1 /* Primitive operations on floating point for GNU Emacs Lisp interpreter.
2 Copyright (C) 1988, 1992 Free Software Foundation, Inc.
4 This file is part of GNU Emacs.
6 GNU Emacs is free software; you can redistribute it and/or modify
7 it under the terms of the GNU General Public License as published by
8 the Free Software Foundation; either version 2, or (at your option)
11 GNU Emacs is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 GNU General Public License for more details.
16 You should have received a copy of the GNU General Public License
17 along with GNU Emacs; see the file COPYING. If not, write to
18 the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. */
21 /* ANSI C requires only these float functions:
22 acos, asin, atan, atan2, ceil, cos, cosh, exp, fabs, floor, fmod,
23 frexp, ldexp, log, log10, modf, pow, sin, sinh, sqrt, tan, tanh.
25 Define HAVE_INVERSE_HYPERBOLIC if you have acosh, asinh, and atanh.
26 Define HAVE_CBRT if you have cbrt.
27 Define HAVE_RINT if you have rint.
28 If you don't define these, then the appropriate routines will be simulated.
30 Define HAVE_MATHERR if on a system supporting the SysV matherr callback.
31 (This should happen automatically.)
33 Define FLOAT_CHECK_ERRNO if the float library routines set errno.
34 This has no effect if HAVE_MATHERR is defined.
36 Define FLOAT_CATCH_SIGILL if the float library routines signal SIGILL.
37 (What systems actually do this? Please let us know.)
39 Define FLOAT_CHECK_DOMAIN if the float library doesn't handle errors by
40 either setting errno, or signalling SIGFPE/SIGILL. Otherwise, domain and
41 range checking will happen before calling the float routines. This has
42 no effect if HAVE_MATHERR is defined (since matherr will be called when
43 a domain error occurs.)
50 #include "syssignal.h"
52 Lisp_Object Qarith_error
;
54 #ifdef LISP_FLOAT_TYPE
58 #if defined(DOMAIN) && defined(SING) && defined(OVERFLOW)
59 /* If those are defined, then this is probably a `matherr' machine. */
66 # ifdef FLOAT_CHECK_ERRNO
67 # undef FLOAT_CHECK_ERRNO
69 # ifdef FLOAT_CHECK_DOMAIN
70 # undef FLOAT_CHECK_DOMAIN
74 #ifndef NO_FLOAT_CHECK_ERRNO
75 #define FLOAT_CHECK_ERRNO
78 #ifdef FLOAT_CHECK_ERRNO
84 /* Avoid traps on VMS from sinh and cosh.
85 All the other functions set errno instead. */
90 #define cosh(x) ((exp(x)+exp(-x))*0.5)
91 #define sinh(x) ((exp(x)-exp(-x))*0.5)
95 #define rint(x) (floor((x)+0.5))
98 static SIGTYPE
float_error ();
100 /* Nonzero while executing in floating point.
101 This tells float_error what to do. */
105 /* If an argument is out of range for a mathematical function,
106 here is the actual argument value to use in the error message. */
108 static Lisp_Object float_error_arg
, float_error_arg2
;
110 static char *float_error_fn_name
;
112 /* Evaluate the floating point expression D, recording NUM
113 as the original argument for error messages.
114 D is normally an assignment expression.
115 Handle errors which may result in signals or may set errno.
117 Note that float_error may be declared to return void, so you can't
118 just cast the zero after the colon to (SIGTYPE) to make the types
121 #ifdef FLOAT_CHECK_ERRNO
122 #define IN_FLOAT(d, name, num) \
124 float_error_arg = num; \
125 float_error_fn_name = name; \
126 in_float = 1; errno = 0; (d); in_float = 0; \
129 case EDOM: domain_error (float_error_fn_name, float_error_arg); \
130 case ERANGE: range_error (float_error_fn_name, float_error_arg); \
131 default: arith_error (float_error_fn_name, float_error_arg); \
134 #define IN_FLOAT2(d, name, num, num2) \
136 float_error_arg = num; \
137 float_error_arg2 = num2; \
138 float_error_fn_name = name; \
139 in_float = 1; errno = 0; (d); in_float = 0; \
142 case EDOM: domain_error (float_error_fn_name, float_error_arg); \
143 case ERANGE: range_error (float_error_fn_name, float_error_arg); \
144 default: arith_error (float_error_fn_name, float_error_arg); \
148 #define IN_FLOAT2(d, name, num, num2) (in_float = 1, (d), in_float = 0)
151 #define arith_error(op,arg) \
152 Fsignal (Qarith_error, Fcons (build_string ((op)), Fcons ((arg), Qnil)))
153 #define range_error(op,arg) \
154 Fsignal (Qrange_error, Fcons (build_string ((op)), Fcons ((arg), Qnil)))
155 #define domain_error(op,arg) \
156 Fsignal (Qdomain_error, Fcons (build_string ((op)), Fcons ((arg), Qnil)))
157 #define domain_error2(op,a1,a2) \
158 Fsignal (Qdomain_error, Fcons (build_string ((op)), Fcons ((a1), Fcons ((a2), Qnil))))
160 /* Extract a Lisp number as a `double', or signal an error. */
166 CHECK_NUMBER_OR_FLOAT (num
, 0);
168 if (XTYPE (num
) == Lisp_Float
)
169 return XFLOAT (num
)->data
;
170 return (double) XINT (num
);
173 /* Trig functions. */
175 DEFUN ("acos", Facos
, Sacos
, 1, 1, 0,
176 "Return the inverse cosine of ARG.")
178 register Lisp_Object arg
;
180 double d
= extract_float (arg
);
181 #ifdef FLOAT_CHECK_DOMAIN
182 if (d
> 1.0 || d
< -1.0)
183 domain_error ("acos", arg
);
185 IN_FLOAT (d
= acos (d
), "acos", arg
);
186 return make_float (d
);
189 DEFUN ("asin", Fasin
, Sasin
, 1, 1, 0,
190 "Return the inverse sine of ARG.")
192 register Lisp_Object arg
;
194 double d
= extract_float (arg
);
195 #ifdef FLOAT_CHECK_DOMAIN
196 if (d
> 1.0 || d
< -1.0)
197 domain_error ("asin", arg
);
199 IN_FLOAT (d
= asin (d
), "asin", arg
);
200 return make_float (d
);
203 DEFUN ("atan", Fatan
, Satan
, 1, 1, 0,
204 "Return the inverse tangent of ARG.")
206 register Lisp_Object arg
;
208 double d
= extract_float (arg
);
209 IN_FLOAT (d
= atan (d
), "atan", arg
);
210 return make_float (d
);
213 DEFUN ("cos", Fcos
, Scos
, 1, 1, 0,
214 "Return the cosine of ARG.")
216 register Lisp_Object arg
;
218 double d
= extract_float (arg
);
219 IN_FLOAT (d
= cos (d
), "cos", arg
);
220 return make_float (d
);
223 DEFUN ("sin", Fsin
, Ssin
, 1, 1, 0,
224 "Return the sine of ARG.")
226 register Lisp_Object arg
;
228 double d
= extract_float (arg
);
229 IN_FLOAT (d
= sin (d
), "sin", arg
);
230 return make_float (d
);
233 DEFUN ("tan", Ftan
, Stan
, 1, 1, 0,
234 "Return the tangent of ARG.")
236 register Lisp_Object arg
;
238 double d
= extract_float (arg
);
240 #ifdef FLOAT_CHECK_DOMAIN
242 domain_error ("tan", arg
);
244 IN_FLOAT (d
= sin (d
) / c
, "tan", arg
);
245 return make_float (d
);
248 #if 0 /* Leave these out unless we find there's a reason for them. */
250 DEFUN ("bessel-j0", Fbessel_j0
, Sbessel_j0
, 1, 1, 0,
251 "Return the bessel function j0 of ARG.")
253 register Lisp_Object arg
;
255 double d
= extract_float (arg
);
256 IN_FLOAT (d
= j0 (d
), "bessel-j0", arg
);
257 return make_float (d
);
260 DEFUN ("bessel-j1", Fbessel_j1
, Sbessel_j1
, 1, 1, 0,
261 "Return the bessel function j1 of ARG.")
263 register Lisp_Object arg
;
265 double d
= extract_float (arg
);
266 IN_FLOAT (d
= j1 (d
), "bessel-j1", arg
);
267 return make_float (d
);
270 DEFUN ("bessel-jn", Fbessel_jn
, Sbessel_jn
, 2, 2, 0,
271 "Return the order N bessel function output jn of ARG.\n\
272 The first arg (the order) is truncated to an integer.")
274 register Lisp_Object arg1
, arg2
;
276 int i1
= extract_float (arg1
);
277 double f2
= extract_float (arg2
);
279 IN_FLOAT (f2
= jn (i1
, f2
), "bessel-jn", arg1
);
280 return make_float (f2
);
283 DEFUN ("bessel-y0", Fbessel_y0
, Sbessel_y0
, 1, 1, 0,
284 "Return the bessel function y0 of ARG.")
286 register Lisp_Object arg
;
288 double d
= extract_float (arg
);
289 IN_FLOAT (d
= y0 (d
), "bessel-y0", arg
);
290 return make_float (d
);
293 DEFUN ("bessel-y1", Fbessel_y1
, Sbessel_y1
, 1, 1, 0,
294 "Return the bessel function y1 of ARG.")
296 register Lisp_Object arg
;
298 double d
= extract_float (arg
);
299 IN_FLOAT (d
= y1 (d
), "bessel-y0", arg
);
300 return make_float (d
);
303 DEFUN ("bessel-yn", Fbessel_yn
, Sbessel_yn
, 2, 2, 0,
304 "Return the order N bessel function output yn of ARG.\n\
305 The first arg (the order) is truncated to an integer.")
307 register Lisp_Object arg1
, arg2
;
309 int i1
= extract_float (arg1
);
310 double f2
= extract_float (arg2
);
312 IN_FLOAT (f2
= yn (i1
, f2
), "bessel-yn", arg1
);
313 return make_float (f2
);
318 #if 0 /* Leave these out unless we see they are worth having. */
320 DEFUN ("erf", Ferf
, Serf
, 1, 1, 0,
321 "Return the mathematical error function of ARG.")
323 register Lisp_Object arg
;
325 double d
= extract_float (arg
);
326 IN_FLOAT (d
= erf (d
), "erf", arg
);
327 return make_float (d
);
330 DEFUN ("erfc", Ferfc
, Serfc
, 1, 1, 0,
331 "Return the complementary error function of ARG.")
333 register Lisp_Object arg
;
335 double d
= extract_float (arg
);
336 IN_FLOAT (d
= erfc (d
), "erfc", arg
);
337 return make_float (d
);
340 DEFUN ("log-gamma", Flog_gamma
, Slog_gamma
, 1, 1, 0,
341 "Return the log gamma of ARG.")
343 register Lisp_Object arg
;
345 double d
= extract_float (arg
);
346 IN_FLOAT (d
= lgamma (d
), "log-gamma", arg
);
347 return make_float (d
);
350 DEFUN ("cube-root", Fcube_root
, Scube_root
, 1, 1, 0,
351 "Return the cube root of ARG.")
353 register Lisp_Object arg
;
355 double d
= extract_float (arg
);
357 IN_FLOAT (d
= cbrt (d
), "cube-root", arg
);
360 IN_FLOAT (d
= pow (d
, 1.0/3.0), "cube-root", arg
);
362 IN_FLOAT (d
= -pow (-d
, 1.0/3.0), "cube-root", arg
);
364 return make_float (d
);
369 DEFUN ("exp", Fexp
, Sexp
, 1, 1, 0,
370 "Return the exponential base e of ARG.")
372 register Lisp_Object arg
;
374 double d
= extract_float (arg
);
375 #ifdef FLOAT_CHECK_DOMAIN
376 if (d
> 709.7827) /* Assume IEEE doubles here */
377 range_error ("exp", arg
);
379 return make_float (0.0);
382 IN_FLOAT (d
= exp (d
), "exp", arg
);
383 return make_float (d
);
386 DEFUN ("expt", Fexpt
, Sexpt
, 2, 2, 0,
387 "Return the exponential X ** Y.")
389 register Lisp_Object arg1
, arg2
;
393 CHECK_NUMBER_OR_FLOAT (arg1
, 0);
394 CHECK_NUMBER_OR_FLOAT (arg2
, 0);
395 if ((XTYPE (arg1
) == Lisp_Int
) && /* common lisp spec */
396 (XTYPE (arg2
) == Lisp_Int
)) /* don't promote, if both are ints */
397 { /* this can be improved by pre-calculating */
398 int acc
, x
, y
; /* some binary powers of x then acumulating */
399 /* these, therby saving some time. -wsr */
409 acc
= (y
& 1) ? -1 : 1;
421 y
= (unsigned)y
>> 1;
424 XSET (x
, Lisp_Int
, acc
);
427 f1
= (XTYPE (arg1
) == Lisp_Float
) ? XFLOAT (arg1
)->data
: XINT (arg1
);
428 f2
= (XTYPE (arg2
) == Lisp_Float
) ? XFLOAT (arg2
)->data
: XINT (arg2
);
429 /* Really should check for overflow, too */
430 if (f1
== 0.0 && f2
== 0.0)
432 #ifdef FLOAT_CHECK_DOMAIN
433 else if ((f1
== 0.0 && f2
< 0.0) || (f1
< 0 && f2
!= floor(f2
)))
434 domain_error2 ("expt", arg1
, arg2
);
436 IN_FLOAT (f1
= pow (f1
, f2
), "expt", arg1
);
437 return make_float (f1
);
440 DEFUN ("log", Flog
, Slog
, 1, 2, 0,
441 "Return the natural logarithm of ARG.\n\
442 If second optional argument BASE is given, return log ARG using that base.")
444 register Lisp_Object arg
, base
;
446 double d
= extract_float (arg
);
448 #ifdef FLOAT_CHECK_DOMAIN
450 domain_error2 ("log", arg
, base
);
453 IN_FLOAT (d
= log (d
), "log", arg
);
456 double b
= extract_float (base
);
458 #ifdef FLOAT_CHECK_DOMAIN
459 if (b
<= 0.0 || b
== 1.0)
460 domain_error2 ("log", arg
, base
);
463 IN_FLOAT2 (d
= log10 (d
), "log", arg
, base
);
465 IN_FLOAT2 (d
= log (arg
) / log (b
), "log", arg
, base
);
467 return make_float (d
);
470 DEFUN ("log10", Flog10
, Slog10
, 1, 1, 0,
471 "Return the logarithm base 10 of ARG.")
473 register Lisp_Object arg
;
475 double d
= extract_float (arg
);
476 #ifdef FLOAT_CHECK_DOMAIN
478 domain_error ("log10", arg
);
480 IN_FLOAT (d
= log10 (d
), "log10", arg
);
481 return make_float (d
);
484 DEFUN ("sqrt", Fsqrt
, Ssqrt
, 1, 1, 0,
485 "Return the square root of ARG.")
487 register Lisp_Object arg
;
489 double d
= extract_float (arg
);
490 #ifdef FLOAT_CHECK_DOMAIN
492 domain_error ("sqrt", arg
);
494 IN_FLOAT (d
= sqrt (d
), "sqrt", arg
);
495 return make_float (d
);
498 #if 0 /* Not clearly worth adding. */
500 DEFUN ("acosh", Facosh
, Sacosh
, 1, 1, 0,
501 "Return the inverse hyperbolic cosine of ARG.")
503 register Lisp_Object arg
;
505 double d
= extract_float (arg
);
506 #ifdef FLOAT_CHECK_DOMAIN
508 domain_error ("acosh", arg
);
510 #ifdef HAVE_INVERSE_HYPERBOLIC
511 IN_FLOAT (d
= acosh (d
), "acosh", arg
);
513 IN_FLOAT (d
= log (d
+ sqrt (d
*d
- 1.0)), "acosh", arg
);
515 return make_float (d
);
518 DEFUN ("asinh", Fasinh
, Sasinh
, 1, 1, 0,
519 "Return the inverse hyperbolic sine of ARG.")
521 register Lisp_Object arg
;
523 double d
= extract_float (arg
);
524 #ifdef HAVE_INVERSE_HYPERBOLIC
525 IN_FLOAT (d
= asinh (d
), "asinh", arg
);
527 IN_FLOAT (d
= log (d
+ sqrt (d
*d
+ 1.0)), "asinh", arg
);
529 return make_float (d
);
532 DEFUN ("atanh", Fatanh
, Satanh
, 1, 1, 0,
533 "Return the inverse hyperbolic tangent of ARG.")
535 register Lisp_Object arg
;
537 double d
= extract_float (arg
);
538 #ifdef FLOAT_CHECK_DOMAIN
539 if (d
>= 1.0 || d
<= -1.0)
540 domain_error ("atanh", arg
);
542 #ifdef HAVE_INVERSE_HYPERBOLIC
543 IN_FLOAT (d
= atanh (d
), "atanh", arg
);
545 IN_FLOAT (d
= 0.5 * log ((1.0 + d
) / (1.0 - d
)), "atanh", arg
);
547 return make_float (d
);
550 DEFUN ("cosh", Fcosh
, Scosh
, 1, 1, 0,
551 "Return the hyperbolic cosine of ARG.")
553 register Lisp_Object arg
;
555 double d
= extract_float (arg
);
556 #ifdef FLOAT_CHECK_DOMAIN
557 if (d
> 710.0 || d
< -710.0)
558 range_error ("cosh", arg
);
560 IN_FLOAT (d
= cosh (d
), "cosh", arg
);
561 return make_float (d
);
564 DEFUN ("sinh", Fsinh
, Ssinh
, 1, 1, 0,
565 "Return the hyperbolic sine of ARG.")
567 register Lisp_Object arg
;
569 double d
= extract_float (arg
);
570 #ifdef FLOAT_CHECK_DOMAIN
571 if (d
> 710.0 || d
< -710.0)
572 range_error ("sinh", arg
);
574 IN_FLOAT (d
= sinh (d
), "sinh", arg
);
575 return make_float (d
);
578 DEFUN ("tanh", Ftanh
, Stanh
, 1, 1, 0,
579 "Return the hyperbolic tangent of ARG.")
581 register Lisp_Object arg
;
583 double d
= extract_float (arg
);
584 IN_FLOAT (d
= tanh (d
), "tanh", arg
);
585 return make_float (d
);
589 DEFUN ("abs", Fabs
, Sabs
, 1, 1, 0,
590 "Return the absolute value of ARG.")
592 register Lisp_Object arg
;
594 CHECK_NUMBER_OR_FLOAT (arg
, 0);
596 if (XTYPE (arg
) == Lisp_Float
)
597 IN_FLOAT (arg
= make_float (fabs (XFLOAT (arg
)->data
)), "abs", arg
);
598 else if (XINT (arg
) < 0)
599 XSETINT (arg
, - XFASTINT (arg
));
604 DEFUN ("float", Ffloat
, Sfloat
, 1, 1, 0,
605 "Return the floating point number equal to ARG.")
607 register Lisp_Object arg
;
609 CHECK_NUMBER_OR_FLOAT (arg
, 0);
611 if (XTYPE (arg
) == Lisp_Int
)
612 return make_float ((double) XINT (arg
));
613 else /* give 'em the same float back */
617 DEFUN ("logb", Flogb
, Slogb
, 1, 1, 0,
618 "Returns the integer not greater than the base 2 log of the magnitude of ARG.\n\
619 This is the same as the exponent of a float.")
624 error ("SYSV apparently doesn't have a logb function; what to do?");
627 double f
= extract_float (num
);
629 IN_FLOAT (val
= logb (f
), "logb", num
);
630 XSET (val
, Lisp_Int
, val
);
635 /* the rounding functions */
637 DEFUN ("ceiling", Fceiling
, Sceiling
, 1, 1, 0,
638 "Return the smallest integer no less than ARG. (Round toward +inf.)")
640 register Lisp_Object arg
;
642 CHECK_NUMBER_OR_FLOAT (arg
, 0);
644 if (XTYPE (arg
) == Lisp_Float
)
645 IN_FLOAT (XSET (arg
, Lisp_Int
, ceil (XFLOAT (arg
)->data
)), "celing", arg
);
650 DEFUN ("floor", Ffloor
, Sfloor
, 1, 1, 0,
651 "Return the largest integer no greater than ARG. (Round towards -inf.)")
653 register Lisp_Object arg
;
655 CHECK_NUMBER_OR_FLOAT (arg
, 0);
657 if (XTYPE (arg
) == Lisp_Float
)
658 IN_FLOAT (XSET (arg
, Lisp_Int
, floor (XFLOAT (arg
)->data
)), "floor", arg
);
663 DEFUN ("round", Fround
, Sround
, 1, 1, 0,
664 "Return the nearest integer to ARG.")
666 register Lisp_Object arg
;
668 CHECK_NUMBER_OR_FLOAT (arg
, 0);
670 if (XTYPE (arg
) == Lisp_Float
)
671 /* Screw the prevailing rounding mode. */
672 IN_FLOAT (XSET (arg
, Lisp_Int
, rint (XFLOAT (arg
)->data
)), "round", arg
);
677 DEFUN ("truncate", Ftruncate
, Struncate
, 1, 1, 0,
678 "Truncate a floating point number to an int.\n\
679 Rounds the value toward zero.")
681 register Lisp_Object arg
;
683 CHECK_NUMBER_OR_FLOAT (arg
, 0);
685 if (XTYPE (arg
) == Lisp_Float
)
686 XSET (arg
, Lisp_Int
, (int) XFLOAT (arg
)->data
);
692 /* It's not clear these are worth adding. */
694 DEFUN ("fceiling", Ffceiling
, Sfceiling
, 1, 1, 0,
695 "Return the smallest integer no less than ARG, as a float.\n\
696 \(Round toward +inf.\)")
698 register Lisp_Object arg
;
700 double d
= extract_float (arg
);
701 IN_FLOAT (d
= ceil (d
), "fceiling", arg
);
702 return make_float (d
);
705 DEFUN ("ffloor", Fffloor
, Sffloor
, 1, 1, 0,
706 "Return the largest integer no greater than ARG, as a float.\n\
707 \(Round towards -inf.\)")
709 register Lisp_Object arg
;
711 double d
= extract_float (arg
);
712 IN_FLOAT (d
= floor (d
), "ffloor", arg
);
713 return make_float (d
);
716 DEFUN ("fround", Ffround
, Sfround
, 1, 1, 0,
717 "Return the nearest integer to ARG, as a float.")
719 register Lisp_Object arg
;
721 double d
= extract_float (arg
);
722 IN_FLOAT (d
= rint (XFLOAT (arg
)->data
), "fround", arg
);
723 return make_float (d
);
726 DEFUN ("ftruncate", Fftruncate
, Sftruncate
, 1, 1, 0,
727 "Truncate a floating point number to an integral float value.\n\
728 Rounds the value toward zero.")
730 register Lisp_Object arg
;
732 double d
= extract_float (arg
);
734 IN_FLOAT (d
= floor (d
), "ftruncate", arg
);
736 IN_FLOAT (d
= ceil (d
), arg
);
737 return make_float (d
);
741 #ifdef FLOAT_CATCH_SIGILL
747 fatal_error_signal (signo
);
752 #else /* not BSD4_1 */
753 sigsetmask (SIGEMPTYMASK
);
754 #endif /* not BSD4_1 */
756 /* Must reestablish handler each time it is called. */
757 signal (SIGILL
, float_error
);
762 Fsignal (Qarith_error
, Fcons (float_error_arg
, Qnil
));
765 /* Another idea was to replace the library function `infnan'
766 where SIGILL is signaled. */
768 #endif /* FLOAT_CATCH_SIGILL */
777 /* Not called from emacs-lisp float routines; do the default thing. */
779 if (!strcmp (x
->name
, "pow"))
783 = Fcons (build_string (x
->name
),
784 Fcons (make_float (x
->arg1
),
785 ((!strcmp (x
->name
, "log") || !strcmp (x
->name
, "pow"))
786 ? Fcons (make_float (x
->arg2
), Qnil
)
790 case DOMAIN
: Fsignal (Qdomain_error
, args
); break;
791 case SING
: Fsignal (Qsingularity_error
, args
); break;
792 case OVERFLOW
: Fsignal (Qoverflow_error
, args
); break;
793 case UNDERFLOW
: Fsignal (Qunderflow_error
, args
); break;
794 default: Fsignal (Qarith_error
, args
); break;
796 return (1); /* don't set errno or print a message */
798 #endif /* HAVE_MATHERR */
802 #ifdef FLOAT_CATCH_SIGILL
803 signal (SIGILL
, float_error
);
823 defsubr (&Sbessel_y0
);
824 defsubr (&Sbessel_y1
);
825 defsubr (&Sbessel_yn
);
826 defsubr (&Sbessel_j0
);
827 defsubr (&Sbessel_j1
);
828 defsubr (&Sbessel_jn
);
831 defsubr (&Slog_gamma
);
832 defsubr (&Scube_root
);
833 defsubr (&Sfceiling
);
836 defsubr (&Sftruncate
);
850 defsubr (&Struncate
);
853 #else /* not LISP_FLOAT_TYPE */
861 #endif /* not LISP_FLOAT_TYPE */