--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/floatfns.c	Mon Aug 13 08:45:50 2007 +0200
@@ -0,0 +1,1103 @@
+/* Primitive operations on floating point for XEmacs Lisp interpreter.
+   Copyright (C) 1988, 1993, 1994 Free Software Foundation, Inc.
+
+This file is part of XEmacs.
+
+XEmacs is free software; you can redistribute it and/or modify it
+under the terms of the GNU General Public License as published by the
+Free Software Foundation; either version 2, or (at your option) any
+later version.
+
+XEmacs 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 General Public License
+for more details.
+
+You should have received a copy of the GNU General Public License
+along with XEmacs; see the file COPYING.  If not, write to
+the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+Boston, MA 02111-1307, USA.  */
+
+/* Synched up with: FSF 19.30. */
+
+/* ANSI C requires only these float functions:
+   acos, asin, atan, atan2, ceil, cos, cosh, exp, fabs, floor, fmod,
+   frexp, ldexp, log, log10, modf, pow, sin, sinh, sqrt, tan, tanh.
+
+   Define HAVE_INVERSE_HYPERBOLIC if you have acosh, asinh, and atanh.
+   Define HAVE_CBRT if you have cbrt().
+   Define HAVE_RINT if you have rint().
+   If you don't define these, then the appropriate routines will be simulated.
+
+   Define HAVE_MATHERR if on a system supporting the SysV matherr() callback.
+   (This should happen automatically.)
+
+   Define FLOAT_CHECK_ERRNO if the float library routines set errno.
+   This has no effect if HAVE_MATHERR is defined.
+
+   Define FLOAT_CATCH_SIGILL if the float library routines signal SIGILL.
+   (What systems actually do this?  Let me know. -jwz)
+
+   Define FLOAT_CHECK_DOMAIN if the float library doesn't handle errors by
+   either setting errno, or signalling SIGFPE/SIGILL.  Otherwise, domain and
+   range checking will happen before calling the float routines.  This has
+   no effect if HAVE_MATHERR is defined (since matherr will be called when
+   a domain error occurs).
+ */
+
+#include <config.h>
+#include "lisp.h"
+#include "syssignal.h"
+
+#ifdef LISP_FLOAT_TYPE
+
+/* Need to define a differentiating symbol -- see sysfloat.h */
+#define THIS_FILENAME floatfns
+#include "sysfloat.h"
+
+#ifndef HAVE_RINT
+static double
+rint (double x)
+{
+  double r = floor (x + 0.5);
+  double diff = fabs (r - x);
+  /* Round to even and correct for any roundoff errors.  */
+  if (diff >= 0.5 && (diff > 0.5 || r != 2.0 * floor (r / 2.0)))
+    r += r < x ? 1.0 : -1.0;
+  return r;
+}
+#endif
+
+/* Nonzero while executing in floating point.
+   This tells float_error what to do.  */
+static int in_float;
+
+/* If an argument is out of range for a mathematical function,
+   here is the actual argument value to use in the error message.  */
+static Lisp_Object float_error_arg, float_error_arg2;
+static CONST char *float_error_fn_name;
+
+/* Evaluate the floating point expression D, recording NUM
+   as the original argument for error messages.
+   D is normally an assignment expression.
+   Handle errors which may result in signals or may set errno.
+
+   Note that float_error may be declared to return void, so you can't
+   just cast the zero after the colon to (SIGTYPE) to make the types
+   check properly.  */
+#ifdef FLOAT_CHECK_ERRNO
+#define IN_FLOAT(d, name, num)				\
+  do {							\
+    float_error_arg = num;				\
+    float_error_fn_name = name;				\
+    in_float = 1; errno = 0; (d); in_float = 0;		\
+    if (errno != 0) in_float_error ();			\
+  } while (0)
+#define IN_FLOAT2(d, name, num, num2)			\
+  do {							\
+    float_error_arg = num;				\
+    float_error_arg2 = num2;				\
+    float_error_fn_name = name;				\
+    in_float = 2; errno = 0; (d); in_float = 0;		\
+    if (errno != 0) in_float_error ();			\
+  } while (0)
+#else
+#define IN_FLOAT(d, name, num) (in_float = 1, (d), in_float = 0)
+#define IN_FLOAT2(d, name, num, num2) (in_float = 2, (d), in_float = 0)
+#endif
+
+
+#define arith_error(op,arg) \
+  Fsignal (Qarith_error, list2 (build_string ((op)), (arg)))
+#define range_error(op,arg) \
+  Fsignal (Qrange_error, list2 (build_string ((op)), (arg)))
+#define range_error2(op,a1,a2) \
+  Fsignal (Qrange_error, list3 (build_string ((op)), (a1), (a2)))
+#define domain_error(op,arg) \
+  Fsignal (Qdomain_error, list2 (build_string ((op)), (arg)))
+#define domain_error2(op,a1,a2) \
+  Fsignal (Qdomain_error, list3 (build_string ((op)), (a1), (a2)))
+
+
+/* Convert float to Lisp_Int if it fits, else signal a range error
+   using the given arguments.  */
+static Lisp_Object
+float_to_int (double x, CONST char *name, Lisp_Object num, Lisp_Object num2)
+{
+  if (x >= ((EMACS_INT) 1 << (VALBITS-1))
+      || x <= - ((EMACS_INT) 1 << (VALBITS-1)) - (EMACS_INT) 1)
+  {
+    if (!UNBOUNDP (num2))
+      range_error2 (name, num, num2);
+    else
+      range_error (name, num);
+  }
+  return (make_int ((EMACS_INT) x));
+}
+
+
+static void
+in_float_error (void)
+{
+  switch (errno)
+  {
+  case 0: 
+    break;
+  case EDOM:
+    if (in_float == 2)
+      domain_error2 (float_error_fn_name, float_error_arg, float_error_arg2);
+    else
+      domain_error (float_error_fn_name, float_error_arg);
+    break;
+  case ERANGE:
+    range_error (float_error_fn_name, float_error_arg);
+    break;
+  default:
+    arith_error (float_error_fn_name, float_error_arg);
+    break;
+  }
+}
+
+  
+
+static Lisp_Object mark_float (Lisp_Object, void (*) (Lisp_Object));
+extern void print_float (Lisp_Object, Lisp_Object, int);
+static int float_equal (Lisp_Object o1, Lisp_Object o2, int depth);
+static unsigned long float_hash (Lisp_Object obj, int depth);
+DEFINE_BASIC_LRECORD_IMPLEMENTATION ("float", float,
+				     mark_float, print_float, 0, float_equal,
+				     float_hash, struct Lisp_Float);
+
+static Lisp_Object
+mark_float (Lisp_Object obj, void (*markobj) (Lisp_Object))
+{
+  return (Qnil);
+}
+
+static int
+float_equal (Lisp_Object o1, Lisp_Object o2, int depth)
+{
+  return (extract_float (o1) == extract_float (o2));
+}
+
+static unsigned long
+float_hash (Lisp_Object obj, int depth)
+{
+  /* mod the value down to 32-bit range */
+  /* #### change for 64-bit machines */
+  return (unsigned long) fmod (extract_float (obj), 4e9);
+}
+
+
+/* Extract a Lisp number as a `double', or signal an error.  */
+
+double
+extract_float (Lisp_Object num)
+{
+  CHECK_INT_OR_FLOAT (num);
+
+  if (FLOATP (num))
+    return (float_data (XFLOAT (num)));
+  return (double) XINT (num);
+}
+#endif /* LISP_FLOAT_TYPE */
+
+
+/* Trig functions.  */
+#ifdef LISP_FLOAT_TYPE
+
+DEFUN ("acos", Facos, Sacos, 1, 1, 0 /*
+Return the inverse cosine of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+#ifdef FLOAT_CHECK_DOMAIN
+  if (d > 1.0 || d < -1.0)
+    domain_error ("acos", arg);
+#endif
+  IN_FLOAT (d = acos (d), "acos", arg);
+  return make_float (d);
+}
+
+DEFUN ("asin", Fasin, Sasin, 1, 1, 0 /*
+Return the inverse sine of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+#ifdef FLOAT_CHECK_DOMAIN
+  if (d > 1.0 || d < -1.0)
+    domain_error ("asin", arg);
+#endif
+  IN_FLOAT (d = asin (d), "asin", arg);
+  return make_float (d);
+}
+
+DEFUN ("atan", Fatan, Satan, 1, 2, 0 /*
+Return the inverse tangent of ARG.
+*/ )
+  (arg1, arg2)
+     Lisp_Object arg1, arg2;
+{
+  double d = extract_float (arg1);
+
+  if (NILP (arg2))
+    IN_FLOAT (d = atan (d), "atan", arg1);
+  else
+    {
+      double d2 = extract_float (arg2);
+#ifdef FLOAT_CHECK_DOMAIN
+      if (d == 0.0 && d2 == 0.0)
+	domain_error2 ("atan", arg1, arg2);
+#endif
+      IN_FLOAT2 (d = atan2 (d, d2), "atan", arg1, arg2);
+    }
+  return make_float (d);
+}
+
+DEFUN ("cos", Fcos, Scos, 1, 1, 0 /*
+Return the cosine of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  IN_FLOAT (d = cos (d), "cos", arg);
+  return make_float (d);
+}
+
+DEFUN ("sin", Fsin, Ssin, 1, 1, 0 /*
+Return the sine of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  IN_FLOAT (d = sin (d), "sin", arg);
+  return make_float (d);
+}
+
+DEFUN ("tan", Ftan, Stan, 1, 1, 0 /*
+Return the tangent of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  double c = cos (d);
+#ifdef FLOAT_CHECK_DOMAIN
+  if (c == 0.0)
+    domain_error ("tan", arg);
+#endif
+  IN_FLOAT (d = (sin (d) / c), "tan", arg);
+  return make_float (d);
+}
+#endif /* LISP_FLOAT_TYPE (trig functions) */
+
+
+/* Bessel functions */
+#if 0 /* Leave these out unless we find there's a reason for them.  */
+/* #ifdef LISP_FLOAT_TYPE */
+
+DEFUN ("bessel-j0", Fbessel_j0, Sbessel_j0, 1, 1, 0 /*
+Return the bessel function j0 of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  IN_FLOAT (d = j0 (d), "bessel-j0", arg);
+  return make_float (d);
+}
+
+DEFUN ("bessel-j1", Fbessel_j1, Sbessel_j1, 1, 1, 0 /*
+Return the bessel function j1 of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  IN_FLOAT (d = j1 (d), "bessel-j1", arg);
+  return make_float (d);
+}
+
+DEFUN ("bessel-jn", Fbessel_jn, Sbessel_jn, 2, 2, 0 /*
+Return the order N bessel function output jn of ARG.
+The first arg (the order) is truncated to an integer.
+*/ )
+  (arg1, arg2)
+     Lisp_Object arg1, arg2;
+{
+  int i1 = extract_float (arg1);
+  double f2 = extract_float (arg2);
+
+  IN_FLOAT (f2 = jn (i1, f2), "bessel-jn", arg1);
+  return make_float (f2);
+}
+
+DEFUN ("bessel-y0", Fbessel_y0, Sbessel_y0, 1, 1, 0 /*
+Return the bessel function y0 of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  IN_FLOAT (d = y0 (d), "bessel-y0", arg);
+  return make_float (d);
+}
+
+DEFUN ("bessel-y1", Fbessel_y1, Sbessel_y1, 1, 1, 0 /*
+Return the bessel function y1 of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  IN_FLOAT (d = y1 (d), "bessel-y0", arg);
+  return make_float (d);
+}
+
+DEFUN ("bessel-yn", Fbessel_yn, Sbessel_yn, 2, 2, 0 /*
+Return the order N bessel function output yn of ARG.
+The first arg (the order) is truncated to an integer.
+*/ )
+  (arg1, arg2)
+     Lisp_Object arg1, arg2;
+{
+  int i1 = extract_float (arg1);
+  double f2 = extract_float (arg2);
+
+  IN_FLOAT (f2 = yn (i1, f2), "bessel-yn", arg1);
+  return make_float (f2);
+}
+
+#endif /* 0 (bessel functions) */
+
+/* Error functions. */
+#if 0 /* Leave these out unless we see they are worth having.  */
+/* #ifdef LISP_FLOAT_TYPE */
+
+DEFUN ("erf", Ferf, Serf, 1, 1, 0 /*
+Return the mathematical error function of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  IN_FLOAT (d = erf (d), "erf", arg);
+  return make_float (d);
+}
+
+DEFUN ("erfc", Ferfc, Serfc, 1, 1, 0 /*
+Return the complementary error function of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  IN_FLOAT (d = erfc (d), "erfc", arg);
+  return make_float (d);
+}
+
+DEFUN ("log-gamma", Flog_gamma, Slog_gamma, 1, 1, 0 /*
+Return the log gamma of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  IN_FLOAT (d = lgamma (d), "log-gamma", arg);
+  return make_float (d);
+}
+
+#endif /* 0 (error functions) */
+
+
+/* Root and Log functions. */
+
+#ifdef LISP_FLOAT_TYPE
+DEFUN ("exp", Fexp, Sexp, 1, 1, 0 /*
+Return the exponential base e of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+#ifdef FLOAT_CHECK_DOMAIN
+  if (d > 709.7827)   /* Assume IEEE doubles here */
+    range_error ("exp", arg);
+  else if (d < -709.0)
+    return make_float (0.0);
+  else
+#endif
+    IN_FLOAT (d = exp (d), "exp", arg);
+  return make_float (d);
+}
+#endif /* LISP_FLOAT_TYPE */
+
+
+DEFUN ("expt", Fexpt, Sexpt, 2, 2, 0 /*
+Return the exponential ARG1 ** ARG2.
+*/ )
+  (arg1, arg2)
+     Lisp_Object arg1, arg2;
+{
+  double f1, f2;
+
+  CHECK_INT_OR_FLOAT (arg1);
+  CHECK_INT_OR_FLOAT (arg2);
+  if ((INTP (arg1)) && /* common lisp spec */
+      (INTP (arg2))) /* don't promote, if both are ints */
+    {
+      EMACS_INT acc, x, y;
+      x = XINT (arg1);
+      y = XINT (arg2);
+      
+      if (y < 0)
+	{
+	  if (x == 1)
+	    acc = 1;
+	  else if (x == -1)
+	    acc = (y & 1) ? -1 : 1;
+	  else
+	    acc = 0;
+	}
+      else
+	{
+	  acc = 1;
+	  while (y > 0)
+	    {
+	      if (y & 1)
+		acc *= x;
+	      x *= x;
+	      y = (unsigned EMACS_INT) y >> 1;
+	    }
+	}
+      return (make_int (acc));
+    }
+#ifdef LISP_FLOAT_TYPE
+  f1 = (FLOATP (arg1)) ? float_data (XFLOAT (arg1)) : XINT (arg1);
+  f2 = (FLOATP (arg2)) ? float_data (XFLOAT (arg2)) : XINT (arg2);
+  /* Really should check for overflow, too */
+  if (f1 == 0.0 && f2 == 0.0)
+    f1 = 1.0;
+# ifdef FLOAT_CHECK_DOMAIN
+  else if ((f1 == 0.0 && f2 < 0.0) || (f1 < 0 && f2 != floor(f2)))
+    domain_error2 ("expt", arg1, arg2);
+# endif /* FLOAT_CHECK_DOMAIN */
+  IN_FLOAT2 (f1 = pow (f1, f2), "expt", arg1, arg2);
+  return make_float (f1);
+#else  /* !LISP_FLOAT_TYPE */
+  abort ();
+#endif /* LISP_FLOAT_TYPE */
+}
+
+#ifdef LISP_FLOAT_TYPE
+DEFUN ("log", Flog, Slog, 1, 2, 0 /*
+Return the natural logarithm of ARG.
+If second optional argument BASE is given, return log ARG using that base.
+*/ )
+  (arg, base)
+     Lisp_Object arg, base;
+{
+  double d = extract_float (arg);
+#ifdef FLOAT_CHECK_DOMAIN
+  if (d <= 0.0)
+    domain_error2 ("log", arg, base);
+#endif
+  if (NILP (base))
+    IN_FLOAT (d = log (d), "log", arg);
+  else
+    {
+      double b = extract_float (base);
+#ifdef FLOAT_CHECK_DOMAIN
+      if (b <= 0.0 || b == 1.0)
+	domain_error2 ("log", arg, base);
+#endif
+      if (b == 10.0)
+	IN_FLOAT2 (d = log10 (d), "log", arg, base);
+      else
+	IN_FLOAT2 (d = (log (d) / log (b)), "log", arg, base);
+    }
+  return make_float (d);
+}
+
+
+DEFUN ("log10", Flog10, Slog10, 1, 1, 0 /*
+Return the logarithm base 10 of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+#ifdef FLOAT_CHECK_DOMAIN
+  if (d <= 0.0)
+    domain_error ("log10", arg);
+#endif
+  IN_FLOAT (d = log10 (d), "log10", arg);
+  return make_float (d);
+}
+
+
+DEFUN ("sqrt", Fsqrt, Ssqrt, 1, 1, 0 /*
+Return the square root of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+#ifdef FLOAT_CHECK_DOMAIN
+  if (d < 0.0)
+    domain_error ("sqrt", arg);
+#endif
+  IN_FLOAT (d = sqrt (d), "sqrt", arg);
+  return make_float (d);
+}
+
+
+DEFUN ("cube-root", Fcube_root, Scube_root, 1, 1, 0 /*
+Return the cube root of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+#ifdef HAVE_CBRT
+  IN_FLOAT (d = cbrt (d), "cube-root", arg);
+#else
+  if (d >= 0.0)
+    IN_FLOAT (d = pow (d, 1.0/3.0), "cube-root", arg);
+  else
+    IN_FLOAT (d = -pow (-d, 1.0/3.0), "cube-root", arg);
+#endif
+  return make_float (d);
+}
+#endif /* LISP_FLOAT_TYPE */
+
+
+/* Inverse trig functions. */
+#ifdef LISP_FLOAT_TYPE
+/* #if 0  Not clearly worth adding...  */
+
+DEFUN ("acosh", Facosh, Sacosh, 1, 1, 0 /*
+Return the inverse hyperbolic cosine of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+#ifdef FLOAT_CHECK_DOMAIN
+  if (d < 1.0)
+    domain_error ("acosh", arg);
+#endif
+#ifdef HAVE_INVERSE_HYPERBOLIC
+  IN_FLOAT (d = acosh (d), "acosh", arg);
+#else
+  IN_FLOAT (d = log (d + sqrt (d*d - 1.0)), "acosh", arg);
+#endif
+  return make_float (d);
+}
+
+DEFUN ("asinh", Fasinh, Sasinh, 1, 1, 0 /*
+Return the inverse hyperbolic sine of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+#ifdef HAVE_INVERSE_HYPERBOLIC
+  IN_FLOAT (d = asinh (d), "asinh", arg);
+#else
+  IN_FLOAT (d = log (d + sqrt (d*d + 1.0)), "asinh", arg);
+#endif
+  return make_float (d);
+}
+
+DEFUN ("atanh", Fatanh, Satanh, 1, 1, 0 /*
+Return the inverse hyperbolic tangent of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+#ifdef FLOAT_CHECK_DOMAIN
+  if (d >= 1.0 || d <= -1.0)
+    domain_error ("atanh", arg);
+#endif
+#ifdef HAVE_INVERSE_HYPERBOLIC
+  IN_FLOAT (d = atanh (d), "atanh", arg);
+#else
+  IN_FLOAT (d = 0.5 * log ((1.0 + d) / (1.0 - d)), "atanh", arg);
+#endif
+  return make_float (d);
+}
+
+DEFUN ("cosh", Fcosh, Scosh, 1, 1, 0 /*
+Return the hyperbolic cosine of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+#ifdef FLOAT_CHECK_DOMAIN
+  if (d > 710.0 || d < -710.0)
+    range_error ("cosh", arg);
+#endif
+  IN_FLOAT (d = cosh (d), "cosh", arg);
+  return make_float (d);
+}
+
+DEFUN ("sinh", Fsinh, Ssinh, 1, 1, 0 /*
+Return the hyperbolic sine of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+#ifdef FLOAT_CHECK_DOMAIN
+  if (d > 710.0 || d < -710.0)
+    range_error ("sinh", arg);
+#endif
+  IN_FLOAT (d = sinh (d), "sinh", arg);
+  return make_float (d);
+}
+
+DEFUN ("tanh", Ftanh, Stanh, 1, 1, 0 /*
+Return the hyperbolic tangent of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  IN_FLOAT (d = tanh (d), "tanh", arg);
+  return make_float (d);
+}
+#endif /* LISP_FLOAT_TYPE (inverse trig functions) */
+
+/* Rounding functions */
+
+DEFUN ("abs", Fabs, Sabs, 1, 1, 0 /*
+Return the absolute value of ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  CHECK_INT_OR_FLOAT (arg);
+
+#ifdef LISP_FLOAT_TYPE
+  if (FLOATP (arg))
+  {
+    IN_FLOAT (arg = make_float ((double) fabs (float_data (XFLOAT (arg)))),
+              "abs", arg);
+    return (arg);
+  }
+  else
+#endif /* LISP_FLOAT_TYPE */
+    if (XINT (arg) < 0)
+      return (make_int (- XINT (arg)));
+    else
+      return (arg);
+}
+
+#ifdef LISP_FLOAT_TYPE
+DEFUN ("float", Ffloat, Sfloat, 1, 1, 0 /*
+Return the floating point number equal to ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  CHECK_INT_OR_FLOAT (arg);
+
+  if (INTP (arg))
+    return make_float ((double) XINT (arg));
+  else				/* give 'em the same float back */
+    return arg;
+}
+#endif /* LISP_FLOAT_TYPE */
+
+
+#ifdef LISP_FLOAT_TYPE
+DEFUN ("logb", Flogb, Slogb, 1, 1, 0 /*
+Return largest integer <= the base 2 log of the magnitude of ARG.
+This is the same as the exponent of a float.
+*/ )
+     (arg)
+     Lisp_Object arg;
+{
+  double f = extract_float (arg);
+
+  if (f == 0.0)
+    return (make_int (- (((EMACS_UINT) 1) << (VALBITS - 1)))); /* most-negative-fixnum */
+#ifdef HAVE_LOGB
+  {
+    Lisp_Object val;
+    IN_FLOAT (val = make_int (logb (f)), "logb", arg);
+    return (val);
+  }
+#else
+#ifdef HAVE_FREXP
+  {
+    int exqp;  
+    IN_FLOAT (frexp (f, &exqp), "logb", arg);
+    return (make_int (exqp - 1));
+  }
+#else
+  {
+    int i;
+    double d;
+    EMACS_INT val;
+    if (f < 0.0)
+      f = -f;
+    val = -1;
+    while (f < 0.5)
+      {
+        for (i = 1, d = 0.5; d * d >= f; i += i)
+          d *= d;
+        f /= d;
+        val -= i;
+      }
+    while (f >= 1.0)
+      {
+        for (i = 1, d = 2.0; d * d <= f; i += i)
+          d *= d;
+        f /= d;
+        val += i;
+      }
+    return (make_int (val));
+  }
+#endif /* ! HAVE_FREXP */
+#endif /* ! HAVE_LOGB */
+}
+#endif /* LISP_FLOAT_TYPE */
+
+
+DEFUN ("ceiling", Fceiling, Sceiling, 1, 1, 0 /*
+Return the smallest integer no less than ARG.  (Round toward +inf.)
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  CHECK_INT_OR_FLOAT (arg);
+
+#ifdef LISP_FLOAT_TYPE
+  if (FLOATP (arg))
+  {
+    double d;
+    IN_FLOAT ((d = ceil (float_data (XFLOAT (arg)))), "ceiling", arg);
+    return (float_to_int (d, "ceiling", arg, Qunbound));
+  }
+#endif /* LISP_FLOAT_TYPE */
+
+  return arg;
+}
+
+
+DEFUN ("floor", Ffloor, Sfloor, 1, 2, 0 /*
+Return the largest integer no greater than ARG.  (Round towards -inf.)
+With optional DIVISOR, return the largest integer no greater than ARG/DIVISOR.
+*/ )
+  (arg, divisor)
+     Lisp_Object arg, divisor;
+{
+  CHECK_INT_OR_FLOAT (arg);
+
+  if (! NILP (divisor))
+    {
+      EMACS_INT i1, i2;
+
+      CHECK_INT_OR_FLOAT (divisor);
+
+#ifdef LISP_FLOAT_TYPE
+      if (FLOATP (arg) || FLOATP (divisor))
+	{
+	  double f1, f2;
+
+	  f1 = ((FLOATP (arg)) ? float_data (XFLOAT (arg)) : XINT (arg));
+	  f2 = ((FLOATP (divisor)) ? float_data (XFLOAT (divisor)) : XINT (divisor));
+	  if (f2 == 0)
+	    Fsignal (Qarith_error, Qnil);
+
+	  IN_FLOAT2 (f1 = floor (f1 / f2), "floor", arg, divisor);
+	  return float_to_int (f1, "floor", arg, divisor);
+	}
+#endif /* LISP_FLOAT_TYPE */
+
+      i1 = XINT (arg);
+      i2 = XINT (divisor);
+
+      if (i2 == 0)
+	Fsignal (Qarith_error, Qnil);
+
+      /* With C's /, the result is implementation-defined if either operand
+	 is negative, so use only nonnegative operands.  */
+      i1 = (i2 < 0
+	    ? (i1 <= 0  ?  -i1 / -i2  :  -1 - ((i1 - 1) / -i2))
+	    : (i1 < 0  ?  -1 - ((-1 - i1) / i2)  :  i1 / i2));
+
+      return (make_int (i1));
+    }
+
+#ifdef LISP_FLOAT_TYPE
+  if (FLOATP (arg))
+  {
+    double d;
+    IN_FLOAT ((d = floor (float_data (XFLOAT (arg)))), "floor", arg);
+    return (float_to_int (d, "floor", arg, Qunbound));
+  }
+#endif /* LISP_FLOAT_TYPE */
+
+  return arg;
+}
+
+DEFUN ("round", Fround, Sround, 1, 1, 0 /*
+Return the nearest integer to ARG.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  CHECK_INT_OR_FLOAT (arg);
+
+#ifdef LISP_FLOAT_TYPE
+  if (FLOATP (arg))
+  {
+    double d;
+    /* Screw the prevailing rounding mode.  */
+    IN_FLOAT ((d = rint (float_data (XFLOAT (arg)))), "round", arg);
+    return (float_to_int (d, "round", arg, Qunbound));
+  }
+#endif /* LISP_FLOAT_TYPE */
+
+  return arg;
+}
+
+DEFUN ("truncate", Ftruncate, Struncate, 1, 1, 0 /*
+Truncate a floating point number to an integer.
+Rounds the value toward zero.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  CHECK_INT_OR_FLOAT (arg);
+
+#ifdef LISP_FLOAT_TYPE
+  if (FLOATP (arg))
+    return (float_to_int (float_data (XFLOAT (arg)),
+                          "truncate", arg, Qunbound));
+#endif /* LISP_FLOAT_TYPE */
+
+  return arg;
+}
+
+/* Float-rounding functions. */
+#ifdef LISP_FLOAT_TYPE
+/* #if 1  It's not clear these are worth adding... */
+
+DEFUN ("fceiling", Ffceiling, Sfceiling, 1, 1, 0 /*
+Return the smallest integer no less than ARG, as a float.
+\(Round toward +inf.\)
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  IN_FLOAT (d = ceil (d), "fceiling", arg);
+  return make_float (d);
+}
+
+DEFUN ("ffloor", Fffloor, Sffloor, 1, 1, 0 /*
+Return the largest integer no greater than ARG, as a float.
+\(Round towards -inf.\)
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  IN_FLOAT (d = floor (d), "ffloor", arg);
+  return make_float (d);
+}
+
+DEFUN ("fround", Ffround, Sfround, 1, 1, 0 /*
+Return the nearest integer to ARG, as a float.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  IN_FLOAT (d = rint (d), "fround", arg);
+  return make_float (d);
+}
+
+DEFUN ("ftruncate", Fftruncate, Sftruncate, 1, 1, 0 /*
+Truncate a floating point number to an integral float value.
+Rounds the value toward zero.
+*/ )
+  (arg)
+     Lisp_Object arg;
+{
+  double d = extract_float (arg);
+  if (d >= 0.0)
+    IN_FLOAT (d = floor (d), "ftruncate", arg);
+  else
+    IN_FLOAT (d = ceil (d), "ftruncate", arg);
+  return make_float (d);
+}
+
+#endif /* LISP_FLOAT_TYPE (float-rounding functions) */
+
+
+#ifdef LISP_FLOAT_TYPE
+#ifdef FLOAT_CATCH_SIGILL
+static SIGTYPE
+float_error (int signo)
+{
+  if (! in_float)
+    fatal_error_signal (signo);
+
+  EMACS_REESTABLISH_SIGNAL (signo, arith_error);
+  EMACS_UNBLOCK_SIGNAL (signo);
+
+  in_float = 0;
+
+  /* Was Fsignal(), but it just doesn't make sense for an error
+     occurring inside a signal handler to be restartable, considering
+     that anything could happen when the error is signaled and trapped
+     and considering the asynchronous nature of signal handlers. */
+  signal_error (Qarith_error, list1 (float_error_arg));
+}
+
+/* Another idea was to replace the library function `infnan'
+   where SIGILL is signaled.  */
+
+#endif /* FLOAT_CATCH_SIGILL */
+
+#ifdef HAVE_MATHERR
+int 
+matherr (struct exception *x)
+{
+  Lisp_Object args;
+  if (! in_float)
+    /* Not called from emacs-lisp float routines; do the default thing. */
+    return 0;
+
+  /* if (!strcmp (x->name, "pow")) x->name = "expt"; */
+
+  args = Fcons (build_string (x->name),
+                Fcons (make_float (x->arg1),
+                       ((in_float == 2)
+                        ? Fcons (make_float (x->arg2), Qnil)
+                        : Qnil)));
+  switch (x->type)
+    {
+    case DOMAIN:	Fsignal (Qdomain_error, args);		break;
+    case SING:		Fsignal (Qsingularity_error, args);	break;
+    case OVERFLOW:	Fsignal (Qoverflow_error, args);	break;
+    case UNDERFLOW:	Fsignal (Qunderflow_error, args);	break;
+    default:		Fsignal (Qarith_error, args);		break;
+    }
+  return (1);	/* don't set errno or print a message */
+}
+#endif /* HAVE_MATHERR */
+#endif /* LISP_FLOAT_TYPE */
+
+
+void
+init_floatfns_very_early (void)
+{
+#ifdef LISP_FLOAT_TYPE
+# ifdef FLOAT_CATCH_SIGILL
+  signal (SIGILL, float_error);
+# endif 
+  in_float = 0;
+#endif /* LISP_FLOAT_TYPE */
+}
+
+void
+syms_of_floatfns (void)
+{
+  
+  /* Trig functions.  */
+  
+#ifdef LISP_FLOAT_TYPE
+  defsubr (&Sacos);
+  defsubr (&Sasin);
+  defsubr (&Satan);
+  defsubr (&Scos);
+  defsubr (&Ssin);
+  defsubr (&Stan);
+#endif /* LISP_FLOAT_TYPE */
+
+  /* Bessel functions */
+  
+#if 0
+  defsubr (&Sbessel_y0);
+  defsubr (&Sbessel_y1);
+  defsubr (&Sbessel_yn);
+  defsubr (&Sbessel_j0);
+  defsubr (&Sbessel_j1);
+  defsubr (&Sbessel_jn);
+#endif /* 0 */
+
+  /* Error functions. */
+
+#if 0
+  defsubr (&Serf);
+  defsubr (&Serfc);
+  defsubr (&Slog_gamma);
+#endif /* 0 */
+
+  /* Root and Log functions. */
+
+#ifdef LISP_FLOAT_TYPE
+  defsubr (&Sexp);
+#endif /* LISP_FLOAT_TYPE */
+  defsubr (&Sexpt);
+#ifdef LISP_FLOAT_TYPE
+  defsubr (&Slog);
+  defsubr (&Slog10);
+  defsubr (&Ssqrt);
+  defsubr (&Scube_root);
+#endif /* LISP_FLOAT_TYPE */
+
+  /* Inverse trig functions. */
+
+#ifdef LISP_FLOAT_TYPE
+  defsubr (&Sacosh);
+  defsubr (&Sasinh);
+  defsubr (&Satanh);
+  defsubr (&Scosh);
+  defsubr (&Ssinh);
+  defsubr (&Stanh);
+#endif /* LISP_FLOAT_TYPE */
+
+  /* Rounding functions */
+
+  defsubr (&Sabs);
+#ifdef LISP_FLOAT_TYPE
+  defsubr (&Sfloat);
+  defsubr (&Slogb);
+#endif /* LISP_FLOAT_TYPE */
+  defsubr (&Sceiling);
+  defsubr (&Sfloor);
+  defsubr (&Sround);
+  defsubr (&Struncate);
+
+  /* Float-rounding functions. */
+
+#ifdef LISP_FLOAT_TYPE
+  defsubr (&Sfceiling);
+  defsubr (&Sffloor);
+  defsubr (&Sfround);
+  defsubr (&Sftruncate);
+#endif /* LISP_FLOAT_TYPE */
+}
+
+void
+vars_of_floatfns (void)
+{
+#ifdef LISP_FLOAT_TYPE
+  Fprovide (intern ("lisp-float-type"));
+#endif
+}