xref: /llvm-project/libcxx/include/cmath (revision b9a2658a3e8bd13b0f9e7a8a440832a95b377216)
1// -*- C++ -*-
2//===----------------------------------------------------------------------===//
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
207double         hermite(unsigned n, double x);                    // C++17
208float          hermite(unsigned n, float x);                     // C++17
209long double    hermite(unsigned n, long double x);               // C++17
210float          hermitef(unsigned n, float x);                    // C++17
211long double    hermitel(unsigned n, long double x);              // C++17
212template <class Integer>
213double         hermite(unsigned n, Integer x);                   // C++17
214
215floating_point hypot (arithmetic x, arithmetic y);
216float          hypotf(float x, float y);
217long double    hypotl(long double x, long double y);
218
219double       hypot(double x, double y, double z);                // C++17
220float        hypot(float x, float y, float z);                   // C++17
221long double  hypot(long double x, long double y, long double z); // C++17
222
223int ilogb (arithmetic x);
224int ilogbf(float x);
225int ilogbl(long double x);
226
227floating_point lgamma (arithmetic x);
228float          lgammaf(float x);
229long double    lgammal(long double x);
230
231long long llrint (arithmetic x);
232long long llrintf(float x);
233long long llrintl(long double x);
234
235long long llround (arithmetic x);
236long long llroundf(float x);
237long long llroundl(long double x);
238
239floating_point log1p (arithmetic x);
240float          log1pf(float x);
241long double    log1pl(long double x);
242
243floating_point log2 (arithmetic x);
244float          log2f(float x);
245long double    log2l(long double x);
246
247floating_point logb (arithmetic x);
248float          logbf(float x);
249long double    logbl(long double x);
250
251long lrint (arithmetic x);
252long lrintf(float x);
253long lrintl(long double x);
254
255long lround (arithmetic x);
256long lroundf(float x);
257long lroundl(long double x);
258
259double      nan (const char* str);
260float       nanf(const char* str);
261long double nanl(const char* str);
262
263floating_point nearbyint (arithmetic x);
264float          nearbyintf(float x);
265long double    nearbyintl(long double x);
266
267floating_point nextafter (arithmetic x, arithmetic y);
268float          nextafterf(float x, float y);
269long double    nextafterl(long double x, long double y);
270
271floating_point nexttoward (arithmetic x, long double y);
272float          nexttowardf(float x, long double y);
273long double    nexttowardl(long double x, long double y);
274
275floating_point remainder (arithmetic x, arithmetic y);
276float          remainderf(float x, float y);
277long double    remainderl(long double x, long double y);
278
279floating_point remquo (arithmetic x, arithmetic y, int* pquo);
280float          remquof(float x, float y, int* pquo);
281long double    remquol(long double x, long double y, int* pquo);
282
283floating_point rint (arithmetic x);
284float          rintf(float x);
285long double    rintl(long double x);
286
287floating_point round (arithmetic x);
288float          roundf(float x);
289long double    roundl(long double x);
290
291floating_point scalbln (arithmetic x, long ex);
292float          scalblnf(float x, long ex);
293long double    scalblnl(long double x, long ex);
294
295floating_point scalbn (arithmetic x, int ex);
296float          scalbnf(float x, int ex);
297long double    scalbnl(long double x, int ex);
298
299floating_point tgamma (arithmetic x);
300float          tgammaf(float x);
301long double    tgammal(long double x);
302
303floating_point trunc (arithmetic x);
304float          truncf(float x);
305long double    truncl(long double x);
306
307constexpr float       lerp(float a, float b, float t) noexcept;                   // C++20
308constexpr double      lerp(double a, double b, double t) noexcept;                // C++20
309constexpr long double lerp(long double a, long double b, long double t) noexcept; // C++20
310
311}  // std
312
313*/
314
315#if __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS)
316#  include <__cxx03/cmath>
317#else
318#  include <__config>
319#  include <__math/hypot.h>
320#  include <__type_traits/enable_if.h>
321#  include <__type_traits/is_arithmetic.h>
322#  include <__type_traits/is_constant_evaluated.h>
323#  include <__type_traits/is_floating_point.h>
324#  include <__type_traits/is_same.h>
325#  include <__type_traits/promote.h>
326#  include <__type_traits/remove_cv.h>
327#  include <limits>
328#  include <version>
329
330#  include <__math/special_functions.h>
331#  include <math.h>
332
333#  ifndef _LIBCPP_MATH_H
334#   error <cmath> tried including <math.h> but didn't find libc++'s <math.h> header. \
335          This usually means that your header search paths are not configured properly. \
336          The header search paths should contain the C++ Standard Library headers before \
337          any C Standard Library, and you are probably using compiler flags that make that \
338          not be the case.
339#  endif
340
341#  if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
342#    pragma GCC system_header
343#  endif
344
345_LIBCPP_PUSH_MACROS
346#  include <__undef_macros>
347
348_LIBCPP_BEGIN_NAMESPACE_STD
349
350using ::signbit _LIBCPP_USING_IF_EXISTS;
351using ::fpclassify _LIBCPP_USING_IF_EXISTS;
352using ::isfinite _LIBCPP_USING_IF_EXISTS;
353using ::isinf _LIBCPP_USING_IF_EXISTS;
354using ::isnan _LIBCPP_USING_IF_EXISTS;
355using ::isnormal _LIBCPP_USING_IF_EXISTS;
356using ::isgreater _LIBCPP_USING_IF_EXISTS;
357using ::isgreaterequal _LIBCPP_USING_IF_EXISTS;
358using ::isless _LIBCPP_USING_IF_EXISTS;
359using ::islessequal _LIBCPP_USING_IF_EXISTS;
360using ::islessgreater _LIBCPP_USING_IF_EXISTS;
361using ::isunordered _LIBCPP_USING_IF_EXISTS;
362using ::isunordered _LIBCPP_USING_IF_EXISTS;
363
364using ::float_t _LIBCPP_USING_IF_EXISTS;
365using ::double_t _LIBCPP_USING_IF_EXISTS;
366
367using ::abs _LIBCPP_USING_IF_EXISTS;
368
369using ::acos _LIBCPP_USING_IF_EXISTS;
370using ::acosf _LIBCPP_USING_IF_EXISTS;
371using ::asin _LIBCPP_USING_IF_EXISTS;
372using ::asinf _LIBCPP_USING_IF_EXISTS;
373using ::atan _LIBCPP_USING_IF_EXISTS;
374using ::atanf _LIBCPP_USING_IF_EXISTS;
375using ::atan2 _LIBCPP_USING_IF_EXISTS;
376using ::atan2f _LIBCPP_USING_IF_EXISTS;
377using ::ceil _LIBCPP_USING_IF_EXISTS;
378using ::ceilf _LIBCPP_USING_IF_EXISTS;
379using ::cos _LIBCPP_USING_IF_EXISTS;
380using ::cosf _LIBCPP_USING_IF_EXISTS;
381using ::cosh _LIBCPP_USING_IF_EXISTS;
382using ::coshf _LIBCPP_USING_IF_EXISTS;
383
384using ::exp _LIBCPP_USING_IF_EXISTS;
385using ::expf _LIBCPP_USING_IF_EXISTS;
386
387using ::fabs _LIBCPP_USING_IF_EXISTS;
388using ::fabsf _LIBCPP_USING_IF_EXISTS;
389using ::floor _LIBCPP_USING_IF_EXISTS;
390using ::floorf _LIBCPP_USING_IF_EXISTS;
391
392using ::fmod _LIBCPP_USING_IF_EXISTS;
393using ::fmodf _LIBCPP_USING_IF_EXISTS;
394
395using ::frexp _LIBCPP_USING_IF_EXISTS;
396using ::frexpf _LIBCPP_USING_IF_EXISTS;
397using ::ldexp _LIBCPP_USING_IF_EXISTS;
398using ::ldexpf _LIBCPP_USING_IF_EXISTS;
399
400using ::log _LIBCPP_USING_IF_EXISTS;
401using ::logf _LIBCPP_USING_IF_EXISTS;
402
403using ::log10 _LIBCPP_USING_IF_EXISTS;
404using ::log10f _LIBCPP_USING_IF_EXISTS;
405using ::modf _LIBCPP_USING_IF_EXISTS;
406using ::modff _LIBCPP_USING_IF_EXISTS;
407
408using ::pow _LIBCPP_USING_IF_EXISTS;
409using ::powf _LIBCPP_USING_IF_EXISTS;
410
411using ::sin _LIBCPP_USING_IF_EXISTS;
412using ::sinf _LIBCPP_USING_IF_EXISTS;
413using ::sinh _LIBCPP_USING_IF_EXISTS;
414using ::sinhf _LIBCPP_USING_IF_EXISTS;
415
416using ::sqrt _LIBCPP_USING_IF_EXISTS;
417using ::sqrtf _LIBCPP_USING_IF_EXISTS;
418using ::tan _LIBCPP_USING_IF_EXISTS;
419using ::tanf _LIBCPP_USING_IF_EXISTS;
420
421using ::tanh _LIBCPP_USING_IF_EXISTS;
422using ::tanhf _LIBCPP_USING_IF_EXISTS;
423
424using ::acosh _LIBCPP_USING_IF_EXISTS;
425using ::acoshf _LIBCPP_USING_IF_EXISTS;
426using ::asinh _LIBCPP_USING_IF_EXISTS;
427using ::asinhf _LIBCPP_USING_IF_EXISTS;
428using ::atanh _LIBCPP_USING_IF_EXISTS;
429using ::atanhf _LIBCPP_USING_IF_EXISTS;
430using ::cbrt _LIBCPP_USING_IF_EXISTS;
431using ::cbrtf _LIBCPP_USING_IF_EXISTS;
432
433using ::copysign _LIBCPP_USING_IF_EXISTS;
434using ::copysignf _LIBCPP_USING_IF_EXISTS;
435
436using ::erf _LIBCPP_USING_IF_EXISTS;
437using ::erff _LIBCPP_USING_IF_EXISTS;
438using ::erfc _LIBCPP_USING_IF_EXISTS;
439using ::erfcf _LIBCPP_USING_IF_EXISTS;
440using ::exp2 _LIBCPP_USING_IF_EXISTS;
441using ::exp2f _LIBCPP_USING_IF_EXISTS;
442using ::expm1 _LIBCPP_USING_IF_EXISTS;
443using ::expm1f _LIBCPP_USING_IF_EXISTS;
444using ::fdim _LIBCPP_USING_IF_EXISTS;
445using ::fdimf _LIBCPP_USING_IF_EXISTS;
446using ::fmaf _LIBCPP_USING_IF_EXISTS;
447using ::fma _LIBCPP_USING_IF_EXISTS;
448using ::fmax _LIBCPP_USING_IF_EXISTS;
449using ::fmaxf _LIBCPP_USING_IF_EXISTS;
450using ::fmin _LIBCPP_USING_IF_EXISTS;
451using ::fminf _LIBCPP_USING_IF_EXISTS;
452using ::hypot _LIBCPP_USING_IF_EXISTS;
453using ::hypotf _LIBCPP_USING_IF_EXISTS;
454using ::ilogb _LIBCPP_USING_IF_EXISTS;
455using ::ilogbf _LIBCPP_USING_IF_EXISTS;
456using ::lgamma _LIBCPP_USING_IF_EXISTS;
457using ::lgammaf _LIBCPP_USING_IF_EXISTS;
458using ::llrint _LIBCPP_USING_IF_EXISTS;
459using ::llrintf _LIBCPP_USING_IF_EXISTS;
460using ::llround _LIBCPP_USING_IF_EXISTS;
461using ::llroundf _LIBCPP_USING_IF_EXISTS;
462using ::log1p _LIBCPP_USING_IF_EXISTS;
463using ::log1pf _LIBCPP_USING_IF_EXISTS;
464using ::log2 _LIBCPP_USING_IF_EXISTS;
465using ::log2f _LIBCPP_USING_IF_EXISTS;
466using ::logb _LIBCPP_USING_IF_EXISTS;
467using ::logbf _LIBCPP_USING_IF_EXISTS;
468using ::lrint _LIBCPP_USING_IF_EXISTS;
469using ::lrintf _LIBCPP_USING_IF_EXISTS;
470using ::lround _LIBCPP_USING_IF_EXISTS;
471using ::lroundf _LIBCPP_USING_IF_EXISTS;
472
473using ::nan _LIBCPP_USING_IF_EXISTS;
474using ::nanf _LIBCPP_USING_IF_EXISTS;
475
476using ::nearbyint _LIBCPP_USING_IF_EXISTS;
477using ::nearbyintf _LIBCPP_USING_IF_EXISTS;
478using ::nextafter _LIBCPP_USING_IF_EXISTS;
479using ::nextafterf _LIBCPP_USING_IF_EXISTS;
480using ::nexttoward _LIBCPP_USING_IF_EXISTS;
481using ::nexttowardf _LIBCPP_USING_IF_EXISTS;
482using ::remainder _LIBCPP_USING_IF_EXISTS;
483using ::remainderf _LIBCPP_USING_IF_EXISTS;
484using ::remquo _LIBCPP_USING_IF_EXISTS;
485using ::remquof _LIBCPP_USING_IF_EXISTS;
486using ::rint _LIBCPP_USING_IF_EXISTS;
487using ::rintf _LIBCPP_USING_IF_EXISTS;
488using ::round _LIBCPP_USING_IF_EXISTS;
489using ::roundf _LIBCPP_USING_IF_EXISTS;
490using ::scalbln _LIBCPP_USING_IF_EXISTS;
491using ::scalblnf _LIBCPP_USING_IF_EXISTS;
492using ::scalbn _LIBCPP_USING_IF_EXISTS;
493using ::scalbnf _LIBCPP_USING_IF_EXISTS;
494using ::tgamma _LIBCPP_USING_IF_EXISTS;
495using ::tgammaf _LIBCPP_USING_IF_EXISTS;
496using ::trunc _LIBCPP_USING_IF_EXISTS;
497using ::truncf _LIBCPP_USING_IF_EXISTS;
498
499using ::acosl _LIBCPP_USING_IF_EXISTS;
500using ::asinl _LIBCPP_USING_IF_EXISTS;
501using ::atanl _LIBCPP_USING_IF_EXISTS;
502using ::atan2l _LIBCPP_USING_IF_EXISTS;
503using ::ceill _LIBCPP_USING_IF_EXISTS;
504using ::cosl _LIBCPP_USING_IF_EXISTS;
505using ::coshl _LIBCPP_USING_IF_EXISTS;
506using ::expl _LIBCPP_USING_IF_EXISTS;
507using ::fabsl _LIBCPP_USING_IF_EXISTS;
508using ::floorl _LIBCPP_USING_IF_EXISTS;
509using ::fmodl _LIBCPP_USING_IF_EXISTS;
510using ::frexpl _LIBCPP_USING_IF_EXISTS;
511using ::ldexpl _LIBCPP_USING_IF_EXISTS;
512using ::logl _LIBCPP_USING_IF_EXISTS;
513using ::log10l _LIBCPP_USING_IF_EXISTS;
514using ::modfl _LIBCPP_USING_IF_EXISTS;
515using ::powl _LIBCPP_USING_IF_EXISTS;
516using ::sinl _LIBCPP_USING_IF_EXISTS;
517using ::sinhl _LIBCPP_USING_IF_EXISTS;
518using ::sqrtl _LIBCPP_USING_IF_EXISTS;
519using ::tanl _LIBCPP_USING_IF_EXISTS;
520
521using ::tanhl _LIBCPP_USING_IF_EXISTS;
522using ::acoshl _LIBCPP_USING_IF_EXISTS;
523using ::asinhl _LIBCPP_USING_IF_EXISTS;
524using ::atanhl _LIBCPP_USING_IF_EXISTS;
525using ::cbrtl _LIBCPP_USING_IF_EXISTS;
526
527using ::copysignl _LIBCPP_USING_IF_EXISTS;
528
529using ::erfl _LIBCPP_USING_IF_EXISTS;
530using ::erfcl _LIBCPP_USING_IF_EXISTS;
531using ::exp2l _LIBCPP_USING_IF_EXISTS;
532using ::expm1l _LIBCPP_USING_IF_EXISTS;
533using ::fdiml _LIBCPP_USING_IF_EXISTS;
534using ::fmal _LIBCPP_USING_IF_EXISTS;
535using ::fmaxl _LIBCPP_USING_IF_EXISTS;
536using ::fminl _LIBCPP_USING_IF_EXISTS;
537using ::hypotl _LIBCPP_USING_IF_EXISTS;
538using ::ilogbl _LIBCPP_USING_IF_EXISTS;
539using ::lgammal _LIBCPP_USING_IF_EXISTS;
540using ::llrintl _LIBCPP_USING_IF_EXISTS;
541using ::llroundl _LIBCPP_USING_IF_EXISTS;
542using ::log1pl _LIBCPP_USING_IF_EXISTS;
543using ::log2l _LIBCPP_USING_IF_EXISTS;
544using ::logbl _LIBCPP_USING_IF_EXISTS;
545using ::lrintl _LIBCPP_USING_IF_EXISTS;
546using ::lroundl _LIBCPP_USING_IF_EXISTS;
547using ::nanl _LIBCPP_USING_IF_EXISTS;
548using ::nearbyintl _LIBCPP_USING_IF_EXISTS;
549using ::nextafterl _LIBCPP_USING_IF_EXISTS;
550using ::nexttowardl _LIBCPP_USING_IF_EXISTS;
551using ::remainderl _LIBCPP_USING_IF_EXISTS;
552using ::remquol _LIBCPP_USING_IF_EXISTS;
553using ::rintl _LIBCPP_USING_IF_EXISTS;
554using ::roundl _LIBCPP_USING_IF_EXISTS;
555using ::scalblnl _LIBCPP_USING_IF_EXISTS;
556using ::scalbnl _LIBCPP_USING_IF_EXISTS;
557using ::tgammal _LIBCPP_USING_IF_EXISTS;
558using ::truncl _LIBCPP_USING_IF_EXISTS;
559
560template <class _A1, __enable_if_t<is_floating_point<_A1>::value, int> = 0>
561_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isinf(_A1 __lcpp_x) _NOEXCEPT {
562#  if __has_builtin(__builtin_isinf)
563  return __builtin_isinf(__lcpp_x);
564#  else
565  return isinf(__lcpp_x);
566#  endif
567}
568
569template <class _A1, __enable_if_t<!is_floating_point<_A1>::value, int> = 0>
570_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isinf(_A1 __lcpp_x) _NOEXCEPT {
571  return std::isinf(__lcpp_x);
572}
573
574#  if _LIBCPP_STD_VER >= 20
575template <typename _Fp>
576_LIBCPP_HIDE_FROM_ABI constexpr _Fp __lerp(_Fp __a, _Fp __b, _Fp __t) noexcept {
577  if ((__a <= 0 && __b >= 0) || (__a >= 0 && __b <= 0))
578    return __t * __b + (1 - __t) * __a;
579
580  if (__t == 1)
581    return __b;
582  const _Fp __x = __a + __t * (__b - __a);
583  if ((__t > 1) == (__b > __a))
584    return __b < __x ? __x : __b;
585  else
586    return __x < __b ? __x : __b;
587}
588
589_LIBCPP_HIDE_FROM_ABI inline constexpr float lerp(float __a, float __b, float __t) _NOEXCEPT {
590  return __lerp(__a, __b, __t);
591}
592
593_LIBCPP_HIDE_FROM_ABI inline constexpr double lerp(double __a, double __b, double __t) _NOEXCEPT {
594  return __lerp(__a, __b, __t);
595}
596
597_LIBCPP_HIDE_FROM_ABI inline constexpr long double lerp(long double __a, long double __b, long double __t) _NOEXCEPT {
598  return __lerp(__a, __b, __t);
599}
600
601template <class _A1, class _A2, class _A3>
602inline _LIBCPP_HIDE_FROM_ABI constexpr
603    typename enable_if_t< is_arithmetic<_A1>::value && is_arithmetic<_A2>::value && is_arithmetic<_A3>::value,
604                          __promote<_A1, _A2, _A3> >::type
605    lerp(_A1 __a, _A2 __b, _A3 __t) noexcept {
606  typedef typename __promote<_A1, _A2, _A3>::type __result_type;
607  static_assert(!(
608      _IsSame<_A1, __result_type>::value && _IsSame<_A2, __result_type>::value && _IsSame<_A3, __result_type>::value));
609  return std::__lerp((__result_type)__a, (__result_type)__b, (__result_type)__t);
610}
611#  endif // _LIBCPP_STD_VER >= 20
612
613_LIBCPP_END_NAMESPACE_STD
614
615_LIBCPP_POP_MACROS
616
617#  if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20
618#    include <type_traits>
619#  endif
620#endif // __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS)
621
622#endif // _LIBCPP_CMATH
623