671 lines
21 KiB
C
671 lines
21 KiB
C
/****************************************************************************
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* libs/libm/newlib/include/math.h
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*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership. The
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* ASF licenses this file to you under the Apache License, Version 2.0 (the
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* "License"); you may not use this file except in compliance with the
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* License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
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* License for the specific language governing permissions and limitations
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* under the License.
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*
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****************************************************************************/
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#ifndef _MATH_H_
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#define _MATH_H_
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/****************************************************************************
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* Included Files
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****************************************************************************/
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#include <machine/ieeefp.h>
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#include <stdint.h>
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#ifdef __cplusplus
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extern "C"
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{
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#endif
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/* Macro to test version of GCC. Returns 0 for non-GCC or too old GCC. */
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#ifndef __GNUC_PREREQ
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# if defined __GNUC__ && defined __GNUC_MINOR__
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# define __GNUC_PREREQ(maj, min) \
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((__GNUC__ << 16) + __GNUC_MINOR__ >= ((maj) << 16) + (min))
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# else
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# define __GNUC_PREREQ(maj, min) 0
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# endif
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#endif /* __GNUC_PREREQ */
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#ifndef __has_extension
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# ifdef __has_feature
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# define __has_extension __has_feature
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# else
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# define __has_extension(x) 0
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# endif
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#endif
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#if !__has_extension(c_thread_local)
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/* XXX: Some compilers (Clang 3.3, GCC 4.7) falsely announce C++11 mode
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* without actually supporting the thread_local keyword. Don't check for
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* the presence of C++11 when defining _Thread_local.
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*/
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# if /* (defined(__cplusplus) && __cplusplus >= 201103L) || */ \
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__has_extension(cxx_thread_local)
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# define _Thread_local thread_local
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# else
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# define _Thread_local __thread
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# endif
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#endif
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/* Newlib doesn't fully support long double math functions so far.
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* On platforms where long double equals double the long double functions
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* let's define _LDBL_EQ_DBL to simply call the double functions.
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*/
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#define _LDBL_EQ_DBL 1
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extern _Thread_local int _tls_gamma_signgam;
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#define _REENT_SIGNGAM(ptr) _tls_gamma_signgam
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/* Natural log of 2 */
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#define _M_LN2 0.693147180559945309417
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#if __GNUC_PREREQ (3, 3)
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/* gcc >= 3.3 implicitly defines builtins for HUGE_VALx values. */
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# ifndef HUGE_VAL
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# define HUGE_VAL (__builtin_huge_val())
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# endif
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# ifndef HUGE_VALF
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# define HUGE_VALF (__builtin_huge_valf())
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# endif
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# ifndef HUGE_VALL
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# define HUGE_VALL (__builtin_huge_vall())
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# endif
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# ifndef INFINITY
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# define INFINITY (__builtin_inff())
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# endif
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# ifndef NAN
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# define NAN (__builtin_nanf(""))
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# endif
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#else /* !gcc >= 3.3 */
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/* No builtins. Use fixed defines instead. (All 3 HUGE plus the INFINITY
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* and NAN macros are required to be constant expressions. Using a variable--
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* even a static const--does not meet this requirement, as it cannot be
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* evaluated at translation time.)
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* The infinities are done using numbers that are far in excess of
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* something that would be expected to be encountered in a floating-point
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* implementation. (A more certain way uses values from float.h, but that is
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* avoided because system includes are not supposed to include each other.)
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* This method might produce warnings from some compilers. (It does in
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* newer GCCs, but not for ones that would hit this #else.) If this happens,
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* please report details to the Newlib mailing list.
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*/
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#ifndef HUGE_VAL
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#define HUGE_VAL (1.0e999999999)
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#endif
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#ifndef HUGE_VALF
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#define HUGE_VALF (1.0e999999999F)
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#endif
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#if !defined(HUGE_VALL) && defined(_HAVE_LONG_DOUBLE)
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#define HUGE_VALL (1.0e999999999L)
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#endif
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#if !defined(INFINITY)
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#define INFINITY (HUGE_VALF)
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#endif
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#if !defined(NAN)
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#define NAN (0.0F/0.0F)
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#endif
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#endif /* !gcc >= 3.3 */
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/* Reentrant ANSI C functions. */
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#ifndef __math_68881
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extern double atan (double);
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extern double cos (double);
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extern double sin (double);
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extern double tan (double);
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extern double tanh (double);
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extern double frexp (double, int *);
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extern double modf (double, double *);
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extern double ceil (double);
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extern double fabs (double);
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extern double floor (double);
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#endif /* ! defined (__math_68881) */
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/* Non reentrant ANSI C functions. */
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#ifndef __math_68881
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extern double acos (double);
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extern double asin (double);
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extern double atan2 (double, double);
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extern double cosh (double);
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extern double sinh (double);
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extern double exp (double);
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extern double ldexp (double, int);
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extern double log (double);
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extern double log10 (double);
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extern double pow (double, double);
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extern double sqrt (double);
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extern double fmod (double, double);
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#endif /* ! defined (__math_68881) */
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extern int finite (double);
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extern int finitef (float);
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extern int finitel (long double);
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extern int isinff (float);
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extern int isnanf (float);
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#ifdef __CYGWIN__ /* not implemented in newlib yet */
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extern int isinfl (long double);
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extern int isnanl (long double);
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#endif
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#if !defined(__cplusplus) || __cplusplus < 201103L
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extern int isinf (double);
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#endif
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#if !defined(__cplusplus) || __cplusplus < 201103L
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extern int isnan (double);
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#endif
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/* ISO C99 types and macros. */
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/* FIXME: FLT_EVAL_METHOD should somehow be gotten from float.h (which is
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* hard, considering that the standard says the includes it defines should
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* not include other includes that it defines) and that value used. (This
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* can be solved, but autoconf has a bug which makes the solution more
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* difficult, so it has been skipped for now.)
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*/
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#if !defined(FLT_EVAL_METHOD) && defined(__FLT_EVAL_METHOD__)
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#define FLT_EVAL_METHOD __FLT_EVAL_METHOD__
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#define __TMP_FLT_EVAL_METHOD
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#endif /* FLT_EVAL_METHOD */
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#if defined FLT_EVAL_METHOD
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/* FLT_EVAL_METHOD == 16 has meaning as defined in ISO/IEC TS 18661-3,
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* which provides non-compliant extensions to C and POSIX (by adding
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* additional positive values for FLT_EVAL_METHOD). It effectively has
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* same meaning as the C99 and C11 definitions for value 0, while also
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* serving as a flag that the _Float16 (float16_t) type exists.
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*
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* FLT_EVAL_METHOD could be any number of bits of supported floating point
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* format (e.g. 32, 64, 128), but currently only AArch64 and few other
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* targets might define that as 16.
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*/
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#if (FLT_EVAL_METHOD == 0) \
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|| (FLT_EVAL_METHOD == 16)
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typedef float float_t;
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typedef double double_t;
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#elif FLT_EVAL_METHOD == 1
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typedef double float_t;
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typedef double double_t;
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#elif FLT_EVAL_METHOD == 2
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typedef long double float_t;
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typedef long double double_t;
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#else
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/* Implementation-defined. Assume float_t and double_t have been
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* defined previously for this configuration (e.g. config.h).
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*/
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/* If __DOUBLE_TYPE is defined (__FLOAT_TYPE is then supposed to be
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* defined as well) float_t and double_t definition is suggested by
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* an arch specific header.
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*/
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#ifdef __DOUBLE_TYPE
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typedef __DOUBLE_TYPE double_t;
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typedef __FLOAT_TYPE float_t;
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#endif
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/* Assume config.h has provided these types. */
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#endif
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#else
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/* Assume basic definitions. */
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typedef float float_t;
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typedef double double_t;
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#endif
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#if defined(__TMP_FLT_EVAL_METHOD)
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#undef FLT_EVAL_METHOD
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#endif
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#define FP_NAN 0
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#define FP_INFINITE 1
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#define FP_ZERO 2
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#define FP_SUBNORMAL 3
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#define FP_NORMAL 4
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#ifndef FP_ILOGB0
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# define FP_ILOGB0 (-__INT_MAX__)
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#endif
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#ifndef FP_ILOGBNAN
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# define FP_ILOGBNAN __INT_MAX__
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#endif
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#ifndef MATH_ERRNO
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# define MATH_ERRNO 1
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#endif
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#ifndef MATH_ERREXCEPT
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# define MATH_ERREXCEPT 2
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#endif
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#ifndef math_errhandling
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# ifdef _IEEE_LIBM
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# define _MATH_ERRHANDLING_ERRNO 0
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# else
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# define _MATH_ERRHANDLING_ERRNO MATH_ERRNO
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# endif
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# ifdef _SUPPORTS_ERREXCEPT
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# define _MATH_ERRHANDLING_ERREXCEPT MATH_ERREXCEPT
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# else
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# define _MATH_ERRHANDLING_ERREXCEPT 0
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# endif
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# define math_errhandling (_MATH_ERRHANDLING_ERRNO | _MATH_ERRHANDLING_ERREXCEPT)
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#endif
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extern int __isinff (float);
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extern int __isinfd (double);
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extern int __isnanf (float);
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extern int __isnand (double);
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extern int __fpclassifyf (float);
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extern int __fpclassifyd (double);
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extern int __signbitf (float);
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extern int __signbitd (double);
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/* Note: isinf and isnan were once functions in newlib that took double
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* arguments. C99 specifies that these names are reserved for macros
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* supporting multiple floating point types. Thus, they are
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* now defined as macros. Implementations of the old functions
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* taking double arguments still exist for compatibility purposes
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* (prototypes for them are earlier in this header).
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*/
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#if __GNUC_PREREQ (4, 4)
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#define fpclassify(__x) (__builtin_fpclassify (FP_NAN, FP_INFINITE, \
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FP_NORMAL, FP_SUBNORMAL, \
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FP_ZERO, __x))
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#ifndef isfinite
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#define isfinite(__x) (__builtin_isfinite (__x))
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#endif
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#ifndef isinf
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#define isinf(__x) (__builtin_isinf_sign (__x))
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#endif
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#ifndef isnan
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#define isnan(__x) (__builtin_isnan (__x))
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#endif
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#define isnormal(__x) (__builtin_isnormal (__x))
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#else
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#define fpclassify(__x) \
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((sizeof(__x) == sizeof(float)) ? __fpclassifyf(__x) : \
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__fpclassifyd(__x))
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#ifndef isfinite
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#define isfinite(__y) \
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(__extension__ ({int __cy = fpclassify(__y); \
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__cy != FP_INFINITE && __cy != FP_NAN;}))
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#endif
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#ifndef isinf
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#define isinf(__x) (fpclassify(__x) == FP_INFINITE)
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#endif
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#ifndef isnan
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#define isnan(__x) (fpclassify(__x) == FP_NAN)
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#endif
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#define isnormal(__x) (fpclassify(__x) == FP_NORMAL)
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#endif
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#if __GNUC_PREREQ (4, 0)
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#if defined(_HAVE_LONG_DOUBLE)
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#define signbit(__x) \
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((sizeof(__x) == sizeof(float)) ? __builtin_signbitf(__x) : \
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(sizeof(__x) == sizeof(double)) ? __builtin_signbit (__x) : \
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__builtin_signbitl(__x))
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#else
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#define signbit(__x) \
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((sizeof(__x) == sizeof(float)) ? __builtin_signbitf(__x) : \
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__builtin_signbit (__x))
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#endif
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#else
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#define signbit(__x) \
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((sizeof(__x) == sizeof(float)) ? __signbitf(__x) : \
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__signbitd(__x))
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#endif
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#if __GNUC_PREREQ (2, 97)
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#define isgreater(__x,__y) (__builtin_isgreater (__x, __y))
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#define isgreaterequal(__x,__y) (__builtin_isgreaterequal (__x, __y))
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#define isless(__x,__y) (__builtin_isless (__x, __y))
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#define islessequal(__x,__y) (__builtin_islessequal (__x, __y))
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#define islessgreater(__x,__y) (__builtin_islessgreater (__x, __y))
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#define isunordered(__x,__y) (__builtin_isunordered (__x, __y))
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#else
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#define isgreater(x,y) \
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(__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \
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!isunordered(__x,__y) && (__x > __y);}))
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#define isgreaterequal(x,y) \
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(__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \
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!isunordered(__x,__y) && (__x >= __y);}))
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#define isless(x,y) \
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(__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \
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!isunordered(__x,__y) && (__x < __y);}))
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#define islessequal(x,y) \
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(__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \
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!isunordered(__x,__y) && (__x <= __y);}))
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#define islessgreater(x,y) \
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(__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \
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!isunordered(__x,__y) && (__x < __y || __x > __y);}))
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#define isunordered(a,b) \
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(__extension__ ({__typeof__(a) __a = (a); __typeof__(b) __b = (b); \
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fpclassify(__a) == FP_NAN || fpclassify(__b) == FP_NAN;}))
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#endif
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/* Non ANSI double precision functions. */
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extern double infinity (void);
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extern double nan (const char *);
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extern double copysign (double, double);
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extern double logb (double);
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extern int ilogb (double);
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extern double asinh (double);
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extern double cbrt (double);
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extern double nextafter (double, double);
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extern double rint (double);
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extern double scalbn (double, int);
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extern double exp2 (double);
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extern double scalbln (double, long int);
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extern double tgamma (double);
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extern double nearbyint (double);
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extern long int lrint (double);
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extern long long int llrint (double);
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extern double round (double);
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extern long int lround (double);
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extern long long int llround (double);
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extern double trunc (double);
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extern double remquo (double, double, int *);
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extern double fdim (double, double);
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extern double fmax (double, double);
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extern double fmin (double, double);
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extern double fma (double, double, double);
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#ifndef __math_68881
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extern double log1p (double);
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extern double expm1 (double);
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#endif /* ! defined (__math_68881) */
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extern double acosh (double);
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extern double atanh (double);
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extern double remainder (double, double);
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extern double gamma (double);
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extern double lgamma (double);
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extern double erf (double);
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extern double erfc (double);
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extern double log2 (double);
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#if !defined(__cplusplus)
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#define log2(x) (log (x) / _M_LN2)
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#endif
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#ifndef __math_68881
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extern double hypot (double, double);
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#endif
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/* Single precision versions of ANSI functions. */
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extern float atanf (float);
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extern float cosf (float);
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extern float sinf (float);
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extern float tanf (float);
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extern float tanhf (float);
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extern float frexpf (float, int *);
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extern float modff (float, float *);
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extern float ceilf (float);
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extern float fabsf (float);
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extern float floorf (float);
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extern float acosf (float);
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extern float asinf (float);
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extern float atan2f (float, float);
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extern float coshf (float);
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extern float sinhf (float);
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extern float expf (float);
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extern float ldexpf (float, int);
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extern float logf (float);
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extern float log10f (float);
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extern float powf (float, float);
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extern float sqrtf (float);
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extern float fmodf (float, float);
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/* Other single precision functions. */
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extern float exp2f (float);
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extern float scalblnf (float, long int);
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extern float tgammaf (float);
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extern float nearbyintf (float);
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extern long int lrintf (float);
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extern long long int llrintf (float);
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extern float roundf (float);
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extern long int lroundf (float);
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extern long long int llroundf (float);
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extern float truncf (float);
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extern float remquof (float, float, int *);
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extern float fdimf (float, float);
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extern float fmaxf (float, float);
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extern float fminf (float, float);
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extern float fmaf (float, float, float);
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extern float infinityf (void);
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extern float nanf (const char *);
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extern float copysignf (float, float);
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extern float logbf (float);
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extern int ilogbf (float);
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extern float asinhf (float);
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extern float cbrtf (float);
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extern float nextafterf (float, float);
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extern float rintf (float);
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extern float scalbnf (float, int);
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extern float log1pf (float);
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extern float expm1f (float);
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extern float acoshf (float);
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extern float atanhf (float);
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extern float remainderf (float, float);
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extern float gammaf (float);
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extern float lgammaf (float);
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extern float erff (float);
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extern float erfcf (float);
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extern float log2f (float);
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extern float hypotf (float, float);
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/* Newlib doesn't fully support long double math functions so far.
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* On platforms where long double equals double the long double functions
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* simply call the double functions. On Cygwin the long double functions
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* are implemented independently from newlib to be able to use optimized
|
|
* assembler functions despite using the Microsoft x86_64 ABI.
|
|
*/
|
|
|
|
#if defined (_LDBL_EQ_DBL) || defined (__CYGWIN__)
|
|
/* Reentrant ANSI C functions. */
|
|
#ifndef __math_68881
|
|
extern long double atanl (long double);
|
|
extern long double cosl (long double);
|
|
extern long double sinl (long double);
|
|
extern long double tanl (long double);
|
|
extern long double tanhl (long double);
|
|
extern long double frexpl (long double, int *);
|
|
extern long double modfl (long double, long double *);
|
|
extern long double ceill (long double);
|
|
extern long double fabsl (long double);
|
|
extern long double floorl (long double);
|
|
extern long double log1pl (long double);
|
|
extern long double expm1l (long double);
|
|
#endif /* ! defined (__math_68881) */
|
|
/* Non reentrant ANSI C functions. */
|
|
#ifndef __math_68881
|
|
extern long double acosl (long double);
|
|
extern long double asinl (long double);
|
|
extern long double atan2l (long double, long double);
|
|
extern long double coshl (long double);
|
|
extern long double sinhl (long double);
|
|
extern long double expl (long double);
|
|
extern long double ldexpl (long double, int);
|
|
extern long double logl (long double);
|
|
extern long double log10l (long double);
|
|
extern long double powl (long double, long double);
|
|
extern long double sqrtl (long double);
|
|
extern long double fmodl (long double, long double);
|
|
extern long double hypotl (long double, long double);
|
|
#endif /* ! defined (__math_68881) */
|
|
extern long double copysignl (long double, long double);
|
|
extern long double nanl (const char *);
|
|
extern int ilogbl (long double);
|
|
extern long double asinhl (long double);
|
|
extern long double cbrtl (long double);
|
|
extern long double nextafterl (long double, long double);
|
|
extern float nexttowardf (float, long double);
|
|
extern double nexttoward (double, long double);
|
|
extern long double nexttowardl (long double, long double);
|
|
extern long double logbl (long double);
|
|
extern long double log2l (long double);
|
|
extern long double rintl (long double);
|
|
extern long double scalbnl (long double, int);
|
|
extern long double exp2l (long double);
|
|
extern long double scalblnl (long double, long);
|
|
extern long double tgammal (long double);
|
|
extern long double nearbyintl (long double);
|
|
extern long int lrintl (long double);
|
|
extern long long int llrintl (long double);
|
|
extern long double roundl (long double);
|
|
extern long lroundl (long double);
|
|
extern long long int llroundl (long double);
|
|
extern long double truncl (long double);
|
|
extern long double remquol (long double, long double, int *);
|
|
extern long double fdiml (long double, long double);
|
|
extern long double fmaxl (long double, long double);
|
|
extern long double fminl (long double, long double);
|
|
extern long double fmal (long double, long double, long double);
|
|
extern long double acoshl (long double);
|
|
extern long double atanhl (long double);
|
|
extern long double remainderl (long double, long double);
|
|
extern long double lgammal (long double);
|
|
extern long double erfl (long double);
|
|
extern long double erfcl (long double);
|
|
#else /* !_LDBL_EQ_DBL && !__CYGWIN__ */
|
|
extern long double hypotl (long double, long double);
|
|
extern long double sqrtl (long double);
|
|
extern long double frexpl (long double, int *);
|
|
#ifdef __i386__
|
|
/* Other long double precision functions. */
|
|
|
|
extern _LONG_DOUBLE rintl (_LONG_DOUBLE);
|
|
extern long int lrintl (_LONG_DOUBLE);
|
|
extern long long int llrintl (_LONG_DOUBLE);
|
|
#endif /* __i386__ */
|
|
#endif /* !_LDBL_EQ_DBL && !__CYGWIN__ */
|
|
|
|
extern double drem (double, double);
|
|
extern float dremf (float, float);
|
|
#ifdef __CYGWIN__
|
|
extern float dreml (long double, long double);
|
|
#endif /* __CYGWIN__ */
|
|
extern double gamma_r (double, int *);
|
|
extern double lgamma_r (double, int *);
|
|
extern float gammaf_r (float, int *);
|
|
extern float lgammaf_r (float, int *);
|
|
|
|
extern double y0 (double);
|
|
extern double y1 (double);
|
|
extern double yn (int, double);
|
|
extern double j0 (double);
|
|
extern double j1 (double);
|
|
extern double jn (int, double);
|
|
|
|
extern float y0f (float);
|
|
extern float y1f (float);
|
|
extern float ynf (int, float);
|
|
extern float j0f (float);
|
|
extern float j1f (float);
|
|
extern float jnf (int, float);
|
|
|
|
/* GNU extensions */
|
|
|
|
extern void sincos (double, double *, double *);
|
|
extern void sincosf (float, float *, float *);
|
|
#ifdef __CYGWIN__
|
|
extern void sincosl (long double, long double *, long double *);
|
|
#endif /* __CYGWIN__ */
|
|
# ifndef exp10
|
|
extern double exp10 (double);
|
|
# endif
|
|
# ifndef pow10
|
|
extern double pow10 (double);
|
|
# endif
|
|
# ifndef exp10f
|
|
extern float exp10f (float);
|
|
# endif
|
|
# ifndef pow10f
|
|
extern float pow10f (float);
|
|
# endif
|
|
#ifdef __CYGWIN__
|
|
# ifndef exp10l
|
|
extern float exp10l (float);
|
|
# endif
|
|
# ifndef pow10l
|
|
extern float pow10l (float);
|
|
# endif
|
|
#endif /* __CYGWIN__ */
|
|
|
|
/* The gamma functions use a global variable, signgam. */
|
|
#define signgam (*__signgam())
|
|
extern int *__signgam (void);
|
|
|
|
#define __signgam_r(ptr) _REENT_SIGNGAM(ptr)
|
|
|
|
/* Useful constants. */
|
|
|
|
#define MAXFLOAT 3.40282347e+38F
|
|
|
|
#define M_E 2.7182818284590452354
|
|
#define M_LOG2E 1.4426950408889634074
|
|
#define M_LOG10E 0.43429448190325182765
|
|
#define M_LN2 _M_LN2
|
|
#define M_LN10 2.30258509299404568402
|
|
#define M_PI 3.14159265358979323846
|
|
#define M_PI_2 1.57079632679489661923
|
|
#define M_PI_4 0.78539816339744830962
|
|
#define M_1_PI 0.31830988618379067154
|
|
#define M_2_PI 0.63661977236758134308
|
|
#define M_2_SQRTPI 1.12837916709551257390
|
|
#define M_SQRT2 1.41421356237309504880
|
|
#define M_SQRT1_2 0.70710678118654752440
|
|
|
|
#define M_TWOPI (M_PI * 2.0)
|
|
#define M_3PI_4 2.3561944901923448370E0
|
|
#define M_SQRTPI 1.77245385090551602792981
|
|
#define M_LN2LO 1.9082149292705877000E-10
|
|
#define M_LN2HI 6.9314718036912381649E-1
|
|
#define M_SQRT3 1.73205080756887719000
|
|
#define M_IVLN10 0.43429448190325182765 /* 1 / log(10) */
|
|
#define M_LOG2_E _M_LN2
|
|
#define M_INVLN2 1.4426950408889633870E0 /* 1 / log(2) */
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|
|
|
|
#endif /* _MATH_H_ */
|