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-rw-r--r--usr/src/lib/libm/common/R/besself.c807
1 files changed, 807 insertions, 0 deletions
diff --git a/usr/src/lib/libm/common/R/besself.c b/usr/src/lib/libm/common/R/besself.c
new file mode 100644
index 0000000000..720e4eb47f
--- /dev/null
+++ b/usr/src/lib/libm/common/R/besself.c
@@ -0,0 +1,807 @@
+/*
+ * CDDL HEADER START
+ *
+ * The contents of this file are subject to the terms of the
+ * Common Development and Distribution License (the "License").
+ * You may not use this file except in compliance with the License.
+ *
+ * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
+ * or http://www.opensolaris.org/os/licensing.
+ * See the License for the specific language governing permissions
+ * and limitations under the License.
+ *
+ * When distributing Covered Code, include this CDDL HEADER in each
+ * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
+ * If applicable, add the following below this CDDL HEADER, with the
+ * fields enclosed by brackets "[]" replaced with your own identifying
+ * information: Portions Copyright [yyyy] [name of copyright owner]
+ *
+ * CDDL HEADER END
+ */
+/*
+ * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
+ */
+/*
+ * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
+ * Use is subject to license terms.
+ */
+
+#pragma weak j0f = __j0f
+#pragma weak j1f = __j1f
+#pragma weak jnf = __jnf
+#pragma weak y0f = __y0f
+#pragma weak y1f = __y1f
+#pragma weak ynf = __ynf
+
+#include "libm.h"
+#include <float.h>
+
+#if defined(__i386) && !defined(__amd64)
+extern int __swapRP(int);
+#endif
+
+static const float
+ zerof = 0.0f,
+ onef = 1.0f;
+
+static const double C[] = {
+ 0.0,
+ -0.125,
+ 0.25,
+ 0.375,
+ 0.5,
+ 1.0,
+ 2.0,
+ 8.0,
+ 0.5641895835477562869480794515607725858441, /* 1/sqrt(pi) */
+ 0.636619772367581343075535053490057448, /* 2/pi */
+ 1.0e9,
+};
+
+#define zero C[0]
+#define neighth C[1]
+#define quarter C[2]
+#define three8 C[3]
+#define half C[4]
+#define one C[5]
+#define two C[6]
+#define eight C[7]
+#define isqrtpi C[8]
+#define tpi C[9]
+#define big C[10]
+
+static const double Cj0y0[] = {
+ 0.4861344183386052721391238447e5, /* pr */
+ 0.1377662549407112278133438945e6,
+ 0.1222466364088289731869114004e6,
+ 0.4107070084315176135583353374e5,
+ 0.5026073801860637125889039915e4,
+ 0.1783193659125479654541542419e3,
+ 0.88010344055383421691677564e0,
+ 0.4861344183386052721414037058e5, /* ps */
+ 0.1378196632630384670477582699e6,
+ 0.1223967185341006542748936787e6,
+ 0.4120150243795353639995862617e5,
+ 0.5068271181053546392490184353e4,
+ 0.1829817905472769960535671664e3,
+ 1.0,
+ -0.1731210995701068539185611951e3, /* qr */
+ -0.5522559165936166961235240613e3,
+ -0.5604935606637346590614529613e3,
+ -0.2200430300226009379477365011e3,
+ -0.323869355375648849771296746e2,
+ -0.14294979207907956223499258e1,
+ -0.834690374102384988158918e-2,
+ 0.1107975037248683865326709645e5, /* qs */
+ 0.3544581680627082674651471873e5,
+ 0.3619118937918394132179019059e5,
+ 0.1439895563565398007471485822e5,
+ 0.2190277023344363955930226234e4,
+ 0.106695157020407986137501682e3,
+ 1.0,
+};
+
+#define pr Cj0y0
+#define ps (Cj0y0+7)
+#define qr (Cj0y0+14)
+#define qs (Cj0y0+21)
+
+static const double Cj0[] = {
+ -2.500000000000003622131880894830476755537e-0001, /* r0 */
+ 1.095597547334830263234433855932375353303e-0002,
+ -1.819734750463320921799187258987098087697e-0004,
+ 9.977001946806131657544212501069893930846e-0007,
+ 1.0, /* s0 */
+ 1.867609810662950169966782360588199673741e-0002,
+ 1.590389206181565490878430827706972074208e-0004,
+ 6.520867386742583632375520147714499522721e-0007,
+ 9.999999999999999942156495584397047660949e-0001, /* r1 */
+ -2.389887722731319130476839836908143731281e-0001,
+ 1.293359476138939027791270393439493640570e-0002,
+ -2.770985642343140122168852400228563364082e-0004,
+ 2.905241575772067678086738389169625218912e-0006,
+ -1.636846356264052597969042009265043251279e-0008,
+ 5.072306160724884775085431059052611737827e-0011,
+ -8.187060730684066824228914775146536139112e-0014,
+ 5.422219326959949863954297860723723423842e-0017,
+ 1.0, /* s1 */
+ 1.101122772686807702762104741932076228349e-0002,
+ 6.140169310641649223411427764669143978228e-0005,
+ 2.292035877515152097976946119293215705250e-0007,
+ 6.356910426504644334558832036362219583789e-0010,
+ 1.366626326900219555045096999553948891401e-0012,
+ 2.280399586866739522891837985560481180088e-0015,
+ 2.801559820648939665270492520004836611187e-0018,
+ 2.073101088320349159764410261466350732968e-0021,
+};
+
+#define r0 Cj0
+#define s0 (Cj0+4)
+#define r1 (Cj0+8)
+#define s1 (Cj0+17)
+
+static const double Cy0[] = {
+ -7.380429510868722526754723020704317641941e-0002, /* u0 */
+ 1.772607102684869924301459663049874294814e-0001,
+ -1.524370666542713828604078090970799356306e-0002,
+ 4.650819100693891757143771557629924591915e-0004,
+ -7.125768872339528975036316108718239946022e-0006,
+ 6.411017001656104598327565004771515257146e-0008,
+ -3.694275157433032553021246812379258781665e-0010,
+ 1.434364544206266624252820889648445263842e-0012,
+ -3.852064731859936455895036286874139896861e-0015,
+ 7.182052899726138381739945881914874579696e-0018,
+ -9.060556574619677567323741194079797987200e-0021,
+ 7.124435467408860515265552217131230511455e-0024,
+ -2.709726774636397615328813121715432044771e-0027,
+ 1.0, /* v0 */
+ 4.678678931512549002587702477349214886475e-0003,
+ 9.486828955529948534822800829497565178985e-0006,
+ 1.001495929158861646659010844136682454906e-0008,
+ 4.725338116256021660204443235685358593611e-0012,
+};
+
+#define u0 Cy0
+#define v0 (Cy0+13)
+
+static const double Cj1y1[] = {
+ -0.4435757816794127857114720794e7, /* pr0 */
+ -0.9942246505077641195658377899e7,
+ -0.6603373248364939109255245434e7,
+ -0.1523529351181137383255105722e7,
+ -0.1098240554345934672737413139e6,
+ -0.1611616644324610116477412898e4,
+ -0.4435757816794127856828016962e7, /* ps0 */
+ -0.9934124389934585658967556309e7,
+ -0.6585339479723087072826915069e7,
+ -0.1511809506634160881644546358e7,
+ -0.1072638599110382011903063867e6,
+ -0.1455009440190496182453565068e4,
+ 0.3322091340985722351859704442e5, /* qr0 */
+ 0.8514516067533570196555001171e5,
+ 0.6617883658127083517939992166e5,
+ 0.1849426287322386679652009819e5,
+ 0.1706375429020768002061283546e4,
+ 0.3526513384663603218592175580e2,
+ 0.7087128194102874357377502472e6, /* qs0 */
+ 0.1819458042243997298924553839e7,
+ 0.1419460669603720892855755253e7,
+ 0.4002944358226697511708610813e6,
+ 0.3789022974577220264142952256e5,
+ 0.8638367769604990967475517183e3,
+};
+
+#define pr0 Cj1y1
+#define ps0 (Cj1y1+6)
+#define qr0 (Cj1y1+12)
+#define qs0 (Cj1y1+18)
+
+static const double Cj1[] = {
+ -6.250000000000002203053200981413218949548e-0002, /* a0 */
+ 1.600998455640072901321605101981501263762e-0003,
+ -1.963888815948313758552511884390162864930e-0005,
+ 8.263917341093549759781339713418201620998e-0008,
+ 1.0e0, /* b0 */
+ 1.605069137643004242395356851797873766927e-0002,
+ 1.149454623251299996428500249509098499383e-0004,
+ 3.849701673735260970379681807910852327825e-0007,
+ 4.999999999999999995517408894340485471724e-0001,
+ -6.003825028120475684835384519945468075423e-0002,
+ 2.301719899263321828388344461995355419832e-0003,
+ -4.208494869238892934859525221654040304068e-0005,
+ 4.377745135188837783031540029700282443388e-0007,
+ -2.854106755678624335145364226735677754179e-0009,
+ 1.234002865443952024332943901323798413689e-0011,
+ -3.645498437039791058951273508838177134310e-0014,
+ 7.404320596071797459925377103787837414422e-0017,
+ -1.009457448277522275262808398517024439084e-0019,
+ 8.520158355824819796968771418801019930585e-0023,
+ -3.458159926081163274483854614601091361424e-0026,
+ 1.0e0, /* b1 */
+ 4.923499437590484879081138588998986303306e-0003,
+ 1.054389489212184156499666953501976688452e-0005,
+ 1.180768373106166527048240364872043816050e-0008,
+ 5.942665743476099355323245707680648588540e-0012,
+};
+
+#define a0 Cj1
+#define b0 (Cj1+4)
+#define a1 (Cj1+8)
+#define b1 (Cj1+20)
+
+static const double Cy1[] = {
+ -1.960570906462389461018983259589655961560e-0001, /* c0 */
+ 4.931824118350661953459180060007970291139e-0002,
+ -1.626975871565393656845930125424683008677e-0003,
+ 1.359657517926394132692884168082224258360e-0005,
+ 1.0e0, /* d0 */
+ 2.565807214838390835108224713630901653793e-0002,
+ 3.374175208978404268650522752520906231508e-0004,
+ 2.840368571306070719539936935220728843177e-0006,
+ 1.396387402048998277638900944415752207592e-0008,
+ -1.960570906462389473336339614647555351626e-0001, /* c1 */
+ 5.336268030335074494231369159933012844735e-0002,
+ -2.684137504382748094149184541866332033280e-0003,
+ 5.737671618979185736981543498580051903060e-0005,
+ -6.642696350686335339171171785557663224892e-0007,
+ 4.692417922568160354012347591960362101664e-0009,
+ -2.161728635907789319335231338621412258355e-0011,
+ 6.727353419738316107197644431844194668702e-0014,
+ -1.427502986803861372125234355906790573422e-0016,
+ 2.020392498726806769468143219616642940371e-0019,
+ -1.761371948595104156753045457888272716340e-0022,
+ 7.352828391941157905175042420249225115816e-0026,
+ 1.0e0, /* d1 */
+ 5.029187436727947764916247076102283399442e-0003,
+ 1.102693095808242775074856548927801750627e-0005,
+ 1.268035774543174837829534603830227216291e-0008,
+ 6.579416271766610825192542295821308730206e-0012,
+};
+
+#define c0 Cy1
+#define d0 (Cy1+4)
+#define c1 (Cy1+9)
+#define d1 (Cy1+21)
+
+
+/* core of j0f computation; assumes fx is finite */
+static double
+__k_j0f(float fx)
+{
+ double x, z, s, c, ss, cc, r, t, p0, q0;
+ int ix, i;
+
+ ix = *(int *)&fx & ~0x80000000;
+ x = fabs((double)fx);
+ if (ix > 0x41000000) {
+ /* x > 8; see comments in j0.c */
+ s = sin(x);
+ c = cos(x);
+ if (signbit(s) != signbit(c)) {
+ ss = s - c;
+ cc = -cos(x + x) / ss;
+ } else {
+ cc = s + c;
+ ss = -cos(x + x) / cc;
+ }
+ if (ix > 0x501502f9) {
+ /* x > 1.0e10 */
+ p0 = one;
+ q0 = neighth / x;
+ } else {
+ t = eight / x;
+ z = t * t;
+ p0 = (pr[0] + z * (pr[1] + z * (pr[2] + z * (pr[3] +
+ z * (pr[4] + z * (pr[5] + z * pr[6])))))) /
+ (ps[0] + z * (ps[1] + z * (ps[2] + z * (ps[3] +
+ z * (ps[4] + z * (ps[5] + z))))));
+ q0 = ((qr[0] + z * (qr[1] + z * (qr[2] + z * (qr[3] +
+ z * (qr[4] + z * (qr[5] + z * qr[6])))))) /
+ (qs[0] + z * (qs[1] + z * (qs[2] + z * (qs[3] +
+ z * (qs[4] + z * (qs[5] + z))))))) * t;
+ }
+ return (isqrtpi * (p0 * cc - q0 * ss) / sqrt(x));
+ }
+ if (ix <= 0x3727c5ac) {
+ /* x <= 1.0e-5 */
+ if (ix <= 0x219392ef) /* x <= 1.0e-18 */
+ return (one - x);
+ return (one - x * x * quarter);
+ }
+ z = x * x;
+ if (ix <= 0x3fa3d70a) {
+ /* x <= 1.28 */
+ r = r0[0] + z * (r0[1] + z * (r0[2] + z * r0[3]));
+ s = s0[0] + z * (s0[1] + z * (s0[2] + z * s0[3]));
+ return (one + z * (r / s));
+ }
+ r = r1[8];
+ s = s1[8];
+ for (i = 7; i >= 0; i--) {
+ r = r * z + r1[i];
+ s = s * z + s1[i];
+ }
+ return (r / s);
+}
+
+float
+j0f(float fx)
+{
+ float f;
+ int ix;
+#if defined(__i386) && !defined(__amd64)
+ int rp;
+#endif
+
+ ix = *(int *)&fx & ~0x80000000;
+ if (ix >= 0x7f800000) { /* nan or inf */
+ if (ix > 0x7f800000)
+ return (fx * fx);
+ return (zerof);
+ }
+
+#if defined(__i386) && !defined(__amd64)
+ rp = __swapRP(fp_extended);
+#endif
+ f = (float)__k_j0f(fx);
+#if defined(__i386) && !defined(__amd64)
+ if (rp != fp_extended)
+ (void) __swapRP(rp);
+#endif
+ return (f);
+}
+
+/* core of y0f computation; assumes fx is finite and positive */
+static double
+__k_y0f(float fx)
+{
+ double x, z, s, c, ss, cc, t, p0, q0, u, v;
+ int ix, i;
+
+ ix = *(int *)&fx;
+ x = (double)fx;
+ if (ix > 0x41000000) {
+ /* x > 8; see comments in j0.c */
+ s = sin(x);
+ c = cos(x);
+ if (signbit(s) != signbit(c)) {
+ ss = s - c;
+ cc = -cos(x + x) / ss;
+ } else {
+ cc = s + c;
+ ss = -cos(x + x) / cc;
+ }
+ if (ix > 0x501502f9) {
+ /* x > 1.0e10 */
+ p0 = one;
+ q0 = neighth / x;
+ } else {
+ t = eight / x;
+ z = t * t;
+ p0 = (pr[0] + z * (pr[1] + z * (pr[2] + z * (pr[3] +
+ z * (pr[4] + z * (pr[5] + z * pr[6])))))) /
+ (ps[0] + z * (ps[1] + z * (ps[2] + z * (ps[3] +
+ z * (ps[4] + z * (ps[5] + z))))));
+ q0 = ((qr[0] + z * (qr[1] + z * (qr[2] + z * (qr[3] +
+ z * (qr[4] + z * (qr[5] + z * qr[6])))))) /
+ (qs[0] + z * (qs[1] + z * (qs[2] + z * (qs[3] +
+ z * (qs[4] + z * (qs[5] + z))))))) * t;
+ }
+ return (isqrtpi * (p0 * ss + q0 * cc) / sqrt(x));
+ }
+ if (ix <= 0x219392ef) /* x <= 1.0e-18 */
+ return (u0[0] + tpi * log(x));
+ z = x * x;
+ u = u0[12];
+ for (i = 11; i >= 0; i--)
+ u = u * z + u0[i];
+ v = v0[0] + z * (v0[1] + z * (v0[2] + z * (v0[3] + z * v0[4])));
+ return (u / v + tpi * (__k_j0f(fx) * log(x)));
+}
+
+float
+y0f(float fx)
+{
+ float f;
+ int ix;
+#if defined(__i386) && !defined(__amd64)
+ int rp;
+#endif
+
+ ix = *(int *)&fx;
+ if ((ix & ~0x80000000) > 0x7f800000) /* nan */
+ return (fx * fx);
+ if (ix <= 0) { /* zero or negative */
+ if ((ix << 1) == 0)
+ return (-onef / zerof);
+ return (zerof / zerof);
+ }
+ if (ix == 0x7f800000) /* +inf */
+ return (zerof);
+
+#if defined(__i386) && !defined(__amd64)
+ rp = __swapRP(fp_extended);
+#endif
+ f = (float)__k_y0f(fx);
+#if defined(__i386) && !defined(__amd64)
+ if (rp != fp_extended)
+ (void) __swapRP(rp);
+#endif
+ return (f);
+}
+
+/* core of j1f computation; assumes fx is finite */
+static double
+__k_j1f(float fx)
+{
+ double x, z, s, c, ss, cc, r, t, p1, q1;
+ int i, ix, sgn;
+
+ ix = *(int *)&fx;
+ sgn = (unsigned)ix >> 31;
+ ix &= ~0x80000000;
+ x = fabs((double)fx);
+ if (ix > 0x41000000) {
+ /* x > 8; see comments in j1.c */
+ s = sin(x);
+ c = cos(x);
+ if (signbit(s) != signbit(c)) {
+ cc = s - c;
+ ss = cos(x + x) / cc;
+ } else {
+ ss = -s - c;
+ cc = cos(x + x) / ss;
+ }
+ if (ix > 0x501502f9) {
+ /* x > 1.0e10 */
+ p1 = one;
+ q1 = three8 / x;
+ } else {
+ t = eight / x;
+ z = t * t;
+ p1 = (pr0[0] + z * (pr0[1] + z * (pr0[2] + z *
+ (pr0[3] + z * (pr0[4] + z * pr0[5]))))) /
+ (ps0[0] + z * (ps0[1] + z * (ps0[2] + z *
+ (ps0[3] + z * (ps0[4] + z * (ps0[5] + z))))));
+ q1 = ((qr0[0] + z * (qr0[1] + z * (qr0[2] + z *
+ (qr0[3] + z * (qr0[4] + z * qr0[5]))))) /
+ (qs0[0] + z * (qs0[1] + z * (qs0[2] + z *
+ (qs0[3] + z * (qs0[4] + z * (qs0[5] + z))))))) * t;
+ }
+ t = isqrtpi * (p1 * cc - q1 * ss) / sqrt(x);
+ return ((sgn)? -t : t);
+ }
+ if (ix <= 0x3727c5ac) {
+ /* x <= 1.0e-5 */
+ if (ix <= 0x219392ef) /* x <= 1.0e-18 */
+ t = half * x;
+ else
+ t = x * (half + neighth * x * x);
+ return ((sgn)? -t : t);
+ }
+ z = x * x;
+ if (ix < 0x3fa3d70a) {
+ /* x < 1.28 */
+ r = a0[0] + z * (a0[1] + z * (a0[2] + z * a0[3]));
+ s = b0[0] + z * (b0[1] + z * (b0[2] + z * b0[3]));
+ t = x * half + x * (z * (r / s));
+ } else {
+ r = a1[11];
+ for (i = 10; i >= 0; i--)
+ r = r * z + a1[i];
+ s = b1[0] + z * (b1[1] + z * (b1[2] + z * (b1[3] + z * b1[4])));
+ t = x * (r / s);
+ }
+ return ((sgn)? -t : t);
+}
+
+float
+j1f(float fx)
+{
+ float f;
+ int ix;
+#if defined(__i386) && !defined(__amd64)
+ int rp;
+#endif
+
+ ix = *(int *)&fx & ~0x80000000;
+ if (ix >= 0x7f800000) /* nan or inf */
+ return (onef / fx);
+
+#if defined(__i386) && !defined(__amd64)
+ rp = __swapRP(fp_extended);
+#endif
+ f = (float)__k_j1f(fx);
+#if defined(__i386) && !defined(__amd64)
+ if (rp != fp_extended)
+ (void) __swapRP(rp);
+#endif
+ return (f);
+}
+
+/* core of y1f computation; assumes fx is finite and positive */
+static double
+__k_y1f(float fx)
+{
+ double x, z, s, c, ss, cc, u, v, p1, q1, t;
+ int i, ix;
+
+ ix = *(int *)&fx;
+ x = (double)fx;
+ if (ix > 0x41000000) {
+ /* x > 8; see comments in j1.c */
+ s = sin(x);
+ c = cos(x);
+ if (signbit(s) != signbit(c)) {
+ cc = s - c;
+ ss = cos(x + x) / cc;
+ } else {
+ ss = -s - c;
+ cc = cos(x + x) / ss;
+ }
+ if (ix > 0x501502f9) {
+ /* x > 1.0e10 */
+ p1 = one;
+ q1 = three8 / x;
+ } else {
+ t = eight / x;
+ z = t * t;
+ p1 = (pr0[0] + z * (pr0[1] + z * (pr0[2] + z *
+ (pr0[3] + z * (pr0[4] + z * pr0[5]))))) /
+ (ps0[0] + z * (ps0[1] + z * (ps0[2] + z *
+ (ps0[3] + z * (ps0[4] + z * (ps0[5] + z))))));
+ q1 = ((qr0[0] + z * (qr0[1] + z * (qr0[2] + z *
+ (qr0[3] + z * (qr0[4] + z * qr0[5]))))) /
+ (qs0[0] + z * (qs0[1] + z * (qs0[2] + z *
+ (qs0[3] + z * (qs0[4] + z * (qs0[5] + z))))))) * t;
+ }
+ return (isqrtpi * (p1 * ss + q1 * cc) / sqrt(x));
+ }
+ if (ix <= 0x219392ef) /* x <= 1.0e-18 */
+ return (-tpi / x);
+ z = x * x;
+ if (ix < 0x3fa3d70a) {
+ /* x < 1.28 */
+ u = c0[0] + z * (c0[1] + z * (c0[2] + z * c0[3]));
+ v = d0[0] + z * (d0[1] + z * (d0[2] + z * (d0[3] + z * d0[4])));
+ } else {
+ u = c1[11];
+ for (i = 10; i >= 0; i--)
+ u = u * z + c1[i];
+ v = d1[0] + z * (d1[1] + z * (d1[2] + z * (d1[3] + z * d1[4])));
+ }
+ return (x * (u / v) + tpi * (__k_j1f(fx) * log(x) - one / x));
+}
+
+float
+y1f(float fx)
+{
+ float f;
+ int ix;
+#if defined(__i386) && !defined(__amd64)
+ int rp;
+#endif
+
+ ix = *(int *)&fx;
+ if ((ix & ~0x80000000) > 0x7f800000) /* nan */
+ return (fx * fx);
+ if (ix <= 0) { /* zero or negative */
+ if ((ix << 1) == 0)
+ return (-onef / zerof);
+ return (zerof / zerof);
+ }
+ if (ix == 0x7f800000) /* +inf */
+ return (zerof);
+
+#if defined(__i386) && !defined(__amd64)
+ rp = __swapRP(fp_extended);
+#endif
+ f = (float)__k_y1f(fx);
+#if defined(__i386) && !defined(__amd64)
+ if (rp != fp_extended)
+ (void) __swapRP(rp);
+#endif
+ return (f);
+}
+
+float
+jnf(int n, float fx)
+{
+ double a, b, temp, x, z, w, t, q0, q1, h;
+ float f;
+ int i, ix, sgn, m, k;
+#if defined(__i386) && !defined(__amd64)
+ int rp;
+#endif
+
+ if (n < 0) {
+ n = -n;
+ fx = -fx;
+ }
+ if (n == 0)
+ return (j0f(fx));
+ if (n == 1)
+ return (j1f(fx));
+
+ ix = *(int *)&fx;
+ sgn = (n & 1)? ((unsigned)ix >> 31) : 0;
+ ix &= ~0x80000000;
+ if (ix >= 0x7f800000) { /* nan or inf */
+ if (ix > 0x7f800000)
+ return (fx * fx);
+ return ((sgn)? -zerof : zerof);
+ }
+ if ((ix << 1) == 0)
+ return ((sgn)? -zerof : zerof);
+
+#if defined(__i386) && !defined(__amd64)
+ rp = __swapRP(fp_extended);
+#endif
+ fx = fabsf(fx);
+ x = (double)fx;
+ if ((double)n <= x) {
+ /* safe to use J(n+1,x) = 2n/x * J(n,x) - J(n-1,x) */
+ a = __k_j0f(fx);
+ b = __k_j1f(fx);
+ for (i = 1; i < n; i++) {
+ temp = b;
+ b = b * ((double)(i + i) / x) - a;
+ a = temp;
+ }
+ f = (float)b;
+#if defined(__i386) && !defined(__amd64)
+ if (rp != fp_extended)
+ (void) __swapRP(rp);
+#endif
+ return ((sgn)? -f : f);
+ }
+ if (ix < 0x3089705f) {
+ /* x < 1.0e-9; use J(n,x) = 1/n! * (x / 2)^n */
+ if (n > 6)
+ n = 6; /* result underflows to zero for n >= 6 */
+ b = t = half * x;
+ a = one;
+ for (i = 2; i <= n; i++) {
+ b *= t;
+ a *= (double)i;
+ }
+ b /= a;
+ } else {
+ /*
+ * Use the backward recurrence:
+ *
+ * x x^2 x^2
+ * J(n,x)/J(n-1,x) = ---- - ------ - ------ .....
+ * 2n 2(n+1) 2(n+2)
+ *
+ * Let w = 2n/x and h = 2/x. Then the above quotient
+ * is equal to the continued fraction:
+ * 1
+ * = -----------------------
+ * 1
+ * w - -----------------
+ * 1
+ * w+h - ---------
+ * w+2h - ...
+ *
+ * To determine how many terms are needed, run the
+ * recurrence
+ *
+ * Q(0) = w,
+ * Q(1) = w(w+h) - 1,
+ * Q(k) = (w+k*h)*Q(k-1) - Q(k-2).
+ *
+ * Then when Q(k) > 1e4, k is large enough for single
+ * precision.
+ */
+/* XXX NOT DONE - rework this */
+ w = (n + n) / x;
+ h = two / x;
+ q0 = w;
+ z = w + h;
+ q1 = w * z - one;
+ k = 1;
+ while (q1 < big) {
+ k++;
+ z += h;
+ temp = z * q1 - q0;
+ q0 = q1;
+ q1 = temp;
+ }
+ m = n + n;
+ t = zero;
+ for (i = (n + k) << 1; i >= m; i -= 2)
+ t = one / ((double)i / x - t);
+ a = t;
+ b = one;
+ /*
+ * estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
+ * hence, if n*(log(2n/x)) > ...
+ * single 8.8722839355e+01
+ * double 7.09782712893383973096e+02
+ * then recurrent value may overflow and the result is
+ * likely underflow to zero
+ */
+ temp = (double)n;
+ temp *= log((two / x) * temp);
+ if (temp < 7.09782712893383973096e+02) {
+ for (i = n - 1; i > 0; i--) {
+ temp = b;
+ b = b * ((double)(i + i) / x) - a;
+ a = temp;
+ }
+ } else {
+ for (i = n - 1; i > 0; i--) {
+ temp = b;
+ b = b * ((double)(i + i) / x) - a;
+ a = temp;
+ if (b > 1.0e100) {
+ a /= b;
+ t /= b;
+ b = one;
+ }
+ }
+ }
+ b = (t * __k_j0f(fx) / b);
+ }
+ f = (float)b;
+#if defined(__i386) && !defined(__amd64)
+ if (rp != fp_extended)
+ (void) __swapRP(rp);
+#endif
+ return ((sgn)? -f : f);
+}
+
+float
+ynf(int n, float fx)
+{
+ double a, b, temp, x;
+ float f;
+ int i, sign, ix;
+#if defined(__i386) && !defined(__amd64)
+ int rp;
+#endif
+
+ sign = 0;
+ if (n < 0) {
+ n = -n;
+ if (n & 1)
+ sign = 1;
+ }
+ if (n == 0)
+ return (y0f(fx));
+ if (n == 1)
+ return ((sign)? -y1f(fx) : y1f(fx));
+
+ ix = *(int *)&fx;
+ if ((ix & ~0x80000000) > 0x7f800000) /* nan */
+ return (fx * fx);
+ if (ix <= 0) { /* zero or negative */
+ if ((ix << 1) == 0)
+ return (-onef / zerof);
+ return (zerof / zerof);
+ }
+ if (ix == 0x7f800000) /* +inf */
+ return (zerof);
+
+#if defined(__i386) && !defined(__amd64)
+ rp = __swapRP(fp_extended);
+#endif
+ a = __k_y0f(fx);
+ b = __k_y1f(fx);
+ x = (double)fx;
+ for (i = 1; i < n; i++) {
+ temp = b;
+ b *= (double)(i + i) / x;
+ if (b <= -DBL_MAX)
+ break;
+ b -= a;
+ a = temp;
+ }
+ f = (float)b;
+#if defined(__i386) && !defined(__amd64)
+ if (rp != fp_extended)
+ (void) __swapRP(rp);
+#endif
+ return ((sign)? -f : f);
+}
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