xref: /llvm-project-15.0.7/libcxx/include/cmath (revision e8b659fc) 
1// -*- C++ -*-
2//===---------------------------- cmath -----------------------------------===//
3//
4// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5// See https://llvm.org/LICENSE.txt for license information.
6// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
7//
8//===----------------------------------------------------------------------===//
9
10#ifndef _LIBCPP_CMATH
11#define _LIBCPP_CMATH
12
13/*
14    cmath synopsis
15
16Macros:
17
18    HUGE_VAL
19    HUGE_VALF               // C99
20    HUGE_VALL               // C99
21    INFINITY                // C99
22    NAN                     // C99
23    FP_INFINITE             // C99
24    FP_NAN                  // C99
25    FP_NORMAL               // C99
26    FP_SUBNORMAL            // C99
27    FP_ZERO                 // C99
28    FP_FAST_FMA             // C99
29    FP_FAST_FMAF            // C99
30    FP_FAST_FMAL            // C99
31    FP_ILOGB0               // C99
32    FP_ILOGBNAN             // C99
33    MATH_ERRNO              // C99
34    MATH_ERREXCEPT          // C99
35    math_errhandling        // C99
36
37namespace std
38{
39
40Types:
41
42    float_t                 // C99
43    double_t                // C99
44
45// C90
46
47floating_point abs(floating_point x);
48
49floating_point acos (arithmetic x);
50float          acosf(float x);
51long double    acosl(long double x);
52
53floating_point asin (arithmetic x);
54float          asinf(float x);
55long double    asinl(long double x);
56
57floating_point atan (arithmetic x);
58float          atanf(float x);
59long double    atanl(long double x);
60
61floating_point atan2 (arithmetic y, arithmetic x);
62float          atan2f(float y, float x);
63long double    atan2l(long double y, long double x);
64
65floating_point ceil (arithmetic x);
66float          ceilf(float x);
67long double    ceill(long double x);
68
69floating_point cos (arithmetic x);
70float          cosf(float x);
71long double    cosl(long double x);
72
73floating_point cosh (arithmetic x);
74float          coshf(float x);
75long double    coshl(long double x);
76
77floating_point exp (arithmetic x);
78float          expf(float x);
79long double    expl(long double x);
80
81floating_point fabs (arithmetic x);
82float          fabsf(float x);
83long double    fabsl(long double x);
84
85floating_point floor (arithmetic x);
86float          floorf(float x);
87long double    floorl(long double x);
88
89floating_point fmod (arithmetic x, arithmetic y);
90float          fmodf(float x, float y);
91long double    fmodl(long double x, long double y);
92
93floating_point frexp (arithmetic value, int* exp);
94float          frexpf(float value, int* exp);
95long double    frexpl(long double value, int* exp);
96
97floating_point ldexp (arithmetic value, int exp);
98float          ldexpf(float value, int exp);
99long double    ldexpl(long double value, int exp);
100
101floating_point log (arithmetic x);
102float          logf(float x);
103long double    logl(long double x);
104
105floating_point log10 (arithmetic x);
106float          log10f(float x);
107long double    log10l(long double x);
108
109floating_point modf (floating_point value, floating_point* iptr);
110float          modff(float value, float* iptr);
111long double    modfl(long double value, long double* iptr);
112
113floating_point pow (arithmetic x, arithmetic y);
114float          powf(float x, float y);
115long double    powl(long double x, long double y);
116
117floating_point sin (arithmetic x);
118float          sinf(float x);
119long double    sinl(long double x);
120
121floating_point sinh (arithmetic x);
122float          sinhf(float x);
123long double    sinhl(long double x);
124
125floating_point sqrt (arithmetic x);
126float          sqrtf(float x);
127long double    sqrtl(long double x);
128
129floating_point tan (arithmetic x);
130float          tanf(float x);
131long double    tanl(long double x);
132
133floating_point tanh (arithmetic x);
134float          tanhf(float x);
135long double    tanhl(long double x);
136
137//  C99
138
139bool signbit(arithmetic x);
140
141int fpclassify(arithmetic x);
142
143bool isfinite(arithmetic x);
144bool isinf(arithmetic x);
145bool isnan(arithmetic x);
146bool isnormal(arithmetic x);
147
148bool isgreater(arithmetic x, arithmetic y);
149bool isgreaterequal(arithmetic x, arithmetic y);
150bool isless(arithmetic x, arithmetic y);
151bool islessequal(arithmetic x, arithmetic y);
152bool islessgreater(arithmetic x, arithmetic y);
153bool isunordered(arithmetic x, arithmetic y);
154
155floating_point acosh (arithmetic x);
156float          acoshf(float x);
157long double    acoshl(long double x);
158
159floating_point asinh (arithmetic x);
160float          asinhf(float x);
161long double    asinhl(long double x);
162
163floating_point atanh (arithmetic x);
164float          atanhf(float x);
165long double    atanhl(long double x);
166
167floating_point cbrt (arithmetic x);
168float          cbrtf(float x);
169long double    cbrtl(long double x);
170
171floating_point copysign (arithmetic x, arithmetic y);
172float          copysignf(float x, float y);
173long double    copysignl(long double x, long double y);
174
175floating_point erf (arithmetic x);
176float          erff(float x);
177long double    erfl(long double x);
178
179floating_point erfc (arithmetic x);
180float          erfcf(float x);
181long double    erfcl(long double x);
182
183floating_point exp2 (arithmetic x);
184float          exp2f(float x);
185long double    exp2l(long double x);
186
187floating_point expm1 (arithmetic x);
188float          expm1f(float x);
189long double    expm1l(long double x);
190
191floating_point fdim (arithmetic x, arithmetic y);
192float          fdimf(float x, float y);
193long double    fdiml(long double x, long double y);
194
195floating_point fma (arithmetic x, arithmetic y, arithmetic z);
196float          fmaf(float x, float y, float z);
197long double    fmal(long double x, long double y, long double z);
198
199floating_point fmax (arithmetic x, arithmetic y);
200float          fmaxf(float x, float y);
201long double    fmaxl(long double x, long double y);
202
203floating_point fmin (arithmetic x, arithmetic y);
204float          fminf(float x, float y);
205long double    fminl(long double x, long double y);
206
207floating_point hypot (arithmetic x, arithmetic y);
208float          hypotf(float x, float y);
209long double    hypotl(long double x, long double y);
210
211double       hypot(double x, double y, double z);                // C++17
212float        hypot(float x, float y, float z);                   // C++17
213long double  hypot(long double x, long double y, long double z); // C++17
214
215int ilogb (arithmetic x);
216int ilogbf(float x);
217int ilogbl(long double x);
218
219floating_point lgamma (arithmetic x);
220float          lgammaf(float x);
221long double    lgammal(long double x);
222
223long long llrint (arithmetic x);
224long long llrintf(float x);
225long long llrintl(long double x);
226
227long long llround (arithmetic x);
228long long llroundf(float x);
229long long llroundl(long double x);
230
231floating_point log1p (arithmetic x);
232float          log1pf(float x);
233long double    log1pl(long double x);
234
235floating_point log2 (arithmetic x);
236float          log2f(float x);
237long double    log2l(long double x);
238
239floating_point logb (arithmetic x);
240float          logbf(float x);
241long double    logbl(long double x);
242
243long lrint (arithmetic x);
244long lrintf(float x);
245long lrintl(long double x);
246
247long lround (arithmetic x);
248long lroundf(float x);
249long lroundl(long double x);
250
251double      nan (const char* str);
252float       nanf(const char* str);
253long double nanl(const char* str);
254
255floating_point nearbyint (arithmetic x);
256float          nearbyintf(float x);
257long double    nearbyintl(long double x);
258
259floating_point nextafter (arithmetic x, arithmetic y);
260float          nextafterf(float x, float y);
261long double    nextafterl(long double x, long double y);
262
263floating_point nexttoward (arithmetic x, long double y);
264float          nexttowardf(float x, long double y);
265long double    nexttowardl(long double x, long double y);
266
267floating_point remainder (arithmetic x, arithmetic y);
268float          remainderf(float x, float y);
269long double    remainderl(long double x, long double y);
270
271floating_point remquo (arithmetic x, arithmetic y, int* pquo);
272float          remquof(float x, float y, int* pquo);
273long double    remquol(long double x, long double y, int* pquo);
274
275floating_point rint (arithmetic x);
276float          rintf(float x);
277long double    rintl(long double x);
278
279floating_point round (arithmetic x);
280float          roundf(float x);
281long double    roundl(long double x);
282
283floating_point scalbln (arithmetic x, long ex);
284float          scalblnf(float x, long ex);
285long double    scalblnl(long double x, long ex);
286
287floating_point scalbn (arithmetic x, int ex);
288float          scalbnf(float x, int ex);
289long double    scalbnl(long double x, int ex);
290
291floating_point tgamma (arithmetic x);
292float          tgammaf(float x);
293long double    tgammal(long double x);
294
295floating_point trunc (arithmetic x);
296float          truncf(float x);
297long double    truncl(long double x);
298
299}  // std
300
301*/
302
303#include <__config>
304#include <math.h>
305#include <version>
306
307#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
308#pragma GCC system_header
309#endif
310
311_LIBCPP_BEGIN_NAMESPACE_STD
312
313using ::signbit;
314using ::fpclassify;
315using ::isfinite;
316using ::isinf;
317using ::isnan;
318using ::isnormal;
319using ::isgreater;
320using ::isgreaterequal;
321using ::isless;
322using ::islessequal;
323using ::islessgreater;
324using ::isunordered;
325using ::isunordered;
326
327using ::float_t;
328using ::double_t;
329
330#ifndef _AIX
331using ::abs;
332#endif
333
334using ::acos;
335using ::acosf;
336using ::asin;
337using ::asinf;
338using ::atan;
339using ::atanf;
340using ::atan2;
341using ::atan2f;
342using ::ceil;
343using ::ceilf;
344using ::cos;
345using ::cosf;
346using ::cosh;
347using ::coshf;
348
349using ::exp;
350using ::expf;
351
352using ::fabs;
353using ::fabsf;
354using ::floor;
355using ::floorf;
356
357using ::fmod;
358using ::fmodf;
359
360using ::frexp;
361using ::frexpf;
362using ::ldexp;
363using ::ldexpf;
364
365using ::log;
366using ::logf;
367
368using ::log10;
369using ::log10f;
370using ::modf;
371using ::modff;
372
373using ::pow;
374using ::powf;
375
376using ::sin;
377using ::sinf;
378using ::sinh;
379using ::sinhf;
380
381using ::sqrt;
382using ::sqrtf;
383using ::tan;
384using ::tanf;
385
386using ::tanh;
387using ::tanhf;
388
389using ::acosh;
390using ::acoshf;
391using ::asinh;
392using ::asinhf;
393using ::atanh;
394using ::atanhf;
395using ::cbrt;
396using ::cbrtf;
397
398using ::copysign;
399using ::copysignf;
400
401using ::erf;
402using ::erff;
403using ::erfc;
404using ::erfcf;
405using ::exp2;
406using ::exp2f;
407using ::expm1;
408using ::expm1f;
409using ::fdim;
410using ::fdimf;
411using ::fmaf;
412using ::fma;
413using ::fmax;
414using ::fmaxf;
415using ::fmin;
416using ::fminf;
417using ::hypot;
418using ::hypotf;
419using ::ilogb;
420using ::ilogbf;
421using ::lgamma;
422using ::lgammaf;
423using ::llrint;
424using ::llrintf;
425using ::llround;
426using ::llroundf;
427using ::log1p;
428using ::log1pf;
429using ::log2;
430using ::log2f;
431using ::logb;
432using ::logbf;
433using ::lrint;
434using ::lrintf;
435using ::lround;
436using ::lroundf;
437
438using ::nan;
439using ::nanf;
440
441using ::nearbyint;
442using ::nearbyintf;
443using ::nextafter;
444using ::nextafterf;
445using ::nexttoward;
446using ::nexttowardf;
447using ::remainder;
448using ::remainderf;
449using ::remquo;
450using ::remquof;
451using ::rint;
452using ::rintf;
453using ::round;
454using ::roundf;
455using ::scalbln;
456using ::scalblnf;
457using ::scalbn;
458using ::scalbnf;
459using ::tgamma;
460using ::tgammaf;
461using ::trunc;
462using ::truncf;
463
464using ::acosl;
465using ::asinl;
466using ::atanl;
467using ::atan2l;
468using ::ceill;
469using ::cosl;
470using ::coshl;
471using ::expl;
472using ::fabsl;
473using ::floorl;
474using ::fmodl;
475using ::frexpl;
476using ::ldexpl;
477using ::logl;
478using ::log10l;
479using ::modfl;
480using ::powl;
481using ::sinl;
482using ::sinhl;
483using ::sqrtl;
484using ::tanl;
485
486using ::tanhl;
487using ::acoshl;
488using ::asinhl;
489using ::atanhl;
490using ::cbrtl;
491
492using ::copysignl;
493
494using ::erfl;
495using ::erfcl;
496using ::exp2l;
497using ::expm1l;
498using ::fdiml;
499using ::fmal;
500using ::fmaxl;
501using ::fminl;
502using ::hypotl;
503using ::ilogbl;
504using ::lgammal;
505using ::llrintl;
506using ::llroundl;
507using ::log1pl;
508using ::log2l;
509using ::logbl;
510using ::lrintl;
511using ::lroundl;
512using ::nanl;
513using ::nearbyintl;
514using ::nextafterl;
515using ::nexttowardl;
516using ::remainderl;
517using ::remquol;
518using ::rintl;
519using ::roundl;
520using ::scalblnl;
521using ::scalbnl;
522using ::tgammal;
523using ::truncl;
524
525#if _LIBCPP_STD_VER > 14
526inline _LIBCPP_INLINE_VISIBILITY float       hypot(       float x,       float y,       float z ) { return sqrt(x*x + y*y + z*z); }
527inline _LIBCPP_INLINE_VISIBILITY double      hypot(      double x,      double y,      double z ) { return sqrt(x*x + y*y + z*z); }
528inline _LIBCPP_INLINE_VISIBILITY long double hypot( long double x, long double y, long double z ) { return sqrt(x*x + y*y + z*z); }
529
530template <class _A1, class _A2, class _A3>
531inline _LIBCPP_INLINE_VISIBILITY
532typename _EnableIf
533<
534    is_arithmetic<_A1>::value &&
535    is_arithmetic<_A2>::value &&
536    is_arithmetic<_A3>::value,
537    __promote<_A1, _A2, _A3>
538>::type
539hypot(_A1 __lcpp_x, _A2 __lcpp_y, _A3 __lcpp_z) _NOEXCEPT
540{
541    typedef typename __promote<_A1, _A2, _A3>::type __result_type;
542    static_assert((!(is_same<_A1, __result_type>::value &&
543                     is_same<_A2, __result_type>::value &&
544                     is_same<_A3, __result_type>::value)), "");
545    return hypot((__result_type)__lcpp_x, (__result_type)__lcpp_y, (__result_type)__lcpp_z);
546}
547#endif
548
549template <class _A1>
550_LIBCPP_INLINE_VISIBILITY
551_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
552__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT
553{
554#if __has_builtin(__builtin_isnan)
555    return __builtin_isnan(__lcpp_x);
556#else
557    return isnan(__lcpp_x);
558#endif
559}
560
561template <class _A1>
562_LIBCPP_INLINE_VISIBILITY
563_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
564__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT
565{
566    return isnan(__lcpp_x);
567}
568
569template <class _A1>
570_LIBCPP_INLINE_VISIBILITY
571_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
572__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT
573{
574#if __has_builtin(__builtin_isinf)
575    return __builtin_isinf(__lcpp_x);
576#else
577    return isinf(__lcpp_x);
578#endif
579}
580
581template <class _A1>
582_LIBCPP_INLINE_VISIBILITY
583_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
584__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT
585{
586    return isinf(__lcpp_x);
587}
588
589template <class _A1>
590_LIBCPP_INLINE_VISIBILITY
591_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
592__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT
593{
594#if __has_builtin(__builtin_isfinite)
595    return __builtin_isfinite(__lcpp_x);
596#else
597    return isfinite(__lcpp_x);
598#endif
599}
600
601template <class _A1>
602_LIBCPP_INLINE_VISIBILITY
603_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
604__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT
605{
606    return isfinite(__lcpp_x);
607}
608
609#if _LIBCPP_STD_VER > 17
610template <typename _Fp>
611constexpr
612_Fp __lerp(_Fp __a, _Fp __b, _Fp __t) noexcept {
613    if ((__a <= 0 && __b >= 0) || (__a >= 0 && __b <= 0))
614        return __t * __b + (1 - __t) * __a;
615
616    if (__t == 1) return __b;
617    const _Fp __x = __a + __t * (__b - __a);
618    if (__t > 1 == __b > __a)
619    	return __b < __x ? __x : __b;
620    else
621    	return __x < __b ? __x : __b;
622}
623
624constexpr float
625lerp(float __a, float __b, float __t)                   _NOEXCEPT { return __lerp(__a, __b, __t); }
626
627constexpr double
628lerp(double __a, double __b, double __t)                _NOEXCEPT { return __lerp(__a, __b, __t); }
629
630constexpr long double
631lerp(long double __a, long double __b, long double __t) _NOEXCEPT { return __lerp(__a, __b, __t); }
632
633#endif // _LIBCPP_STD_VER > 17
634
635_LIBCPP_END_NAMESPACE_STD
636
637#endif  // _LIBCPP_CMATH
638