1da2e3ebdSchin #include "FEATURE/uwin"
2da2e3ebdSchin
3da2e3ebdSchin #if !_UWIN || _lib_erf
4da2e3ebdSchin
_STUB_erf()5da2e3ebdSchin void _STUB_erf(){}
6da2e3ebdSchin
7da2e3ebdSchin #else
8da2e3ebdSchin
9da2e3ebdSchin /*-
10da2e3ebdSchin * Copyright (c) 1992, 1993
11da2e3ebdSchin * The Regents of the University of California. All rights reserved.
12da2e3ebdSchin *
13da2e3ebdSchin * Redistribution and use in source and binary forms, with or without
14da2e3ebdSchin * modification, are permitted provided that the following conditions
15da2e3ebdSchin * are met:
16da2e3ebdSchin * 1. Redistributions of source code must retain the above copyright
17da2e3ebdSchin * notice, this list of conditions and the following disclaimer.
18da2e3ebdSchin * 2. Redistributions in binary form must reproduce the above copyright
19da2e3ebdSchin * notice, this list of conditions and the following disclaimer in the
20da2e3ebdSchin * documentation and/or other materials provided with the distribution.
21da2e3ebdSchin * 3. Neither the name of the University nor the names of its contributors
22da2e3ebdSchin * may be used to endorse or promote products derived from this software
23da2e3ebdSchin * without specific prior written permission.
24da2e3ebdSchin *
25da2e3ebdSchin * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
26da2e3ebdSchin * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27da2e3ebdSchin * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
28da2e3ebdSchin * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
29da2e3ebdSchin * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
30da2e3ebdSchin * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
31da2e3ebdSchin * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
32da2e3ebdSchin * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
33da2e3ebdSchin * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
34da2e3ebdSchin * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
35da2e3ebdSchin * SUCH DAMAGE.
36da2e3ebdSchin */
37da2e3ebdSchin
38da2e3ebdSchin #ifndef lint
39da2e3ebdSchin static char sccsid[] = "@(#)erf.c 8.1 (Berkeley) 6/4/93";
40da2e3ebdSchin #endif /* not lint */
41da2e3ebdSchin
42da2e3ebdSchin /* Modified Nov 30, 1992 P. McILROY:
43da2e3ebdSchin * Replaced expansions for x >= 1.25 (error 1.7ulp vs ~6ulp)
44da2e3ebdSchin * Replaced even+odd with direct calculation for x < .84375,
45da2e3ebdSchin * to avoid destructive cancellation.
46da2e3ebdSchin *
47da2e3ebdSchin * Performance of erfc(x):
48da2e3ebdSchin * In 300000 trials in the range [.83, .84375] the
49da2e3ebdSchin * maximum observed error was 3.6ulp.
50da2e3ebdSchin *
51da2e3ebdSchin * In [.84735,1.25] the maximum observed error was <2.5ulp in
52da2e3ebdSchin * 100000 runs in the range [1.2, 1.25].
53da2e3ebdSchin *
54da2e3ebdSchin * In [1.25,26] (Not including subnormal results)
55da2e3ebdSchin * the error is < 1.7ulp.
56da2e3ebdSchin */
57da2e3ebdSchin
58da2e3ebdSchin /* double erf(double x)
59da2e3ebdSchin * double erfc(double x)
60da2e3ebdSchin * x
61da2e3ebdSchin * 2 |\
62da2e3ebdSchin * erf(x) = --------- | exp(-t*t)dt
63da2e3ebdSchin * sqrt(pi) \|
64da2e3ebdSchin * 0
65da2e3ebdSchin *
66da2e3ebdSchin * erfc(x) = 1-erf(x)
67da2e3ebdSchin *
68da2e3ebdSchin * Method:
69da2e3ebdSchin * 1. Reduce x to |x| by erf(-x) = -erf(x)
70da2e3ebdSchin * 2. For x in [0, 0.84375]
71da2e3ebdSchin * erf(x) = x + x*P(x^2)
72da2e3ebdSchin * erfc(x) = 1 - erf(x) if x<=0.25
73da2e3ebdSchin * = 0.5 + ((0.5-x)-x*P) if x in [0.25,0.84375]
74da2e3ebdSchin * where
75da2e3ebdSchin * 2 2 4 20
76da2e3ebdSchin * P = P(x ) = (p0 + p1 * x + p2 * x + ... + p10 * x )
77da2e3ebdSchin * is an approximation to (erf(x)-x)/x with precision
78da2e3ebdSchin *
79da2e3ebdSchin * -56.45
80da2e3ebdSchin * | P - (erf(x)-x)/x | <= 2
81da2e3ebdSchin *
82da2e3ebdSchin *
83da2e3ebdSchin * Remark. The formula is derived by noting
84da2e3ebdSchin * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
85da2e3ebdSchin * and that
86da2e3ebdSchin * 2/sqrt(pi) = 1.128379167095512573896158903121545171688
87da2e3ebdSchin * is close to one. The interval is chosen because the fixed
88da2e3ebdSchin * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
89da2e3ebdSchin * near 0.6174), and by some experiment, 0.84375 is chosen to
90da2e3ebdSchin * guarantee the error is less than one ulp for erf.
91da2e3ebdSchin *
92da2e3ebdSchin * 3. For x in [0.84375,1.25], let s = x - 1, and
93da2e3ebdSchin * c = 0.84506291151 rounded to single (24 bits)
94da2e3ebdSchin * erf(x) = c + P1(s)/Q1(s)
95da2e3ebdSchin * erfc(x) = (1-c) - P1(s)/Q1(s)
96da2e3ebdSchin * |P1/Q1 - (erf(x)-c)| <= 2**-59.06
97da2e3ebdSchin * Remark: here we use the taylor series expansion at x=1.
98da2e3ebdSchin * erf(1+s) = erf(1) + s*Poly(s)
99da2e3ebdSchin * = 0.845.. + P1(s)/Q1(s)
100da2e3ebdSchin * That is, we use rational approximation to approximate
101da2e3ebdSchin * erf(1+s) - (c = (single)0.84506291151)
102da2e3ebdSchin * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
103da2e3ebdSchin * where
104da2e3ebdSchin * P1(s) = degree 6 poly in s
105da2e3ebdSchin * Q1(s) = degree 6 poly in s
106da2e3ebdSchin *
107da2e3ebdSchin * 4. For x in [1.25, 2]; [2, 4]
108da2e3ebdSchin * erf(x) = 1.0 - tiny
109da2e3ebdSchin * erfc(x) = (1/x)exp(-x*x-(.5*log(pi) -.5z + R(z)/S(z))
110da2e3ebdSchin *
111da2e3ebdSchin * Where z = 1/(x*x), R is degree 9, and S is degree 3;
112da2e3ebdSchin *
113da2e3ebdSchin * 5. For x in [4,28]
114da2e3ebdSchin * erf(x) = 1.0 - tiny
115da2e3ebdSchin * erfc(x) = (1/x)exp(-x*x-(.5*log(pi)+eps + zP(z))
116da2e3ebdSchin *
117da2e3ebdSchin * Where P is degree 14 polynomial in 1/(x*x).
118da2e3ebdSchin *
119da2e3ebdSchin * Notes:
120da2e3ebdSchin * Here 4 and 5 make use of the asymptotic series
121da2e3ebdSchin * exp(-x*x)
122da2e3ebdSchin * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) );
123da2e3ebdSchin * x*sqrt(pi)
124da2e3ebdSchin *
125da2e3ebdSchin * where for z = 1/(x*x)
126da2e3ebdSchin * P(z) ~ z/2*(-1 + z*3/2*(1 + z*5/2*(-1 + z*7/2*(1 +...))))
127da2e3ebdSchin *
128da2e3ebdSchin * Thus we use rational approximation to approximate
129da2e3ebdSchin * erfc*x*exp(x*x) ~ 1/sqrt(pi);
130da2e3ebdSchin *
131da2e3ebdSchin * The error bound for the target function, G(z) for
132da2e3ebdSchin * the interval
133da2e3ebdSchin * [4, 28]:
134da2e3ebdSchin * |eps + 1/(z)P(z) - G(z)| < 2**(-56.61)
135da2e3ebdSchin * for [2, 4]:
136da2e3ebdSchin * |R(z)/S(z) - G(z)| < 2**(-58.24)
137da2e3ebdSchin * for [1.25, 2]:
138da2e3ebdSchin * |R(z)/S(z) - G(z)| < 2**(-58.12)
139da2e3ebdSchin *
140da2e3ebdSchin * 6. For inf > x >= 28
141da2e3ebdSchin * erf(x) = 1 - tiny (raise inexact)
142da2e3ebdSchin * erfc(x) = tiny*tiny (raise underflow)
143da2e3ebdSchin *
144da2e3ebdSchin * 7. Special cases:
145da2e3ebdSchin * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
146da2e3ebdSchin * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
147da2e3ebdSchin * erfc/erf(NaN) is NaN
148da2e3ebdSchin */
149da2e3ebdSchin
150da2e3ebdSchin #if defined(vax) || defined(tahoe)
151da2e3ebdSchin #define _IEEE 0
152da2e3ebdSchin #define TRUNC(x) (double) (float) (x)
153da2e3ebdSchin #else
154da2e3ebdSchin #define _IEEE 1
155da2e3ebdSchin #define TRUNC(x) *(((int *) &x) + 1) &= 0xf8000000
156da2e3ebdSchin #define infnan(x) 0.0
157da2e3ebdSchin #endif
158da2e3ebdSchin
159da2e3ebdSchin #ifdef _IEEE_LIBM
160da2e3ebdSchin /*
161da2e3ebdSchin * redefining "___function" to "function" in _IEEE_LIBM mode
162da2e3ebdSchin */
163da2e3ebdSchin #include "ieee_libm.h"
164da2e3ebdSchin #endif
165da2e3ebdSchin #include "mathimpl.h"
166da2e3ebdSchin
167da2e3ebdSchin static double
168da2e3ebdSchin tiny = 1e-300,
169da2e3ebdSchin half = 0.5,
170da2e3ebdSchin one = 1.0,
171da2e3ebdSchin two = 2.0,
172da2e3ebdSchin c = 8.45062911510467529297e-01, /* (float)0.84506291151 */
173da2e3ebdSchin /*
174da2e3ebdSchin * Coefficients for approximation to erf in [0,0.84375]
175da2e3ebdSchin */
176da2e3ebdSchin p0t8 = 1.02703333676410051049867154944018394163280,
177da2e3ebdSchin p0 = 1.283791670955125638123339436800229927041e-0001,
178da2e3ebdSchin p1 = -3.761263890318340796574473028946097022260e-0001,
179da2e3ebdSchin p2 = 1.128379167093567004871858633779992337238e-0001,
180da2e3ebdSchin p3 = -2.686617064084433642889526516177508374437e-0002,
181da2e3ebdSchin p4 = 5.223977576966219409445780927846432273191e-0003,
182da2e3ebdSchin p5 = -8.548323822001639515038738961618255438422e-0004,
183da2e3ebdSchin p6 = 1.205520092530505090384383082516403772317e-0004,
184da2e3ebdSchin p7 = -1.492214100762529635365672665955239554276e-0005,
185da2e3ebdSchin p8 = 1.640186161764254363152286358441771740838e-0006,
186da2e3ebdSchin p9 = -1.571599331700515057841960987689515895479e-0007,
187da2e3ebdSchin p10= 1.073087585213621540635426191486561494058e-0008;
188da2e3ebdSchin /*
189da2e3ebdSchin * Coefficients for approximation to erf in [0.84375,1.25]
190da2e3ebdSchin */
191da2e3ebdSchin static double
192da2e3ebdSchin pa0 = -2.362118560752659485957248365514511540287e-0003,
193da2e3ebdSchin pa1 = 4.148561186837483359654781492060070469522e-0001,
194da2e3ebdSchin pa2 = -3.722078760357013107593507594535478633044e-0001,
195da2e3ebdSchin pa3 = 3.183466199011617316853636418691420262160e-0001,
196da2e3ebdSchin pa4 = -1.108946942823966771253985510891237782544e-0001,
197da2e3ebdSchin pa5 = 3.547830432561823343969797140537411825179e-0002,
198da2e3ebdSchin pa6 = -2.166375594868790886906539848893221184820e-0003,
199da2e3ebdSchin qa1 = 1.064208804008442270765369280952419863524e-0001,
200da2e3ebdSchin qa2 = 5.403979177021710663441167681878575087235e-0001,
201da2e3ebdSchin qa3 = 7.182865441419627066207655332170665812023e-0002,
202da2e3ebdSchin qa4 = 1.261712198087616469108438860983447773726e-0001,
203da2e3ebdSchin qa5 = 1.363708391202905087876983523620537833157e-0002,
204da2e3ebdSchin qa6 = 1.198449984679910764099772682882189711364e-0002;
205da2e3ebdSchin /*
206da2e3ebdSchin * log(sqrt(pi)) for large x expansions.
207da2e3ebdSchin * The tail (lsqrtPI_lo) is included in the rational
208da2e3ebdSchin * approximations.
209da2e3ebdSchin */
210da2e3ebdSchin static double
211da2e3ebdSchin lsqrtPI_hi = .5723649429247000819387380943226;
212da2e3ebdSchin /*
213da2e3ebdSchin * lsqrtPI_lo = .000000000000000005132975581353913;
214da2e3ebdSchin *
215da2e3ebdSchin * Coefficients for approximation to erfc in [2, 4]
216da2e3ebdSchin */
217da2e3ebdSchin static double
218da2e3ebdSchin rb0 = -1.5306508387410807582e-010, /* includes lsqrtPI_lo */
219da2e3ebdSchin rb1 = 2.15592846101742183841910806188e-008,
220da2e3ebdSchin rb2 = 6.24998557732436510470108714799e-001,
221da2e3ebdSchin rb3 = 8.24849222231141787631258921465e+000,
222da2e3ebdSchin rb4 = 2.63974967372233173534823436057e+001,
223da2e3ebdSchin rb5 = 9.86383092541570505318304640241e+000,
224da2e3ebdSchin rb6 = -7.28024154841991322228977878694e+000,
225da2e3ebdSchin rb7 = 5.96303287280680116566600190708e+000,
226da2e3ebdSchin rb8 = -4.40070358507372993983608466806e+000,
227da2e3ebdSchin rb9 = 2.39923700182518073731330332521e+000,
228da2e3ebdSchin rb10 = -6.89257464785841156285073338950e-001,
229da2e3ebdSchin sb1 = 1.56641558965626774835300238919e+001,
230da2e3ebdSchin sb2 = 7.20522741000949622502957936376e+001,
231da2e3ebdSchin sb3 = 9.60121069770492994166488642804e+001;
232da2e3ebdSchin /*
233da2e3ebdSchin * Coefficients for approximation to erfc in [1.25, 2]
234da2e3ebdSchin */
235da2e3ebdSchin static double
236da2e3ebdSchin rc0 = -2.47925334685189288817e-007, /* includes lsqrtPI_lo */
237da2e3ebdSchin rc1 = 1.28735722546372485255126993930e-005,
238da2e3ebdSchin rc2 = 6.24664954087883916855616917019e-001,
239da2e3ebdSchin rc3 = 4.69798884785807402408863708843e+000,
240da2e3ebdSchin rc4 = 7.61618295853929705430118701770e+000,
241da2e3ebdSchin rc5 = 9.15640208659364240872946538730e-001,
242da2e3ebdSchin rc6 = -3.59753040425048631334448145935e-001,
243da2e3ebdSchin rc7 = 1.42862267989304403403849619281e-001,
244da2e3ebdSchin rc8 = -4.74392758811439801958087514322e-002,
245da2e3ebdSchin rc9 = 1.09964787987580810135757047874e-002,
246da2e3ebdSchin rc10 = -1.28856240494889325194638463046e-003,
247da2e3ebdSchin sc1 = 9.97395106984001955652274773456e+000,
248da2e3ebdSchin sc2 = 2.80952153365721279953959310660e+001,
249da2e3ebdSchin sc3 = 2.19826478142545234106819407316e+001;
250da2e3ebdSchin /*
251da2e3ebdSchin * Coefficients for approximation to erfc in [4,28]
252da2e3ebdSchin */
253da2e3ebdSchin static double
254da2e3ebdSchin rd0 = -2.1491361969012978677e-016, /* includes lsqrtPI_lo */
255da2e3ebdSchin rd1 = -4.99999999999640086151350330820e-001,
256da2e3ebdSchin rd2 = 6.24999999772906433825880867516e-001,
257da2e3ebdSchin rd3 = -1.54166659428052432723177389562e+000,
258da2e3ebdSchin rd4 = 5.51561147405411844601985649206e+000,
259da2e3ebdSchin rd5 = -2.55046307982949826964613748714e+001,
260da2e3ebdSchin rd6 = 1.43631424382843846387913799845e+002,
261da2e3ebdSchin rd7 = -9.45789244999420134263345971704e+002,
262da2e3ebdSchin rd8 = 6.94834146607051206956384703517e+003,
263da2e3ebdSchin rd9 = -5.27176414235983393155038356781e+004,
264da2e3ebdSchin rd10 = 3.68530281128672766499221324921e+005,
265da2e3ebdSchin rd11 = -2.06466642800404317677021026611e+006,
266da2e3ebdSchin rd12 = 7.78293889471135381609201431274e+006,
267da2e3ebdSchin rd13 = -1.42821001129434127360582351685e+007;
268da2e3ebdSchin
269da2e3ebdSchin extern double erf(x)
270da2e3ebdSchin double x;
271da2e3ebdSchin {
272da2e3ebdSchin double R,S,P,Q,ax,s,y,z,r,fabs(),exp();
273da2e3ebdSchin if(!finite(x)) { /* erf(nan)=nan */
274da2e3ebdSchin if (isnan(x))
275da2e3ebdSchin return(x);
276da2e3ebdSchin return (x > 0 ? one : -one); /* erf(+/-inf)= +/-1 */
277da2e3ebdSchin }
278da2e3ebdSchin if ((ax = x) < 0)
279da2e3ebdSchin ax = - ax;
280da2e3ebdSchin if (ax < .84375) {
281da2e3ebdSchin if (ax < 3.7e-09) {
282da2e3ebdSchin if (ax < 1.0e-308)
283da2e3ebdSchin return 0.125*(8.0*x+p0t8*x); /*avoid underflow */
284da2e3ebdSchin return x + p0*x;
285da2e3ebdSchin }
286da2e3ebdSchin y = x*x;
287da2e3ebdSchin r = y*(p1+y*(p2+y*(p3+y*(p4+y*(p5+
288da2e3ebdSchin y*(p6+y*(p7+y*(p8+y*(p9+y*p10)))))))));
289da2e3ebdSchin return x + x*(p0+r);
290da2e3ebdSchin }
291da2e3ebdSchin if (ax < 1.25) { /* 0.84375 <= |x| < 1.25 */
292da2e3ebdSchin s = fabs(x)-one;
293da2e3ebdSchin P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
294da2e3ebdSchin Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
295da2e3ebdSchin if (x>=0)
296da2e3ebdSchin return (c + P/Q);
297da2e3ebdSchin else
298da2e3ebdSchin return (-c - P/Q);
299da2e3ebdSchin }
300da2e3ebdSchin if (ax >= 6.0) { /* inf>|x|>=6 */
301da2e3ebdSchin if (x >= 0.0)
302da2e3ebdSchin return (one-tiny);
303da2e3ebdSchin else
304da2e3ebdSchin return (tiny-one);
305da2e3ebdSchin }
306da2e3ebdSchin /* 1.25 <= |x| < 6 */
307da2e3ebdSchin z = -ax*ax;
308da2e3ebdSchin s = -one/z;
309da2e3ebdSchin if (ax < 2.0) {
310da2e3ebdSchin R = rc0+s*(rc1+s*(rc2+s*(rc3+s*(rc4+s*(rc5+
311da2e3ebdSchin s*(rc6+s*(rc7+s*(rc8+s*(rc9+s*rc10)))))))));
312da2e3ebdSchin S = one+s*(sc1+s*(sc2+s*sc3));
313da2e3ebdSchin } else {
314da2e3ebdSchin R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+
315da2e3ebdSchin s*(rb6+s*(rb7+s*(rb8+s*(rb9+s*rb10)))))))));
316da2e3ebdSchin S = one+s*(sb1+s*(sb2+s*sb3));
317da2e3ebdSchin }
318da2e3ebdSchin y = (R/S -.5*s) - lsqrtPI_hi;
319da2e3ebdSchin z += y;
320da2e3ebdSchin z = exp(z)/ax;
321da2e3ebdSchin if (x >= 0)
322da2e3ebdSchin return (one-z);
323da2e3ebdSchin else
324da2e3ebdSchin return (z-one);
325da2e3ebdSchin }
326da2e3ebdSchin
327da2e3ebdSchin extern double erfc(x)
328da2e3ebdSchin double x;
329da2e3ebdSchin {
330da2e3ebdSchin double R,S,P,Q,s,ax,y,z,r,fabs(),__exp__D();
331da2e3ebdSchin if (!finite(x)) {
332da2e3ebdSchin if (isnan(x)) /* erfc(NaN) = NaN */
333da2e3ebdSchin return(x);
334da2e3ebdSchin else if (x > 0) /* erfc(+-inf)=0,2 */
335da2e3ebdSchin return 0.0;
336da2e3ebdSchin else
337da2e3ebdSchin return 2.0;
338da2e3ebdSchin }
339da2e3ebdSchin if ((ax = x) < 0)
340da2e3ebdSchin ax = -ax;
341da2e3ebdSchin if (ax < .84375) { /* |x|<0.84375 */
342da2e3ebdSchin if (ax < 1.38777878078144568e-17) /* |x|<2**-56 */
343da2e3ebdSchin return one-x;
344da2e3ebdSchin y = x*x;
345da2e3ebdSchin r = y*(p1+y*(p2+y*(p3+y*(p4+y*(p5+
346da2e3ebdSchin y*(p6+y*(p7+y*(p8+y*(p9+y*p10)))))))));
347da2e3ebdSchin if (ax < .0625) { /* |x|<2**-4 */
348da2e3ebdSchin return (one-(x+x*(p0+r)));
349da2e3ebdSchin } else {
350da2e3ebdSchin r = x*(p0+r);
351da2e3ebdSchin r += (x-half);
352da2e3ebdSchin return (half - r);
353da2e3ebdSchin }
354da2e3ebdSchin }
355da2e3ebdSchin if (ax < 1.25) { /* 0.84375 <= |x| < 1.25 */
356da2e3ebdSchin s = ax-one;
357da2e3ebdSchin P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
358da2e3ebdSchin Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
359da2e3ebdSchin if (x>=0) {
360da2e3ebdSchin z = one-c; return z - P/Q;
361da2e3ebdSchin } else {
362da2e3ebdSchin z = c+P/Q; return one+z;
363da2e3ebdSchin }
364da2e3ebdSchin }
365da2e3ebdSchin if (ax >= 28) /* Out of range */
366da2e3ebdSchin if (x>0)
367da2e3ebdSchin return (tiny*tiny);
368da2e3ebdSchin else
369da2e3ebdSchin return (two-tiny);
370da2e3ebdSchin z = ax;
371da2e3ebdSchin TRUNC(z);
372da2e3ebdSchin y = z - ax; y *= (ax+z);
373da2e3ebdSchin z *= -z; /* Here z + y = -x^2 */
374da2e3ebdSchin s = one/(-z-y); /* 1/(x*x) */
375da2e3ebdSchin if (ax >= 4) { /* 6 <= ax */
376da2e3ebdSchin R = s*(rd1+s*(rd2+s*(rd3+s*(rd4+s*(rd5+
377da2e3ebdSchin s*(rd6+s*(rd7+s*(rd8+s*(rd9+s*(rd10
378da2e3ebdSchin +s*(rd11+s*(rd12+s*rd13))))))))))));
379da2e3ebdSchin y += rd0;
380da2e3ebdSchin } else if (ax >= 2) {
381da2e3ebdSchin R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+
382da2e3ebdSchin s*(rb6+s*(rb7+s*(rb8+s*(rb9+s*rb10)))))))));
383da2e3ebdSchin S = one+s*(sb1+s*(sb2+s*sb3));
384da2e3ebdSchin y += R/S;
385da2e3ebdSchin R = -.5*s;
386da2e3ebdSchin } else {
387da2e3ebdSchin R = rc0+s*(rc1+s*(rc2+s*(rc3+s*(rc4+s*(rc5+
388da2e3ebdSchin s*(rc6+s*(rc7+s*(rc8+s*(rc9+s*rc10)))))))));
389da2e3ebdSchin S = one+s*(sc1+s*(sc2+s*sc3));
390da2e3ebdSchin y += R/S;
391da2e3ebdSchin R = -.5*s;
392da2e3ebdSchin }
393da2e3ebdSchin /* return exp(-x^2 - lsqrtPI_hi + R + y)/x; */
394da2e3ebdSchin s = ((R + y) - lsqrtPI_hi) + z;
395da2e3ebdSchin y = (((z-s) - lsqrtPI_hi) + R) + y;
396da2e3ebdSchin r = __exp__D(s, y)/x;
397da2e3ebdSchin if (x>0)
398da2e3ebdSchin return r;
399da2e3ebdSchin else
400da2e3ebdSchin return two-r;
401da2e3ebdSchin }
402da2e3ebdSchin
403da2e3ebdSchin #endif
404