/* Primitive operations on floating point for GNU Emacs Lisp interpreter.
- Copyright (C) 1988, 1993 Free Software Foundation, Inc.
+ Copyright (C) 1988, 1993, 1994, 1999 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., 59 Temple Place - Suite 330,
+Boston, MA 02111-1307, USA. */
/* ANSI C requires only these float functions:
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.
+ 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.
(What systems actually do this? Please let us know.)
Define FLOAT_CHECK_DOMAIN if the float library doesn't handle errors by
- either setting errno, or signalling SIGFPE/SIGILL. Otherwise, domain and
+ 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 "config.h"
#include "lisp.h"
#include "syssignal.h"
-Lisp_Object Qarith_error;
+#if STDC_HEADERS
+#include <float.h>
+#endif
+
+/* 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
-#ifdef LISP_FLOAT_TYPE
+/* 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>
-#ifndef hpux
-/* These declarations are omitted on some systems, like Ultrix. */
+/* This declaration is omitted on some systems, like Ultrix. */
+#if !defined (HPUX) && defined (HAVE_LOGB) && !defined (logb)
extern double logb ();
-#endif
+#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. */
#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 */
-#ifndef HAVE_RINT
-#define rint(x) (floor((x)+0.5))
-#endif
-
static SIGTYPE float_error ();
/* Nonzero while executing in floating point.
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;
} \
} 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
+/* 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 ((x) >= (((EMACS_INT) 1) << (VALBITS-1)) || \
+ (x) <= - (((EMACS_INT) 1) << (VALBITS-1)) - 1) \
+ range_error (name, num); \
+ XSETINT (i, (EMACS_INT)(x)); \
+ } \
+ while (0)
+#define FLOAT_TO_INT2(x, i, name, num1, num2) \
+ do \
+ { \
+ if ((x) >= (((EMACS_INT) 1) << (VALBITS-1)) || \
+ (x) <= - (((EMACS_INT) 1) << (VALBITS-1)) - 1) \
+ 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))))
+ Fsignal (Qdomain_error, Fcons (build_string ((op)), \
+ Fcons ((a1), Fcons ((a2), Qnil))))
/* Extract a Lisp number as a `double', or signal an error. */
{
CHECK_NUMBER_OR_FLOAT (num, 0);
- if (XTYPE (num) == Lisp_Float)
- return XFLOAT (num)->data;
+ if (FLOATP (num))
+ return XFLOAT_DATA (num);
return (double) XINT (num);
}
\f
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.")
- (arg1, arg2)
- register Lisp_Object arg1, arg2;
+ (n, arg)
+ register Lisp_Object n, arg;
{
- int i1 = extract_float (arg1);
- double f2 = extract_float (arg2);
+ int i1 = extract_float (n);
+ double f2 = extract_float (arg);
- IN_FLOAT (f2 = jn (i1, f2), "bessel-jn", arg1);
+ IN_FLOAT (f2 = jn (i1, f2), "bessel-jn", n);
return make_float (f2);
}
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.")
- (arg1, arg2)
- register Lisp_Object arg1, arg2;
+ (n, arg)
+ register Lisp_Object n, arg;
{
- int i1 = extract_float (arg1);
- double f2 = extract_float (arg2);
+ int i1 = extract_float (n);
+ double f2 = extract_float (arg);
- IN_FLOAT (f2 = yn (i1, f2), "bessel-yn", arg1);
+ IN_FLOAT (f2 = yn (i1, f2), "bessel-yn", n);
return make_float (f2);
}
}
DEFUN ("expt", Fexpt, Sexpt, 2, 2, 0,
- "Return the exponential X ** Y.")
+ "Return the exponential ARG1 ** ARG2.")
(arg1, arg2)
register Lisp_Object arg1, arg2;
{
CHECK_NUMBER_OR_FLOAT (arg1, 0);
CHECK_NUMBER_OR_FLOAT (arg2, 0);
- if ((XTYPE (arg1) == Lisp_Int) && /* common lisp spec */
- (XTYPE (arg2) == Lisp_Int)) /* don't promote, if both are ints */
+ if (INTEGERP (arg1) /* common lisp spec */
+ && INTEGERP (arg2)) /* don't promote, if both are ints */
{ /* this can be improved by pre-calculating */
- int acc, x, y; /* some binary powers of x then acumulating */
- /* these, therby saving some time. -wsr */
+ EMACS_INT acc, x, y; /* some binary powers of x then accumulating */
+ Lisp_Object val;
+
x = XINT (arg1);
y = XINT (arg2);
acc = 1;
}
else
{
- for (; y > 0; y--)
while (y > 0)
{
if (y & 1)
y = (unsigned)y >> 1;
}
}
- XSET (x, Lisp_Int, acc);
- return x;
+ XSETINT (val, acc);
+ return val;
}
- f1 = (XTYPE (arg1) == Lisp_Float) ? XFLOAT (arg1)->data : XINT (arg1);
- f2 = (XTYPE (arg2) == Lisp_Float) ? XFLOAT (arg2)->data : XINT (arg2);
+ 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;
else if ((f1 == 0.0 && f2 < 0.0) || (f1 < 0 && f2 != floor(f2)))
domain_error2 ("expt", arg1, arg2);
#endif
- IN_FLOAT (f1 = pow (f1, f2), "expt", arg1);
+ IN_FLOAT2 (f1 = pow (f1, f2), "expt", arg1, arg2);
return make_float (f1);
}
if (b == 10.0)
IN_FLOAT2 (d = log10 (d), "log", arg, base);
else
- IN_FLOAT2 (d = log (arg) / log (b), "log", arg, base);
+ IN_FLOAT2 (d = log (d) / log (b), "log", arg, base);
}
return make_float (d);
}
{
CHECK_NUMBER_OR_FLOAT (arg, 0);
- if (XTYPE (arg) == Lisp_Float)
- IN_FLOAT (arg = make_float (fabs (XFLOAT (arg)->data)), "abs", arg);
+ if (FLOATP (arg))
+ IN_FLOAT (arg = make_float (fabs (XFLOAT_DATA (arg))), "abs", arg);
else if (XINT (arg) < 0)
- XSETINT (arg, - XFASTINT (arg));
+ XSETINT (arg, - XINT (arg));
return arg;
}
{
CHECK_NUMBER_OR_FLOAT (arg, 0);
- if (XTYPE (arg) == Lisp_Int)
+ if (INTEGERP (arg))
return make_float ((double) XINT (arg));
else /* give 'em the same float back */
return arg;
}
DEFUN ("logb", Flogb, Slogb, 1, 1, 0,
- "Returns the integer not greater than the base 2 log of the magnitude of ARG.\n\
+ "Returns largest integer <= the base 2 log of the magnitude of ARG.\n\
This is the same as the exponent of a float.")
(arg)
Lisp_Object arg;
{
Lisp_Object val;
- int value;
+ EMACS_INT value;
double f = extract_float (arg);
-#ifdef USG
- {
- int exp;
-
- IN_FLOAT (frexp (f, &exp), "logb", arg);
- XSET (val, Lisp_Int, exp-1);
- }
+ if (f == 0.0)
+ value = -(VALMASK >> 1);
+ 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
- IN_FLOAT (value = logb (f), "logb", arg);
- XSET (val, Lisp_Int, value);
+ 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.)")
- (arg)
- register Lisp_Object arg;
+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 (arg, 0);
- if (XTYPE (arg) == Lisp_Float)
- IN_FLOAT (XSET (arg, Lisp_Int, ceil (XFLOAT (arg)->data)), "celing", arg);
+ if (! NILP (divisor))
+ {
+ EMACS_INT i1, i2;
+
+ CHECK_NUMBER_OR_FLOAT (divisor, 1);
+
+ 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);
+
+ 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.)")
- (arg)
- register Lisp_Object arg;
+/* 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 (arg, 0);
+ return (i2 < 0
+ ? (i1 < 0 ? ((-1 - i1) / -i2) + 1 : - (i1 / -i2))
+ : (i1 <= 0 ? - (-i1 / i2) : ((i1 - 1) / i2) + 1));
+}
- if (XTYPE (arg) == Lisp_Float)
- IN_FLOAT (XSET (arg, Lisp_Int, floor (XFLOAT (arg)->data)), "floor", arg);
+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 arg;
+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.")
- (arg)
- register Lisp_Object arg;
+static EMACS_INT
+round2 (i1, i2)
+ EMACS_INT i1, i2;
{
- CHECK_NUMBER_OR_FLOAT (arg, 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);
+}
+
+/* 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
+static double
+emacs_rint (d)
+ double d;
+{
+ return floor (d + 0.5);
+}
+#endif
+
+static double
+double_identity (d)
+ double d;
+{
+ return d;
+}
- if (XTYPE (arg) == Lisp_Float)
- /* Screw the prevailing rounding mode. */
- IN_FLOAT (XSET (arg, Lisp_Int, rint (XFLOAT (arg)->data)), "round", arg);
+DEFUN ("ceiling", Fceiling, Sceiling, 1, 2, 0,
+ "Return the smallest integer no less than ARG. (Round toward +inf.)\n\
+With optional DIVISOR, return the smallest integer no less than ARG/DIVISOR.")
+ (arg, divisor)
+ Lisp_Object arg, divisor;
+{
+ return rounding_driver (arg, divisor, ceil, ceiling2, "ceiling");
+}
- return arg;
+DEFUN ("floor", Ffloor, Sfloor, 1, 2, 0,
+ "Return the largest integer no greater than ARG. (Round towards -inf.)\n\
+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");
+}
+
+DEFUN ("round", Fround, Sround, 1, 2, 0,
+ "Return the nearest integer to ARG.\n\
+With optional DIVISOR, return the nearest integer to ARG/DIVISOR.")
+ (arg, divisor)
+ Lisp_Object arg, divisor;
+{
+ return rounding_driver (arg, divisor, emacs_rint, round2, "round");
}
-DEFUN ("truncate", Ftruncate, Struncate, 1, 1, 0,
+DEFUN ("truncate", Ftruncate, Struncate, 1, 2, 0,
"Truncate a floating point number to an int.\n\
-Rounds the value toward zero.")
- (arg)
- register Lisp_Object arg;
+Rounds ARG toward zero.\n\
+With optional DIVISOR, truncate ARG/DIVISOR.")
+ (arg, divisor)
+ Lisp_Object arg, divisor;
{
- CHECK_NUMBER_OR_FLOAT (arg, 0);
+ return rounding_driver (arg, divisor, double_identity, truncate2,
+ "truncate");
+}
- if (XTYPE (arg) == Lisp_Float)
- XSET (arg, Lisp_Int, (int) XFLOAT (arg)->data);
- return arg;
+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
-#if 0
/* It's not clear these are worth adding. */
DEFUN ("fceiling", Ffceiling, Sfceiling, 1, 1, 0,
register Lisp_Object arg;
{
double d = extract_float (arg);
- IN_FLOAT (d = rint (XFLOAT (arg)->data), "fround", arg);
+ IN_FLOAT (d = emacs_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.\n\
+ "Truncate a floating point number to an integral float value.\n\
Rounds the value toward zero.")
(arg)
register Lisp_Object arg;
if (d >= 0.0)
IN_FLOAT (d = floor (d), "ftruncate", arg);
else
- IN_FLOAT (d = ceil (d), arg);
+ IN_FLOAT (d = ceil (d), "ftruncate", arg);
return make_float (d);
}
-#endif
\f
#ifdef FLOAT_CATCH_SIGILL
static SIGTYPE
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 */
in_float = 0;
}
#endif /* HAVE_MATHERR */
+void
init_floatfns ()
{
#ifdef FLOAT_CATCH_SIGILL
in_float = 0;
}
+void
syms_of_floatfns ()
{
defsubr (&Sacos);
defsubr (&Serfc);
defsubr (&Slog_gamma);
defsubr (&Scube_root);
+#endif
defsubr (&Sfceiling);
defsubr (&Sffloor);
defsubr (&Sfround);
defsubr (&Sftruncate);
-#endif
defsubr (&Sexp);
defsubr (&Sexpt);
defsubr (&Slog);
defsubr (&Sround);
defsubr (&Struncate);
}
-
-#else /* not LISP_FLOAT_TYPE */
-
-init_floatfns ()
-{}
-
-syms_of_floatfns ()
-{}
-
-#endif /* not LISP_FLOAT_TYPE */