1// -*- C++ -*-
2//===---------------------------- cmath -----------------------------------===//
3//
4//                     The LLVM Compiler Infrastructure
5//
6// This file is dual licensed under the MIT and the University of Illinois Open
7// Source Licenses. See LICENSE.TXT for details.
8//
9//===----------------------------------------------------------------------===//
10
11#ifndef _LIBCPP_CMATH
12#define _LIBCPP_CMATH
13
14/*
15    cmath synopsis
16
17Macros:
18
19    HUGE_VAL
20    HUGE_VALF               // C99
21    HUGE_VALL               // C99
22    INFINITY                // C99
23    NAN                     // C99
24    FP_INFINITE             // C99
25    FP_NAN                  // C99
26    FP_NORMAL               // C99
27    FP_SUBNORMAL            // C99
28    FP_ZERO                 // C99
29    FP_FAST_FMA             // C99
30    FP_FAST_FMAF            // C99
31    FP_FAST_FMAL            // C99
32    FP_ILOGB0               // C99
33    FP_ILOGBNAN             // C99
34    MATH_ERRNO              // C99
35    MATH_ERREXCEPT          // C99
36    math_errhandling        // C99
37
38namespace std
39{
40
41Types:
42
43    float_t                 // C99
44    double_t                // C99
45
46// C90
47
48floating_point abs(floating_point x);
49
50floating_point acos (arithmetic x);
51float          acosf(float x);
52long double    acosl(long double x);
53
54floating_point asin (arithmetic x);
55float          asinf(float x);
56long double    asinl(long double x);
57
58floating_point atan (arithmetic x);
59float          atanf(float x);
60long double    atanl(long double x);
61
62floating_point atan2 (arithmetic y, arithmetic x);
63float          atan2f(float y, float x);
64long double    atan2l(long double y, long double x);
65
66floating_point ceil (arithmetic x);
67float          ceilf(float x);
68long double    ceill(long double x);
69
70floating_point cos (arithmetic x);
71float          cosf(float x);
72long double    cosl(long double x);
73
74floating_point cosh (arithmetic x);
75float          coshf(float x);
76long double    coshl(long double x);
77
78floating_point exp (arithmetic x);
79float          expf(float x);
80long double    expl(long double x);
81
82floating_point fabs (arithmetic x);
83float          fabsf(float x);
84long double    fabsl(long double x);
85
86floating_point floor (arithmetic x);
87float          floorf(float x);
88long double    floorl(long double x);
89
90floating_point fmod (arithmetic x, arithmetic y);
91float          fmodf(float x, float y);
92long double    fmodl(long double x, long double y);
93
94floating_point frexp (arithmetic value, int* exp);
95float          frexpf(float value, int* exp);
96long double    frexpl(long double value, int* exp);
97
98floating_point ldexp (arithmetic value, int exp);
99float          ldexpf(float value, int exp);
100long double    ldexpl(long double value, int exp);
101
102floating_point log (arithmetic x);
103float          logf(float x);
104long double    logl(long double x);
105
106floating_point log10 (arithmetic x);
107float          log10f(float x);
108long double    log10l(long double x);
109
110floating_point modf (floating_point value, floating_point* iptr);
111float          modff(float value, float* iptr);
112long double    modfl(long double value, long double* iptr);
113
114floating_point pow (arithmetic x, arithmetic y);
115float          powf(float x, float y);
116long double    powl(long double x, long double y);
117
118floating_point sin (arithmetic x);
119float          sinf(float x);
120long double    sinl(long double x);
121
122floating_point sinh (arithmetic x);
123float          sinhf(float x);
124long double    sinhl(long double x);
125
126floating_point sqrt (arithmetic x);
127float          sqrtf(float x);
128long double    sqrtl(long double x);
129
130floating_point tan (arithmetic x);
131float          tanf(float x);
132long double    tanl(long double x);
133
134floating_point tanh (arithmetic x);
135float          tanhf(float x);
136long double    tanhl(long double x);
137
138//  C99
139
140bool signbit(arithmetic x);
141
142int fpclassify(arithmetic x);
143
144bool isfinite(arithmetic x);
145bool isinf(arithmetic x);
146bool isnan(arithmetic x);
147bool isnormal(arithmetic x);
148
149bool isgreater(arithmetic x, arithmetic y);
150bool isgreaterequal(arithmetic x, arithmetic y);
151bool isless(arithmetic x, arithmetic y);
152bool islessequal(arithmetic x, arithmetic y);
153bool islessgreater(arithmetic x, arithmetic y);
154bool isunordered(arithmetic x, arithmetic y);
155
156floating_point acosh (arithmetic x);
157float          acoshf(float x);
158long double    acoshl(long double x);
159
160floating_point asinh (arithmetic x);
161float          asinhf(float x);
162long double    asinhl(long double x);
163
164floating_point atanh (arithmetic x);
165float          atanhf(float x);
166long double    atanhl(long double x);
167
168floating_point cbrt (arithmetic x);
169float          cbrtf(float x);
170long double    cbrtl(long double x);
171
172floating_point copysign (arithmetic x, arithmetic y);
173float          copysignf(float x, float y);
174long double    copysignl(long double x, long double y);
175
176floating_point erf (arithmetic x);
177float          erff(float x);
178long double    erfl(long double x);
179
180floating_point erfc (arithmetic x);
181float          erfcf(float x);
182long double    erfcl(long double x);
183
184floating_point exp2 (arithmetic x);
185float          exp2f(float x);
186long double    exp2l(long double x);
187
188floating_point expm1 (arithmetic x);
189float          expm1f(float x);
190long double    expm1l(long double x);
191
192floating_point fdim (arithmetic x, arithmetic y);
193float          fdimf(float x, float y);
194long double    fdiml(long double x, long double y);
195
196floating_point fma (arithmetic x, arithmetic y, arithmetic z);
197float          fmaf(float x, float y, float z);
198long double    fmal(long double x, long double y, long double z);
199
200floating_point fmax (arithmetic x, arithmetic y);
201float          fmaxf(float x, float y);
202long double    fmaxl(long double x, long double y);
203
204floating_point fmin (arithmetic x, arithmetic y);
205float          fminf(float x, float y);
206long double    fminl(long double x, long double y);
207
208floating_point hypot (arithmetic x, arithmetic y);
209float          hypotf(float x, float y);
210long double    hypotl(long double x, long double y);
211
212double       hypot(double x, double y, double z);                // C++17
213float        hypot(float x, float y, float z);                   // C++17
214long double  hypot(long double x, long double y, long double z); // C++17
215
216int ilogb (arithmetic x);
217int ilogbf(float x);
218int ilogbl(long double x);
219
220floating_point lgamma (arithmetic x);
221float          lgammaf(float x);
222long double    lgammal(long double x);
223
224long long llrint (arithmetic x);
225long long llrintf(float x);
226long long llrintl(long double x);
227
228long long llround (arithmetic x);
229long long llroundf(float x);
230long long llroundl(long double x);
231
232floating_point log1p (arithmetic x);
233float          log1pf(float x);
234long double    log1pl(long double x);
235
236floating_point log2 (arithmetic x);
237float          log2f(float x);
238long double    log2l(long double x);
239
240floating_point logb (arithmetic x);
241float          logbf(float x);
242long double    logbl(long double x);
243
244long lrint (arithmetic x);
245long lrintf(float x);
246long lrintl(long double x);
247
248long lround (arithmetic x);
249long lroundf(float x);
250long lroundl(long double x);
251
252double      nan (const char* str);
253float       nanf(const char* str);
254long double nanl(const char* str);
255
256floating_point nearbyint (arithmetic x);
257float          nearbyintf(float x);
258long double    nearbyintl(long double x);
259
260floating_point nextafter (arithmetic x, arithmetic y);
261float          nextafterf(float x, float y);
262long double    nextafterl(long double x, long double y);
263
264floating_point nexttoward (arithmetic x, long double y);
265float          nexttowardf(float x, long double y);
266long double    nexttowardl(long double x, long double y);
267
268floating_point remainder (arithmetic x, arithmetic y);
269float          remainderf(float x, float y);
270long double    remainderl(long double x, long double y);
271
272floating_point remquo (arithmetic x, arithmetic y, int* pquo);
273float          remquof(float x, float y, int* pquo);
274long double    remquol(long double x, long double y, int* pquo);
275
276floating_point rint (arithmetic x);
277float          rintf(float x);
278long double    rintl(long double x);
279
280floating_point round (arithmetic x);
281float          roundf(float x);
282long double    roundl(long double x);
283
284floating_point scalbln (arithmetic x, long ex);
285float          scalblnf(float x, long ex);
286long double    scalblnl(long double x, long ex);
287
288floating_point scalbn (arithmetic x, int ex);
289float          scalbnf(float x, int ex);
290long double    scalbnl(long double x, int ex);
291
292floating_point tgamma (arithmetic x);
293float          tgammaf(float x);
294long double    tgammal(long double x);
295
296floating_point trunc (arithmetic x);
297float          truncf(float x);
298long double    truncl(long double x);
299
300}  // std
301
302*/
303
304#include <__config>
305#include <math.h>
306#include <version>
307#include <type_traits>
308
309#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
310#pragma GCC system_header
311#endif
312
313_LIBCPP_PUSH_MACROS
314#include <__undef_macros>
315
316_LIBCPP_BEGIN_NAMESPACE_STD
317
318using ::signbit;
319using ::fpclassify;
320using ::isfinite;
321using ::isinf;
322using ::isnan;
323using ::isnormal;
324using ::isgreater;
325using ::isgreaterequal;
326using ::isless;
327using ::islessequal;
328using ::islessgreater;
329using ::isunordered;
330using ::isunordered;
331
332using ::float_t;
333using ::double_t;
334
335#ifndef _AIX
336using ::abs;
337#endif
338
339using ::acos;
340using ::acosf;
341using ::asin;
342using ::asinf;
343using ::atan;
344using ::atanf;
345using ::atan2;
346using ::atan2f;
347using ::ceil;
348using ::ceilf;
349using ::cos;
350using ::cosf;
351using ::cosh;
352using ::coshf;
353
354using ::exp;
355using ::expf;
356
357using ::fabs;
358using ::fabsf;
359using ::floor;
360using ::floorf;
361
362using ::fmod;
363using ::fmodf;
364
365using ::frexp;
366using ::frexpf;
367using ::ldexp;
368using ::ldexpf;
369
370using ::log;
371using ::logf;
372
373using ::log10;
374using ::log10f;
375using ::modf;
376using ::modff;
377
378using ::pow;
379using ::powf;
380
381using ::sin;
382using ::sinf;
383using ::sinh;
384using ::sinhf;
385
386using ::sqrt;
387using ::sqrtf;
388using ::tan;
389using ::tanf;
390
391using ::tanh;
392using ::tanhf;
393
394using ::acosh;
395using ::acoshf;
396using ::asinh;
397using ::asinhf;
398using ::atanh;
399using ::atanhf;
400using ::cbrt;
401using ::cbrtf;
402
403using ::copysign;
404using ::copysignf;
405
406using ::erf;
407using ::erff;
408using ::erfc;
409using ::erfcf;
410using ::exp2;
411using ::exp2f;
412using ::expm1;
413using ::expm1f;
414using ::fdim;
415using ::fdimf;
416using ::fmaf;
417using ::fma;
418using ::fmax;
419using ::fmaxf;
420using ::fmin;
421using ::fminf;
422using ::hypot;
423using ::hypotf;
424using ::ilogb;
425using ::ilogbf;
426using ::lgamma;
427using ::lgammaf;
428using ::llrint;
429using ::llrintf;
430using ::llround;
431using ::llroundf;
432using ::log1p;
433using ::log1pf;
434using ::log2;
435using ::log2f;
436using ::logb;
437using ::logbf;
438using ::lrint;
439using ::lrintf;
440using ::lround;
441using ::lroundf;
442
443using ::nan;
444using ::nanf;
445
446using ::nearbyint;
447using ::nearbyintf;
448using ::nextafter;
449using ::nextafterf;
450using ::nexttoward;
451using ::nexttowardf;
452using ::remainder;
453using ::remainderf;
454using ::remquo;
455using ::remquof;
456using ::rint;
457using ::rintf;
458using ::round;
459using ::roundf;
460using ::scalbln;
461using ::scalblnf;
462using ::scalbn;
463using ::scalbnf;
464using ::tgamma;
465using ::tgammaf;
466using ::trunc;
467using ::truncf;
468
469using ::acosl;
470using ::asinl;
471using ::atanl;
472using ::atan2l;
473using ::ceill;
474using ::cosl;
475using ::coshl;
476using ::expl;
477using ::fabsl;
478using ::floorl;
479using ::fmodl;
480using ::frexpl;
481using ::ldexpl;
482using ::logl;
483using ::log10l;
484using ::modfl;
485using ::powl;
486using ::sinl;
487using ::sinhl;
488using ::sqrtl;
489using ::tanl;
490
491using ::tanhl;
492using ::acoshl;
493using ::asinhl;
494using ::atanhl;
495using ::cbrtl;
496
497using ::copysignl;
498
499using ::erfl;
500using ::erfcl;
501using ::exp2l;
502using ::expm1l;
503using ::fdiml;
504using ::fmal;
505using ::fmaxl;
506using ::fminl;
507using ::hypotl;
508using ::ilogbl;
509using ::lgammal;
510using ::llrintl;
511using ::llroundl;
512using ::log1pl;
513using ::log2l;
514using ::logbl;
515using ::lrintl;
516using ::lroundl;
517using ::nanl;
518using ::nearbyintl;
519using ::nextafterl;
520using ::nexttowardl;
521using ::remainderl;
522using ::remquol;
523using ::rintl;
524using ::roundl;
525using ::scalblnl;
526using ::scalbnl;
527using ::tgammal;
528using ::truncl;
529
530#if _LIBCPP_STD_VER > 14
531inline _LIBCPP_INLINE_VISIBILITY float       hypot(       float x,       float y,       float z ) { return sqrt(x*x + y*y + z*z); }
532inline _LIBCPP_INLINE_VISIBILITY double      hypot(      double x,      double y,      double z ) { return sqrt(x*x + y*y + z*z); }
533inline _LIBCPP_INLINE_VISIBILITY long double hypot( long double x, long double y, long double z ) { return sqrt(x*x + y*y + z*z); }
534
535template <class _A1, class _A2, class _A3>
536inline _LIBCPP_INLINE_VISIBILITY
537typename __lazy_enable_if
538<
539    is_arithmetic<_A1>::value &&
540    is_arithmetic<_A2>::value &&
541    is_arithmetic<_A3>::value,
542    __promote<_A1, _A2, _A3>
543>::type
544hypot(_A1 __lcpp_x, _A2 __lcpp_y, _A3 __lcpp_z) _NOEXCEPT
545{
546    typedef typename __promote<_A1, _A2, _A3>::type __result_type;
547    static_assert((!(is_same<_A1, __result_type>::value &&
548                     is_same<_A2, __result_type>::value &&
549                     is_same<_A3, __result_type>::value)), "");
550    return hypot((__result_type)__lcpp_x, (__result_type)__lcpp_y, (__result_type)__lcpp_z);
551}
552#endif
553
554template <class _A1>
555_LIBCPP_INLINE_VISIBILITY
556_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
557__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT
558{
559#if __has_builtin(__builtin_isnan)
560    return __builtin_isnan(__lcpp_x);
561#else
562    return isnan(__lcpp_x);
563#endif
564}
565
566template <class _A1>
567_LIBCPP_INLINE_VISIBILITY
568_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
569__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT
570{
571    return isnan(__lcpp_x);
572}
573
574template <class _A1>
575_LIBCPP_INLINE_VISIBILITY
576_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
577__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT
578{
579#if __has_builtin(__builtin_isinf)
580    return __builtin_isinf(__lcpp_x);
581#else
582    return isinf(__lcpp_x);
583#endif
584}
585
586template <class _A1>
587_LIBCPP_INLINE_VISIBILITY
588_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
589__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT
590{
591    return isinf(__lcpp_x);
592}
593
594template <class _A1>
595_LIBCPP_INLINE_VISIBILITY
596_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
597__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT
598{
599#if __has_builtin(__builtin_isfinite)
600    return __builtin_isfinite(__lcpp_x);
601#else
602    return isfinite(__lcpp_x);
603#endif
604}
605
606template <class _A1>
607_LIBCPP_INLINE_VISIBILITY
608_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
609__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT
610{
611    return isfinite(__lcpp_x);
612}
613
614template <class _IntT, class _FloatT,
615    bool _FloatBigger = (numeric_limits<_FloatT>::digits > numeric_limits<_IntT>::digits),
616    int _Bits = (numeric_limits<_IntT>::digits - numeric_limits<_FloatT>::digits)>
617_LIBCPP_INLINE_VISIBILITY
618_LIBCPP_CONSTEXPR _IntT __max_representable_int_for_float() _NOEXCEPT {
619  static_assert(is_floating_point<_FloatT>::value, "must be a floating point type");
620  static_assert(is_integral<_IntT>::value, "must be an integral type");
621  static_assert(numeric_limits<_FloatT>::radix == 2, "FloatT has incorrect radix");
622  static_assert(is_same<_FloatT, float>::value || is_same<_FloatT, double>::value
623               || is_same<_FloatT,long double>::value, "unsupported floating point type");
624  return _FloatBigger ? numeric_limits<_IntT>::max() :  (numeric_limits<_IntT>::max() >> _Bits << _Bits);
625}
626
627// Convert a floating point number to the specified integral type after
628// clamping to the integral types representable range.
629//
630// The behavior is undefined if `__r` is NaN.
631template <class _IntT, class _RealT>
632_LIBCPP_INLINE_VISIBILITY
633_IntT __clamp_to_integral(_RealT __r) _NOEXCEPT {
634  using _Lim = std::numeric_limits<_IntT>;
635  const _IntT _MaxVal = std::__max_representable_int_for_float<_IntT, _RealT>();
636  if (__r >= ::nextafter(static_cast<_RealT>(_MaxVal), INFINITY)) {
637    return _Lim::max();
638  } else if (__r <= _Lim::lowest()) {
639    return _Lim::min();
640  }
641  return static_cast<_IntT>(__r);
642}
643
644_LIBCPP_END_NAMESPACE_STD
645
646_LIBCPP_POP_MACROS
647
648#endif  // _LIBCPP_CMATH
649