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tools/tcp_stream: Set message size on both send and receive sides
[dragonfly.git] / contrib / openbsd_libm / src / e_j0f.c
blob8e323ba797f19a0cf4fcbe3baf74314bce204b0a
1 /* e_j0f.c -- float version of e_j0.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 */
4
5 /*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16 #include "math.h"
17 #include "math_private.h"
18
19 static float pzerof(float), qzerof(float);
20
21 static const float
22 huge = 1e30,
23 one = 1.0,
24 invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
25 tpi = 6.3661974669e-01, /* 0x3f22f983 */
26 /* R0/S0 on [0, 2.00] */
27 R02 = 1.5625000000e-02, /* 0x3c800000 */
28 R03 = -1.8997929874e-04, /* 0xb947352e */
29 R04 = 1.8295404516e-06, /* 0x35f58e88 */
30 R05 = -4.6183270541e-09, /* 0xb19eaf3c */
31 S01 = 1.5619102865e-02, /* 0x3c7fe744 */
32 S02 = 1.1692678527e-04, /* 0x38f53697 */
33 S03 = 5.1354652442e-07, /* 0x3509daa6 */
34 S04 = 1.1661400734e-09; /* 0x30a045e8 */
35
36 static const float zero = 0.0;
37
38 float
39 j0f(float x)
40 {
41 float z, s,c,ss,cc,r,u,v;
42 int32_t hx,ix;
43
44 GET_FLOAT_WORD(hx,x);
45 ix = hx&0x7fffffff;
46 if(ix>=0x7f800000) return one/(x*x);
47 x = fabsf(x);
48 if(ix >= 0x40000000) { /* |x| >= 2.0 */
49 s = sinf(x);
50 c = cosf(x);
51 ss = s-c;
52 cc = s+c;
53 if(ix<0x7f000000) { /* make sure x+x not overflow */
54 z = -cosf(x+x);
55 if ((s*c)<zero) cc = z/ss;
56 else ss = z/cc;
57 }
58 /*
59 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
60 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
61 */
62 if((u_int32_t)ix>0x80000000U) z = (invsqrtpi*cc)/sqrtf(x);
63 else {
64 u = pzerof(x); v = qzerof(x);
65 z = invsqrtpi*(u*cc-v*ss)/sqrtf(x);
66 }
67 return z;
68 }
69 if(ix<0x39000000) { /* |x| < 2**-13 */
70 if(huge+x>one) { /* raise inexact if x != 0 */
71 if(ix<0x32000000) return one; /* |x|<2**-27 */
72 else return one - (float)0.25*x*x;
73 }
74 }
75 z = x*x;
76 r = z*(R02+z*(R03+z*(R04+z*R05)));
77 s = one+z*(S01+z*(S02+z*(S03+z*S04)));
78 if(ix < 0x3F800000) { /* |x| < 1.00 */
79 return one + z*((float)-0.25+(r/s));
80 } else {
81 u = (float)0.5*x;
82 return((one+u)*(one-u)+z*(r/s));
83 }
84 }
85
86 static const float
87 u00 = -7.3804296553e-02, /* 0xbd9726b5 */
88 u01 = 1.7666645348e-01, /* 0x3e34e80d */
89 u02 = -1.3818567619e-02, /* 0xbc626746 */
90 u03 = 3.4745343146e-04, /* 0x39b62a69 */
91 u04 = -3.8140706238e-06, /* 0xb67ff53c */
92 u05 = 1.9559013964e-08, /* 0x32a802ba */
93 u06 = -3.9820518410e-11, /* 0xae2f21eb */
94 v01 = 1.2730483897e-02, /* 0x3c509385 */
95 v02 = 7.6006865129e-05, /* 0x389f65e0 */
96 v03 = 2.5915085189e-07, /* 0x348b216c */
97 v04 = 4.4111031494e-10; /* 0x2ff280c2 */
98
99 float
100 y0f(float x)
101 {
102 float z, s,c,ss,cc,u,v;
103 int32_t hx,ix;
104
105 GET_FLOAT_WORD(hx,x);
106 ix = 0x7fffffff&hx;
107 /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
108 if(ix>=0x7f800000) return one/(x+x*x);
109 if(ix==0) return -one/zero;
110 if(hx<0) return zero/zero;
111 if(ix >= 0x40000000) { /* |x| >= 2.0 */
112 /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
113 * where x0 = x-pi/4
114 * Better formula:
115 * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
116 * = 1/sqrt(2) * (sin(x) + cos(x))
117 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
118 * = 1/sqrt(2) * (sin(x) - cos(x))
119 * To avoid cancellation, use
120 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
121 * to compute the worse one.
122 */
123 s = sinf(x);
124 c = cosf(x);
125 ss = s-c;
126 cc = s+c;
127 /*
128 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
129 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
130 */
131 if(ix<0x7f000000) { /* make sure x+x not overflow */
132 z = -cosf(x+x);
133 if ((s*c)<zero) cc = z/ss;
134 else ss = z/cc;
135 }
136 if((u_int32_t)ix>0x80000000U) z = (invsqrtpi*ss)/sqrtf(x);
137 else {
138 u = pzerof(x); v = qzerof(x);
139 z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
140 }
141 return z;
142 }
143 if(ix<=0x32000000) { /* x < 2**-27 */
144 return(u00 + tpi*logf(x));
145 }
146 z = x*x;
147 u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
148 v = one+z*(v01+z*(v02+z*(v03+z*v04)));
149 return(u/v + tpi*(j0f(x)*logf(x)));
150 }
151
152 /* The asymptotic expansions of pzero is
153 * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
154 * For x >= 2, We approximate pzero by
155 * pzero(x) = 1 + (R/S)
156 * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
157 * S = 1 + pS0*s^2 + ... + pS4*s^10
158 * and
159 * | pzero(x)-1-R/S | <= 2 ** ( -60.26)
160 */
161 static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
162 0.0000000000e+00, /* 0x00000000 */
163 -7.0312500000e-02, /* 0xbd900000 */
164 -8.0816707611e+00, /* 0xc1014e86 */
165 -2.5706311035e+02, /* 0xc3808814 */
166 -2.4852163086e+03, /* 0xc51b5376 */
167 -5.2530439453e+03, /* 0xc5a4285a */
168 };
169 static const float pS8[5] = {
170 1.1653436279e+02, /* 0x42e91198 */
171 3.8337448730e+03, /* 0x456f9beb */
172 4.0597855469e+04, /* 0x471e95db */
173 1.1675296875e+05, /* 0x47e4087c */
174 4.7627726562e+04, /* 0x473a0bba */
175 };
176 static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
177 -1.1412546255e-11, /* 0xad48c58a */
178 -7.0312492549e-02, /* 0xbd8fffff */
179 -4.1596107483e+00, /* 0xc0851b88 */
180 -6.7674766541e+01, /* 0xc287597b */
181 -3.3123129272e+02, /* 0xc3a59d9b */
182 -3.4643338013e+02, /* 0xc3ad3779 */
183 };
184 static const float pS5[5] = {
185 6.0753936768e+01, /* 0x42730408 */
186 1.0512523193e+03, /* 0x44836813 */
187 5.9789707031e+03, /* 0x45bad7c4 */
188 9.6254453125e+03, /* 0x461665c8 */
189 2.4060581055e+03, /* 0x451660ee */
190 };
191
192 static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
193 -2.5470459075e-09, /* 0xb12f081b */
194 -7.0311963558e-02, /* 0xbd8fffb8 */
195 -2.4090321064e+00, /* 0xc01a2d95 */
196 -2.1965976715e+01, /* 0xc1afba52 */
197 -5.8079170227e+01, /* 0xc2685112 */
198 -3.1447946548e+01, /* 0xc1fb9565 */
199 };
200 static const float pS3[5] = {
201 3.5856033325e+01, /* 0x420f6c94 */
202 3.6151397705e+02, /* 0x43b4c1ca */
203 1.1936077881e+03, /* 0x44953373 */
204 1.1279968262e+03, /* 0x448cffe6 */
205 1.7358093262e+02, /* 0x432d94b8 */
206 };
207
208 static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
209 -8.8753431271e-08, /* 0xb3be98b7 */
210 -7.0303097367e-02, /* 0xbd8ffb12 */
211 -1.4507384300e+00, /* 0xbfb9b1cc */
212 -7.6356959343e+00, /* 0xc0f4579f */
213 -1.1193166733e+01, /* 0xc1331736 */
214 -3.2336456776e+00, /* 0xc04ef40d */
215 };
216 static const float pS2[5] = {
217 2.2220300674e+01, /* 0x41b1c32d */
218 1.3620678711e+02, /* 0x430834f0 */
219 2.7047027588e+02, /* 0x43873c32 */
220 1.5387539673e+02, /* 0x4319e01a */
221 1.4657617569e+01, /* 0x416a859a */
222 };
223
224 static float
225 pzerof(float x)
226 {
227 const float *p,*q;
228 float z,r,s;
229 int32_t ix;
230 GET_FLOAT_WORD(ix,x);
231 ix &= 0x7fffffff;
232 if(ix>=0x41000000) {p = pR8; q= pS8;}
233 else if(ix>=0x40f71c58){p = pR5; q= pS5;}
234 else if(ix>=0x4036db68){p = pR3; q= pS3;}
235 else /*if(ix>=0x40000000)*/ {p = pR2; q= pS2;}
236 z = one/(x*x);
237 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
238 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
239 return one+ r/s;
240 }
241
242
243 /* For x >= 8, the asymptotic expansions of qzero is
244 * -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
245 * We approximate pzero by
246 * qzero(x) = s*(-1.25 + (R/S))
247 * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
248 * S = 1 + qS0*s^2 + ... + qS5*s^12
249 * and
250 * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
251 */
252 static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
253 0.0000000000e+00, /* 0x00000000 */
254 7.3242187500e-02, /* 0x3d960000 */
255 1.1768206596e+01, /* 0x413c4a93 */
256 5.5767340088e+02, /* 0x440b6b19 */
257 8.8591972656e+03, /* 0x460a6cca */
258 3.7014625000e+04, /* 0x471096a0 */
259 };
260 static const float qS8[6] = {
261 1.6377603149e+02, /* 0x4323c6aa */
262 8.0983447266e+03, /* 0x45fd12c2 */
263 1.4253829688e+05, /* 0x480b3293 */
264 8.0330925000e+05, /* 0x49441ed4 */
265 8.4050156250e+05, /* 0x494d3359 */
266 -3.4389928125e+05, /* 0xc8a7eb69 */
267 };
268
269 static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
270 1.8408595828e-11, /* 0x2da1ec79 */
271 7.3242180049e-02, /* 0x3d95ffff */
272 5.8356351852e+00, /* 0x40babd86 */
273 1.3511157227e+02, /* 0x43071c90 */
274 1.0272437744e+03, /* 0x448067cd */
275 1.9899779053e+03, /* 0x44f8bf4b */
276 };
277 static const float qS5[6] = {
278 8.2776611328e+01, /* 0x42a58da0 */
279 2.0778142090e+03, /* 0x4501dd07 */
280 1.8847289062e+04, /* 0x46933e94 */
281 5.6751113281e+04, /* 0x475daf1d */
282 3.5976753906e+04, /* 0x470c88c1 */
283 -5.3543427734e+03, /* 0xc5a752be */
284 };
285
286 static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
287 4.3774099900e-09, /* 0x3196681b */
288 7.3241114616e-02, /* 0x3d95ff70 */
289 3.3442313671e+00, /* 0x405607e3 */
290 4.2621845245e+01, /* 0x422a7cc5 */
291 1.7080809021e+02, /* 0x432acedf */
292 1.6673394775e+02, /* 0x4326bbe4 */
293 };
294 static const float qS3[6] = {
295 4.8758872986e+01, /* 0x42430916 */
296 7.0968920898e+02, /* 0x44316c1c */
297 3.7041481934e+03, /* 0x4567825f */
298 6.4604252930e+03, /* 0x45c9e367 */
299 2.5163337402e+03, /* 0x451d4557 */
300 -1.4924745178e+02, /* 0xc3153f59 */
301 };
302
303 static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
304 1.5044444979e-07, /* 0x342189db */
305 7.3223426938e-02, /* 0x3d95f62a */
306 1.9981917143e+00, /* 0x3fffc4bf */
307 1.4495602608e+01, /* 0x4167edfd */
308 3.1666231155e+01, /* 0x41fd5471 */
309 1.6252708435e+01, /* 0x4182058c */
310 };
311 static const float qS2[6] = {
312 3.0365585327e+01, /* 0x41f2ecb8 */
313 2.6934811401e+02, /* 0x4386ac8f */
314 8.4478375244e+02, /* 0x44533229 */
315 8.8293585205e+02, /* 0x445cbbe5 */
316 2.1266638184e+02, /* 0x4354aa98 */
317 -5.3109550476e+00, /* 0xc0a9f358 */
318 };
319
320 static float
321 qzerof(float x)
322 {
323 const float *p,*q;
324 float s,r,z;
325 int32_t ix;
326 GET_FLOAT_WORD(ix,x);
327 ix &= 0x7fffffff;
328 if(ix>=0x41000000) {p = qR8; q= qS8;}
329 else if(ix>=0x40f71c58){p = qR5; q= qS5;}
330 else if(ix>=0x4036db68){p = qR3; q= qS3;}
331 else /*if(ix>=0x40000000)*/ {p = qR2; q= qS2;}
332 z = one/(x*x);
333 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
334 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
335 return (-(float).125 + r/s)/x;
336 }
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