This file is indexed.

/usr/mipsel-linux-gnu/include/math.h is in libc6-dev-mipsel-cross 2.27-3ubuntu1cross1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

   1
   2
   3
   4
   5
   6
   7
   8
   9
  10
  11
  12
  13
  14
  15
  16
  17
  18
  19
  20
  21
  22
  23
  24
  25
  26
  27
  28
  29
  30
  31
  32
  33
  34
  35
  36
  37
  38
  39
  40
  41
  42
  43
  44
  45
  46
  47
  48
  49
  50
  51
  52
  53
  54
  55
  56
  57
  58
  59
  60
  61
  62
  63
  64
  65
  66
  67
  68
  69
  70
  71
  72
  73
  74
  75
  76
  77
  78
  79
  80
  81
  82
  83
  84
  85
  86
  87
  88
  89
  90
  91
  92
  93
  94
  95
  96
  97
  98
  99
 100
 101
 102
 103
 104
 105
 106
 107
 108
 109
 110
 111
 112
 113
 114
 115
 116
 117
 118
 119
 120
 121
 122
 123
 124
 125
 126
 127
 128
 129
 130
 131
 132
 133
 134
 135
 136
 137
 138
 139
 140
 141
 142
 143
 144
 145
 146
 147
 148
 149
 150
 151
 152
 153
 154
 155
 156
 157
 158
 159
 160
 161
 162
 163
 164
 165
 166
 167
 168
 169
 170
 171
 172
 173
 174
 175
 176
 177
 178
 179
 180
 181
 182
 183
 184
 185
 186
 187
 188
 189
 190
 191
 192
 193
 194
 195
 196
 197
 198
 199
 200
 201
 202
 203
 204
 205
 206
 207
 208
 209
 210
 211
 212
 213
 214
 215
 216
 217
 218
 219
 220
 221
 222
 223
 224
 225
 226
 227
 228
 229
 230
 231
 232
 233
 234
 235
 236
 237
 238
 239
 240
 241
 242
 243
 244
 245
 246
 247
 248
 249
 250
 251
 252
 253
 254
 255
 256
 257
 258
 259
 260
 261
 262
 263
 264
 265
 266
 267
 268
 269
 270
 271
 272
 273
 274
 275
 276
 277
 278
 279
 280
 281
 282
 283
 284
 285
 286
 287
 288
 289
 290
 291
 292
 293
 294
 295
 296
 297
 298
 299
 300
 301
 302
 303
 304
 305
 306
 307
 308
 309
 310
 311
 312
 313
 314
 315
 316
 317
 318
 319
 320
 321
 322
 323
 324
 325
 326
 327
 328
 329
 330
 331
 332
 333
 334
 335
 336
 337
 338
 339
 340
 341
 342
 343
 344
 345
 346
 347
 348
 349
 350
 351
 352
 353
 354
 355
 356
 357
 358
 359
 360
 361
 362
 363
 364
 365
 366
 367
 368
 369
 370
 371
 372
 373
 374
 375
 376
 377
 378
 379
 380
 381
 382
 383
 384
 385
 386
 387
 388
 389
 390
 391
 392
 393
 394
 395
 396
 397
 398
 399
 400
 401
 402
 403
 404
 405
 406
 407
 408
 409
 410
 411
 412
 413
 414
 415
 416
 417
 418
 419
 420
 421
 422
 423
 424
 425
 426
 427
 428
 429
 430
 431
 432
 433
 434
 435
 436
 437
 438
 439
 440
 441
 442
 443
 444
 445
 446
 447
 448
 449
 450
 451
 452
 453
 454
 455
 456
 457
 458
 459
 460
 461
 462
 463
 464
 465
 466
 467
 468
 469
 470
 471
 472
 473
 474
 475
 476
 477
 478
 479
 480
 481
 482
 483
 484
 485
 486
 487
 488
 489
 490
 491
 492
 493
 494
 495
 496
 497
 498
 499
 500
 501
 502
 503
 504
 505
 506
 507
 508
 509
 510
 511
 512
 513
 514
 515
 516
 517
 518
 519
 520
 521
 522
 523
 524
 525
 526
 527
 528
 529
 530
 531
 532
 533
 534
 535
 536
 537
 538
 539
 540
 541
 542
 543
 544
 545
 546
 547
 548
 549
 550
 551
 552
 553
 554
 555
 556
 557
 558
 559
 560
 561
 562
 563
 564
 565
 566
 567
 568
 569
 570
 571
 572
 573
 574
 575
 576
 577
 578
 579
 580
 581
 582
 583
 584
 585
 586
 587
 588
 589
 590
 591
 592
 593
 594
 595
 596
 597
 598
 599
 600
 601
 602
 603
 604
 605
 606
 607
 608
 609
 610
 611
 612
 613
 614
 615
 616
 617
 618
 619
 620
 621
 622
 623
 624
 625
 626
 627
 628
 629
 630
 631
 632
 633
 634
 635
 636
 637
 638
 639
 640
 641
 642
 643
 644
 645
 646
 647
 648
 649
 650
 651
 652
 653
 654
 655
 656
 657
 658
 659
 660
 661
 662
 663
 664
 665
 666
 667
 668
 669
 670
 671
 672
 673
 674
 675
 676
 677
 678
 679
 680
 681
 682
 683
 684
 685
 686
 687
 688
 689
 690
 691
 692
 693
 694
 695
 696
 697
 698
 699
 700
 701
 702
 703
 704
 705
 706
 707
 708
 709
 710
 711
 712
 713
 714
 715
 716
 717
 718
 719
 720
 721
 722
 723
 724
 725
 726
 727
 728
 729
 730
 731
 732
 733
 734
 735
 736
 737
 738
 739
 740
 741
 742
 743
 744
 745
 746
 747
 748
 749
 750
 751
 752
 753
 754
 755
 756
 757
 758
 759
 760
 761
 762
 763
 764
 765
 766
 767
 768
 769
 770
 771
 772
 773
 774
 775
 776
 777
 778
 779
 780
 781
 782
 783
 784
 785
 786
 787
 788
 789
 790
 791
 792
 793
 794
 795
 796
 797
 798
 799
 800
 801
 802
 803
 804
 805
 806
 807
 808
 809
 810
 811
 812
 813
 814
 815
 816
 817
 818
 819
 820
 821
 822
 823
 824
 825
 826
 827
 828
 829
 830
 831
 832
 833
 834
 835
 836
 837
 838
 839
 840
 841
 842
 843
 844
 845
 846
 847
 848
 849
 850
 851
 852
 853
 854
 855
 856
 857
 858
 859
 860
 861
 862
 863
 864
 865
 866
 867
 868
 869
 870
 871
 872
 873
 874
 875
 876
 877
 878
 879
 880
 881
 882
 883
 884
 885
 886
 887
 888
 889
 890
 891
 892
 893
 894
 895
 896
 897
 898
 899
 900
 901
 902
 903
 904
 905
 906
 907
 908
 909
 910
 911
 912
 913
 914
 915
 916
 917
 918
 919
 920
 921
 922
 923
 924
 925
 926
 927
 928
 929
 930
 931
 932
 933
 934
 935
 936
 937
 938
 939
 940
 941
 942
 943
 944
 945
 946
 947
 948
 949
 950
 951
 952
 953
 954
 955
 956
 957
 958
 959
 960
 961
 962
 963
 964
 965
 966
 967
 968
 969
 970
 971
 972
 973
 974
 975
 976
 977
 978
 979
 980
 981
 982
 983
 984
 985
 986
 987
 988
 989
 990
 991
 992
 993
 994
 995
 996
 997
 998
 999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
/* Declarations for math functions.
   Copyright (C) 1991-2018 Free Software Foundation, Inc.
   This file is part of the GNU C Library.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, see
   <http://www.gnu.org/licenses/>.  */

/*
 *	ISO C99 Standard: 7.12 Mathematics	<math.h>
 */

#ifndef	_MATH_H
#define	_MATH_H	1

#define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
#include <bits/libc-header-start.h>

#if defined log && defined __GNUC__
# warning A macro called log was already defined when <math.h> was included.
# warning This will cause compilation problems.
#endif

__BEGIN_DECLS

/* Get definitions of __intmax_t and __uintmax_t.  */
#include <bits/types.h>

/* Get machine-dependent vector math functions declarations.  */
#include <bits/math-vector.h>

/* Gather machine dependent type support.  */
#include <bits/floatn.h>

/* Value returned on overflow.  With IEEE 754 floating point, this is
   +Infinity, otherwise the largest representable positive value.  */
#if __GNUC_PREREQ (3, 3)
# define HUGE_VAL (__builtin_huge_val ())
#else
/* This may provoke compiler warnings, and may not be rounded to
   +Infinity in all IEEE 754 rounding modes, but is the best that can
   be done in ISO C while remaining a constant expression.  10,000 is
   greater than the maximum (decimal) exponent for all supported
   floating-point formats and widths.  */
# define HUGE_VAL 1e10000
#endif
#ifdef __USE_ISOC99
# if __GNUC_PREREQ (3, 3)
#  define HUGE_VALF (__builtin_huge_valf ())
#  define HUGE_VALL (__builtin_huge_vall ())
# else
#  define HUGE_VALF 1e10000f
#  define HUGE_VALL 1e10000L
# endif
#endif
#if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define HUGE_VAL_F16 (__builtin_huge_valf16 ())
#endif
#if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define HUGE_VAL_F32 (__builtin_huge_valf32 ())
#endif
#if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define HUGE_VAL_F64 (__builtin_huge_valf64 ())
#endif
#if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define HUGE_VAL_F128 (__builtin_huge_valf128 ())
#endif
#if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define HUGE_VAL_F32X (__builtin_huge_valf32x ())
#endif
#if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define HUGE_VAL_F64X (__builtin_huge_valf64x ())
#endif
#if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define HUGE_VAL_F128X (__builtin_huge_valf128x ())
#endif

#ifdef __USE_ISOC99
/* IEEE positive infinity.  */
# if __GNUC_PREREQ (3, 3)
#  define INFINITY (__builtin_inff ())
# else
#  define INFINITY HUGE_VALF
# endif

/* IEEE Not A Number.  */
# if __GNUC_PREREQ (3, 3)
#  define NAN (__builtin_nanf (""))
# else
/* This will raise an "invalid" exception outside static initializers,
   but is the best that can be done in ISO C while remaining a
   constant expression.  */
#  define NAN (0.0f / 0.0f)
# endif
#endif /* __USE_ISOC99 */

#if __GLIBC_USE (IEC_60559_BFP_EXT)
/* Signaling NaN macros, if supported.  */
# if __GNUC_PREREQ (3, 3)
#  define SNANF (__builtin_nansf (""))
#  define SNAN (__builtin_nans (""))
#  define SNANL (__builtin_nansl (""))
# endif
#endif
#if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define SNANF16 (__builtin_nansf16 (""))
#endif
#if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define SNANF32 (__builtin_nansf32 (""))
#endif
#if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define SNANF64 (__builtin_nansf64 (""))
#endif
#if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define SNANF128 (__builtin_nansf128 (""))
#endif
#if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define SNANF32X (__builtin_nansf32x (""))
#endif
#if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define SNANF64X (__builtin_nansf64x (""))
#endif
#if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)
# define SNANF128X (__builtin_nansf128x (""))
#endif

/* Get __GLIBC_FLT_EVAL_METHOD.  */
#include <bits/flt-eval-method.h>

#ifdef __USE_ISOC99
/* Define the following typedefs.

    float_t	floating-point type at least as wide as `float' used
		to evaluate `float' expressions
    double_t	floating-point type at least as wide as `double' used
		to evaluate `double' expressions
*/
# if __GLIBC_FLT_EVAL_METHOD == 0 || __GLIBC_FLT_EVAL_METHOD == 16
typedef float float_t;
typedef double double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 1
typedef double float_t;
typedef double double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 2
typedef long double float_t;
typedef long double double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 32
typedef _Float32 float_t;
typedef double double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 33
typedef _Float32x float_t;
typedef _Float32x double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 64
typedef _Float64 float_t;
typedef _Float64 double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 65
typedef _Float64x float_t;
typedef _Float64x double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 128
typedef _Float128 float_t;
typedef _Float128 double_t;
# elif __GLIBC_FLT_EVAL_METHOD == 129
typedef _Float128x float_t;
typedef _Float128x double_t;
# else
#  error "Unknown __GLIBC_FLT_EVAL_METHOD"
# endif
#endif

/* Define macros for the return values of ilogb and llogb, based on
   __FP_LOGB0_IS_MIN and __FP_LOGBNAN_IS_MIN.

    FP_ILOGB0	Expands to a value returned by `ilogb (0.0)'.
    FP_ILOGBNAN	Expands to a value returned by `ilogb (NAN)'.
    FP_LLOGB0	Expands to a value returned by `llogb (0.0)'.
    FP_LLOGBNAN	Expands to a value returned by `llogb (NAN)'.

*/

#include <bits/fp-logb.h>
#ifdef __USE_ISOC99
# if __FP_LOGB0_IS_MIN
#  define FP_ILOGB0	(-2147483647 - 1)
# else
#  define FP_ILOGB0	(-2147483647)
# endif
# if __FP_LOGBNAN_IS_MIN
#  define FP_ILOGBNAN	(-2147483647 - 1)
# else
#  define FP_ILOGBNAN	2147483647
# endif
#endif
#if __GLIBC_USE (IEC_60559_BFP_EXT)
# if __WORDSIZE == 32
#  define __FP_LONG_MAX 0x7fffffffL
# else
#  define __FP_LONG_MAX 0x7fffffffffffffffL
# endif
# if __FP_LOGB0_IS_MIN
#  define FP_LLOGB0	(-__FP_LONG_MAX - 1)
# else
#  define FP_LLOGB0	(-__FP_LONG_MAX)
# endif
# if __FP_LOGBNAN_IS_MIN
#  define FP_LLOGBNAN	(-__FP_LONG_MAX - 1)
# else
#  define FP_LLOGBNAN	__FP_LONG_MAX
# endif
#endif

/* Get the architecture specific values describing the floating-point
   evaluation.  The following symbols will get defined:

    FP_FAST_FMA
    FP_FAST_FMAF
    FP_FAST_FMAL
		If defined it indicates that the `fma' function
		generally executes about as fast as a multiply and an add.
		This macro is defined only iff the `fma' function is
		implemented directly with a hardware multiply-add instructions.
*/

#include <bits/fp-fast.h>

#if __GLIBC_USE (IEC_60559_BFP_EXT)
/* Rounding direction macros for fromfp functions.  */
enum
  {
    FP_INT_UPWARD =
# define FP_INT_UPWARD 0
      FP_INT_UPWARD,
    FP_INT_DOWNWARD =
# define FP_INT_DOWNWARD 1
      FP_INT_DOWNWARD,
    FP_INT_TOWARDZERO =
# define FP_INT_TOWARDZERO 2
      FP_INT_TOWARDZERO,
    FP_INT_TONEARESTFROMZERO =
# define FP_INT_TONEARESTFROMZERO 3
      FP_INT_TONEARESTFROMZERO,
    FP_INT_TONEAREST =
# define FP_INT_TONEAREST 4
      FP_INT_TONEAREST,
  };
#endif

/* The file <bits/mathcalls.h> contains the prototypes for all the
   actual math functions.  These macros are used for those prototypes,
   so we can easily declare each function as both `name' and `__name',
   and can declare the float versions `namef' and `__namef'.  */

#define __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)

#define __MATHCALL_VEC(function, suffix, args) 	\
  __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
  __MATHCALL (function, suffix, args)

#define __MATHDECL_VEC(type, function,suffix, args) \
  __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
  __MATHDECL(type, function,suffix, args)

#define __MATHCALL(function,suffix, args)	\
  __MATHDECL (_Mdouble_,function,suffix, args)
#define __MATHDECL(type, function,suffix, args) \
  __MATHDECL_1(type, function,suffix, args); \
  __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
#define __MATHCALLX(function,suffix, args, attrib)	\
  __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
#define __MATHDECLX(type, function,suffix, args, attrib) \
  __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
  __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
#define __MATHDECL_1(type, function,suffix, args) \
  extern type __MATH_PRECNAME(function,suffix) args __THROW

#define _Mdouble_		double
#define __MATH_PRECNAME(name,r)	__CONCAT(name,r)
#define __MATH_DECLARING_DOUBLE  1
#define __MATH_DECLARING_FLOATN  0
#include <bits/mathcalls-helper-functions.h>
#include <bits/mathcalls.h>
#undef	_Mdouble_
#undef	__MATH_PRECNAME
#undef __MATH_DECLARING_DOUBLE
#undef __MATH_DECLARING_FLOATN

#ifdef __USE_ISOC99


/* Include the file of declarations again, this time using `float'
   instead of `double' and appending f to each function name.  */

# define _Mdouble_		float
# define __MATH_PRECNAME(name,r) name##f##r
# define __MATH_DECLARING_DOUBLE  0
# define __MATH_DECLARING_FLOATN  0
# include <bits/mathcalls-helper-functions.h>
# include <bits/mathcalls.h>
# undef	_Mdouble_
# undef	__MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN

# if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
     || defined __LDBL_COMPAT \
     || defined _LIBC_TEST
#  ifdef __LDBL_COMPAT

#   ifdef __USE_ISOC99
extern float __nldbl_nexttowardf (float __x, long double __y)
				  __THROW __attribute__ ((__const__));
#    ifdef __REDIRECT_NTH
extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
			     __nldbl_nexttowardf)
     __attribute__ ((__const__));
extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
			      nextafter) __attribute__ ((__const__));
extern long double __REDIRECT_NTH (nexttowardl,
				   (long double __x, long double __y),
				   nextafter) __attribute__ ((__const__));
#    endif
#   endif

#   undef __MATHDECL_1
#   define __MATHDECL_2(type, function,suffix, args, alias) \
  extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
			     args, alias)
#   define __MATHDECL_1(type, function,suffix, args) \
  __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
#  endif

/* Include the file of declarations again, this time using `long double'
   instead of `double' and appending l to each function name.  */

#  define _Mdouble_		long double
#  define __MATH_PRECNAME(name,r) name##l##r
#  define __MATH_DECLARING_DOUBLE  0
#  define __MATH_DECLARING_FLOATN  0
#  define __MATH_DECLARE_LDOUBLE   1
#  include <bits/mathcalls-helper-functions.h>
#  include <bits/mathcalls.h>
#  undef _Mdouble_
#  undef __MATH_PRECNAME
#  undef __MATH_DECLARING_DOUBLE
#  undef __MATH_DECLARING_FLOATN

# endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */

#endif	/* Use ISO C99.  */

/* Include the file of declarations for _FloatN and _FloatNx
   types.  */

#if __HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !defined _LIBC)
# define _Mdouble_		_Float16
# define __MATH_PRECNAME(name,r) name##f16##r
# define __MATH_DECLARING_DOUBLE  0
# define __MATH_DECLARING_FLOATN  1
# if __HAVE_DISTINCT_FLOAT16
#  include <bits/mathcalls-helper-functions.h>
# endif
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
#  include <bits/mathcalls.h>
# endif
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
#endif /* __HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !_LIBC).  */

#if __HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !defined _LIBC)
# define _Mdouble_		_Float32
# define __MATH_PRECNAME(name,r) name##f32##r
# define __MATH_DECLARING_DOUBLE  0
# define __MATH_DECLARING_FLOATN  1
# if __HAVE_DISTINCT_FLOAT32
#  include <bits/mathcalls-helper-functions.h>
# endif
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
#  include <bits/mathcalls.h>
# endif
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
#endif /* __HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !_LIBC).  */

#if __HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !defined _LIBC)
# define _Mdouble_		_Float64
# define __MATH_PRECNAME(name,r) name##f64##r
# define __MATH_DECLARING_DOUBLE  0
# define __MATH_DECLARING_FLOATN  1
# if __HAVE_DISTINCT_FLOAT64
#  include <bits/mathcalls-helper-functions.h>
# endif
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
#  include <bits/mathcalls.h>
# endif
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
#endif /* __HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !_LIBC).  */

#if __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC)
# define _Mdouble_		_Float128
# define __MATH_PRECNAME(name,r) name##f128##r
# define __MATH_DECLARING_DOUBLE  0
# define __MATH_DECLARING_FLOATN  1
# if __HAVE_DISTINCT_FLOAT128
#  include <bits/mathcalls-helper-functions.h>
# endif
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
#  include <bits/mathcalls.h>
# endif
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
#endif /* __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !_LIBC).  */

#if __HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !defined _LIBC)
# define _Mdouble_		_Float32x
# define __MATH_PRECNAME(name,r) name##f32x##r
# define __MATH_DECLARING_DOUBLE  0
# define __MATH_DECLARING_FLOATN  1
# if __HAVE_DISTINCT_FLOAT32X
#  include <bits/mathcalls-helper-functions.h>
# endif
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
#  include <bits/mathcalls.h>
# endif
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
#endif /* __HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !_LIBC).  */

#if __HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !defined _LIBC)
# define _Mdouble_		_Float64x
# define __MATH_PRECNAME(name,r) name##f64x##r
# define __MATH_DECLARING_DOUBLE  0
# define __MATH_DECLARING_FLOATN  1
# if __HAVE_DISTINCT_FLOAT64X
#  include <bits/mathcalls-helper-functions.h>
# endif
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
#  include <bits/mathcalls.h>
# endif
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
#endif /* __HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !_LIBC).  */

#if __HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !defined _LIBC)
# define _Mdouble_		_Float128x
# define __MATH_PRECNAME(name,r) name##f128x##r
# define __MATH_DECLARING_DOUBLE  0
# define __MATH_DECLARING_FLOATN  1
# if __HAVE_DISTINCT_FLOAT128X
#  include <bits/mathcalls-helper-functions.h>
# endif
# if __GLIBC_USE (IEC_60559_TYPES_EXT)
#  include <bits/mathcalls.h>
# endif
# undef _Mdouble_
# undef __MATH_PRECNAME
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
#endif /* __HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !_LIBC).  */

#undef	__MATHDECL_1
#undef	__MATHDECL
#undef	__MATHCALL


#if defined __USE_MISC || defined __USE_XOPEN
/* This variable is used by `gamma' and `lgamma'.  */
extern int signgam;
#endif

#if (__HAVE_DISTINCT_FLOAT16			\
     || __HAVE_DISTINCT_FLOAT32			\
     || __HAVE_DISTINCT_FLOAT64			\
     || __HAVE_DISTINCT_FLOAT32X		\
     || __HAVE_DISTINCT_FLOAT64X		\
     || __HAVE_DISTINCT_FLOAT128X)
# error "Unsupported _FloatN or _FloatNx types for <math.h>."
#endif

/* Depending on the type of TG_ARG, call an appropriately suffixed
   version of FUNC with arguments (including parentheses) ARGS.
   Suffixed functions may not exist for long double if it has the same
   format as double, or for other types with the same format as float,
   double or long double.  The behavior is undefined if the argument
   does not have a real floating type.  The definition may use a
   conditional expression, so all suffixed versions of FUNC must
   return the same type (FUNC may include a cast if necessary rather
   than being a single identifier).  */
#ifdef __NO_LONG_DOUBLE_MATH
# if __HAVE_DISTINCT_FLOAT128
#  error "Distinct _Float128 without distinct long double not supported."
# endif
# define __MATH_TG(TG_ARG, FUNC, ARGS)					\
  (sizeof (TG_ARG) == sizeof (float) ? FUNC ## f ARGS : FUNC ARGS)
#elif __HAVE_DISTINCT_FLOAT128
# if __HAVE_GENERIC_SELECTION
#  if __HAVE_FLOATN_NOT_TYPEDEF && __HAVE_FLOAT32
#   define __MATH_TG_F32(FUNC, ARGS) _Float32: FUNC ## f ARGS,
#  else
#   define __MATH_TG_F32(FUNC, ARGS)
#  endif
#  if __HAVE_FLOATN_NOT_TYPEDEF && __HAVE_FLOAT64X
#   if __HAVE_FLOAT64X_LONG_DOUBLE
#    define __MATH_TG_F64X(FUNC, ARGS) _Float64x: FUNC ## l ARGS,
#   else
#    define __MATH_TG_F64X(FUNC, ARGS) _Float64x: FUNC ## f128 ARGS,
#   endif
#  else
#   define __MATH_TG_F64X(FUNC, ARGS)
#  endif
#  define __MATH_TG(TG_ARG, FUNC, ARGS)	\
     _Generic ((TG_ARG),			\
	       float: FUNC ## f ARGS,		\
	       __MATH_TG_F32 (FUNC, ARGS)	\
	       default: FUNC ARGS,		\
	       long double: FUNC ## l ARGS,	\
	       __MATH_TG_F64X (FUNC, ARGS)	\
	       _Float128: FUNC ## f128 ARGS)
# else
#  if __HAVE_FLOATN_NOT_TYPEDEF
#   error "Non-typedef _FloatN but no _Generic."
#  endif
#  define __MATH_TG(TG_ARG, FUNC, ARGS)					\
     __builtin_choose_expr						\
     (__builtin_types_compatible_p (__typeof (TG_ARG), float),		\
      FUNC ## f ARGS,							\
      __builtin_choose_expr						\
      (__builtin_types_compatible_p (__typeof (TG_ARG), double),	\
       FUNC ARGS,							\
       __builtin_choose_expr						\
       (__builtin_types_compatible_p (__typeof (TG_ARG), long double),	\
	FUNC ## l ARGS,							\
	FUNC ## f128 ARGS)))
# endif
#else
# define __MATH_TG(TG_ARG, FUNC, ARGS)		\
  (sizeof (TG_ARG) == sizeof (float)		\
   ? FUNC ## f ARGS				\
   : sizeof (TG_ARG) == sizeof (double)		\
   ? FUNC ARGS					\
   : FUNC ## l ARGS)
#endif

/* ISO C99 defines some generic macros which work on any data type.  */
#ifdef __USE_ISOC99

/* All floating-point numbers can be put in one of these categories.  */
enum
  {
    FP_NAN =
# define FP_NAN 0
      FP_NAN,
    FP_INFINITE =
# define FP_INFINITE 1
      FP_INFINITE,
    FP_ZERO =
# define FP_ZERO 2
      FP_ZERO,
    FP_SUBNORMAL =
# define FP_SUBNORMAL 3
      FP_SUBNORMAL,
    FP_NORMAL =
# define FP_NORMAL 4
      FP_NORMAL
  };

/* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
   so disable builtins if this is enabled.  When fixed in a newer GCC,
   the __SUPPORT_SNAN__ check may be skipped for those versions.  */

/* Return number of classification appropriate for X.  */
# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__			      \
     && (!defined __OPTIMIZE_SIZE__ || defined __cplusplus)
     /* The check for __cplusplus allows the use of the builtin, even
	when optimization for size is on.  This is provided for
	libstdc++, only to let its configure test work when it is built
	with -Os.  No further use of this definition of fpclassify is
	expected in C++ mode, since libstdc++ provides its own version
	of fpclassify in cmath (which undefines fpclassify).  */
#  define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE,	      \
     FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
# else
#  define fpclassify(x) __MATH_TG ((x), __fpclassify, (x))
# endif

/* Return nonzero value if sign of X is negative.  */
# if __GNUC_PREREQ (6,0)
#  define signbit(x) __builtin_signbit (x)
# elif defined __cplusplus
  /* In C++ mode, __MATH_TG cannot be used, because it relies on
     __builtin_types_compatible_p, which is a C-only builtin.
     The check for __cplusplus allows the use of the builtin instead of
     __MATH_TG. This is provided for libstdc++, only to let its configure
     test work. No further use of this definition of signbit is expected
     in C++ mode, since libstdc++ provides its own version of signbit
     in cmath (which undefines signbit). */
#  define signbit(x) __builtin_signbitl (x)
# elif __GNUC_PREREQ (4,0)
#  define signbit(x) __MATH_TG ((x), __builtin_signbit, (x))
# else
#  define signbit(x) __MATH_TG ((x), __signbit, (x))
# endif

/* Return nonzero value if X is not +-Inf or NaN.  */
# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
#  define isfinite(x) __builtin_isfinite (x)
# else
#  define isfinite(x) __MATH_TG ((x), __finite, (x))
# endif

/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
#  define isnormal(x) __builtin_isnormal (x)
# else
#  define isnormal(x) (fpclassify (x) == FP_NORMAL)
# endif

/* Return nonzero value if X is a NaN.  We could use `fpclassify' but
   we already have this functions `__isnan' and it is faster.  */
# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
#  define isnan(x) __builtin_isnan (x)
# else
#  define isnan(x) __MATH_TG ((x), __isnan, (x))
# endif

/* Return nonzero value if X is positive or negative infinity.  */
# if __HAVE_DISTINCT_FLOAT128 && !__GNUC_PREREQ (7,0) \
     && !defined __SUPPORT_SNAN__ && !defined __cplusplus
   /* Since __builtin_isinf_sign is broken for float128 before GCC 7.0,
      use the helper function, __isinff128, with older compilers.  This is
      only provided for C mode, because in C++ mode, GCC has no support
      for __builtin_types_compatible_p (and when in C++ mode, this macro is
      not used anyway, because libstdc++ headers undefine it).  */
#  define isinf(x) \
    (__builtin_types_compatible_p (__typeof (x), _Float128) \
     ? __isinff128 (x) : __builtin_isinf_sign (x))
# elif __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
#  define isinf(x) __builtin_isinf_sign (x)
# else
#  define isinf(x) __MATH_TG ((x), __isinf, (x))
# endif

/* Bitmasks for the math_errhandling macro.  */
# define MATH_ERRNO	1	/* errno set by math functions.  */
# define MATH_ERREXCEPT	2	/* Exceptions raised by math functions.  */

/* By default all math functions support both errno and exception handling
   (except for soft floating point implementations which may only support
   errno handling).  If errno handling is disabled, exceptions are still
   supported by GLIBC.  Set math_errhandling to 0 with -ffast-math (this is
   nonconforming but it is more useful than leaving it undefined).  */
# ifdef __FAST_MATH__
#  define math_errhandling	0
# elif defined __NO_MATH_ERRNO__
#  define math_errhandling	(MATH_ERREXCEPT)
# else
#  define math_errhandling	(MATH_ERRNO | MATH_ERREXCEPT)
# endif

#endif /* Use ISO C99.  */

#if __GLIBC_USE (IEC_60559_BFP_EXT)
# include <bits/iscanonical.h>

/* Return nonzero value if X is a signaling NaN.  */
# ifndef __cplusplus
#  define issignaling(x) __MATH_TG ((x), __issignaling, (x))
# else
   /* In C++ mode, __MATH_TG cannot be used, because it relies on
      __builtin_types_compatible_p, which is a C-only builtin.  On the
      other hand, overloading provides the means to distinguish between
      the floating-point types.  The overloading resolution will match
      the correct parameter (regardless of type qualifiers (i.e.: const
      and volatile)).  */
extern "C++" {
inline int issignaling (float __val) { return __issignalingf (__val); }
inline int issignaling (double __val) { return __issignaling (__val); }
inline int
issignaling (long double __val)
{
#  ifdef __NO_LONG_DOUBLE_MATH
  return __issignaling (__val);
#  else
  return __issignalingl (__val);
#  endif
}
#  if __HAVE_DISTINCT_FLOAT128
inline int issignaling (_Float128 __val) { return __issignalingf128 (__val); }
#  endif
} /* extern C++ */
# endif

/* Return nonzero value if X is subnormal.  */
# define issubnormal(x) (fpclassify (x) == FP_SUBNORMAL)

/* Return nonzero value if X is zero.  */
# ifndef __cplusplus
#  ifdef __SUPPORT_SNAN__
#   define iszero(x) (fpclassify (x) == FP_ZERO)
#  else
#   define iszero(x) (((__typeof (x)) (x)) == 0)
#  endif
# else	/* __cplusplus */
extern "C++" {
#  ifdef __SUPPORT_SNAN__
inline int
iszero (float __val)
{
  return __fpclassifyf (__val) == FP_ZERO;
}
inline int
iszero (double __val)
{
  return __fpclassify (__val) == FP_ZERO;
}
inline int
iszero (long double __val)
{
#   ifdef __NO_LONG_DOUBLE_MATH
  return __fpclassify (__val) == FP_ZERO;
#   else
  return __fpclassifyl (__val) == FP_ZERO;
#   endif
}
#   if __HAVE_DISTINCT_FLOAT128
inline int
iszero (_Float128 __val)
{
  return __fpclassifyf128 (__val) == FP_ZERO;
}
#   endif
#  else
template <class __T> inline bool
iszero (__T __val)
{
  return __val == 0;
}
#  endif
} /* extern C++ */
# endif	/* __cplusplus */
#endif /* Use IEC_60559_BFP_EXT.  */

#ifdef __USE_XOPEN
/* X/Open wants another strange constant.  */
# define MAXFLOAT	3.40282347e+38F
#endif


/* Some useful constants.  */
#if defined __USE_MISC || defined __USE_XOPEN
# define M_E		2.7182818284590452354	/* e */
# define M_LOG2E	1.4426950408889634074	/* log_2 e */
# define M_LOG10E	0.43429448190325182765	/* log_10 e */
# define M_LN2		0.69314718055994530942	/* log_e 2 */
# define M_LN10		2.30258509299404568402	/* log_e 10 */
# define M_PI		3.14159265358979323846	/* pi */
# define M_PI_2		1.57079632679489661923	/* pi/2 */
# define M_PI_4		0.78539816339744830962	/* pi/4 */
# define M_1_PI		0.31830988618379067154	/* 1/pi */
# define M_2_PI		0.63661977236758134308	/* 2/pi */
# define M_2_SQRTPI	1.12837916709551257390	/* 2/sqrt(pi) */
# define M_SQRT2	1.41421356237309504880	/* sqrt(2) */
# define M_SQRT1_2	0.70710678118654752440	/* 1/sqrt(2) */
#endif

/* The above constants are not adequate for computation using `long double's.
   Therefore we provide as an extension constants with similar names as a
   GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
#ifdef __USE_GNU
# define M_El		2.718281828459045235360287471352662498L /* e */
# define M_LOG2El	1.442695040888963407359924681001892137L /* log_2 e */
# define M_LOG10El	0.434294481903251827651128918916605082L /* log_10 e */
# define M_LN2l		0.693147180559945309417232121458176568L /* log_e 2 */
# define M_LN10l	2.302585092994045684017991454684364208L /* log_e 10 */
# define M_PIl		3.141592653589793238462643383279502884L /* pi */
# define M_PI_2l	1.570796326794896619231321691639751442L /* pi/2 */
# define M_PI_4l	0.785398163397448309615660845819875721L /* pi/4 */
# define M_1_PIl	0.318309886183790671537767526745028724L /* 1/pi */
# define M_2_PIl	0.636619772367581343075535053490057448L /* 2/pi */
# define M_2_SQRTPIl	1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
# define M_SQRT2l	1.414213562373095048801688724209698079L /* sqrt(2) */
# define M_SQRT1_2l	0.707106781186547524400844362104849039L /* 1/sqrt(2) */
#endif

#if __HAVE_FLOAT16 && defined __USE_GNU
# define M_Ef16		__f16 (2.718281828459045235360287471352662498) /* e */
# define M_LOG2Ef16	__f16 (1.442695040888963407359924681001892137) /* log_2 e */
# define M_LOG10Ef16	__f16 (0.434294481903251827651128918916605082) /* log_10 e */
# define M_LN2f16	__f16 (0.693147180559945309417232121458176568) /* log_e 2 */
# define M_LN10f16	__f16 (2.302585092994045684017991454684364208) /* log_e 10 */
# define M_PIf16	__f16 (3.141592653589793238462643383279502884) /* pi */
# define M_PI_2f16	__f16 (1.570796326794896619231321691639751442) /* pi/2 */
# define M_PI_4f16	__f16 (0.785398163397448309615660845819875721) /* pi/4 */
# define M_1_PIf16	__f16 (0.318309886183790671537767526745028724) /* 1/pi */
# define M_2_PIf16	__f16 (0.636619772367581343075535053490057448) /* 2/pi */
# define M_2_SQRTPIf16	__f16 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
# define M_SQRT2f16	__f16 (1.414213562373095048801688724209698079) /* sqrt(2) */
# define M_SQRT1_2f16	__f16 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
#endif

#if __HAVE_FLOAT32 && defined __USE_GNU
# define M_Ef32		__f32 (2.718281828459045235360287471352662498) /* e */
# define M_LOG2Ef32	__f32 (1.442695040888963407359924681001892137) /* log_2 e */
# define M_LOG10Ef32	__f32 (0.434294481903251827651128918916605082) /* log_10 e */
# define M_LN2f32	__f32 (0.693147180559945309417232121458176568) /* log_e 2 */
# define M_LN10f32	__f32 (2.302585092994045684017991454684364208) /* log_e 10 */
# define M_PIf32	__f32 (3.141592653589793238462643383279502884) /* pi */
# define M_PI_2f32	__f32 (1.570796326794896619231321691639751442) /* pi/2 */
# define M_PI_4f32	__f32 (0.785398163397448309615660845819875721) /* pi/4 */
# define M_1_PIf32	__f32 (0.318309886183790671537767526745028724) /* 1/pi */
# define M_2_PIf32	__f32 (0.636619772367581343075535053490057448) /* 2/pi */
# define M_2_SQRTPIf32	__f32 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
# define M_SQRT2f32	__f32 (1.414213562373095048801688724209698079) /* sqrt(2) */
# define M_SQRT1_2f32	__f32 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
#endif

#if __HAVE_FLOAT64 && defined __USE_GNU
# define M_Ef64		__f64 (2.718281828459045235360287471352662498) /* e */
# define M_LOG2Ef64	__f64 (1.442695040888963407359924681001892137) /* log_2 e */
# define M_LOG10Ef64	__f64 (0.434294481903251827651128918916605082) /* log_10 e */
# define M_LN2f64	__f64 (0.693147180559945309417232121458176568) /* log_e 2 */
# define M_LN10f64	__f64 (2.302585092994045684017991454684364208) /* log_e 10 */
# define M_PIf64	__f64 (3.141592653589793238462643383279502884) /* pi */
# define M_PI_2f64	__f64 (1.570796326794896619231321691639751442) /* pi/2 */
# define M_PI_4f64	__f64 (0.785398163397448309615660845819875721) /* pi/4 */
# define M_1_PIf64	__f64 (0.318309886183790671537767526745028724) /* 1/pi */
# define M_2_PIf64	__f64 (0.636619772367581343075535053490057448) /* 2/pi */
# define M_2_SQRTPIf64	__f64 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
# define M_SQRT2f64	__f64 (1.414213562373095048801688724209698079) /* sqrt(2) */
# define M_SQRT1_2f64	__f64 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
#endif

#if __HAVE_FLOAT128 && defined __USE_GNU
# define M_Ef128	__f128 (2.718281828459045235360287471352662498) /* e */
# define M_LOG2Ef128	__f128 (1.442695040888963407359924681001892137) /* log_2 e */
# define M_LOG10Ef128	__f128 (0.434294481903251827651128918916605082) /* log_10 e */
# define M_LN2f128	__f128 (0.693147180559945309417232121458176568) /* log_e 2 */
# define M_LN10f128	__f128 (2.302585092994045684017991454684364208) /* log_e 10 */
# define M_PIf128	__f128 (3.141592653589793238462643383279502884) /* pi */
# define M_PI_2f128	__f128 (1.570796326794896619231321691639751442) /* pi/2 */
# define M_PI_4f128	__f128 (0.785398163397448309615660845819875721) /* pi/4 */
# define M_1_PIf128	__f128 (0.318309886183790671537767526745028724) /* 1/pi */
# define M_2_PIf128	__f128 (0.636619772367581343075535053490057448) /* 2/pi */
# define M_2_SQRTPIf128	__f128 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
# define M_SQRT2f128	__f128 (1.414213562373095048801688724209698079) /* sqrt(2) */
# define M_SQRT1_2f128	__f128 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
#endif

#if __HAVE_FLOAT32X && defined __USE_GNU
# define M_Ef32x	__f32x (2.718281828459045235360287471352662498) /* e */
# define M_LOG2Ef32x	__f32x (1.442695040888963407359924681001892137) /* log_2 e */
# define M_LOG10Ef32x	__f32x (0.434294481903251827651128918916605082) /* log_10 e */
# define M_LN2f32x	__f32x (0.693147180559945309417232121458176568) /* log_e 2 */
# define M_LN10f32x	__f32x (2.302585092994045684017991454684364208) /* log_e 10 */
# define M_PIf32x	__f32x (3.141592653589793238462643383279502884) /* pi */
# define M_PI_2f32x	__f32x (1.570796326794896619231321691639751442) /* pi/2 */
# define M_PI_4f32x	__f32x (0.785398163397448309615660845819875721) /* pi/4 */
# define M_1_PIf32x	__f32x (0.318309886183790671537767526745028724) /* 1/pi */
# define M_2_PIf32x	__f32x (0.636619772367581343075535053490057448) /* 2/pi */
# define M_2_SQRTPIf32x	__f32x (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
# define M_SQRT2f32x	__f32x (1.414213562373095048801688724209698079) /* sqrt(2) */
# define M_SQRT1_2f32x	__f32x (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
#endif

#if __HAVE_FLOAT64X && defined __USE_GNU
# define M_Ef64x	__f64x (2.718281828459045235360287471352662498) /* e */
# define M_LOG2Ef64x	__f64x (1.442695040888963407359924681001892137) /* log_2 e */
# define M_LOG10Ef64x	__f64x (0.434294481903251827651128918916605082) /* log_10 e */
# define M_LN2f64x	__f64x (0.693147180559945309417232121458176568) /* log_e 2 */
# define M_LN10f64x	__f64x (2.302585092994045684017991454684364208) /* log_e 10 */
# define M_PIf64x	__f64x (3.141592653589793238462643383279502884) /* pi */
# define M_PI_2f64x	__f64x (1.570796326794896619231321691639751442) /* pi/2 */
# define M_PI_4f64x	__f64x (0.785398163397448309615660845819875721) /* pi/4 */
# define M_1_PIf64x	__f64x (0.318309886183790671537767526745028724) /* 1/pi */
# define M_2_PIf64x	__f64x (0.636619772367581343075535053490057448) /* 2/pi */
# define M_2_SQRTPIf64x	__f64x (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
# define M_SQRT2f64x	__f64x (1.414213562373095048801688724209698079) /* sqrt(2) */
# define M_SQRT1_2f64x	__f64x (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
#endif

#if __HAVE_FLOAT128X && defined __USE_GNU
# error "M_* values needed for _Float128x"
#endif

/* When compiling in strict ISO C compatible mode we must not use the
   inline functions since they, among other things, do not set the
   `errno' variable correctly.  */
#if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
# define __NO_MATH_INLINES	1
#endif

#ifdef __USE_ISOC99
# if __GNUC_PREREQ (3, 1)
/* ISO C99 defines some macros to compare number while taking care for
   unordered numbers.  Many FPUs provide special instructions to support
   these operations.  Generic support in GCC for these as builtins went
   in 2.97, but not all cpus added their patterns until 3.1.  Therefore
   we enable the builtins from 3.1 onwards and use a generic implementation
   othwerwise.  */
#  define isgreater(x, y)	__builtin_isgreater(x, y)
#  define isgreaterequal(x, y)	__builtin_isgreaterequal(x, y)
#  define isless(x, y)		__builtin_isless(x, y)
#  define islessequal(x, y)	__builtin_islessequal(x, y)
#  define islessgreater(x, y)	__builtin_islessgreater(x, y)
#  define isunordered(x, y)	__builtin_isunordered(x, y)
# else
#  define isgreater(x, y) \
  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
		    !isunordered (__x, __y) && __x > __y; }))
#  define isgreaterequal(x, y) \
  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
		    !isunordered (__x, __y) && __x >= __y; }))
#  define isless(x, y) \
  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
		    !isunordered (__x, __y) && __x < __y; }))
#  define islessequal(x, y) \
  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
		    !isunordered (__x, __y) && __x <= __y; }))
#  define islessgreater(x, y) \
  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
		    !isunordered (__x, __y) && __x != __y; }))
/* isunordered must always check both operands first for signaling NaNs.  */
#  define isunordered(x, y) \
  (__extension__ ({ __typeof__ (x) __u = (x); __typeof__ (y) __v = (y); \
		    __u != __v && (__u != __u || __v != __v); }))
# endif
#endif

/* Get machine-dependent inline versions (if there are any).  */
#ifdef __USE_EXTERN_INLINES
# include <bits/mathinline.h>
#endif

/* Define special entry points to use when the compiler got told to
   only expect finite results.  */
#if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0

/* Include bits/math-finite.h for double.  */
# define _Mdouble_ double
# define __MATH_DECLARING_DOUBLE 1
# define __MATH_DECLARING_FLOATN 0
# define __REDIRFROM_X(function, reentrant) \
  function ## reentrant
# define __REDIRTO_X(function, reentrant) \
   __ ## function ## reentrant ## _finite
# include <bits/math-finite.h>
# undef _Mdouble_
# undef __MATH_DECLARING_DOUBLE
# undef __MATH_DECLARING_FLOATN
# undef __REDIRFROM_X
# undef __REDIRTO_X

/* When __USE_ISOC99 is defined, include math-finite for float and
   long double, as well.  */
# ifdef __USE_ISOC99

/* Include bits/math-finite.h for float.  */
#  define _Mdouble_ float
#  define __MATH_DECLARING_DOUBLE 0
#  define __MATH_DECLARING_FLOATN 0
#  define __REDIRFROM_X(function, reentrant) \
  function ## f ## reentrant
#  define __REDIRTO_X(function, reentrant) \
   __ ## function ## f ## reentrant ## _finite
#  include <bits/math-finite.h>
#  undef _Mdouble_
#  undef __MATH_DECLARING_DOUBLE
#  undef __MATH_DECLARING_FLOATN
#  undef __REDIRFROM_X
#  undef __REDIRTO_X

/* Include bits/math-finite.h for long double.  */
#  ifdef __MATH_DECLARE_LDOUBLE
#   define _Mdouble_ long double
#   define __MATH_DECLARING_DOUBLE 0
#   define __MATH_DECLARING_FLOATN 0
#   define __REDIRFROM_X(function, reentrant) \
  function ## l ## reentrant
#   ifdef __NO_LONG_DOUBLE_MATH
#    define __REDIRTO_X(function, reentrant) \
   __ ## function ## reentrant ## _finite
#   else
#    define __REDIRTO_X(function, reentrant) \
   __ ## function ## l ## reentrant ## _finite
#   endif
#   include <bits/math-finite.h>
#   undef _Mdouble_
#   undef __MATH_DECLARING_DOUBLE
#   undef __MATH_DECLARING_FLOATN
#   undef __REDIRFROM_X
#   undef __REDIRTO_X
#  endif

# endif /* __USE_ISOC99.  */

/* Include bits/math-finite.h for _FloatN and _FloatNx.  */

# if (__HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !defined _LIBC))	\
      && __GLIBC_USE (IEC_60559_TYPES_EXT)
#  define _Mdouble_ _Float16
#  define __MATH_DECLARING_DOUBLE 0
#  define __MATH_DECLARING_FLOATN 1
#  define __REDIRFROM_X(function, reentrant) \
  function ## f16 ## reentrant
#  if __HAVE_DISTINCT_FLOAT16
#   define __REDIRTO_X(function, reentrant) \
   __ ## function ## f16 ## reentrant ## _finite
#  else
#   error "non-disinct _Float16"
#  endif
#  include <bits/math-finite.h>
#  undef _Mdouble_
#  undef __MATH_DECLARING_DOUBLE
#  undef __MATH_DECLARING_FLOATN
#  undef __REDIRFROM_X
#  undef __REDIRTO_X
# endif

# if (__HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !defined _LIBC))	\
      && __GLIBC_USE (IEC_60559_TYPES_EXT)
#  define _Mdouble_ _Float32
#  define __MATH_DECLARING_DOUBLE 0
#  define __MATH_DECLARING_FLOATN 1
#  define __REDIRFROM_X(function, reentrant) \
  function ## f32 ## reentrant
#  if __HAVE_DISTINCT_FLOAT32
#   define __REDIRTO_X(function, reentrant) \
   __ ## function ## f32 ## reentrant ## _finite
#  else
#   define __REDIRTO_X(function, reentrant) \
   __ ## function ## f ## reentrant ## _finite
#  endif
#  include <bits/math-finite.h>
#  undef _Mdouble_
#  undef __MATH_DECLARING_DOUBLE
#  undef __MATH_DECLARING_FLOATN
#  undef __REDIRFROM_X
#  undef __REDIRTO_X
# endif

# if (__HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !defined _LIBC))	\
      && __GLIBC_USE (IEC_60559_TYPES_EXT)
#  define _Mdouble_ _Float64
#  define __MATH_DECLARING_DOUBLE 0
#  define __MATH_DECLARING_FLOATN 1
#  define __REDIRFROM_X(function, reentrant) \
  function ## f64 ## reentrant
#  if __HAVE_DISTINCT_FLOAT64
#   define __REDIRTO_X(function, reentrant) \
   __ ## function ## f64 ## reentrant ## _finite
#  else
#   define __REDIRTO_X(function, reentrant) \
   __ ## function ## reentrant ## _finite
#  endif
#  include <bits/math-finite.h>
#  undef _Mdouble_
#  undef __MATH_DECLARING_DOUBLE
#  undef __MATH_DECLARING_FLOATN
#  undef __REDIRFROM_X
#  undef __REDIRTO_X
# endif

# if (__HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC))	\
      && __GLIBC_USE (IEC_60559_TYPES_EXT)
#  define _Mdouble_ _Float128
#  define __MATH_DECLARING_DOUBLE 0
#  define __MATH_DECLARING_FLOATN 1
#  define __REDIRFROM_X(function, reentrant) \
  function ## f128 ## reentrant
#  if __HAVE_DISTINCT_FLOAT128
#   define __REDIRTO_X(function, reentrant) \
   __ ## function ## f128 ## reentrant ## _finite
#  else
#   define __REDIRTO_X(function, reentrant) \
   __ ## function ## l ## reentrant ## _finite
#  endif
#  include <bits/math-finite.h>
#  undef _Mdouble_
#  undef __MATH_DECLARING_DOUBLE
#  undef __MATH_DECLARING_FLOATN
#  undef __REDIRFROM_X
#  undef __REDIRTO_X
# endif

# if (__HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !defined _LIBC))	\
      && __GLIBC_USE (IEC_60559_TYPES_EXT)
#  define _Mdouble_ _Float32x
#  define __MATH_DECLARING_DOUBLE 0
#  define __MATH_DECLARING_FLOATN 1
#  define __REDIRFROM_X(function, reentrant) \
  function ## f32x ## reentrant
#  if __HAVE_DISTINCT_FLOAT32X
#   define __REDIRTO_X(function, reentrant) \
   __ ## function ## f32x ## reentrant ## _finite
#  else
#   define __REDIRTO_X(function, reentrant) \
   __ ## function ## reentrant ## _finite
#  endif
#  include <bits/math-finite.h>
#  undef _Mdouble_
#  undef __MATH_DECLARING_DOUBLE
#  undef __MATH_DECLARING_FLOATN
#  undef __REDIRFROM_X
#  undef __REDIRTO_X
# endif

# if (__HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !defined _LIBC))	\
      && __GLIBC_USE (IEC_60559_TYPES_EXT)
#  define _Mdouble_ _Float64x
#  define __MATH_DECLARING_DOUBLE 0
#  define __MATH_DECLARING_FLOATN 1
#  define __REDIRFROM_X(function, reentrant) \
  function ## f64x ## reentrant
#  if __HAVE_DISTINCT_FLOAT64X
#   define __REDIRTO_X(function, reentrant) \
   __ ## function ## f64x ## reentrant ## _finite
#  elif __HAVE_FLOAT64X_LONG_DOUBLE
#   define __REDIRTO_X(function, reentrant) \
   __ ## function ## l ## reentrant ## _finite
#  else
#   define __REDIRTO_X(function, reentrant) \
   __ ## function ## f128 ## reentrant ## _finite
#  endif
#  include <bits/math-finite.h>
#  undef _Mdouble_
#  undef __MATH_DECLARING_DOUBLE
#  undef __MATH_DECLARING_FLOATN
#  undef __REDIRFROM_X
#  undef __REDIRTO_X
# endif

# if (__HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !defined _LIBC)) \
      && __GLIBC_USE (IEC_60559_TYPES_EXT)
#  define _Mdouble_ _Float128x
#  define __MATH_DECLARING_DOUBLE 0
#  define __MATH_DECLARING_FLOATN 1
#  define __REDIRFROM_X(function, reentrant) \
  function ## f128x ## reentrant
#  if __HAVE_DISTINCT_FLOAT128X
#   define __REDIRTO_X(function, reentrant) \
   __ ## function ## f128x ## reentrant ## _finite
#  else
#   error "non-disinct _Float128x"
#  endif
#  include <bits/math-finite.h>
#  undef _Mdouble_
#  undef __MATH_DECLARING_DOUBLE
#  undef __MATH_DECLARING_FLOATN
#  undef __REDIRFROM_X
#  undef __REDIRTO_X
# endif

#endif /* __FINITE_MATH_ONLY__ > 0.  */

#if __GLIBC_USE (IEC_60559_BFP_EXT)
/* An expression whose type has the widest of the evaluation formats
   of X and Y (which are of floating-point types).  */
# if __FLT_EVAL_METHOD__ == 2 || __FLT_EVAL_METHOD__ > 64
#  define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0L)
# elif __FLT_EVAL_METHOD__ == 1 || __FLT_EVAL_METHOD__ > 32
#  define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0)
# elif __FLT_EVAL_METHOD__ == 0 || __FLT_EVAL_METHOD__ == 32
#  define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0f)
# else
#  define __MATH_EVAL_FMT2(x, y) ((x) + (y))
# endif

/* Return X == Y but raising "invalid" and setting errno if X or Y is
   a NaN.  */
# if !defined __cplusplus || (__cplusplus < 201103L && !defined __GNUC__)
#  define iseqsig(x, y) \
   __MATH_TG (__MATH_EVAL_FMT2 (x, y), __iseqsig, ((x), (y)))
# else
/* In C++ mode, __MATH_TG cannot be used, because it relies on
   __builtin_types_compatible_p, which is a C-only builtin.  Moreover,
   the comparison macros from ISO C take two floating-point arguments,
   which need not have the same type.  Choosing what underlying function
   to call requires evaluating the formats of the arguments, then
   selecting which is wider.  The macro __MATH_EVAL_FMT2 provides this
   information, however, only the type of the macro expansion is
   relevant (actually evaluating the expression would be incorrect).
   Thus, the type is used as a template parameter for __iseqsig_type,
   which calls the appropriate underlying function.  */
extern "C++" {
template<typename> struct __iseqsig_type;

template<> struct __iseqsig_type<float>
{
  static int __call (float __x, float __y) throw ()
  {
    return __iseqsigf (__x, __y);
  }
};

template<> struct __iseqsig_type<double>
{
  static int __call (double __x, double __y) throw ()
  {
    return __iseqsig (__x, __y);
  }
};

template<> struct __iseqsig_type<long double>
{
  static int __call (double __x, double __y) throw ()
  {
#  ifndef __NO_LONG_DOUBLE_MATH
    return __iseqsigl (__x, __y);
#  else
    return __iseqsig (__x, __y);
#  endif
  }
};

#  if __HAVE_DISTINCT_FLOAT128
template<> struct __iseqsig_type<_Float128>
{
  static int __call (_Float128 __x, _Float128 __y) throw ()
  {
    return __iseqsigf128 (__x, __y);
  }
};
#  endif

template<typename _T1, typename _T2>
inline int
iseqsig (_T1 __x, _T2 __y) throw ()
{
#  if __cplusplus >= 201103L
  typedef decltype (__MATH_EVAL_FMT2 (__x, __y)) _T3;
#  else
  typedef __typeof (__MATH_EVAL_FMT2 (__x, __y)) _T3;
#  endif
  return __iseqsig_type<_T3>::__call (__x, __y);
}

} /* extern "C++" */
# endif /* __cplusplus */

#endif

__END_DECLS


#endif /* math.h  */