X-Git-Url: http://git.hcoop.net/bpt/guile.git/blobdiff_plain/3eb7e6ee5eec319c27fd8e3a20f654be0d3e28ab..9e6fc585b28869b547de3f8d460f19d96e85b17e:/libguile/numbers.c?ds=sidebyside diff --git a/libguile/numbers.c b/libguile/numbers.c dissimilarity index 63% index 769562829..2b2cedbff 100644 --- a/libguile/numbers.c +++ b/libguile/numbers.c @@ -1,4819 +1,4544 @@ -/* Copyright (C) 1995,1996,1997,1998, 1999 Free Software Foundation, Inc. - - * This program 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. - * - * This program 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 this software; see the file COPYING. If not, write to - * the Free Software Foundation, Inc., 59 Temple Place, Suite 330, - * Boston, MA 02111-1307 USA - * - * As a special exception, the Free Software Foundation gives permission - * for additional uses of the text contained in its release of GUILE. - * - * The exception is that, if you link the GUILE library with other files - * to produce an executable, this does not by itself cause the - * resulting executable to be covered by the GNU General Public License. - * Your use of that executable is in no way restricted on account of - * linking the GUILE library code into it. - * - * This exception does not however invalidate any other reasons why - * the executable file might be covered by the GNU General Public License. - * - * This exception applies only to the code released by the - * Free Software Foundation under the name GUILE. If you copy - * code from other Free Software Foundation releases into a copy of - * GUILE, as the General Public License permits, the exception does - * not apply to the code that you add in this way. To avoid misleading - * anyone as to the status of such modified files, you must delete - * this exception notice from them. - * - * If you write modifications of your own for GUILE, it is your choice - * whether to permit this exception to apply to your modifications. - * If you do not wish that, delete this exception notice. */ - - -#include -#include -#include "_scm.h" -#include "genio.h" -#include "unif.h" -#include "feature.h" -#include "smob.h" - -#include "numbers.h" - -#define DIGITS '0':case '1':case '2':case '3':case '4':\ - case '5':case '6':case '7':case '8':case '9' - - -/* IS_INF tests its floating point number for infiniteness - */ -#ifndef IS_INF -#define IS_INF(x) ((x) == (x) / 2) -#endif - -/* Return true if X is not infinite and is not a NaN - */ -#ifndef isfinite -#define isfinite(x) (!IS_INF (x) && (x) == (x)) -#endif - -/* MAXEXP is the maximum double precision expontent - * FLTMAX is less than or scm_equal the largest single precision float - */ - -#ifdef SCM_FLOATS -#ifdef STDC_HEADERS -#ifndef GO32 -#include -#endif /* ndef GO32 */ -#endif /* def STDC_HEADERS */ -#ifdef DBL_MAX_10_EXP -#define MAXEXP DBL_MAX_10_EXP -#else -#define MAXEXP 308 /* IEEE doubles */ -#endif /* def DBL_MAX_10_EXP */ -#ifdef FLT_MAX -#define FLTMAX FLT_MAX -#else -#define FLTMAX 1e+23 -#endif /* def FLT_MAX */ -#endif /* def SCM_FLOATS */ - - - -SCM_PROC (s_exact_p, "exact?", 1, 0, 0, scm_exact_p); - -SCM -scm_exact_p (x) - SCM x; -{ - if (SCM_INUMP (x)) - return SCM_BOOL_T; -#ifdef SCM_BIGDIG - if (SCM_NIMP (x) && SCM_BIGP (x)) - return SCM_BOOL_T; -#endif - return SCM_BOOL_F; -} - -SCM_PROC (s_odd_p, "odd?", 1, 0, 0, scm_odd_p); - -SCM -scm_odd_p (n) - SCM n; -{ -#ifdef SCM_BIGDIG - if (SCM_NINUMP (n)) - { - SCM_ASSERT (SCM_NIMP (n) && SCM_BIGP (n), n, SCM_ARG1, s_odd_p); - return (1 & SCM_BDIGITS (n)[0]) ? SCM_BOOL_T : SCM_BOOL_F; - } -#else - SCM_ASSERT (SCM_INUMP (n), n, SCM_ARG1, s_odd_p); -#endif - return (4 & (int) n) ? SCM_BOOL_T : SCM_BOOL_F; -} - -SCM_PROC (s_even_p, "even?", 1, 0, 0, scm_even_p); - -SCM -scm_even_p (n) - SCM n; -{ -#ifdef SCM_BIGDIG - if (SCM_NINUMP (n)) - { - SCM_ASSERT (SCM_NIMP (n) && SCM_BIGP (n), n, SCM_ARG1, s_even_p); - return (1 & SCM_BDIGITS (n)[0]) ? SCM_BOOL_F : SCM_BOOL_T; - } -#else - SCM_ASSERT (SCM_INUMP (n), n, SCM_ARG1, s_even_p); -#endif - return (4 & (int) n) ? SCM_BOOL_F : SCM_BOOL_T; -} - -SCM_GPROC (s_abs, "abs", 1, 0, 0, scm_abs, g_abs); - -SCM -scm_abs (x) - SCM x; -{ -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - SCM_GASSERT1 (SCM_NIMP (x) && SCM_BIGP (x), g_abs, x, SCM_ARG1, s_abs); - if (SCM_TYP16 (x) == scm_tc16_bigpos) - return x; - return scm_copybig (x, 0); - } -#else - SCM_GASSERT1 (SCM_INUMP (x), g_abs, x, SCM_ARG1, s_abs); -#endif - if (SCM_INUM (x) >= 0) - return x; - x = - SCM_INUM (x); - if (!SCM_POSFIXABLE (x)) -#ifdef SCM_BIGDIG - return scm_long2big (x); -#else - scm_num_overflow (s_abs); -#endif - return SCM_MAKINUM (x); -} - -SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient); - -SCM -scm_quotient (x, y) - SCM x; - SCM y; -{ - register long z; -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - long w; - SCM_GASSERT2 (SCM_NIMP (x) && SCM_BIGP (x), - g_quotient, x, y, SCM_ARG1, s_quotient); - if (SCM_NINUMP (y)) - { - SCM_ASRTGO (SCM_NIMP (y) && SCM_BIGP (y), bady); - return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - SCM_BDIGITS (y), SCM_NUMDIGS (y), - SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y), 2); - } - z = SCM_INUM (y); - SCM_ASRTGO (z, ov); - if (1 == z) - return x; - if (z < 0) - z = -z; - if (z < SCM_BIGRAD) - { - w = scm_copybig (x, SCM_BIGSIGN (x) ? (y > 0) : (y < 0)); - scm_divbigdig (SCM_BDIGITS (w), SCM_NUMDIGS (w), (SCM_BIGDIG) z); - return scm_normbig (w); - } -#ifndef SCM_DIGSTOOBIG - w = scm_pseudolong (z); - return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - (SCM_BIGDIG *) & w, SCM_DIGSPERLONG, - SCM_BIGSIGN (x) ? (y > 0) : (y < 0), 2); -#else - { - SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; - scm_longdigs (z, zdigs); - return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - zdigs, SCM_DIGSPERLONG, - SCM_BIGSIGN (x) ? (y > 0) : (y < 0), 2); - } -#endif - } - if (SCM_NINUMP (y)) - { - if (!(SCM_NIMP (y) && SCM_BIGP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); - } - return SCM_INUM0; - } -#else - SCM_GASSERT2 (SCM_INUMP (x), g_quotient, x, y, SCM_ARG1, s_quotient); - SCM_GASSERT2 (SCM_INUMP (y), g_quotient, x, y, SCM_ARG2, s_quotient); -#endif - if ((z = SCM_INUM (y)) == 0) - { - ov: - scm_num_overflow (s_quotient); - } - z = SCM_INUM (x) / z; -#ifdef BADIVSGNS - { -#if (__TURBOC__ == 1) - long t = ((y < 0) ? -SCM_INUM (x) : SCM_INUM (x)) % SCM_INUM (y); -#else - long t = SCM_INUM (x) % SCM_INUM (y); -#endif - if (t == 0); - else if (t < 0) - if (x < 0); - else - z--; - else if (x < 0) - z++; - } -#endif - if (!SCM_FIXABLE (z)) -#ifdef SCM_BIGDIG - return scm_long2big (z); -#else - scm_num_overflow (s_quotient); -#endif - return SCM_MAKINUM (z); -} - -SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder); - -SCM -scm_remainder (x, y) - SCM x; - SCM y; -{ - register long z; -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - SCM_GASSERT2 (SCM_NIMP (x) && SCM_BIGP (x), - g_remainder, x, y, SCM_ARG1, s_remainder); - if (SCM_NINUMP (y)) - { - SCM_ASRTGO (SCM_NIMP (y) && SCM_BIGP (y), bady); - return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - SCM_BDIGITS (y), SCM_NUMDIGS (y), - SCM_BIGSIGN (x), 0); - } - if (!(z = SCM_INUM (y))) - goto ov; - return scm_divbigint (x, z, SCM_BIGSIGN (x), 0); - } - if (SCM_NINUMP (y)) - { - if (!(SCM_NIMP (y) && SCM_BIGP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); - } - return x; - } -#else - SCM_GASSERT2 (SCM_INUMP (x), g_remainder, x, y, SCM_ARG1, s_remainder); - SCM_GASSERT2 (SCM_INUMP (y), g_remainder, x, y, SCM_ARG2, s_remainder); -#endif - if (!(z = SCM_INUM (y))) - { - ov: - scm_num_overflow (s_remainder); - } -#if (__TURBOC__ == 1) - if (z < 0) - z = -z; -#endif - z = SCM_INUM (x) % z; -#ifdef BADIVSGNS - if (!z); - else if (z < 0) - if (x < 0); - else - z += SCM_INUM (y); - else if (x < 0) - z -= SCM_INUM (y); -#endif - return SCM_MAKINUM (z); -} - -SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo); - -SCM -scm_modulo (x, y) - SCM x; - SCM y; -{ - register long yy, z; -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - SCM_GASSERT2 (SCM_NIMP (x) && SCM_BIGP (x), - g_modulo, x, y, SCM_ARG1, s_modulo); - if (SCM_NINUMP (y)) - { - SCM_ASRTGO (SCM_NIMP (y) && SCM_BIGP (y), bady); - return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - SCM_BDIGITS (y), SCM_NUMDIGS (y), - SCM_BIGSIGN (y), - (SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y)) ? 1 : 0); - } - if (!(z = SCM_INUM (y))) - goto ov; - return scm_divbigint (x, z, y < 0, - (SCM_BIGSIGN (x) ? (y > 0) : (y < 0)) ? 1 : 0); - } - if (SCM_NINUMP (y)) - { - if (!(SCM_NIMP (y) && SCM_BIGP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); - } - return (SCM_BIGSIGN (y) ? (x > 0) : (x < 0)) ? scm_sum (x, y) : x; - } -#else - SCM_GASSERT1 (SCM_INUMP (x), g_modulo, x, y, SCM_ARG1, s_modulo); - SCM_GASSERT2 (SCM_INUMP (y), g_modulo, x, y, SCM_ARG2, s_modulo); -#endif - if (!(yy = SCM_INUM (y))) - { - ov: - scm_num_overflow (s_modulo); - } -#if (__TURBOC__==1) - z = SCM_INUM (x); - z = ((yy < 0) ? -z : z) % yy; -#else - z = SCM_INUM (x) % yy; -#endif - return SCM_MAKINUM (((yy < 0) ? (z > 0) : (z < 0)) ? z + yy : z); -} - -SCM_GPROC1 (s_gcd, "gcd", scm_tc7_asubr, scm_gcd, g_gcd); - -SCM -scm_gcd (x, y) - SCM x; - SCM y; -{ - register long u, v, k, t; - if (SCM_UNBNDP (y)) - return SCM_UNBNDP (x) ? SCM_INUM0 : x; - tailrec: -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - big_gcd: - SCM_GASSERT2 (SCM_NIMP (x) && SCM_BIGP (x), - g_gcd, x, y, SCM_ARG1, s_gcd); - if (SCM_BIGSIGN (x)) - x = scm_copybig (x, 0); - newy: - if (SCM_NINUMP (y)) - { - SCM_GASSERT2 (SCM_NIMP (y) && SCM_BIGP (y), - g_gcd, x, y, SCM_ARGn, s_gcd); - if (SCM_BIGSIGN (y)) - y = scm_copybig (y, 0); - switch (scm_bigcomp (x, y)) - { - case -1: - swaprec: - t = scm_remainder (x, y); - x = y; - y = t; - goto tailrec; - case 0: - return x; - case 1: - y = scm_remainder (y, x); - goto newy; - } - /* instead of the switch, we could just - return scm_gcd (y, scm_modulo (x, y)); */ - } - if (SCM_INUM0 == y) - return x; - goto swaprec; - } - if (SCM_NINUMP (y)) - { - t = x; - x = y; - y = t; - goto big_gcd; - } -#else - SCM_GASSERT2 (SCM_INUMP (x), g_gcd, x, y, SCM_ARG1, s_gcd); - SCM_GASSERT2 (SCM_INUMP (y), g_gcd, x, y, SCM_ARGn, s_gcd); -#endif - u = SCM_INUM (x); - if (u < 0) - u = -u; - v = SCM_INUM (y); - if (v < 0) - v = -v; - else if (0 == v) - goto getout; - if (0 == u) - { - u = v; - goto getout; - } - for (k = 1; !(1 & ((int) u | (int) v)); k <<= 1, u >>= 1, v >>= 1); - if (1 & (int) u) - t = -v; - else - { - t = u; - b3: - t = SCM_SRS (t, 1); - } - if (!(1 & (int) t)) - goto b3; - if (t > 0) - u = t; - else - v = -t; - if ((t = u - v)) - goto b3; - u = u * k; - getout: - if (!SCM_POSFIXABLE (u)) -#ifdef SCM_BIGDIG - return scm_long2big (u); -#else - scm_num_overflow (s_gcd); -#endif - return SCM_MAKINUM (u); -} - -SCM_GPROC1 (s_lcm, "lcm", scm_tc7_asubr, scm_lcm, g_lcm); - -SCM -scm_lcm (n1, n2) - SCM n1; - SCM n2; -{ - SCM d; -#ifndef SCM_BIGDIG - SCM_GASSERT2 (SCM_INUMP (n1) || SCM_UNBNDP (n1), - g_lcm, n1, n2, SCM_ARG1, s_lcm); - SCM_GASSERT2 (SCM_INUMP (n2) || SCM_UNBNDP (n2), - g_lcm, n1, n2, SCM_ARGn, s_lcm); -#else - SCM_GASSERT2 (SCM_INUMP (n1) - || SCM_UNBNDP (n1) - || (SCM_NIMP (n1) && SCM_BIGP (n1)), - g_lcm, n1, n2, SCM_ARG1, s_lcm); - SCM_GASSERT2 (SCM_INUMP (n2) - || SCM_UNBNDP (n2) - || (SCM_NIMP (n2) && SCM_BIGP (n2)), - g_lcm, n1, n2, SCM_ARGn, s_lcm); -#endif - if (SCM_UNBNDP (n2)) - { - n2 = SCM_MAKINUM (1L); - if (SCM_UNBNDP (n1)) - return n2; - } - - d = scm_gcd (n1, n2); - if (SCM_INUM0 == d) - return d; - return scm_abs (scm_product (n1, scm_quotient (n2, d))); -} - -#ifndef SCM_BIGDIG -#ifndef SCM_FLOATS -#define scm_long2num SCM_MAKINUM -#endif -#endif - -#ifndef scm_long2num -SCM_PROC1 (s_logand, "logand", scm_tc7_asubr, scm_logand); - -SCM -scm_logand (n1, n2) - SCM n1; - SCM n2; -{ - if (SCM_UNBNDP (n2)) - { - if (SCM_UNBNDP (n1)) - return SCM_MAKINUM (-1); - return n1; - } - return scm_ulong2num (scm_num2ulong (n1, (char *) SCM_ARG1, s_logand) - & scm_num2ulong (n2, (char *) SCM_ARG2, s_logand)); -} - -SCM_PROC1 (s_logior, "logior", scm_tc7_asubr, scm_logior); - -SCM -scm_logior (n1, n2) - SCM n1; - SCM n2; -{ - if (SCM_UNBNDP (n2)) - { - if (SCM_UNBNDP (n1)) - return SCM_INUM0; - return n1; - } - return scm_ulong2num (scm_num2ulong (n1, (char *) SCM_ARG1, s_logior) - | scm_num2ulong (n2, (char *) SCM_ARG2, s_logior)); -} - -SCM_PROC1 (s_logxor, "logxor", scm_tc7_asubr, scm_logxor); - -SCM -scm_logxor (n1, n2) - SCM n1; - SCM n2; -{ - if (SCM_UNBNDP (n2)) - { - if (SCM_UNBNDP (n1)) - return SCM_INUM0; - return n1; - } - return scm_ulong2num (scm_num2ulong (n1, (char *) SCM_ARG1, s_logxor) - ^ scm_num2ulong (n2, (char *) SCM_ARG2, s_logxor)); -} - -SCM_PROC (s_logtest, "logtest", 2, 0, 0, scm_logtest); - -SCM -scm_logtest (n1, n2) - SCM n1; - SCM n2; -{ - return ((scm_num2ulong (n1, (char *) SCM_ARG1, s_logtest) - & scm_num2ulong (n2, (char *) SCM_ARG2, s_logtest)) - ? SCM_BOOL_T : SCM_BOOL_F); -} - - -SCM_PROC (s_logbit_p, "logbit?", 2, 0, 0, scm_logbit_p); - -SCM -scm_logbit_p (n1, n2) - SCM n1; - SCM n2; -{ - return (((1 << scm_num2long (n1, (char *) SCM_ARG1, s_logtest)) - & scm_num2ulong (n2, (char *) SCM_ARG2, s_logtest)) - ? SCM_BOOL_T : SCM_BOOL_F); -} - -#else - -SCM_PROC1 (s_logand, "logand", scm_tc7_asubr, scm_logand); - -SCM -scm_logand (n1, n2) - SCM n1; - SCM n2; -{ - if (SCM_UNBNDP (n2)) - { - if (SCM_UNBNDP (n1)) - return SCM_MAKINUM (-1); - return n1; - } - return SCM_MAKINUM (SCM_INUM (n1) & SCM_INUM (n2)); -} - -SCM_PROC1 (s_logior, "logior", scm_tc7_asubr, scm_logior); - -SCM -scm_logior (n1, n2) - SCM n1; - SCM n2; -{ - if (SCM_UNBNDP (n2)) - { - if (SCM_UNBNDP (n1)) - return SCM_INUM0; - return n1; - } - return SCM_MAKINUM (SCM_INUM (n1) | SCM_INUM (n2)); -} - -SCM_PROC1 (s_logxor, "logxor", scm_tc7_asubr, scm_logxor); - -SCM -scm_logxor (n1, n2) - SCM n1; - SCM n2; -{ - if (SCM_UNBNDP (n2)) - { - if (SCM_UNBNDP (n1)) - return SCM_INUM0; - return n1; - } - return SCM_MAKINUM (SCM_INUM (n1) ^ SCM_INUM (n2)); -} - -SCM_PROC (s_logtest, "logtest", 2, 0, 0, scm_logtest); - -SCM -scm_logtest (n1, n2) - SCM n1; - SCM n2; -{ - SCM_ASSERT (SCM_INUMP (n1), n1, SCM_ARG1, s_logtest); - SCM_ASSERT (SCM_INUMP (n2), n2, SCM_ARG2, s_logtest); - return (SCM_INUM (n1) & SCM_INUM (n2)) ? SCM_BOOL_T : SCM_BOOL_F; -} - -SCM_PROC (s_logbit_p, "logbit?", 2, 0, 0, scm_logbit_p); - -SCM -scm_logbit_p (n1, n2) - SCM n1; - SCM n2; -{ - SCM_ASSERT (SCM_INUMP (n1) && SCM_INUM (n1) >= 0, n1, SCM_ARG1, s_logbit_p); - SCM_ASSERT (SCM_INUMP (n2), n2, SCM_ARG2, s_logbit_p); - return ((1 << SCM_INUM (n1)) & SCM_INUM (n2)) ? SCM_BOOL_T : SCM_BOOL_F; -} -#endif - -SCM_PROC (s_lognot, "lognot", 1, 0, 0, scm_lognot); - -SCM -scm_lognot (n) - SCM n; -{ - SCM_ASSERT (SCM_INUMP (n), n, SCM_ARG1, s_lognot); - return scm_difference (SCM_MAKINUM (-1L), n); -} - -SCM_PROC (s_integer_expt, "integer-expt", 2, 0, 0, scm_integer_expt); - -SCM -scm_integer_expt (z1, z2) - SCM z1; - SCM z2; -{ - SCM acc = SCM_MAKINUM (1L); -#ifdef SCM_BIGDIG - if (SCM_INUM0 == z1 || acc == z1) - return z1; - else if (SCM_MAKINUM (-1L) == z1) - return SCM_BOOL_F == scm_even_p (z2) ? z1 : acc; -#endif - SCM_ASSERT (SCM_INUMP (z2), z2, SCM_ARG2, s_integer_expt); - z2 = SCM_INUM (z2); - if (z2 < 0) - { - z2 = -z2; - z1 = scm_divide (z1, SCM_UNDEFINED); - } - while (1) - { - if (0 == z2) - return acc; - if (1 == z2) - return scm_product (acc, z1); - if (z2 & 1) - acc = scm_product (acc, z1); - z1 = scm_product (z1, z1); - z2 >>= 1; - } -} - -SCM_PROC (s_ash, "ash", 2, 0, 0, scm_ash); - -SCM -scm_ash (n, cnt) - SCM n; - SCM cnt; -{ - SCM res = SCM_INUM (n); - SCM_ASSERT (SCM_INUMP (cnt), cnt, SCM_ARG2, s_ash); -#ifdef SCM_BIGDIG - if (cnt < 0) - { - res = scm_integer_expt (SCM_MAKINUM (2), SCM_MAKINUM (-SCM_INUM (cnt))); - if (SCM_NFALSEP (scm_negative_p (n))) - return scm_sum (SCM_MAKINUM (-1L), - scm_quotient (scm_sum (SCM_MAKINUM (1L), n), res)); - else - return scm_quotient (n, res); - } - else - return scm_product (n, scm_integer_expt (SCM_MAKINUM (2), cnt)); -#else - SCM_ASSERT (SCM_INUMP (n), n, SCM_ARG1, s_ash); - cnt = SCM_INUM (cnt); - if (cnt < 0) - return SCM_MAKINUM (SCM_SRS (res, -cnt)); - res = SCM_MAKINUM (res << cnt); - if (SCM_INUM (res) >> cnt != SCM_INUM (n)) - scm_num_overflow (s_ash); - return res; -#endif -} - -SCM_PROC (s_bit_extract, "bit-extract", 3, 0, 0, scm_bit_extract); - -SCM -scm_bit_extract (n, start, end) - SCM n; - SCM start; - SCM end; -{ - SCM_ASSERT (SCM_INUMP (start), start, SCM_ARG2, s_bit_extract); - SCM_ASSERT (SCM_INUMP (end), end, SCM_ARG3, s_bit_extract); - start = SCM_INUM (start); - end = SCM_INUM (end); - SCM_ASSERT (end >= start, SCM_MAKINUM (end), SCM_OUTOFRANGE, s_bit_extract); -#ifdef SCM_BIGDIG - if (SCM_NINUMP (n)) - return - scm_logand (scm_difference (scm_integer_expt (SCM_MAKINUM (2), - SCM_MAKINUM (end - start)), - SCM_MAKINUM (1L)), - scm_ash (n, SCM_MAKINUM (-start))); -#else - SCM_ASSERT (SCM_INUMP (n), n, SCM_ARG1, s_bit_extract); -#endif - return SCM_MAKINUM ((SCM_INUM (n) >> start) & ((1L << (end - start)) - 1)); -} - -static const char scm_logtab[] = { - 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 -}; -SCM_PROC (s_logcount, "logcount", 1, 0, 0, scm_logcount); - -SCM -scm_logcount (n) - SCM n; -{ - register unsigned long c = 0; - register long nn; -#ifdef SCM_BIGDIG - if (SCM_NINUMP (n)) - { - scm_sizet i; - SCM_BIGDIG *ds, d; - SCM_ASSERT (SCM_NIMP (n) && SCM_BIGP (n), n, SCM_ARG1, s_logcount); - if (SCM_BIGSIGN (n)) - return scm_logcount (scm_difference (SCM_MAKINUM (-1L), n)); - ds = SCM_BDIGITS (n); - for (i = SCM_NUMDIGS (n); i--;) - for (d = ds[i]; d; d >>= 4) - c += scm_logtab[15 & d]; - return SCM_MAKINUM (c); - } -#else - SCM_ASSERT (SCM_INUMP (n), n, SCM_ARG1, s_logcount); -#endif - if ((nn = SCM_INUM (n)) < 0) - nn = -1 - nn; - for (; nn; nn >>= 4) - c += scm_logtab[15 & nn]; - return SCM_MAKINUM (c); -} - -static const char scm_ilentab[] = { - 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 -}; -SCM_PROC (s_integer_length, "integer-length", 1, 0, 0, scm_integer_length); - -SCM -scm_integer_length (n) - SCM n; -{ - register unsigned long c = 0; - register long nn; - unsigned int l = 4; -#ifdef SCM_BIGDIG - if (SCM_NINUMP (n)) - { - SCM_BIGDIG *ds, d; - SCM_ASSERT (SCM_NIMP (n) && SCM_BIGP (n), n, SCM_ARG1, s_integer_length); - if (SCM_BIGSIGN (n)) - return scm_integer_length (scm_difference (SCM_MAKINUM (-1L), n)); - ds = SCM_BDIGITS (n); - d = ds[c = SCM_NUMDIGS (n) - 1]; - for (c *= SCM_BITSPERDIG; d; d >>= 4) - { - c += 4; - l = scm_ilentab[15 & d]; - } - return SCM_MAKINUM (c - 4 + l); - } -#else - SCM_ASSERT (SCM_INUMP (n), n, SCM_ARG1, s_integer_length); -#endif - if ((nn = SCM_INUM (n)) < 0) - nn = -1 - nn; - for (; nn; nn >>= 4) - { - c += 4; - l = scm_ilentab[15 & nn]; - } - return SCM_MAKINUM (c - 4 + l); -} - - -#ifdef SCM_BIGDIG -static const char s_bignum[] = "bignum"; - -SCM -scm_mkbig (nlen, sign) - scm_sizet nlen; - int sign; -{ - SCM v = nlen; - /* Cast to SCM to avoid signed/unsigned comparison warnings. */ - if (((v << 16) >> 16) != (SCM) nlen) - scm_wta (SCM_MAKINUM (nlen), (char *) SCM_NALLOC, s_bignum); - SCM_NEWCELL (v); - SCM_DEFER_INTS; - SCM_SETCHARS (v, scm_must_malloc ((long) (nlen * sizeof (SCM_BIGDIG)), - s_bignum)); - SCM_SETNUMDIGS (v, nlen, sign ? scm_tc16_bigneg : scm_tc16_bigpos); - SCM_ALLOW_INTS; - return v; -} - - -SCM -scm_big2inum (b, l) - SCM b; - scm_sizet l; -{ - unsigned long num = 0; - SCM_BIGDIG *tmp = SCM_BDIGITS (b); - while (l--) - num = SCM_BIGUP (num) + tmp[l]; - if (SCM_TYP16 (b) == scm_tc16_bigpos) - { - if (SCM_POSFIXABLE (num)) - return SCM_MAKINUM (num); - } - else if (SCM_UNEGFIXABLE (num)) - return SCM_MAKINUM (-num); - return b; -} - - -static const char s_adjbig[] = "scm_adjbig"; - -SCM -scm_adjbig (b, nlen) - SCM b; - scm_sizet nlen; -{ - scm_sizet nsiz = nlen; - if (((nsiz << 16) >> 16) != nlen) - scm_wta (scm_ulong2num (nsiz), (char *) SCM_NALLOC, s_adjbig); - - SCM_DEFER_INTS; - { - SCM_BIGDIG *digits - = ((SCM_BIGDIG *) - scm_must_realloc ((char *) SCM_CHARS (b), - (long) (SCM_NUMDIGS (b) * sizeof (SCM_BIGDIG)), - (long) (nsiz * sizeof (SCM_BIGDIG)), s_adjbig)); - - SCM_SETCHARS (b, digits); - SCM_SETNUMDIGS (b, nsiz, SCM_TYP16 (b)); - } - SCM_ALLOW_INTS; - return b; -} - - - -SCM -scm_normbig (b) - SCM b; -{ -#ifndef _UNICOS - scm_sizet nlen = SCM_NUMDIGS (b); -#else - int nlen = SCM_NUMDIGS (b); /* unsigned nlen breaks on Cray when nlen => 0 */ -#endif - SCM_BIGDIG *zds = SCM_BDIGITS (b); - while (nlen-- && !zds[nlen]); - nlen++; - if (nlen * SCM_BITSPERDIG / SCM_CHAR_BIT <= sizeof (SCM)) - if (SCM_INUMP (b = scm_big2inum (b, (scm_sizet) nlen))) - return b; - if (SCM_NUMDIGS (b) == nlen) - return b; - return scm_adjbig (b, (scm_sizet) nlen); -} - - - -SCM -scm_copybig (b, sign) - SCM b; - int sign; -{ - scm_sizet i = SCM_NUMDIGS (b); - SCM ans = scm_mkbig (i, sign); - SCM_BIGDIG *src = SCM_BDIGITS (b), *dst = SCM_BDIGITS (ans); - while (i--) - dst[i] = src[i]; - return ans; -} - - - -SCM -scm_long2big (n) - long n; -{ - scm_sizet i = 0; - SCM_BIGDIG *digits; - SCM ans = scm_mkbig (SCM_DIGSPERLONG, n < 0); - digits = SCM_BDIGITS (ans); - if (n < 0) - n = -n; - while (i < SCM_DIGSPERLONG) - { - digits[i++] = SCM_BIGLO (n); - n = SCM_BIGDN ((unsigned long) n); - } - return ans; -} - -#ifdef LONGLONGS - -SCM -scm_long_long2big (n) - long_long n; -{ - scm_sizet i; - SCM_BIGDIG *digits; - SCM ans; - int n_digits; - - { - long tn; - tn = (long) n; - if ((long long) tn == n) - return scm_long2big (tn); - } - - { - long_long tn; - - for (tn = n, n_digits = 0; - tn; - ++n_digits, tn = SCM_BIGDN ((ulong_long) tn)) - ; - } - - i = 0; - ans = scm_mkbig (n_digits, n < 0); - digits = SCM_BDIGITS (ans); - if (n < 0) - n = -n; - while (i < n_digits) - { - digits[i++] = SCM_BIGLO (n); - n = SCM_BIGDN ((ulong_long) n); - } - return ans; -} -#endif - - -SCM -scm_2ulong2big (np) - unsigned long *np; -{ - unsigned long n; - scm_sizet i; - SCM_BIGDIG *digits; - SCM ans; - - ans = scm_mkbig (2 * SCM_DIGSPERLONG, 0); - digits = SCM_BDIGITS (ans); - - n = np[0]; - for (i = 0; i < SCM_DIGSPERLONG; ++i) - { - digits[i] = SCM_BIGLO (n); - n = SCM_BIGDN ((unsigned long) n); - } - n = np[1]; - for (i = 0; i < SCM_DIGSPERLONG; ++i) - { - digits[i + SCM_DIGSPERLONG] = SCM_BIGLO (n); - n = SCM_BIGDN ((unsigned long) n); - } - return ans; -} - - - -SCM -scm_ulong2big (n) - unsigned long n; -{ - scm_sizet i = 0; - SCM_BIGDIG *digits; - SCM ans = scm_mkbig (SCM_DIGSPERLONG, 0); - digits = SCM_BDIGITS (ans); - while (i < SCM_DIGSPERLONG) - { - digits[i++] = SCM_BIGLO (n); - n = SCM_BIGDN (n); - } - return ans; -} - - - -int -scm_bigcomp (x, y) - SCM x; - SCM y; -{ - int xsign = SCM_BIGSIGN (x); - int ysign = SCM_BIGSIGN (y); - scm_sizet xlen, ylen; - - /* Look at the signs, first. */ - if (ysign < xsign) - return 1; - if (ysign > xsign) - return -1; - - /* They're the same sign, so see which one has more digits. Note - that, if they are negative, the longer number is the lesser. */ - ylen = SCM_NUMDIGS (y); - xlen = SCM_NUMDIGS (x); - if (ylen > xlen) - return (xsign) ? -1 : 1; - if (ylen < xlen) - return (xsign) ? 1 : -1; - - /* They have the same number of digits, so find the most significant - digit where they differ. */ - while (xlen) - { - --xlen; - if (SCM_BDIGITS (y)[xlen] != SCM_BDIGITS (x)[xlen]) - /* Make the discrimination based on the digit that differs. */ - return ((SCM_BDIGITS (y)[xlen] > SCM_BDIGITS (x)[xlen]) - ? (xsign ? -1 : 1) - : (xsign ? 1 : -1)); - } - - /* The numbers are identical. */ - return 0; -} - -#ifndef SCM_DIGSTOOBIG - - -long -scm_pseudolong (x) - long x; -{ - union - { - long l; - SCM_BIGDIG bd[SCM_DIGSPERLONG]; - } - p; - scm_sizet i = 0; - if (x < 0) - x = -x; - while (i < SCM_DIGSPERLONG) - { - p.bd[i++] = SCM_BIGLO (x); - x = SCM_BIGDN (x); - } - /* p.bd[0] = SCM_BIGLO(x); p.bd[1] = SCM_BIGDN(x); */ - return p.l; -} - -#else - - -void -scm_longdigs (x, digs) - long x; - SCM_BIGDIG digs[]; -{ - scm_sizet i = 0; - if (x < 0) - x = -x; - while (i < SCM_DIGSPERLONG) - { - digs[i++] = SCM_BIGLO (x); - x = SCM_BIGDN (x); - } -} -#endif - - - -SCM -scm_addbig (x, nx, xsgn, bigy, sgny) - SCM_BIGDIG *x; - scm_sizet nx; - int xsgn; - SCM bigy; - int sgny; -{ - /* Assumes nx <= SCM_NUMDIGS(bigy) */ - /* Assumes xsgn and sgny scm_equal either 0 or 0x0100 */ - long num = 0; - scm_sizet i = 0, ny = SCM_NUMDIGS (bigy); - SCM z = scm_copybig (bigy, SCM_BIGSIGN (bigy) ^ sgny); - SCM_BIGDIG *zds = SCM_BDIGITS (z); - if (xsgn ^ SCM_BIGSIGN (z)) - { - do - { - num += (long) zds[i] - x[i]; - if (num < 0) - { - zds[i] = num + SCM_BIGRAD; - num = -1; - } - else - { - zds[i] = SCM_BIGLO (num); - num = 0; - } - } - while (++i < nx); - if (num && nx == ny) - { - num = 1; - i = 0; - SCM_SETCAR (z, SCM_CAR (z) ^ 0x0100); - do - { - num += (SCM_BIGRAD - 1) - zds[i]; - zds[i++] = SCM_BIGLO (num); - num = SCM_BIGDN (num); - } - while (i < ny); - } - else - while (i < ny) - { - num += zds[i]; - if (num < 0) - { - zds[i++] = num + SCM_BIGRAD; - num = -1; - } - else - { - zds[i++] = SCM_BIGLO (num); - num = 0; - } - } - } - else - { - do - { - num += (long) zds[i] + x[i]; - zds[i++] = SCM_BIGLO (num); - num = SCM_BIGDN (num); - } - while (i < nx); - if (!num) - return z; - while (i < ny) - { - num += zds[i]; - zds[i++] = SCM_BIGLO (num); - num = SCM_BIGDN (num); - if (!num) - return z; - } - if (num) - { - z = scm_adjbig (z, ny + 1); - SCM_BDIGITS (z)[ny] = num; - return z; - } - } - return scm_normbig (z); -} - - -SCM -scm_mulbig (x, nx, y, ny, sgn) - SCM_BIGDIG *x; - scm_sizet nx; - SCM_BIGDIG *y; - scm_sizet ny; - int sgn; -{ - scm_sizet i = 0, j = nx + ny; - unsigned long n = 0; - SCM z = scm_mkbig (j, sgn); - SCM_BIGDIG *zds = SCM_BDIGITS (z); - while (j--) - zds[j] = 0; - do - { - j = 0; - if (x[i]) - { - do - { - n += zds[i + j] + ((unsigned long) x[i] * y[j]); - zds[i + j++] = SCM_BIGLO (n); - n = SCM_BIGDN (n); - } - while (j < ny); - if (n) - { - zds[i + j] = n; - n = 0; - } - } - } - while (++i < nx); - return scm_normbig (z); -} - - -/* Sun's compiler complains about the fact that this function has an - ANSI prototype in numbers.h, but a K&R declaration here, and the - two specify different promotions for the third argument. I'm going - to turn this into an ANSI declaration, and see if anyone complains - about it not being K&R. */ - -unsigned int -scm_divbigdig (SCM_BIGDIG * ds, - scm_sizet h, - SCM_BIGDIG div) -{ - register unsigned long t2 = 0; - while (h--) - { - t2 = SCM_BIGUP (t2) + ds[h]; - ds[h] = t2 / div; - t2 %= div; - } - return t2; -} - - - -SCM -scm_divbigint (x, z, sgn, mode) - SCM x; - long z; - int sgn; - int mode; -{ - if (z < 0) - z = -z; - if (z < SCM_BIGRAD) - { - register unsigned long t2 = 0; - register SCM_BIGDIG *ds = SCM_BDIGITS (x); - scm_sizet nd = SCM_NUMDIGS (x); - while (nd--) - t2 = (SCM_BIGUP (t2) + ds[nd]) % z; - if (mode && t2) - t2 = z - t2; - return SCM_MAKINUM (sgn ? -t2 : t2); - } - { -#ifndef SCM_DIGSTOOBIG - unsigned long t2 = scm_pseudolong (z); - return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - (SCM_BIGDIG *) & t2, SCM_DIGSPERLONG, - sgn, mode); -#else - SCM_BIGDIG t2[SCM_DIGSPERLONG]; - scm_longdigs (z, t2); - return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - t2, SCM_DIGSPERLONG, - sgn, mode); -#endif - } -} - - -SCM -scm_divbigbig (x, nx, y, ny, sgn, modes) - SCM_BIGDIG *x; - scm_sizet nx; - SCM_BIGDIG *y; - scm_sizet ny; - int sgn; - int modes; -{ - /* modes description - 0 remainder - 1 scm_modulo - 2 quotient - 3 quotient but returns 0 if division is not exact. */ - scm_sizet i = 0, j = 0; - long num = 0; - unsigned long t2 = 0; - SCM z, newy; - SCM_BIGDIG d = 0, qhat, *zds, *yds; - /* algorithm requires nx >= ny */ - if (nx < ny) - switch (modes) - { - case 0: /* remainder -- just return x */ - z = scm_mkbig (nx, sgn); - zds = SCM_BDIGITS (z); - do - { - zds[i] = x[i]; - } - while (++i < nx); - return z; - case 1: /* scm_modulo -- return y-x */ - z = scm_mkbig (ny, sgn); - zds = SCM_BDIGITS (z); - do - { - num += (long) y[i] - x[i]; - if (num < 0) - { - zds[i] = num + SCM_BIGRAD; - num = -1; - } - else - { - zds[i] = num; - num = 0; - } - } - while (++i < nx); - while (i < ny) - { - num += y[i]; - if (num < 0) - { - zds[i++] = num + SCM_BIGRAD; - num = -1; - } - else - { - zds[i++] = num; - num = 0; - } - } - goto doadj; - case 2: - return SCM_INUM0; /* quotient is zero */ - case 3: - return 0; /* the division is not exact */ - } - - z = scm_mkbig (nx == ny ? nx + 2 : nx + 1, sgn); - zds = SCM_BDIGITS (z); - if (nx == ny) - zds[nx + 1] = 0; - while (!y[ny - 1]) - ny--; /* in case y came in as a psuedolong */ - if (y[ny - 1] < (SCM_BIGRAD >> 1)) - { /* normalize operands */ - d = SCM_BIGRAD / (y[ny - 1] + 1); - newy = scm_mkbig (ny, 0); - yds = SCM_BDIGITS (newy); - while (j < ny) - { - t2 += (unsigned long) y[j] * d; - yds[j++] = SCM_BIGLO (t2); - t2 = SCM_BIGDN (t2); - } - y = yds; - j = 0; - t2 = 0; - while (j < nx) - { - t2 += (unsigned long) x[j] * d; - zds[j++] = SCM_BIGLO (t2); - t2 = SCM_BIGDN (t2); - } - zds[j] = t2; - } - else - { - zds[j = nx] = 0; - while (j--) - zds[j] = x[j]; - } - j = nx == ny ? nx + 1 : nx; /* dividend needs more digits than divisor */ - do - { /* loop over digits of quotient */ - if (zds[j] == y[ny - 1]) - qhat = SCM_BIGRAD - 1; - else - qhat = (SCM_BIGUP (zds[j]) + zds[j - 1]) / y[ny - 1]; - if (!qhat) - continue; - i = 0; - num = 0; - t2 = 0; - do - { /* multiply and subtract */ - t2 += (unsigned long) y[i] * qhat; - num += zds[j - ny + i] - SCM_BIGLO (t2); - if (num < 0) - { - zds[j - ny + i] = num + SCM_BIGRAD; - num = -1; - } - else - { - zds[j - ny + i] = num; - num = 0; - } - t2 = SCM_BIGDN (t2); - } - while (++i < ny); - num += zds[j - ny + i] - t2; /* borrow from high digit; don't update */ - while (num) - { /* "add back" required */ - i = 0; - num = 0; - qhat--; - do - { - num += (long) zds[j - ny + i] + y[i]; - zds[j - ny + i] = SCM_BIGLO (num); - num = SCM_BIGDN (num); - } - while (++i < ny); - num--; - } - if (modes & 2) - zds[j] = qhat; - } - while (--j >= ny); - switch (modes) - { - case 3: /* check that remainder==0 */ - for (j = ny; j && !zds[j - 1]; --j); - if (j) - return 0; - case 2: /* move quotient down in z */ - j = (nx == ny ? nx + 2 : nx + 1) - ny; - for (i = 0; i < j; i++) - zds[i] = zds[i + ny]; - ny = i; - break; - case 1: /* subtract for scm_modulo */ - i = 0; - num = 0; - j = 0; - do - { - num += y[i] - zds[i]; - j = j | zds[i]; - if (num < 0) - { - zds[i] = num + SCM_BIGRAD; - num = -1; - } - else - { - zds[i] = num; - num = 0; - } - } - while (++i < ny); - if (!j) - return SCM_INUM0; - case 0: /* just normalize remainder */ - if (d) - scm_divbigdig (zds, ny, d); - } - doadj: - for (j = ny; j && !zds[j - 1]; --j); - if (j * SCM_BITSPERDIG <= sizeof (SCM) * SCM_CHAR_BIT) - if (SCM_INUMP (z = scm_big2inum (z, j))) - return z; - return scm_adjbig (z, j); -} -#endif - - - - - -/*** NUMBERS -> STRINGS ***/ -#ifdef SCM_FLOATS -int scm_dblprec; -static const double fx[] = -{ 0.0, 5e-1, 5e-2, 5e-3, 5e-4, 5e-5, - 5e-6, 5e-7, 5e-8, 5e-9, 5e-10, - 5e-11, 5e-12, 5e-13, 5e-14, 5e-15, - 5e-16, 5e-17, 5e-18, 5e-19, 5e-20}; - - - - -static scm_sizet idbl2str SCM_P ((double f, char *a)); - -static scm_sizet -idbl2str (f, a) - double f; - char *a; -{ - int efmt, dpt, d, i, wp = scm_dblprec; - scm_sizet ch = 0; - int exp = 0; - - if (f == 0.0) - goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ - if (f < 0.0) - { - f = -f; - a[ch++] = '-'; - } - else if (f > 0.0); - else - goto funny; - if (IS_INF (f)) - { - if (ch == 0) - a[ch++] = '+'; - funny: - a[ch++] = '#'; - a[ch++] = '.'; - a[ch++] = '#'; - return ch; - } -#ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from - make-uniform-vector, from causing infinite loops. */ - while (f < 1.0) - { - f *= 10.0; - if (exp-- < DBL_MIN_10_EXP) - goto funny; - } - while (f > 10.0) - { - f *= 0.10; - if (exp++ > DBL_MAX_10_EXP) - goto funny; - } -#else - while (f < 1.0) - { - f *= 10.0; - exp--; - } - while (f > 10.0) - { - f /= 10.0; - exp++; - } -#endif - if (f + fx[wp] >= 10.0) - { - f = 1.0; - exp++; - } - zero: -#ifdef ENGNOT - dpt = (exp + 9999) % 3; - exp -= dpt++; - efmt = 1; -#else - efmt = (exp < -3) || (exp > wp + 2); - if (!efmt) - { - if (exp < 0) - { - a[ch++] = '0'; - a[ch++] = '.'; - dpt = exp; - while (++dpt) - a[ch++] = '0'; - } - else - dpt = exp + 1; - } - else - dpt = 1; -#endif - - do - { - d = f; - f -= d; - a[ch++] = d + '0'; - if (f < fx[wp]) - break; - if (f + fx[wp] >= 1.0) - { - a[ch - 1]++; - break; - } - f *= 10.0; - if (!(--dpt)) - a[ch++] = '.'; - } - while (wp--); - - if (dpt > 0) - { -#ifndef ENGNOT - if ((dpt > 4) && (exp > 6)) - { - d = (a[0] == '-' ? 2 : 1); - for (i = ch++; i > d; i--) - a[i] = a[i - 1]; - a[d] = '.'; - efmt = 1; - } - else -#endif - { - while (--dpt) - a[ch++] = '0'; - a[ch++] = '.'; - } - } - if (a[ch - 1] == '.') - a[ch++] = '0'; /* trailing zero */ - if (efmt && exp) - { - a[ch++] = 'e'; - if (exp < 0) - { - exp = -exp; - a[ch++] = '-'; - } - for (i = 10; i <= exp; i *= 10); - for (i /= 10; i; i /= 10) - { - a[ch++] = exp / i + '0'; - exp %= i; - } - } - return ch; -} - - -static scm_sizet iflo2str SCM_P ((SCM flt, char *str)); - -static scm_sizet -iflo2str (flt, str) - SCM flt; - char *str; -{ - scm_sizet i; -#ifdef SCM_SINGLES - if (SCM_SINGP (flt)) - i = idbl2str (SCM_FLO (flt), str); - else -#endif - i = idbl2str (SCM_REAL (flt), str); - if (SCM_CPLXP (flt)) - { - if (0 <= SCM_IMAG (flt)) /* jeh */ - str[i++] = '+'; /* jeh */ - i += idbl2str (SCM_IMAG (flt), &str[i]); - str[i++] = 'i'; - } - return i; -} -#endif /* SCM_FLOATS */ - - -scm_sizet -scm_iint2str (num, rad, p) - long num; - int rad; - char *p; -{ - scm_sizet j; - register int i = 1, d; - register long n = num; - if (n < 0) - { - n = -n; - i++; - } - for (n /= rad; n > 0; n /= rad) - i++; - j = i; - n = num; - if (n < 0) - { - n = -n; - *p++ = '-'; - i--; - } - while (i--) - { - d = n % rad; - n /= rad; - p[i] = d + ((d < 10) ? '0' : 'a' - 10); - } - return j; -} - - -#ifdef SCM_BIGDIG - -static SCM big2str SCM_P ((SCM b, register unsigned int radix)); - -static SCM -big2str (b, radix) - SCM b; - register unsigned int radix; -{ - SCM t = scm_copybig (b, 0); /* sign of temp doesn't matter */ - register SCM_BIGDIG *ds = SCM_BDIGITS (t); - scm_sizet i = SCM_NUMDIGS (t); - scm_sizet j = radix == 16 ? (SCM_BITSPERDIG * i) / 4 + 2 - : radix >= 10 ? (SCM_BITSPERDIG * i * 241L) / 800 + 2 - : (SCM_BITSPERDIG * i) + 2; - scm_sizet k = 0; - scm_sizet radct = 0; - scm_sizet ch; /* jeh */ - SCM_BIGDIG radpow = 1, radmod = 0; - SCM ss = scm_makstr ((long) j, 0); - char *s = SCM_CHARS (ss), c; - while ((long) radpow * radix < SCM_BIGRAD) - { - radpow *= radix; - radct++; - } - s[0] = scm_tc16_bigneg == SCM_TYP16 (b) ? '-' : '+'; - while ((i || radmod) && j) - { - if (k == 0) - { - radmod = (SCM_BIGDIG) scm_divbigdig (ds, i, radpow); - k = radct; - if (!ds[i - 1]) - i--; - } - c = radmod % radix; - radmod /= radix; - k--; - s[--j] = c < 10 ? c + '0' : c + 'a' - 10; - } - ch = s[0] == '-' ? 1 : 0; /* jeh */ - if (ch < j) - { /* jeh */ - for (i = j; j < SCM_LENGTH (ss); j++) - s[ch + j - i] = s[j]; /* jeh */ - scm_vector_set_length_x (ss, /* jeh */ - (SCM) SCM_MAKINUM (ch + SCM_LENGTH (ss) - i)); - } - - return scm_return_first (ss, t); -} -#endif - - -SCM_PROC (s_number_to_string, "number->string", 1, 1, 0, scm_number_to_string); - -SCM -scm_number_to_string (x, radix) - SCM x; - SCM radix; -{ - if (SCM_UNBNDP (radix)) - radix = SCM_MAKINUM (10L); - else - { - SCM_ASSERT (SCM_INUMP (radix), radix, SCM_ARG2, s_number_to_string); - SCM_ASSERT (SCM_INUM (radix) >= 2, radix, SCM_OUTOFRANGE, - s_number_to_string); - } -#ifdef SCM_FLOATS - if (SCM_NINUMP (x)) - { - char num_buf[SCM_FLOBUFLEN]; -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (x), badx); - if (SCM_BIGP (x)) - return big2str (x, (unsigned int) SCM_INUM (radix)); -#ifndef SCM_RECKLESS - if (!(SCM_INEXP (x))) - { - badx: - scm_wta (x, (char *) SCM_ARG1, s_number_to_string); - } -#endif -#else - SCM_ASSERT (SCM_NIMP (x) && SCM_INEXP (x), - x, SCM_ARG1, s_number_to_string); -#endif - return scm_makfromstr (num_buf, iflo2str (x, num_buf), 0); - } -#else -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - SCM_ASSERT (SCM_NIMP (x) && SCM_BIGP (x), - x, SCM_ARG1, s_number_to_string); - return big2str (x, (unsigned int) SCM_INUM (radix)); - } -#else - SCM_ASSERT (SCM_INUMP (x), x, SCM_ARG1, s_number_to_string); -#endif -#endif - { - char num_buf[SCM_INTBUFLEN]; - return scm_makfromstr (num_buf, - scm_iint2str (SCM_INUM (x), - (int) SCM_INUM (radix), - num_buf), - 0); - } -} - - -/* These print routines are stubbed here so that scm_repl.c doesn't need - SCM_FLOATS or SCM_BIGDIGs conditionals */ - -int -scm_floprint (sexp, port, pstate) - SCM sexp; - SCM port; - scm_print_state *pstate; -{ -#ifdef SCM_FLOATS - char num_buf[SCM_FLOBUFLEN]; - scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port); -#else - scm_ipruk ("float", sexp, port); -#endif - return !0; -} - - - -int -scm_bigprint (exp, port, pstate) - SCM exp; - SCM port; - scm_print_state *pstate; -{ -#ifdef SCM_BIGDIG - exp = big2str (exp, (unsigned int) 10); - scm_lfwrite (SCM_CHARS (exp), (scm_sizet) SCM_LENGTH (exp), port); -#else - scm_ipruk ("bignum", exp, port); -#endif - return !0; -} -/*** END nums->strs ***/ - -/*** STRINGS -> NUMBERS ***/ - -static SCM scm_small_istr2int SCM_P ((char *str, long len, long radix)); - -static SCM -scm_small_istr2int (str, len, radix) - char *str; - long len; - long radix; -{ - register long n = 0, ln; - register int c; - register int i = 0; - int lead_neg = 0; - if (0 >= len) - return SCM_BOOL_F; /* zero scm_length */ - switch (*str) - { /* leading sign */ - case '-': - lead_neg = 1; - case '+': - if (++i == len) - return SCM_BOOL_F; /* bad if lone `+' or `-' */ - } - - do - { - switch (c = str[i++]) - { - case DIGITS: - c = c - '0'; - goto accumulate; - case 'A': - case 'B': - case 'C': - case 'D': - case 'E': - case 'F': - c = c - 'A' + 10; - goto accumulate; - case 'a': - case 'b': - case 'c': - case 'd': - case 'e': - case 'f': - c = c - 'a' + 10; - accumulate: - if (c >= radix) - return SCM_BOOL_F; /* bad digit for radix */ - ln = n; - n = n * radix - c; - /* Negation is a workaround for HP700 cc bug */ - if (n > ln || (-n > -SCM_MOST_NEGATIVE_FIXNUM)) - goto ovfl; - break; - default: - return SCM_BOOL_F; /* not a digit */ - } - } - while (i < len); - if (!lead_neg) - if ((n = -n) > SCM_MOST_POSITIVE_FIXNUM) - goto ovfl; - return SCM_MAKINUM (n); - ovfl: /* overflow scheme integer */ - return SCM_BOOL_F; -} - - - -SCM -scm_istr2int (str, len, radix) - char *str; - long len; - long radix; -{ - scm_sizet j; - register scm_sizet k, blen = 1; - scm_sizet i = 0; - int c; - SCM res; - register SCM_BIGDIG *ds; - register unsigned long t2; - - if (0 >= len) - return SCM_BOOL_F; /* zero scm_length */ - - /* Short numbers we parse directly into an int, to avoid the overhead - of creating a bignum. */ - if (len < 6) - return scm_small_istr2int (str, len, radix); - - if (16 == radix) - j = 1 + (4 * len * sizeof (char)) / (SCM_BITSPERDIG); - else if (10 <= radix) - j = 1 + (84 * len * sizeof (char)) / (SCM_BITSPERDIG * 25); - else - j = 1 + (len * sizeof (char)) / (SCM_BITSPERDIG); - switch (str[0]) - { /* leading sign */ - case '-': - case '+': - if (++i == (unsigned) len) - return SCM_BOOL_F; /* bad if lone `+' or `-' */ - } - res = scm_mkbig (j, '-' == str[0]); - ds = SCM_BDIGITS (res); - for (k = j; k--;) - ds[k] = 0; - do - { - switch (c = str[i++]) - { - case DIGITS: - c = c - '0'; - goto accumulate; - case 'A': - case 'B': - case 'C': - case 'D': - case 'E': - case 'F': - c = c - 'A' + 10; - goto accumulate; - case 'a': - case 'b': - case 'c': - case 'd': - case 'e': - case 'f': - c = c - 'a' + 10; - accumulate: - if (c >= radix) - return SCM_BOOL_F; /* bad digit for radix */ - k = 0; - t2 = c; - moretodo: - while (k < blen) - { -/* printf ("k = %d, blen = %d, t2 = %ld, ds[k] = %d\n", k, blen, t2, ds[k]); */ - t2 += ds[k] * radix; - ds[k++] = SCM_BIGLO (t2); - t2 = SCM_BIGDN (t2); - } - if (blen > j) - scm_num_overflow ("bignum"); - if (t2) - { - blen++; - goto moretodo; - } - break; - default: - return SCM_BOOL_F; /* not a digit */ - } - } - while (i < (unsigned) len); - if (blen * SCM_BITSPERDIG / SCM_CHAR_BIT <= sizeof (SCM)) - if (SCM_INUMP (res = scm_big2inum (res, blen))) - return res; - if (j == blen) - return res; - return scm_adjbig (res, blen); -} - -#ifdef SCM_FLOATS - -SCM -scm_istr2flo (str, len, radix) - char *str; - long len; - long radix; -{ - register int c, i = 0; - double lead_sgn; - double res = 0.0, tmp = 0.0; - int flg = 0; - int point = 0; - SCM second; - - if (i >= len) - return SCM_BOOL_F; /* zero scm_length */ - - switch (*str) - { /* leading sign */ - case '-': - lead_sgn = -1.0; - i++; - break; - case '+': - lead_sgn = 1.0; - i++; - break; - default: - lead_sgn = 0.0; - } - if (i == len) - return SCM_BOOL_F; /* bad if lone `+' or `-' */ - - if (str[i] == 'i' || str[i] == 'I') - { /* handle `+i' and `-i' */ - if (lead_sgn == 0.0) - return SCM_BOOL_F; /* must have leading sign */ - if (++i < len) - return SCM_BOOL_F; /* `i' not last character */ - return scm_makdbl (0.0, lead_sgn); - } - do - { /* check initial digits */ - switch (c = str[i]) - { - case DIGITS: - c = c - '0'; - goto accum1; - case 'D': - case 'E': - case 'F': - if (radix == 10) - goto out1; /* must be exponent */ - case 'A': - case 'B': - case 'C': - c = c - 'A' + 10; - goto accum1; - case 'd': - case 'e': - case 'f': - if (radix == 10) - goto out1; - case 'a': - case 'b': - case 'c': - c = c - 'a' + 10; - accum1: - if (c >= radix) - return SCM_BOOL_F; /* bad digit for radix */ - res = res * radix + c; - flg = 1; /* res is valid */ - break; - default: - goto out1; - } - } - while (++i < len); - out1: - - /* if true, then we did see a digit above, and res is valid */ - if (i == len) - goto done; - - /* By here, must have seen a digit, - or must have next char be a `.' with radix==10 */ - if (!flg) - if (!(str[i] == '.' && radix == 10)) - return SCM_BOOL_F; - - while (str[i] == '#') - { /* optional sharps */ - res *= radix; - if (++i == len) - goto done; - } - - if (str[i] == '/') - { - while (++i < len) - { - switch (c = str[i]) - { - case DIGITS: - c = c - '0'; - goto accum2; - case 'A': - case 'B': - case 'C': - case 'D': - case 'E': - case 'F': - c = c - 'A' + 10; - goto accum2; - case 'a': - case 'b': - case 'c': - case 'd': - case 'e': - case 'f': - c = c - 'a' + 10; - accum2: - if (c >= radix) - return SCM_BOOL_F; - tmp = tmp * radix + c; - break; - default: - goto out2; - } - } - out2: - if (tmp == 0.0) - return SCM_BOOL_F; /* `slash zero' not allowed */ - if (i < len) - while (str[i] == '#') - { /* optional sharps */ - tmp *= radix; - if (++i == len) - break; - } - res /= tmp; - goto done; - } - - if (str[i] == '.') - { /* decimal point notation */ - if (radix != 10) - return SCM_BOOL_F; /* must be radix 10 */ - while (++i < len) - { - switch (c = str[i]) - { - case DIGITS: - point--; - res = res * 10.0 + c - '0'; - flg = 1; - break; - default: - goto out3; - } - } - out3: - if (!flg) - return SCM_BOOL_F; /* no digits before or after decimal point */ - if (i == len) - goto adjust; - while (str[i] == '#') - { /* ignore remaining sharps */ - if (++i == len) - goto adjust; - } - } - - switch (str[i]) - { /* exponent */ - case 'd': - case 'D': - case 'e': - case 'E': - case 'f': - case 'F': - case 'l': - case 'L': - case 's': - case 'S': - { - int expsgn = 1, expon = 0; - if (radix != 10) - return SCM_BOOL_F; /* only in radix 10 */ - if (++i == len) - return SCM_BOOL_F; /* bad exponent */ - switch (str[i]) - { - case '-': - expsgn = (-1); - case '+': - if (++i == len) - return SCM_BOOL_F; /* bad exponent */ - } - if (str[i] < '0' || str[i] > '9') - return SCM_BOOL_F; /* bad exponent */ - do - { - switch (c = str[i]) - { - case DIGITS: - expon = expon * 10 + c - '0'; - if (expon > MAXEXP) - return SCM_BOOL_F; /* exponent too large */ - break; - default: - goto out4; - } - } - while (++i < len); - out4: - point += expsgn * expon; - } - } - - adjust: - if (point >= 0) - while (point--) - res *= 10.0; - else -#ifdef _UNICOS - while (point++) - res *= 0.1; -#else - while (point++) - res /= 10.0; -#endif - - done: - /* at this point, we have a legitimate floating point result */ - if (lead_sgn == -1.0) - res = -res; - if (i == len) - return scm_makdbl (res, 0.0); - - if (str[i] == 'i' || str[i] == 'I') - { /* pure imaginary number */ - if (lead_sgn == 0.0) - return SCM_BOOL_F; /* must have leading sign */ - if (++i < len) - return SCM_BOOL_F; /* `i' not last character */ - return scm_makdbl (0.0, res); - } - - switch (str[i++]) - { - case '-': - lead_sgn = -1.0; - break; - case '+': - lead_sgn = 1.0; - break; - case '@': - { /* polar input for complex number */ - /* get a `real' for scm_angle */ - second = scm_istr2flo (&str[i], (long) (len - i), radix); - if (!(SCM_NIMP (second) && SCM_INEXP (second))) - return SCM_BOOL_F; /* not `real' */ - if (SCM_CPLXP (second)) - return SCM_BOOL_F; /* not `real' */ - tmp = SCM_REALPART (second); - return scm_makdbl (res * cos (tmp), res * sin (tmp)); - } - default: - return SCM_BOOL_F; - } - - /* at this point, last char must be `i' */ - if (str[len - 1] != 'i' && str[len - 1] != 'I') - return SCM_BOOL_F; - /* handles `x+i' and `x-i' */ - if (i == (len - 1)) - return scm_makdbl (res, lead_sgn); - /* get a `ureal' for complex part */ - second = scm_istr2flo (&str[i], (long) ((len - i) - 1), radix); - if (! (SCM_NIMP (second) && SCM_INEXP (second))) - return SCM_BOOL_F; /* not `ureal' */ - if (SCM_CPLXP (second)) - return SCM_BOOL_F; /* not `ureal' */ - tmp = SCM_REALPART (second); - if (tmp < 0.0) - return SCM_BOOL_F; /* not `ureal' */ - return scm_makdbl (res, (lead_sgn * tmp)); -} -#endif /* SCM_FLOATS */ - - - -SCM -scm_istring2number (str, len, radix) - char *str; - long len; - long radix; -{ - int i = 0; - char ex = 0; - char ex_p = 0, rx_p = 0; /* Only allow 1 exactness and 1 radix prefix */ - SCM res; - if (len == 1) - if (*str == '+' || *str == '-') /* Catches lone `+' and `-' for speed */ - return SCM_BOOL_F; - - while ((len - i) >= 2 && str[i] == '#' && ++i) - switch (str[i++]) - { - case 'b': - case 'B': - if (rx_p++) - return SCM_BOOL_F; - radix = 2; - break; - case 'o': - case 'O': - if (rx_p++) - return SCM_BOOL_F; - radix = 8; - break; - case 'd': - case 'D': - if (rx_p++) - return SCM_BOOL_F; - radix = 10; - break; - case 'x': - case 'X': - if (rx_p++) - return SCM_BOOL_F; - radix = 16; - break; - case 'i': - case 'I': - if (ex_p++) - return SCM_BOOL_F; - ex = 2; - break; - case 'e': - case 'E': - if (ex_p++) - return SCM_BOOL_F; - ex = 1; - break; - default: - return SCM_BOOL_F; - } - - switch (ex) - { - case 1: - return scm_istr2int (&str[i], len - i, radix); - case 0: - res = scm_istr2int (&str[i], len - i, radix); - if (SCM_NFALSEP (res)) - return res; -#ifdef SCM_FLOATS - case 2: - return scm_istr2flo (&str[i], len - i, radix); -#endif - } - return SCM_BOOL_F; -} - - -SCM_PROC (s_string_to_number, "string->number", 1, 1, 0, scm_string_to_number); - -SCM -scm_string_to_number (str, radix) - SCM str; - SCM radix; -{ - SCM answer; - if (SCM_UNBNDP (radix)) - radix = SCM_MAKINUM (10L); - else - { - SCM_ASSERT (SCM_INUMP (radix), radix, SCM_ARG2, s_string_to_number); - SCM_ASSERT (SCM_INUM (radix) >= 2, radix, SCM_OUTOFRANGE, - s_number_to_string); - } - SCM_ASSERT (SCM_NIMP (str) && SCM_ROSTRINGP (str), - str, SCM_ARG1, s_string_to_number); - answer = scm_istring2number (SCM_ROCHARS (str), - SCM_ROLENGTH (str), - SCM_INUM (radix)); - return scm_return_first (answer, str); -} -/*** END strs->nums ***/ - -#ifdef SCM_FLOATS - -SCM -scm_makdbl (x, y) - double x; - double y; -{ - SCM z; - if ((y == 0.0) && (x == 0.0)) - return scm_flo0; - SCM_DEFER_INTS; - if (y == 0.0) - { -#ifdef SCM_SINGLES - float fx = x; -#ifndef SCM_SINGLESONLY - if ((-FLTMAX < x) && (x < FLTMAX) && (fx == x)) -#endif - { - SCM_NEWSMOB(z,scm_tc_flo,NULL); - SCM_FLO (z) = x; - SCM_ALLOW_INTS; - return z; - } -#endif /* def SCM_SINGLES */ - SCM_NEWSMOB(z,scm_tc_dblr,scm_must_malloc (1L * sizeof (double), "real")); - } - else - { - SCM_NEWSMOB(z,scm_tc_dblc,scm_must_malloc (2L * sizeof (double), "comkplex")); - SCM_IMAG (z) = y; - } - SCM_REAL (z) = x; - SCM_ALLOW_INTS; - return z; -} -#endif - - - -SCM -scm_bigequal (x, y) - SCM x; - SCM y; -{ -#ifdef SCM_BIGDIG - if (0 == scm_bigcomp (x, y)) - return SCM_BOOL_T; -#endif - return SCM_BOOL_F; -} - - - -SCM -scm_floequal (x, y) - SCM x; - SCM y; -{ -#ifdef SCM_FLOATS - if (SCM_REALPART (x) != SCM_REALPART (y)) - return SCM_BOOL_F; - if (!(SCM_CPLXP (x) && (SCM_IMAG (x) != SCM_IMAG (y)))) - return SCM_BOOL_T; -#endif - return SCM_BOOL_F; -} - - - - -SCM_PROC (s_number_p, "number?", 1, 0, 0, scm_number_p); -SCM_PROC (s_complex_p, "complex?", 1, 0, 0, scm_number_p); - -SCM -scm_number_p (x) - SCM x; -{ - if (SCM_INUMP (x)) - return SCM_BOOL_T; -#ifdef SCM_FLOATS - if (SCM_NIMP (x) && SCM_NUMP (x)) - return SCM_BOOL_T; -#else -#ifdef SCM_BIGDIG - if (SCM_NIMP (x) && SCM_NUMP (x)) - return SCM_BOOL_T; -#endif -#endif - return SCM_BOOL_F; -} - - - -#ifdef SCM_FLOATS -SCM_PROC (s_real_p, "real?", 1, 0, 0, scm_real_p); -SCM_PROC (s_rational_p, "rational?", 1, 0, 0, scm_real_p); - -SCM -scm_real_p (x) - SCM x; -{ - if (SCM_INUMP (x)) - return SCM_BOOL_T; - if (SCM_IMP (x)) - return SCM_BOOL_F; - if (SCM_REALP (x)) - return SCM_BOOL_T; -#ifdef SCM_BIGDIG - if (SCM_BIGP (x)) - return SCM_BOOL_T; -#endif - return SCM_BOOL_F; -} - - - -SCM_PROC (s_int_p, "integer?", 1, 0, 0, scm_integer_p); - -SCM -scm_integer_p (x) - SCM x; -{ - double r; - if (SCM_INUMP (x)) - return SCM_BOOL_T; - if (SCM_IMP (x)) - return SCM_BOOL_F; -#ifdef SCM_BIGDIG - if (SCM_BIGP (x)) - return SCM_BOOL_T; -#endif - if (!SCM_INEXP (x)) - return SCM_BOOL_F; - if (SCM_CPLXP (x)) - return SCM_BOOL_F; - r = SCM_REALPART (x); - if (r == floor (r)) - return SCM_BOOL_T; - return SCM_BOOL_F; -} - - - -#endif /* SCM_FLOATS */ - -SCM_PROC (s_inexact_p, "inexact?", 1, 0, 0, scm_inexact_p); - -SCM -scm_inexact_p (x) - SCM x; -{ -#ifdef SCM_FLOATS - if (SCM_NIMP (x) && SCM_INEXP (x)) - return SCM_BOOL_T; -#endif - return SCM_BOOL_F; -} - - - - -SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p); - -SCM -scm_num_eq_p (x, y) - SCM x; - SCM y; -{ -#ifdef SCM_FLOATS - SCM t; - if (SCM_NINUMP (x)) - { -#ifdef SCM_BIGDIG - if (!(SCM_NIMP (x))) - { - badx: - SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p); - } - if (SCM_BIGP (x)) - { - if (SCM_INUMP (y)) - return SCM_BOOL_F; - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - return (0 == scm_bigcomp (x, y)) ? SCM_BOOL_T : SCM_BOOL_F; - SCM_ASRTGO (SCM_INEXP (y), bady); - bigreal: - return ((SCM_REALP (y) && (scm_big2dbl (x) == SCM_REALPART (y))) - ? SCM_BOOL_T - : SCM_BOOL_F); - } - SCM_ASRTGO (SCM_INEXP (x), badx); -#else - SCM_GASSERT2 (SCM_NIMP (x) && SCM_INEXP (x), - g_eq_p, x, y, SCM_ARG1, s_eq_p); -#endif - if (SCM_INUMP (y)) - { - t = x; - x = y; - y = t; - goto realint; - } -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - { - t = x; - x = y; - y = t; - goto bigreal; - } - SCM_ASRTGO (SCM_INEXP (y), bady); -#else - SCM_ASRTGO (SCM_NIMP (y) && SCM_INEXP (y), bady); -#endif - if (SCM_REALPART (x) != SCM_REALPART (y)) - return SCM_BOOL_F; - if (SCM_CPLXP (x)) - return ((SCM_CPLXP (y) && (SCM_IMAG (x) == SCM_IMAG (y))) - ? SCM_BOOL_T - : SCM_BOOL_F); - return SCM_CPLXP (y) ? SCM_BOOL_F : SCM_BOOL_T; - } - if (SCM_NINUMP (y)) - { -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - return SCM_BOOL_F; - if (!(SCM_INEXP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); - } -#else - if (!(SCM_NIMP (y) && SCM_INEXP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); - } -#endif - realint: - return ((SCM_REALP (y) && (((double) SCM_INUM (x)) == SCM_REALPART (y))) - ? SCM_BOOL_T - : SCM_BOOL_F); - } -#else -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - SCM_GASSERT2 (SCM_NIMP (x) && SCM_BIGP (x), - g_eq_p, x, y, SCM_ARG1, s_eq_p); - if (SCM_INUMP (y)) - return SCM_BOOL_F; - SCM_ASRTGO (SCM_NIMP (y) && SCM_BIGP (y), bady); - return (0 == scm_bigcomp (x, y)) ? SCM_BOOL_T : SCM_BOOL_F; - } - if (SCM_NINUMP (y)) - { - if (!(SCM_NIMP (y) && SCM_BIGP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); - } - return SCM_BOOL_F; - } -#else - SCM_GASSERT2 (SCM_INUMP (x), g_eq_p, x, y, SCM_ARG1, s_eq_p); - SCM_GASSERT2 (SCM_INUMP (y), g_eq_p, x, y, SCM_ARGn, s_eq_p); -#endif -#endif - return ((long) x == (long) y) ? SCM_BOOL_T : SCM_BOOL_F; -} - - - -SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p); - -SCM -scm_less_p (x, y) - SCM x; - SCM y; -{ -#ifdef SCM_FLOATS - if (SCM_NINUMP (x)) - { -#ifdef SCM_BIGDIG - if (!(SCM_NIMP (x))) - { - badx: - SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p); - } - if (SCM_BIGP (x)) - { - if (SCM_INUMP (y)) - return SCM_BIGSIGN (x) ? SCM_BOOL_T : SCM_BOOL_F; - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - return (1 == scm_bigcomp (x, y)) ? SCM_BOOL_T : SCM_BOOL_F; - SCM_ASRTGO (SCM_REALP (y), bady); - return ((scm_big2dbl (x) < SCM_REALPART (y)) - ? SCM_BOOL_T - : SCM_BOOL_F); - } - SCM_ASRTGO (SCM_REALP (x), badx); -#else - SCM_GASSERT2 (SCM_NIMP (x) && SCM_REALP (x), - g_less_p, x, y, SCM_ARG1, s_less_p); -#endif - if (SCM_INUMP (y)) - return ((SCM_REALPART (x) < ((double) SCM_INUM (y))) - ? SCM_BOOL_T - : SCM_BOOL_F); -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - return (SCM_REALPART (x) < scm_big2dbl (y)) ? SCM_BOOL_T : SCM_BOOL_F; - SCM_ASRTGO (SCM_REALP (y), bady); -#else - SCM_ASRTGO (SCM_NIMP (y) && SCM_REALP (y), bady); -#endif - return (SCM_REALPART (x) < SCM_REALPART (y)) ? SCM_BOOL_T : SCM_BOOL_F; - } - if (SCM_NINUMP (y)) - { -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - return SCM_BIGSIGN (y) ? SCM_BOOL_F : SCM_BOOL_T; - if (!(SCM_REALP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); - } -#else - if (!(SCM_NIMP (y) && SCM_REALP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); - } -#endif - return ((((double) SCM_INUM (x)) < SCM_REALPART (y)) - ? SCM_BOOL_T - : SCM_BOOL_F); - } -#else -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - SCM_GASSERT2 (SCM_NIMP (x) && SCM_BIGP (x), - g_less_p, x, y, SCM_ARG1, s_less_p); - if (SCM_INUMP (y)) - return SCM_BIGSIGN (x) ? SCM_BOOL_T : SCM_BOOL_F; - SCM_ASRTGO (SCM_NIMP (y) && SCM_BIGP (y), bady); - return (1 == scm_bigcomp (x, y)) ? SCM_BOOL_T : SCM_BOOL_F; - } - if (SCM_NINUMP (y)) - { - if (!(SCM_NIMP (y) && SCM_BIGP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); - } - return SCM_BIGSIGN (y) ? SCM_BOOL_F : SCM_BOOL_T; - } -#else - SCM_GASSERT2 (SCM_INUMP (x), g_less_p, x, y, SCM_ARG1, s_less_p); - SCM_GASSERT2 (SCM_INUMP (y), g_less_p, x, y, SCM_ARGn, s_less_p); -#endif -#endif - return ((long) x < (long) y) ? SCM_BOOL_T : SCM_BOOL_F; -} - - -SCM_PROC1 (s_gr_p, ">", scm_tc7_rpsubr, scm_gr_p); - -SCM -scm_gr_p (x, y) - SCM x; - SCM y; -{ - return scm_less_p (y, x); -} - - - -SCM_PROC1 (s_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p); - -SCM -scm_leq_p (x, y) - SCM x; - SCM y; -{ - return SCM_BOOL_NOT (scm_less_p (y, x)); -} - - - -SCM_PROC1 (s_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p); - -SCM -scm_geq_p (x, y) - SCM x; - SCM y; -{ - return SCM_BOOL_NOT (scm_less_p (x, y)); -} - - - -SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); - -SCM -scm_zero_p (z) - SCM z; -{ -#ifdef SCM_FLOATS - if (SCM_NINUMP (z)) - { -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (z), badz); - if (SCM_BIGP (z)) - return SCM_BOOL_F; - if (!(SCM_INEXP (z))) - { - badz: - SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); - } -#else - SCM_GASSERT1 (SCM_NIMP (z) && SCM_INEXP (z), - g_zero_p, z, SCM_ARG1, s_zero_p); -#endif - return (z == scm_flo0) ? SCM_BOOL_T : SCM_BOOL_F; - } -#else -#ifdef SCM_BIGDIG - if (SCM_NINUMP (z)) - { - SCM_GASSERT1 (SCM_NIMP (z) && SCM_BIGP (z), - g_zero_p, z, SCM_ARG1, s_zero_p); - return SCM_BOOL_F; - } -#else - SCM_GASSERT1 (SCM_INUMP (z), g_zero_p, z, SCM_ARG1, s_zero_p); -#endif -#endif - return (z == SCM_INUM0) ? SCM_BOOL_T : SCM_BOOL_F; -} - - - -SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); - -SCM -scm_positive_p (x) - SCM x; -{ -#ifdef SCM_FLOATS - if (SCM_NINUMP (x)) - { -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (x), badx); - if (SCM_BIGP (x)) - return SCM_TYP16 (x) == scm_tc16_bigpos ? SCM_BOOL_T : SCM_BOOL_F; - if (!(SCM_REALP (x))) - { - badx: - SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); - } -#else - SCM_GASSERT1 (SCM_NIMP (x) && SCM_REALP (x), - g_positive_p, x, SCM_ARG1, s_positive_p); -#endif - return (SCM_REALPART (x) > 0.0) ? SCM_BOOL_T : SCM_BOOL_F; - } -#else -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - SCM_GASSERT1 (SCM_NIMP (x) && SCM_BIGP (x), - g_positive_p, x, SCM_ARG1, s_positive_p); - return SCM_TYP16 (x) == scm_tc16_bigpos ? SCM_BOOL_T : SCM_BOOL_F; - } -#else - SCM_GASSERT1 (SCM_INUMP (x), g_positive_p, x, SCM_ARG1, s_positive_p); -#endif -#endif - return (x > SCM_INUM0) ? SCM_BOOL_T : SCM_BOOL_F; -} - - - -SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); - -SCM -scm_negative_p (x) - SCM x; -{ -#ifdef SCM_FLOATS - if (SCM_NINUMP (x)) - { -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (x), badx); - if (SCM_BIGP (x)) - return SCM_TYP16 (x) == scm_tc16_bigpos ? SCM_BOOL_F : SCM_BOOL_T; - if (!(SCM_REALP (x))) - { - badx: - SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); - } -#else - SCM_GASSERT1 (SCM_NIMP (x) && SCM_REALP (x), - g_negative_p, x, SCM_ARG1, s_negative_p); -#endif - return (SCM_REALPART (x) < 0.0) ? SCM_BOOL_T : SCM_BOOL_F; - } -#else -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - SCM_GASSERT1 (SCM_NIMP (x) && SCM_BIGP (x), - g_negative_p, x, SCM_ARG1, s_negative_p); - return (SCM_TYP16 (x) == scm_tc16_bigneg) ? SCM_BOOL_T : SCM_BOOL_F; - } -#else - SCM_GASSERT1 (SCM_INUMP (x), g_negative_p, x, SCM_ARG1, s_negative_p); -#endif -#endif - return (x < SCM_INUM0) ? SCM_BOOL_T : SCM_BOOL_F; -} - - -SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max); - -SCM -scm_max (x, y) - SCM x; - SCM y; -{ -#ifdef SCM_FLOATS - double z; -#endif - if (SCM_UNBNDP (y)) - { - SCM_GASSERT0 (!SCM_UNBNDP (x), - g_max, scm_makfrom0str (s_max), SCM_WNA, 0); - SCM_GASSERT1 (SCM_NUMBERP (x), g_max, x, SCM_ARG1, s_max); - return x; - } -#ifdef SCM_FLOATS - if (SCM_NINUMP (x)) - { -#ifdef SCM_BIGDIG - if (!SCM_NIMP (x)) - { - badx2: - SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); - } - if (SCM_BIGP (x)) - { - if (SCM_INUMP (y)) - return SCM_BIGSIGN (x) ? y : x; - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - return (1 == scm_bigcomp (x, y)) ? y : x; - SCM_ASRTGO (SCM_REALP (y), bady); - z = scm_big2dbl (x); - return (z < SCM_REALPART (y)) ? y : scm_makdbl (z, 0.0); - } - SCM_ASRTGO (SCM_REALP (x), badx2); -#else - SCM_GASSERT2 (SCM_NIMP (x) && SCM_REALP (x), - g_max, x, y, SCM_ARG1, s_max); -#endif - if (SCM_INUMP (y)) - return ((SCM_REALPART (x) < (z = SCM_INUM (y))) - ? scm_makdbl (z, 0.0) - : x); -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - return ((SCM_REALPART (x) < (z = scm_big2dbl (y))) - ? scm_makdbl (z, 0.0) - : x); - SCM_ASRTGO (SCM_REALP (y), bady); -#else - SCM_ASRTGO (SCM_NIMP (y) && SCM_REALP (y), bady); -#endif - return (SCM_REALPART (x) < SCM_REALPART (y)) ? y : x; - } - if (SCM_NINUMP (y)) - { -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - return SCM_BIGSIGN (y) ? x : y; - if (!(SCM_REALP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); - } -#else - if (!(SCM_NIMP (y) && SCM_REALP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); - } -#endif - return (((z = SCM_INUM (x)) < SCM_REALPART (y)) - ? y - : scm_makdbl (z, 0.0)); - } -#else -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - SCM_GASSERT2 (SCM_NIMP (x) && SCM_BIGP (x), - g_max, x, y, SCM_ARG1, s_max); - if (SCM_INUMP (y)) - return SCM_BIGSIGN (x) ? y : x; - SCM_ASRTGO (SCM_NIMP (y) && SCM_BIGP (y), bady); - return (1 == scm_bigcomp (x, y)) ? y : x; - } - if (SCM_NINUMP (y)) - { - if (!(SCM_NIMP (y) && SCM_BIGP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); - } - return SCM_BIGSIGN (y) ? x : y; - } -#else - SCM_GASSERT2 (SCM_INUMP (x), g_max, x, y, SCM_ARG1, s_max); - SCM_GASSERT2 (SCM_INUMP (y), g_max, x, y, SCM_ARGn, s_max); -#endif -#endif - return ((long) x < (long) y) ? y : x; -} - - - - -SCM_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min); - -SCM -scm_min (x, y) - SCM x; - SCM y; -{ -#ifdef SCM_FLOATS - double z; -#endif - if (SCM_UNBNDP (y)) - { - SCM_GASSERT0 (!SCM_UNBNDP (x), - g_min, scm_makfrom0str (s_min), SCM_WNA, 0); - SCM_GASSERT1 (SCM_NUMBERP (x), g_min, x, SCM_ARG1, s_min); - return x; - } -#ifdef SCM_FLOATS - if (SCM_NINUMP (x)) - { -#ifdef SCM_BIGDIG - if (!(SCM_NIMP (x))) - { - badx2: - SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); - } - if (SCM_BIGP (x)) - { - if (SCM_INUMP (y)) - return SCM_BIGSIGN (x) ? x : y; - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - return (-1 == scm_bigcomp (x, y)) ? y : x; - SCM_ASRTGO (SCM_REALP (y), bady); - z = scm_big2dbl (x); - return (z > SCM_REALPART (y)) ? y : scm_makdbl (z, 0.0); - } - SCM_ASRTGO (SCM_REALP (x), badx2); -#else - SCM_GASSERT2 (SCM_NIMP (x) && SCM_REALP (x), - g_min, x, y, SCM_ARG1, s_min); -#endif - if (SCM_INUMP (y)) - return ((SCM_REALPART (x) > (z = SCM_INUM (y))) - ? scm_makdbl (z, 0.0) - : x); -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - return ((SCM_REALPART (x) > (z = scm_big2dbl (y))) - ? scm_makdbl (z, 0.0) - : x); - SCM_ASRTGO (SCM_REALP (y), bady); -#else - SCM_ASRTGO (SCM_NIMP (y) && SCM_REALP (y), bady); -#endif - return (SCM_REALPART (x) > SCM_REALPART (y)) ? y : x; - } - if (SCM_NINUMP (y)) - { -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - return SCM_BIGSIGN (y) ? y : x; - if (!(SCM_REALP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); - } -#else - if (!(SCM_NIMP (y) && SCM_REALP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); - } -#endif - return (((z = SCM_INUM (x)) > SCM_REALPART (y)) - ? y - : scm_makdbl (z, 0.0)); - } -#else -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - SCM_GASSERT2 (SCM_NIMP (x) && SCM_BIGP (x), - g_min, x, y, SCM_ARG1, s_min); - if (SCM_INUMP (y)) - return SCM_BIGSIGN (x) ? x : y; - SCM_ASRTGO (SCM_NIMP (y) && SCM_BIGP (y), bady); - return (-1 == scm_bigcomp (x, y)) ? y : x; - } - if (SCM_NINUMP (y)) - { - if (!(SCM_NIMP (y) && SCM_BIGP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); - } - return SCM_BIGSIGN (y) ? y : x; - } -#else - SCM_GASSERT2 (SCM_INUMP (x), g_min, x, y, SCM_ARG1, s_min); - SCM_GASSERT2 (SCM_INUMP (y), g_min, x, y, SCM_ARGn, s_min); -#endif -#endif - return ((long) x > (long) y) ? y : x; -} - - - - -SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum); - -SCM -scm_sum (x, y) - SCM x; - SCM y; -{ - if (SCM_UNBNDP (y)) - { - if (SCM_UNBNDP (x)) - return SCM_INUM0; - SCM_GASSERT1 (SCM_NUMBERP (x), g_sum, x, SCM_ARG1, s_sum); - return x; - } -#ifdef SCM_FLOATS - if (SCM_NINUMP (x)) - { - SCM t; -#ifdef SCM_BIGDIG - if (!SCM_NIMP (x)) - { - badx2: - SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); - } - if (SCM_BIGP (x)) - { - if (SCM_INUMP (y)) - { - t = x; - x = y; - y = t; - goto intbig; - } - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - { - if (SCM_NUMDIGS (x) > SCM_NUMDIGS (y)) - { - t = x; - x = y; - y = t; - } - return scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - SCM_BIGSIGN (x), - y, 0); - } - SCM_ASRTGO (SCM_INEXP (y), bady); - bigreal: - return scm_makdbl (scm_big2dbl (x) + SCM_REALPART (y), - SCM_CPLXP (y) ? SCM_IMAG (y) : 0.0); - } - SCM_ASRTGO (SCM_INEXP (x), badx2); -#else - SCM_ASRTGO (SCM_NIMP (x) && SCM_INEXP (x), badx2); -#endif - if (SCM_INUMP (y)) - { - t = x; - x = y; - y = t; - goto intreal; - } -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - { - t = x; - x = y; - y = t; - goto bigreal; - } - else if (!(SCM_INEXP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); - } -#else - if (!(SCM_NIMP (y) && SCM_INEXP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); - } -#endif - { - double i = 0.0; - if (SCM_CPLXP (x)) - i = SCM_IMAG (x); - if (SCM_CPLXP (y)) - i += SCM_IMAG (y); - return scm_makdbl (SCM_REALPART (x) + SCM_REALPART (y), i); - } - } - if (SCM_NINUMP (y)) - { -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - { - intbig: - { -#ifndef SCM_DIGSTOOBIG - long z = scm_pseudolong (SCM_INUM (x)); - return scm_addbig ((SCM_BIGDIG *) & z, - SCM_DIGSPERLONG, - (x < 0) ? 0x0100 : 0, - y, 0); -#else - SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; - scm_longdigs (SCM_INUM (x), zdigs); - return scm_addbig (zdigs, SCM_DIGSPERLONG, (x < 0) ? 0x0100 : 0, - y, 0); -#endif - } - } - SCM_ASRTGO (SCM_INEXP (y), bady); -#else - SCM_ASRTGO (SCM_NIMP (y) && SCM_INEXP (y), bady); -#endif - intreal: - return scm_makdbl (SCM_INUM (x) + SCM_REALPART (y), - SCM_CPLXP (y) ? SCM_IMAG (y) : 0.0); - } -#else -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - SCM t; - SCM_ASRTGO (SCM_NIMP (x) && SCM_BIGP (x), badx2); - if (SCM_INUMP (y)) - { - t = x; - x = y; - y = t; - goto intbig; - } - SCM_ASRTGO (SCM_NIMP (y) && SCM_BIGP (y), bady); - if (SCM_NUMDIGS (x) > SCM_NUMDIGS (y)) - { - t = x; - x = y; - y = t; - } - return scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), SCM_BIGSIGN (x), - y, 0); - } - if (SCM_NINUMP (y)) - { - if (!(SCM_NIMP (y) && SCM_BIGP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); - } - intbig: - { -#ifndef SCM_DIGSTOOBIG - long z = scm_pseudolong (SCM_INUM (x)); - return scm_addbig (&z, SCM_DIGSPERLONG, (x < 0) ? 0x0100 : 0, y, 0); -#else - SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; - scm_longdigs (SCM_INUM (x), zdigs); - return scm_addbig (zdigs, SCM_DIGSPERLONG, (x < 0) ? 0x0100 : 0, y, 0); -#endif - } - } -#else - SCM_ASRTGO (SCM_INUMP (x), badx2); - SCM_GASSERT2 (SCM_INUMP (y), g_sum, x, y, SCM_ARGn, s_sum); -#endif -#endif - x = SCM_INUM (x) + SCM_INUM (y); - if (SCM_FIXABLE (x)) - return SCM_MAKINUM (x); -#ifdef SCM_BIGDIG - return scm_long2big (x); -#else -#ifdef SCM_FLOATS - return scm_makdbl ((double) x, 0.0); -#else - scm_num_overflow (s_sum); - return SCM_UNSPECIFIED; -#endif -#endif -} - - - - -SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference); - -SCM -scm_difference (x, y) - SCM x; - SCM y; -{ -#ifdef SCM_FLOATS - if (SCM_NINUMP (x)) - { - if (!(SCM_NIMP (x))) - { - if (SCM_UNBNDP (y)) - { - SCM_GASSERT0 (!SCM_UNBNDP (x), g_difference, - scm_makfrom0str (s_difference), SCM_WNA, 0); - badx: - SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); - } - else - { - badx2: - SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); - } - } - if (SCM_UNBNDP (y)) - { -#ifdef SCM_BIGDIG - if (SCM_BIGP (x)) - { - x = scm_copybig (x, !SCM_BIGSIGN (x)); - return (SCM_NUMDIGS (x) * SCM_BITSPERDIG / SCM_CHAR_BIT - <= sizeof (SCM) - ? scm_big2inum (x, SCM_NUMDIGS (x)) - : x); - } -#endif - SCM_ASRTGO (SCM_INEXP (x), badx); - return scm_makdbl (- SCM_REALPART (x), - SCM_CPLXP (x) ? -SCM_IMAG (x) : 0.0); - } - if (SCM_INUMP (y)) - return scm_sum (x, SCM_MAKINUM (- SCM_INUM (y))); -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (x)) - { - if (SCM_BIGP (y)) - return ((SCM_NUMDIGS (x) < SCM_NUMDIGS (y)) - ? scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - SCM_BIGSIGN (x), - y, 0x0100) - : scm_addbig (SCM_BDIGITS (y), SCM_NUMDIGS (y), - SCM_BIGSIGN (y) ^ 0x0100, - x, 0)); - SCM_ASRTGO (SCM_INEXP (y), bady); - return scm_makdbl (scm_big2dbl (x) - SCM_REALPART (y), - SCM_CPLXP (y) ? -SCM_IMAG (y) : 0.0); - } - SCM_ASRTGO (SCM_INEXP (x), badx2); - if (SCM_BIGP (y)) - return scm_makdbl (SCM_REALPART (x) - scm_big2dbl (y), - SCM_CPLXP (x) ? SCM_IMAG (x) : 0.0); - SCM_ASRTGO (SCM_INEXP (y), bady); -#else - SCM_ASRTGO (SCM_INEXP (x), badx2); - SCM_ASRTGO (SCM_NIMP (y) && SCM_INEXP (y), bady); -#endif - if (SCM_CPLXP (x)) - { - if (SCM_CPLXP (y)) - return scm_makdbl (SCM_REAL (x) - SCM_REAL (y), - SCM_IMAG (x) - SCM_IMAG (y)); - else - return scm_makdbl (SCM_REAL (x) - SCM_REALPART (y), SCM_IMAG (x)); - } - return scm_makdbl (SCM_REALPART (x) - SCM_REALPART (y), - SCM_CPLXP (y) ? - SCM_IMAG (y) : 0.0); - } - if (SCM_UNBNDP (y)) - { - x = -SCM_INUM (x); - goto checkx; - } - if (SCM_NINUMP (y)) - { -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - { -#ifndef SCM_DIGSTOOBIG - long z = scm_pseudolong (SCM_INUM (x)); - return scm_addbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, - (x < 0) ? 0x0100 : 0, - y, 0x0100); -#else - SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; - scm_longdigs (SCM_INUM (x), zdigs); - return scm_addbig (zdigs, SCM_DIGSPERLONG, (x < 0) ? 0x0100 : 0, - y, 0x0100); -#endif - } - if (!(SCM_INEXP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); - } -#else - if (!(SCM_NIMP (y) && SCM_INEXP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); - } -#endif - return scm_makdbl (SCM_INUM (x) - SCM_REALPART (y), - SCM_CPLXP (y) ? -SCM_IMAG (y) : 0.0); - } -#else -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - SCM_GASSERT2 (SCM_NIMP (x) && SCM_BIGP (x), - g_difference, x, y, SCM_ARG1, s_difference); - if (SCM_UNBNDP (y)) - { - x = scm_copybig (x, !SCM_BIGSIGN (x)); - return (SCM_NUMDIGS (x) * SCM_BITSPERDIG / SCM_CHAR_BIT - <= sizeof (SCM) - ? scm_big2inum (x, SCM_NUMDIGS (x)) - : x); - } - if (SCM_INUMP (y)) - { -#ifndef SCM_DIGSTOOBIG - long z = scm_pseudolong (SCM_INUM (y)); - return scm_addbig (&z, SCM_DIGSPERLONG, (y < 0) ? 0 : 0x0100, x, 0); -#else - SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; - scm_longdigs (SCM_INUM (x), zdigs); - return scm_addbig (zdigs, SCM_DIGSPERLONG, (y < 0) ? 0 : 0x0100, - x, 0); -#endif - } - SCM_ASRTGO (SCM_NIMP (y) && SCM_BIGP (y), bady); - return (SCM_NUMDIGS (x) < SCM_NUMDIGS (y)) ? - scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), SCM_BIGSIGN (x), - y, 0x0100) : - scm_addbig (SCM_BDIGITS (y), SCM_NUMDIGS (y), SCM_BIGSIGN (y) ^ 0x0100, - x, 0); - } - if (SCM_UNBNDP (y)) - { - x = -SCM_INUM (x); - goto checkx; - } - if (SCM_NINUMP (y)) - { - if (!(SCM_NIMP (y) && SCM_BIGP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); - } - { -#ifndef SCM_DIGSTOOBIG - long z = scm_pseudolong (SCM_INUM (x)); - return scm_addbig (&z, SCM_DIGSPERLONG, (x < 0) ? 0x0100 : 0, - y, 0x0100); -#else - SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; - scm_longdigs (SCM_INUM (x), zdigs); - return scm_addbig (zdigs, SCM_DIGSPERLONG, (x < 0) ? 0x0100 : 0, - y, 0x0100); -#endif - } - } -#else - SCM_GASSERT2 (SCM_INUMP (x), g_difference, x, y, SCM_ARG1, s_difference); - if (SCM_UNBNDP (y)) - { - x = -SCM_INUM (x); - goto checkx; - } - SCM_GASSERT2 (SCM_INUMP (y), g_difference, x, y, SCM_ARGn, s_difference); -#endif -#endif - x = SCM_INUM (x) - SCM_INUM (y); - checkx: - if (SCM_FIXABLE (x)) - return SCM_MAKINUM (x); -#ifdef SCM_BIGDIG - return scm_long2big (x); -#else -#ifdef SCM_FLOATS - return scm_makdbl ((double) x, 0.0); -#else - scm_num_overflow (s_difference); - return SCM_UNSPECIFIED; -#endif -#endif -} - - - - -SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product); - -SCM -scm_product (x, y) - SCM x; - SCM y; -{ - if (SCM_UNBNDP (y)) - { - if (SCM_UNBNDP (x)) - return SCM_MAKINUM (1L); - SCM_GASSERT1 (SCM_NUMBERP (x), g_product, x, SCM_ARG1, s_product); - return x; - } -#ifdef SCM_FLOATS - if (SCM_NINUMP (x)) - { - SCM t; -#ifdef SCM_BIGDIG - if (!SCM_NIMP (x)) - { - badx2: - SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); - } - if (SCM_BIGP (x)) - { - if (SCM_INUMP (y)) - { - t = x; - x = y; - y = t; - goto intbig; - } - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - return scm_mulbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - SCM_BDIGITS (y), SCM_NUMDIGS (y), - SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y)); - SCM_ASRTGO (SCM_INEXP (y), bady); - bigreal: - { - double bg = scm_big2dbl (x); - return scm_makdbl (bg * SCM_REALPART (y), - SCM_CPLXP (y) ? bg * SCM_IMAG (y) : 0.0); - } - } - SCM_ASRTGO (SCM_INEXP (x), badx2); -#else - SCM_ASRTGO (SCM_NIMP (x) && SCM_INEXP (x), badx2); -#endif - if (SCM_INUMP (y)) - { - t = x; - x = y; - y = t; - goto intreal; - } -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - { - t = x; - x = y; - y = t; - goto bigreal; - } - else if (!(SCM_INEXP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); - } -#else - if (!(SCM_NIMP (y) && SCM_INEXP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); - } -#endif - if (SCM_CPLXP (x)) - { - if (SCM_CPLXP (y)) - return scm_makdbl (SCM_REAL (x) * SCM_REAL (y) - - SCM_IMAG (x) * SCM_IMAG (y), - SCM_REAL (x) * SCM_IMAG (y) - + SCM_IMAG (x) * SCM_REAL (y)); - else - return scm_makdbl (SCM_REAL (x) * SCM_REALPART (y), - SCM_IMAG (x) * SCM_REALPART (y)); - } - return scm_makdbl (SCM_REALPART (x) * SCM_REALPART (y), - SCM_CPLXP (y) - ? SCM_REALPART (x) * SCM_IMAG (y) - : 0.0); - } - if (SCM_NINUMP (y)) - { -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - { - intbig: - if (SCM_INUM0 == x) - return x; - if (SCM_MAKINUM (1L) == x) - return y; - { -#ifndef SCM_DIGSTOOBIG - long z = scm_pseudolong (SCM_INUM (x)); - return scm_mulbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, - SCM_BDIGITS (y), SCM_NUMDIGS (y), - SCM_BIGSIGN (y) ? (x > 0) : (x < 0)); -#else - SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; - scm_longdigs (SCM_INUM (x), zdigs); - return scm_mulbig (zdigs, SCM_DIGSPERLONG, - SCM_BDIGITS (y), SCM_NUMDIGS (y), - SCM_BIGSIGN (y) ? (x > 0) : (x < 0)); -#endif - } - } - SCM_ASRTGO (SCM_INEXP (y), bady); -#else - SCM_ASRTGO (SCM_NIMP (y) && SCM_INEXP (y), bady); -#endif - intreal: - return scm_makdbl (SCM_INUM (x) * SCM_REALPART (y), - SCM_CPLXP (y) ? SCM_INUM (x) * SCM_IMAG (y) : 0.0); - } -#else -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - SCM_ASRTGO (SCM_NIMP (x) && SCM_BIGP (x), badx2); - if (SCM_INUMP (y)) - { - SCM t = x; - x = y; - y = t; - goto intbig; - } - SCM_ASRTGO (SCM_NIMP (y) && SCM_BIGP (y), bady); - return scm_mulbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - SCM_BDIGITS (y), SCM_NUMDIGS (y), - SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y)); - } - if (SCM_NINUMP (y)) - { - if (!(SCM_NIMP (y) && SCM_BIGP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); - } - intbig: - if (SCM_INUM0 == x) - return x; - if (SCM_MAKINUM (1L) == x) - return y; - { -#ifndef SCM_DIGSTOOBIG - long z = scm_pseudolong (SCM_INUM (x)); - return scm_mulbig (&z, SCM_DIGSPERLONG, - SCM_BDIGITS (y), SCM_NUMDIGS (y), - SCM_BIGSIGN (y) ? (x > 0) : (x < 0)); -#else - SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; - scm_longdigs (SCM_INUM (x), zdigs); - return scm_mulbig (zdigs, SCM_DIGSPERLONG, - SCM_BDIGITS (y), SCM_NUMDIGS (y), - SCM_BIGSIGN (y) ? (x > 0) : (x < 0)); -#endif - } - } -#else - SCM_ASRTGO (SCM_INUMP (x), badx2); - SCM_GASSERT (SCM_INUMP (y), g_product, x, y, SCM_ARGn, s_product); -#endif -#endif - { - long i, j, k; - i = SCM_INUM (x); - if (0 == i) - return x; - j = SCM_INUM (y); - k = i * j; - y = SCM_MAKINUM (k); - if (k != SCM_INUM (y) || k / i != j) -#ifdef SCM_BIGDIG - { - int sgn = (i < 0) ^ (j < 0); -#ifndef SCM_DIGSTOOBIG - i = scm_pseudolong (i); - j = scm_pseudolong (j); - return scm_mulbig ((SCM_BIGDIG *) & i, SCM_DIGSPERLONG, - (SCM_BIGDIG *) & j, SCM_DIGSPERLONG, sgn); -#else /* SCM_DIGSTOOBIG */ - SCM_BIGDIG idigs[SCM_DIGSPERLONG]; - SCM_BIGDIG jdigs[SCM_DIGSPERLONG]; - scm_longdigs (i, idigs); - scm_longdigs (j, jdigs); - return scm_mulbig (idigs, SCM_DIGSPERLONG, - jdigs, SCM_DIGSPERLONG, - sgn); -#endif - } -#else -#ifdef SCM_FLOATS - return scm_makdbl (((double) i) * ((double) j), 0.0); -#else - scm_num_overflow (s_product); -#endif -#endif - return y; - } -} - - - -double -scm_num2dbl (a, why) - SCM a; - const char *why; -{ - if (SCM_INUMP (a)) - return (double) SCM_INUM (a); -#ifdef SCM_FLOATS - SCM_ASSERT (SCM_NIMP (a), a, "wrong type argument", why); - if (SCM_REALP (a)) - return (SCM_REALPART (a)); -#endif -#ifdef SCM_BIGDIG - return scm_big2dbl (a); -#endif - SCM_ASSERT (0, a, "wrong type argument", why); - return SCM_UNSPECIFIED; -} - - -SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide); - -SCM -scm_divide (x, y) - SCM x; - SCM y; -{ -#ifdef SCM_FLOATS - double d, r, i, a; - if (SCM_NINUMP (x)) - { - if (!(SCM_NIMP (x))) - { - if (SCM_UNBNDP (y)) - { - SCM_GASSERT0 (!SCM_UNBNDP (x), - g_divide, scm_makfrom0str (s_divide), SCM_WNA, 0); - badx: - SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); - } - else - { - badx2: - SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); - } - } - if (SCM_UNBNDP (y)) - { -#ifdef SCM_BIGDIG - if (SCM_BIGP (x)) - return scm_makdbl (1.0 / scm_big2dbl (x), 0.0); -#endif - SCM_ASRTGO (SCM_INEXP (x), badx); - if (SCM_REALP (x)) - return scm_makdbl (1.0 / SCM_REALPART (x), 0.0); - r = SCM_REAL (x); - i = SCM_IMAG (x); - d = r * r + i * i; - return scm_makdbl (r / d, -i / d); - } -#ifdef SCM_BIGDIG - if (SCM_BIGP (x)) - { - SCM z; - if (SCM_INUMP (y)) - { - z = SCM_INUM (y); -#ifndef SCM_RECKLESS - if (!z) - scm_num_overflow (s_divide); -#endif - if (1 == z) - return x; - if (z < 0) - z = -z; - if (z < SCM_BIGRAD) - { - SCM w = scm_copybig (x, SCM_BIGSIGN (x) ? (y > 0) : (y < 0)); - return (scm_divbigdig (SCM_BDIGITS (w), SCM_NUMDIGS (w), - (SCM_BIGDIG) z) - ? scm_makdbl (scm_big2dbl (x) / SCM_INUM (y), 0.0) - : scm_normbig (w)); - } -#ifndef SCM_DIGSTOOBIG - z = scm_pseudolong (z); - z = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - (SCM_BIGDIG *) & z, SCM_DIGSPERLONG, - SCM_BIGSIGN (x) ? (y > 0) : (y < 0), 3); -#else - { - SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; - scm_longdigs (z, zdigs); - z = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - zdigs, SCM_DIGSPERLONG, - SCM_BIGSIGN (x) ? (y > 0) : (y < 0), 3); - } -#endif - return z ? z : scm_makdbl (scm_big2dbl (x) / SCM_INUM (y), 0.0); - } - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - { - z = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - SCM_BDIGITS (y), SCM_NUMDIGS (y), - SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y), 3); - return z ? z : scm_makdbl (scm_big2dbl (x) / scm_big2dbl (y), - 0.0); - } - SCM_ASRTGO (SCM_INEXP (y), bady); - if (SCM_REALP (y)) - return scm_makdbl (scm_big2dbl (x) / SCM_REALPART (y), 0.0); - a = scm_big2dbl (x); - goto complex_div; - } -#endif - SCM_ASRTGO (SCM_INEXP (x), badx2); - if (SCM_INUMP (y)) - { - d = SCM_INUM (y); - goto basic_div; - } -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - { - d = scm_big2dbl (y); - goto basic_div; - } - SCM_ASRTGO (SCM_INEXP (y), bady); -#else - SCM_ASRTGO (SCM_NIMP (y) && SCM_INEXP (y), bady); -#endif - if (SCM_REALP (y)) - { - d = SCM_REALPART (y); - basic_div: - return scm_makdbl (SCM_REALPART (x) / d, - SCM_CPLXP (x) ? SCM_IMAG (x) / d : 0.0); - } - a = SCM_REALPART (x); - if (SCM_REALP (x)) - goto complex_div; - r = SCM_REAL (y); - i = SCM_IMAG (y); - d = r * r + i * i; - return scm_makdbl ((a * r + SCM_IMAG (x) * i) / d, - (SCM_IMAG (x) * r - a * i) / d); - } - if (SCM_UNBNDP (y)) - { - if ((SCM_MAKINUM (1L) == x) || (SCM_MAKINUM (-1L) == x)) - return x; - return scm_makdbl (1.0 / ((double) SCM_INUM (x)), 0.0); - } - if (SCM_NINUMP (y)) - { -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (y), bady); - if (SCM_BIGP (y)) - return scm_makdbl (SCM_INUM (x) / scm_big2dbl (y), 0.0); - if (!(SCM_INEXP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); - } -#else - if (!(SCM_NIMP (y) && SCM_INEXP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); - } -#endif - if (SCM_REALP (y)) - return scm_makdbl (SCM_INUM (x) / SCM_REALPART (y), 0.0); - a = SCM_INUM (x); - complex_div: - r = SCM_REAL (y); - i = SCM_IMAG (y); - d = r * r + i * i; - return scm_makdbl ((a * r) / d, (-a * i) / d); - } -#else -#ifdef SCM_BIGDIG - if (SCM_NINUMP (x)) - { - SCM z; - SCM_GASSERT2 (SCM_NIMP (x) && SCM_BIGP (x), - g_divide, x, y, SCM_ARG1, s_divide); - if (SCM_UNBNDP (y)) - goto ov; - if (SCM_INUMP (y)) - { - z = SCM_INUM (y); - if (!z) - goto ov; - if (1 == z) - return x; - if (z < 0) - z = -z; - if (z < SCM_BIGRAD) - { - SCM w = scm_copybig (x, SCM_BIGSIGN (x) ? (y > 0) : (y < 0)); - if (scm_divbigdig (SCM_BDIGITS (w), SCM_NUMDIGS (w), - (SCM_BIGDIG) z)) - goto ov; - return w; - } -#ifndef SCM_DIGSTOOBIG - z = scm_pseudolong (z); - z = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - &z, SCM_DIGSPERLONG, - SCM_BIGSIGN (x) ? (y > 0) : (y < 0), 3); -#else - { - SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; - scm_longdigs (z, zdigs); - z = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - zdigs, SCM_DIGSPERLONG, - SCM_BIGSIGN (x) ? (y > 0) : (y < 0), 3); - } -#endif - } - else - { - SCM_ASRTGO (SCM_NIMP (y) && SCM_BIGP (y), bady); - z = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), - SCM_BDIGITS (y), SCM_NUMDIGS (y), - SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y), 3); - } - if (!z) - goto ov; - return z; - } - if (SCM_UNBNDP (y)) - { - if ((SCM_MAKINUM (1L) == x) || (SCM_MAKINUM (-1L) == x)) - return x; - goto ov; - } - if (SCM_NINUMP (y)) - { - if (!(SCM_NIMP (y) && SCM_BIGP (y))) - { - bady: - SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); - } - goto ov; - } -#else - SCM_GASSERT2 (SCM_INUMP (x), g_divide, x, y, SCM_ARG1, s_divide); - if (SCM_UNBNDP (y)) - { - if ((SCM_MAKINUM (1L) == x) || (SCM_MAKINUM (-1L) == x)) - return x; - goto ov; - } - SCM_GASSERT2 (SCM_INUMP (y), g_divide, x, y, SCM_ARGn, s_divide); -#endif -#endif - { - long z = SCM_INUM (y); - if ((0 == z) || SCM_INUM (x) % z) - goto ov; - z = SCM_INUM (x) / z; - if (SCM_FIXABLE (z)) - return SCM_MAKINUM (z); -#ifdef SCM_BIGDIG - return scm_long2big (z); -#endif -#ifdef SCM_FLOATS - ov: - return scm_makdbl (((double) SCM_INUM (x)) / ((double) SCM_INUM (y)), 0.0); -#else - ov: - scm_num_overflow (s_divide); - return SCM_UNSPECIFIED; -#endif - } -} - - - - -#ifdef SCM_FLOATS -SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_cxr, (SCM (*)()) scm_asinh, g_asinh); - -double -scm_asinh (x) - double x; -{ - return log (x + sqrt (x * x + 1)); -} - - - - -SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_cxr, (SCM (*)()) scm_acosh, g_acosh); - -double -scm_acosh (x) - double x; -{ - return log (x + sqrt (x * x - 1)); -} - - - - -SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_cxr, (SCM (*)()) scm_atanh, g_atanh); - -double -scm_atanh (x) - double x; -{ - return 0.5 * log ((1 + x) / (1 - x)); -} - - - - -SCM_GPROC1 (s_truncate, "truncate", scm_tc7_cxr, (SCM (*)()) scm_truncate, g_truncate); - -double -scm_truncate (x) - double x; -{ - if (x < 0.0) - return -floor (-x); - return floor (x); -} - - - -SCM_GPROC1 (s_round, "round", scm_tc7_cxr, (SCM (*)()) scm_round, g_round); - -double -scm_round (x) - double x; -{ - double plus_half = x + 0.5; - double result = floor (plus_half); - /* Adjust so that the scm_round is towards even. */ - return (plus_half == result && plus_half / 2 != floor (plus_half / 2)) - ? result - 1 : result; -} - - - -SCM_GPROC1 (s_exact_to_inexact, "exact->inexact", scm_tc7_cxr, (SCM (*)()) scm_exact_to_inexact, g_exact_to_inexact); - -double -scm_exact_to_inexact (z) - double z; -{ - return z; -} - - -SCM_GPROC1 (s_i_floor, "floor", scm_tc7_cxr, (SCM (*)()) floor, g_i_floor); -SCM_GPROC1 (s_i_ceil, "ceiling", scm_tc7_cxr, (SCM (*)()) ceil, g_i_ceil); -SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_cxr, (SCM (*)()) sqrt, g_i_sqrt); -SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_cxr, (SCM (*)()) fabs, g_i_abs); -SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_cxr, (SCM (*)()) exp, g_i_exp); -SCM_GPROC1 (s_i_log, "$log", scm_tc7_cxr, (SCM (*)()) log, g_i_log); -SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_cxr, (SCM (*)()) sin, g_i_sin); -SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_cxr, (SCM (*)()) cos, g_i_cos); -SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_cxr, (SCM (*)()) tan, g_i_tan); -SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_cxr, (SCM (*)()) asin, g_i_asin); -SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_cxr, (SCM (*)()) acos, g_i_acos); -SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_cxr, (SCM (*)()) atan, g_i_atan); -SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_cxr, (SCM (*)()) sinh, g_i_sinh); -SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_cxr, (SCM (*)()) cosh, g_i_cosh); -SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_cxr, (SCM (*)()) tanh, g_i_tanh); - -struct dpair -{ - double x, y; -}; - -static void scm_two_doubles (SCM z1, - SCM z2, - const char *sstring, - struct dpair * xy); - -static void -scm_two_doubles (z1, z2, sstring, xy) - SCM z1, z2; - const char *sstring; - struct dpair *xy; -{ - if (SCM_INUMP (z1)) - xy->x = SCM_INUM (z1); - else - { -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (z1), badz1); - if (SCM_BIGP (z1)) - xy->x = scm_big2dbl (z1); - else - { -#ifndef SCM_RECKLESS - if (!(SCM_REALP (z1))) - badz1:scm_wta (z1, (char *) SCM_ARG1, sstring); -#endif - xy->x = SCM_REALPART (z1); - } -#else - { - SCM_ASSERT (SCM_NIMP (z1) && SCM_REALP (z1), z1, SCM_ARG1, sstring); - xy->x = SCM_REALPART (z1); - } -#endif - } - if (SCM_INUMP (z2)) - xy->y = SCM_INUM (z2); - else - { -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (z2), badz2); - if (SCM_BIGP (z2)) - xy->y = scm_big2dbl (z2); - else - { -#ifndef SCM_RECKLESS - if (!(SCM_REALP (z2))) - badz2:scm_wta (z2, (char *) SCM_ARG2, sstring); -#endif - xy->y = SCM_REALPART (z2); - } -#else - { - SCM_ASSERT (SCM_NIMP (z2) && SCM_REALP (z2), z2, SCM_ARG2, sstring); - xy->y = SCM_REALPART (z2); - } -#endif - } -} - - - - -SCM_PROC (s_sys_expt, "$expt", 2, 0, 0, scm_sys_expt); - -SCM -scm_sys_expt (z1, z2) - SCM z1; - SCM z2; -{ - struct dpair xy; - scm_two_doubles (z1, z2, s_sys_expt, &xy); - return scm_makdbl (pow (xy.x, xy.y), 0.0); -} - - - -SCM_PROC (s_sys_atan2, "$atan2", 2, 0, 0, scm_sys_atan2); - -SCM -scm_sys_atan2 (z1, z2) - SCM z1; - SCM z2; -{ - struct dpair xy; - scm_two_doubles (z1, z2, s_sys_atan2, &xy); - return scm_makdbl (atan2 (xy.x, xy.y), 0.0); -} - - - -SCM_PROC (s_make_rectangular, "make-rectangular", 2, 0, 0, scm_make_rectangular); - -SCM -scm_make_rectangular (z1, z2) - SCM z1; - SCM z2; -{ - struct dpair xy; - scm_two_doubles (z1, z2, s_make_rectangular, &xy); - return scm_makdbl (xy.x, xy.y); -} - - - -SCM_PROC (s_make_polar, "make-polar", 2, 0, 0, scm_make_polar); - -SCM -scm_make_polar (z1, z2) - SCM z1; - SCM z2; -{ - struct dpair xy; - scm_two_doubles (z1, z2, s_make_polar, &xy); - return scm_makdbl (xy.x * cos (xy.y), xy.x * sin (xy.y)); -} - - - - -SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); - -SCM -scm_real_part (z) - SCM z; -{ - if (SCM_NINUMP (z)) - { -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (z), badz); - if (SCM_BIGP (z)) - return z; - if (!(SCM_INEXP (z))) - { - badz: - SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); - } -#else - SCM_GASSERT1 (SCM_NIMP (z) && SCM_INEXP (z), - g_real_part, z, SCM_ARG1, s_real_part); -#endif - if (SCM_CPLXP (z)) - return scm_makdbl (SCM_REAL (z), 0.0); - } - return z; -} - - - -SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); - -SCM -scm_imag_part (z) - SCM z; -{ - if (SCM_INUMP (z)) - return SCM_INUM0; -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (z), badz); - if (SCM_BIGP (z)) - return SCM_INUM0; - if (!(SCM_INEXP (z))) - { - badz: - SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); - } -#else - SCM_GASSERT1 (SCM_NIMP (z) && SCM_INEXP (z), - g_imag_part, z, SCM_ARG1, s_imag_part); -#endif - if (SCM_CPLXP (z)) - return scm_makdbl (SCM_IMAG (z), 0.0); - return scm_flo0; -} - - - -SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); - -SCM -scm_magnitude (z) - SCM z; -{ - if (SCM_INUMP (z)) - return scm_abs (z); -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (z), badz); - if (SCM_BIGP (z)) - return scm_abs (z); - if (!(SCM_INEXP (z))) - { - badz: - SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); - } -#else - SCM_GASSERT1 (SCM_NIMP (z) && SCM_INEXP (z), - g_magnitude, z, SCM_ARG1, s_magnitude); -#endif - if (SCM_CPLXP (z)) - { - double i = SCM_IMAG (z), r = SCM_REAL (z); - return scm_makdbl (sqrt (i * i + r * r), 0.0); - } - return scm_makdbl (fabs (SCM_REALPART (z)), 0.0); -} - - - - -SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); - -SCM -scm_angle (z) - SCM z; -{ - double x, y = 0.0; - if (SCM_INUMP (z)) - { - x = (z >= SCM_INUM0) ? 1.0 : -1.0; - goto do_angle; - } -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (z), badz); - if (SCM_BIGP (z)) - { - x = (SCM_TYP16 (z) == scm_tc16_bigpos) ? 1.0 : -1.0; - goto do_angle; - } - if (!(SCM_INEXP (z))) - { - badz: - SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); - } -#else - SCM_GASSERT1 (SCM_NIMP (z) && SCM_INEXP (z), g_angle, z, SCM_ARG1, s_angle); -#endif - if (SCM_REALP (z)) - { - x = SCM_REALPART (z); - goto do_angle; - } - x = SCM_REAL (z); - y = SCM_IMAG (z); - do_angle: - return scm_makdbl (atan2 (y, x), 0.0); -} - - -SCM_PROC (s_inexact_to_exact, "inexact->exact", 1, 0, 0, scm_inexact_to_exact); - -SCM -scm_inexact_to_exact (z) - SCM z; -{ - if (SCM_INUMP (z)) - return z; -#ifdef SCM_BIGDIG - SCM_ASRTGO (SCM_NIMP (z), badz); - if (SCM_BIGP (z)) - return z; -#ifndef SCM_RECKLESS - if (!(SCM_REALP (z))) - { - badz: - scm_wta (z, (char *) SCM_ARG1, s_inexact_to_exact); - } -#endif -#else - SCM_ASSERT (SCM_NIMP (z) && SCM_REALP (z), z, SCM_ARG1, s_inexact_to_exact); -#endif -#ifdef SCM_BIGDIG - { - double u = floor (SCM_REALPART (z) + 0.5); - if ((u <= SCM_MOST_POSITIVE_FIXNUM) && (-u <= -SCM_MOST_NEGATIVE_FIXNUM)) - { - /* Negation is a workaround for HP700 cc bug */ - SCM ans = SCM_MAKINUM ((long) u); - if (SCM_INUM (ans) == (long) u) - return ans; - } - SCM_ASRTGO (isfinite (u), badz); /* problem? */ - return scm_dbl2big (u); - } -#else - return SCM_MAKINUM ((long) floor (SCM_REALPART (z) + 0.5)); -#endif -} - - - -#else /* ~SCM_FLOATS */ -SCM_GPROC (s_trunc, "truncate", 1, 0, 0, scm_trunc, g_trunc); - -SCM -scm_trunc (x) - SCM x; -{ - SCM_GASSERT2 (SCM_INUMP (x), g_trunc, x, y, SCM_ARG1, s_truncate); - return x; -} - - - -#endif /* SCM_FLOATS */ - -#ifdef SCM_BIGDIG -#ifdef SCM_FLOATS -/* d must be integer */ - -SCM -scm_dbl2big (d) - double d; -{ - scm_sizet i = 0; - long c; - SCM_BIGDIG *digits; - SCM ans; - double u = (d < 0) ? -d : d; - while (0 != floor (u)) - { - u /= SCM_BIGRAD; - i++; - } - ans = scm_mkbig (i, d < 0); - digits = SCM_BDIGITS (ans); - while (i--) - { - u *= SCM_BIGRAD; - c = floor (u); - u -= c; - digits[i] = c; - } -#ifndef SCM_RECKLESS - if (u != 0) - scm_num_overflow ("dbl2big"); -#endif - return ans; -} - - - -double -scm_big2dbl (b) - SCM b; -{ - double ans = 0.0; - scm_sizet i = SCM_NUMDIGS (b); - SCM_BIGDIG *digits = SCM_BDIGITS (b); - while (i--) - ans = digits[i] + SCM_BIGRAD * ans; - if (scm_tc16_bigneg == SCM_TYP16 (b)) - return -ans; - return ans; -} -#endif -#endif - - -SCM -scm_long2num (sl) - long sl; -{ - if (!SCM_FIXABLE (sl)) - { -#ifdef SCM_BIGDIG - return scm_long2big (sl); -#else -#ifdef SCM_FLOATS - return scm_makdbl ((double) sl, 0.0); -#else - return SCM_BOOL_F; -#endif -#endif - } - return SCM_MAKINUM (sl); -} - - -#ifdef LONGLONGS - -SCM -scm_long_long2num (sl) - long_long sl; -{ - if (!SCM_FIXABLE (sl)) - { -#ifdef SCM_BIGDIG - return scm_long_long2big (sl); -#else -#ifdef SCM_FLOATS - return scm_makdbl ((double) sl, 0.0); -#else - return SCM_BOOL_F; -#endif -#endif - } - return SCM_MAKINUM (sl); -} -#endif - - - -SCM -scm_ulong2num (sl) - unsigned long sl; -{ - if (!SCM_POSFIXABLE (sl)) - { -#ifdef SCM_BIGDIG - return scm_ulong2big (sl); -#else -#ifdef SCM_FLOATS - return scm_makdbl ((double) sl, 0.0); -#else - return SCM_BOOL_F; -#endif -#endif - } - return SCM_MAKINUM (sl); -} - - -long -scm_num2long (num, pos, s_caller) - SCM num; - char *pos; - const char *s_caller; -{ - long res; - if (SCM_INUMP (num)) - { - res = SCM_INUM (num); - return res; - } - SCM_ASRTGO (SCM_NIMP (num), errout); -#ifdef SCM_FLOATS - if (SCM_REALP (num)) - { - double u = SCM_REALPART (num); - res = u; - if ((double) res == u) - { - return res; - } - } -#endif -#ifdef SCM_BIGDIG - if (SCM_BIGP (num)) - { - long oldres; - scm_sizet l; - res = 0; - oldres = 0; - for (l = SCM_NUMDIGS (num); l--;) - { - res = SCM_BIGUP (res) + SCM_BDIGITS (num)[l]; - if (res < oldres) - goto errout; - oldres = res; - } - if (SCM_TYP16 (num) == scm_tc16_bigpos) - return res; - else - return -res; - } -#endif - errout: - scm_wta (num, pos, s_caller); - return SCM_UNSPECIFIED; -} - - - -#ifdef LONGLONGS - -long_long -scm_num2long_long (num, pos, s_caller) - SCM num; - char *pos; - const char *s_caller; -{ - long_long res; - if (SCM_INUMP (num)) - { - res = SCM_INUM ((long_long) num); - return res; - } - SCM_ASRTGO (SCM_NIMP (num), errout); -#ifdef SCM_FLOATS - if (SCM_REALP (num)) - { - double u = SCM_REALPART (num); - if (((SCM_MOST_NEGATIVE_FIXNUM * 4) <= u) - && (u <= (SCM_MOST_POSITIVE_FIXNUM * 4 + 3))) - { - res = u; - return res; - } - } -#endif -#ifdef SCM_BIGDIG - if (SCM_BIGP (num)) - { - scm_sizet l = SCM_NUMDIGS (num); - SCM_ASRTGO (SCM_DIGSPERLONGLONG >= l, errout); - res = 0; - for (; l--;) - res = SCM_LONGLONGBIGUP (res) + SCM_BDIGITS (num)[l]; - return res; - } -#endif - errout: - scm_wta (num, pos, s_caller); - return SCM_UNSPECIFIED; -} -#endif - - - -unsigned long -scm_num2ulong (num, pos, s_caller) - SCM num; - char *pos; - const char *s_caller; -{ - unsigned long res; - if (SCM_INUMP (num)) - { - res = SCM_INUM ((unsigned long) num); - return res; - } - SCM_ASRTGO (SCM_NIMP (num), errout); -#ifdef SCM_FLOATS - if (SCM_REALP (num)) - { - double u = SCM_REALPART (num); - if ((0 <= u) && (u <= (unsigned long) ~0L)) - { - res = u; - return res; - } - } -#endif -#ifdef SCM_BIGDIG - if (SCM_BIGP (num)) - { - unsigned long oldres; - scm_sizet l; - res = 0; - oldres = 0; - for (l = SCM_NUMDIGS (num); l--;) - { - res = SCM_BIGUP (res) + SCM_BDIGITS (num)[l]; - if (res < oldres) - goto errout; - oldres = res; - } - return res; - } -#endif - errout: - scm_wta (num, pos, s_caller); - return SCM_UNSPECIFIED; -} - - -#ifdef SCM_FLOATS -#ifndef DBL_DIG -static void add1 SCM_P ((double f, double *fsum)); -static void -add1 (f, fsum) - double f, *fsum; -{ - *fsum = f + 1.0; -} -#endif -#endif - - - -void -scm_init_numbers () -{ - scm_add_feature("complex"); -#ifdef SCM_FLOATS - scm_add_feature("inexact"); -#ifdef SCM_SINGLES - SCM_NEWSMOB(scm_flo0,scm_tc_flo,NULL); -#else - SCM_NEWSMOB(scm_flo0,scm_tc_dblr,scm_must_malloc (1L * sizeof (double), "real")); - SCM_REAL (scm_flo0) = 0.0; -#endif -#ifdef DBL_DIG - scm_dblprec = (DBL_DIG > 20) ? 20 : DBL_DIG; -#else - { /* determine floating point precision */ - double f = 0.1; - double fsum = 1.0 + f; - while (fsum != 1.0) - { - f /= 10.0; - if (++scm_dblprec > 20) - break; - add1 (f, &fsum); - } - scm_dblprec = scm_dblprec - 1; - } -#endif /* DBL_DIG */ -#endif -#include "numbers.x" -} +/* Copyright (C) 1995,1996,1997,1998,1999,2000 Free Software Foundation, Inc. + * + * This program 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. + * + * This program 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 this software; see the file COPYING. If not, write to + * the Free Software Foundation, Inc., 59 Temple Place, Suite 330, + * Boston, MA 02111-1307 USA + * + * As a special exception, the Free Software Foundation gives permission + * for additional uses of the text contained in its release of GUILE. + * + * The exception is that, if you link the GUILE library with other files + * to produce an executable, this does not by itself cause the + * resulting executable to be covered by the GNU General Public License. + * Your use of that executable is in no way restricted on account of + * linking the GUILE library code into it. + * + * This exception does not however invalidate any other reasons why + * the executable file might be covered by the GNU General Public License. + * + * This exception applies only to the code released by the + * Free Software Foundation under the name GUILE. If you copy + * code from other Free Software Foundation releases into a copy of + * GUILE, as the General Public License permits, the exception does + * not apply to the code that you add in this way. To avoid misleading + * anyone as to the status of such modified files, you must delete + * this exception notice from them. + * + * If you write modifications of your own for GUILE, it is your choice + * whether to permit this exception to apply to your modifications. + * If you do not wish that, delete this exception notice. */ + +/* Software engineering face-lift by Greg J. Badros, 11-Dec-1999, + gjb@cs.washington.edu, http://www.cs.washington.edu/homes/gjb */ + + + +#include +#include +#include "libguile/_scm.h" +#include "libguile/feature.h" +#include "libguile/ports.h" +#include "libguile/root.h" +#include "libguile/smob.h" +#include "libguile/strings.h" + +#include "libguile/validate.h" +#include "libguile/numbers.h" + + + +static SCM scm_divbigbig (SCM_BIGDIG *x, scm_sizet nx, SCM_BIGDIG *y, scm_sizet ny, int sgn, int modes); +static SCM scm_divbigint (SCM x, long z, int sgn, int mode); + + +#define DIGITS '0':case '1':case '2':case '3':case '4':\ + case '5':case '6':case '7':case '8':case '9' + + +#define SCM_SWAP(x,y) do { SCM __t = x; x = y; y = __t; } while (0) + + +#if (SCM_DEBUG_DEPRECATED == 1) /* not defined in header yet? */ + +/* SCM_FLOBUFLEN is the maximum number of characters neccessary for the + * printed or scm_string representation of an inexact number. + */ +#define SCM_FLOBUFLEN (10+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) + +#endif /* SCM_DEBUG_DEPRECATED == 1 */ + + +/* IS_INF tests its floating point number for infiniteness + Dirk:FIXME:: This test does not work if x == 0 + */ +#ifndef IS_INF +#define IS_INF(x) ((x) == (x) / 2) +#endif + + +/* Return true if X is not infinite and is not a NaN + Dirk:FIXME:: Since IS_INF is broken, this test does not work if x == 0 + */ +#ifndef isfinite +#define isfinite(x) (!IS_INF (x) && (x) == (x)) +#endif + + + +static SCM abs_most_negative_fixnum; + + + + +SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0, + (SCM x), + "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" + "otherwise.") +#define FUNC_NAME s_scm_exact_p +{ + if (SCM_INUMP (x)) { + return SCM_BOOL_T; + } else if (SCM_BIGP (x)) { + return SCM_BOOL_T; + } else { + return SCM_BOOL_F; + } +} +#undef FUNC_NAME + + +SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0, + (SCM n), + "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" + "otherwise.") +#define FUNC_NAME s_scm_odd_p +{ + if (SCM_INUMP (n)) { + return SCM_BOOL ((4 & SCM_UNPACK (n)) != 0); + } else if (SCM_BIGP (n)) { + return SCM_BOOL ((1 & SCM_BDIGITS (n) [0]) != 0); + } else { + SCM_WRONG_TYPE_ARG (1, n); + } +} +#undef FUNC_NAME + + +SCM_DEFINE (scm_even_p, "even?", 1, 0, 0, + (SCM n), + "Return @code{#t} if @var{n} is an even number, @code{#f}\n" + "otherwise.") +#define FUNC_NAME s_scm_even_p +{ + if (SCM_INUMP (n)) { + return SCM_BOOL ((4 & SCM_UNPACK (n)) == 0); + } else if (SCM_BIGP (n)) { + return SCM_BOOL ((1 & SCM_BDIGITS (n) [0]) == 0); + } else { + SCM_WRONG_TYPE_ARG (1, n); + } +} +#undef FUNC_NAME + + +SCM_GPROC (s_abs, "abs", 1, 0, 0, scm_abs, g_abs); +/* "Return the absolute value of @var{x}." + */ +SCM +scm_abs (SCM x) +{ + if (SCM_INUMP (x)) { + long int xx = SCM_INUM (x); + if (xx >= 0) { + return x; + } else if (SCM_POSFIXABLE (-xx)) { + return SCM_MAKINUM (-xx); + } else { +#ifdef SCM_BIGDIG + return scm_long2big (-xx); +#else + scm_num_overflow (s_abs); +#endif + } + } else if (SCM_BIGP (x)) { + if (!SCM_BIGSIGN (x)) { + return x; + } else { + return scm_copybig (x, 0); + } + } else if (SCM_REALP (x)) { + return scm_make_real (fabs (SCM_REAL_VALUE (x))); + } else { + SCM_WTA_DISPATCH_1 (g_abs, x, 1, s_abs); + } +} + + +SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient); +/* "Return the quotient of the numbers @var{x} and @var{y}." + */ +SCM +scm_quotient (SCM x, SCM y) +{ + if (SCM_INUMP (x)) { + long xx = SCM_INUM (x); + if (SCM_INUMP (y)) { + long yy = SCM_INUM (y); + if (yy == 0) { + scm_num_overflow (s_quotient); + } else { + long z = xx / yy; + if (SCM_FIXABLE (z)) { + return SCM_MAKINUM (z); + } else { +#ifdef SCM_BIGDIG + return scm_long2big (z); +#else + scm_num_overflow (s_quotient); +#endif + } + } + } else if (SCM_BIGP (y)) { + if (SCM_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM + && scm_bigcomp (abs_most_negative_fixnum, y) == 0) + { + /* Special case: x == fixnum-min && y == abs (fixnum-min) */ + return SCM_MAKINUM (-1); + } + else + return SCM_MAKINUM (0); + } else { + SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); + } + } else if (SCM_BIGP (x)) { + if (SCM_INUMP (y)) { + long yy = SCM_INUM (y); + if (yy == 0) { + scm_num_overflow (s_quotient); + } else if (yy == 1) { + return x; + } else { + long z = yy < 0 ? -yy : yy; + + if (z < SCM_BIGRAD) { + SCM sw = scm_copybig (x, SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0)); + scm_divbigdig (SCM_BDIGITS (sw), SCM_NUMDIGS (sw), (SCM_BIGDIG) z); + return scm_normbig (sw); + } else { +#ifndef SCM_DIGSTOOBIG + long w = scm_pseudolong (z); + return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), + (SCM_BIGDIG *) & w, SCM_DIGSPERLONG, + SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0), 2); +#else + SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; + scm_longdigs (z, zdigs); + return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), + zdigs, SCM_DIGSPERLONG, + SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0), 2); +#endif + } + } + } else if (SCM_BIGP (y)) { + return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), + SCM_BDIGITS (y), SCM_NUMDIGS (y), + SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y), 2); + } else { + SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); + } + } else { + SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient); + } +} + + +SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder); +/* "Return the remainder of the numbers @var{x} and @var{y}.\n" + * "@lisp\n" + * "(remainder 13 4) @result{} 1\n" + * "(remainder -13 4) @result{} -1\n" + * "@end lisp" + */ +SCM +scm_remainder (SCM x, SCM y) +{ + if (SCM_INUMP (x)) { + if (SCM_INUMP (y)) { + long yy = SCM_INUM (y); + if (yy == 0) { + scm_num_overflow (s_remainder); + } else { + long z = SCM_INUM (x) % yy; + return SCM_MAKINUM (z); + } + } else if (SCM_BIGP (y)) { + if (SCM_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM + && scm_bigcomp (abs_most_negative_fixnum, y) == 0) + { + /* Special case: x == fixnum-min && y == abs (fixnum-min) */ + return SCM_MAKINUM (0); + } + else + return x; + } else { + SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); + } + } else if (SCM_BIGP (x)) { + if (SCM_INUMP (y)) { + long yy = SCM_INUM (y); + if (yy == 0) { + scm_num_overflow (s_remainder); + } else { + return scm_divbigint (x, yy, SCM_BIGSIGN (x), 0); + } + } else if (SCM_BIGP (y)) { + return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), + SCM_BDIGITS (y), SCM_NUMDIGS (y), + SCM_BIGSIGN (x), 0); + } else { + SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); + } + } else { + SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder); + } +} + + +SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo); +/* "Return the modulo of the numbers @var{x} and @var{y}.\n" + * "@lisp\n" + * "(modulo 13 4) @result{} 1\n" + * "(modulo -13 4) @result{} 3\n" + * "@end lisp" + */ +SCM +scm_modulo (SCM x, SCM y) +{ + if (SCM_INUMP (x)) { + long xx = SCM_INUM (x); + if (SCM_INUMP (y)) { + long yy = SCM_INUM (y); + if (yy == 0) { + scm_num_overflow (s_modulo); + } else { + long z = xx % yy; + return SCM_MAKINUM (((yy < 0) ? (z > 0) : (z < 0)) ? z + yy : z); + } + } else if (SCM_BIGP (y)) { + return (SCM_BIGSIGN (y) ? (xx > 0) : (xx < 0)) ? scm_sum (x, y) : x; + } else { + SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); + } + } else if (SCM_BIGP (x)) { + if (SCM_INUMP (y)) { + long yy = SCM_INUM (y); + if (yy == 0) { + scm_num_overflow (s_modulo); + } else { + return scm_divbigint (x, yy, yy < 0, + (SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0)) ? 1 : 0); + } + } else if (SCM_BIGP (y)) { + return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), + SCM_BDIGITS (y), SCM_NUMDIGS (y), + SCM_BIGSIGN (y), + (SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y)) ? 1 : 0); + } else { + SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); + } + } else { + SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo); + } +} + + +SCM_GPROC1 (s_gcd, "gcd", scm_tc7_asubr, scm_gcd, g_gcd); +/* "Return the greatest common divisor of all arguments.\n" + * "If called without arguments, 0 is returned." + */ +SCM +scm_gcd (SCM x, SCM y) +{ + if (SCM_UNBNDP (y)) { + if (SCM_UNBNDP (x)) { + return SCM_INUM0; + } else { + return x; + } + } + + tailrec: + if (SCM_INUMP (x)) { + if (SCM_INUMP (y)) { + long xx = SCM_INUM (x); + long yy = SCM_INUM (y); + long u = xx < 0 ? -xx : xx; + long v = yy < 0 ? -yy : yy; + long result; + + if (xx == 0) { + result = v; + } else if (yy == 0) { + result = u; + } else { + int k = 1; + long t; + + /* Determine a common factor 2^k */ + while (!(1 & (u | v))) { + k <<= 1; + u >>= 1; + v >>= 1; + } + + /* Now, any factor 2^n can be eliminated */ + if (u & 1) { + t = -v; + } else { + t = u; + b3: + t = SCM_SRS (t, 1); + } + if (!(1 & t)) + goto b3; + if (t > 0) + u = t; + else + v = -t; + t = u - v; + if (t != 0) + goto b3; + + result = u * k; + } + if (SCM_POSFIXABLE (result)) { + return SCM_MAKINUM (result); + } else { +#ifdef SCM_BIGDIG + return scm_long2big (result); +#else + scm_num_overflow (s_gcd); +#endif + } + } else if (SCM_BIGP (y)) { + SCM_SWAP (x, y); + goto big_gcd; + } else { + SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); + } + } else if (SCM_BIGP (x)) { + big_gcd: + if (SCM_BIGSIGN (x)) + x = scm_copybig (x, 0); + newy: + if (SCM_INUMP (y)) { + if (SCM_EQ_P (y, SCM_INUM0)) { + return x; + } else { + goto swaprec; + } + } else if (SCM_BIGP (y)) { + if (SCM_BIGSIGN (y)) + y = scm_copybig (y, 0); + switch (scm_bigcomp (x, y)) + { + case -1: /* x > y */ + swaprec: + { + SCM t = scm_remainder (x, y); + x = y; + y = t; + } + goto tailrec; + case 1: /* x < y */ + y = scm_remainder (y, x); + goto newy; + default: /* x == y */ + return x; + } + /* instead of the switch, we could just + return scm_gcd (y, scm_modulo (x, y)); */ + } else { + SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); + } + } else { + SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); + } +} + + +SCM_GPROC1 (s_lcm, "lcm", scm_tc7_asubr, scm_lcm, g_lcm); +/* "Return the least common multiple of the arguments.\n" + * "If called without arguments, 1 is returned." + */ +SCM +scm_lcm (SCM n1, SCM n2) +{ + if (SCM_UNBNDP (n2)) { + if (SCM_UNBNDP (n1)) { + return SCM_MAKINUM (1L); + } else { + n2 = SCM_MAKINUM (1L); + } + }; + +#ifndef SCM_BIGDIG + SCM_GASSERT2 (SCM_INUMP (n1), g_lcm, n1, n2, SCM_ARG1, s_lcm); + SCM_GASSERT2 (SCM_INUMP (n2), g_lcm, n1, n2, SCM_ARGn, s_lcm); +#else + SCM_GASSERT2 (SCM_INUMP (n1) || SCM_BIGP (n1), + g_lcm, n1, n2, SCM_ARG1, s_lcm); + SCM_GASSERT2 (SCM_INUMP (n2) || SCM_BIGP (n2), + g_lcm, n1, n2, SCM_ARGn, s_lcm); +#endif + + { + SCM d = scm_gcd (n1, n2); + if (SCM_EQ_P (d, SCM_INUM0)) { + return d; + } else { + return scm_abs (scm_product (n1, scm_quotient (n2, d))); + } + } +} + + +#ifndef scm_long2num +#define SCM_LOGOP_RETURN(x) scm_ulong2num(x) +#else +#define SCM_LOGOP_RETURN(x) SCM_MAKINUM(x) +#endif + + +/* Emulating 2's complement bignums with sign magnitude arithmetic: + + Logand: + X Y Result Method: + (len) + + + + x (map digit:logand X Y) + + - + x (map digit:logand X (lognot (+ -1 Y))) + - + + y (map digit:logand (lognot (+ -1 X)) Y) + - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) + + Logior: + X Y Result Method: + + + + + (map digit:logior X Y) + + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) + - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) + - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) + + Logxor: + X Y Result Method: + + + + + (map digit:logxor X Y) + + - - (+ 1 (map digit:logxor X (+ -1 Y))) + - + - (+ 1 (map digit:logxor (+ -1 X) Y)) + - - + (map digit:logxor (+ -1 X) (+ -1 Y)) + + Logtest: + X Y Result + + + + (any digit:logand X Y) + + - (any digit:logand X (lognot (+ -1 Y))) + - + (any digit:logand (lognot (+ -1 X)) Y) + - - #t + +*/ + +#ifdef SCM_BIGDIG + +SCM scm_copy_big_dec(SCM b, int sign); +SCM scm_copy_smaller(SCM_BIGDIG *x, scm_sizet nx, int zsgn); +SCM scm_big_ior(SCM_BIGDIG *x, scm_sizet nx, int xsgn, SCM bigy); +SCM scm_big_xor(SCM_BIGDIG *x, scm_sizet nx, int xsgn, SCM bigy); +SCM scm_big_and(SCM_BIGDIG *x, scm_sizet nx, int xsgn, SCM bigy, int zsgn); +SCM scm_big_test(SCM_BIGDIG *x, scm_sizet nx, int xsgn, SCM bigy); + +SCM scm_copy_big_dec(SCM b, int sign) +{ + long num = -1; + scm_sizet nx = SCM_NUMDIGS(b); + scm_sizet i = 0; + SCM ans = scm_mkbig(nx, sign); + SCM_BIGDIG *src = SCM_BDIGITS(b), *dst = SCM_BDIGITS(ans); + if SCM_BIGSIGN(b) do { + num += src[i]; + if (num < 0) {dst[i] = num + SCM_BIGRAD; num = -1;} + else {dst[i] = SCM_BIGLO(num); num = 0;} + } while (++i < nx); + else + while (nx--) dst[nx] = src[nx]; + return ans; +} + +SCM scm_copy_smaller(SCM_BIGDIG *x, scm_sizet nx, int zsgn) +{ + long num = -1; + scm_sizet i = 0; + SCM z = scm_mkbig(nx, zsgn); + SCM_BIGDIG *zds = SCM_BDIGITS(z); + if (zsgn) do { + num += x[i]; + if (num < 0) {zds[i] = num + SCM_BIGRAD; num = -1;} + else {zds[i] = SCM_BIGLO(num); num = 0;} + } while (++i < nx); + else do zds[i] = x[i]; while (++i < nx); + return z; +} + +SCM scm_big_ior(SCM_BIGDIG *x, scm_sizet nx, int xsgn, SCM bigy) +/* Assumes nx <= SCM_NUMDIGS(bigy) */ +/* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */ +{ + long num = -1; + scm_sizet i = 0, ny = SCM_NUMDIGS(bigy); + SCM z = scm_copy_big_dec (bigy, xsgn & SCM_BIGSIGN (bigy)); + SCM_BIGDIG *zds = SCM_BDIGITS(z); + if (xsgn) { + do { + num += x[i]; + if (num < 0) {zds[i] |= num + SCM_BIGRAD; num = -1;} + else {zds[i] |= SCM_BIGLO(num); num = 0;} + } while (++i < nx); + /* ========= Need to increment zds now =========== */ + i = 0; num = 1; + while (i < ny) { + num += zds[i]; + zds[i++] = SCM_BIGLO(num); + num = SCM_BIGDN(num); + if (!num) return z; + } + scm_adjbig(z, 1 + ny); /* OOPS, overflowed into next digit. */ + SCM_BDIGITS(z)[ny] = 1; + return z; + } + else do zds[i] = zds[i] | x[i]; while (++i < nx); + return z; +} + +SCM scm_big_xor(SCM_BIGDIG *x, scm_sizet nx, int xsgn, SCM bigy) +/* Assumes nx <= SCM_NUMDIGS(bigy) */ +/* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */ +{ + long num = -1; + scm_sizet i = 0, ny = SCM_NUMDIGS(bigy); + SCM z = scm_copy_big_dec(bigy, xsgn ^ SCM_BIGSIGN(bigy)); + SCM_BIGDIG *zds = SCM_BDIGITS(z); + if (xsgn) do { + num += x[i]; + if (num < 0) {zds[i] ^= num + SCM_BIGRAD; num = -1;} + else {zds[i] ^= SCM_BIGLO(num); num = 0;} + } while (++i < nx); + else do { + zds[i] = zds[i] ^ x[i]; + } while (++i < nx); + + if (xsgn ^ SCM_BIGSIGN(bigy)) { + /* ========= Need to increment zds now =========== */ + i = 0; num = 1; + while (i < ny) { + num += zds[i]; + zds[i++] = SCM_BIGLO(num); + num = SCM_BIGDN(num); + if (!num) return scm_normbig(z); + } + } + return scm_normbig(z); +} + +SCM scm_big_and(SCM_BIGDIG *x, scm_sizet nx, int xsgn, SCM bigy, int zsgn) +/* Assumes nx <= SCM_NUMDIGS(bigy) */ +/* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */ +/* return sign equals either 0 or SCM_BIGSIGNFLAG */ +{ + long num = -1; + scm_sizet i = 0; + SCM z; + SCM_BIGDIG *zds; + if (xsgn==zsgn) { + z = scm_copy_smaller(x, nx, zsgn); + x = SCM_BDIGITS(bigy); + xsgn = SCM_BIGSIGN(bigy); + } + else z = scm_copy_big_dec(bigy, zsgn); + zds = SCM_BDIGITS(z); + + if (zsgn) { + if (xsgn) do { + num += x[i]; + if (num < 0) {zds[i] &= num + SCM_BIGRAD; num = -1;} + else {zds[i] &= SCM_BIGLO(num); num = 0;} + } while (++i < nx); + else do zds[i] = zds[i] & ~x[i]; while (++i < nx); + /* ========= need to increment zds now =========== */ + i = 0; num = 1; + while (i < nx) { + num += zds[i]; + zds[i++] = SCM_BIGLO(num); + num = SCM_BIGDN(num); + if (!num) return scm_normbig(z); + } + } + else if (xsgn) { + unsigned long int carry = 1; + do { + unsigned long int mask = (SCM_BIGDIG) ~x[i] + carry; + zds[i] = zds[i] & (SCM_BIGDIG) mask; + carry = (mask >= SCM_BIGRAD) ? 1 : 0; + } while (++i < nx); + } else do zds[i] = zds[i] & x[i]; while (++i < nx); + return scm_normbig(z); +} + +SCM scm_big_test(SCM_BIGDIG *x, scm_sizet nx, int xsgn, SCM bigy) +/* Assumes nx <= SCM_NUMDIGS(bigy) */ +/* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */ +{ + SCM_BIGDIG *y; + scm_sizet i = 0; + long num = -1; + if (SCM_BIGSIGN(bigy) & xsgn) return SCM_BOOL_T; + if (SCM_NUMDIGS(bigy) != nx && xsgn) return SCM_BOOL_T; + y = SCM_BDIGITS(bigy); + if (xsgn) + do { + num += x[i]; + if (num < 0) { + if (y[i] & ~(num + SCM_BIGRAD)) return SCM_BOOL_T; + num = -1; + } + else { + if (y[i] & ~SCM_BIGLO(num)) return SCM_BOOL_T; + num = 0; + } + } while (++i < nx); + else if SCM_BIGSIGN(bigy) + do { + num += y[i]; + if (num < 0) { + if (x[i] & ~(num + SCM_BIGRAD)) return SCM_BOOL_T; + num = -1; + } + else { + if (x[i] & ~SCM_BIGLO(num)) return SCM_BOOL_T; + num = 0; + } + } while (++i < nx); + else + do if (x[i] & y[i]) return SCM_BOOL_T; + while (++i < nx); + return SCM_BOOL_F; +} + +#endif + + +SCM_DEFINE1 (scm_logand, "logand", scm_tc7_asubr, + (SCM n1, SCM n2), + "Returns the integer which is the bit-wise AND of the two integer\n" + "arguments.\n\n" + "Example:\n" + "@lisp\n" + "(number->string (logand #b1100 #b1010) 2)\n" + " @result{} \"1000\"\n" + "@end lisp") +#define FUNC_NAME s_scm_logand +{ + long int nn1; + + if (SCM_UNBNDP (n2)) { + if (SCM_UNBNDP (n1)) { + return SCM_MAKINUM (-1); + } else if (!SCM_NUMBERP (n1)) { + SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); +#ifndef SCM_RECKLESS + } else if (SCM_NUMBERP (n1)) { + return n1; + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); +#else + } else { + return n1; +#endif + } + } + + if (SCM_INUMP (n1)) { + nn1 = SCM_INUM (n1); + if (SCM_INUMP (n2)) { + long nn2 = SCM_INUM (n2); + return SCM_MAKINUM (nn1 & nn2); + } else if SCM_BIGP (n2) { + intbig: + { +# ifndef SCM_DIGSTOOBIG + long z = scm_pseudolong (nn1); + if ((nn1 < 0) && SCM_BIGSIGN (n2)) { + return scm_big_ior ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, + SCM_BIGSIGNFLAG, n2); + } else { + return scm_big_and ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, + (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, 0); + } +# else + SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; + scm_longdigs (nn1, zdigs); + if ((nn1 < 0) && SCM_BIGSIGN (n2)) { + return scm_big_ior (zdigs, SCM_DIGSPERLONG, SCM_BIGSIGNFLAG, n2); + } else { + return scm_big_and (zdigs, SCM_DIGSPERLONG, + (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, 0); + } +# endif + } + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); + } + } else if (SCM_BIGP (n1)) { + if (SCM_INUMP (n2)) { + SCM_SWAP (n1, n2); + nn1 = SCM_INUM (n1); + goto intbig; + } else if (SCM_BIGP (n2)) { + if (SCM_NUMDIGS (n1) > SCM_NUMDIGS (n2)) { + SCM_SWAP (n1, n2); + }; + if ((SCM_BIGSIGN (n1)) && SCM_BIGSIGN (n2)) { + return scm_big_ior (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), + SCM_BIGSIGNFLAG, n2); + } else { + return scm_big_and (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), + SCM_BIGSIGN (n1), n2, 0); + } + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); + } + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); + } +} +#undef FUNC_NAME + + +SCM_DEFINE1 (scm_logior, "logior", scm_tc7_asubr, + (SCM n1, SCM n2), + "Returns the integer which is the bit-wise OR of the two integer\n" + "arguments.\n\n" + "Example:\n" + "@lisp\n" + "(number->string (logior #b1100 #b1010) 2)\n" + " @result{} \"1110\"\n" + "@end lisp") +#define FUNC_NAME s_scm_logior +{ + long int nn1; + + if (SCM_UNBNDP (n2)) { + if (SCM_UNBNDP (n1)) { + return SCM_INUM0; +#ifndef SCM_RECKLESS + } else if (SCM_NUMBERP (n1)) { + return n1; + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); +#else + } else { + return n1; +#endif + } + } + + if (SCM_INUMP (n1)) { + nn1 = SCM_INUM (n1); + if (SCM_INUMP (n2)) { + long nn2 = SCM_INUM (n2); + return SCM_MAKINUM (nn1 | nn2); + } else if (SCM_BIGP (n2)) { + intbig: + { +# ifndef SCM_DIGSTOOBIG + long z = scm_pseudolong (nn1); + if ((!(nn1 < 0)) && !SCM_BIGSIGN (n2)) { + return scm_big_ior ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, + (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2); + } else { + return scm_big_and ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, + (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, SCM_BIGSIGNFLAG); + } +# else + SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; + scm_longdigs (nn1, zdigs); + if ((!(nn1 < 0)) && !SCM_BIGSIGN (n2)) { + return scm_big_ior (zdigs, SCM_DIGSPERLONG, + (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2); + } else { + return scm_big_and (zdigs, SCM_DIGSPERLONG, + (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, SCM_BIGSIGNFLAG); + } +# endif + } + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); + } + } else if (SCM_BIGP (n1)) { + if (SCM_INUMP (n2)) { + SCM_SWAP (n1, n2); + nn1 = SCM_INUM (n1); + goto intbig; + } else if (SCM_BIGP (n2)) { + if (SCM_NUMDIGS (n1) > SCM_NUMDIGS (n2)) { + SCM_SWAP (n1, n2); + }; + if ((!SCM_BIGSIGN (n1)) && !SCM_BIGSIGN (n2)) { + return scm_big_ior (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), + SCM_BIGSIGN (n1), n2); + } else { + return scm_big_and (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), + SCM_BIGSIGN (n1), n2, SCM_BIGSIGNFLAG); + } + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); + } + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); + } +} +#undef FUNC_NAME + + +SCM_DEFINE1 (scm_logxor, "logxor", scm_tc7_asubr, + (SCM n1, SCM n2), + "Returns the integer which is the bit-wise XOR of the two integer\n" + "arguments.\n\n" + "Example:\n" + "@lisp\n" + "(number->string (logxor #b1100 #b1010) 2)\n" + " @result{} \"110\"\n" + "@end lisp") +#define FUNC_NAME s_scm_logxor +{ + long int nn1; + + if (SCM_UNBNDP (n2)) { + if (SCM_UNBNDP (n1)) { + return SCM_INUM0; +#ifndef SCM_RECKLESS + } else if (SCM_NUMBERP (n1)) { + return n1; + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); +#else + } else { + return n1; +#endif + } + } + + if (SCM_INUMP (n1)) { + nn1 = SCM_INUM (n1); + if (SCM_INUMP (n2)) { + long nn2 = SCM_INUM (n2); + return SCM_MAKINUM (nn1 ^ nn2); + } else if (SCM_BIGP (n2)) { + intbig: + { +# ifndef SCM_DIGSTOOBIG + long z = scm_pseudolong (nn1); + return scm_big_xor ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, + (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2); +# else + SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; + scm_longdigs (nn1, zdigs); + return scm_big_xor (zdigs, SCM_DIGSPERLONG, + (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2); +# endif + } + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); + } + } else if (SCM_BIGP (n1)) { + if (SCM_INUMP (n2)) { + SCM_SWAP (n1, n2); + nn1 = SCM_INUM (n1); + goto intbig; + } else if (SCM_BIGP (n2)) { + if (SCM_NUMDIGS(n1) > SCM_NUMDIGS(n2)) { + SCM_SWAP (n1, n2); + } + return scm_big_xor (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), + SCM_BIGSIGN (n1), n2); + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); + } + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); + } +} +#undef FUNC_NAME + + +SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, + (SCM n1, SCM n2), + "@example\n" + "(logtest j k) @equiv{} (not (zero? (logand j k)))\n\n" + "(logtest #b0100 #b1011) @result{} #f\n" + "(logtest #b0100 #b0111) @result{} #t\n" + "@end example") +#define FUNC_NAME s_scm_logtest +{ + long int nn1; + + if (SCM_INUMP (n1)) { + nn1 = SCM_INUM (n1); + if (SCM_INUMP (n2)) { + long nn2 = SCM_INUM (n2); + return SCM_BOOL (nn1 & nn2); + } else if (SCM_BIGP (n2)) { + intbig: + { +# ifndef SCM_DIGSTOOBIG + long z = scm_pseudolong (nn1); + return scm_big_test ((SCM_BIGDIG *)&z, SCM_DIGSPERLONG, + (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2); +# else + SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; + scm_longdigs (nn1, zdigs); + return scm_big_test (zdigs, SCM_DIGSPERLONG, + (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2); +# endif + } + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); + } + } else if (SCM_BIGP (n1)) { + if (SCM_INUMP (n2)) { + SCM_SWAP (n1, n2); + nn1 = SCM_INUM (n1); + goto intbig; + } else if (SCM_BIGP (n2)) { + if (SCM_NUMDIGS (n1) > SCM_NUMDIGS (n2)) { + SCM_SWAP (n1, n2); + } + return scm_big_test (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), + SCM_BIGSIGN (n1), n2); + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); + } + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); + } +} +#undef FUNC_NAME + + +SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, + (SCM index, SCM j), + "@example\n" + "(logbit? index j) @equiv{} (logtest (integer-expt 2 index) j)\n\n" + "(logbit? 0 #b1101) @result{} #t\n" + "(logbit? 1 #b1101) @result{} #f\n" + "(logbit? 2 #b1101) @result{} #t\n" + "(logbit? 3 #b1101) @result{} #t\n" + "(logbit? 4 #b1101) @result{} #f\n" + "@end example") +#define FUNC_NAME s_scm_logbit_p +{ + unsigned long int iindex; + + SCM_VALIDATE_INUM_MIN (SCM_ARG1, index, 0); + iindex = (unsigned long int) SCM_INUM (index); + + if (SCM_INUMP (j)) { + return SCM_BOOL ((1L << iindex) & SCM_INUM (j)); + } else if (SCM_BIGP (j)) { + if (SCM_NUMDIGS (j) * SCM_BITSPERDIG < iindex) { + return SCM_BOOL_F; + } else if (SCM_BIGSIGN (j)) { + long num = -1; + scm_sizet i = 0; + SCM_BIGDIG * x = SCM_BDIGITS (j); + scm_sizet nx = iindex / SCM_BITSPERDIG; + while (1) { + num += x[i]; + if (nx == i++) { + return SCM_BOOL (((1L << (iindex % SCM_BITSPERDIG)) & num) == 0); + } else if (num < 0) { + num = -1; + } else { + num = 0; + } + } + } else { + return SCM_BOOL (SCM_BDIGITS (j) [iindex / SCM_BITSPERDIG] + & (1L << (iindex % SCM_BITSPERDIG))); + } + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG2, j); + } +} +#undef FUNC_NAME + + +SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, + (SCM n), + "Returns the integer which is the 2s-complement of the integer argument.\n\n" + "Example:\n" + "@lisp\n" + "(number->string (lognot #b10000000) 2)\n" + " @result{} \"-10000001\"\n" + "(number->string (lognot #b0) 2)\n" + " @result{} \"-1\"\n" + "@end lisp\n") +#define FUNC_NAME s_scm_lognot +{ + return scm_difference (SCM_MAKINUM (-1L), n); +} +#undef FUNC_NAME + +SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, + (SCM n, SCM k), + "Returns @var{n} raised to the non-negative integer exponent @var{k}.\n\n" + "Example:\n" + "@lisp\n" + "(integer-expt 2 5)\n" + " @result{} 32\n" + "(integer-expt -3 3)\n" + " @result{} -27\n" + "@end lisp") +#define FUNC_NAME s_scm_integer_expt +{ + SCM acc = SCM_MAKINUM (1L); + int i2; +#ifdef SCM_BIGDIG + if (SCM_EQ_P (n, SCM_INUM0) || SCM_EQ_P (n, acc)) + return n; + else if (SCM_EQ_P (n, SCM_MAKINUM (-1L))) + return SCM_FALSEP (scm_even_p (k)) ? n : acc; +#endif + SCM_VALIDATE_ULONG_COPY (2,k,i2); + if (i2 < 0) + { + i2 = -i2; + n = scm_divide (n, SCM_UNDEFINED); + } + while (1) + { + if (0 == i2) + return acc; + if (1 == i2) + return scm_product (acc, n); + if (i2 & 1) + acc = scm_product (acc, n); + n = scm_product (n, n); + i2 >>= 1; + } +} +#undef FUNC_NAME + +SCM_DEFINE (scm_ash, "ash", 2, 0, 0, + (SCM n, SCM cnt), + "The function ash performs an arithmetic shift left by @var{CNT}\n" + "bits (or shift right, if @var{cnt} is negative).\n" + "'Arithmetic' means, that the function does not guarantee to\n" + "keep the bit structure of @var{n}, but rather guarantees that\n" + "the result will always be rounded towards minus infinity.\n" + "Therefore, the results of ash and a corresponding bitwise\n" + "shift will differ if N is negative.\n\n" + "Formally, the function returns an integer equivalent to\n" + "@code{(inexact->exact (floor (* @var{n} (expt 2 @var{cnt}))))}.\n\n" + "Example:\n" + "@lisp\n" + "(number->string (ash #b1 3) 2)\n" + " @result{} \"1000\"\n" + "(number->string (ash #b1010 -1) 2)\n" + " @result{} \"101\"\n" + "@end lisp") +#define FUNC_NAME s_scm_ash +{ + long bits_to_shift; + +#ifndef SCM_BIGDIG + SCM_VALIDATE_INUM (1, n) +#endif + SCM_VALIDATE_INUM (2, cnt); + + bits_to_shift = SCM_INUM (cnt); +#ifdef SCM_BIGDIG + if (bits_to_shift < 0) { + /* Shift right by abs(cnt) bits. This is realized as a division by + div:=2^abs(cnt). However, to guarantee the floor rounding, negative + values require some special treatment. + */ + SCM div = scm_integer_expt (SCM_MAKINUM (2), SCM_MAKINUM (-bits_to_shift)); + if (SCM_FALSEP (scm_negative_p (n))) + return scm_quotient (n, div); + else + return scm_sum (SCM_MAKINUM (-1L), + scm_quotient (scm_sum (SCM_MAKINUM (1L), n), div)); + } else + /* Shift left is done by multiplication with 2^CNT */ + return scm_product (n, scm_integer_expt (SCM_MAKINUM (2), cnt)); +#else + if (bits_to_shift < 0) + /* Signed right shift (SCM_SRS does it right) by abs(cnt) bits. */ + return SCM_MAKINUM (SCM_SRS (SCM_INUM (n), -bits_to_shift)); + else { + /* Shift left, but make sure not to leave the range of inums */ + SCM res = SCM_MAKINUM (SCM_INUM (n) << cnt); + if (SCM_INUM (res) >> cnt != SCM_INUM (n)) + scm_num_overflow (FUNC_NAME); + return res; + } +#endif +} +#undef FUNC_NAME + + +SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, + (SCM n, SCM start, SCM end), + "Returns the integer composed of the @var{start} (inclusive) through\n" + "@var{end} (exclusive) bits of @var{n}. The @var{start}th bit becomes\n" + "the 0-th bit in the result.@refill\n\n" + "Example:\n" + "@lisp\n" + "(number->string (bit-extract #b1101101010 0 4) 2)\n" + " @result{} \"1010\"\n" + "(number->string (bit-extract #b1101101010 4 9) 2)\n" + " @result{} \"10110\"\n" + "@end lisp") +#define FUNC_NAME s_scm_bit_extract +{ + unsigned long int istart, iend; + SCM_VALIDATE_INUM_MIN_COPY (2,start,0,istart); + SCM_VALIDATE_INUM_MIN_COPY (3, end, 0, iend); + SCM_ASSERT_RANGE (3, end, (iend >= istart)); + + if (SCM_INUMP (n)) { + long int in = SCM_INUM (n); + unsigned long int bits = iend - istart; + + if (in < 0 && bits >= SCM_FIXNUM_BIT) + { + /* Since we emulate two's complement encoded numbers, this special + * case requires us to produce a result that has more bits than can be + * stored in a fixnum. Thus, we fall back to the more general + * algorithm that is used for bignums. + */ + goto generalcase; + } + + if (istart < SCM_FIXNUM_BIT) + { + in = in >> istart; + if (bits < SCM_FIXNUM_BIT) + return SCM_MAKINUM (in & ((1L << bits) - 1)); + else /* we know: in >= 0 */ + return SCM_MAKINUM (in); + } + else if (in < 0) + { + return SCM_MAKINUM (-1L & ((1L << bits) - 1)); + } + else + { + return SCM_MAKINUM (0); + } + } else if (SCM_BIGP (n)) { + generalcase: + { + SCM num1 = SCM_MAKINUM (1L); + SCM num2 = SCM_MAKINUM (2L); + SCM bits = SCM_MAKINUM (iend - istart); + SCM mask = scm_difference (scm_integer_expt (num2, bits), num1); + return scm_logand (mask, scm_ash (n, SCM_MAKINUM (-istart))); + } + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG1, n); + } +} +#undef FUNC_NAME + + +static const char scm_logtab[] = { + 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 +}; + +SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, + (SCM n), + "Returns the number of bits in integer @var{n}. If integer is positive,\n" + "the 1-bits in its binary representation are counted. If negative, the\n" + "0-bits in its two's-complement binary representation are counted. If 0,\n" + "0 is returned.\n\n" + "Example:\n" + "@lisp\n" + "(logcount #b10101010)\n" + " @result{} 4\n" + "(logcount 0)\n" + " @result{} 0\n" + "(logcount -2)\n" + " @result{} 1\n" + "@end lisp") +#define FUNC_NAME s_scm_logcount +{ + if (SCM_INUMP (n)) { + unsigned long int c = 0; + long int nn = SCM_INUM (n); + if (nn < 0) { + nn = -1 - nn; + }; + while (nn) { + c += scm_logtab[15 & nn]; + nn >>= 4; + }; + return SCM_MAKINUM (c); + } else if (SCM_BIGP (n)) { + if (SCM_BIGSIGN (n)) { + return scm_logcount (scm_difference (SCM_MAKINUM (-1L), n)); + } else { + unsigned long int c = 0; + scm_sizet i = SCM_NUMDIGS (n); + SCM_BIGDIG * ds = SCM_BDIGITS (n); + while (i--) { + SCM_BIGDIG d; + for (d = ds[i]; d; d >>= 4) { + c += scm_logtab[15 & d]; + } + } + return SCM_MAKINUM (c); + } + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG1, n); + } +} +#undef FUNC_NAME + + +static const char scm_ilentab[] = { + 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 +}; + +SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, + (SCM n), + "Returns the number of bits neccessary to represent @var{n}.\n\n" + "Example:\n" + "@lisp\n" + "(integer-length #b10101010)\n" + " @result{} 8\n" + "(integer-length 0)\n" + " @result{} 0\n" + "(integer-length #b1111)\n" + " @result{} 4\n" + "@end lisp") +#define FUNC_NAME s_scm_integer_length +{ + if (SCM_INUMP (n)) { + unsigned long int c = 0; + unsigned int l = 4; + long int nn = SCM_INUM (n); + if (nn < 0) { + nn = -1 - nn; + }; + while (nn) { + c += 4; + l = scm_ilentab [15 & nn]; + nn >>= 4; + }; + return SCM_MAKINUM (c - 4 + l); + } else if (SCM_BIGP (n)) { + if (SCM_BIGSIGN (n)) { + return scm_integer_length (scm_difference (SCM_MAKINUM (-1L), n)); + } else { + unsigned long int digs = SCM_NUMDIGS (n) - 1; + unsigned long int c = digs * SCM_BITSPERDIG; + unsigned int l = 4; + SCM_BIGDIG * ds = SCM_BDIGITS (n); + SCM_BIGDIG d = ds [digs]; + while (d) { + c += 4; + l = scm_ilentab [15 & d]; + d >>= 4; + }; + return SCM_MAKINUM (c - 4 + l); + } + } else { + SCM_WRONG_TYPE_ARG (SCM_ARG1, n); + } +} +#undef FUNC_NAME + + +#ifdef SCM_BIGDIG +static const char s_bignum[] = "bignum"; + +SCM +scm_mkbig (scm_sizet nlen, int sign) +{ + SCM v; + /* Cast to long int to avoid signed/unsigned comparison warnings. */ + if ((( ((long int) nlen) << SCM_BIGSIZEFIELD) >> SCM_BIGSIZEFIELD) + != (long int) nlen) + scm_memory_error (s_bignum); + + SCM_NEWCELL (v); + SCM_DEFER_INTS; + SCM_SET_BIGNUM_BASE (v, scm_must_malloc (nlen * sizeof (SCM_BIGDIG), s_bignum)); + SCM_SETNUMDIGS (v, nlen, sign); + SCM_ALLOW_INTS; + return v; +} + + +SCM +scm_big2inum (SCM b, scm_sizet l) +{ + unsigned long num = 0; + SCM_BIGDIG *tmp = SCM_BDIGITS (b); + while (l--) + num = SCM_BIGUP (num) + tmp[l]; + if (!SCM_BIGSIGN (b)) + { + if (SCM_POSFIXABLE (num)) + return SCM_MAKINUM (num); + } + else if (num <= -SCM_MOST_NEGATIVE_FIXNUM) + return SCM_MAKINUM (-num); + return b; +} + + +static const char s_adjbig[] = "scm_adjbig"; + +SCM +scm_adjbig (SCM b, scm_sizet nlen) +{ + scm_sizet nsiz = nlen; + if (((nsiz << SCM_BIGSIZEFIELD) >> SCM_BIGSIZEFIELD) != nlen) + scm_memory_error (s_adjbig); + + SCM_DEFER_INTS; + { + SCM_BIGDIG *digits + = ((SCM_BIGDIG *) + scm_must_realloc ((char *) SCM_BDIGITS (b), + (long) (SCM_NUMDIGS (b) * sizeof (SCM_BIGDIG)), + (long) (nsiz * sizeof (SCM_BIGDIG)), s_bignum)); + + SCM_SET_BIGNUM_BASE (b, digits); + SCM_SETNUMDIGS (b, nsiz, SCM_BIGSIGN (b)); + } + SCM_ALLOW_INTS; + return b; +} + + + +SCM +scm_normbig (SCM b) +{ +#ifndef _UNICOS + scm_sizet nlen = SCM_NUMDIGS (b); +#else + int nlen = SCM_NUMDIGS (b); /* unsigned nlen breaks on Cray when nlen => 0 */ +#endif + SCM_BIGDIG *zds = SCM_BDIGITS (b); + while (nlen-- && !zds[nlen]); + nlen++; + if (nlen * SCM_BITSPERDIG / SCM_CHAR_BIT <= sizeof (SCM)) + if (SCM_INUMP (b = scm_big2inum (b, (scm_sizet) nlen))) + return b; + if (SCM_NUMDIGS (b) == nlen) + return b; + return scm_adjbig (b, (scm_sizet) nlen); +} + + + +SCM +scm_copybig (SCM b, int sign) +{ + scm_sizet i = SCM_NUMDIGS (b); + SCM ans = scm_mkbig (i, sign); + SCM_BIGDIG *src = SCM_BDIGITS (b), *dst = SCM_BDIGITS (ans); + while (i--) + dst[i] = src[i]; + return ans; +} + + + +SCM +scm_long2big (long n) +{ + scm_sizet i = 0; + SCM_BIGDIG *digits; + SCM ans = scm_mkbig (SCM_DIGSPERLONG, n < 0); + digits = SCM_BDIGITS (ans); + if (n < 0) + n = -n; + while (i < SCM_DIGSPERLONG) + { + digits[i++] = SCM_BIGLO (n); + n = SCM_BIGDN ((unsigned long) n); + } + return ans; +} + +#ifdef HAVE_LONG_LONGS + +SCM +scm_long_long2big (long_long n) +{ + scm_sizet i; + SCM_BIGDIG *digits; + SCM ans; + int n_digits; + + { + long tn; + tn = (long) n; + if ((long long) tn == n) + return scm_long2big (tn); + } + + { + long_long tn; + + for (tn = n, n_digits = 0; + tn; + ++n_digits, tn = SCM_BIGDN ((ulong_long) tn)) + ; + } + + i = 0; + ans = scm_mkbig (n_digits, n < 0); + digits = SCM_BDIGITS (ans); + if (n < 0) + n = -n; + while (i < n_digits) + { + digits[i++] = SCM_BIGLO (n); + n = SCM_BIGDN ((ulong_long) n); + } + return ans; +} +#endif /* HAVE_LONG_LONGS */ + + +SCM +scm_2ulong2big (unsigned long *np) +{ + unsigned long n; + scm_sizet i; + SCM_BIGDIG *digits; + SCM ans; + + ans = scm_mkbig (2 * SCM_DIGSPERLONG, 0); + digits = SCM_BDIGITS (ans); + + n = np[0]; + for (i = 0; i < SCM_DIGSPERLONG; ++i) + { + digits[i] = SCM_BIGLO (n); + n = SCM_BIGDN ((unsigned long) n); + } + n = np[1]; + for (i = 0; i < SCM_DIGSPERLONG; ++i) + { + digits[i + SCM_DIGSPERLONG] = SCM_BIGLO (n); + n = SCM_BIGDN ((unsigned long) n); + } + return ans; +} + + + +SCM +scm_ulong2big (unsigned long n) +{ + scm_sizet i = 0; + SCM_BIGDIG *digits; + SCM ans = scm_mkbig (SCM_DIGSPERLONG, 0); + digits = SCM_BDIGITS (ans); + while (i < SCM_DIGSPERLONG) + { + digits[i++] = SCM_BIGLO (n); + n = SCM_BIGDN (n); + } + return ans; +} + + + +int +scm_bigcomp (SCM x, SCM y) +{ + int xsign = SCM_BIGSIGN (x); + int ysign = SCM_BIGSIGN (y); + scm_sizet xlen, ylen; + + /* Look at the signs, first. */ + if (ysign < xsign) + return 1; + if (ysign > xsign) + return -1; + + /* They're the same sign, so see which one has more digits. Note + that, if they are negative, the longer number is the lesser. */ + ylen = SCM_NUMDIGS (y); + xlen = SCM_NUMDIGS (x); + if (ylen > xlen) + return (xsign) ? -1 : 1; + if (ylen < xlen) + return (xsign) ? 1 : -1; + + /* They have the same number of digits, so find the most significant + digit where they differ. */ + while (xlen) + { + --xlen; + if (SCM_BDIGITS (y)[xlen] != SCM_BDIGITS (x)[xlen]) + /* Make the discrimination based on the digit that differs. */ + return ((SCM_BDIGITS (y)[xlen] > SCM_BDIGITS (x)[xlen]) + ? (xsign ? -1 : 1) + : (xsign ? 1 : -1)); + } + + /* The numbers are identical. */ + return 0; +} + +#ifndef SCM_DIGSTOOBIG + + +long +scm_pseudolong (long x) +{ + union + { + long l; + SCM_BIGDIG bd[SCM_DIGSPERLONG]; + } + p; + scm_sizet i = 0; + if (x < 0) + x = -x; + while (i < SCM_DIGSPERLONG) + { + p.bd[i++] = SCM_BIGLO (x); + x = SCM_BIGDN (x); + } + /* p.bd[0] = SCM_BIGLO(x); p.bd[1] = SCM_BIGDN(x); */ + return p.l; +} + +#else + + +void +scm_longdigs (long x, SCM_BIGDIG digs[]) +{ + scm_sizet i = 0; + if (x < 0) + x = -x; + while (i < SCM_DIGSPERLONG) + { + digs[i++] = SCM_BIGLO (x); + x = SCM_BIGDN (x); + } +} +#endif + + + +SCM +scm_addbig (SCM_BIGDIG *x, scm_sizet nx, int xsgn, SCM bigy, int sgny) +{ + /* Assumes nx <= SCM_NUMDIGS(bigy) */ + /* Assumes xsgn and sgny scm_equal either 0 or SCM_BIGSIGNFLAG */ + long num = 0; + scm_sizet i = 0, ny = SCM_NUMDIGS (bigy); + SCM z = scm_copybig (bigy, SCM_BIGSIGN (bigy) ^ sgny); + SCM_BIGDIG *zds = SCM_BDIGITS (z); + if (xsgn ^ SCM_BIGSIGN (z)) + { + do + { + num += (long) zds[i] - x[i]; + if (num < 0) + { + zds[i] = num + SCM_BIGRAD; + num = -1; + } + else + { + zds[i] = SCM_BIGLO (num); + num = 0; + } + } + while (++i < nx); + if (num && nx == ny) + { + num = 1; + i = 0; + SCM_SET_CELL_WORD_0 (z, SCM_CELL_WORD_0 (z) ^ SCM_BIGSIGNFLAG); + do + { + num += (SCM_BIGRAD - 1) - zds[i]; + zds[i++] = SCM_BIGLO (num); + num = SCM_BIGDN (num); + } + while (i < ny); + } + else + while (i < ny) + { + num += zds[i]; + if (num < 0) + { + zds[i++] = num + SCM_BIGRAD; + num = -1; + } + else + { + zds[i++] = SCM_BIGLO (num); + num = 0; + } + } + } + else + { + do + { + num += (long) zds[i] + x[i]; + zds[i++] = SCM_BIGLO (num); + num = SCM_BIGDN (num); + } + while (i < nx); + if (!num) + return z; + while (i < ny) + { + num += zds[i]; + zds[i++] = SCM_BIGLO (num); + num = SCM_BIGDN (num); + if (!num) + return z; + } + if (num) + { + z = scm_adjbig (z, ny + 1); + SCM_BDIGITS (z)[ny] = num; + return z; + } + } + return scm_normbig (z); +} + + +SCM +scm_mulbig (SCM_BIGDIG *x, scm_sizet nx, SCM_BIGDIG *y, scm_sizet ny, int sgn) +{ + scm_sizet i = 0, j = nx + ny; + unsigned long n = 0; + SCM z = scm_mkbig (j, sgn); + SCM_BIGDIG *zds = SCM_BDIGITS (z); + while (j--) + zds[j] = 0; + do + { + j = 0; + if (x[i]) + { + do + { + n += zds[i + j] + ((unsigned long) x[i] * y[j]); + zds[i + j++] = SCM_BIGLO (n); + n = SCM_BIGDN (n); + } + while (j < ny); + if (n) + { + zds[i + j] = n; + n = 0; + } + } + } + while (++i < nx); + return scm_normbig (z); +} + + +unsigned int +scm_divbigdig (SCM_BIGDIG * ds, scm_sizet h, SCM_BIGDIG div) +{ + register unsigned long t2 = 0; + while (h--) + { + t2 = SCM_BIGUP (t2) + ds[h]; + ds[h] = t2 / div; + t2 %= div; + } + return t2; +} + + + +static SCM +scm_divbigint (SCM x, long z, int sgn, int mode) +{ + if (z < 0) + z = -z; + if (z < SCM_BIGRAD) + { + register unsigned long t2 = 0; + register SCM_BIGDIG *ds = SCM_BDIGITS (x); + scm_sizet nd = SCM_NUMDIGS (x); + while (nd--) + t2 = (SCM_BIGUP (t2) + ds[nd]) % z; + if (mode && t2) + t2 = z - t2; + return SCM_MAKINUM (sgn ? -t2 : t2); + } + { +#ifndef SCM_DIGSTOOBIG + unsigned long t2 = scm_pseudolong (z); + return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), + (SCM_BIGDIG *) & t2, SCM_DIGSPERLONG, + sgn, mode); +#else + SCM_BIGDIG t2[SCM_DIGSPERLONG]; + scm_longdigs (z, t2); + return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), + t2, SCM_DIGSPERLONG, + sgn, mode); +#endif + } +} + + +static SCM +scm_divbigbig (SCM_BIGDIG *x, scm_sizet nx, SCM_BIGDIG *y, scm_sizet ny, int sgn, int modes) +{ + /* modes description + 0 remainder + 1 scm_modulo + 2 quotient + 3 quotient but returns SCM_UNDEFINED if division is not exact. */ + scm_sizet i = 0, j = 0; + long num = 0; + unsigned long t2 = 0; + SCM z, newy; + SCM_BIGDIG d = 0, qhat, *zds, *yds; + /* algorithm requires nx >= ny */ + if (nx < ny) + switch (modes) + { + case 0: /* remainder -- just return x */ + z = scm_mkbig (nx, sgn); + zds = SCM_BDIGITS (z); + do + { + zds[i] = x[i]; + } + while (++i < nx); + return z; + case 1: /* scm_modulo -- return y-x */ + z = scm_mkbig (ny, sgn); + zds = SCM_BDIGITS (z); + do + { + num += (long) y[i] - x[i]; + if (num < 0) + { + zds[i] = num + SCM_BIGRAD; + num = -1; + } + else + { + zds[i] = num; + num = 0; + } + } + while (++i < nx); + while (i < ny) + { + num += y[i]; + if (num < 0) + { + zds[i++] = num + SCM_BIGRAD; + num = -1; + } + else + { + zds[i++] = num; + num = 0; + } + } + goto doadj; + case 2: + return SCM_INUM0; /* quotient is zero */ + case 3: + return SCM_UNDEFINED; /* the division is not exact */ + } + + z = scm_mkbig (nx == ny ? nx + 2 : nx + 1, sgn); + zds = SCM_BDIGITS (z); + if (nx == ny) + zds[nx + 1] = 0; + while (!y[ny - 1]) + ny--; /* in case y came in as a psuedolong */ + if (y[ny - 1] < (SCM_BIGRAD >> 1)) + { /* normalize operands */ + d = SCM_BIGRAD / (y[ny - 1] + 1); + newy = scm_mkbig (ny, 0); + yds = SCM_BDIGITS (newy); + while (j < ny) + { + t2 += (unsigned long) y[j] * d; + yds[j++] = SCM_BIGLO (t2); + t2 = SCM_BIGDN (t2); + } + y = yds; + j = 0; + t2 = 0; + while (j < nx) + { + t2 += (unsigned long) x[j] * d; + zds[j++] = SCM_BIGLO (t2); + t2 = SCM_BIGDN (t2); + } + zds[j] = t2; + } + else + { + zds[j = nx] = 0; + while (j--) + zds[j] = x[j]; + } + j = nx == ny ? nx + 1 : nx; /* dividend needs more digits than divisor */ + do + { /* loop over digits of quotient */ + if (zds[j] == y[ny - 1]) + qhat = SCM_BIGRAD - 1; + else + qhat = (SCM_BIGUP (zds[j]) + zds[j - 1]) / y[ny - 1]; + if (!qhat) + continue; + i = 0; + num = 0; + t2 = 0; + do + { /* multiply and subtract */ + t2 += (unsigned long) y[i] * qhat; + num += zds[j - ny + i] - SCM_BIGLO (t2); + if (num < 0) + { + zds[j - ny + i] = num + SCM_BIGRAD; + num = -1; + } + else + { + zds[j - ny + i] = num; + num = 0; + } + t2 = SCM_BIGDN (t2); + } + while (++i < ny); + num += zds[j - ny + i] - t2; /* borrow from high digit; don't update */ + while (num) + { /* "add back" required */ + i = 0; + num = 0; + qhat--; + do + { + num += (long) zds[j - ny + i] + y[i]; + zds[j - ny + i] = SCM_BIGLO (num); + num = SCM_BIGDN (num); + } + while (++i < ny); + num--; + } + if (modes & 2) + zds[j] = qhat; + } + while (--j >= ny); + switch (modes) + { + case 3: /* check that remainder==0 */ + for (j = ny; j && !zds[j - 1]; --j); + if (j) + return SCM_UNDEFINED; + case 2: /* move quotient down in z */ + j = (nx == ny ? nx + 2 : nx + 1) - ny; + for (i = 0; i < j; i++) + zds[i] = zds[i + ny]; + ny = i; + break; + case 1: /* subtract for scm_modulo */ + i = 0; + num = 0; + j = 0; + do + { + num += y[i] - zds[i]; + j = j | zds[i]; + if (num < 0) + { + zds[i] = num + SCM_BIGRAD; + num = -1; + } + else + { + zds[i] = num; + num = 0; + } + } + while (++i < ny); + if (!j) + return SCM_INUM0; + case 0: /* just normalize remainder */ + if (d) + scm_divbigdig (zds, ny, d); + } + doadj: + for (j = ny; j && !zds[j - 1]; --j); + if (j * SCM_BITSPERDIG <= sizeof (SCM) * SCM_CHAR_BIT) + if (SCM_INUMP (z = scm_big2inum (z, j))) + return z; + return scm_adjbig (z, j); +} +#endif + + + + + +/*** NUMBERS -> STRINGS ***/ +int scm_dblprec; +static const double fx[] = +{ 0.0, 5e-1, 5e-2, 5e-3, 5e-4, 5e-5, + 5e-6, 5e-7, 5e-8, 5e-9, 5e-10, + 5e-11, 5e-12, 5e-13, 5e-14, 5e-15, + 5e-16, 5e-17, 5e-18, 5e-19, 5e-20}; + + + + +static scm_sizet +idbl2str (double f, char *a) +{ + int efmt, dpt, d, i, wp = scm_dblprec; + scm_sizet ch = 0; + int exp = 0; + + if (f == 0.0) + goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ + if (f < 0.0) + { + f = -f; + a[ch++] = '-'; + } + else if (f > 0.0); + else + goto funny; + if (IS_INF (f)) + { + if (ch == 0) + a[ch++] = '+'; + funny: + a[ch++] = '#'; + a[ch++] = '.'; + a[ch++] = '#'; + return ch; + } +#ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from + make-uniform-vector, from causing infinite loops. */ + while (f < 1.0) + { + f *= 10.0; + if (exp-- < DBL_MIN_10_EXP) + goto funny; + } + while (f > 10.0) + { + f *= 0.10; + if (exp++ > DBL_MAX_10_EXP) + goto funny; + } +#else + while (f < 1.0) + { + f *= 10.0; + exp--; + } + while (f > 10.0) + { + f /= 10.0; + exp++; + } +#endif + if (f + fx[wp] >= 10.0) + { + f = 1.0; + exp++; + } + zero: +#ifdef ENGNOT + dpt = (exp + 9999) % 3; + exp -= dpt++; + efmt = 1; +#else + efmt = (exp < -3) || (exp > wp + 2); + if (!efmt) + { + if (exp < 0) + { + a[ch++] = '0'; + a[ch++] = '.'; + dpt = exp; + while (++dpt) + a[ch++] = '0'; + } + else + dpt = exp + 1; + } + else + dpt = 1; +#endif + + do + { + d = f; + f -= d; + a[ch++] = d + '0'; + if (f < fx[wp]) + break; + if (f + fx[wp] >= 1.0) + { + a[ch - 1]++; + break; + } + f *= 10.0; + if (!(--dpt)) + a[ch++] = '.'; + } + while (wp--); + + if (dpt > 0) + { +#ifndef ENGNOT + if ((dpt > 4) && (exp > 6)) + { + d = (a[0] == '-' ? 2 : 1); + for (i = ch++; i > d; i--) + a[i] = a[i - 1]; + a[d] = '.'; + efmt = 1; + } + else +#endif + { + while (--dpt) + a[ch++] = '0'; + a[ch++] = '.'; + } + } + if (a[ch - 1] == '.') + a[ch++] = '0'; /* trailing zero */ + if (efmt && exp) + { + a[ch++] = 'e'; + if (exp < 0) + { + exp = -exp; + a[ch++] = '-'; + } + for (i = 10; i <= exp; i *= 10); + for (i /= 10; i; i /= 10) + { + a[ch++] = exp / i + '0'; + exp %= i; + } + } + return ch; +} + + +static scm_sizet +iflo2str (SCM flt, char *str) +{ + scm_sizet i; + if (SCM_SLOPPY_REALP (flt)) + i = idbl2str (SCM_REAL_VALUE (flt), str); + else + { + i = idbl2str (SCM_COMPLEX_REAL (flt), str); + if (SCM_COMPLEX_IMAG (flt) != 0.0) + { + if (0 <= SCM_COMPLEX_IMAG (flt)) + str[i++] = '+'; + i += idbl2str (SCM_COMPLEX_IMAG (flt), &str[i]); + str[i++] = 'i'; + } + } + return i; +} + +/* convert a long to a string (unterminated). returns the number of + characters in the result. + rad is output base + p is destination: worst case (base 2) is SCM_INTBUFLEN */ +scm_sizet +scm_iint2str (long num, int rad, char *p) +{ + scm_sizet j = 1; + scm_sizet i; + unsigned long n = (num < 0) ? -num : num; + + for (n /= rad; n > 0; n /= rad) + j++; + + i = j; + if (num < 0) + { + *p++ = '-'; + j++; + n = -num; + } + else + n = num; + while (i--) + { + int d = n % rad; + + n /= rad; + p[i] = d + ((d < 10) ? '0' : 'a' - 10); + } + return j; +} + + +#ifdef SCM_BIGDIG + +static SCM +big2str (SCM b, unsigned int radix) +{ + SCM t = scm_copybig (b, 0); /* sign of temp doesn't matter */ + register SCM_BIGDIG *ds = SCM_BDIGITS (t); + scm_sizet i = SCM_NUMDIGS (t); + scm_sizet j = radix == 16 ? (SCM_BITSPERDIG * i) / 4 + 2 + : radix >= 10 ? (SCM_BITSPERDIG * i * 241L) / 800 + 2 + : (SCM_BITSPERDIG * i) + 2; + scm_sizet k = 0; + scm_sizet radct = 0; + SCM_BIGDIG radpow = 1, radmod = 0; + SCM ss = scm_makstr ((long) j, 0); + char *s = SCM_STRING_CHARS (ss), c; + while ((long) radpow * radix < SCM_BIGRAD) + { + radpow *= radix; + radct++; + } + while ((i || radmod) && j) + { + if (k == 0) + { + radmod = (SCM_BIGDIG) scm_divbigdig (ds, i, radpow); + k = radct; + if (!ds[i - 1]) + i--; + } + c = radmod % radix; + radmod /= radix; + k--; + s[--j] = c < 10 ? c + '0' : c + 'a' - 10; + } + + if (SCM_BIGSIGN (b)) + s[--j] = '-'; + + if (j > 0) + { + /* The pre-reserved string length was too large. */ + unsigned long int length = SCM_STRING_LENGTH (ss); + ss = scm_substring (ss, SCM_MAKINUM (j), SCM_MAKINUM (length)); + } + + return scm_return_first (ss, t); +} +#endif + + +SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, + (SCM n, SCM radix), + "Return a string holding the external representation of the\n" + "number @var{n} in the given @var{radix}. If @var{n} is\n" + "inexact, a radix of 10 will be used.") +#define FUNC_NAME s_scm_number_to_string +{ + int base; + + if (SCM_UNBNDP (radix)) { + base = 10; + } else { + SCM_VALIDATE_INUM (2, radix); + base = SCM_INUM (radix); + SCM_ASSERT_RANGE (2, radix, base >= 2); + } + + if (SCM_INUMP (n)) { + char num_buf [SCM_INTBUFLEN]; + scm_sizet length = scm_iint2str (SCM_INUM (n), base, num_buf); + return scm_makfromstr (num_buf, length, 0); + } else if (SCM_BIGP (n)) { + return big2str (n, (unsigned int) base); + } else if (SCM_INEXACTP (n)) { + char num_buf [SCM_FLOBUFLEN]; + return scm_makfromstr (num_buf, iflo2str (n, num_buf), 0); + } else { + SCM_WRONG_TYPE_ARG (1, n); + } +} +#undef FUNC_NAME + + +/* These print routines are stubbed here so that scm_repl.c doesn't need + SCM_BIGDIG conditionals */ + +int +scm_print_real (SCM sexp, SCM port, scm_print_state *pstate) +{ + char num_buf[SCM_FLOBUFLEN]; + scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port); + return !0; +} + +int +scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate) +{ + char num_buf[SCM_FLOBUFLEN]; + scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port); + return !0; +} + +int +scm_bigprint (SCM exp, SCM port, scm_print_state *pstate) +{ +#ifdef SCM_BIGDIG + exp = big2str (exp, (unsigned int) 10); + scm_lfwrite (SCM_STRING_CHARS (exp), (scm_sizet) SCM_STRING_LENGTH (exp), port); +#else + scm_ipruk ("bignum", exp, port); +#endif + return !0; +} +/*** END nums->strs ***/ + +/*** STRINGS -> NUMBERS ***/ + +static SCM +scm_small_istr2int (char *str, long len, long radix) +{ + register long n = 0, ln; + register int c; + register int i = 0; + int lead_neg = 0; + if (0 >= len) + return SCM_BOOL_F; /* zero scm_length */ + switch (*str) + { /* leading sign */ + case '-': + lead_neg = 1; + case '+': + if (++i == len) + return SCM_BOOL_F; /* bad if lone `+' or `-' */ + } + + do + { + switch (c = str[i++]) + { + case DIGITS: + c = c - '0'; + goto accumulate; + case 'A': + case 'B': + case 'C': + case 'D': + case 'E': + case 'F': + c = c - 'A' + 10; + goto accumulate; + case 'a': + case 'b': + case 'c': + case 'd': + case 'e': + case 'f': + c = c - 'a' + 10; + accumulate: + if (c >= radix) + return SCM_BOOL_F; /* bad digit for radix */ + ln = n; + n = n * radix - c; + /* Negation is a workaround for HP700 cc bug */ + if (n > ln || (-n > -SCM_MOST_NEGATIVE_FIXNUM)) + goto ovfl; + break; + default: + return SCM_BOOL_F; /* not a digit */ + } + } + while (i < len); + if (!lead_neg) + if ((n = -n) > SCM_MOST_POSITIVE_FIXNUM) + goto ovfl; + return SCM_MAKINUM (n); + ovfl: /* overflow scheme integer */ + return SCM_BOOL_F; +} + + + +SCM +scm_istr2int (char *str, long len, long radix) +{ + scm_sizet j; + register scm_sizet k, blen = 1; + scm_sizet i = 0; + int c; + SCM res; + register SCM_BIGDIG *ds; + register unsigned long t2; + + if (0 >= len) + return SCM_BOOL_F; /* zero scm_length */ + + /* Short numbers we parse directly into an int, to avoid the overhead + of creating a bignum. */ + if (len < 6) + return scm_small_istr2int (str, len, radix); + + if (16 == radix) + j = 1 + (4 * len * sizeof (char)) / (SCM_BITSPERDIG); + else if (10 <= radix) + j = 1 + (84 * len * sizeof (char)) / (SCM_BITSPERDIG * 25); + else + j = 1 + (len * sizeof (char)) / (SCM_BITSPERDIG); + switch (str[0]) + { /* leading sign */ + case '-': + case '+': + if (++i == (unsigned) len) + return SCM_BOOL_F; /* bad if lone `+' or `-' */ + } + res = scm_mkbig (j, '-' == str[0]); + ds = SCM_BDIGITS (res); + for (k = j; k--;) + ds[k] = 0; + do + { + switch (c = str[i++]) + { + case DIGITS: + c = c - '0'; + goto accumulate; + case 'A': + case 'B': + case 'C': + case 'D': + case 'E': + case 'F': + c = c - 'A' + 10; + goto accumulate; + case 'a': + case 'b': + case 'c': + case 'd': + case 'e': + case 'f': + c = c - 'a' + 10; + accumulate: + if (c >= radix) + return SCM_BOOL_F; /* bad digit for radix */ + k = 0; + t2 = c; + moretodo: + while (k < blen) + { +/* printf ("k = %d, blen = %d, t2 = %ld, ds[k] = %d\n", k, blen, t2, ds[k]); */ + t2 += ds[k] * radix; + ds[k++] = SCM_BIGLO (t2); + t2 = SCM_BIGDN (t2); + } + if (blen > j) + scm_num_overflow ("bignum"); + if (t2) + { + blen++; + goto moretodo; + } + break; + default: + return SCM_BOOL_F; /* not a digit */ + } + } + while (i < (unsigned) len); + if (blen * SCM_BITSPERDIG / SCM_CHAR_BIT <= sizeof (SCM)) + if (SCM_INUMP (res = scm_big2inum (res, blen))) + return res; + if (j == blen) + return res; + return scm_adjbig (res, blen); +} + +SCM +scm_istr2flo (char *str, long len, long radix) +{ + register int c, i = 0; + double lead_sgn; + double res = 0.0, tmp = 0.0; + int flg = 0; + int point = 0; + SCM second; + + if (i >= len) + return SCM_BOOL_F; /* zero scm_length */ + + switch (*str) + { /* leading sign */ + case '-': + lead_sgn = -1.0; + i++; + break; + case '+': + lead_sgn = 1.0; + i++; + break; + default: + lead_sgn = 0.0; + } + if (i == len) + return SCM_BOOL_F; /* bad if lone `+' or `-' */ + + if (str[i] == 'i' || str[i] == 'I') + { /* handle `+i' and `-i' */ + if (lead_sgn == 0.0) + return SCM_BOOL_F; /* must have leading sign */ + if (++i < len) + return SCM_BOOL_F; /* `i' not last character */ + return scm_make_complex (0.0, lead_sgn); + } + do + { /* check initial digits */ + switch (c = str[i]) + { + case DIGITS: + c = c - '0'; + goto accum1; + case 'D': + case 'E': + case 'F': + if (radix == 10) + goto out1; /* must be exponent */ + case 'A': + case 'B': + case 'C': + c = c - 'A' + 10; + goto accum1; + case 'd': + case 'e': + case 'f': + if (radix == 10) + goto out1; + case 'a': + case 'b': + case 'c': + c = c - 'a' + 10; + accum1: + if (c >= radix) + return SCM_BOOL_F; /* bad digit for radix */ + res = res * radix + c; + flg = 1; /* res is valid */ + break; + default: + goto out1; + } + } + while (++i < len); + out1: + + /* if true, then we did see a digit above, and res is valid */ + if (i == len) + goto done; + + /* By here, must have seen a digit, + or must have next char be a `.' with radix==10 */ + if (!flg) + if (!(str[i] == '.' && radix == 10)) + return SCM_BOOL_F; + + while (str[i] == '#') + { /* optional sharps */ + res *= radix; + if (++i == len) + goto done; + } + + if (str[i] == '/') + { + while (++i < len) + { + switch (c = str[i]) + { + case DIGITS: + c = c - '0'; + goto accum2; + case 'A': + case 'B': + case 'C': + case 'D': + case 'E': + case 'F': + c = c - 'A' + 10; + goto accum2; + case 'a': + case 'b': + case 'c': + case 'd': + case 'e': + case 'f': + c = c - 'a' + 10; + accum2: + if (c >= radix) + return SCM_BOOL_F; + tmp = tmp * radix + c; + break; + default: + goto out2; + } + } + out2: + if (tmp == 0.0) + return SCM_BOOL_F; /* `slash zero' not allowed */ + if (i < len) + while (str[i] == '#') + { /* optional sharps */ + tmp *= radix; + if (++i == len) + break; + } + res /= tmp; + goto done; + } + + if (str[i] == '.') + { /* decimal point notation */ + if (radix != 10) + return SCM_BOOL_F; /* must be radix 10 */ + while (++i < len) + { + switch (c = str[i]) + { + case DIGITS: + point--; + res = res * 10.0 + c - '0'; + flg = 1; + break; + default: + goto out3; + } + } + out3: + if (!flg) + return SCM_BOOL_F; /* no digits before or after decimal point */ + if (i == len) + goto adjust; + while (str[i] == '#') + { /* ignore remaining sharps */ + if (++i == len) + goto adjust; + } + } + + switch (str[i]) + { /* exponent */ + case 'd': + case 'D': + case 'e': + case 'E': + case 'f': + case 'F': + case 'l': + case 'L': + case 's': + case 'S': + { + int expsgn = 1, expon = 0; + if (radix != 10) + return SCM_BOOL_F; /* only in radix 10 */ + if (++i == len) + return SCM_BOOL_F; /* bad exponent */ + switch (str[i]) + { + case '-': + expsgn = (-1); + case '+': + if (++i == len) + return SCM_BOOL_F; /* bad exponent */ + } + if (str[i] < '0' || str[i] > '9') + return SCM_BOOL_F; /* bad exponent */ + do + { + switch (c = str[i]) + { + case DIGITS: + expon = expon * 10 + c - '0'; + if (expon > SCM_MAXEXP) + scm_out_of_range ("string->number", SCM_MAKINUM (expon)); + break; + default: + goto out4; + } + } + while (++i < len); + out4: + point += expsgn * expon; + } + } + + adjust: + if (point >= 0) + while (point--) + res *= 10.0; + else +#ifdef _UNICOS + while (point++) + res *= 0.1; +#else + while (point++) + res /= 10.0; +#endif + + done: + /* at this point, we have a legitimate floating point result */ + if (lead_sgn == -1.0) + res = -res; + if (i == len) + return scm_make_real (res); + + if (str[i] == 'i' || str[i] == 'I') + { /* pure imaginary number */ + if (lead_sgn == 0.0) + return SCM_BOOL_F; /* must have leading sign */ + if (++i < len) + return SCM_BOOL_F; /* `i' not last character */ + return scm_make_complex (0.0, res); + } + + switch (str[i++]) + { + case '-': + lead_sgn = -1.0; + break; + case '+': + lead_sgn = 1.0; + break; + case '@': + { /* polar input for complex number */ + /* get a `real' for scm_angle */ + second = scm_istr2flo (&str[i], (long) (len - i), radix); + if (!SCM_SLOPPY_INEXACTP (second)) + return SCM_BOOL_F; /* not `real' */ + if (SCM_SLOPPY_COMPLEXP (second)) + return SCM_BOOL_F; /* not `real' */ + tmp = SCM_REAL_VALUE (second); + return scm_make_complex (res * cos (tmp), res * sin (tmp)); + } + default: + return SCM_BOOL_F; + } + + /* at this point, last char must be `i' */ + if (str[len - 1] != 'i' && str[len - 1] != 'I') + return SCM_BOOL_F; + /* handles `x+i' and `x-i' */ + if (i == (len - 1)) + return scm_make_complex (res, lead_sgn); + /* get a `ureal' for complex part */ + second = scm_istr2flo (&str[i], (long) ((len - i) - 1), radix); + if (!SCM_INEXACTP (second)) + return SCM_BOOL_F; /* not `ureal' */ + if (SCM_SLOPPY_COMPLEXP (second)) + return SCM_BOOL_F; /* not `ureal' */ + tmp = SCM_REAL_VALUE (second); + if (tmp < 0.0) + return SCM_BOOL_F; /* not `ureal' */ + return scm_make_complex (res, (lead_sgn * tmp)); +} + + + +SCM +scm_istring2number (char *str, long len, long radix) +{ + int i = 0; + char ex = 0; + char ex_p = 0, rx_p = 0; /* Only allow 1 exactness and 1 radix prefix */ + SCM res; + if (len == 1) + if (*str == '+' || *str == '-') /* Catches lone `+' and `-' for speed */ + return SCM_BOOL_F; + + while ((len - i) >= 2 && str[i] == '#' && ++i) + switch (str[i++]) + { + case 'b': + case 'B': + if (rx_p++) + return SCM_BOOL_F; + radix = 2; + break; + case 'o': + case 'O': + if (rx_p++) + return SCM_BOOL_F; + radix = 8; + break; + case 'd': + case 'D': + if (rx_p++) + return SCM_BOOL_F; + radix = 10; + break; + case 'x': + case 'X': + if (rx_p++) + return SCM_BOOL_F; + radix = 16; + break; + case 'i': + case 'I': + if (ex_p++) + return SCM_BOOL_F; + ex = 2; + break; + case 'e': + case 'E': + if (ex_p++) + return SCM_BOOL_F; + ex = 1; + break; + default: + return SCM_BOOL_F; + } + + switch (ex) + { + case 1: + return scm_istr2int (&str[i], len - i, radix); + case 0: + res = scm_istr2int (&str[i], len - i, radix); + if (SCM_NFALSEP (res)) + return res; + case 2: + return scm_istr2flo (&str[i], len - i, radix); + } + return SCM_BOOL_F; +} + + +SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, + (SCM string, SCM radix), + "Returns a number of the maximally precise representation\n" + "expressed by the given @var{string}. @var{radix} must be an\n" + "exact integer, either 2, 8, 10, or 16. If supplied, @var{RADIX}\n" + "is a default radix that may be overridden by an explicit\n" + "radix prefix in @var{string} (e.g. \"#o177\"). If @var{radix}\n" + "is not supplied, then the default radix is 10. If string is\n" + "not a syntactically valid notation for a number, then\n" + "@code{string->number} returns @code{#f}. (r5rs)") +#define FUNC_NAME s_scm_string_to_number +{ + SCM answer; + int base; + SCM_VALIDATE_STRING (1, string); + SCM_VALIDATE_INUM_MIN_DEF_COPY (2,radix,2,10,base); + answer = scm_istring2number (SCM_STRING_CHARS (string), + SCM_STRING_LENGTH (string), + base); + return scm_return_first (answer, string); +} +#undef FUNC_NAME +/*** END strs->nums ***/ + + +SCM +scm_make_real (double x) +{ + SCM z; + SCM_NEWCELL2 (z); + SCM_SET_CELL_TYPE (z, scm_tc16_real); + SCM_REAL_VALUE (z) = x; + return z; +} + + +SCM +scm_make_complex (double x, double y) +{ + if (y == 0.0) { + return scm_make_real (x); + } else { + SCM z; + SCM_NEWSMOB (z, scm_tc16_complex, scm_must_malloc (2L * sizeof (double), "complex")); + SCM_COMPLEX_REAL (z) = x; + SCM_COMPLEX_IMAG (z) = y; + return z; + } +} + + +SCM +scm_bigequal (SCM x, SCM y) +{ +#ifdef SCM_BIGDIG + if (0 == scm_bigcomp (x, y)) + return SCM_BOOL_T; +#endif + return SCM_BOOL_F; +} + +SCM +scm_real_equalp (SCM x, SCM y) +{ + return SCM_BOOL (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); +} + +SCM +scm_complex_equalp (SCM x, SCM y) +{ + return SCM_BOOL (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y) + && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)); +} + + + +SCM_REGISTER_PROC (s_number_p, "number?", 1, 0, 0, scm_number_p); +/* "Return @code{#t} if @var{x} is a number, @code{#f}\n" + * "else. Note that the sets of complex, real, rational and\n" + * "integer values form subsets of the set of numbers, i. e. the\n" + * "predicate will be fulfilled for any number." + */ +SCM_DEFINE (scm_number_p, "complex?", 1, 0, 0, + (SCM x), + "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" + "else. Note that the sets of real, rational and integer\n" + "values form subsets of the set of complex numbers, i. e. the\n" + "predicate will also be fulfilled if @var{x} is a real,\n" + "rational or integer number.") +#define FUNC_NAME s_scm_number_p +{ + return SCM_BOOL (SCM_NUMBERP (x)); +} +#undef FUNC_NAME + + +SCM_REGISTER_PROC (s_real_p, "real?", 1, 0, 0, scm_real_p); +/* "Return @code{#t} if @var{x} is a real number, @code{#f} else.\n" + * "Note that the sets of integer and rational values form a subset\n" + * "of the set of real numbers, i. e. the predicate will also\n" + * "be fulfilled if @var{x} is an integer or a rational number." + */ +SCM_DEFINE (scm_real_p, "rational?", 1, 0, 0, + (SCM x), + "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" + "else. Note that the set of integer values forms a subset of\n" + "the set of rational numbers, i. e. the predicate will also be\n" + "fulfilled if @var{x} is an integer number. Real numbers\n" + "will also satisfy this predicate, because of their limited\n" + "precision.") +#define FUNC_NAME s_scm_real_p +{ + if (SCM_INUMP (x)) { + return SCM_BOOL_T; + } else if (SCM_IMP (x)) { + return SCM_BOOL_F; + } else if (SCM_SLOPPY_REALP (x)) { + return SCM_BOOL_T; + } else if (SCM_BIGP (x)) { + return SCM_BOOL_T; + } else { + return SCM_BOOL_F; + } +} +#undef FUNC_NAME + + +SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, + (SCM x), + "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" + "else.") +#define FUNC_NAME s_scm_integer_p +{ + double r; + if (SCM_INUMP (x)) + return SCM_BOOL_T; + if (SCM_IMP (x)) + return SCM_BOOL_F; + if (SCM_BIGP (x)) + return SCM_BOOL_T; + if (!SCM_SLOPPY_INEXACTP (x)) + return SCM_BOOL_F; + if (SCM_SLOPPY_COMPLEXP (x)) + return SCM_BOOL_F; + r = SCM_REAL_VALUE (x); + if (r == floor (r)) + return SCM_BOOL_T; + return SCM_BOOL_F; +} +#undef FUNC_NAME + + +SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, + (SCM x), + "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" + "else.") +#define FUNC_NAME s_scm_inexact_p +{ + return SCM_BOOL (SCM_INEXACTP (x)); +} +#undef FUNC_NAME + + +SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p); +/* "Return @code{#t} if all parameters are numerically equal." */ +SCM +scm_num_eq_p (SCM x, SCM y) +{ + if (SCM_INUMP (x)) { + long xx = SCM_INUM (x); + if (SCM_INUMP (y)) { + long yy = SCM_INUM (y); + return SCM_BOOL (xx == yy); + } else if (SCM_BIGP (y)) { + return SCM_BOOL_F; + } else if (SCM_REALP (y)) { + return SCM_BOOL ((double) xx == SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + return SCM_BOOL (((double) xx == SCM_COMPLEX_REAL (y)) + && (0.0 == SCM_COMPLEX_IMAG (y))); + } else { + SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); + } + } else if (SCM_BIGP (x)) { + if (SCM_INUMP (y)) { + return SCM_BOOL_F; + } else if (SCM_BIGP (y)) { + return SCM_BOOL (0 == scm_bigcomp (x, y)); + } else if (SCM_REALP (y)) { + return SCM_BOOL (scm_big2dbl (x) == SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + return SCM_BOOL ((scm_big2dbl (x) == SCM_COMPLEX_REAL (y)) + && (0.0 == SCM_COMPLEX_IMAG (y))); + } else { + SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); + } + } else if (SCM_REALP (x)) { + if (SCM_INUMP (y)) { + return SCM_BOOL (SCM_REAL_VALUE (x) == (double) SCM_INUM (y)); + } else if (SCM_BIGP (y)) { + return SCM_BOOL (SCM_REAL_VALUE (x) == scm_big2dbl (y)); + } else if (SCM_REALP (y)) { + return SCM_BOOL (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + return SCM_BOOL ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) + && (0.0 == SCM_COMPLEX_IMAG (y))); + } else { + SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); + } + } else if (SCM_COMPLEXP (x)) { + if (SCM_INUMP (y)) { + return SCM_BOOL ((SCM_COMPLEX_REAL (x) == (double) SCM_INUM (y)) + && (SCM_COMPLEX_IMAG (x) == 0.0)); + } else if (SCM_BIGP (y)) { + return SCM_BOOL ((SCM_COMPLEX_REAL (x) == scm_big2dbl (y)) + && (SCM_COMPLEX_IMAG (x) == 0.0)); + } else if (SCM_REALP (y)) { + return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) + && (SCM_COMPLEX_IMAG (x) == 0.0)); + } else if (SCM_COMPLEXP (y)) { + return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) + && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); + } else { + SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); + } + } else { + SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p); + } +} + + +SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p); +/* "Return @code{#t} if the list of parameters is monotonically\n" + * "increasing." + */ +SCM +scm_less_p (SCM x, SCM y) +{ + if (SCM_INUMP (x)) { + long xx = SCM_INUM (x); + if (SCM_INUMP (y)) { + long yy = SCM_INUM (y); + return SCM_BOOL (xx < yy); + } else if (SCM_BIGP (y)) { + return SCM_BOOL (!SCM_BIGSIGN (y)); + } else if (SCM_REALP (y)) { + return SCM_BOOL ((double) xx < SCM_REAL_VALUE (y)); + } else { + SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); + } + } else if (SCM_BIGP (x)) { + if (SCM_INUMP (y)) { + return SCM_BOOL (SCM_BIGSIGN (x)); + } else if (SCM_BIGP (y)) { + return SCM_BOOL (1 == scm_bigcomp (x, y)); + } else if (SCM_REALP (y)) { + return SCM_BOOL (scm_big2dbl (x) < SCM_REAL_VALUE (y)); + } else { + SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); + } + } else if (SCM_REALP (x)) { + if (SCM_INUMP (y)) { + return SCM_BOOL (SCM_REAL_VALUE (x) < (double) SCM_INUM (y)); + } else if (SCM_BIGP (y)) { + return SCM_BOOL (SCM_REAL_VALUE (x) < scm_big2dbl (y)); + } else if (SCM_REALP (y)) { + return SCM_BOOL (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); + } else { + SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); + } + } else { + SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p); + } +} + + +SCM_GPROC1 (s_scm_gr_p, ">", scm_tc7_rpsubr, scm_gr_p, g_gr_p); +/* "Return @code{#t} if the list of parameters is monotonically\n" + * "decreasing." + */ +#define FUNC_NAME s_scm_gr_p +SCM +scm_gr_p (SCM x, SCM y) +{ + if (!SCM_NUMBERP (x)) + SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG1, FUNC_NAME); + else if (!SCM_NUMBERP (y)) + SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG2, FUNC_NAME); + else + return scm_less_p (y, x); +} +#undef FUNC_NAME + + +SCM_GPROC1 (s_scm_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p, g_leq_p); +/* "Return @code{#t} if the list of parameters is monotonically\n" + * "non-decreasing." + */ +#define FUNC_NAME s_scm_leq_p +SCM +scm_leq_p (SCM x, SCM y) +{ + if (!SCM_NUMBERP (x)) + SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG1, FUNC_NAME); + else if (!SCM_NUMBERP (y)) + SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG2, FUNC_NAME); + else + return SCM_BOOL_NOT (scm_less_p (y, x)); +} +#undef FUNC_NAME + + +SCM_GPROC1 (s_scm_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p, g_geq_p); +/* "Return @code{#t} if the list of parameters is monotonically\n" + * "non-increasing." + */ +#define FUNC_NAME s_scm_geq_p +SCM +scm_geq_p (SCM x, SCM y) +{ + if (!SCM_NUMBERP (x)) + SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG1, FUNC_NAME); + else if (!SCM_NUMBERP (y)) + SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG2, FUNC_NAME); + else + return SCM_BOOL_NOT (scm_less_p (x, y)); +} +#undef FUNC_NAME + + +SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); +/* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" + * "zero." + */ +SCM +scm_zero_p (SCM z) +{ + if (SCM_INUMP (z)) { + return SCM_BOOL (SCM_EQ_P (z, SCM_INUM0)); + } else if (SCM_BIGP (z)) { + return SCM_BOOL_F; + } else if (SCM_REALP (z)) { + return SCM_BOOL (SCM_REAL_VALUE (z) == 0.0); + } else if (SCM_COMPLEXP (z)) { + return SCM_BOOL (SCM_COMPLEX_REAL (z) == 0.0 + && SCM_COMPLEX_IMAG (z) == 0.0); + } else { + SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); + } +} + + +SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); +/* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" + * "zero." + */ +SCM +scm_positive_p (SCM x) +{ + if (SCM_INUMP (x)) { + return SCM_BOOL (SCM_INUM (x) > 0); + } else if (SCM_BIGP (x)) { + return SCM_BOOL (!SCM_BIGSIGN (x)); + } else if (SCM_REALP (x)) { + return SCM_BOOL(SCM_REAL_VALUE (x) > 0.0); + } else { + SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); + } +} + + +SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); +/* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" + * "zero." + */ +SCM +scm_negative_p (SCM x) +{ + if (SCM_INUMP (x)) { + return SCM_BOOL (SCM_INUM (x) < 0); + } else if (SCM_BIGP (x)) { + return SCM_BOOL (SCM_BIGSIGN (x)); + } else if (SCM_REALP (x)) { + return SCM_BOOL(SCM_REAL_VALUE (x) < 0.0); + } else { + SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); + } +} + + +SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max); +/* "Return the maximum of all parameter values." + */ +SCM +scm_max (SCM x, SCM y) +{ + if (SCM_UNBNDP (y)) { + if (SCM_UNBNDP (x)) { + SCM_WTA_DISPATCH_0 (g_max, x, SCM_ARG1, s_max); + } else if (SCM_NUMBERP (x)) { + return x; + } else { + SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); + } + } + + if (SCM_INUMP (x)) { + long xx = SCM_INUM (x); + if (SCM_INUMP (y)) { + long yy = SCM_INUM (y); + return (xx < yy) ? y : x; + } else if (SCM_BIGP (y)) { + return SCM_BIGSIGN (y) ? x : y; + } else if (SCM_REALP (y)) { + double z = xx; + return (z <= SCM_REAL_VALUE (y)) ? y : scm_make_real (z); + } else { + SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); + } + } else if (SCM_BIGP (x)) { + if (SCM_INUMP (y)) { + return SCM_BIGSIGN (x) ? y : x; + } else if (SCM_BIGP (y)) { + return (1 == scm_bigcomp (x, y)) ? y : x; + } else if (SCM_REALP (y)) { + double z = scm_big2dbl (x); + return (z <= SCM_REAL_VALUE (y)) ? y : scm_make_real (z); + } else { + SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); + } + } else if (SCM_REALP (x)) { + if (SCM_INUMP (y)) { + double z = SCM_INUM (y); + return (SCM_REAL_VALUE (x) < z) ? scm_make_real (z) : x; + } else if (SCM_BIGP (y)) { + double z = scm_big2dbl (y); + return (SCM_REAL_VALUE (x) < z) ? scm_make_real (z) : x; + } else if (SCM_REALP (y)) { + return (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)) ? y : x; + } else { + SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); + } + } else { + SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); + } +} + + +SCM_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min); +/* "Return the minium of all parameter values." + */ +SCM +scm_min (SCM x, SCM y) +{ + if (SCM_UNBNDP (y)) { + if (SCM_UNBNDP (x)) { + SCM_WTA_DISPATCH_0 (g_min, x, SCM_ARG1, s_min); + } else if (SCM_NUMBERP (x)) { + return x; + } else { + SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); + } + } + + if (SCM_INUMP (x)) { + long xx = SCM_INUM (x); + if (SCM_INUMP (y)) { + long yy = SCM_INUM (y); + return (xx < yy) ? x : y; + } else if (SCM_BIGP (y)) { + return SCM_BIGSIGN (y) ? y : x; + } else if (SCM_REALP (y)) { + double z = xx; + return (z < SCM_REAL_VALUE (y)) ? scm_make_real (z) : y; + } else { + SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); + } + } else if (SCM_BIGP (x)) { + if (SCM_INUMP (y)) { + return SCM_BIGSIGN (x) ? x : y; + } else if (SCM_BIGP (y)) { + return (-1 == scm_bigcomp (x, y)) ? y : x; + } else if (SCM_REALP (y)) { + double z = scm_big2dbl (x); + return (z < SCM_REAL_VALUE (y)) ? scm_make_real (z) : y; + } else { + SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); + } + } else if (SCM_REALP (x)) { + if (SCM_INUMP (y)) { + double z = SCM_INUM (y); + return (SCM_REAL_VALUE (x) <= z) ? x : scm_make_real (z); + } else if (SCM_BIGP (y)) { + double z = scm_big2dbl (y); + return (SCM_REAL_VALUE (x) <= z) ? x : scm_make_real (z); + } else if (SCM_REALP (y)) { + return (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)) ? x : y; + } else { + SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); + } + } else { + SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); + } +} + + +SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum); +/* "Return the sum of all parameter values. Return 0 if called without\n" + * "any parameters." + */ +SCM +scm_sum (SCM x, SCM y) +{ + if (SCM_UNBNDP (y)) { + if (SCM_UNBNDP (x)) { + return SCM_INUM0; + } else if (SCM_NUMBERP (x)) { + return x; + } else { + SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); + } + } + + if (SCM_INUMP (x)) { + long int xx = SCM_INUM (x); + if (SCM_INUMP (y)) { + long int yy = SCM_INUM (y); + long int z = xx + yy; + if (SCM_FIXABLE (z)) { + return SCM_MAKINUM (z); + } else { +#ifdef SCM_BIGDIG + return scm_long2big (z); +#else /* SCM_BIGDIG */ + return scm_make_real ((double) z); +#endif /* SCM_BIGDIG */ + } + } else if (SCM_BIGP (y)) { + intbig: + { + long int xx = SCM_INUM (x); +#ifndef SCM_DIGSTOOBIG + long z = scm_pseudolong (xx); + return scm_addbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, + (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, 0); +#else /* SCM_DIGSTOOBIG */ + SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; + scm_longdigs (xx, zdigs); + return scm_addbig (zdigs, SCM_DIGSPERLONG, + (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, 0); +#endif /* SCM_DIGSTOOBIG */ + } + } else if (SCM_REALP (y)) { + return scm_make_real (xx + SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + return scm_make_complex (xx + SCM_COMPLEX_REAL (y), + SCM_COMPLEX_IMAG (y)); + } else { + SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); + } + } else if (SCM_BIGP (x)) { + if (SCM_INUMP (y)) { + SCM_SWAP (x, y); + goto intbig; + } else if (SCM_BIGP (y)) { + if (SCM_NUMDIGS (x) > SCM_NUMDIGS (y)) { + SCM_SWAP (x, y); + } + return scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), + SCM_BIGSIGN (x), y, 0); + } else if (SCM_REALP (y)) { + return scm_make_real (scm_big2dbl (x) + SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + return scm_make_complex (scm_big2dbl (x) + SCM_COMPLEX_REAL (y), + SCM_COMPLEX_IMAG (y)); + } else { + SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); + } + } else if (SCM_REALP (x)) { + if (SCM_INUMP (y)) { + return scm_make_real (SCM_REAL_VALUE (x) + SCM_INUM (y)); + } else if (SCM_BIGP (y)) { + return scm_make_real (SCM_REAL_VALUE (x) + scm_big2dbl (y)); + } else if (SCM_REALP (y)) { + return scm_make_real (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + return scm_make_complex (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), + SCM_COMPLEX_IMAG (y)); + } else { + SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); + } + } else if (SCM_COMPLEXP (x)) { + if (SCM_INUMP (y)) { + return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_INUM (y), + SCM_COMPLEX_IMAG (x)); + } else if (SCM_BIGP (y)) { + return scm_make_complex (SCM_COMPLEX_REAL (x) + scm_big2dbl (y), + SCM_COMPLEX_IMAG (x)); + } else if (SCM_REALP (y)) { + return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), + SCM_COMPLEX_IMAG (x)); + } else if (SCM_COMPLEXP (y)) { + return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), + SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); + } else { + SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); + } + } else { + SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); + } +} + + +SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference); +/* "If called without arguments, 0 is returned. Otherwise the sum of\n" + * "all but the first argument are subtracted from the first\n" + * "argument." + */ +SCM +scm_difference (SCM x, SCM y) +{ + if (SCM_UNBNDP (y)) { + if (SCM_INUMP (x)) { + long xx = -SCM_INUM (x); + if (SCM_FIXABLE (xx)) { + return SCM_MAKINUM (xx); + } else { +#ifdef SCM_BIGDIG + return scm_long2big (xx); +#else + return scm_make_real ((double) xx); +#endif + } + } else if (SCM_BIGP (x)) { + SCM z = scm_copybig (x, !SCM_BIGSIGN (x)); + unsigned int digs = SCM_NUMDIGS (z); + unsigned int size = digs * SCM_BITSPERDIG / SCM_CHAR_BIT; + return size <= sizeof (SCM) ? scm_big2inum (z, digs) : z; + } else if (SCM_REALP (x)) { + return scm_make_real (-SCM_REAL_VALUE (x)); + } else if (SCM_COMPLEXP (x)) { + return scm_make_complex (-SCM_COMPLEX_REAL (x), -SCM_COMPLEX_IMAG (x)); + } else { + SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); + } + } + + if (SCM_INUMP (x)) { + long int xx = SCM_INUM (x); + if (SCM_INUMP (y)) { + long int yy = SCM_INUM (y); + long int z = xx - yy; + if (SCM_FIXABLE (z)) { + return SCM_MAKINUM (z); + } else { +#ifdef SCM_BIGDIG + return scm_long2big (z); +#else + return scm_make_real ((double) z); +#endif + } + } else if (SCM_BIGP (y)) { +#ifndef SCM_DIGSTOOBIG + long z = scm_pseudolong (xx); + return scm_addbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, + (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, SCM_BIGSIGNFLAG); +#else + SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; + scm_longdigs (xx, zdigs); + return scm_addbig (zdigs, SCM_DIGSPERLONG, + (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, SCM_BIGSIGNFLAG); +#endif + } else if (SCM_REALP (y)) { + return scm_make_real (xx - SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + return scm_make_complex (xx - SCM_COMPLEX_REAL (y), + -SCM_COMPLEX_IMAG (y)); + } else { + SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); + } + } else if (SCM_BIGP (x)) { + if (SCM_INUMP (y)) { + long int yy = SCM_INUM (y); +#ifndef SCM_DIGSTOOBIG + long z = scm_pseudolong (yy); + return scm_addbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, + (yy < 0) ? 0 : SCM_BIGSIGNFLAG, x, 0); +#else + SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; + scm_longdigs (yy, zdigs); + return scm_addbig (zdigs, SCM_DIGSPERLONG, + (yy < 0) ? 0 : SCM_BIGSIGNFLAG, x, 0); +#endif + } else if (SCM_BIGP (y)) { + return (SCM_NUMDIGS (x) < SCM_NUMDIGS (y)) + ? scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), + SCM_BIGSIGN (x), y, SCM_BIGSIGNFLAG) + : scm_addbig (SCM_BDIGITS (y), SCM_NUMDIGS (y), + SCM_BIGSIGN (y) ^ SCM_BIGSIGNFLAG, x, 0); + } else if (SCM_REALP (y)) { + return scm_make_real (scm_big2dbl (x) - SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + return scm_make_complex (scm_big2dbl (x) - SCM_COMPLEX_REAL (y), + - SCM_COMPLEX_IMAG (y)); + } else { + SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); + } + } else if (SCM_REALP (x)) { + if (SCM_INUMP (y)) { + return scm_make_real (SCM_REAL_VALUE (x) - SCM_INUM (y)); + } else if (SCM_BIGP (y)) { + return scm_make_real (SCM_REAL_VALUE (x) - scm_big2dbl (y)); + } else if (SCM_REALP (y)) { + return scm_make_real (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + return scm_make_complex (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), + -SCM_COMPLEX_IMAG (y)); + } else { + SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); + } + } else if (SCM_COMPLEXP (x)) { + if (SCM_INUMP (y)) { + return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_INUM (y), + SCM_COMPLEX_IMAG (x)); + } else if (SCM_BIGP (y)) { + return scm_make_complex (SCM_COMPLEX_REAL (x) - scm_big2dbl (y), + SCM_COMPLEX_IMAG (x)); + } else if (SCM_REALP (y)) { + return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), + SCM_COMPLEX_IMAG (x)); + } else if (SCM_COMPLEXP (y)) { + return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), + SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); + } else { + SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); + } + } else { + SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); + } +} + + +SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product); +/* "Return the product of all arguments. If called without arguments,\n" + * "1 is returned." + */ +SCM +scm_product (SCM x, SCM y) +{ + if (SCM_UNBNDP (y)) { + if (SCM_UNBNDP (x)) { + return SCM_MAKINUM (1L); + } else if (SCM_NUMBERP (x)) { + return x; + } else { + SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); + } + } + + if (SCM_INUMP (x)) { + long xx; + + intbig: + xx = SCM_INUM (x); + + if (xx == 0) { + return x; + } else if (xx == 1) { + return y; + } + + if (SCM_INUMP (y)) { + long yy = SCM_INUM (y); + long kk = xx * yy; + SCM k = SCM_MAKINUM (kk); + if (kk != SCM_INUM (k) || kk / xx != yy) { +#ifdef SCM_BIGDIG + int sgn = (xx < 0) ^ (yy < 0); +#ifndef SCM_DIGSTOOBIG + long i = scm_pseudolong (xx); + long j = scm_pseudolong (yy); + return scm_mulbig ((SCM_BIGDIG *) & i, SCM_DIGSPERLONG, + (SCM_BIGDIG *) & j, SCM_DIGSPERLONG, sgn); +#else /* SCM_DIGSTOOBIG */ + SCM_BIGDIG xdigs [SCM_DIGSPERLONG]; + SCM_BIGDIG ydigs [SCM_DIGSPERLONG]; + scm_longdigs (xx, xdigs); + scm_longdigs (yy, ydigs); + return scm_mulbig (xdigs, SCM_DIGSPERLONG, + ydigs, SCM_DIGSPERLONG, + sgn); +#endif +#else + return scm_make_real (((double) xx) * ((double) yy)); +#endif + } else { + return k; + } + } else if (SCM_BIGP (y)) { +#ifndef SCM_DIGSTOOBIG + long z = scm_pseudolong (xx); + return scm_mulbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, + SCM_BDIGITS (y), SCM_NUMDIGS (y), + SCM_BIGSIGN (y) ? (xx > 0) : (xx < 0)); +#else + SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; + scm_longdigs (xx, zdigs); + return scm_mulbig (zdigs, SCM_DIGSPERLONG, + SCM_BDIGITS (y), SCM_NUMDIGS (y), + SCM_BIGSIGN (y) ? (xx > 0) : (xx < 0)); +#endif + } else if (SCM_REALP (y)) { + return scm_make_real (xx * SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + return scm_make_complex (xx * SCM_COMPLEX_REAL (y), + xx * SCM_COMPLEX_IMAG (y)); + } else { + SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); + } + } else if (SCM_BIGP (x)) { + if (SCM_INUMP (y)) { + SCM_SWAP (x, y); + goto intbig; + } else if (SCM_BIGP (y)) { + return scm_mulbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), + SCM_BDIGITS (y), SCM_NUMDIGS (y), + SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y)); + } else if (SCM_REALP (y)) { + return scm_make_real (scm_big2dbl (x) * SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + double z = scm_big2dbl (x); + return scm_make_complex (z * SCM_COMPLEX_REAL (y), + z * SCM_COMPLEX_IMAG (y)); + } else { + SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); + } + } else if (SCM_REALP (x)) { + if (SCM_INUMP (y)) { + return scm_make_real (SCM_INUM (y) * SCM_REAL_VALUE (x)); + } else if (SCM_BIGP (y)) { + return scm_make_real (scm_big2dbl (y) * SCM_REAL_VALUE (x)); + } else if (SCM_REALP (y)) { + return scm_make_real (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + return scm_make_complex (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), + SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); + } else { + SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); + } + } else if (SCM_COMPLEXP (x)) { + if (SCM_INUMP (y)) { + return scm_make_complex (SCM_INUM (y) * SCM_COMPLEX_REAL (x), + SCM_INUM (y) * SCM_COMPLEX_IMAG (x)); + } else if (SCM_BIGP (y)) { + double z = scm_big2dbl (y); + return scm_make_complex (z * SCM_COMPLEX_REAL (x), + z * SCM_COMPLEX_IMAG (x)); + } else if (SCM_REALP (y)) { + return scm_make_complex (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), + SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); + } else if (SCM_COMPLEXP (y)) { + return scm_make_complex (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) + - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), + SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) + + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); + } else { + SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); + } + } else { + SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); + } +} + + +double +scm_num2dbl (SCM a, const char *why) +#define FUNC_NAME why +{ + if (SCM_INUMP (a)) { + return (double) SCM_INUM (a); + } else if (SCM_BIGP (a)) { + return scm_big2dbl (a); + } else if (SCM_REALP (a)) { + return (SCM_REAL_VALUE (a)); + } else { + SCM_WRONG_TYPE_ARG (SCM_ARGn, a); + } +} +#undef FUNC_NAME + + +SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide); +/* "Divide the first argument by the product of the remaining arguments." + */ +SCM +scm_divide (SCM x, SCM y) +{ + double a; + + if (SCM_UNBNDP (y)) { + if (SCM_UNBNDP (x)) { + SCM_WTA_DISPATCH_0 (g_divide, x, SCM_ARG1, s_divide); + } else if (SCM_INUMP (x)) { + if (SCM_EQ_P (x, SCM_MAKINUM (1L)) || SCM_EQ_P (x, SCM_MAKINUM (-1L))) { + return x; + } else { + return scm_make_real (1.0 / (double) SCM_INUM (x)); + } + } else if (SCM_BIGP (x)) { + return scm_make_real (1.0 / scm_big2dbl (x)); + } else if (SCM_REALP (x)) { + return scm_make_real (1.0 / SCM_REAL_VALUE (x)); + } else if (SCM_COMPLEXP (x)) { + double r = SCM_COMPLEX_REAL (x); + double i = SCM_COMPLEX_IMAG (x); + double d = r * r + i * i; + return scm_make_complex (r / d, -i / d); + } else { + SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); + } + } + + if (SCM_INUMP (x)) { + long xx = SCM_INUM (x); + if (SCM_INUMP (y)) { + long yy = SCM_INUM (y); + if (yy == 0) { + scm_num_overflow (s_divide); + } else if (xx % yy != 0) { + return scm_make_real ((double) xx / (double) yy); + } else { + long z = xx / yy; + if (SCM_FIXABLE (z)) { + return SCM_MAKINUM (z); + } else { +#ifdef SCM_BIGDIG + return scm_long2big (z); +#else + return scm_make_real ((double) xx / (double) yy); +#endif + } + } + } else if (SCM_BIGP (y)) { + return scm_make_real ((double) xx / scm_big2dbl (y)); + } else if (SCM_REALP (y)) { + return scm_make_real ((double) xx / SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + a = xx; + complex_div: /* y _must_ be a complex number */ + { + double r = SCM_COMPLEX_REAL (y); + double i = SCM_COMPLEX_IMAG (y); + double d = r * r + i * i; + return scm_make_complex ((a * r) / d, (-a * i) / d); + } + } else { + SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); + } + } else if (SCM_BIGP (x)) { + if (SCM_INUMP (y)) { + long int yy = SCM_INUM (y); + if (yy == 0) { + scm_num_overflow (s_divide); + } else if (yy == 1) { + return x; + } else { + long z = yy < 0 ? -yy : yy; + if (z < SCM_BIGRAD) { + SCM w = scm_copybig (x, SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0)); + return scm_divbigdig (SCM_BDIGITS (w), SCM_NUMDIGS (w), + (SCM_BIGDIG) z) + ? scm_make_real (scm_big2dbl (x) / (double) yy) + : scm_normbig (w); + } else { + SCM w; +#ifndef SCM_DIGSTOOBIG + z = scm_pseudolong (z); + w = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), + (SCM_BIGDIG *) & z, SCM_DIGSPERLONG, + SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0), 3); +#else + SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; + scm_longdigs (z, zdigs); + w = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), + zdigs, SCM_DIGSPERLONG, + SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0), 3); +#endif + return (!SCM_UNBNDP (w)) + ? w + : scm_make_real (scm_big2dbl (x) / (double) yy); + } + } + } else if (SCM_BIGP (y)) { + SCM w = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), + SCM_BDIGITS (y), SCM_NUMDIGS (y), + SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y), 3); + return (!SCM_UNBNDP (w)) + ? w + : scm_make_real (scm_big2dbl (x) / scm_big2dbl (y)); + } else if (SCM_REALP (y)) { + return scm_make_real (scm_big2dbl (x) / SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + a = scm_big2dbl (x); + goto complex_div; + } else { + SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); + } + } else if (SCM_REALP (x)) { + double rx = SCM_REAL_VALUE (x); + if (SCM_INUMP (y)) { + return scm_make_real (rx / (double) SCM_INUM (y)); + } else if (SCM_BIGP (y)) { + return scm_make_real (rx / scm_big2dbl (y)); + } else if (SCM_REALP (y)) { + return scm_make_real (rx / SCM_REAL_VALUE (y)); + } else if (SCM_COMPLEXP (y)) { + a = rx; + goto complex_div; + } else { + SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); + } + } else if (SCM_COMPLEXP (x)) { + double rx = SCM_COMPLEX_REAL (x); + double ix = SCM_COMPLEX_IMAG (x); + if (SCM_INUMP (y)) { + double d = SCM_INUM (y); + return scm_make_complex (rx / d, ix / d); + } else if (SCM_BIGP (y)) { + double d = scm_big2dbl (y); + return scm_make_complex (rx / d, ix / d); + } else if (SCM_REALP (y)) { + double d = SCM_REAL_VALUE (y); + return scm_make_complex (rx / d, ix / d); + } else if (SCM_COMPLEXP (y)) { + double ry = SCM_COMPLEX_REAL (y); + double iy = SCM_COMPLEX_IMAG (y); + double d = ry * ry + iy * iy; + return scm_make_complex ((rx * ry + ix * iy) / d, + (ix * ry - rx * iy) / d); + } else { + SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); + } + } else { + SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); + } +} + + +SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_cxr, (SCM (*)()) scm_asinh, g_asinh); +/* "Return the inverse hyperbolic sine of @var{x}." + */ +double +scm_asinh (double x) +{ + return log (x + sqrt (x * x + 1)); +} + + + + +SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_cxr, (SCM (*)()) scm_acosh, g_acosh); +/* "Return the inverse hyperbolic cosine of @var{x}." + */ +double +scm_acosh (double x) +{ + return log (x + sqrt (x * x - 1)); +} + + + + +SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_cxr, (SCM (*)()) scm_atanh, g_atanh); +/* "Return the inverse hyperbolic tangent of @var{x}." + */ +double +scm_atanh (double x) +{ + return 0.5 * log ((1 + x) / (1 - x)); +} + + + + +SCM_GPROC1 (s_truncate, "truncate", scm_tc7_cxr, (SCM (*)()) scm_truncate, g_truncate); +/* "Round the inexact number @var{x} towards zero." + */ +double +scm_truncate (double x) +{ + if (x < 0.0) + return -floor (-x); + return floor (x); +} + + + +SCM_GPROC1 (s_round, "round", scm_tc7_cxr, (SCM (*)()) scm_round, g_round); +/* "Round the inexact number @var{x}. If @var{x} is halfway between two\n" + * "numbers, round towards even." + */ +double +scm_round (double x) +{ + double plus_half = x + 0.5; + double result = floor (plus_half); + /* Adjust so that the scm_round is towards even. */ + return (plus_half == result && plus_half / 2 != floor (plus_half / 2)) + ? result - 1 : result; +} + + + +SCM_GPROC1 (s_exact_to_inexact, "exact->inexact", scm_tc7_cxr, (SCM (*)()) scm_exact_to_inexact, g_exact_to_inexact); +/* Convert the number @var{x} to its inexact representation.\n" + */ +double +scm_exact_to_inexact (double z) +{ + return z; +} + + +SCM_GPROC1 (s_i_floor, "floor", scm_tc7_cxr, (SCM (*)()) floor, g_i_floor); +/* "Round the number @var{x} towards minus infinity." + */ +SCM_GPROC1 (s_i_ceil, "ceiling", scm_tc7_cxr, (SCM (*)()) ceil, g_i_ceil); +/* "Round the number @var{x} towards infinity." + */ +SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_cxr, (SCM (*)()) sqrt, g_i_sqrt); +/* "Return the square root of the real number @var{x}." + */ +SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_cxr, (SCM (*)()) fabs, g_i_abs); +/* "Return the absolute value of the real number @var{x}." + */ +SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_cxr, (SCM (*)()) exp, g_i_exp); +/* "Return the @var{x}th power of e." + */ +SCM_GPROC1 (s_i_log, "$log", scm_tc7_cxr, (SCM (*)()) log, g_i_log); +/* "Return the natural logarithm of the real number@var{x}." + */ +SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_cxr, (SCM (*)()) sin, g_i_sin); +/* "Return the sine of the real number @var{x}." + */ +SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_cxr, (SCM (*)()) cos, g_i_cos); +/* "Return the cosine of the real number @var{x}." + */ +SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_cxr, (SCM (*)()) tan, g_i_tan); +/* "Return the tangent of the real number @var{x}." + */ +SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_cxr, (SCM (*)()) asin, g_i_asin); +/* "Return the arc sine of the real number @var{x}." + */ +SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_cxr, (SCM (*)()) acos, g_i_acos); +/* "Return the arc cosine of the real number @var{x}." + */ +SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_cxr, (SCM (*)()) atan, g_i_atan); +/* "Return the arc tangent of the real number @var{x}." + */ +SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_cxr, (SCM (*)()) sinh, g_i_sinh); +/* "Return the hyperbolic sine of the real number @var{x}." + */ +SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_cxr, (SCM (*)()) cosh, g_i_cosh); +/* "Return the hyperbolic cosine of the real number @var{x}." + */ +SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_cxr, (SCM (*)()) tanh, g_i_tanh); +/* "Return the hyperbolic tangent of the real number @var{x}." + */ + +struct dpair +{ + double x, y; +}; + +static void scm_two_doubles (SCM x, + SCM y, + const char *sstring, + struct dpair * xy); + +static void +scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy) +{ + if (SCM_INUMP (x)) { + xy->x = SCM_INUM (x); + } else if (SCM_BIGP (x)) { + xy->x = scm_big2dbl (x); + } else if (SCM_REALP (x)) { + xy->x = SCM_REAL_VALUE (x); + } else { + scm_wrong_type_arg (sstring, SCM_ARG1, x); + } + + if (SCM_INUMP (y)) { + xy->y = SCM_INUM (y); + } else if (SCM_BIGP (y)) { + xy->y = scm_big2dbl (y); + } else if (SCM_REALP (y)) { + xy->y = SCM_REAL_VALUE (y); + } else { + scm_wrong_type_arg (sstring, SCM_ARG2, y); + } +} + + +SCM_DEFINE (scm_sys_expt, "$expt", 2, 0, 0, + (SCM x, SCM y), + "Return @var{x} raised to the power of @var{y}. This\n" + "procedure does not accept complex arguments.") +#define FUNC_NAME s_scm_sys_expt +{ + struct dpair xy; + scm_two_doubles (x, y, FUNC_NAME, &xy); + return scm_make_real (pow (xy.x, xy.y)); +} +#undef FUNC_NAME + + +SCM_DEFINE (scm_sys_atan2, "$atan2", 2, 0, 0, + (SCM x, SCM y), + "Return the arc tangent of the two arguments @var{x} and\n" + "@var{y}. This is similar to calculating the arc tangent of\n" + "@var{x} / @var{y}, except that the signs of both arguments\n" + "are used to determine the quadrant of the result. This\n" + "procedure does not accept complex arguments.") +#define FUNC_NAME s_scm_sys_atan2 +{ + struct dpair xy; + scm_two_doubles (x, y, FUNC_NAME, &xy); + return scm_make_real (atan2 (xy.x, xy.y)); +} +#undef FUNC_NAME + + +SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, + (SCM real, SCM imaginary), + "Return a complex number constructed of the given @var{real} and\n" + "@var{imaginary} parts.") +#define FUNC_NAME s_scm_make_rectangular +{ + struct dpair xy; + scm_two_doubles (real, imaginary, FUNC_NAME, &xy); + return scm_make_complex (xy.x, xy.y); +} +#undef FUNC_NAME + + + +SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, + (SCM x, SCM y), + "Return the complex number @var{x} * e^(i * @var{y}).") +#define FUNC_NAME s_scm_make_polar +{ + struct dpair xy; + scm_two_doubles (x, y, FUNC_NAME, &xy); + return scm_make_complex (xy.x * cos (xy.y), xy.x * sin (xy.y)); +} +#undef FUNC_NAME + + +SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); +/* "Return the real part of the number @var{z}." + */ +SCM +scm_real_part (SCM z) +{ + if (SCM_INUMP (z)) { + return z; + } else if (SCM_BIGP (z)) { + return z; + } else if (SCM_REALP (z)) { + return z; + } else if (SCM_COMPLEXP (z)) { + return scm_make_real (SCM_COMPLEX_REAL (z)); + } else { + SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); + } +} + + +SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); +/* "Return the imaginary part of the number @var{z}." + */ +SCM +scm_imag_part (SCM z) +{ + if (SCM_INUMP (z)) { + return SCM_INUM0; + } else if (SCM_BIGP (z)) { + return SCM_INUM0; + } else if (SCM_REALP (z)) { + return scm_flo0; + } else if (SCM_COMPLEXP (z)) { + return scm_make_real (SCM_COMPLEX_IMAG (z)); + } else { + SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); + } +} + + +SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); +/* "Return the magnitude of the number @var{z}. This is the same as\n" + * "@code{abs} for real arguments, but also allows complex numbers." + */ +SCM +scm_magnitude (SCM z) +{ + if (SCM_INUMP (z)) { + long int zz = SCM_INUM (z); + if (zz >= 0) { + return z; + } else if (SCM_POSFIXABLE (-zz)) { + return SCM_MAKINUM (-zz); + } else { +#ifdef SCM_BIGDIG + return scm_long2big (-zz); +#else + scm_num_overflow (s_magnitude); +#endif + } + } else if (SCM_BIGP (z)) { + if (!SCM_BIGSIGN (z)) { + return z; + } else { + return scm_copybig (z, 0); + } + } else if (SCM_REALP (z)) { + return scm_make_real (fabs (SCM_REAL_VALUE (z))); + } else if (SCM_COMPLEXP (z)) { + double r = SCM_COMPLEX_REAL (z); + double i = SCM_COMPLEX_IMAG (z); + return scm_make_real (sqrt (i * i + r * r)); + } else { + SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); + } +} + + +SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); +/* "Return the angle of the complex number @var{z}." + */ +SCM +scm_angle (SCM z) +{ + if (SCM_INUMP (z)) { + if (SCM_INUM (z) >= 0) { + return scm_make_real (atan2 (0.0, 1.0)); + } else { + return scm_make_real (atan2 (0.0, -1.0)); + } + } else if (SCM_BIGP (z)) { + if (SCM_BIGSIGN (z)) { + return scm_make_real (atan2 (0.0, -1.0)); + } else { + return scm_make_real (atan2 (0.0, 1.0)); + } + } else if (SCM_REALP (z)) { + return scm_make_real (atan2 (0.0, SCM_REAL_VALUE (z))); + } else if (SCM_COMPLEXP (z)) { + return scm_make_real (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); + } else { + SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); + } +} + + +SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, + (SCM z), + "Returns an exact number that is numerically closest to @var{z}.") +#define FUNC_NAME s_scm_inexact_to_exact +{ + if (SCM_INUMP (z)) { + return z; + } else if (SCM_BIGP (z)) { + return z; + } else if (SCM_REALP (z)) { + double u = floor (SCM_REAL_VALUE (z) + 0.5); + long lu = (long) u; + if (SCM_FIXABLE (lu)) { + return SCM_MAKINUM (lu); +#ifdef SCM_BIGDIG + } else if (isfinite (u)) { + return scm_dbl2big (u); +#endif + } else { + scm_num_overflow (s_scm_inexact_to_exact); + } + } else { + SCM_WRONG_TYPE_ARG (1, z); + } +} +#undef FUNC_NAME + + +#ifdef SCM_BIGDIG +/* d must be integer */ + +SCM +scm_dbl2big (double d) +{ + scm_sizet i = 0; + long c; + SCM_BIGDIG *digits; + SCM ans; + double u = (d < 0) ? -d : d; + while (0 != floor (u)) + { + u /= SCM_BIGRAD; + i++; + } + ans = scm_mkbig (i, d < 0); + digits = SCM_BDIGITS (ans); + while (i--) + { + u *= SCM_BIGRAD; + c = floor (u); + u -= c; + digits[i] = c; + } +#ifndef SCM_RECKLESS + if (u != 0) + scm_num_overflow ("dbl2big"); +#endif + return ans; +} + + + +double +scm_big2dbl (SCM b) +{ + double ans = 0.0; + scm_sizet i = SCM_NUMDIGS (b); + SCM_BIGDIG *digits = SCM_BDIGITS (b); + while (i--) + ans = digits[i] + SCM_BIGRAD * ans; + if (SCM_BIGSIGN (b)) + return - ans; + return ans; +} +#endif + + +SCM +scm_long2num (long sl) +{ + if (!SCM_FIXABLE (sl)) + { +#ifdef SCM_BIGDIG + return scm_long2big (sl); +#else + return scm_make_real ((double) sl); +#endif + } + return SCM_MAKINUM (sl); +} + + +#ifdef HAVE_LONG_LONGS + +SCM +scm_long_long2num (long_long sl) +{ + if (!SCM_FIXABLE (sl)) + { +#ifdef SCM_BIGDIG + return scm_long_long2big (sl); +#else + return scm_make_real ((double) sl); +#endif + } + else + { + /* we know that sl fits into an inum */ + return SCM_MAKINUM ((scm_bits_t) sl); + } +} + +#endif /* HAVE_LONG_LONGS */ + + +SCM +scm_ulong2num (unsigned long sl) +{ + if (!SCM_POSFIXABLE (sl)) + { +#ifdef SCM_BIGDIG + return scm_ulong2big (sl); +#else + return scm_make_real ((double) sl); +#endif + } + return SCM_MAKINUM (sl); +} + + +long +scm_num2long (SCM num, char *pos, const char *s_caller) +{ + if (SCM_INUMP (num)) { + return SCM_INUM (num); + } else if (SCM_BIGP (num)) { + long int res; + /* can't use res directly in case num is -2^31. */ + unsigned long int pos_res = 0; + unsigned long int old_res = 0; + scm_sizet l; + + for (l = SCM_NUMDIGS (num); l--;) { + pos_res = SCM_BIGUP (pos_res) + SCM_BDIGITS (num)[l]; + if (pos_res >= old_res) { + old_res = pos_res; + } else { + /* overflow. */ + scm_out_of_range (s_caller, num); + } + } + if (SCM_BIGSIGN (num)) { + res = -pos_res; + if (res <= 0) { + return res; + } else { + scm_out_of_range (s_caller, num); + } + } else { + res = pos_res; + if (res >= 0) { + return res; + } else { + scm_out_of_range (s_caller, num); + } + } + } else if (SCM_REALP (num)) { + double u = SCM_REAL_VALUE (num); + long int res = u; + if ((double) res == u) { + return res; + } else { + scm_out_of_range (s_caller, num); + } + } else { + scm_wrong_type_arg (s_caller, (int) pos, num); + } +} + + +#ifdef HAVE_LONG_LONGS + +long_long +scm_num2long_long (SCM num, char *pos, const char *s_caller) +{ + if (SCM_INUMP (num)) { + return SCM_INUM (num); + } else if (SCM_BIGP (num)) { + long long res; + /* can't use res directly in case num is -2^63. */ + unsigned long long int pos_res = 0; + unsigned long long int old_res = 0; + scm_sizet l; + + for (l = SCM_NUMDIGS (num); l--;) { + pos_res = SCM_LONGLONGBIGUP (pos_res) + SCM_BDIGITS (num)[l]; + if (pos_res >= old_res) { + old_res = pos_res; + } else { + /* overflow. */ + scm_out_of_range (s_caller, num); + } + } + if (SCM_BIGSIGN (num)) { + res = -pos_res; + if (res <= 0) { + return res; + } else { + scm_out_of_range (s_caller, num); + } + } else { + res = pos_res; + if (res >= 0) { + return res; + } else { + scm_out_of_range (s_caller, num); + } + } + } else if (SCM_REALP (num)) { + double u = SCM_REAL_VALUE (num); + long long int res = u; + if ((double) res == u) { + return res; + } else { + scm_out_of_range (s_caller, num); + } + } else { + scm_wrong_type_arg (s_caller, (int) pos, num); + } +} + +#endif /* HAVE_LONG_LONGS */ + + +unsigned long +scm_num2ulong (SCM num, char *pos, const char *s_caller) +{ + if (SCM_INUMP (num)) { + long nnum = SCM_INUM (num); + if (nnum >= 0) { + return nnum; + } else { + scm_out_of_range (s_caller, num); + } + } else if (SCM_BIGP (num)) { + unsigned long int res = 0; + unsigned long int old_res = 0; + scm_sizet l; + + for (l = SCM_NUMDIGS (num); l--;) { + res = SCM_BIGUP (res) + SCM_BDIGITS (num)[l]; + if (res >= old_res) { + old_res = res; + } else { + scm_out_of_range (s_caller, num); + } + } + return res; + } else if (SCM_REALP (num)) { + double u = SCM_REAL_VALUE (num); + unsigned long int res = u; + if ((double) res == u) { + return res; + } else { + scm_out_of_range (s_caller, num); + } + } else { + scm_wrong_type_arg (s_caller, (int) pos, num); + } +} + + +void +scm_init_numbers () +{ + abs_most_negative_fixnum = scm_long2big (- SCM_MOST_NEGATIVE_FIXNUM); + scm_permanent_object (abs_most_negative_fixnum); + + /* It may be possible to tune the performance of some algorithms by using + * the following constants to avoid the creation of bignums. Please, before + * using these values, remember the two rules of program optimization: + * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ + scm_sysintern ("most-positive-fixnum", SCM_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); + scm_sysintern ("most-negative-fixnum", SCM_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); + + scm_add_feature ("complex"); + scm_add_feature ("inexact"); + scm_flo0 = scm_make_real (0.0); +#ifdef DBL_DIG + scm_dblprec = (DBL_DIG > 20) ? 20 : DBL_DIG; +#else + { /* determine floating point precision */ + double f = 0.1; + double fsum = 1.0 + f; + while (fsum != 1.0) { + if (++scm_dblprec > 20) { + fsum = 1.0; + } else { + f /= 10.0; + fsum = f + 1.0; + } + } + scm_dblprec = scm_dblprec - 1; + } +#endif /* DBL_DIG */ +#ifndef SCM_MAGIC_SNARFER +#include "libguile/numbers.x" +#endif +} + +/* + Local Variables: + c-file-style: "gnu" + End: +*/