ReactOS 0.4.15-dev-8146-gdc0ed6d
sinh.c File Reference
#include "libm.h"
#include "libm_util.h"
#include "libm_inlines.h"
#include "libm_errno.h"
Include dependency graph for sinh.c:

Go to the source code of this file.

Macros

#define USE_SPLITEXP
 
#define USE_SCALEDOUBLE_1
 
#define USE_SCALEDOUBLE_2
 
#define USE_INFINITY_WITH_FLAGS
 
#define USE_VAL_WITH_FLAGS
 
#define USE_HANDLE_ERROR
 

Functions

double sinh (double x)
 

Macro Definition Documentation

◆ USE_HANDLE_ERROR

#define USE_HANDLE_ERROR

Definition at line 35 of file sinh.c.

◆ USE_INFINITY_WITH_FLAGS

#define USE_INFINITY_WITH_FLAGS

Definition at line 33 of file sinh.c.

◆ USE_SCALEDOUBLE_1

#define USE_SCALEDOUBLE_1

Definition at line 31 of file sinh.c.

◆ USE_SCALEDOUBLE_2

#define USE_SCALEDOUBLE_2

Definition at line 32 of file sinh.c.

◆ USE_SPLITEXP

#define USE_SPLITEXP

Definition at line 30 of file sinh.c.

◆ USE_VAL_WITH_FLAGS

#define USE_VAL_WITH_FLAGS

Definition at line 34 of file sinh.c.

Function Documentation

◆ sinh()

double sinh ( double  x)

Definition at line 50 of file sinh.c.

51{
52 /*
53 After dealing with special cases the computation is split into
54 regions as follows:
55
56 abs(x) >= max_sinh_arg:
57 sinh(x) = sign(x)*Inf
58
59 abs(x) >= small_threshold:
60 sinh(x) = sign(x)*exp(abs(x))/2 computed using the
61 splitexp and scaleDouble functions as for exp_amd().
62
63 abs(x) < small_threshold:
64 compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0)))
65 sinh(x) is then sign(x)*z. */
66
67 static const double
68 max_sinh_arg = 7.10475860073943977113e+02, /* 0x408633ce8fb9f87e */
69 thirtytwo_by_log2 = 4.61662413084468283841e+01, /* 0x40471547652b82fe */
70 log2_by_32_lead = 2.16608493356034159660e-02, /* 0x3f962e42fe000000 */
71 log2_by_32_tail = 5.68948749532545630390e-11, /* 0x3dcf473de6af278e */
72 small_threshold = 8*BASEDIGITS_DP64*0.30102999566398119521373889;
73 /* (8*BASEDIGITS_DP64*log10of2) ' exp(-x) insignificant c.f. exp(x) */
74
75 /* Lead and tail tabulated values of sinh(i) and cosh(i)
76 for i = 0,...,36. The lead part has 26 leading bits. */
77
78 static const double sinh_lead[37] = {
79 0.00000000000000000000e+00, /* 0x0000000000000000 */
80 1.17520117759704589844e+00, /* 0x3ff2cd9fc0000000 */
81 3.62686038017272949219e+00, /* 0x400d03cf60000000 */
82 1.00178747177124023438e+01, /* 0x40240926e0000000 */
83 2.72899169921875000000e+01, /* 0x403b4a3800000000 */
84 7.42032089233398437500e+01, /* 0x40528d0160000000 */
85 2.01713153839111328125e+02, /* 0x406936d228000000 */
86 5.48316116333007812500e+02, /* 0x4081228768000000 */
87 1.49047882080078125000e+03, /* 0x409749ea50000000 */
88 4.05154187011718750000e+03, /* 0x40afa71570000000 */
89 1.10132326660156250000e+04, /* 0x40c5829dc8000000 */
90 2.99370708007812500000e+04, /* 0x40dd3c4488000000 */
91 8.13773945312500000000e+04, /* 0x40f3de1650000000 */
92 2.21206695312500000000e+05, /* 0x410b00b590000000 */
93 6.01302140625000000000e+05, /* 0x412259ac48000000 */
94 1.63450865625000000000e+06, /* 0x4138f0cca8000000 */
95 4.44305525000000000000e+06, /* 0x4150f2ebd0000000 */
96 1.20774762500000000000e+07, /* 0x4167093488000000 */
97 3.28299845000000000000e+07, /* 0x417f4f2208000000 */
98 8.92411500000000000000e+07, /* 0x419546d8f8000000 */
99 2.42582596000000000000e+08, /* 0x41aceb0888000000 */
100 6.59407856000000000000e+08, /* 0x41c3a6e1f8000000 */
101 1.79245641600000000000e+09, /* 0x41dab5adb8000000 */
102 4.87240166400000000000e+09, /* 0x41f226af30000000 */
103 1.32445608960000000000e+10, /* 0x4208ab7fb0000000 */
104 3.60024494080000000000e+10, /* 0x4220c3d390000000 */
105 9.78648043520000000000e+10, /* 0x4236c93268000000 */
106 2.66024116224000000000e+11, /* 0x424ef822f0000000 */
107 7.23128516608000000000e+11, /* 0x42650bba30000000 */
108 1.96566712320000000000e+12, /* 0x427c9aae40000000 */
109 5.34323724288000000000e+12, /* 0x4293704708000000 */
110 1.45244246507520000000e+13, /* 0x42aa6b7658000000 */
111 3.94814795284480000000e+13, /* 0x42c1f43fc8000000 */
112 1.07321789251584000000e+14, /* 0x42d866f348000000 */
113 2.91730863685632000000e+14, /* 0x42f0953e28000000 */
114 7.93006722514944000000e+14, /* 0x430689e220000000 */
115 2.15561576592179200000e+15}; /* 0x431ea215a0000000 */
116
117 static const double sinh_tail[37] = {
118 0.00000000000000000000e+00, /* 0x0000000000000000 */
119 1.60467555584448807892e-08, /* 0x3e513ae6096a0092 */
120 2.76742892754807136947e-08, /* 0x3e5db70cfb79a640 */
121 2.09697499555224576530e-07, /* 0x3e8c2526b66dc067 */
122 2.04940252448908240062e-07, /* 0x3e8b81b18647f380 */
123 1.65444891522700935932e-06, /* 0x3ebbc1cdd1e1eb08 */
124 3.53116789999998198721e-06, /* 0x3ecd9f201534fb09 */
125 6.94023870987375490695e-06, /* 0x3edd1c064a4e9954 */
126 4.98876893611587449271e-06, /* 0x3ed4eca65d06ea74 */
127 3.19656024605152215752e-05, /* 0x3f00c259bcc0ecc5 */
128 2.08687768377236501204e-04, /* 0x3f2b5a6647cf9016 */
129 4.84668088325403796299e-05, /* 0x3f09691adefb0870 */
130 1.17517985422733832468e-03, /* 0x3f53410fc29cde38 */
131 6.90830086959560562415e-04, /* 0x3f46a31a50b6fb3c */
132 1.45697262451506548420e-03, /* 0x3f57defc71805c40 */
133 2.99859023684906737806e-02, /* 0x3f9eb49fd80e0bab */
134 1.02538800507941396667e-02, /* 0x3f84fffc7bcd5920 */
135 1.26787628407699110022e-01, /* 0x3fc03a93b6c63435 */
136 6.86652479544033744752e-02, /* 0x3fb1940bb255fd1c */
137 4.81593627621056619148e-01, /* 0x3fded26e14260b50 */
138 1.70489513795397629181e+00, /* 0x3ffb47401fc9f2a2 */
139 1.12416073482258713767e+01, /* 0x40267bb3f55634f1 */
140 7.06579578070110514432e+00, /* 0x401c435ff8194ddc */
141 5.91244512999659974639e+01, /* 0x404d8fee052ba63a */
142 1.68921736147050694399e+02, /* 0x40651d7edccde3f6 */
143 2.60692936262073658327e+02, /* 0x40704b1644557d1a */
144 3.62419382134885609048e+02, /* 0x4076a6b5ca0a9dc4 */
145 4.07689930834187271103e+03, /* 0x40afd9cc72249aba */
146 1.55377375868385224749e+04, /* 0x40ce58de693edab5 */
147 2.53720210371943067003e+04, /* 0x40d8c70158ac6363 */
148 4.78822310734952334315e+04, /* 0x40e7614764f43e20 */
149 1.81871712615542812273e+05, /* 0x4106337db36fc718 */
150 5.62892347580489004031e+05, /* 0x41212d98b1f611e2 */
151 6.41374032312148716301e+05, /* 0x412392bc108b37cc */
152 7.57809544070145115256e+06, /* 0x415ce87bdc3473dc */
153 3.64177136406482197344e+06, /* 0x414bc8d5ae99ad14 */
154 7.63580561355670914054e+06}; /* 0x415d20d76744835c */
155
156 static const double cosh_lead[37] = {
157 1.00000000000000000000e+00, /* 0x3ff0000000000000 */
158 1.54308062791824340820e+00, /* 0x3ff8b07550000000 */
159 3.76219564676284790039e+00, /* 0x400e18fa08000000 */
160 1.00676617622375488281e+01, /* 0x402422a490000000 */
161 2.73082327842712402344e+01, /* 0x403b4ee858000000 */
162 7.42099475860595703125e+01, /* 0x40528d6fc8000000 */
163 2.01715633392333984375e+02, /* 0x406936e678000000 */
164 5.48317031860351562500e+02, /* 0x4081228948000000 */
165 1.49047915649414062500e+03, /* 0x409749eaa8000000 */
166 4.05154199218750000000e+03, /* 0x40afa71580000000 */
167 1.10132329101562500000e+04, /* 0x40c5829dd0000000 */
168 2.99370708007812500000e+04, /* 0x40dd3c4488000000 */
169 8.13773945312500000000e+04, /* 0x40f3de1650000000 */
170 2.21206695312500000000e+05, /* 0x410b00b590000000 */
171 6.01302140625000000000e+05, /* 0x412259ac48000000 */
172 1.63450865625000000000e+06, /* 0x4138f0cca8000000 */
173 4.44305525000000000000e+06, /* 0x4150f2ebd0000000 */
174 1.20774762500000000000e+07, /* 0x4167093488000000 */
175 3.28299845000000000000e+07, /* 0x417f4f2208000000 */
176 8.92411500000000000000e+07, /* 0x419546d8f8000000 */
177 2.42582596000000000000e+08, /* 0x41aceb0888000000 */
178 6.59407856000000000000e+08, /* 0x41c3a6e1f8000000 */
179 1.79245641600000000000e+09, /* 0x41dab5adb8000000 */
180 4.87240166400000000000e+09, /* 0x41f226af30000000 */
181 1.32445608960000000000e+10, /* 0x4208ab7fb0000000 */
182 3.60024494080000000000e+10, /* 0x4220c3d390000000 */
183 9.78648043520000000000e+10, /* 0x4236c93268000000 */
184 2.66024116224000000000e+11, /* 0x424ef822f0000000 */
185 7.23128516608000000000e+11, /* 0x42650bba30000000 */
186 1.96566712320000000000e+12, /* 0x427c9aae40000000 */
187 5.34323724288000000000e+12, /* 0x4293704708000000 */
188 1.45244246507520000000e+13, /* 0x42aa6b7658000000 */
189 3.94814795284480000000e+13, /* 0x42c1f43fc8000000 */
190 1.07321789251584000000e+14, /* 0x42d866f348000000 */
191 2.91730863685632000000e+14, /* 0x42f0953e28000000 */
192 7.93006722514944000000e+14, /* 0x430689e220000000 */
193 2.15561576592179200000e+15}; /* 0x431ea215a0000000 */
194
195 static const double cosh_tail[37] = {
196 0.00000000000000000000e+00, /* 0x0000000000000000 */
197 6.89700037027478056904e-09, /* 0x3e3d9f5504c2bd28 */
198 4.43207835591715833630e-08, /* 0x3e67cb66f0a4c9fd */
199 2.33540217013828929694e-07, /* 0x3e8f58617928e588 */
200 5.17452463948269748331e-08, /* 0x3e6bc7d000c38d48 */
201 9.38728274131605919153e-07, /* 0x3eaf7f9d4e329998 */
202 2.73012191010840495544e-06, /* 0x3ec6e6e464885269 */
203 3.29486051438996307950e-06, /* 0x3ecba3a8b946c154 */
204 4.75803746362771416375e-06, /* 0x3ed3f4e76110d5a4 */
205 3.33050940471947692369e-05, /* 0x3f017622515a3e2b */
206 9.94707313972136215365e-06, /* 0x3ee4dc4b528af3d0 */
207 6.51685096227860253398e-05, /* 0x3f11156278615e10 */
208 1.18132406658066663359e-03, /* 0x3f535ad50ed821f5 */
209 6.93090416366541877541e-04, /* 0x3f46b61055f2935c */
210 1.45780415323416845386e-03, /* 0x3f57e2794a601240 */
211 2.99862082708111758744e-02, /* 0x3f9eb4b45f6aadd3 */
212 1.02539925859688602072e-02, /* 0x3f85000b967b3698 */
213 1.26787669807076286421e-01, /* 0x3fc03a940fadc092 */
214 6.86652631843830962843e-02, /* 0x3fb1940bf3bf874c */
215 4.81593633223853068159e-01, /* 0x3fded26e1a2a2110 */
216 1.70489514001513020602e+00, /* 0x3ffb4740205796d6 */
217 1.12416073489841270572e+01, /* 0x40267bb3f55cb85d */
218 7.06579578098005001152e+00, /* 0x401c435ff81e18ac */
219 5.91244513000686140458e+01, /* 0x404d8fee052bdea4 */
220 1.68921736147088438429e+02, /* 0x40651d7edccde926 */
221 2.60692936262087528121e+02, /* 0x40704b1644557e0e */
222 3.62419382134890611269e+02, /* 0x4076a6b5ca0a9e1c */
223 4.07689930834187453002e+03, /* 0x40afd9cc72249abe */
224 1.55377375868385224749e+04, /* 0x40ce58de693edab5 */
225 2.53720210371943103382e+04, /* 0x40d8c70158ac6364 */
226 4.78822310734952334315e+04, /* 0x40e7614764f43e20 */
227 1.81871712615542812273e+05, /* 0x4106337db36fc718 */
228 5.62892347580489004031e+05, /* 0x41212d98b1f611e2 */
229 6.41374032312148716301e+05, /* 0x412392bc108b37cc */
230 7.57809544070145115256e+06, /* 0x415ce87bdc3473dc */
231 3.64177136406482197344e+06, /* 0x414bc8d5ae99ad14 */
232 7.63580561355670914054e+06}; /* 0x415d20d76744835c */
233
234 unsigned long long ux, aux, xneg;
235 double y, z, z1, z2;
236 int m;
237
238 /* Special cases */
239
240 GET_BITS_DP64(x, ux);
241 aux = ux & ~SIGNBIT_DP64;
242 if (aux < 0x3e30000000000000) /* |x| small enough that sinh(x) = x */
243 {
244 if (aux == 0)
245 /* with no inexact */
246 return x;
247 else
248 return val_with_flags(x, AMD_F_INEXACT);
249 }
250 else if (aux >= 0x7ff0000000000000) /* |x| is NaN or Inf */
251 {
252 if (aux > 0x7ff0000000000000)
253 /* x is NaN */
254 return _handle_error("sinh", OP_SINH, ux|0x0008000000000000, _DOMAIN,
255 0, EDOM, x, 0.0, 1);
256 else
257 return x + x;
258 }
259
260
261 xneg = (aux != ux);
262
263 y = x;
264 if (xneg) y = -x;
265
266 if (y >= max_sinh_arg)
267 {
268 if (xneg)
269 return _handle_error("sinh", OP_SINH, NINFBITPATT_DP64, _OVERFLOW,
270 AMD_F_OVERFLOW, ERANGE, x, 0.0, 1);
271 else
272 return _handle_error("sinh", OP_SINH, PINFBITPATT_DP64, _OVERFLOW,
273 AMD_F_OVERFLOW, ERANGE, x, 0.0, 1);
274 }
275 else if (y >= small_threshold)
276 {
277 /* In this range y is large enough so that
278 the negative exponential is negligible,
279 so sinh(y) is approximated by sign(x)*exp(y)/2. The
280 code below is an inlined version of that from
281 exp() with two changes (it operates on
282 y instead of x, and the division by 2 is
283 done by reducing m by 1). */
284
285 splitexp(y, 1.0, thirtytwo_by_log2, log2_by_32_lead,
286 log2_by_32_tail, &m, &z1, &z2);
287 m -= 1;
288
289 if (m >= EMIN_DP64 && m <= EMAX_DP64)
290 z = scaleDouble_1((z1+z2),m);
291 else
292 z = scaleDouble_2((z1+z2),m);
293 }
294 else
295 {
296 /* In this range we find the integer part y0 of y
297 and the increment dy = y - y0. We then compute
298
299 z = sinh(y) = sinh(y0)cosh(dy) + cosh(y0)sinh(dy)
300
301 where sinh(y0) and cosh(y0) are tabulated above. */
302
303 int ind;
304 double dy, dy2, sdy, cdy, sdy1, sdy2;
305
306 ind = (int)y;
307 dy = y - ind;
308
309 dy2 = dy*dy;
310 sdy = dy*dy2*(0.166666666666666667013899e0 +
311 (0.833333333333329931873097e-2 +
312 (0.198412698413242405162014e-3 +
313 (0.275573191913636406057211e-5 +
314 (0.250521176994133472333666e-7 +
315 (0.160576793121939886190847e-9 +
316 0.7746188980094184251527126e-12*dy2)*dy2)*dy2)*dy2)*dy2)*dy2);
317
318 cdy = dy2*(0.500000000000000005911074e0 +
319 (0.416666666666660876512776e-1 +
320 (0.138888888889814854814536e-2 +
321 (0.248015872460622433115785e-4 +
322 (0.275573350756016588011357e-6 +
323 (0.208744349831471353536305e-8 +
324 0.1163921388172173692062032e-10*dy2)*dy2)*dy2)*dy2)*dy2)*dy2);
325
326 /* At this point sinh(dy) is approximated by dy + sdy.
327 Shift some significant bits from dy to sdy. */
328
329 GET_BITS_DP64(dy, ux);
330 ux &= 0xfffffffff8000000;
331 PUT_BITS_DP64(ux, sdy1);
332 sdy2 = sdy + (dy - sdy1);
333
334 z = ((((((cosh_tail[ind]*sdy2 + sinh_tail[ind]*cdy)
335 + cosh_tail[ind]*sdy1) + sinh_tail[ind])
336 + cosh_lead[ind]*sdy2) + sinh_lead[ind]*cdy)
337 + cosh_lead[ind]*sdy1) + sinh_lead[ind];
338 }
339
340 if (xneg) z = - z;
341 return z;
342}
double __cdecl _handle_error(char *fname, int opcode, unsigned long long value, int type, int flags, int error, double arg1, double arg2, int nargs)
Handles an error condition.
Definition: _handle_error.c:34
#define ERANGE
Definition: acclib.h:92
unsigned int(__cdecl typeof(jpeg_read_scanlines))(struct jpeg_decompress_struct *
Definition: typeof.h:31
#define EDOM
Definition: errno.h:39
GLint GLint GLint GLint GLint x
Definition: gl.h:1548
GLint GLint GLint GLint GLint GLint y
Definition: gl.h:1548
GLdouble GLdouble z
Definition: glext.h:5874
const GLfloat * m
Definition: glext.h:10848
#define _DOMAIN
Definition: math.h:39
#define _OVERFLOW
Definition: math.h:41
#define AMD_F_INEXACT
Definition: libm_new.h:82
#define AMD_F_OVERFLOW
Definition: libm_new.h:83
#define NINFBITPATT_DP64
Definition: libm_util.h:54
#define GET_BITS_DP64(x, ux)
Definition: libm_util.h:118
#define PINFBITPATT_DP64
Definition: libm_util.h:53
#define EMAX_DP64
Definition: libm_util.h:60
#define EMIN_DP64
Definition: libm_util.h:58
#define PUT_BITS_DP64(ux, x)
Definition: libm_util.h:124
#define BASEDIGITS_DP64
Definition: libm_util.h:63
GLint dy
Definition: linetemp.h:97
static const WCHAR aux[]