/* Primitive operations on floating point for GNU Emacs Lisp interpreter.
- Copyright (C) 1988, 1992 Free Software Foundation, Inc.
+ Copyright (C) 1988, 1993, 1994, 1999, 2002, 2003, 2004,
+ 2005, 2006 Free Software Foundation, Inc.
This file is part of GNU Emacs.
You should have received a copy of the GNU General Public License
along with GNU Emacs; see the file COPYING. If not, write to
-the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. */
+the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+Boston, MA 02110-1301, USA. */
-#include <signal.h>
+/* 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 a working 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? Please let us know.)
-#include "config.h"
+ Define FLOAT_CHECK_DOMAIN if the float library doesn't handle errors by
+ either setting errno, or signaling 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 <signal.h>
#include "lisp.h"
#include "syssignal.h"
-Lisp_Object Qarith_error;
+#if STDC_HEADERS
+#include <float.h>
+#endif
-#ifdef LISP_FLOAT_TYPE
+/* If IEEE_FLOATING_POINT isn't defined, default it from FLT_*. */
+#ifndef IEEE_FLOATING_POINT
+#if (FLT_RADIX == 2 && FLT_MANT_DIG == 24 \
+ && FLT_MIN_EXP == -125 && FLT_MAX_EXP == 128)
+#define IEEE_FLOATING_POINT 1
+#else
+#define IEEE_FLOATING_POINT 0
+#endif
+#endif
+
+/* Work around a problem that happens because math.h on hpux 7
+ defines two static variables--which, in Emacs, are not really static,
+ because `static' is defined as nothing. The problem is that they are
+ defined both here and in lread.c.
+ These macros prevent the name conflict. */
+#if defined (HPUX) && !defined (HPUX8)
+#define _MAXLDBL floatfns_maxldbl
+#define _NMAXLDBL floatfns_nmaxldbl
+#endif
#include <math.h>
-#include <errno.h>
+/* This declaration is omitted on some systems, like Ultrix. */
+#if !defined (HPUX) && defined (HAVE_LOGB) && !defined (logb)
+extern double logb ();
+#endif /* not HPUX and HAVE_LOGB and no logb macro */
+
+#if defined(DOMAIN) && defined(SING) && defined(OVERFLOW)
+ /* If those are defined, then this is probably a `matherr' machine. */
+# ifndef HAVE_MATHERR
+# define HAVE_MATHERR
+# endif
+#endif
+
+#ifdef NO_MATHERR
+#undef HAVE_MATHERR
+#endif
+
+#ifdef HAVE_MATHERR
+# ifdef FLOAT_CHECK_ERRNO
+# undef FLOAT_CHECK_ERRNO
+# endif
+# ifdef FLOAT_CHECK_DOMAIN
+# undef FLOAT_CHECK_DOMAIN
+# endif
+#endif
+
+#ifndef NO_FLOAT_CHECK_ERRNO
+#define FLOAT_CHECK_ERRNO
+#endif
+
+#ifdef FLOAT_CHECK_ERRNO
+# include <errno.h>
+
+#ifndef USE_CRT_DLL
extern int errno;
+#endif
+#endif
/* Avoid traps on VMS from sinh and cosh.
All the other functions set errno instead. */
#define sinh(x) ((exp(x)-exp(-x))*0.5)
#endif /* VMS */
+#ifdef FLOAT_CATCH_SIGILL
static SIGTYPE float_error ();
+#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. */
+ here is the actual argument value to use in the error message.
+ These variables are used only across the floating point library call
+ so there is no need to staticpro them. */
+
+static Lisp_Object float_error_arg, float_error_arg2;
-static Lisp_Object float_error_arg;
+static 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. */
+ 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; \
+ switch (errno) { \
+ case 0: break; \
+ case EDOM: domain_error (float_error_fn_name, float_error_arg); \
+ case ERANGE: range_error (float_error_fn_name, float_error_arg); \
+ default: arith_error (float_error_fn_name, float_error_arg); \
+ } \
+ } 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 = 1; errno = 0; (d); in_float = 0; \
+ switch (errno) { \
+ case 0: break; \
+ case EDOM: domain_error (float_error_fn_name, float_error_arg); \
+ case ERANGE: range_error (float_error_fn_name, float_error_arg); \
+ default: arith_error (float_error_fn_name, float_error_arg); \
+ } \
+ } 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 = 1, (d), in_float = 0)
+#endif
-#define IN_FLOAT(D, NUM) \
-(in_float = 1, errno = 0, float_error_arg = NUM, (D), \
- (errno == ERANGE || errno == EDOM ? float_error () : (SIGTYPE) 0), \
- in_float = 0)
+/* Convert float to Lisp_Int if it fits, else signal a range error
+ using the given arguments. */
+#define FLOAT_TO_INT(x, i, name, num) \
+ do \
+ { \
+ if (FIXNUM_OVERFLOW_P (x)) \
+ range_error (name, num); \
+ XSETINT (i, (EMACS_INT)(x)); \
+ } \
+ while (0)
+#define FLOAT_TO_INT2(x, i, name, num1, num2) \
+ do \
+ { \
+ if (FIXNUM_OVERFLOW_P (x)) \
+ range_error2 (name, num1, num2); \
+ XSETINT (i, (EMACS_INT)(x)); \
+ } \
+ while (0)
+
+#define arith_error(op,arg) \
+ Fsignal (Qarith_error, Fcons (build_string ((op)), Fcons ((arg), Qnil)))
+#define range_error(op,arg) \
+ Fsignal (Qrange_error, Fcons (build_string ((op)), Fcons ((arg), Qnil)))
+#define range_error2(op,a1,a2) \
+ Fsignal (Qrange_error, Fcons (build_string ((op)), \
+ Fcons ((a1), Fcons ((a2), Qnil))))
+#define domain_error(op,arg) \
+ Fsignal (Qdomain_error, Fcons (build_string ((op)), Fcons ((arg), Qnil)))
+#define domain_error2(op,a1,a2) \
+ Fsignal (Qdomain_error, Fcons (build_string ((op)), \
+ Fcons ((a1), Fcons ((a2), Qnil))))
/* Extract a Lisp number as a `double', or signal an error. */
extract_float (num)
Lisp_Object num;
{
- CHECK_NUMBER_OR_FLOAT (num, 0);
+ CHECK_NUMBER_OR_FLOAT (num);
- if (XTYPE (num) == Lisp_Float)
- return XFLOAT (num)->data;
+ if (FLOATP (num))
+ return XFLOAT_DATA (num);
return (double) XINT (num);
}
\f
/* Trig functions. */
DEFUN ("acos", Facos, Sacos, 1, 1, 0,
- "Return the inverse cosine of ARG.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the inverse cosine of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = acos (d), num);
+ 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.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the inverse sine of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = asin (d), num);
+ 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, 1, 0,
- "Return the inverse tangent of ARG.")
- (num)
- register Lisp_Object num;
+DEFUN ("atan", Fatan, Satan, 1, 2, 0,
+ doc: /* Return the inverse tangent of the arguments.
+If only one argument Y is given, return the inverse tangent of Y.
+If two arguments Y and X are given, return the inverse tangent of Y
+divided by X, i.e. the angle in radians between the vector (X, Y)
+and the x-axis. */)
+ (y, x)
+ register Lisp_Object y, x;
{
- double d = extract_float (num);
- IN_FLOAT (d = atan (d), num);
+ double d = extract_float (y);
+
+ if (NILP (x))
+ IN_FLOAT (d = atan (d), "atan", y);
+ else
+ {
+ double d2 = extract_float (x);
+
+ IN_FLOAT2 (d = atan2 (d, d2), "atan", y, x);
+ }
return make_float (d);
}
DEFUN ("cos", Fcos, Scos, 1, 1, 0,
- "Return the cosine of ARG.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the cosine of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = cos (d), num);
+ 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.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the sine of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = sin (d), num);
+ 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.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the tangent of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = tan (d), num);
+ 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);
}
\f
#if 0 /* Leave these out unless we find there's a reason for them. */
DEFUN ("bessel-j0", Fbessel_j0, Sbessel_j0, 1, 1, 0,
- "Return the bessel function j0 of ARG.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the bessel function j0 of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = j0 (d), num);
+ 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.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the bessel function j1 of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = j1 (d), num);
+ 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.\n\
-The first arg (the order) is truncated to an integer.")
- (num1, num2)
- register Lisp_Object num1, num2;
+ doc: /* Return the order N bessel function output jn of ARG.
+The first arg (the order) is truncated to an integer. */)
+ (n, arg)
+ register Lisp_Object n, arg;
{
- int i1 = extract_float (num1);
- double f2 = extract_float (num2);
+ int i1 = extract_float (n);
+ double f2 = extract_float (arg);
- IN_FLOAT (f2 = jn (i1, f2), num1);
+ IN_FLOAT (f2 = jn (i1, f2), "bessel-jn", n);
return make_float (f2);
}
DEFUN ("bessel-y0", Fbessel_y0, Sbessel_y0, 1, 1, 0,
- "Return the bessel function y0 of ARG.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the bessel function y0 of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = y0 (d), num);
+ 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.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the bessel function y1 of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = y1 (d), num);
+ 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.\n\
-The first arg (the order) is truncated to an integer.")
- (num1, num2)
- register Lisp_Object num1, num2;
+ doc: /* Return the order N bessel function output yn of ARG.
+The first arg (the order) is truncated to an integer. */)
+ (n, arg)
+ register Lisp_Object n, arg;
{
- int i1 = extract_float (num1);
- double f2 = extract_float (num2);
+ int i1 = extract_float (n);
+ double f2 = extract_float (arg);
- IN_FLOAT (f2 = yn (i1, f2), num1);
+ IN_FLOAT (f2 = yn (i1, f2), "bessel-yn", n);
return make_float (f2);
}
#if 0 /* Leave these out unless we see they are worth having. */
DEFUN ("erf", Ferf, Serf, 1, 1, 0,
- "Return the mathematical error function of ARG.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the mathematical error function of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = erf (d), num);
+ 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.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the complementary error function of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = erfc (d), num);
+ 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.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the log gamma of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = lgamma (d), num);
+ double d = extract_float (arg);
+ IN_FLOAT (d = lgamma (d), "log-gamma", arg);
return make_float (d);
}
-DEFUN ("cbrt", Fcbrt, Scbrt, 1, 1, 0,
- "Return the cube root of ARG.")
- (num)
- register Lisp_Object num;
+DEFUN ("cube-root", Fcube_root, Scube_root, 1, 1, 0,
+ doc: /* Return the cube root of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = cbrt (d), num);
+ 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
\f
DEFUN ("exp", Fexp, Sexp, 1, 1, 0,
- "Return the exponential base e of ARG.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the exponential base e of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = exp (d), num);
+ 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);
}
DEFUN ("expt", Fexpt, Sexpt, 2, 2, 0,
- "Return the exponential X ** Y.")
- (num1, num2)
- register Lisp_Object num1, num2;
+ doc: /* Return the exponential ARG1 ** ARG2. */)
+ (arg1, arg2)
+ register Lisp_Object arg1, arg2;
{
double f1, f2;
- CHECK_NUMBER_OR_FLOAT (num1, 0);
- CHECK_NUMBER_OR_FLOAT (num2, 0);
- if ((XTYPE (num1) == Lisp_Int) && /* common lisp spec */
- (XTYPE (num2) == Lisp_Int)) /* don't promote, if both are ints */
+ CHECK_NUMBER_OR_FLOAT (arg1);
+ CHECK_NUMBER_OR_FLOAT (arg2);
+ if (INTEGERP (arg1) /* common lisp spec */
+ && INTEGERP (arg2) /* don't promote, if both are ints, and */
+ && 0 <= XINT (arg2)) /* we are sure the result is not fractional */
{ /* this can be improved by pre-calculating */
- int acc, x, y; /* some binary powers of x then acumulating */
- /* these, therby saving some time. -wsr */
- x = XINT (num1);
- y = XINT (num2);
+ EMACS_INT acc, x, y; /* some binary powers of x then accumulating */
+ Lisp_Object val;
+
+ x = XINT (arg1);
+ y = XINT (arg2);
acc = 1;
-
+
if (y < 0)
{
- for (; y < 0; y++)
- acc /= x;
+ if (x == 1)
+ acc = 1;
+ else if (x == -1)
+ acc = (y & 1) ? -1 : 1;
+ else
+ acc = 0;
}
else
{
- for (; y > 0; y--)
- acc *= x;
+ while (y > 0)
+ {
+ if (y & 1)
+ acc *= x;
+ x *= x;
+ y = (unsigned)y >> 1;
+ }
}
- XFASTINT (x) = acc;
- return x;
+ XSETINT (val, acc);
+ return val;
}
- f1 = (XTYPE (num1) == Lisp_Float) ? XFLOAT (num1)->data : XINT (num1);
- f2 = (XTYPE (num2) == Lisp_Float) ? XFLOAT (num2)->data : XINT (num2);
- IN_FLOAT (f1 = pow (f1, f2), num1);
+ f1 = FLOATP (arg1) ? XFLOAT_DATA (arg1) : XINT (arg1);
+ f2 = FLOATP (arg2) ? XFLOAT_DATA (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
+ IN_FLOAT2 (f1 = pow (f1, f2), "expt", arg1, arg2);
return make_float (f1);
}
DEFUN ("log", Flog, Slog, 1, 2, 0,
- "Return the natural logarithm of NUM.\n\
-If second optional argument BASE is given, return log NUM using that base.")
- (num, base)
- register Lisp_Object num, base;
+ doc: /* Return the natural logarithm of ARG.
+If the optional argument BASE is given, return log ARG using that base. */)
+ (arg, base)
+ register Lisp_Object arg, base;
{
- double d = extract_float (num);
+ 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), num);
+ IN_FLOAT (d = log (d), "log", arg);
else
{
double b = extract_float (base);
- IN_FLOAT (d = log (num) / log (b), num);
+#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.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the logarithm base 10 of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = log10 (d), num);
+ 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.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the square root of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = sqrt (d), num);
+ 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);
}
\f
#if 0 /* Not clearly worth adding. */
DEFUN ("acosh", Facosh, Sacosh, 1, 1, 0,
- "Return the inverse hyperbolic cosine of ARG.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the inverse hyperbolic cosine of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = acosh (d), num);
+ 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.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the inverse hyperbolic sine of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = asinh (d), num);
+ 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.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the inverse hyperbolic tangent of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = atanh (d), num);
+ 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.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the hyperbolic cosine of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = cosh (d), num);
+ 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.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the hyperbolic sine of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = sinh (d), num);
+ 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.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the hyperbolic tangent of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- double d = extract_float (num);
- IN_FLOAT (d = tanh (d), num);
+ double d = extract_float (arg);
+ IN_FLOAT (d = tanh (d), "tanh", arg);
return make_float (d);
}
#endif
\f
DEFUN ("abs", Fabs, Sabs, 1, 1, 0,
- "Return the absolute value of ARG.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the absolute value of ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- CHECK_NUMBER_OR_FLOAT (num, 0);
+ CHECK_NUMBER_OR_FLOAT (arg);
- if (XTYPE (num) == Lisp_Float)
- IN_FLOAT (num = make_float (fabs (XFLOAT (num)->data)), num);
- else if (XINT (num) < 0)
- XSETINT (num, - XFASTINT (num));
+ if (FLOATP (arg))
+ IN_FLOAT (arg = make_float (fabs (XFLOAT_DATA (arg))), "abs", arg);
+ else if (XINT (arg) < 0)
+ XSETINT (arg, - XINT (arg));
- return num;
+ return arg;
}
DEFUN ("float", Ffloat, Sfloat, 1, 1, 0,
- "Return the floating point number equal to ARG.")
- (num)
- register Lisp_Object num;
+ doc: /* Return the floating point number equal to ARG. */)
+ (arg)
+ register Lisp_Object arg;
{
- CHECK_NUMBER_OR_FLOAT (num, 0);
+ CHECK_NUMBER_OR_FLOAT (arg);
- if (XTYPE (num) == Lisp_Int)
- return make_float ((double) XINT (num));
+ if (INTEGERP (arg))
+ return make_float ((double) XINT (arg));
else /* give 'em the same float back */
- return num;
+ return arg;
}
DEFUN ("logb", Flogb, Slogb, 1, 1, 0,
- "Returns the integer that is the base 2 log of ARG.\n\
-This is the same as the exponent of a float.")
- (num)
-Lisp_Object num;
-{
-#ifdef USG
- /* System V apparently doesn't have a `logb' function. */
- return Flog (num, make_number (2));
-#else
+ doc: /* Returns 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;
+{
Lisp_Object val;
- double f = extract_float (num);
+ EMACS_INT value;
+ double f = extract_float (arg);
- IN_FLOAT (val = logb (f), num);
- XSET (val, Lisp_Int, val);
- return val;
+ if (f == 0.0)
+ value = MOST_NEGATIVE_FIXNUM;
+ else
+ {
+#ifdef HAVE_LOGB
+ IN_FLOAT (value = logb (f), "logb", arg);
+#else
+#ifdef HAVE_FREXP
+ int ivalue;
+ IN_FLOAT (frexp (f, &ivalue), "logb", arg);
+ value = ivalue - 1;
+#else
+ int i;
+ double d;
+ if (f < 0.0)
+ f = -f;
+ value = -1;
+ while (f < 0.5)
+ {
+ for (i = 1, d = 0.5; d * d >= f; i += i)
+ d *= d;
+ f /= d;
+ value -= i;
+ }
+ while (f >= 1.0)
+ {
+ for (i = 1, d = 2.0; d * d <= f; i += i)
+ d *= d;
+ f /= d;
+ value += i;
+ }
#endif
+#endif
+ }
+ XSETINT (val, value);
+ return val;
}
+
/* the rounding functions */
-DEFUN ("ceiling", Fceiling, Sceiling, 1, 1, 0,
- "Return the smallest integer no less than ARG. (Round toward +inf.)")
- (num)
- register Lisp_Object num;
+static Lisp_Object
+rounding_driver (arg, divisor, double_round, int_round2, name)
+ register Lisp_Object arg, divisor;
+ double (*double_round) ();
+ EMACS_INT (*int_round2) ();
+ char *name;
{
- CHECK_NUMBER_OR_FLOAT (num, 0);
+ CHECK_NUMBER_OR_FLOAT (arg);
- if (XTYPE (num) == Lisp_Float)
- IN_FLOAT (XSET (num, Lisp_Int, ceil (XFLOAT (num)->data)), num);
+ if (! NILP (divisor))
+ {
+ EMACS_INT i1, i2;
+
+ CHECK_NUMBER_OR_FLOAT (divisor);
+
+ if (FLOATP (arg) || FLOATP (divisor))
+ {
+ double f1, f2;
+
+ f1 = FLOATP (arg) ? XFLOAT_DATA (arg) : XINT (arg);
+ f2 = (FLOATP (divisor) ? XFLOAT_DATA (divisor) : XINT (divisor));
+ if (! IEEE_FLOATING_POINT && f2 == 0)
+ Fsignal (Qarith_error, Qnil);
- return num;
+ IN_FLOAT2 (f1 = (*double_round) (f1 / f2), name, arg, divisor);
+ FLOAT_TO_INT2 (f1, arg, name, arg, divisor);
+ return arg;
+ }
+
+ i1 = XINT (arg);
+ i2 = XINT (divisor);
+
+ if (i2 == 0)
+ Fsignal (Qarith_error, Qnil);
+
+ XSETINT (arg, (*int_round2) (i1, i2));
+ return arg;
+ }
+
+ if (FLOATP (arg))
+ {
+ double d;
+
+ IN_FLOAT (d = (*double_round) (XFLOAT_DATA (arg)), name, arg);
+ FLOAT_TO_INT (d, arg, name, arg);
+ }
+
+ return arg;
}
-DEFUN ("floor", Ffloor, Sfloor, 1, 1, 0,
- "Return the largest integer no greater than ARG. (Round towards -inf.)")
- (num)
- register Lisp_Object num;
+/* With C's /, the result is implementation-defined if either operand
+ is negative, so take care with negative operands in the following
+ integer functions. */
+
+static EMACS_INT
+ceiling2 (i1, i2)
+ EMACS_INT i1, i2;
{
- CHECK_NUMBER_OR_FLOAT (num, 0);
+ return (i2 < 0
+ ? (i1 < 0 ? ((-1 - i1) / -i2) + 1 : - (i1 / -i2))
+ : (i1 <= 0 ? - (-i1 / i2) : ((i1 - 1) / i2) + 1));
+}
- if (XTYPE (num) == Lisp_Float)
- IN_FLOAT (XSET (num, Lisp_Int, floor (XFLOAT (num)->data)), num);
+static EMACS_INT
+floor2 (i1, i2)
+ EMACS_INT i1, i2;
+{
+ return (i2 < 0
+ ? (i1 <= 0 ? -i1 / -i2 : -1 - ((i1 - 1) / -i2))
+ : (i1 < 0 ? -1 - ((-1 - i1) / i2) : i1 / i2));
+}
- return num;
+static EMACS_INT
+truncate2 (i1, i2)
+ EMACS_INT i1, i2;
+{
+ return (i2 < 0
+ ? (i1 < 0 ? -i1 / -i2 : - (i1 / -i2))
+ : (i1 < 0 ? - (-i1 / i2) : i1 / i2));
}
-DEFUN ("round", Fround, Sround, 1, 1, 0,
- "Return the nearest integer to ARG.")
- (num)
- register Lisp_Object num;
+static EMACS_INT
+round2 (i1, i2)
+ EMACS_INT i1, i2;
{
- CHECK_NUMBER_OR_FLOAT (num, 0);
+ /* The C language's division operator gives us one remainder R, but
+ we want the remainder R1 on the other side of 0 if R1 is closer
+ to 0 than R is; because we want to round to even, we also want R1
+ if R and R1 are the same distance from 0 and if C's quotient is
+ odd. */
+ EMACS_INT q = i1 / i2;
+ EMACS_INT r = i1 % i2;
+ EMACS_INT abs_r = r < 0 ? -r : r;
+ EMACS_INT abs_r1 = (i2 < 0 ? -i2 : i2) - abs_r;
+ return q + (abs_r + (q & 1) <= abs_r1 ? 0 : (i2 ^ r) < 0 ? -1 : 1);
+}
- if (XTYPE (num) == Lisp_Float)
- {
-#ifdef USG
- /* Screw the prevailing rounding mode. */
- IN_FLOAT (XSET (num, Lisp_Int, floor (XFLOAT (num)->data + 0.5)), num);
+/* The code uses emacs_rint, so that it works to undefine HAVE_RINT
+ if `rint' exists but does not work right. */
+#ifdef HAVE_RINT
+#define emacs_rint rint
#else
- IN_FLOAT (XSET (num, Lisp_Int, rint (XFLOAT (num)->data)), num);
+static double
+emacs_rint (d)
+ double d;
+{
+ return floor (d + 0.5);
+}
#endif
- }
- return num;
+static double
+double_identity (d)
+ double d;
+{
+ return d;
}
-DEFUN ("truncate", Ftruncate, Struncate, 1, 1, 0,
- "Truncate a floating point number to an int.\n\
-Rounds the value toward zero.")
- (num)
- register Lisp_Object num;
+DEFUN ("ceiling", Fceiling, Sceiling, 1, 2, 0,
+ doc: /* Return the smallest integer no less than ARG.
+This rounds the value towards +inf.
+With optional DIVISOR, return the smallest integer no less than ARG/DIVISOR. */)
+ (arg, divisor)
+ Lisp_Object arg, divisor;
{
- CHECK_NUMBER_OR_FLOAT (num, 0);
+ return rounding_driver (arg, divisor, ceil, ceiling2, "ceiling");
+}
- if (XTYPE (num) == Lisp_Float)
- XSET (num, Lisp_Int, (int) XFLOAT (num)->data);
+DEFUN ("floor", Ffloor, Sfloor, 1, 2, 0,
+ doc: /* Return the largest integer no greater than ARG.
+This rounds the value towards -inf.
+With optional DIVISOR, return the largest integer no greater than ARG/DIVISOR. */)
+ (arg, divisor)
+ Lisp_Object arg, divisor;
+{
+ return rounding_driver (arg, divisor, floor, floor2, "floor");
+}
- return num;
+DEFUN ("round", Fround, Sround, 1, 2, 0,
+ doc: /* Return the nearest integer to ARG.
+With optional DIVISOR, return the nearest integer to ARG/DIVISOR.
+
+Rounding a value equidistant between two integers may choose the
+integer closer to zero, or it may prefer an even integer, depending on
+your machine. For example, \(round 2.5\) can return 3 on some
+systems, but 2 on others. */)
+ (arg, divisor)
+ Lisp_Object arg, divisor;
+{
+ return rounding_driver (arg, divisor, emacs_rint, round2, "round");
+}
+
+DEFUN ("truncate", Ftruncate, Struncate, 1, 2, 0,
+ doc: /* Truncate a floating point number to an int.
+Rounds ARG toward zero.
+With optional DIVISOR, truncate ARG/DIVISOR. */)
+ (arg, divisor)
+ Lisp_Object arg, divisor;
+{
+ return rounding_driver (arg, divisor, double_identity, truncate2,
+ "truncate");
+}
+
+
+Lisp_Object
+fmod_float (x, y)
+ register Lisp_Object x, y;
+{
+ double f1, f2;
+
+ f1 = FLOATP (x) ? XFLOAT_DATA (x) : XINT (x);
+ f2 = FLOATP (y) ? XFLOAT_DATA (y) : XINT (y);
+
+ if (! IEEE_FLOATING_POINT && f2 == 0)
+ Fsignal (Qarith_error, Qnil);
+
+ /* If the "remainder" comes out with the wrong sign, fix it. */
+ IN_FLOAT2 ((f1 = fmod (f1, f2),
+ f1 = (f2 < 0 ? f1 > 0 : f1 < 0) ? f1 + f2 : f1),
+ "mod", x, y);
+ return make_float (f1);
}
\f
+/* It's not clear these are worth adding. */
+
+DEFUN ("fceiling", Ffceiling, Sfceiling, 1, 1, 0,
+ doc: /* Return the smallest integer no less than ARG, as a float.
+\(Round toward +inf.\) */)
+ (arg)
+ register 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,
+ doc: /* Return the largest integer no greater than ARG, as a float.
+\(Round towards -inf.\) */)
+ (arg)
+ register 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,
+ doc: /* Return the nearest integer to ARG, as a float. */)
+ (arg)
+ register Lisp_Object arg;
+{
+ double d = extract_float (arg);
+ IN_FLOAT (d = emacs_rint (d), "fround", arg);
+ return make_float (d);
+}
+
+DEFUN ("ftruncate", Fftruncate, Sftruncate, 1, 1, 0,
+ doc: /* Truncate a floating point number to an integral float value.
+Rounds the value toward zero. */)
+ (arg)
+ register 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);
+}
+\f
+#ifdef FLOAT_CATCH_SIGILL
static SIGTYPE
float_error (signo)
int signo;
if (! in_float)
fatal_error_signal (signo);
-#ifdef BSD
+#ifdef BSD_SYSTEM
#ifdef BSD4_1
sigrelse (SIGILL);
#else /* not BSD4_1 */
#else
/* Must reestablish handler each time it is called. */
signal (SIGILL, float_error);
-#endif /* BSD */
+#endif /* BSD_SYSTEM */
+ SIGNAL_THREAD_CHECK (signo);
in_float = 0;
Fsignal (Qarith_error, Fcons (float_error_arg, Qnil));
}
+/* Another idea was to replace the library function `infnan'
+ where SIGILL is signaled. */
+
+#endif /* FLOAT_CATCH_SIGILL */
+
+#ifdef HAVE_MATHERR
+int
+matherr (x)
+ 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),
+ ((!strcmp (x->name, "log") || !strcmp (x->name, "pow"))
+ ? 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 */
+
+void
init_floatfns ()
{
+#ifdef FLOAT_CATCH_SIGILL
signal (SIGILL, float_error);
+#endif
in_float = 0;
}
+void
syms_of_floatfns ()
{
defsubr (&Sacos);
defsubr (&Serf);
defsubr (&Serfc);
defsubr (&Slog_gamma);
- defsubr (&Scbrt);
+ defsubr (&Scube_root);
#endif
+ defsubr (&Sfceiling);
+ defsubr (&Sffloor);
+ defsubr (&Sfround);
+ defsubr (&Sftruncate);
defsubr (&Sexp);
defsubr (&Sexpt);
defsubr (&Slog);
defsubr (&Struncate);
}
-#else /* not LISP_FLOAT_TYPE */
-
-init_floatfns ()
-{}
-
-syms_of_floatfns ()
-{}
-
-#endif /* not LISP_FLOAT_TYPE */
+/* arch-tag: be05bf9d-049e-4e31-91b9-e6153d483ae7
+ (do not change this comment) */