1 /* GCC Quad-Precision Math Library
2 Copyright (C) 2010, 2011 Free Software Foundation, Inc.
3 Written by Francois-Xavier Coudert <fxcoudert@gcc.gnu.org>
4
5 This file is part of the libquadmath library.
6 Libquadmath is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Library General Public
8 License as published by the Free Software Foundation; either
9 version 2 of the License, or (at your option) any later version.
10
11 Libquadmath is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Library General Public License for more details.
15
16 You should have received a copy of the GNU Library General Public
17 License along with libquadmath; see the file COPYING.LIB. If
18 not, write to the Free Software Foundation, Inc., 51 Franklin Street - Fifth Floor,
19 Boston, MA 02110-1301, USA. */
20
21 #ifndef QUADMATH_IMP_H
22 #define QUADMATH_IMP_H
23
24 #include <errno.h>
25 #include <limits.h>
26 #include <stdbool.h>
27 #include <stdint.h>
28 #include <stdlib.h>
29 #include "quadmath.h"
30 #include "config.h"
31 #ifdef HAVE_FENV_H
32 # include <fenv.h>
33 #endif
34
35
36 /* Under IEEE 754, an architecture may determine tininess of
37 floating-point results either "before rounding" or "after
38 rounding", but must do so in the same way for all operations
39 returning binary results. Define TININESS_AFTER_ROUNDING to 1 for
40 "after rounding" architectures, 0 for "before rounding"
41 architectures. */
42
43 #define TININESS_AFTER_ROUNDING 1
44
45 #define HIGH_ORDER_BIT_IS_SET_FOR_SNAN 0
46
47 #define FIX_FLT128_LONG_CONVERT_OVERFLOW 0
48 #define FIX_FLT128_LLONG_CONVERT_OVERFLOW 0
49
50 /* Prototypes for internal functions. */
51 extern int32_t __quadmath_rem_pio2q (__float128, __float128 *);
52 extern void __quadmath_kernel_sincosq (__float128, __float128, __float128 *,
53 __float128 *, int);
54 extern __float128 __quadmath_kernel_sinq (__float128, __float128, int);
55 extern __float128 __quadmath_kernel_cosq (__float128, __float128);
56 extern __float128 __quadmath_kernel_tanq (__float128, __float128, int);
57 extern __float128 __quadmath_gamma_productq (__float128, __float128, int,
58 __float128 *);
59 extern __float128 __quadmath_gammaq_r (__float128, int *);
60 extern __float128 __quadmath_lgamma_negq (__float128, int *);
61 extern __float128 __quadmath_lgamma_productq (__float128, __float128,
62 __float128, int);
63 extern __float128 __quadmath_lgammaq_r (__float128, int *);
64 extern __float128 __quadmath_x2y2m1q (__float128 x, __float128 y);
65 extern __complex128 __quadmath_kernel_casinhq (__complex128, int);
66
67 static inline void
68 mul_splitq (__float128 *hi, __float128 *lo, __float128 x, __float128 y)
69 {
70 /* Fast built-in fused multiply-add. */
71 *hi = x * y;
72 *lo = fmaq (x, y, -*hi);
73 }
74
75
76
77
78 /* Frankly, if you have __float128, you have 64-bit integers, right? */
79 #ifndef UINT64_C
80 # error "No way!"
81 #endif
82
83
84 /* Main union type we use to manipulate the floating-point type. */
85 typedef union
86 {
87 __float128 value;
88
89 struct
90 #ifdef __MINGW32__
91 /* On mingw targets the ms-bitfields option is active by default.
92 Therefore enforce gnu-bitfield style. */
93 __attribute__ ((gcc_struct))
94 #endif
95 {
96 #if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
97 unsigned negative:1;
98 unsigned exponent:15;
99 unsigned mantissa0:16;
100 unsigned mantissa1:32;
101 unsigned mantissa2:32;
102 unsigned mantissa3:32;
103 #else
104 unsigned mantissa3:32;
105 unsigned mantissa2:32;
106 unsigned mantissa1:32;
107 unsigned mantissa0:16;
108 unsigned exponent:15;
109 unsigned negative:1;
110 #endif
111 } ieee;
112
113 struct
114 {
115 #if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
116 uint64_t high;
117 uint64_t low;
118 #else
119 uint64_t low;
120 uint64_t high;
121 #endif
122 } words64;
123
124 struct
125 {
126 #if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
127 uint32_t w0;
128 uint32_t w1;
129 uint32_t w2;
130 uint32_t w3;
131 #else
132 uint32_t w3;
133 uint32_t w2;
134 uint32_t w1;
135 uint32_t w0;
136 #endif
137 } words32;
138
139 struct
140 #ifdef __MINGW32__
141 /* Make sure we are using gnu-style bitfield handling. */
142 __attribute__ ((gcc_struct))
143 #endif
144 {
145 #if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
146 unsigned negative:1;
147 unsigned exponent:15;
148 unsigned quiet_nan:1;
149 unsigned mantissa0:15;
150 unsigned mantissa1:32;
151 unsigned mantissa2:32;
152 unsigned mantissa3:32;
153 #else
154 unsigned mantissa3:32;
155 unsigned mantissa2:32;
156 unsigned mantissa1:32;
157 unsigned mantissa0:15;
158 unsigned quiet_nan:1;
159 unsigned exponent:15;
160 unsigned negative:1;
161 #endif
162 } ieee_nan;
163
164 } ieee854_float128;
165
166
167 /* Get two 64 bit ints from a long double. */
168 #define GET_FLT128_WORDS64(ix0,ix1,d) \
169 do { \
170 ieee854_float128 u; \
171 u.value = (d); \
172 (ix0) = u.words64.high; \
173 (ix1) = u.words64.low; \
174 } while (0)
175
176 /* Set a long double from two 64 bit ints. */
177 #define SET_FLT128_WORDS64(d,ix0,ix1) \
178 do { \
179 ieee854_float128 u; \
180 u.words64.high = (ix0); \
181 u.words64.low = (ix1); \
182 (d) = u.value; \
183 } while (0)
184
185 /* Get the more significant 64 bits of a long double mantissa. */
186 #define GET_FLT128_MSW64(v,d) \
187 do { \
188 ieee854_float128 u; \
189 u.value = (d); \
190 (v) = u.words64.high; \
191 } while (0)
192
193 /* Set the more significant 64 bits of a long double mantissa from an int. */
194 #define SET_FLT128_MSW64(d,v) \
195 do { \
196 ieee854_float128 u; \
197 u.value = (d); \
198 u.words64.high = (v); \
199 (d) = u.value; \
200 } while (0)
201
202 /* Get the least significant 64 bits of a long double mantissa. */
203 #define GET_FLT128_LSW64(v,d) \
204 do { \
205 ieee854_float128 u; \
206 u.value = (d); \
207 (v) = u.words64.low; \
208 } while (0)
209
210
211 #define IEEE854_FLOAT128_BIAS 0x3fff
212
213 #define QUADFP_NAN 0
214 #define QUADFP_INFINITE 1
215 #define QUADFP_ZERO 2
216 #define QUADFP_SUBNORMAL 3
217 #define QUADFP_NORMAL 4
218 #define fpclassifyq(x) \
219 __builtin_fpclassify (QUADFP_NAN, QUADFP_INFINITE, QUADFP_NORMAL, \
220 QUADFP_SUBNORMAL, QUADFP_ZERO, x)
221
222 #ifndef math_opt_barrier
223 # define math_opt_barrier(x) \
224 ({ __typeof (x) __x = (x); __asm ("" : "+m" (__x)); __x; })
225 # define math_force_eval(x) \
226 ({ __typeof (x) __x = (x); __asm __volatile__ ("" : : "m" (__x)); })
227 #endif
228
229 /* math_narrow_eval reduces its floating-point argument to the range
230 and precision of its semantic type. (The original evaluation may
231 still occur with excess range and precision, so the result may be
232 affected by double rounding.) */
233 #define math_narrow_eval(x) (x)
234
235 /* If X (which is not a NaN) is subnormal, force an underflow
236 exception. */
237 #define math_check_force_underflow(x) \
238 do \
239 { \
240 __float128 force_underflow_tmp = (x); \
241 if (fabsq (force_underflow_tmp) < FLT128_MIN) \
242 { \
243 __float128 force_underflow_tmp2 \
244 = force_underflow_tmp * force_underflow_tmp; \
245 math_force_eval (force_underflow_tmp2); \
246 } \
247 } \
248 while (0)
249 /* Likewise, but X is also known to be nonnegative. */
250 #define math_check_force_underflow_nonneg(x) \
251 do \
252 { \
253 __float128 force_underflow_tmp = (x); \
254 if (force_underflow_tmp < FLT128_MIN) \
255 { \
256 __float128 force_underflow_tmp2 \
257 = force_underflow_tmp * force_underflow_tmp; \
258 math_force_eval (force_underflow_tmp2); \
259 } \
260 } \
261 while (0)
262
263 /* Likewise, for both real and imaginary parts of a complex
264 result. */
265 #define math_check_force_underflow_complex(x) \
266 do \
267 { \
268 __typeof (x) force_underflow_complex_tmp = (x); \
269 math_check_force_underflow (__real__ force_underflow_complex_tmp); \
270 math_check_force_underflow (__imag__ force_underflow_complex_tmp); \
271 } \
272 while (0)
273
274 #ifndef HAVE_FENV_H
275 # define feraiseexcept(arg) ((void) 0)
276 typedef int fenv_t;
277 # define feholdexcept(arg) ((void) 0)
278 # define fesetround(arg) ((void) 0)
279 # define feupdateenv(arg) ((void) (arg))
280 # define fesetenv(arg) ((void) (arg))
281 # define fetestexcept(arg) 0
282 # define feclearexcept(arg) ((void) 0)
283 #else
284 # ifndef HAVE_FEHOLDEXCEPT
285 # define feholdexcept(arg) ((void) 0)
286 # endif
287 # ifndef HAVE_FESETROUND
288 # define fesetround(arg) ((void) 0)
289 # endif
290 # ifndef HAVE_FEUPDATEENV
291 # define feupdateenv(arg) ((void) (arg))
292 # endif
293 # ifndef HAVE_FESETENV
294 # define fesetenv(arg) ((void) (arg))
295 # endif
296 # ifndef HAVE_FETESTEXCEPT
297 # define fetestexcept(arg) 0
298 # endif
299 #endif
300
301 #ifndef __glibc_likely
302 # define __glibc_likely(cond) __builtin_expect ((cond), 1)
303 #endif
304
305 #ifndef __glibc_unlikely
306 # define __glibc_unlikely(cond) __builtin_expect ((cond), 0)
307 #endif
308
309 #if defined HAVE_FENV_H && defined HAVE_FESETROUND && defined HAVE_FEUPDATEENV
310 struct rm_ctx
311 {
312 fenv_t env;
313 bool updated_status;
314 };
315
316 # define SET_RESTORE_ROUNDF128(RM) \
317 struct rm_ctx ctx __attribute__((cleanup (libc_feresetround_ctx))); \
318 libc_feholdsetround_ctx (&ctx, (RM))
319
320 static inline __attribute__ ((always_inline)) void
321 libc_feholdsetround_ctx (struct rm_ctx *ctx, int round)
322 {
323 ctx->updated_status = false;
324
325 /* Update rounding mode only if different. */
326 if (__glibc_unlikely (round != fegetround ()))
327 {
328 ctx->updated_status = true;
329 fegetenv (&ctx->env);
330 fesetround (round);
331 }
332 }
333
334 static inline __attribute__ ((always_inline)) void
335 libc_feresetround_ctx (struct rm_ctx *ctx)
336 {
337 /* Restore the rounding mode if updated. */
338 if (__glibc_unlikely (ctx->updated_status))
339 feupdateenv (&ctx->env);
340 }
341 #else
342 # define SET_RESTORE_ROUNDF128(RM) ((void) 0)
343 #endif
344
345 #endif