1 /* file: libm_support.h */
2 
3 
4 /*
5 // Copyright (c) 2000 - 2004, Intel Corporation
6 // All rights reserved.
7 //
8 //
9 // Redistribution and use in source and binary forms, with or without
10 // modification, are permitted provided that the following conditions are
11 // met:
12 //
13 // * Redistributions of source code must retain the above copyright
14 // notice, this list of conditions and the following disclaimer.
15 //
16 // * Redistributions in binary form must reproduce the above copyright
17 // notice, this list of conditions and the following disclaimer in the
18 // documentation and/or other materials provided with the distribution.
19 //
20 // * The name of Intel Corporation may not be used to endorse or promote
21 // products derived from this software without specific prior written
22 // permission.
23 
24 //
25 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
26 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
27 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
28 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
29 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
30 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
31 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
32 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
33 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
34 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
35 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
36 //
37 // Intel Corporation is the author of this code, and requests that all
38 // problem reports or change requests be submitted to it directly at
39 // http://www.intel.com/software/products/opensource/libraries/num.htm.
40 //
41 
42 // History: 02/02/2000 Initial version
43 //          2/28/2000 added tags for logb and nextafter
44 //          3/22/2000 Changes to support _LIB_VERSIONIMF variable
45 //                    and filled some enum gaps. Added support for C99.
46 //          5/31/2000 added prototypes for __libm_frexp_4l/8l
47 //          8/10/2000 Changed declaration of _LIB_VERSIONIMF to work for library
48 //                    builds and other application builds (precompiler directives).
49 //          8/11/2000 Added pointers-to-matherr-functions declarations to allow
50 //                    for user-defined matherr functions in the dll build.
51 //         12/07/2000 Added scalbn error_types values.
52 //          5/01/2001 Added error_types values for C99 nearest integer
53 //                    functions.
54 //          6/07/2001 Added error_types values for fdim.
55 //          6/18/2001 Added include of complex_support.h.
56 //          8/03/2001 Added error_types values for nexttoward, scalbln.
57 //          8/23/2001 Corrected tag numbers from 186 and higher.
58 //          8/27/2001 Added check for long int and long long int definitions.
59 //         12/10/2001 Added error_types for erfc.
60 //         12/27/2001 Added error_types for degree argument functions.
61 //         01/02/2002 Added error_types for tand, cotd.
62 //         01/04/2002 Delete include of complex_support.h
63 //         01/23/2002 Deleted prototypes for __libm_frexp*.  Added check for
64 //                    multiple int, long int, and long long int definitions.
65 //         05/20/2002 Added error_types for cot.
66 //         06/27/2002 Added error_types for sinhcosh.
67 //         12/05/2002 Added error_types for annuity and compound
68 //         04/10/2003 Added error_types for tgammal/tgamma/tgammaf
69 //         05/16/2003 FP-treatment macros copied here from IA32 libm_support.h
70 //         06/02/2003 Added pad into struct fp80 (12/16 bytes).
71 //         08/01/2003 Added struct ker80 and macros for multiprecision addition,
72 //                    subtraction, multiplication, division, square root.
73 //         08/07/2003 History section updated.
74 //         09/03/2003 ALIGN(n) macro added.
75 //         10/01/2003 LDOUBLE_ALIGN and fp80 corrected on linux to 16 bytes.
76 //         11/24/2004 Added ifdef around definitions of INT32/64
77 //         12/15/2004 Added error_types for exp10, nextafter, nexttoward
78 //                    underflow.  Moved error codes into libm_error_codes.h.
79 //
80 */
81 
82 #ifndef __LIBM_SUPPORT_H_INCLUDED__
83 #define __LIBM_SUPPORT_H_INCLUDED__
84 
85 #include <math-svid-compat.h>
86 
87 #ifndef _LIBC
88 #if !(defined(_WIN32) || defined(_WIN64))
89 # pragma const_seg(".rodata") /* place constant data in text (code) section */
90 #endif
91 
92 #if defined(__ICC) || defined(__ICL) || defined(__ECC) || defined(__ECL)
93 # pragma warning( disable : 1682 )	/* #1682: ixplicit conversion of a 64-bit integral type to a smaller integral type (potential portability problem) */
94 # pragma warning( disable : 1683 )	/* #1683: explicit conversion of a 64-bit integral type to a smaller integral type (potential portability problem) */
95 #endif
96 #endif
97 
98 /* macros to form a double value in hex representation (unsigned int type) */
99 
100 #define DOUBLE_HEX(hi,lo) 0x##lo,0x##hi /*LITTLE_ENDIAN*/
101 
102 #include "libm_cpu_defs.h"
103 
104 #if !(defined (IA64))
105 #  include "libm_dll.h"
106 #  include "libm_dispatch.h"
107 #endif
108 
109 #include "libm_error_codes.h"
110 
111 struct exceptionf
112 {
113   int type;
114   char *name;
115   float arg1, arg2, retval;
116 };
117 
118 # ifdef __cplusplus
119 struct __exception
120 {
121   int type;
122   char *name;
123   double arg1, arg2, retval;
124 };
125 # else
126 
127 #  ifndef _LIBC
128 struct exception
129 {
130   int type;
131   char *name;
132   double arg1, arg2, retval;
133 };
134 #  endif
135 # endif
136 
137 struct exceptionl
138 {
139   int type;
140   char *name;
141   long double arg1, arg2, retval;
142 };
143 
144 #if (defined (_MS_) && defined (IA64))
145 #define   MATHERR_F   _matherrf
146 #define   MATHERR_D   _matherr
147 #else
148 #define MATHERR_F   matherrf
149 #define MATHERR_D   matherr
150 #endif
151 
152 # ifdef __cplusplus
153 #define EXC_DECL_D  __exception
154 #else
155 // exception is a reserved name in C++
156 #define EXC_DECL_D  exception
157 #endif
158 
159 extern int MATHERR_F(struct exceptionf*);
160 extern int matherrl(struct exceptionl*);
161 
162 /* memory format definitions (LITTLE_ENDIAN only) */
163 
164 #if !(defined(SIZE_INT_32) || defined(SIZE_INT_64))
165 # error "You need to define SIZE_INT_32 or SIZE_INT_64"
166 #endif
167 
168 #if (defined(SIZE_INT_32) && defined(SIZE_INT_64))
169 #error multiple integer size definitions; define SIZE_INT_32 or SIZE_INT_64
170 #endif
171 
172 #if !(defined(SIZE_LONG_32) || defined(SIZE_LONG_64))
173 # error "You need to define SIZE_LONG_32 or SIZE_LONG_64"
174 #endif
175 
176 #if (defined(SIZE_LONG_32) && defined(SIZE_LONG_64))
177 #error multiple integer size definitions; define SIZE_LONG_32 or SIZE_LONG_64
178 #endif
179 
180 #if !defined(__USE_EXTERNAL_FPMEMTYP_H__)
181 
182 #define BIAS_32  0x007F
183 #define BIAS_64  0x03FF
184 #define BIAS_80  0x3FFF
185 
186 #define MAXEXP_32  0x00FE
187 #define MAXEXP_64  0x07FE
188 #define MAXEXP_80  0x7FFE
189 
190 #define EXPINF_32  0x00FF
191 #define EXPINF_64  0x07FF
192 #define EXPINF_80  0x7FFF
193 
194 struct fp32 { /*// sign:1 exponent:8 significand:23 (implied leading 1)*/
195 #if defined(SIZE_INT_32)
196     unsigned significand:23;
197     unsigned exponent:8;
198     unsigned sign:1;
199 #elif defined(SIZE_INT_64)
200     unsigned significand:23;
201     unsigned exponent:8;
202     unsigned sign:1;
203 #endif
204 };
205 
206 struct fp64 { /*/ sign:1 exponent:11 significand:52 (implied leading 1)*/
207 #if defined(SIZE_INT_32)
208     unsigned lo_significand:32;
209     unsigned hi_significand:20;
210     unsigned exponent:11;
211     unsigned sign:1;
212 #elif defined(SIZE_INT_64)
213     unsigned significand:52;
214     unsigned exponent:11;
215     unsigned sign:1;
216 #endif
217 };
218 
219 struct fp80 { /*/ sign:1 exponent:15 significand:64 (NO implied bits) */
220 #if defined(SIZE_INT_32)
221     unsigned         lo_significand;
222     unsigned         hi_significand;
223     unsigned         exponent:15;
224     unsigned         sign:1;
225 #elif defined(SIZE_INT_64)
226     unsigned         significand;
227     unsigned         exponent:15;
228     unsigned         sign:1;
229 #endif
230     unsigned         pad:16;
231 #if !(defined(__unix__) && defined(__i386__))
232     unsigned         padwin:32;
233 #endif
234 };
235 
236 #endif /*__USE_EXTERNAL_FPMEMTYP_H__*/
237 
238 #if !(defined(opensource))
239 typedef          __int32  INT32;
240 typedef   signed __int32 SINT32;
241 typedef unsigned __int32 UINT32;
242 
243 typedef          __int64  INT64;
244 typedef   signed __int64 SINT64;
245 typedef unsigned __int64 UINT64;
246 #else
247 typedef          int  INT32;
248 typedef   signed int SINT32;
249 typedef unsigned int UINT32;
250 
251 typedef          long long  INT64;
252 typedef   signed long long SINT64;
253 typedef unsigned long long UINT64;
254 #endif
255 
256 #if (defined(_WIN32) || defined(_WIN64))        /* Windows */
257 # define I64CONST(bits) 0x##bits##i64
258 # define U64CONST(bits) 0x##bits##ui64
259 #elif (defined(__linux__) && defined(_M_IA64))  /* Linux,64 */
260 # define I64CONST(bits) 0x##bits##L
261 # define U64CONST(bits) 0x##bits##uL
262 #else                                           /* Linux,32 */
263 # define I64CONST(bits) 0x##bits##LL
264 # define U64CONST(bits) 0x##bits##uLL
265 #endif
266 
267 struct ker80 {
268     union {
269         long double ldhi;
270         struct fp80 fphi;
271     };
272     union {
273         long double ldlo;
274         struct fp80 fplo;
275     };
276     int ex;
277 };
278 
279 /* Addition: x+y                                            */
280 /* The result is sum rhi+rlo                                */
281 /* Temporary variables: t1                                  */
282 /* All variables are in long double precision               */
283 /* Correct if no overflow (algorithm by D.Knuth)           */
284 #define __LIBM_ADDL1_K80( rhi,rlo,x,y, t1 )                 \
285     rhi = x   + y;                                          \
286     rlo = rhi - x;                                          \
287     t1  = rhi - rlo;                                        \
288     rlo = y   - rlo;                                        \
289     t1  = x   - t1;                                         \
290     rlo = rlo + t1;
291 
292 /* Addition: (xhi+xlo) + (yhi+ylo)                          */
293 /* The result is sum rhi+rlo                                */
294 /* Temporary variables: t1                                  */
295 /* All variables are in long double precision               */
296 /* Correct if no overflow (algorithm by T.J.Dekker)         */
297 #define __LIBM_ADDL2_K80( rhi,rlo,xhi,xlo,yhi,ylo, t1 )     \
298     rlo = xhi+yhi;                                          \
299     if ( VALUE_GT_80(FP80(xhi),FP80(yhi)) ) {               \
300         t1=xhi-rlo;t1=t1+yhi;t1=t1+ylo;t1=t1+xlo;           \
301     } else {                                                \
302         t1=yhi-rlo;t1=t1+xhi;t1=t1+xlo;t1=t1+ylo;           \
303     }                                                       \
304     rhi=rlo+t1;                                             \
305     rlo=rlo-rhi;rlo=rlo+t1;
306 
307 /* Addition: r=x+y                                          */
308 /* Variables r,x,y are pointers to struct ker80,            */
309 /* all other variables are in long double precision         */
310 /* Temporary variables: t1                                  */
311 /* Correct if x and y belong to interval [2^-8000;2^8000],  */
312 /* or when one or both of them are zero                     */
313 #if   defined(SIZE_INT_32)
314 #define __LIBM_ADDL_K80(r,x,y, t1)                          \
315     if ( ((y)->ex+(y)->fphi.exponent-134 <                  \
316           (x)->ex+(x)->fphi.exponent)       &&              \
317          ((x)->ex+(x)->fphi.exponent <                      \
318           (y)->ex+(y)->fphi.exponent+134)   &&              \
319          !SIGNIFICAND_ZERO_80(&((x)->fphi)) &&              \
320          !SIGNIFICAND_ZERO_80(&((y)->fphi)) )               \
321     {                                                       \
322         /* y/2^134 < x < y*2^134,               */          \
323         /* and x,y are nonzero finite numbers   */          \
324         if ( (x)->ex != (y)->ex ) {                         \
325             /* adjust x->ex to y->ex */                     \
326             /* t1 = 2^(x->ex - y->ex) */                    \
327             FP80(t1)->sign = 0;                             \
328             FP80(t1)->exponent = BIAS_80 + (x)->ex-(y)->ex; \
329             /*  exponent is correct because             */  \
330             /*  |x->ex - y->ex| =                       */  \
331             /*  = |  (x->ex + x->fphi.exponent) -       */  \
332             /*      -(y->ex + y->fphi.exponent) +       */  \
333             /*              + y->fphi.exponent  -       */  \
334             /*              - x->fphi.exponent     | <  */  \
335             /*  < |  (x->ex+x->fphi.exponent) -         */  \
336             /*      -(y->ex+y->fphi.exponent)      | +  */  \
337             /*   +|  y->fphi.exponent -                 */  \
338             /*      -x->fphi.exponent              | <  */  \
339             /*  < 134 + 16000                           */  \
340             FP80(t1)->hi_significand = 0x80000000;          \
341             FP80(t1)->lo_significand = 0x00000000;          \
342             (x)->ex = (y)->ex;                              \
343             (x)->ldhi *= t1;                                \
344             (x)->ldlo *= t1;                                \
345         }                                                   \
346         /* r==x+y */                                        \
347         (r)->ex = (y)->ex;                                  \
348         __LIBM_ADDL2_K80( (r)->ldhi,(r)->ldlo,              \
349             (x)->ldhi,(x)->ldlo, (y)->ldhi,(y)->ldlo, t1 ); \
350     } else if ( SIGNIFICAND_ZERO_80(&((x)->fphi)) ||        \
351              ((y)->ex+(y)->fphi.exponent-BIAS_80 - 134 >=   \
352               (x)->ex+(x)->fphi.exponent-BIAS_80) )         \
353     {                                                       \
354         /* |x|<<|y| */                                      \
355         *(r) = *(y);                                        \
356     } else {                                                \
357         /* |y|<<|x| */                                      \
358         *(r) = *(x);                                        \
359     }
360 #elif defined(SIZE_INT_64)
361 #define __LIBM_ADDL_K80(r,x,y, t1)                          \
362     if ( ((y)->ex+(y)->fphi.exponent-134 <                  \
363           (x)->ex+(x)->fphi.exponent)       &&              \
364          ((x)->ex+(x)->fphi.exponent <                      \
365           (y)->ex+(y)->fphi.exponent+134)   &&              \
366          !SIGNIFICAND_ZERO_80(&((x)->fphi)) &&              \
367          !SIGNIFICAND_ZERO_80(&((y)->fphi)) )               \
368     {                                                       \
369         /* y/2^134 < x < y*2^134,               */          \
370         /* and x,y are nonzero finite numbers   */          \
371         if ( (x)->ex != (y)->ex ) {                         \
372             /* adjust x->ex to y->ex */                     \
373             /* t1 = 2^(x->ex - y->ex) */                    \
374             FP80(t1)->sign = 0;                             \
375             FP80(t1)->exponent = BIAS_80 + (x)->ex-(y)->ex; \
376             /*  exponent is correct because             */  \
377             /*  |x->ex - y->ex| =                       */  \
378             /*  = |  (x->ex + x->fphi.exponent) -       */  \
379             /*      -(y->ex + y->fphi.exponent) +       */  \
380             /*              + y->fphi.exponent  -       */  \
381             /*              - x->fphi.exponent     | <  */  \
382             /*  < |  (x->ex+x->fphi.exponent) -         */  \
383             /*      -(y->ex+y->fphi.exponent)      | +  */  \
384             /*   +|  y->fphi.exponent -                 */  \
385             /*      -x->fphi.exponent              | <  */  \
386             /*  < 134 + 16000                           */  \
387             FP80(t1)->significand = 0x8000000000000000;     \
388             (x)->ex = (y)->ex;                              \
389             (x)->ldhi *= t1;                                \
390             (x)->ldlo *= t1;                                \
391         }                                                   \
392         /* r==x+y */                                        \
393         (r)->ex = (y)->ex;                                  \
394         __LIBM_ADDL2_K80( (r)->ldhi,(r)->ldlo,              \
395             (x)->ldhi,(x)->ldlo, (y)->ldhi,(y)->ldlo, t1 ); \
396     } else if ( SIGNIFICAND_ZERO_80(&((x)->fphi)) ||        \
397              ((y)->ex+(y)->fphi.exponent-BIAS_80 - 134 >=   \
398               (x)->ex+(x)->fphi.exponent-BIAS_80) )         \
399     {                                                       \
400         /* |x|<<|y| */                                      \
401         *(r) = *(y);                                        \
402     } else {                                                \
403         /* |y|<<|x| */                                      \
404         *(r) = *(x);                                        \
405     }
406 #endif
407 
408 /* Addition: r=x+y                                          */
409 /* Variables r,x,y are pointers to struct ker80,            */
410 /* all other variables are in long double precision         */
411 /* Temporary variables: t1                                  */
412 /* Correct for any finite x and y                           */
413 #define __LIBM_ADDL_NORM_K80(r,x,y, t1)                     \
414     if ( ((x)->fphi.exponent-BIAS_80<-8000) ||              \
415          ((x)->fphi.exponent-BIAS_80>+8000) ||              \
416          ((y)->fphi.exponent-BIAS_80<-8000) ||              \
417          ((y)->fphi.exponent-BIAS_80>+8000) )               \
418     {                                                       \
419         __libm_normalizel_k80(x);                           \
420         __libm_normalizel_k80(y);                           \
421     }                                                       \
422     __LIBM_ADDL_K80(r,x,y, t1)
423 
424 /* Subtraction: x-y                                         */
425 /* The result is sum rhi+rlo                                */
426 /* Temporary variables: t1                                  */
427 /* All variables are in long double precision               */
428 /* Correct if no overflow (algorithm by D.Knuth)           */
429 #define __LIBM_SUBL1_K80( rhi, rlo, x, y, t1 )              \
430     rhi = x   - y;                                          \
431     rlo = rhi - x;                                          \
432     t1  = rhi - rlo;                                        \
433     rlo = y   + rlo;                                        \
434     t1  = x   - t1;                                         \
435     rlo = t1  - rlo;
436 
437 /* Subtraction: (xhi+xlo) - (yhi+ylo)                       */
438 /* The result is sum rhi+rlo                                */
439 /* Temporary variables: t1                                  */
440 /* All variables are in long double precision               */
441 /* Correct if no overflow (algorithm by T.J.Dekker)         */
442 #define __LIBM_SUBL2_K80( rhi,rlo,xhi,xlo,yhi,ylo, t1 )     \
443     rlo = xhi-yhi;                                          \
444     if ( VALUE_GT_80(FP80(xhi),FP80(yhi)) ) {               \
445         t1=xhi-rlo;t1=t1-yhi;t1=t1-ylo;t1=t1+xlo;           \
446     } else {                                                \
447         t1=yhi+rlo;t1=xhi-t1;t1=t1+xlo;t1=t1-ylo;           \
448     }                                                       \
449     rhi=rlo+t1;                                             \
450     rlo=rlo-rhi;rlo=rlo+t1;
451 
452 /* Subtraction: r=x-y                                       */
453 /* Variables r,x,y are pointers to struct ker80,            */
454 /* all other variables are in long double precision         */
455 /* Temporary variables: t1                                  */
456 /* Correct if x and y belong to interval [2^-8000;2^8000],  */
457 /* or when one or both of them are zero                     */
458 #if   defined(SIZE_INT_32)
459 #define __LIBM_SUBL_K80(r,x,y, t1)                          \
460     if ( ((y)->ex+(y)->fphi.exponent-134 <                  \
461           (x)->ex+(x)->fphi.exponent)       &&              \
462          ((x)->ex+(x)->fphi.exponent <                      \
463           (y)->ex+(y)->fphi.exponent+134)   &&              \
464          !SIGNIFICAND_ZERO_80(&((x)->fphi)) &&              \
465          !SIGNIFICAND_ZERO_80(&((y)->fphi)) )               \
466     {                                                       \
467         /* y/2^134 < x < y*2^134,               */          \
468         /* and x,y are nonzero finite numbers   */          \
469         if ( (x)->ex != (y)->ex ) {                         \
470             /* adjust x->ex to y->ex */                     \
471             /* t1 = 2^(x->ex - y->ex) */                    \
472             FP80(t1)->sign = 0;                             \
473             FP80(t1)->exponent = BIAS_80 + (x)->ex-(y)->ex; \
474             /*  exponent is correct because             */  \
475             /*  |x->ex - y->ex| =                       */  \
476             /*  = |  (x->ex + x->fphi.exponent) -       */  \
477             /*      -(y->ex + y->fphi.exponent) +       */  \
478             /*              + y->fphi.exponent  -       */  \
479             /*              - x->fphi.exponent     | <  */  \
480             /*  < |  (x->ex+x->fphi.exponent) -         */  \
481             /*      -(y->ex+y->fphi.exponent)      | +  */  \
482             /*   +|  y->fphi.exponent -                 */  \
483             /*      -x->fphi.exponent              | <  */  \
484             /*  < 134 + 16000                           */  \
485             FP80(t1)->hi_significand = 0x80000000;          \
486             FP80(t1)->lo_significand = 0x00000000;          \
487             (x)->ex = (y)->ex;                              \
488             (x)->ldhi *= t1;                                \
489             (x)->ldlo *= t1;                                \
490         }                                                   \
491         /* r==x+y */                                        \
492         (r)->ex = (y)->ex;                                  \
493         __LIBM_SUBL2_K80( (r)->ldhi,(r)->ldlo,              \
494             (x)->ldhi,(x)->ldlo, (y)->ldhi,(y)->ldlo, t1 ); \
495     } else if ( SIGNIFICAND_ZERO_80(&((x)->fphi)) ||        \
496              ((y)->ex+(y)->fphi.exponent-BIAS_80 - 134 >=   \
497               (x)->ex+(x)->fphi.exponent-BIAS_80) )         \
498     {                                                       \
499         /* |x|<<|y| */                                      \
500         (r)->ex   =   (y)->ex;                              \
501         (r)->ldhi = -((y)->ldhi);                           \
502         (r)->ldlo = -((y)->ldlo);                           \
503     } else {                                                \
504         /* |y|<<|x| */                                      \
505         *(r) = *(x);                                        \
506     }
507 #elif defined(SIZE_INT_64)
508 #define __LIBM_SUBL_K80(r,x,y, t1)                          \
509     if ( ((y)->ex+(y)->fphi.exponent-134 <                  \
510           (x)->ex+(x)->fphi.exponent)       &&              \
511          ((x)->ex+(x)->fphi.exponent <                      \
512           (y)->ex+(y)->fphi.exponent+134)   &&              \
513          !SIGNIFICAND_ZERO_80(&((x)->fphi)) &&              \
514          !SIGNIFICAND_ZERO_80(&((y)->fphi)) )               \
515     {                                                       \
516         /* y/2^134 < x < y*2^134,               */          \
517         /* and x,y are nonzero finite numbers   */          \
518         if ( (x)->ex != (y)->ex ) {                         \
519             /* adjust x->ex to y->ex */                     \
520             /* t1 = 2^(x->ex - y->ex) */                    \
521             FP80(t1)->sign = 0;                             \
522             FP80(t1)->exponent = BIAS_80 + (x)->ex-(y)->ex; \
523             /*  exponent is correct because             */  \
524             /*  |x->ex - y->ex| =                       */  \
525             /*  = |  (x->ex + x->fphi.exponent) -       */  \
526             /*      -(y->ex + y->fphi.exponent) +       */  \
527             /*              + y->fphi.exponent  -       */  \
528             /*              - x->fphi.exponent     | <  */  \
529             /*  < |  (x->ex+x->fphi.exponent) -         */  \
530             /*      -(y->ex+y->fphi.exponent)      | +  */  \
531             /*   +|  y->fphi.exponent -                 */  \
532             /*      -x->fphi.exponent              | <  */  \
533             /*  < 134 + 16000                           */  \
534             FP80(t1)->significand = 0x8000000000000000;     \
535             (x)->ex = (y)->ex;                              \
536             (x)->ldhi *= t1;                                \
537             (x)->ldlo *= t1;                                \
538         }                                                   \
539         /* r==x+y */                                        \
540         (r)->ex = (y)->ex;                                  \
541         __LIBM_SUBL2_K80( (r)->ldhi,(r)->ldlo,              \
542             (x)->ldhi,(x)->ldlo, (y)->ldhi,(y)->ldlo, t1 ); \
543     } else if ( SIGNIFICAND_ZERO_80(&((x)->fphi)) ||        \
544              ((y)->ex+(y)->fphi.exponent-BIAS_80 - 134 >=   \
545               (x)->ex+(x)->fphi.exponent-BIAS_80) )         \
546     {                                                       \
547         /* |x|<<|y| */                                      \
548         (r)->ex   =   (y)->ex;                              \
549         (r)->ldhi = -((y)->ldhi);                           \
550         (r)->ldlo = -((y)->ldlo);                           \
551     } else {                                                \
552         /* |y|<<|x| */                                      \
553         *(r) = *(x);                                        \
554     }
555 #endif
556 
557 /* Subtraction: r=x+y                                       */
558 /* Variables r,x,y are pointers to struct ker80,            */
559 /* all other variables are in long double precision         */
560 /* Temporary variables: t1                                  */
561 /* Correct for any finite x and y                           */
562 #define __LIBM_SUBL_NORM_K80(r,x,y, t1)                     \
563     if ( ((x)->fphi.exponent-BIAS_80<-8000) ||              \
564          ((x)->fphi.exponent-BIAS_80>+8000) ||              \
565          ((y)->fphi.exponent-BIAS_80<-8000) ||              \
566          ((y)->fphi.exponent-BIAS_80>+8000) )               \
567     {                                                       \
568         __libm_normalizel_k80(x);                           \
569         __libm_normalizel_k80(y);                           \
570     }                                                       \
571     __LIBM_SUBL_K80(r,x,y, t1)
572 
573 /* Multiplication: x*y                                      */
574 /* The result is sum rhi+rlo                                */
575 /* Here t32 is the constant 2^32+1                          */
576 /* Temporary variables: t1,t2,t3,t4,t5,t6                   */
577 /* All variables are in long double precision               */
578 /* Correct if no over/underflow (algorithm by T.J.Dekker)   */
579 #define __LIBM_MULL1_K80(rhi,rlo,x,y,                       \
580                                      t32,t1,t2,t3,t4,t5,t6) \
581     t1=(x)*(t32); t3=x-t1; t3=t3+t1; t4=x-t3;               \
582     t1=(y)*(t32); t5=y-t1; t5=t5+t1; t6=y-t5;               \
583     t1=(t3)*(t5);                                           \
584     t2=(t3)*(t6)+(t4)*(t5);                                 \
585     rhi=t1+t2;                                              \
586     rlo=t1-rhi; rlo=rlo+t2; rlo=rlo+(t4*t6);
587 
588 /* Multiplication: (xhi+xlo)*(yhi+ylo)                      */
589 /* The result is sum rhi+rlo                                */
590 /* Here t32 is the constant 2^32+1                          */
591 /* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8             */
592 /* All variables are in long double precision               */
593 /* Correct if no over/underflow (algorithm by T.J.Dekker)   */
594 #define __LIBM_MULL2_K80(rhi,rlo,xhi,xlo,yhi,ylo,           \
595                                t32,t1,t2,t3,t4,t5,t6,t7,t8) \
596     __LIBM_MULL1_K80(t7,t8,xhi,yhi, t32,t1,t2,t3,t4,t5,t6)  \
597     t1=(xhi)*(ylo)+(xlo)*(yhi); t1=t1+t8;                   \
598     rhi=t7+t1;                                              \
599     rlo=t7-rhi; rlo=rlo+t1;
600 
601 /* Multiplication: r=x*y                                    */
602 /* Variables r,x,y are pointers to struct ker80,            */
603 /* all other variables are in long double precision         */
604 /* Here t32 is the constant 2^32+1                          */
605 /* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8             */
606 /* Correct if x and y belong to interval [2^-8000;2^8000]   */
607 #define __LIBM_MULL_K80(r,x,y, t32,t1,t2,t3,t4,t5,t6,t7,t8) \
608     (r)->ex = (x)->ex + (y)->ex;                            \
609     __LIBM_MULL2_K80((r)->ldhi,(r)->ldlo,                   \
610         (x)->ldhi,(x)->ldlo,(y)->ldhi,(y)->ldlo,            \
611         t32,t1,t2,t3,t4,t5,t6,t7,t8)
612 
613 /* Multiplication: r=x*y                                    */
614 /* Variables r,x,y are pointers to struct ker80,            */
615 /* all other variables are in long double precision         */
616 /* Here t32 is the constant 2^32+1                          */
617 /* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8             */
618 /* Correct for any finite x and y                           */
619 #define __LIBM_MULL_NORM_K80(r,x,y,                         \
620                                t32,t1,t2,t3,t4,t5,t6,t7,t8) \
621     if ( ((x)->fphi.exponent-BIAS_80<-8000) ||              \
622          ((x)->fphi.exponent-BIAS_80>+8000) ||              \
623          ((y)->fphi.exponent-BIAS_80<-8000) ||              \
624          ((y)->fphi.exponent-BIAS_80>+8000) )               \
625     {                                                       \
626         __libm_normalizel_k80(x);                           \
627         __libm_normalizel_k80(y);                           \
628     }                                                       \
629     __LIBM_MULL_K80(r,x,y, t32,t1,t2,t3,t4,t5,t6,t7,t8)
630 
631 /* Division: (xhi+xlo)/(yhi+ylo)                            */
632 /* The result is sum rhi+rlo                                */
633 /* Here t32 is the constant 2^32+1                          */
634 /* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8,t9          */
635 /* All variables are in long double precision               */
636 /* Correct if no over/underflow (algorithm by T.J.Dekker)   */
637 #define __LIBM_DIVL2_K80(rhi,rlo,xhi,xlo,yhi,ylo,           \
638                             t32,t1,t2,t3,t4,t5,t6,t7,t8,t9) \
639     t7=(xhi)/(yhi);                                         \
640     __LIBM_MULL1_K80(t8,t9,t7,yhi, t32,t1,t2,t3,t4,t5,t6)   \
641     t1=xhi-t8; t1=t1-t9; t1=t1+xlo; t1=t1-(t7)*(ylo);       \
642     t1=(t1)/(yhi);                                          \
643     rhi=t7+t1;                                              \
644     rlo=t7-rhi; rlo=rlo+t1;
645 
646 /* Division: r=x/y                                          */
647 /* Variables r,x,y are pointers to struct ker80,            */
648 /* all other variables are in long double precision         */
649 /* Here t32 is the constant 2^32+1                          */
650 /* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8,t9          */
651 /* Correct if x and y belong to interval [2^-8000;2^8000]   */
652 #define __LIBM_DIVL_K80(r,x,y,                              \
653                             t32,t1,t2,t3,t4,t5,t6,t7,t8,t9) \
654     (r)->ex = (x)->ex - (y)->ex;                            \
655     __LIBM_DIVL2_K80( (r)->ldhi,(r)->ldlo,                  \
656         (x)->ldhi,(x)->ldlo,(y)->ldhi,(y)->ldlo,            \
657         t32,t1,t2,t3,t4,t5,t6,t7,t8,t9)
658 
659 /* Division: r=x/y                                          */
660 /* Variables r,x,y are pointers to struct ker80,            */
661 /* all other variables are in long double precision         */
662 /* Here t32 is the constant 2^32+1                          */
663 /* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8             */
664 /* Correct for any finite x and y                           */
665 #define __LIBM_DIVL_NORM_K80(r,x,y,                         \
666                             t32,t1,t2,t3,t4,t5,t6,t7,t8,t9) \
667     if ( ((x)->fphi.exponent-BIAS_80<-8000) ||              \
668          ((x)->fphi.exponent-BIAS_80>+8000) ||              \
669          ((y)->fphi.exponent-BIAS_80<-8000) ||              \
670          ((y)->fphi.exponent-BIAS_80>+8000) )               \
671     {                                                       \
672         __libm_normalizel_k80(x);                           \
673         __libm_normalizel_k80(y);                           \
674     }                                                       \
675     __LIBM_DIVL_K80(r,x,y, t32,t1,t2,t3,t4,t5,t6,t7,t8,t9)
676 
677 /* Square root: sqrt(xhi+xlo)                               */
678 /* The result is sum rhi+rlo                                */
679 /* Here t32 is the constant 2^32+1                          */
680 /*      half is the constant 0.5                            */
681 /* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8,t9          */
682 /* All variables are in long double precision               */
683 /* Correct for positive xhi+xlo (algorithm by T.J.Dekker)   */
684 #define __LIBM_SQRTL2_NORM_K80(rhi,rlo,xhi,xlo,             \
685                        t32,half,t1,t2,t3,t4,t5,t6,t7,t8,t9) \
686     t7=sqrtl(xhi);                                          \
687     __LIBM_MULL1_K80(t8,t9,t7,t7, t32,t1,t2,t3,t4,t5,t6)    \
688     t1=xhi-t8; t1=t1-t9; t1=t1+xlo; t1=(t1)*(half);         \
689     t1=(t1)/(t7);                                           \
690     rhi=t7+t1;                                              \
691     rlo=t7-rhi; rlo=rlo+t1;
692 
693 /* Square root: r=sqrt(x)                                   */
694 /* Variables r,x,y are pointers to struct ker80,            */
695 /* all other variables are in long double precision         */
696 /* Here t32 is the constant 2^32+1                          */
697 /*      half is the constant 0.5                            */
698 /* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8,t9          */
699 /* Correct if x belongs to interval [2^-16000;2^16000]      */
700 #define __LIBM_SQRTL_K80(r,x,                               \
701                        t32,half,t1,t2,t3,t4,t5,t6,t7,t8,t9) \
702     if ( ((x)->ex & 1) == 1 ) {                             \
703         (x)->ex    = (x)->ex + 1;                           \
704         (x)->ldhi *= half;                                  \
705         (x)->ldlo *= half;                                  \
706     }                                                       \
707     (r)->ex = (x)->ex >> 1;                                 \
708     __LIBM_SQRTL2_NORM_K80( (r)->ldhi,(r)->ldlo,            \
709         (x)->ldhi,(x)->ldlo,                                \
710         t32,half,t1,t2,t3,t4,t5,t6,t7,t8,t9)
711 
712 /* Square root: r=sqrt(x)                                   */
713 /* Variables r,x,y are pointers to struct ker80,            */
714 /* all other variables are in long double precision         */
715 /* Here t32 is the constant 2^32+1                          */
716 /*      half is the constant 0.5                            */
717 /* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8,t9          */
718 /* Correct for any positive x                               */
719 #define __LIBM_SQRTL_NORM_K80(r,x,                          \
720                        t32,half,t1,t2,t3,t4,t5,t6,t7,t8,t9) \
721     if ( ((x)->fphi.exponent-BIAS_80<-16000) ||             \
722          ((x)->fphi.exponent-BIAS_80>+16000) )              \
723     {                                                       \
724         __libm_normalizel_k80(x);                           \
725     }                                                       \
726     __LIBM_SQRTL_K80(r,x, t32,half,t1,t2,t3,t4,t5,t6,t7,t8,t9)
727 
728 
729 #ifdef __INTEL_COMPILER
730 #define ALIGN(n) __declspec(align(n))
731 #else /* __INTEL_COMPILER */
732 #define ALIGN(n)
733 #endif /* __INTEL_COMPILER */
734 
735 /* macros to form a long double value in hex representation (unsigned short type) */
736 
737 #if (defined(__unix__) && defined(__i386__))
738 # define LDOUBLE_ALIGN 12	/* IA32 Linux: 12-byte alignment */
739 #else	/*__linux__ & IA32*/
740 # define LDOUBLE_ALIGN 16	/* EFI2/IA32 Win or IPF Win/Linux: 16-byte alignment */
741 #endif	/*__linux__ & IA32*/
742 
743 #if (LDOUBLE_ALIGN == 16)
744 #define _XPD_ ,0x0000,0x0000,0x0000
745 #else /*12*/
746 #define _XPD_ ,0x0000
747 #endif
748 
749 #define LDOUBLE_HEX(w4,w3,w2,w1,w0) 0x##w0,0x##w1,0x##w2,0x##w3,0x##w4 _XPD_ /*LITTLE_ENDIAN*/
750 
751 /* macros to sign-expand low 'num' bits of 'val' to native integer */
752 
753 #if defined(SIZE_INT_32)
754 # define SIGN_EXPAND(val,num)  ((int)(val) << (32-(num))) >> (32-(num)) /* sign expand of 'num' LSBs */
755 #elif defined(SIZE_INT_64)
756 # define SIGN_EXPAND(val,num)  ((int)(val) << (64-(num))) >> (64-(num)) /* sign expand of 'num' LSBs */
757 #endif
758 
759 /* macros to form pointers to FP number on-the-fly */
760 
761 #define FP32(f)  ((struct fp32 *)&f)
762 #define FP64(d)  ((struct fp64 *)&d)
763 #define FP80(ld) ((struct fp80 *)&ld)
764 
765 /* macros to extract signed low and high doubleword of long double */
766 
767 #if defined(SIZE_INT_32)
768 # define HI_DWORD_80(ld) ((((FP80(ld)->sign << 15) | FP80(ld)->exponent) << 16) | \
769                           ((FP80(ld)->hi_significand >> 16) & 0xFFFF))
770 # define LO_DWORD_80(ld) SIGN_EXPAND(FP80(ld)->lo_significand, 32)
771 #elif defined(SIZE_INT_64)
772 # define HI_DWORD_80(ld) ((((FP80(ld)->sign << 15) | FP80(ld)->exponent) << 16) | \
773                           ((FP80(ld)->significand >> 48) & 0xFFFF))
774 # define LO_DWORD_80(ld) SIGN_EXPAND(FP80(ld)->significand, 32)
775 #endif
776 
777 /* macros to extract hi bits of significand.
778  * note that explicit high bit do not count (returns as is)
779  */
780 
781 #if defined(SIZE_INT_32)
782 # define HI_SIGNIFICAND_80(X,NBITS) ((X)->hi_significand >> (31 - (NBITS)))
783 #elif defined(SIZE_INT_64)
784 # define HI_SIGNIFICAND_80(X,NBITS) ((X)->significand >> (63 - (NBITS)))
785 #endif
786 
787 /* macros to check, whether a significand bits are all zero, or some of them are non-zero.
788  * note that SIGNIFICAND_ZERO_80 tests high bit also, but SIGNIFICAND_NONZERO_80 does not
789  */
790 
791 #define SIGNIFICAND_ZERO_32(X)     ((X)->significand == 0)
792 #define SIGNIFICAND_NONZERO_32(X)  ((X)->significand != 0)
793 
794 #if defined(SIZE_INT_32)
795 # define SIGNIFICAND_ZERO_64(X)    (((X)->hi_significand == 0) && ((X)->lo_significand == 0))
796 # define SIGNIFICAND_NONZERO_64(X) (((X)->hi_significand != 0) || ((X)->lo_significand != 0))
797 #elif defined(SIZE_INT_64)
798 # define SIGNIFICAND_ZERO_64(X)    ((X)->significand == 0)
799 # define SIGNIFICAND_NONZERO_64(X) ((X)->significand != 0)
800 #endif
801 
802 #if defined(SIZE_INT_32)
803 # define SIGNIFICAND_ZERO_80(X)    (((X)->hi_significand == 0x00000000) && ((X)->lo_significand == 0))
804 # define SIGNIFICAND_NONZERO_80(X) (((X)->hi_significand != 0x80000000) || ((X)->lo_significand != 0))
805 #elif defined(SIZE_INT_64)
806 # define SIGNIFICAND_ZERO_80(X)    ((X)->significand == 0x0000000000000000)
807 # define SIGNIFICAND_NONZERO_80(X) ((X)->significand != 0x8000000000000000)
808 #endif
809 
810 /* macros to compare long double with constant value, represented as hex */
811 
812 #define SIGNIFICAND_EQ_HEX_32(X,BITS) ((X)->significand == 0x ## BITS)
813 #define SIGNIFICAND_GT_HEX_32(X,BITS) ((X)->significand >  0x ## BITS)
814 #define SIGNIFICAND_GE_HEX_32(X,BITS) ((X)->significand >= 0x ## BITS)
815 #define SIGNIFICAND_LT_HEX_32(X,BITS) ((X)->significand <  0x ## BITS)
816 #define SIGNIFICAND_LE_HEX_32(X,BITS) ((X)->significand <= 0x ## BITS)
817 
818 #if defined(SIZE_INT_32)
819 # define SIGNIFICAND_EQ_HEX_64(X,HI,LO) \
820     (((X)->hi_significand == 0x ## HI) && ((X)->lo_significand == 0x ## LO))
821 # define SIGNIFICAND_GT_HEX_64(X,HI,LO) (((X)->hi_significand > 0x ## HI) || \
822     (((X)->hi_significand == 0x ## HI) && ((X)->lo_significand >  0x ## LO)))
823 # define SIGNIFICAND_GE_HEX_64(X,HI,LO) (((X)->hi_significand > 0x ## HI) || \
824     (((X)->hi_significand == 0x ## HI) && ((X)->lo_significand >= 0x ## LO)))
825 # define SIGNIFICAND_LT_HEX_64(X,HI,LO) (((X)->hi_significand < 0x ## HI) || \
826     (((X)->hi_significand == 0x ## HI) && ((X)->lo_significand <  0x ## LO)))
827 # define SIGNIFICAND_LE_HEX_64(X,HI,LO) (((X)->hi_significand < 0x ## HI) || \
828     (((X)->hi_significand == 0x ## HI) && ((X)->lo_significand <= 0x ## LO)))
829 #elif defined(SIZE_INT_64)
830 # define SIGNIFICAND_EQ_HEX_64(X,HI,LO) ((X)->significand == 0x ## HI ## LO)
831 # define SIGNIFICAND_GT_HEX_64(X,HI,LO) ((X)->significand >  0x ## HI ## LO)
832 # define SIGNIFICAND_GE_HEX_64(X,HI,LO) ((X)->significand >= 0x ## HI ## LO)
833 # define SIGNIFICAND_LT_HEX_64(X,HI,LO) ((X)->significand <  0x ## HI ## LO)
834 # define SIGNIFICAND_LE_HEX_64(X,HI,LO) ((X)->significand <= 0x ## HI ## LO)
835 #endif
836 
837 #if defined(SIZE_INT_32)
838 # define SIGNIFICAND_EQ_HEX_80(X,HI,LO) \
839     (((X)->hi_significand == 0x ## HI) && ((X)->lo_significand == 0x ## LO))
840 # define SIGNIFICAND_GT_HEX_80(X,HI,LO) (((X)->hi_significand > 0x ## HI) || \
841     (((X)->hi_significand == 0x ## HI) && ((X)->lo_significand >  0x ## LO)))
842 # define SIGNIFICAND_GE_HEX_80(X,HI,LO) (((X)->hi_significand > 0x ## HI) || \
843     (((X)->hi_significand == 0x ## HI) && ((X)->lo_significand >= 0x ## LO)))
844 # define SIGNIFICAND_LT_HEX_80(X,HI,LO) (((X)->hi_significand < 0x ## HI) || \
845     (((X)->hi_significand == 0x ## HI) && ((X)->lo_significand <  0x ## LO)))
846 # define SIGNIFICAND_LE_HEX_80(X,HI,LO) (((X)->hi_significand < 0x ## HI) || \
847     (((X)->hi_significand == 0x ## HI) && ((X)->lo_significand <= 0x ## LO)))
848 #elif defined(SIZE_INT_64)
849 # define SIGNIFICAND_EQ_HEX_80(X,HI,LO) ((X)->significand == 0x ## HI ## LO)
850 # define SIGNIFICAND_GT_HEX_80(X,HI,LO) ((X)->significand >  0x ## HI ## LO)
851 # define SIGNIFICAND_GE_HEX_80(X,HI,LO) ((X)->significand >= 0x ## HI ## LO)
852 # define SIGNIFICAND_LT_HEX_80(X,HI,LO) ((X)->significand <  0x ## HI ## LO)
853 # define SIGNIFICAND_LE_HEX_80(X,HI,LO) ((X)->significand <= 0x ## HI ## LO)
854 #endif
855 
856 #define VALUE_EQ_HEX_32(X,EXP,BITS) \
857    (((X)->exponent == (EXP)) && (SIGNIFICAND_EQ_HEX_32(X, BITS)))
858 #define VALUE_GT_HEX_32(X,EXP,BITS) (((X)->exponent > (EXP)) || \
859    (((X)->exponent == (EXP)) && (SIGNIFICAND_GT_HEX_32(X, BITS))))
860 #define VALUE_GE_HEX_32(X,EXP,BITS) (((X)->exponent > (EXP)) || \
861    (((X)->exponent == (EXP)) && (SIGNIFICAND_GE_HEX_32(X, BITS))))
862 #define VALUE_LT_HEX_32(X,EXP,BITS) (((X)->exponent < (EXP)) || \
863    (((X)->exponent == (EXP)) && (SIGNIFICAND_LT_HEX_32(X, BITS))))
864 #define VALUE_LE_HEX_32(X,EXP,BITS) (((X)->exponent < (EXP)) || \
865    (((X)->exponent == (EXP)) && (SIGNIFICAND_LE_HEX_32(X, BITS))))
866 
867 #define VALUE_EQ_HEX_64(X,EXP,HI,LO) \
868    (((X)->exponent == (EXP)) && (SIGNIFICAND_EQ_HEX_64(X, HI, LO)))
869 #define VALUE_GT_HEX_64(X,EXP,HI,LO) (((X)->exponent > (EXP)) || \
870    (((X)->exponent == (EXP)) && (SIGNIFICAND_GT_HEX_64(X, HI, LO))))
871 #define VALUE_GE_HEX_64(X,EXP,HI,LO) (((X)->exponent > (EXP)) || \
872    (((X)->exponent == (EXP)) && (SIGNIFICAND_GE_HEX_64(X, HI, LO))))
873 #define VALUE_LT_HEX_64(X,EXP,HI,LO) (((X)->exponent < (EXP)) || \
874    (((X)->exponent == (EXP)) && (SIGNIFICAND_LT_HEX_64(X, HI, LO))))
875 #define VALUE_LE_HEX_64(X,EXP,HI,LO) (((X)->exponent < (EXP)) || \
876    (((X)->exponent == (EXP)) && (SIGNIFICAND_LE_HEX_64(X, HI, LO))))
877 
878 #define VALUE_EQ_HEX_80(X,EXP,HI,LO) \
879    (((X)->exponent == (EXP)) && (SIGNIFICAND_EQ_HEX_80(X, HI, LO)))
880 #define VALUE_GT_HEX_80(X,EXP,HI,LO) (((X)->exponent > (EXP)) || \
881    (((X)->exponent == (EXP)) && (SIGNIFICAND_GT_HEX_80(X, HI, LO))))
882 #define VALUE_GE_HEX_80(X,EXP,HI,LO) (((X)->exponent > (EXP)) || \
883    (((X)->exponent == (EXP)) && (SIGNIFICAND_GE_HEX_80(X, HI, LO))))
884 #define VALUE_LT_HEX_80(X,EXP,HI,LO) (((X)->exponent < (EXP)) || \
885    (((X)->exponent == (EXP)) && (SIGNIFICAND_LT_HEX_80(X, HI, LO))))
886 #define VALUE_LE_HEX_80(X,EXP,HI,LO) (((X)->exponent < (EXP)) || \
887    (((X)->exponent == (EXP)) && (SIGNIFICAND_LE_HEX_80(X, HI, LO))))
888 
889 /* macros to compare two long doubles */
890 
891 #define SIGNIFICAND_EQ_32(X,Y) ((X)->significand == (Y)->significand)
892 #define SIGNIFICAND_GT_32(X,Y) ((X)->significand > (Y)->significand)
893 #define SIGNIFICAND_GE_32(X,Y) ((X)->significand >= (Y)->significand)
894 #define SIGNIFICAND_LT_32(X,Y) ((X)->significand < (Y)->significand)
895 #define SIGNIFICAND_LE_32(X,Y) ((X)->significand <= (Y)->significand)
896 
897 #if defined(SIZE_INT_32)
898 # define SIGNIFICAND_EQ_64(X,Y) \
899   (((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand == (Y)->lo_significand))
900 # define SIGNIFICAND_GT_64(X,Y) (((X)->hi_significand > (Y)->hi_significand) || \
901   (((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand >  (Y)->lo_significand)))
902 # define SIGNIFICAND_GE_64(X,Y) (((X)->hi_significand > (Y)->hi_significand) || \
903   (((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand >= (Y)->lo_significand)))
904 # define SIGNIFICAND_LT_64(X,Y) (((X)->hi_significand < (Y)->hi_significand) || \
905   (((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand <  (Y)->lo_significand)))
906 # define SIGNIFICAND_LE_64(X,Y) (((X)->hi_significand < (Y)->hi_significand) || \
907   (((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand <= (Y)->lo_significand)))
908 #elif defined(SIZE_INT_64)
909 # define SIGNIFICAND_EQ_64(X,Y) ((X)->significand == (Y)->significand)
910 # define SIGNIFICAND_GT_64(X,Y) ((X)->significand >  (Y)->significand)
911 # define SIGNIFICAND_GE_64(X,Y) ((X)->significand >= (Y)->significand)
912 # define SIGNIFICAND_LT_64(X,Y) ((X)->significand <  (Y)->significand)
913 # define SIGNIFICAND_LE_64(X,Y) ((X)->significand <= (Y)->significand)
914 #endif
915 
916 #if defined(SIZE_INT_32)
917 # define SIGNIFICAND_EQ_80(X,Y) \
918     (((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand == (Y)->lo_significand))
919 # define SIGNIFICAND_GT_80(X,Y) (((X)->hi_significand > (Y)->hi_significand) || \
920     (((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand >  (Y)->lo_significand)))
921 # define SIGNIFICAND_GE_80(X,Y) (((X)->hi_significand > (Y)->hi_significand) || \
922     (((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand >= (Y)->lo_significand)))
923 # define SIGNIFICAND_LT_80(X,Y) (((X)->hi_significand < (Y)->hi_significand) || \
924     (((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand <  (Y)->lo_significand)))
925 # define SIGNIFICAND_LE_80(X,Y) (((X)->hi_significand < (Y)->hi_significand) || \
926     (((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand <= (Y)->lo_significand)))
927 #elif defined(SIZE_INT_64)
928 # define SIGNIFICAND_EQ_80(X,Y) ((X)->significand == (Y)->significand)
929 # define SIGNIFICAND_GT_80(X,Y) ((X)->significand >  (Y)->significand)
930 # define SIGNIFICAND_GE_80(X,Y) ((X)->significand >= (Y)->significand)
931 # define SIGNIFICAND_LT_80(X,Y) ((X)->significand <  (Y)->significand)
932 # define SIGNIFICAND_LE_80(X,Y) ((X)->significand <= (Y)->significand)
933 #endif
934 
935 #define VALUE_EQ_32(X,Y) \
936    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_EQ_32(X, Y)))
937 #define VALUE_GT_32(X,Y) (((X)->exponent > (Y)->exponent) || \
938    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GT_32(X, Y))))
939 #define VALUE_GE_32(X,Y) (((X)->exponent > (Y)->exponent) || \
940    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GE_32(X, Y))))
941 #define VALUE_LT_32(X,Y) (((X)->exponent < (Y)->exponent) || \
942    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LT_32(X, Y))))
943 #define VALUE_LE_32(X,Y) (((X)->exponent < (Y)->exponent) || \
944    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LE_32(X, Y))))
945 
946 #define VALUE_EQ_64(X,Y) \
947    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_EQ_64(X, Y)))
948 #define VALUE_GT_64(X,Y) (((X)->exponent > (Y)->exponent) || \
949    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GT_64(X, Y))))
950 #define VALUE_GE_64(X,Y) (((X)->exponent > (Y)->exponent) || \
951    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GE_64(X, Y))))
952 #define VALUE_LT_64(X,Y) (((X)->exponent < (Y)->exponent) || \
953    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LT_64(X, Y))))
954 #define VALUE_LE_64(X,Y) (((X)->exponent < (Y)->exponent) || \
955    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LE_64(X, Y))))
956 
957 #define VALUE_EQ_80(X,Y) \
958    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_EQ_80(X, Y)))
959 #define VALUE_GT_80(X,Y) (((X)->exponent > (Y)->exponent) || \
960    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GT_80(X, Y))))
961 #define VALUE_GE_80(X,Y) (((X)->exponent > (Y)->exponent) || \
962    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GE_80(X, Y))))
963 #define VALUE_LT_80(X,Y) (((X)->exponent < (Y)->exponent) || \
964    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LT_80(X, Y))))
965 #define VALUE_LE_80(X,Y) (((X)->exponent < (Y)->exponent) || \
966    (((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LE_80(X, Y))))
967 
968 /* add/subtract 1 ulp macros */
969 
970 #if defined(SIZE_INT_32)
971 # define ADD_ULP_80(X) \
972     if ((++(X)->lo_significand == 0) && \
973         (++(X)->hi_significand == (((X)->exponent == 0) ? 0x80000000 : 0))) \
974     { \
975         (X)->hi_significand |= 0x80000000; \
976         ++(X)->exponent; \
977     }
978 # define SUB_ULP_80(X) \
979     if (--(X)->lo_significand == 0xFFFFFFFF) { \
980         --(X)->hi_significand; \
981         if (((X)->exponent != 0) && \
982             ((X)->hi_significand == 0x7FFFFFFF) && \
983             (--(X)->exponent != 0)) \
984         { \
985             (X)->hi_significand |= 0x80000000; \
986         } \
987     }
988 #elif defined(SIZE_INT_64)
989 # define ADD_ULP_80(X) \
990     if (++(X)->significand == (((X)->exponent == 0) ? 0x8000000000000000 : 0))) { \
991         (X)->significand |= 0x8000000000000000; \
992         ++(X)->exponent; \
993     }
994 # define SUB_ULP_80(X) \
995     { \
996         --(X)->significand; \
997         if (((X)->exponent != 0) && \
998             ((X)->significand == 0x7FFFFFFFFFFFFFFF) && \
999             (--(X)->exponent != 0)) \
1000         { \
1001             (X)->significand |= 0x8000000000000000; \
1002         } \
1003     }
1004 #endif
1005 
1006 
1007 /* */
1008 
1009 #define VOLATILE_32 /*volatile*/
1010 #define VOLATILE_64 /*volatile*/
1011 #define VOLATILE_80 /*volatile*/
1012 
1013 #define QUAD_TYPE _Quad
1014 
1015 #endif    /*__LIBM_SUPPORT_H_INCLUDED__*/
1016