ipiq: Add simple IPI latency measure sysctls (2)
[dragonfly.git] / lib / libm / src / e_j1f.c
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1/* e_j1f.c -- float version of e_j1.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 *
6ff43c94 15 * $FreeBSD: head/lib/msun/src/e_j1f.c 176451 2008-02-22 02:30:36Z das $
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16 */
17
6ff43c94 18#include "math.h"
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19#include "math_private.h"
20
21static float ponef(float), qonef(float);
22
23static const float
24huge = 1e30,
25one = 1.0,
26invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
27tpi = 6.3661974669e-01, /* 0x3f22f983 */
28 /* R0/S0 on [0,2] */
29r00 = -6.2500000000e-02, /* 0xbd800000 */
30r01 = 1.4070566976e-03, /* 0x3ab86cfd */
31r02 = -1.5995563444e-05, /* 0xb7862e36 */
32r03 = 4.9672799207e-08, /* 0x335557d2 */
33s01 = 1.9153760746e-02, /* 0x3c9ce859 */
34s02 = 1.8594678841e-04, /* 0x3942fab6 */
35s03 = 1.1771846857e-06, /* 0x359dffc2 */
36s04 = 5.0463624390e-09, /* 0x31ad6446 */
37s05 = 1.2354227016e-11; /* 0x2d59567e */
38
39static const float zero = 0.0;
40
41float
6ff43c94 42__ieee754_j1f(float x)
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43{
44 float z, s,c,ss,cc,r,u,v,y;
45 int32_t hx,ix;
46
47 GET_FLOAT_WORD(hx,x);
48 ix = hx&0x7fffffff;
49 if(ix>=0x7f800000) return one/x;
50 y = fabsf(x);
51 if(ix >= 0x40000000) { /* |x| >= 2.0 */
52 s = sinf(y);
53 c = cosf(y);
54 ss = -s-c;
55 cc = s-c;
56 if(ix<0x7f000000) { /* make sure y+y not overflow */
57 z = cosf(y+y);
58 if ((s*c)>zero) cc = z/ss;
59 else ss = z/cc;
60 }
61 /*
62 * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
63 * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
64 */
65 if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(y);
6ff43c94 66 else {
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67 u = ponef(y); v = qonef(y);
68 z = invsqrtpi*(u*cc-v*ss)/sqrtf(y);
69 }
70 if(hx<0) return -z;
71 else return z;
72 }
73 if(ix<0x32000000) { /* |x|<2**-27 */
74 if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */
75 }
76 z = x*x;
77 r = z*(r00+z*(r01+z*(r02+z*r03)));
78 s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
79 r *= x;
80 return(x*(float)0.5+r/s);
81}
82
83static const float U0[5] = {
84 -1.9605709612e-01, /* 0xbe48c331 */
85 5.0443872809e-02, /* 0x3d4e9e3c */
86 -1.9125689287e-03, /* 0xbafaaf2a */
87 2.3525259166e-05, /* 0x37c5581c */
88 -9.1909917899e-08, /* 0xb3c56003 */
89};
90static const float V0[5] = {
91 1.9916731864e-02, /* 0x3ca3286a */
92 2.0255257550e-04, /* 0x3954644b */
93 1.3560879779e-06, /* 0x35b602d4 */
94 6.2274145840e-09, /* 0x31d5f8eb */
95 1.6655924903e-11, /* 0x2d9281cf */
96};
97
98float
6ff43c94 99__ieee754_y1f(float x)
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100{
101 float z, s,c,ss,cc,u,v;
102 int32_t hx,ix;
103
104 GET_FLOAT_WORD(hx,x);
105 ix = 0x7fffffff&hx;
106 /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
107 if(ix>=0x7f800000) return one/(x+x*x);
108 if(ix==0) return -one/zero;
109 if(hx<0) return zero/zero;
110 if(ix >= 0x40000000) { /* |x| >= 2.0 */
111 s = sinf(x);
112 c = cosf(x);
113 ss = -s-c;
114 cc = s-c;
115 if(ix<0x7f000000) { /* make sure x+x not overflow */
116 z = cosf(x+x);
117 if ((s*c)>zero) cc = z/ss;
118 else ss = z/cc;
119 }
120 /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
121 * where x0 = x-3pi/4
122 * Better formula:
123 * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
124 * = 1/sqrt(2) * (sin(x) - cos(x))
125 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
126 * = -1/sqrt(2) * (cos(x) + sin(x))
127 * To avoid cancellation, use
128 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
129 * to compute the worse one.
130 */
131 if(ix>0x48000000) z = (invsqrtpi*ss)/sqrtf(x);
132 else {
133 u = ponef(x); v = qonef(x);
134 z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
135 }
136 return z;
137 }
138 if(ix<=0x24800000) { /* x < 2**-54 */
139 return(-tpi/x);
140 }
141 z = x*x;
142 u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
143 v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
6ff43c94 144 return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(x)-one/x));
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145}
146
147/* For x >= 8, the asymptotic expansions of pone is
148 * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
149 * We approximate pone by
150 * pone(x) = 1 + (R/S)
151 * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
152 * S = 1 + ps0*s^2 + ... + ps4*s^10
153 * and
154 * | pone(x)-1-R/S | <= 2 ** ( -60.06)
155 */
156
157static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
158 0.0000000000e+00, /* 0x00000000 */
159 1.1718750000e-01, /* 0x3df00000 */
160 1.3239480972e+01, /* 0x4153d4ea */
161 4.1205184937e+02, /* 0x43ce06a3 */
162 3.8747453613e+03, /* 0x45722bed */
163 7.9144794922e+03, /* 0x45f753d6 */
164};
165static const float ps8[5] = {
166 1.1420736694e+02, /* 0x42e46a2c */
167 3.6509309082e+03, /* 0x45642ee5 */
168 3.6956207031e+04, /* 0x47105c35 */
169 9.7602796875e+04, /* 0x47bea166 */
170 3.0804271484e+04, /* 0x46f0a88b */
171};
172
173static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
174 1.3199052094e-11, /* 0x2d68333f */
175 1.1718749255e-01, /* 0x3defffff */
176 6.8027510643e+00, /* 0x40d9b023 */
177 1.0830818176e+02, /* 0x42d89dca */
178 5.1763616943e+02, /* 0x440168b7 */
179 5.2871520996e+02, /* 0x44042dc6 */
180};
181static const float ps5[5] = {
182 5.9280597687e+01, /* 0x426d1f55 */
183 9.9140142822e+02, /* 0x4477d9b1 */
184 5.3532670898e+03, /* 0x45a74a23 */
185 7.8446904297e+03, /* 0x45f52586 */
186 1.5040468750e+03, /* 0x44bc0180 */
187};
188
189static const float pr3[6] = {
190 3.0250391081e-09, /* 0x314fe10d */
191 1.1718686670e-01, /* 0x3defffab */
192 3.9329774380e+00, /* 0x407bb5e7 */
193 3.5119403839e+01, /* 0x420c7a45 */
194 9.1055007935e+01, /* 0x42b61c2a */
195 4.8559066772e+01, /* 0x42423c7c */
196};
197static const float ps3[5] = {
198 3.4791309357e+01, /* 0x420b2a4d */
199 3.3676245117e+02, /* 0x43a86198 */
200 1.0468714600e+03, /* 0x4482dbe3 */
201 8.9081134033e+02, /* 0x445eb3ed */
202 1.0378793335e+02, /* 0x42cf936c */
203};
204
205static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
206 1.0771083225e-07, /* 0x33e74ea8 */
207 1.1717621982e-01, /* 0x3deffa16 */
208 2.3685150146e+00, /* 0x401795c0 */
209 1.2242610931e+01, /* 0x4143e1bc */
210 1.7693971634e+01, /* 0x418d8d41 */
211 5.0735230446e+00, /* 0x40a25a4d */
212};
213static const float ps2[5] = {
214 2.1436485291e+01, /* 0x41ab7dec */
215 1.2529022980e+02, /* 0x42fa9499 */
216 2.3227647400e+02, /* 0x436846c7 */
217 1.1767937469e+02, /* 0x42eb5bd7 */
218 8.3646392822e+00, /* 0x4105d590 */
219};
220
6ff43c94 221 static float ponef(float x)
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222{
223 const float *p,*q;
224 float z,r,s;
225 int32_t ix;
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226 GET_FLOAT_WORD(ix,x);
227 ix &= 0x7fffffff;
228 if(ix>=0x41000000) {p = pr8; q= ps8;}
229 else if(ix>=0x40f71c58){p = pr5; q= ps5;}
230 else if(ix>=0x4036db68){p = pr3; q= ps3;}
231 else if(ix>=0x40000000){p = pr2; q= ps2;}
232 z = one/(x*x);
233 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
234 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
235 return one+ r/s;
236}
237
238
239/* For x >= 8, the asymptotic expansions of qone is
240 * 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
241 * We approximate pone by
242 * qone(x) = s*(0.375 + (R/S))
243 * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
244 * S = 1 + qs1*s^2 + ... + qs6*s^12
245 * and
246 * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
247 */
248
249static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
250 0.0000000000e+00, /* 0x00000000 */
251 -1.0253906250e-01, /* 0xbdd20000 */
252 -1.6271753311e+01, /* 0xc1822c8d */
253 -7.5960174561e+02, /* 0xc43de683 */
254 -1.1849806641e+04, /* 0xc639273a */
255 -4.8438511719e+04, /* 0xc73d3683 */
256};
257static const float qs8[6] = {
258 1.6139537048e+02, /* 0x43216537 */
259 7.8253862305e+03, /* 0x45f48b17 */
260 1.3387534375e+05, /* 0x4802bcd6 */
261 7.1965775000e+05, /* 0x492fb29c */
262 6.6660125000e+05, /* 0x4922be94 */
263 -2.9449025000e+05, /* 0xc88fcb48 */
264};
265
266static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
267 -2.0897993405e-11, /* 0xadb7d219 */
268 -1.0253904760e-01, /* 0xbdd1fffe */
269 -8.0564479828e+00, /* 0xc100e736 */
270 -1.8366960144e+02, /* 0xc337ab6b */
271 -1.3731937256e+03, /* 0xc4aba633 */
272 -2.6124443359e+03, /* 0xc523471c */
273};
274static const float qs5[6] = {
275 8.1276550293e+01, /* 0x42a28d98 */
276 1.9917987061e+03, /* 0x44f8f98f */
277 1.7468484375e+04, /* 0x468878f8 */
278 4.9851425781e+04, /* 0x4742bb6d */
279 2.7948074219e+04, /* 0x46da5826 */
280 -4.7191835938e+03, /* 0xc5937978 */
281};
282
6ff43c94 283static const float qr3[6] = {
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284 -5.0783124372e-09, /* 0xb1ae7d4f */
285 -1.0253783315e-01, /* 0xbdd1ff5b */
286 -4.6101160049e+00, /* 0xc0938612 */
287 -5.7847221375e+01, /* 0xc267638e */
288 -2.2824453735e+02, /* 0xc3643e9a */
289 -2.1921012878e+02, /* 0xc35b35cb */
290};
291static const float qs3[6] = {
292 4.7665153503e+01, /* 0x423ea91e */
293 6.7386511230e+02, /* 0x4428775e */
294 3.3801528320e+03, /* 0x45534272 */
295 5.5477290039e+03, /* 0x45ad5dd5 */
296 1.9031191406e+03, /* 0x44ede3d0 */
297 -1.3520118713e+02, /* 0xc3073381 */
298};
299
300static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
301 -1.7838172539e-07, /* 0xb43f8932 */
302 -1.0251704603e-01, /* 0xbdd1f475 */
303 -2.7522056103e+00, /* 0xc0302423 */
304 -1.9663616180e+01, /* 0xc19d4f16 */
305 -4.2325313568e+01, /* 0xc2294d1f */
306 -2.1371921539e+01, /* 0xc1aaf9b2 */
307};
308static const float qs2[6] = {
309 2.9533363342e+01, /* 0x41ec4454 */
310 2.5298155212e+02, /* 0x437cfb47 */
311 7.5750280762e+02, /* 0x443d602e */
312 7.3939318848e+02, /* 0x4438d92a */
313 1.5594900513e+02, /* 0x431bf2f2 */
314 -4.9594988823e+00, /* 0xc09eb437 */
315};
316
6ff43c94 317 static float qonef(float x)
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318{
319 const float *p,*q;
320 float s,r,z;
321 int32_t ix;
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322 GET_FLOAT_WORD(ix,x);
323 ix &= 0x7fffffff;
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324 if(ix>=0x40200000) {p = qr8; q= qs8;}
325 else if(ix>=0x40f71c58){p = qr5; q= qs5;}
326 else if(ix>=0x4036db68){p = qr3; q= qs3;}
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327 else if(ix>=0x40000000){p = qr2; q= qs2;}
328 z = one/(x*x);
329 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
330 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
331 return ((float).375 + r/s)/x;
332}