Lines Matching full:1
36 * erfc(x) = 1-erf(x)
42 * 1. erf(x) = x + x*R(x^2) for |x| in [0, 7/8]
49 * 1a. erf(x) = 1 - erfc(x), for |x| > 1.0
50 * erfc(x) = 1 - erf(x) if |x| < 1/4
52 * 2. For |x| in [7/8, 1], let s = |x| - 1, and
55 * Remark: here we use the taylor series expansion at x=1.
56 * erf(1+s) = erf(1) + s*Poly(s)
60 * 3. For x in [1/4, 5/4],
62 * for const = 1/4, 3/8, ..., 9/8
63 * and 0 <= s <= 1/8 .
66 * erfc(x) = (1/x)*exp(-x*x-0.5625 + R(z))
67 * z=1/x^2
69 * of width 1/8 in 1/x.
80 * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
84 * erf(x) = sign(x) *(1 - tiny) (raise inexact)
89 * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
90 * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
96 /* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */
114 /* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */
134 tiny = 1e-4931L,
137 /* 2/sqrt(pi) - 1 */
138 efx = 1.2837916709551257389615890312154517168810E-1L,
139 /* 8 * (2/sqrt(pi) - 1) */
147 static const long double TN1[NTN1 + 1] =
160 static const long double TD1[NTD1 + 1] =
175 /* erf(z+1) = erf_const + P(z)/Q(z)
180 static const long double TN2[NTN2 + 1] =
190 5.127662277706787664956025545897050896203E-1L
193 static const long double TD2[NTD2 + 1] =
212 static const long double RNr13[NRNr13 + 1] =
225 static const long double RDr13[NRDr13 + 1] =
234 6.469655675326150785692908453094054988938E-1L
246 static const long double RNr14[NRNr14 + 1] =
259 static const long double RDr14[NRDr14 + 1] =
268 7.647745753648996559837591812375456641163E-1L
279 static const long double RNr15[NRNr15 + 1] =
292 static const long double RDr15[NRDr15 + 1] =
312 static const long double RNr16[NRNr16 + 1] =
321 1.370831653033047440345050025876085121231E-1L,
325 static const long double RDr16[NRDr16 + 1] =
345 static const long double RNr17[NRNr17 + 1] =
354 3.631915988567346438830283503729569443642E-1L,
358 static const long double RDr17[NRDr17 + 1] =
379 static const long double RNr18[NRNr18 + 1] =
388 5.933878036611279244654299924101068088582E-1L,
392 static const long double RDr18[NRDr18 + 1] =
412 static const long double RNr19[NRNr19 + 1] =
421 7.533980372789646140112424811291782526263E-1L,
425 static const long double RDr19[NRDr19 + 1] =
445 static const long double RNr20[NRNr20 + 1] =
454 7.573806045289044647727613003096916516475E-1L,
458 static const long double RDr20[NRDr20 + 1] =
474 /* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2))
475 7/8 <= 1/x < 1
478 static const long double RNr8[NRNr8 + 1] =
492 static const long double RDr8[NRDr8 + 1] =
506 /* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2))
507 0.75 <= 1/x <= 0.875
510 static const long double RNr7[NRNr7 + 1] =
524 static const long double RDr7[NRDr7 + 1] =
539 /* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
540 5/8 <= 1/x < 3/4
543 static const long double RNr6[NRNr6 + 1] =
557 static const long double RDr6[NRDr6 + 1] =
572 /* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
573 1/2 <= 1/x < 5/8
576 static const long double RNr5[NRNr5 + 1] =
579 -2.697100758900280402659586595884478660721E-1L,
591 static const long double RDr5[NRDr5 + 1] =
593 3.377879570417399341550710467744693125385E-1L,
606 /* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
607 3/8 <= 1/x < 1/2
610 static const long double RNr4[NRNr4 + 1] =
613 2.987056016877277929720231688689431056567E-1L,
625 static const long double RDr4[NRDr4 + 1] =
627 -3.303141981514540274165450687270180479586E-1L,
641 /* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
642 1/4 <= 1/x < 3/8
645 static const long double RNr3[NRNr3 + 1] =
650 -1.650592646560987700661598877522831234791E-1L,
661 static const long double RDr3[NRDr3 + 1] =
665 2.752657634309886336431266395637285974292E-1L,
677 /* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
678 1/8 <= 1/x < 1/4
681 static const long double RNr2[NRNr2 + 1] =
688 -7.068318854874733315971973707247467326619E-1L,
697 static const long double RDr2[NRDr2 + 1] =
702 1.302040375859768674620410563307838448508E-1L,
713 /* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
714 1/128 <= 1/x < 1/8
717 static const long double RNr1[NRNr1 + 1] =
724 -6.242615227257324746371284637695778043982E-1L,
731 static const long double RDr1[NRDr1 + 1] =
736 1.511222515036021033410078631914783519649E-1L,
759 i = ((sign & 0xffff0000) >> 31) << 1; in erfl()
760 return (long double) (1 - i) + one / x; /* erf(+-inf)=+-1 */ in erfl()
815 return (long double) (((u_int32_t) sign >> 31) << 1) + one / x; in erfcl()
818 if (ix < 0x3ffd0000) /* |x| <1/4 */ in erfcl()
892 case 1: in erfcl()