s = ax-one;  in erfl()
249 	    if(x>=0) RETURNI(erx + P/Q); else RETURNI(-erx - P/Q);  in erfl()
252 	    if(x>=0) RETURNI(one-tiny); else RETURNI(tiny-one);  in erfl()
265 	r=expl(-z*z-0.5625)*expl((z-ax)*(z+ax)+R/S);  in erfl()
266 	if(x>=0) RETURNI(one-r/ax); else RETURNI(r/ax-one);  in erfl()
279 					/* erfcl(+-inf)=0,2 */  in erfcl()
287 	    if(ax < 0x1p-34L)  in erfcl()
288 		RETURNI(one-x);  in erfcl()
294 		RETURNI(one-(x+x*y));  in erfcl()
297 		r += (x-half);  in erfcl()
298 	       RETURNI(half - r);  in erfcl()
302 	    s = ax-one;  in erfcl()
306 	        z  = one-erx; RETURNI(z - P/Q);  in erfcl()
323 		if(x < -7) RETURNI(two-tiny);/* x < -7 */  in erfcl()
328 	    r = expl(-z*z-0.5625)*expl((z-ax)*(z+ax)+R/S);  in erfcl()
329 	    if(x>0) RETURNI(r/ax); else RETURNI(two-r/ax);  in erfcl()
331 	    if(x>0) RETURNI(tiny*tiny); else RETURNI(two-tiny);  in erfcl()