forked from OSchip/llvm-project
674 lines
16 KiB
C++
674 lines
16 KiB
C++
// -*- C++ -*-
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//===---------------------------- cmath -----------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#ifndef _LIBCPP_CMATH
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#define _LIBCPP_CMATH
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/*
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cmath synopsis
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Macros:
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HUGE_VAL
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HUGE_VALF // C99
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HUGE_VALL // C99
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INFINITY // C99
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NAN // C99
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FP_INFINITE // C99
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FP_NAN // C99
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FP_NORMAL // C99
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FP_SUBNORMAL // C99
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FP_ZERO // C99
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FP_FAST_FMA // C99
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FP_FAST_FMAF // C99
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FP_FAST_FMAL // C99
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FP_ILOGB0 // C99
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FP_ILOGBNAN // C99
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MATH_ERRNO // C99
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MATH_ERREXCEPT // C99
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math_errhandling // C99
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namespace std
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{
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Types:
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float_t // C99
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double_t // C99
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// C90
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floating_point abs(floating_point x);
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floating_point acos (arithmetic x);
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float acosf(float x);
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long double acosl(long double x);
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floating_point asin (arithmetic x);
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float asinf(float x);
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long double asinl(long double x);
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floating_point atan (arithmetic x);
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float atanf(float x);
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long double atanl(long double x);
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floating_point atan2 (arithmetic y, arithmetic x);
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float atan2f(float y, float x);
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long double atan2l(long double y, long double x);
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floating_point ceil (arithmetic x);
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float ceilf(float x);
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long double ceill(long double x);
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floating_point cos (arithmetic x);
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float cosf(float x);
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long double cosl(long double x);
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floating_point cosh (arithmetic x);
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float coshf(float x);
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long double coshl(long double x);
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floating_point exp (arithmetic x);
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float expf(float x);
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long double expl(long double x);
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floating_point fabs (arithmetic x);
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float fabsf(float x);
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long double fabsl(long double x);
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floating_point floor (arithmetic x);
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float floorf(float x);
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long double floorl(long double x);
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floating_point fmod (arithmetic x, arithmetic y);
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float fmodf(float x, float y);
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long double fmodl(long double x, long double y);
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floating_point frexp (arithmetic value, int* exp);
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float frexpf(float value, int* exp);
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long double frexpl(long double value, int* exp);
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floating_point ldexp (arithmetic value, int exp);
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float ldexpf(float value, int exp);
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long double ldexpl(long double value, int exp);
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floating_point log (arithmetic x);
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float logf(float x);
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long double logl(long double x);
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floating_point log10 (arithmetic x);
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float log10f(float x);
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long double log10l(long double x);
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floating_point modf (floating_point value, floating_point* iptr);
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float modff(float value, float* iptr);
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long double modfl(long double value, long double* iptr);
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floating_point pow (arithmetic x, arithmetic y);
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float powf(float x, float y);
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long double powl(long double x, long double y);
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floating_point sin (arithmetic x);
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float sinf(float x);
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long double sinl(long double x);
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floating_point sinh (arithmetic x);
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float sinhf(float x);
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long double sinhl(long double x);
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floating_point sqrt (arithmetic x);
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float sqrtf(float x);
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long double sqrtl(long double x);
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floating_point tan (arithmetic x);
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float tanf(float x);
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long double tanl(long double x);
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floating_point tanh (arithmetic x);
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float tanhf(float x);
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long double tanhl(long double x);
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// C99
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bool signbit(arithmetic x);
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int fpclassify(arithmetic x);
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bool isfinite(arithmetic x);
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bool isinf(arithmetic x);
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bool isnan(arithmetic x);
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bool isnormal(arithmetic x);
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bool isgreater(arithmetic x, arithmetic y);
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bool isgreaterequal(arithmetic x, arithmetic y);
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bool isless(arithmetic x, arithmetic y);
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bool islessequal(arithmetic x, arithmetic y);
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bool islessgreater(arithmetic x, arithmetic y);
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bool isunordered(arithmetic x, arithmetic y);
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floating_point acosh (arithmetic x);
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float acoshf(float x);
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long double acoshl(long double x);
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floating_point asinh (arithmetic x);
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float asinhf(float x);
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long double asinhl(long double x);
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floating_point atanh (arithmetic x);
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float atanhf(float x);
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long double atanhl(long double x);
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floating_point cbrt (arithmetic x);
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float cbrtf(float x);
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long double cbrtl(long double x);
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floating_point copysign (arithmetic x, arithmetic y);
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float copysignf(float x, float y);
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long double copysignl(long double x, long double y);
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floating_point erf (arithmetic x);
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float erff(float x);
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long double erfl(long double x);
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floating_point erfc (arithmetic x);
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float erfcf(float x);
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long double erfcl(long double x);
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floating_point exp2 (arithmetic x);
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float exp2f(float x);
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long double exp2l(long double x);
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floating_point expm1 (arithmetic x);
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float expm1f(float x);
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long double expm1l(long double x);
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floating_point fdim (arithmetic x, arithmetic y);
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float fdimf(float x, float y);
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long double fdiml(long double x, long double y);
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floating_point fma (arithmetic x, arithmetic y, arithmetic z);
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float fmaf(float x, float y, float z);
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long double fmal(long double x, long double y, long double z);
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floating_point fmax (arithmetic x, arithmetic y);
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float fmaxf(float x, float y);
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long double fmaxl(long double x, long double y);
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floating_point fmin (arithmetic x, arithmetic y);
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float fminf(float x, float y);
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long double fminl(long double x, long double y);
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floating_point hypot (arithmetic x, arithmetic y);
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float hypotf(float x, float y);
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long double hypotl(long double x, long double y);
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double hypot(double x, double y, double z); // C++17
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float hypot(float x, float y, float z); // C++17
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long double hypot(long double x, long double y, long double z); // C++17
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int ilogb (arithmetic x);
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int ilogbf(float x);
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int ilogbl(long double x);
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floating_point lgamma (arithmetic x);
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float lgammaf(float x);
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long double lgammal(long double x);
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long long llrint (arithmetic x);
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long long llrintf(float x);
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long long llrintl(long double x);
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long long llround (arithmetic x);
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long long llroundf(float x);
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long long llroundl(long double x);
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floating_point log1p (arithmetic x);
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float log1pf(float x);
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long double log1pl(long double x);
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floating_point log2 (arithmetic x);
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float log2f(float x);
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long double log2l(long double x);
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floating_point logb (arithmetic x);
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float logbf(float x);
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long double logbl(long double x);
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long lrint (arithmetic x);
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long lrintf(float x);
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long lrintl(long double x);
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long lround (arithmetic x);
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long lroundf(float x);
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long lroundl(long double x);
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double nan (const char* str);
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float nanf(const char* str);
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long double nanl(const char* str);
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floating_point nearbyint (arithmetic x);
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float nearbyintf(float x);
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long double nearbyintl(long double x);
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floating_point nextafter (arithmetic x, arithmetic y);
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float nextafterf(float x, float y);
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long double nextafterl(long double x, long double y);
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floating_point nexttoward (arithmetic x, long double y);
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float nexttowardf(float x, long double y);
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long double nexttowardl(long double x, long double y);
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floating_point remainder (arithmetic x, arithmetic y);
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float remainderf(float x, float y);
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long double remainderl(long double x, long double y);
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floating_point remquo (arithmetic x, arithmetic y, int* pquo);
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float remquof(float x, float y, int* pquo);
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long double remquol(long double x, long double y, int* pquo);
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floating_point rint (arithmetic x);
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float rintf(float x);
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long double rintl(long double x);
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floating_point round (arithmetic x);
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float roundf(float x);
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long double roundl(long double x);
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floating_point scalbln (arithmetic x, long ex);
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float scalblnf(float x, long ex);
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long double scalblnl(long double x, long ex);
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floating_point scalbn (arithmetic x, int ex);
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float scalbnf(float x, int ex);
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long double scalbnl(long double x, int ex);
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floating_point tgamma (arithmetic x);
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float tgammaf(float x);
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long double tgammal(long double x);
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floating_point trunc (arithmetic x);
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float truncf(float x);
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long double truncl(long double x);
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} // std
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*/
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#include <__config>
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#include <math.h>
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#include <version>
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#include <type_traits>
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#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
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#pragma GCC system_header
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#endif
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_LIBCPP_PUSH_MACROS
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#include <__undef_macros>
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_LIBCPP_BEGIN_NAMESPACE_STD
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using ::signbit;
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using ::fpclassify;
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using ::isfinite;
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using ::isinf;
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using ::isnan;
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using ::isnormal;
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using ::isgreater;
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using ::isgreaterequal;
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using ::isless;
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using ::islessequal;
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using ::islessgreater;
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using ::isunordered;
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using ::isunordered;
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using ::float_t;
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using ::double_t;
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#ifndef _AIX
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using ::abs;
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#endif
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using ::acos;
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using ::acosf;
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using ::asin;
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using ::asinf;
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using ::atan;
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using ::atanf;
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using ::atan2;
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using ::atan2f;
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using ::ceil;
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using ::ceilf;
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using ::cos;
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using ::cosf;
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using ::cosh;
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using ::coshf;
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using ::exp;
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using ::expf;
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using ::fabs;
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using ::fabsf;
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using ::floor;
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using ::floorf;
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using ::fmod;
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using ::fmodf;
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using ::frexp;
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using ::frexpf;
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using ::ldexp;
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using ::ldexpf;
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using ::log;
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using ::logf;
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using ::log10;
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using ::log10f;
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using ::modf;
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using ::modff;
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using ::pow;
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using ::powf;
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using ::sin;
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using ::sinf;
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using ::sinh;
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using ::sinhf;
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using ::sqrt;
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using ::sqrtf;
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using ::tan;
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using ::tanf;
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using ::tanh;
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using ::tanhf;
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using ::acosh;
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using ::acoshf;
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using ::asinh;
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using ::asinhf;
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using ::atanh;
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using ::atanhf;
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using ::cbrt;
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using ::cbrtf;
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using ::copysign;
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using ::copysignf;
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using ::erf;
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using ::erff;
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using ::erfc;
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using ::erfcf;
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using ::exp2;
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using ::exp2f;
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using ::expm1;
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using ::expm1f;
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using ::fdim;
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using ::fdimf;
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using ::fmaf;
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using ::fma;
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using ::fmax;
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using ::fmaxf;
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using ::fmin;
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using ::fminf;
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using ::hypot;
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using ::hypotf;
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using ::ilogb;
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using ::ilogbf;
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using ::lgamma;
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using ::lgammaf;
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using ::llrint;
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using ::llrintf;
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using ::llround;
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using ::llroundf;
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using ::log1p;
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using ::log1pf;
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using ::log2;
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using ::log2f;
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using ::logb;
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using ::logbf;
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using ::lrint;
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using ::lrintf;
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using ::lround;
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using ::lroundf;
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using ::nan;
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using ::nanf;
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using ::nearbyint;
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using ::nearbyintf;
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using ::nextafter;
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using ::nextafterf;
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using ::nexttoward;
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using ::nexttowardf;
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using ::remainder;
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using ::remainderf;
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using ::remquo;
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using ::remquof;
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using ::rint;
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using ::rintf;
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using ::round;
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using ::roundf;
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using ::scalbln;
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using ::scalblnf;
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using ::scalbn;
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using ::scalbnf;
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using ::tgamma;
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using ::tgammaf;
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using ::trunc;
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using ::truncf;
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using ::acosl;
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using ::asinl;
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using ::atanl;
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using ::atan2l;
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using ::ceill;
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using ::cosl;
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using ::coshl;
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using ::expl;
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using ::fabsl;
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using ::floorl;
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using ::fmodl;
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using ::frexpl;
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using ::ldexpl;
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using ::logl;
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using ::log10l;
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using ::modfl;
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using ::powl;
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using ::sinl;
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using ::sinhl;
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using ::sqrtl;
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using ::tanl;
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using ::tanhl;
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using ::acoshl;
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using ::asinhl;
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using ::atanhl;
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using ::cbrtl;
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using ::copysignl;
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using ::erfl;
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using ::erfcl;
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using ::exp2l;
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using ::expm1l;
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using ::fdiml;
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using ::fmal;
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using ::fmaxl;
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using ::fminl;
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using ::hypotl;
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using ::ilogbl;
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using ::lgammal;
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using ::llrintl;
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using ::llroundl;
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using ::log1pl;
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using ::log2l;
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using ::logbl;
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using ::lrintl;
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using ::lroundl;
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using ::nanl;
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using ::nearbyintl;
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using ::nextafterl;
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using ::nexttowardl;
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using ::remainderl;
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using ::remquol;
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using ::rintl;
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using ::roundl;
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using ::scalblnl;
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using ::scalbnl;
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using ::tgammal;
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using ::truncl;
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#if _LIBCPP_STD_VER > 14
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inline _LIBCPP_INLINE_VISIBILITY float hypot( float x, float y, float z ) { return sqrt(x*x + y*y + z*z); }
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inline _LIBCPP_INLINE_VISIBILITY double hypot( double x, double y, double z ) { return sqrt(x*x + y*y + z*z); }
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inline _LIBCPP_INLINE_VISIBILITY long double hypot( long double x, long double y, long double z ) { return sqrt(x*x + y*y + z*z); }
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template <class _A1, class _A2, class _A3>
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inline _LIBCPP_INLINE_VISIBILITY
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typename _EnableIf
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<
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is_arithmetic<_A1>::value &&
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is_arithmetic<_A2>::value &&
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is_arithmetic<_A3>::value,
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__promote<_A1, _A2, _A3>
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>::type
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hypot(_A1 __lcpp_x, _A2 __lcpp_y, _A3 __lcpp_z) _NOEXCEPT
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{
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typedef typename __promote<_A1, _A2, _A3>::type __result_type;
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static_assert((!(is_same<_A1, __result_type>::value &&
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is_same<_A2, __result_type>::value &&
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is_same<_A3, __result_type>::value)), "");
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return hypot((__result_type)__lcpp_x, (__result_type)__lcpp_y, (__result_type)__lcpp_z);
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}
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#endif
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template <class _A1>
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_LIBCPP_INLINE_VISIBILITY
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_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
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__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT
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{
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#if __has_builtin(__builtin_isnan)
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return __builtin_isnan(__lcpp_x);
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#else
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return isnan(__lcpp_x);
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#endif
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}
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|
|
|
template <class _A1>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
|
|
__libcpp_isnan_or_builtin(_A1 __lcpp_x) _NOEXCEPT
|
|
{
|
|
return isnan(__lcpp_x);
|
|
}
|
|
|
|
template <class _A1>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
|
|
__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT
|
|
{
|
|
#if __has_builtin(__builtin_isinf)
|
|
return __builtin_isinf(__lcpp_x);
|
|
#else
|
|
return isinf(__lcpp_x);
|
|
#endif
|
|
}
|
|
|
|
template <class _A1>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
|
|
__libcpp_isinf_or_builtin(_A1 __lcpp_x) _NOEXCEPT
|
|
{
|
|
return isinf(__lcpp_x);
|
|
}
|
|
|
|
template <class _A1>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR typename enable_if<is_floating_point<_A1>::value, bool>::type
|
|
__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT
|
|
{
|
|
#if __has_builtin(__builtin_isfinite)
|
|
return __builtin_isfinite(__lcpp_x);
|
|
#else
|
|
return isfinite(__lcpp_x);
|
|
#endif
|
|
}
|
|
|
|
template <class _A1>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR typename enable_if<!is_floating_point<_A1>::value, bool>::type
|
|
__libcpp_isfinite_or_builtin(_A1 __lcpp_x) _NOEXCEPT
|
|
{
|
|
return isfinite(__lcpp_x);
|
|
}
|
|
|
|
#if _LIBCPP_STD_VER > 17
|
|
template <typename _Fp>
|
|
constexpr
|
|
_Fp __lerp(_Fp __a, _Fp __b, _Fp __t) noexcept {
|
|
if ((__a <= 0 && __b >= 0) || (__a >= 0 && __b <= 0))
|
|
return __t * __b + (1 - __t) * __a;
|
|
|
|
if (__t == 1) return __b;
|
|
const _Fp __x = __a + __t * (__b - __a);
|
|
if (__t > 1 == __b > __a)
|
|
return __b < __x ? __x : __b;
|
|
else
|
|
return __x < __b ? __x : __b;
|
|
}
|
|
|
|
constexpr float
|
|
lerp(float __a, float __b, float __t) _NOEXCEPT { return __lerp(__a, __b, __t); }
|
|
|
|
constexpr double
|
|
lerp(double __a, double __b, double __t) _NOEXCEPT { return __lerp(__a, __b, __t); }
|
|
|
|
constexpr long double
|
|
lerp(long double __a, long double __b, long double __t) _NOEXCEPT { return __lerp(__a, __b, __t); }
|
|
|
|
#endif // _LIBCPP_STD_VER > 17
|
|
|
|
template <class _IntT, class _FloatT,
|
|
bool _FloatBigger = (numeric_limits<_FloatT>::digits > numeric_limits<_IntT>::digits),
|
|
int _Bits = (numeric_limits<_IntT>::digits - numeric_limits<_FloatT>::digits)>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_LIBCPP_CONSTEXPR _IntT __max_representable_int_for_float() _NOEXCEPT {
|
|
static_assert(is_floating_point<_FloatT>::value, "must be a floating point type");
|
|
static_assert(is_integral<_IntT>::value, "must be an integral type");
|
|
static_assert(numeric_limits<_FloatT>::radix == 2, "FloatT has incorrect radix");
|
|
static_assert((_IsSame<_FloatT, float>::value || _IsSame<_FloatT, double>::value
|
|
|| _IsSame<_FloatT,long double>::value), "unsupported floating point type");
|
|
return _FloatBigger ? numeric_limits<_IntT>::max() : (numeric_limits<_IntT>::max() >> _Bits << _Bits);
|
|
}
|
|
|
|
// Convert a floating point number to the specified integral type after
|
|
// clamping to the integral types representable range.
|
|
//
|
|
// The behavior is undefined if `__r` is NaN.
|
|
template <class _IntT, class _RealT>
|
|
_LIBCPP_INLINE_VISIBILITY
|
|
_IntT __clamp_to_integral(_RealT __r) _NOEXCEPT {
|
|
using _Lim = std::numeric_limits<_IntT>;
|
|
const _IntT _MaxVal = std::__max_representable_int_for_float<_IntT, _RealT>();
|
|
if (__r >= ::nextafter(static_cast<_RealT>(_MaxVal), INFINITY)) {
|
|
return _Lim::max();
|
|
} else if (__r <= _Lim::lowest()) {
|
|
return _Lim::min();
|
|
}
|
|
return static_cast<_IntT>(__r);
|
|
}
|
|
|
|
_LIBCPP_END_NAMESPACE_STD
|
|
|
|
_LIBCPP_POP_MACROS
|
|
|
|
#endif // _LIBCPP_CMATH
|