/* Primitive operations on floating point for GNU Emacs Lisp interpreter. Copyright (C) 1988, 1993 Free Software Foundation, Inc. This file is part of GNU Emacs. GNU Emacs 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. GNU Emacs 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 GNU Emacs; see the file COPYING. If not, write to the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. */ /* 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? 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 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 #include "config.h" #include "lisp.h" #include "syssignal.h" Lisp_Object Qarith_error; #ifdef LISP_FLOAT_TYPE #include #ifndef hpux /* These declarations are omitted on some systems, like Ultrix. */ extern double logb (); #endif #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 extern int errno; #endif /* Avoid traps on VMS from sinh and cosh. All the other functions set errno instead. */ #ifdef VMS #undef cosh #undef sinh #define cosh(x) ((exp(x)+exp(-x))*0.5) #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. 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 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; \ 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 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 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. */ double extract_float (num) Lisp_Object num; { CHECK_NUMBER_OR_FLOAT (num, 0); if (XTYPE (num) == Lisp_Float) return XFLOAT (num)->data; return (double) XINT (num); } /* Trig functions. */ DEFUN ("acos", Facos, Sacos, 1, 1, 0, "Return the inverse cosine of ARG.") (arg) register 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) register 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, 1, 0, "Return the inverse tangent of ARG.") (arg) register Lisp_Object arg; { double d = extract_float (arg); IN_FLOAT (d = atan (d), "atan", arg); return make_float (d); } DEFUN ("cos", Fcos, Scos, 1, 1, 0, "Return the cosine of ARG.") (arg) register 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) register 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) register 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); } #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.") (arg) register 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) register 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.\n\ The first arg (the order) is truncated to an integer.") (arg1, arg2) register 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) register 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) register 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.\n\ The first arg (the order) is truncated to an integer.") (arg1, arg2) register 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 #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.") (arg) register 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) register 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) register Lisp_Object arg; { double d = extract_float (arg); IN_FLOAT (d = lgamma (d), "log-gamma", arg); return make_float (d); } DEFUN ("cube-root", Fcube_root, Scube_root, 1, 1, 0, "Return the cube root of ARG.") (arg) register 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 DEFUN ("exp", Fexp, Sexp, 1, 1, 0, "Return the exponential base e of ARG.") (arg) register 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); } DEFUN ("expt", Fexpt, Sexpt, 2, 2, 0, "Return the exponential X ** Y.") (arg1, arg2) register Lisp_Object arg1, arg2; { double f1, f2; 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 */ { /* this can be improved by pre-calculating */ 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) { if (x == 1) acc = 1; else if (x == -1) acc = (y & 1) ? -1 : 1; else acc = 0; } else { for (; y > 0; y--) while (y > 0) { if (y & 1) acc *= x; x *= x; y = (unsigned)y >> 1; } } XSET (val, Lisp_Int, acc); return val; } f1 = (XTYPE (arg1) == Lisp_Float) ? XFLOAT (arg1)->data : XINT (arg1); f2 = (XTYPE (arg2) == Lisp_Float) ? XFLOAT (arg2)->data : 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_FLOAT (f1 = pow (f1, f2), "expt", arg1); return make_float (f1); } DEFUN ("log", Flog, Slog, 1, 2, 0, "Return the natural logarithm of ARG.\n\ If second optional argument BASE is given, return log ARG using that base.") (arg, base) register 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) register 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) register 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); } #if 0 /* Not clearly worth adding. */ DEFUN ("acosh", Facosh, Sacosh, 1, 1, 0, "Return the inverse hyperbolic cosine of ARG.") (arg) register 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) register 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) register 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) register 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) register 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) register Lisp_Object arg; { double d = extract_float (arg); IN_FLOAT (d = tanh (d), "tanh", arg); return make_float (d); } #endif DEFUN ("abs", Fabs, Sabs, 1, 1, 0, "Return the absolute value of ARG.") (arg) register Lisp_Object arg; { CHECK_NUMBER_OR_FLOAT (arg, 0); if (XTYPE (arg) == Lisp_Float) IN_FLOAT (arg = make_float (fabs (XFLOAT (arg)->data)), "abs", arg); else if (XINT (arg) < 0) XSETINT (arg, - XFASTINT (arg)); return arg; } DEFUN ("float", Ffloat, Sfloat, 1, 1, 0, "Return the floating point number equal to ARG.") (arg) register Lisp_Object arg; { CHECK_NUMBER_OR_FLOAT (arg, 0); if (XTYPE (arg) == Lisp_Int) 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\ This is the same as the exponent of a float.") (arg) Lisp_Object arg; { Lisp_Object val; int value; double f = extract_float (arg); #ifdef USG { int exp; IN_FLOAT (frexp (f, &exp), "logb", arg); XSET (val, Lisp_Int, exp-1); } #else IN_FLOAT (value = logb (f), "logb", arg); XSET (val, Lisp_Int, value); #endif 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; { CHECK_NUMBER_OR_FLOAT (arg, 0); if (XTYPE (arg) == Lisp_Float) IN_FLOAT (XSET (arg, Lisp_Int, ceil (XFLOAT (arg)->data)), "ceiling", 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; { CHECK_NUMBER_OR_FLOAT (arg, 0); if (XTYPE (arg) == Lisp_Float) IN_FLOAT (XSET (arg, Lisp_Int, floor (XFLOAT (arg)->data)), "floor", arg); return arg; } DEFUN ("round", Fround, Sround, 1, 1, 0, "Return the nearest integer to ARG.") (arg) register Lisp_Object arg; { CHECK_NUMBER_OR_FLOAT (arg, 0); if (XTYPE (arg) == Lisp_Float) /* Screw the prevailing rounding mode. */ IN_FLOAT (XSET (arg, Lisp_Int, rint (XFLOAT (arg)->data)), "round", arg); return arg; } DEFUN ("truncate", Ftruncate, Struncate, 1, 1, 0, "Truncate a floating point number to an int.\n\ Rounds the value toward zero.") (arg) register Lisp_Object arg; { CHECK_NUMBER_OR_FLOAT (arg, 0); if (XTYPE (arg) == Lisp_Float) XSET (arg, Lisp_Int, (int) XFLOAT (arg)->data); return arg; } #if 0 /* 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.\n\ \(Round toward +inf.\)") (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, "Return the largest integer no greater than ARG, as a float.\n\ \(Round towards -inf.\)") (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, "Return the nearest integer to ARG, as a float.") (arg) register Lisp_Object arg; { double d = extract_float (arg); IN_FLOAT (d = rint (XFLOAT (arg)->data), "fround", arg); return make_float (d); } DEFUN ("ftruncate", Fftruncate, Sftruncate, 1, 1, 0, "Truncate a floating point number to an integral float value.\n\ 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), arg); return make_float (d); } #endif #ifdef FLOAT_CATCH_SIGILL static SIGTYPE float_error (signo) int signo; { if (! in_float) fatal_error_signal (signo); #ifdef BSD #ifdef BSD4_1 sigrelse (SIGILL); #else /* not BSD4_1 */ sigsetmask (SIGEMPTYMASK); #endif /* not BSD4_1 */ #else /* Must reestablish handler each time it is called. */ signal (SIGILL, float_error); #endif /* BSD */ 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 */ init_floatfns () { #ifdef FLOAT_CATCH_SIGILL signal (SIGILL, float_error); #endif in_float = 0; } syms_of_floatfns () { defsubr (&Sacos); defsubr (&Sasin); defsubr (&Satan); defsubr (&Scos); defsubr (&Ssin); defsubr (&Stan); #if 0 defsubr (&Sacosh); defsubr (&Sasinh); defsubr (&Satanh); defsubr (&Scosh); defsubr (&Ssinh); defsubr (&Stanh); defsubr (&Sbessel_y0); defsubr (&Sbessel_y1); defsubr (&Sbessel_yn); defsubr (&Sbessel_j0); defsubr (&Sbessel_j1); defsubr (&Sbessel_jn); defsubr (&Serf); defsubr (&Serfc); defsubr (&Slog_gamma); defsubr (&Scube_root); defsubr (&Sfceiling); defsubr (&Sffloor); defsubr (&Sfround); defsubr (&Sftruncate); #endif defsubr (&Sexp); defsubr (&Sexpt); defsubr (&Slog); defsubr (&Slog10); defsubr (&Ssqrt); defsubr (&Sabs); defsubr (&Sfloat); defsubr (&Slogb); defsubr (&Sceiling); defsubr (&Sfloor); defsubr (&Sround); defsubr (&Struncate); } #else /* not LISP_FLOAT_TYPE */ init_floatfns () {} syms_of_floatfns () {} #endif /* not LISP_FLOAT_TYPE */