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+/* Inline math functions for i387.
+ Copyright (C) 1995, 1996, 1997 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by John C. Bowman <bowman@ipp-garching.mpg.de>, 1995.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Library General Public License as
+ published by the Free Software Foundation; either version 2 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
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public
+ License along with the GNU C Library; see the file COPYING.LIB. If not,
+ write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA. */
+
+#ifndef _BITS_MATHINLINE_H
+#define _BITS_MATHINLINE_H 1
+
+#if defined __GNUG__ && \
+ (__GNUC__ < 2 || (__GNUC__ == 2 && __GNUC_MINOR__ <= 7))
+/* gcc 2.7.2 and 2.7.2.1 have problems with inlining `long double'
+ functions so we disable this now. */
+#undef __NO_MATH_INLINES
+#define __NO_MATH_INLINES
+#endif
+
+#ifdef __GNUC__
+#ifndef __NO_MATH_INLINES
+
+#ifdef __cplusplus
+#define __MATH_INLINE __inline
+#else
+#define __MATH_INLINE extern __inline
+#endif
+
+__MATH_INLINE double cos (double);
+__MATH_INLINE double sin (double);
+
+
+__MATH_INLINE double __expm1 (double __x);
+__MATH_INLINE double
+__expm1 (double __x)
+{
+ register double __value, __exponent, __temp;
+ __asm __volatile__
+ ("fldl2e # e^x - 1 = 2^(x * log2(e)) - 1\n\t"
+ "fmul %%st(1) # x * log2(e)\n\t"
+ "fstl %%st(1)\n\t"
+ "frndint # int(x * log2(e))\n\t"
+ "fxch\n\t"
+ "fsub %%st(1) # fract(x * log2(e))\n\t"
+ "f2xm1 # 2^(fract(x * log2(e))) - 1\n\t"
+ "fscale # 2^(x * log2(e)) - 2^(int(x * log2(e)))\n\t"
+ : "=t" (__value), "=u" (__exponent) : "0" (__x));
+ __asm __volatile__
+ ("fscale # 2^int(x * log2(e))\n\t"
+ : "=t" (__temp) : "0" (1.0), "u" (__exponent));
+ __temp -= 1.0;
+
+ return __temp + __value;
+}
+
+__MATH_INLINE double __sgn1 (double __x);
+__MATH_INLINE double
+__sgn1 (double __x)
+{
+ return __x >= 0.0 ? 1.0 : -1.0;
+}
+
+__MATH_INLINE double sqrt (double __x);
+__MATH_INLINE double
+sqrt (double __x)
+{
+ register double __value;
+ __asm __volatile__
+ ("fsqrt"
+ : "=t" (__value) : "0" (__x));
+
+ return __value;
+}
+
+__MATH_INLINE double fabs (double __x);
+__MATH_INLINE double
+fabs (double __x)
+{
+ register double __value;
+ __asm __volatile__
+ ("fabs"
+ : "=t" (__value) : "0" (__x));
+
+ return __value;
+}
+
+/* The argument range of this inline version is limited. */
+__MATH_INLINE double sin (double __x);
+__MATH_INLINE double
+sin (double __x)
+{
+ register double __value;
+ __asm __volatile__
+ ("fsin"
+ : "=t" (__value) : "0" (__x));
+
+ return __value;
+}
+
+/* The argument range of this inline version is limited. */
+__MATH_INLINE double cos (double __x);
+__MATH_INLINE double
+cos (double __x)
+{
+ register double __value;
+ __asm __volatile__
+ ("fcos"
+ : "=t" (__value): "0" (__x));
+
+ return __value;
+}
+
+__MATH_INLINE double tan (double __x);
+__MATH_INLINE double
+tan (double __x)
+{
+ register double __value;
+ register double __value2 __attribute__ ((unused));
+ __asm __volatile__
+ ("fptan"
+ : "=t" (__value2), "=u" (__value) : "0" (__x));
+
+ return __value;
+}
+
+__MATH_INLINE double atan2 (double __y, double __x);
+__MATH_INLINE double
+atan2 (double __y, double __x)
+{
+ register double __value;
+ __asm __volatile__
+ ("fpatan\n\t"
+ "fldl %%st(0)"
+ : "=t" (__value) : "0" (__x), "u" (__y));
+
+ return __value;
+}
+
+__MATH_INLINE double asin (double __x);
+__MATH_INLINE double
+asin (double __x)
+{
+ return atan2 (__x, sqrt (1.0 - __x * __x));
+}
+
+__MATH_INLINE double acos (double __x);
+__MATH_INLINE double
+acos (double __x)
+{
+ return atan2 (sqrt (1.0 - __x * __x), __x);
+}
+
+__MATH_INLINE double atan (double __x);
+__MATH_INLINE double
+atan (double __x)
+{
+ register double __value;
+ __asm __volatile__
+ ("fld1\n\t"
+ "fpatan"
+ : "=t" (__value) : "0" (__x));
+
+ return __value;
+}
+
+__MATH_INLINE double exp (double __x);
+__MATH_INLINE double
+exp (double __x)
+{
+ register double __value, __exponent;
+ __asm __volatile__
+ ("fldl2e # e^x = 2^(x * log2(e))\n\t"
+ "fmul %%st(1) # x * log2(e)\n\t"
+ "fstl %%st(1)\n\t"
+ "frndint # int(x * log2(e))\n\t"
+ "fxch\n\t"
+ "fsub %%st(1) # fract(x * log2(e))\n\t"
+ "f2xm1 # 2^(fract(x * log2(e))) - 1\n\t"
+ : "=t" (__value), "=u" (__exponent) : "0" (__x));
+ __value += 1.0;
+ __asm __volatile__
+ ("fscale"
+ : "=t" (__value) : "0" (__value), "u" (__exponent));
+
+ return __value;
+}
+
+__MATH_INLINE double sinh (double __x);
+__MATH_INLINE double
+sinh (double __x)
+{
+ register double __exm1 = __expm1 (fabs (__x));
+
+ return 0.5 * (__exm1 / (__exm1 + 1.0) + __exm1) * __sgn1 (__x);
+}
+
+__MATH_INLINE double cosh (double __x);
+__MATH_INLINE double
+cosh (double __x)
+{
+ register double __ex = exp (__x);
+
+ return 0.5 * (__ex + 1.0 / __ex);
+}
+
+__MATH_INLINE double tanh (double __x);
+__MATH_INLINE double
+tanh (double __x)
+{
+ register double __exm1 = __expm1 (-fabs (__x + __x));
+
+ return __exm1 / (__exm1 + 2.0) * __sgn1 (-__x);
+}
+
+__MATH_INLINE double log (double __x);
+__MATH_INLINE double
+log (double __x)
+{
+ register double __value;
+ __asm __volatile__
+ ("fldln2\n\t"
+ "fxch\n\t"
+ "fyl2x"
+ : "=t" (__value) : "0" (__x));
+
+ return __value;
+}
+
+__MATH_INLINE double log10 (double __x);
+__MATH_INLINE double
+log10 (double __x)
+{
+ register double __value;
+ __asm __volatile__
+ ("fldlg2\n\t"
+ "fxch\n\t"
+ "fyl2x"
+ : "=t" (__value) : "0" (__x));
+
+ return __value;
+}
+
+__MATH_INLINE double __log2 (double __x);
+__MATH_INLINE double
+__log2 (double __x)
+{
+ register double __value;
+ __asm __volatile__
+ ("fld1\n\t"
+ "fxch\n\t"
+ "fyl2x"
+ : "=t" (__value) : "0" (__x));
+
+ return __value;
+}
+
+__MATH_INLINE double fmod (double __x, double __y);
+__MATH_INLINE double
+fmod (double __x, double __y)
+{
+ register double __value;
+ __asm __volatile__
+ ("1: fprem\n\t"
+ "fstsw %%ax\n\t"
+ "sahf\n\t"
+ "jp 1b"
+ : "=t" (__value) : "0" (__x), "u" (__y) : "ax", "cc");
+
+ return __value;
+}
+
+__MATH_INLINE double ldexp (double __x, int __y);
+__MATH_INLINE double
+ldexp (double __x, int __y)
+{
+ register double __value;
+ __asm __volatile__
+ ("fscale"
+ : "=t" (__value) : "0" (__x), "u" ((double) __y));
+
+ return __value;
+}
+
+__MATH_INLINE double pow (double __x, double __y);
+__MATH_INLINE double
+pow (double __x, double __y)
+{
+ register double __value, __exponent;
+ long __p = (long) __y;
+
+ if (__x == 0.0 && __y > 0.0)
+ return 0.0;
+ if (__y == (double) __p)
+ {
+ double __r = 1.0;
+ if (__p == 0)
+ return 1.0;
+ if (__p < 0)
+ {
+ __p = -__p;
+ __x = 1.0 / __x;
+ }
+ while (1)
+ {
+ if (__p & 1)
+ __r *= __x;
+ __p >>= 1;
+ if (__p == 0)
+ return __r;
+ __x *= __x;
+ }
+ /* NOTREACHED */
+ }
+ __asm __volatile__
+ ("fmul %%st(1) # y * log2(x)\n\t"
+ "fstl %%st(1)\n\t"
+ "frndint # int(y * log2(x))\n\t"
+ "fxch\n\t"
+ "fsub %%st(1) # fract(y * log2(x))\n\t"
+ "f2xm1 # 2^(fract(y * log2(x))) - 1\n\t"
+ : "=t" (__value), "=u" (__exponent) : "0" (__log2 (__x)), "1" (__y));
+ __value += 1.0;
+ __asm __volatile__
+ ("fscale"
+ : "=t" (__value) : "0" (__value), "u" (__exponent));
+
+ return __value;
+}
+
+__MATH_INLINE double floor (double __x);
+__MATH_INLINE double
+floor (double __x)
+{
+ register double __value;
+ __volatile unsigned short int __cw, __cwtmp;
+
+ __asm __volatile ("fnstcw %0" : "=m" (__cw));
+ __cwtmp = (__cw & 0xf3ff) | 0x0400; /* rounding down */
+ __asm __volatile ("fldcw %0" : : "m" (__cwtmp));
+ __asm __volatile ("frndint" : "=t" (__value) : "0" (__x));
+ __asm __volatile ("fldcw %0" : : "m" (__cw));
+
+ return __value;
+}
+
+__MATH_INLINE double ceil (double __x);
+__MATH_INLINE double
+ceil (double __x)
+{
+ register double __value;
+ __volatile unsigned short int __cw, __cwtmp;
+
+ __asm __volatile ("fnstcw %0" : "=m" (__cw));
+ __cwtmp = (__cw & 0xf3ff) | 0x0800; /* rounding up */
+ __asm __volatile ("fldcw %0" : : "m" (__cwtmp));
+ __asm __volatile ("frndint" : "=t" (__value) : "0" (__x));
+ __asm __volatile ("fldcw %0" : : "m" (__cw));
+
+ return __value;
+}
+
+
+/* Optimized versions for some non-standardized functions. */
+#if defined __USE_ISOC9X || defined __USE_MISC
+
+__MATH_INLINE double hypot (double __x, double __y);
+__MATH_INLINE double
+hypot (double __x, double __y)
+{
+ return sqrt (__x * __x + __y * __y);
+}
+
+/* We cannot rely on M_SQRT being defined. So we do it for ourself
+ here. */
+#define __M_SQRT2 _Mldbl(1.41421356237309504880) /* sqrt(2) */
+
+__MATH_INLINE double log1p (double __x);
+__MATH_INLINE double
+log1p (double __x)
+{
+ register double __value;
+
+ if (fabs (__x) >= 1.0 - 0.5 * __M_SQRT2)
+ __value = log (1.0 + __x);
+ else
+ __asm __volatile__
+ ("fldln2\n\t"
+ "fxch\n\t"
+ "fyl2xp1"
+ : "=t" (__value) : "0" (__x));
+
+ return __value;
+}
+
+__MATH_INLINE double asinh (double __x);
+__MATH_INLINE double
+asinh (double __x)
+{
+ register double __y = fabs (__x);
+
+ return log1p ((__y * __y / (sqrt (__y * __y + 1.0) + 1.0) + __y)
+ * __sgn1 (__x));
+}
+
+__MATH_INLINE double acosh (double __x);
+__MATH_INLINE double
+acosh (double __x)
+{
+ return log (__x + sqrt (__x - 1.0) * sqrt (__x + 1.0));
+}
+
+__MATH_INLINE double atanh (double __x);
+__MATH_INLINE double
+atanh (double __x)
+{
+ register double __y = fabs (__x);
+
+ return -0.5 * __log1p (-(__y + __y) / (1.0 + __y)) * __sgn1 (__x);
+}
+
+__MATH_INLINE double logb (double __x);
+__MATH_INLINE double
+logb (double __x)
+{
+ register double __value, __junk;
+ __asm __volatile__
+ ("fxtract\n\t"
+ : "=t" (__junk), "=u" (__value) : "0" (__x));
+
+ return __value;
+}
+
+__MATH_INLINE double drem (double __x, double __y);
+__MATH_INLINE double
+drem (double __x, double __y)
+{
+ register double __value;
+ __asm __volatile__
+ ("1: fprem1\n\t"
+ "fstsw %%ax\n\t"
+ "sahf\n\t"
+ "jp 1b"
+ : "=t" (__value) : "0" (__x), "u" (__y) : "ax", "cc");
+
+ return __value;
+}
+
+/* This function is used in the `isfinite' macro. */
+__MATH_INLINE int __finite (double __x);
+__MATH_INLINE int
+__finite (double __x)
+{
+ register int __result;
+ __asm__ __volatile__
+ ("orl $0x800fffff, %0\n\t"
+ "incl %0\n\t"
+ "shrl $31, %0"
+ : "=q" (__result) : "0" (((int *) &__x)[1]));
+ return __result;
+}
+
+
+/* ISO C 9X defines some macros to perform unordered comparisons. The
+ ix87 FPU supports this with special opcodes and we should use them.
+ These must not be inline functions since we have to be able to handle
+ all floating-point types. */
+#undef isgreater
+#define isgreater(x, y) \
+ ({ int result; \
+ __asm__ ("fucompp; fnstsw; andb $0x45, %%ah; setz %%al;" \
+ "andl $0xff, %0" \
+ : "=a" (result) : "t" (x), "u" (y) : "cc"); \
+ result; })
+
+#undef isgreaterequal
+#define isgreaterequal(x, y) \
+ ({ int result; \
+ __asm__ ("fucompp; fnstsw; testb $0x05, %%ah; setz %%al;" \
+ "andl $0xff, %0" \
+ : "=a" (result) : "t" (x), "u" (y) : "cc"); \
+ result; })
+
+#undef isless
+#define isless(x, y) \
+ ({ int result; \
+ __asm__ ("fucompp; fnstsw; xorb $0x01, %%ah; testb $0x45, %%ah;" \
+ "setz %%al; andl $0xff, %0" \
+ : "=a" (result) : "t" (x), "u" (y) : "cc"); \
+ result; })
+
+#undef islessequal
+#define islessequal(x, y) \
+ ({ int result; \
+ __asm__ ("fucompp; fnstsw; xorb $0x01, %%ah; testb $0x05, %%ah;" \
+ "setz %%al; andl $0xff, %0" \
+ : "=a" (result) : "t" (x), "u" (y) : "cc"); \
+ result; })
+
+#undef islessgreater
+#define islessgreater(x, y) \
+ ({ int result; \
+ __asm__ ("fucompp; fnstsw; testb $0x44, %%ah; setz %%al;" \
+ "andl $0xff, %0" \
+ : "=a" (result) : "t" (x), "u" (y) : "cc"); \
+ result; })
+
+#undef isunordered
+#define isunordered(x, y) \
+ ({ int result; \
+ __asm__ ("fucompp; fnstsw; sahf; setp %%al; andl $0xff, %0" \
+ : "=a" (result) : "t" (x), "u" (y) : "cc"); \
+ result; })
+#endif
+
+
+#ifdef __USE_MISC
+__MATH_INLINE double coshm1 (double __x);
+__MATH_INLINE double
+coshm1 (double __x)
+{
+ register double __exm1 = __expm1 (fabs (__x));
+
+ return 0.5 * (__exm1 / (__exm1 + 1.0)) * __exm1;
+}
+
+__MATH_INLINE double acosh1p (double __x);
+__MATH_INLINE double
+acosh1p (double __x)
+{
+ return __log1p (__x + sqrt (__x) * sqrt (__x + 2.0));
+}
+
+__MATH_INLINE void sincos (double __x, double *__sinx, double *__cosx);
+__MATH_INLINE void
+sincos (double __x, double *__sinx, double *__cosx)
+{
+ register double __cosr, __sinr;
+ __asm __volatile__
+ ("fsincos\n\t"
+ "fnstsw %%ax\n\t"
+ "testl $0x400, %%eax\n\t"
+ "jz 1f\n\t"
+ "fldpi\n\t"
+ "fadd %%st(0)\n\t"
+ "fxch %%st(1)\n\t"
+ "2: fprem1\n\t"
+ "fnstsw %%ax\n\t"
+ "testl $0x400, %%eax\n\t"
+ "jnz 2b\n\t"
+ "fstp %%st(1)\n\t"
+ "fsincos\n\t"
+ "1:"
+ : "=t" (__cosr), "=u" (__sinr) : "0" (__x));
+
+ *__sinx = __sinr;
+ *__cosx = __cosr;
+}
+
+__MATH_INLINE double sgn (double __x);
+__MATH_INLINE double
+sgn (double __x)
+{
+ return __x == 0.0 ? 0.0 : (__x > 0.0 ? 1.0 : -1.0);
+}
+
+__MATH_INLINE double pow2 (double __x);
+__MATH_INLINE double
+pow2 (double __x)
+{
+ register double __value, __exponent;
+ long __p = (long) __x;
+
+ if (__x == (double) __p)
+ return ldexp (1.0, __p);
+
+ __asm __volatile__
+ ("fldl %%st(0)\n\t"
+ "frndint # int(x)\n\t"
+ "fxch\n\t"
+ "fsub %%st(1) # fract(x)\n\t"
+ "f2xm1 # 2^(fract(x)) - 1\n\t"
+ : "=t" (__value), "=u" (__exponent) : "0" (__x));
+ __value += 1.0;
+ __asm __volatile__
+ ("fscale"
+ : "=t" (__value) : "0" (__value), "u" (__exponent));
+
+ return __value;
+}
+
+#endif /* __USE_MISC */
+
+#endif /* __NO_MATH_INLINES */
+#endif /* __GNUC__ */
+
+#endif /* _BITS_MATHINLINE_H */
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