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+/* Private function declarations for libm.
+ Copyright (C) 2011-2018 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#define __MSUF_X(x, suffix) x ## suffix
+#define __MSUF_S(...) __MSUF_X (__VA_ARGS__)
+#define __MSUF(x) __MSUF_S (x, _MSUF_)
+
+#define __MSUF_R_X(x, suffix) x ## suffix ## _r
+#define __MSUF_R_S(...) __MSUF_R_X (__VA_ARGS__)
+#define __MSUF_R(x) __MSUF_R_S (x, _MSUF_)
+
+/* IEEE style elementary functions. */
+extern _Mdouble_ __MSUF (__ieee754_acos) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_acosh) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_asin) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_atan2) (_Mdouble_, _Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_atanh) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_cosh) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_exp) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_exp10) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_exp2) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_fmod) (_Mdouble_, _Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_gamma) (_Mdouble_);
+extern _Mdouble_ __MSUF_R (__ieee754_gamma) (_Mdouble_, int *);
+extern _Mdouble_ __MSUF (__ieee754_hypot) (_Mdouble_, _Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_j0) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_j1) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_jn) (int, _Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_lgamma) (_Mdouble_);
+extern _Mdouble_ __MSUF_R (__ieee754_lgamma) (_Mdouble_, int *);
+extern _Mdouble_ __MSUF (__ieee754_log) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_log10) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_log2) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_pow) (_Mdouble_, _Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_remainder) (_Mdouble_, _Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_sinh) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_sqrt) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_y0) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_y1) (_Mdouble_);
+extern _Mdouble_ __MSUF (__ieee754_yn) (int, _Mdouble_);
+
+extern _Mdouble_ __MSUF (__ieee754_scalb) (_Mdouble_, _Mdouble_);
+extern int __MSUF (__ieee754_ilogb) (_Mdouble_);
+
+extern int32_t __MSUF (__ieee754_rem_pio2) (_Mdouble_, _Mdouble_ *);
+
+/* fdlibm kernel functions. */
+extern _Mdouble_ __MSUF (__kernel_sin) (_Mdouble_, _Mdouble_, int);
+extern _Mdouble_ __MSUF (__kernel_cos) (_Mdouble_, _Mdouble_);
+extern _Mdouble_ __MSUF (__kernel_tan) (_Mdouble_, _Mdouble_, int);
+
+#if defined __MATH_DECLARING_LONG_DOUBLE || defined __MATH_DECLARING_FLOATN
+extern void __MSUF (__kernel_sincos) (_Mdouble_, _Mdouble_,
+ _Mdouble_ *, _Mdouble_ *, int);
+#endif
+
+#if !defined __MATH_DECLARING_LONG_DOUBLE || defined __MATH_DECLARING_FLOATN
+extern int __MSUF (__kernel_rem_pio2) (_Mdouble_ *, _Mdouble_ *, int,
+ int, int, const int32_t *);
+#endif
+
+/* Internal functions. */
+#if !defined __MATH_DECLARING_LONG_DOUBLE || !defined NO_LONG_DOUBLE
+extern _Mdouble_ __MSUF (__copysign) (_Mdouble_ x, _Mdouble_ __y);
+
+extern inline _Mdouble_
+__MSUF (__copysign) (_Mdouble_ x, _Mdouble_ __y)
+{
+ return __MSUF (__builtin_copysign) (x, __y);
+}
+#endif
+
+/* Return X^2 + Y^2 - 1, computed without large cancellation error.
+ It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >=
+ 0.5. */
+extern _Mdouble_ __MSUF (__x2y2m1) (_Mdouble_ x, _Mdouble_ y);
+
+/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
+ - 1, in the form R * (1 + *EPS) where the return value R is an
+ approximation to the product and *EPS is set to indicate the
+ approximate error in the return value. X is such that all the
+ values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
+ X is small enough that factors quadratic in it can be
+ neglected. */
+extern _Mdouble_ __MSUF (__gamma_product) (_Mdouble_ x, _Mdouble_ x_eps,
+ int n, _Mdouble_ *eps);
+
+/* Compute lgamma of a negative argument X, if it is in a range
+ (depending on the floating-point format) for which expansion around
+ zeros is used, setting *SIGNGAMP accordingly. */
+extern _Mdouble_ __MSUF (__lgamma_neg) (_Mdouble_ x, int *signgamp);
+
+/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
+ 1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that
+ all the values X + 1, ..., X + N - 1 are exactly representable, and
+ X_EPS / X is small enough that factors quadratic in it can be
+ neglected. */
+#if !defined __MATH_DECLARING_FLOAT
+extern _Mdouble_ __MSUF (__lgamma_product) (_Mdouble_ t, _Mdouble_ x,
+ _Mdouble_ x_eps, int n);
+#endif
+
+#undef __MSUF_X
+#undef __MSUF_S
+#undef __MSUF
+
+#undef __MSUF_R_X
+#undef __MSUF_R_S
+#undef __MSUF_R