/* Copyright (C) 1995,1996,1997,1998,1999,2000,2001 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 "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" #include "libguile/deprecation.h" static SCM scm_divbigbig (SCM_BIGDIG *x, size_t nx, SCM_BIGDIG *y, size_t ny, int sgn, int modes); static SCM scm_divbigint (SCM x, long z, int sgn, int mode); #define SCM_SWAP(x,y) do { SCM __t = x; x = y; y = __t; } while (0) /* FLOBUFLEN is the maximum number of characters neccessary for the * printed or scm_string representation of an inexact number. */ #define FLOBUFLEN (10+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) /* 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_i_long2big (-xx); #else scm_num_overflow (s_abs); #endif } } else if (SCM_BIGP (x)) { if (!SCM_BIGSIGN (x)) { return x; } else { return scm_i_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_i_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_i_copybig (x, SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0)); scm_divbigdig (SCM_BDIGITS (sw), SCM_NUMDIGS (sw), (SCM_BIGDIG) z); return scm_i_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 { long 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_i_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_i_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_i_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, size_t nx, int zsgn); SCM scm_big_ior(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy); SCM scm_big_xor(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy); SCM scm_big_and(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy, int zsgn); SCM scm_big_test(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy); SCM scm_copy_big_dec(SCM b, int sign) { long num = -1; size_t nx = SCM_NUMDIGS(b); size_t i = 0; SCM ans = scm_i_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, size_t nx, int zsgn) { long num = -1; size_t i = 0; SCM z = scm_i_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, size_t nx, int xsgn, SCM bigy) /* Assumes nx <= SCM_NUMDIGS(bigy) */ /* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */ { long num = -1; size_t 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_i_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, size_t nx, int xsgn, SCM bigy) /* Assumes nx <= SCM_NUMDIGS(bigy) */ /* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */ { long num = -1; size_t 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_i_normbig(z); } } return scm_i_normbig(z); } SCM scm_big_and(SCM_BIGDIG *x, size_t 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; size_t 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_i_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_i_normbig(z); } SCM scm_big_test(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy) /* Assumes nx <= SCM_NUMDIGS(bigy) */ /* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */ { SCM_BIGDIG *y; size_t 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), "Return the bitwise AND of the integer arguments.\n\n" "@lisp\n" "(logand) @result{} -1\n" "(logand 7) @result{} 7\n" "(logand #b111 #b011 #\b001) @result{} 1\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), "Return the bitwise OR of the integer arguments.\n\n" "@lisp\n" "(logior) @result{} 0\n" "(logior 7) @result{} 7\n" "(logior #b000 #b001 #b011) @result{} 3\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), "Return the bitwise XOR of the integer arguments. A bit is\n" "set in the result if it is set in an odd number of arguments.\n" "@lisp\n" "(logxor) @result{} 0\n" "(logxor 7) @result{} 7\n" "(logxor #b000 #b001 #b011) @result{} 2\n" "(logxor #b000 #b001 #b011 #b011) @result{} 1\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 j, SCM k), "@lisp\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 lisp") #define FUNC_NAME s_scm_logtest { long int nj; if (SCM_INUMP (j)) { nj = SCM_INUM (j); if (SCM_INUMP (k)) { long nk = SCM_INUM (k); return SCM_BOOL (nj & nk); } else if (SCM_BIGP (k)) { intbig: { # ifndef SCM_DIGSTOOBIG long z = scm_pseudolong (nj); return scm_big_test ((SCM_BIGDIG *)&z, SCM_DIGSPERLONG, (nj < 0) ? SCM_BIGSIGNFLAG : 0, k); # else SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; scm_longdigs (nj, zdigs); return scm_big_test (zdigs, SCM_DIGSPERLONG, (nj < 0) ? SCM_BIGSIGNFLAG : 0, k); # endif } } else { SCM_WRONG_TYPE_ARG (SCM_ARG2, k); } } else if (SCM_BIGP (j)) { if (SCM_INUMP (k)) { SCM_SWAP (j, k); nj = SCM_INUM (j); goto intbig; } else if (SCM_BIGP (k)) { if (SCM_NUMDIGS (j) > SCM_NUMDIGS (k)) { SCM_SWAP (j, k); } return scm_big_test (SCM_BDIGITS (j), SCM_NUMDIGS (j), SCM_BIGSIGN (j), k); } else { SCM_WRONG_TYPE_ARG (SCM_ARG2, k); } } else { SCM_WRONG_TYPE_ARG (SCM_ARG1, j); } } #undef FUNC_NAME SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, (SCM index, SCM j), "@lisp\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 lisp") #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; size_t i = 0; SCM_BIGDIG * x = SCM_BDIGITS (j); size_t 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), "Return the integer which is the 2s-complement of the integer\n" "argument.\n" "\n" "@lisp\n" "(number->string (lognot #b10000000) 2)\n" " @result{} \"-10000001\"\n" "(number->string (lognot #b0) 2)\n" " @result{} \"-1\"\n" "@end lisp") #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), "Return @var{n} raised to the non-negative integer exponent\n" "@var{k}.\n" "\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 if (SCM_REALP (k)) { double r = SCM_REAL_VALUE (k); i2 = r; if (i2 != r) SCM_WRONG_TYPE_ARG (2, k); } else 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). 'Arithmetic'\n" "means, that the function does not guarantee to keep the bit\n" "structure of @var{n}, but rather guarantees that the result\n" "will always be rounded towards minus infinity. Therefore, the\n" "results of ash and a corresponding bitwise shift will differ if\n" "@var{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" "@lisp\n" "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" "(number->string (ash #b1010 -1) 2) @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), "Return the integer composed of the @var{start} (inclusive)\n" "through @var{end} (exclusive) bits of @var{n}. The\n" "@var{start}th bit becomes the 0-th bit in the result.\n" "\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_I_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_I_FIXNUM_BIT) { in = in >> istart; if (bits < SCM_I_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), "Return the number of bits in integer @var{n}. If integer is\n" "positive, the 1-bits in its binary representation are counted.\n" "If negative, the 0-bits in its two's-complement binary\n" "representation are counted. If 0, 0 is returned.\n" "\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; size_t 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), "Return the number of bits neccessary to represent @var{n}.\n" "\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_i_mkbig (size_t nlen, int sign) { SCM v; SCM_BIGDIG *base; if (((nlen << SCM_BIGSIZEFIELD) >> SCM_BIGSIZEFIELD) != nlen) scm_memory_error (s_bignum); base = scm_must_malloc (nlen * sizeof (SCM_BIGDIG), s_bignum); SCM_NEWCELL (v); SCM_SET_BIGNUM_BASE (v, base); SCM_SETNUMDIGS (v, nlen, sign); return v; } SCM scm_i_big2inum (SCM b, size_t 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_i_adjbig"; SCM scm_i_adjbig (SCM b, size_t nlen) { size_t 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_i_normbig (SCM b) { #ifndef _UNICOS size_t 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_i_big2inum (b, (size_t) nlen))) return b; if (SCM_NUMDIGS (b) == nlen) return b; return scm_i_adjbig (b, (size_t) nlen); } SCM scm_i_copybig (SCM b, int sign) { size_t i = SCM_NUMDIGS (b); SCM ans = scm_i_mkbig (i, sign); SCM_BIGDIG *src = SCM_BDIGITS (b), *dst = SCM_BDIGITS (ans); while (i--) dst[i] = src[i]; return ans; } int scm_bigcomp (SCM x, SCM y) { int xsign = SCM_BIGSIGN (x); int ysign = SCM_BIGSIGN (y); size_t 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; size_t 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[]) { size_t 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, size_t 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; size_t i = 0, ny = SCM_NUMDIGS (bigy); SCM z = scm_i_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_i_adjbig (z, ny + 1); SCM_BDIGITS (z)[ny] = num; return z; } } return scm_i_normbig (z); } SCM scm_mulbig (SCM_BIGDIG *x, size_t nx, SCM_BIGDIG *y, size_t ny, int sgn) { size_t i = 0, j = nx + ny; unsigned long n = 0; SCM z = scm_i_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_i_normbig (z); } unsigned int scm_divbigdig (SCM_BIGDIG * ds, size_t 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); size_t 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, size_t nx, SCM_BIGDIG *y, size_t 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. */ size_t 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_i_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_i_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_i_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_i_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_i_big2inum (z, j))) return z; return scm_i_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 size_t idbl2str (double f, char *a) { int efmt, dpt, d, i, wp = scm_dblprec; size_t 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 size_t iflo2str (SCM flt, char *str) { size_t i; if (SCM_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 */ size_t scm_iint2str (long num, int rad, char *p) { size_t j = 1; size_t 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_i_copybig (b, 0); /* sign of temp doesn't matter */ register SCM_BIGDIG *ds = SCM_BDIGITS (t); size_t i = SCM_NUMDIGS (t); size_t j = radix == 16 ? (SCM_BITSPERDIG * i) / 4 + 2 : radix >= 10 ? (SCM_BITSPERDIG * i * 241L) / 800 + 2 : (SCM_BITSPERDIG * i) + 2; size_t k = 0; size_t radct = 0; SCM_BIGDIG radpow = 1, radmod = 0; SCM ss = scm_allocate_string (j); 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]; size_t length = scm_iint2str (SCM_INUM (n), base, num_buf); return scm_mem2string (num_buf, length); } else if (SCM_BIGP (n)) { return big2str (n, (unsigned int) base); } else if (SCM_INEXACTP (n)) { char num_buf [FLOBUFLEN]; return scm_mem2string (num_buf, iflo2str (n, num_buf)); } 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 SCM_UNUSED) { char num_buf[FLOBUFLEN]; scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port); return !0; } int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) { char num_buf[FLOBUFLEN]; scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port); return !0; } int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) { #ifdef SCM_BIGDIG exp = big2str (exp, (unsigned int) 10); scm_lfwrite (SCM_STRING_CHARS (exp), (size_t) SCM_STRING_LENGTH (exp), port); #else scm_ipruk ("bignum", exp, port); #endif return !0; } /*** END nums->strs ***/ /*** STRINGS -> NUMBERS ***/ /* The following functions implement the conversion from strings to numbers. * The implementation somehow follows the grammar for numbers as it is given * in R5RS. Thus, the functions resemble syntactic units (, * , ...) that are used to build up numbers in the grammar. Some * points should be noted about the implementation: * * Each function keeps a local index variable 'idx' that points at the * current position within the parsed string. The global index is only * updated if the function could parse the corresponding syntactic unit * successfully. * * Similarly, the functions keep track of indicators of inexactness ('#', * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the * global exactness information is only updated after each part has been * successfully parsed. * * Sequences of digits are parsed into temporary variables holding fixnums. * Only if these fixnums would overflow, the result variables are updated * using the standard functions scm_add, scm_product, scm_divide etc. Then, * the temporary variables holding the fixnums are cleared, and the process * starts over again. If for example fixnums were able to store five decimal * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, * and the result was computed as 12345 * 100000 + 67890. In other words, * only every five digits two bignum operations were performed. */ enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; /* R5RS, section 7.1.1, lexical structure of numbers: . */ /* In non ASCII-style encodings the following macro might not work. */ #define XDIGIT2UINT(d) (isdigit (d) ? (d) - '0' : tolower (d) - 'a' + 10) static SCM mem2uinteger (const char* mem, size_t len, unsigned int *p_idx, unsigned int radix, enum t_exactness *p_exactness) { unsigned int idx = *p_idx; unsigned int hash_seen = 0; scm_t_bits shift = 1; scm_t_bits add = 0; unsigned int digit_value; SCM result; char c; if (idx == len) return SCM_BOOL_F; c = mem[idx]; if (!isxdigit (c)) return SCM_BOOL_F; digit_value = XDIGIT2UINT (c); if (digit_value >= radix) return SCM_BOOL_F; idx++; result = SCM_MAKINUM (digit_value); while (idx != len) { char c = mem[idx]; if (isxdigit (c)) { if (hash_seen) break; digit_value = XDIGIT2UINT (c); if (digit_value >= radix) break; } else if (c == '#') { hash_seen = 1; digit_value = 0; } else break; idx++; if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) { result = scm_product (result, SCM_MAKINUM (shift)); if (add > 0) result = scm_sum (result, SCM_MAKINUM (add)); shift = radix; add = digit_value; } else { shift = shift * radix; add = add * radix + digit_value; } }; if (shift > 1) result = scm_product (result, SCM_MAKINUM (shift)); if (add > 0) result = scm_sum (result, SCM_MAKINUM (add)); *p_idx = idx; if (hash_seen) *p_exactness = INEXACT; return result; } /* R5RS, section 7.1.1, lexical structure of numbers: . Only * covers the parts of the rules that start at a potential point. The value * of the digits up to the point have been parsed by the caller and are given * in variable result. The content of *p_exactness indicates, whether a hash * has already been seen in the digits before the point. */ /* In non ASCII-style encodings the following macro might not work. */ #define DIGIT2UINT(d) ((d) - '0') static SCM mem2decimal_from_point (SCM result, const char* mem, size_t len, unsigned int *p_idx, enum t_exactness *p_exactness) { unsigned int idx = *p_idx; enum t_exactness x = *p_exactness; if (idx == len) return result; if (mem[idx] == '.') { scm_t_bits shift = 1; scm_t_bits add = 0; unsigned int digit_value; SCM big_shift = SCM_MAKINUM (1); idx++; while (idx != len) { char c = mem[idx]; if (isdigit (c)) { if (x == INEXACT) return SCM_BOOL_F; else digit_value = DIGIT2UINT (c); } else if (c == '#') { x = INEXACT; digit_value = 0; } else break; idx++; if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) { big_shift = scm_product (big_shift, SCM_MAKINUM (shift)); result = scm_product (result, SCM_MAKINUM (shift)); if (add > 0) result = scm_sum (result, SCM_MAKINUM (add)); shift = 10; add = digit_value; } else { shift = shift * 10; add = add * 10 + digit_value; } }; if (add > 0) { big_shift = scm_product (big_shift, SCM_MAKINUM (shift)); result = scm_product (result, SCM_MAKINUM (shift)); result = scm_sum (result, SCM_MAKINUM (add)); } result = scm_divide (result, big_shift); /* We've seen a decimal point, thus the value is implicitly inexact. */ x = INEXACT; } if (idx != len) { int sign = 1; unsigned int start; char c; int exponent; SCM e; /* R5RS, section 7.1.1, lexical structure of numbers: */ switch (mem[idx]) { case 'd': case 'D': case 'e': case 'E': case 'f': case 'F': case 'l': case 'L': case 's': case 'S': idx++; start = idx; c = mem[idx]; if (c == '-') { idx++; sign = -1; c = mem[idx]; } else if (c == '+') { idx++; sign = 1; c = mem[idx]; } else sign = 1; if (!isdigit (c)) return SCM_BOOL_F; idx++; exponent = DIGIT2UINT (c); while (idx != len) { char c = mem[idx]; if (isdigit (c)) { idx++; if (exponent <= SCM_MAXEXP) exponent = exponent * 10 + DIGIT2UINT (c); } else break; } if (exponent > SCM_MAXEXP) { size_t exp_len = idx - start; SCM exp_string = scm_mem2string (&mem[start], exp_len); SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); scm_out_of_range ("string->number", exp_num); } e = scm_integer_expt (SCM_MAKINUM (10), SCM_MAKINUM (exponent)); if (sign == 1) result = scm_product (result, e); else result = scm_divide (result, e); /* We've seen an exponent, thus the value is implicitly inexact. */ x = INEXACT; break; default: break; } } *p_idx = idx; if (x == INEXACT) *p_exactness = x; return result; } /* R5RS, section 7.1.1, lexical structure of numbers: */ static SCM mem2ureal (const char* mem, size_t len, unsigned int *p_idx, unsigned int radix, enum t_exactness *p_exactness) { unsigned int idx = *p_idx; if (idx == len) return SCM_BOOL_F; if (mem[idx] == '.') { if (radix != 10) return SCM_BOOL_F; else if (idx + 1 == len) return SCM_BOOL_F; else if (!isdigit (mem[idx + 1])) return SCM_BOOL_F; else return mem2decimal_from_point (SCM_MAKINUM (0), mem, len, p_idx, p_exactness); } else { enum t_exactness x = EXACT; SCM uinteger; SCM result; uinteger = mem2uinteger (mem, len, &idx, radix, &x); if (SCM_FALSEP (uinteger)) return SCM_BOOL_F; if (idx == len) result = uinteger; else if (mem[idx] == '/') { SCM divisor; idx++; divisor = mem2uinteger (mem, len, &idx, radix, &x); if (SCM_FALSEP (divisor)) return SCM_BOOL_F; result = scm_divide (uinteger, divisor); } else if (radix == 10) { result = mem2decimal_from_point (uinteger, mem, len, &idx, &x); if (SCM_FALSEP (result)) return SCM_BOOL_F; } else result = uinteger; *p_idx = idx; if (x == INEXACT) *p_exactness = x; return result; } } /* R5RS, section 7.1.1, lexical structure of numbers: */ static SCM mem2complex (const char* mem, size_t len, unsigned int idx, unsigned int radix, enum t_exactness *p_exactness) { char c; int sign = 0; SCM ureal; if (idx == len) return SCM_BOOL_F; c = mem[idx]; if (c == '+') { idx++; sign = 1; } else if (c == '-') { idx++; sign = -1; } if (idx == len) return SCM_BOOL_F; ureal = mem2ureal (mem, len, &idx, radix, p_exactness); if (SCM_FALSEP (ureal)) { /* input must be either +i or -i */ if (sign == 0) return SCM_BOOL_F; if (mem[idx] == 'i' || mem[idx] == 'I') { idx++; if (idx != len) return SCM_BOOL_F; return scm_make_rectangular (SCM_MAKINUM (0), SCM_MAKINUM (sign)); } else return SCM_BOOL_F; } else { if (sign == -1) ureal = scm_difference (ureal, SCM_UNDEFINED); if (idx == len) return ureal; c = mem[idx]; switch (c) { case 'i': case 'I': /* either +i or -i */ idx++; if (sign == 0) return SCM_BOOL_F; if (idx != len) return SCM_BOOL_F; return scm_make_rectangular (SCM_MAKINUM (0), ureal); case '@': /* polar input: @. */ idx++; if (idx == len) return SCM_BOOL_F; else { int sign; SCM angle; SCM result; c = mem[idx]; if (c == '+') { idx++; sign = 1; } else if (c == '-') { idx++; sign = -1; } else sign = 1; angle = mem2ureal (mem, len, &idx, radix, p_exactness); if (SCM_FALSEP (angle)) return SCM_BOOL_F; if (idx != len) return SCM_BOOL_F; if (sign == -1) angle = scm_difference (angle, SCM_UNDEFINED); result = scm_make_polar (ureal, angle); return result; } case '+': case '-': /* expecting input matching [+-]?i */ idx++; if (idx == len) return SCM_BOOL_F; else { int sign = (c == '+') ? 1 : -1; SCM imag = mem2ureal (mem, len, &idx, radix, p_exactness); if (SCM_FALSEP (imag)) imag = SCM_MAKINUM (sign); else if (sign == -1) imag = scm_difference (imag, SCM_UNDEFINED); if (idx == len) return SCM_BOOL_F; if (mem[idx] != 'i' && mem[idx] != 'I') return SCM_BOOL_F; idx++; if (idx != len) return SCM_BOOL_F; return scm_make_rectangular (ureal, imag); } default: return SCM_BOOL_F; } } } /* R5RS, section 7.1.1, lexical structure of numbers: */ enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; SCM scm_i_mem2number (const char* mem, size_t len, unsigned int default_radix) { unsigned int idx = 0; unsigned int radix = NO_RADIX; enum t_exactness forced_x = NO_EXACTNESS; enum t_exactness implicit_x = EXACT; SCM result; /* R5RS, section 7.1.1, lexical structure of numbers: */ while (idx + 2 < len && mem[idx] == '#') { switch (mem[idx + 1]) { case 'b': case 'B': if (radix != NO_RADIX) return SCM_BOOL_F; radix = DUAL; break; case 'd': case 'D': if (radix != NO_RADIX) return SCM_BOOL_F; radix = DEC; break; case 'i': case 'I': if (forced_x != NO_EXACTNESS) return SCM_BOOL_F; forced_x = INEXACT; break; case 'e': case 'E': if (forced_x != NO_EXACTNESS) return SCM_BOOL_F; forced_x = EXACT; break; case 'o': case 'O': if (radix != NO_RADIX) return SCM_BOOL_F; radix = OCT; break; case 'x': case 'X': if (radix != NO_RADIX) return SCM_BOOL_F; radix = HEX; break; default: return SCM_BOOL_F; } idx += 2; } /* R5RS, section 7.1.1, lexical structure of numbers: */ if (radix == NO_RADIX) result = mem2complex (mem, len, idx, default_radix, &implicit_x); else result = mem2complex (mem, len, idx, (unsigned int) radix, &implicit_x); if (SCM_FALSEP (result)) return SCM_BOOL_F; switch (forced_x) { case EXACT: if (SCM_INEXACTP (result)) /* FIXME: This may change the value. */ return scm_inexact_to_exact (result); else return result; case INEXACT: if (SCM_INEXACTP (result)) return result; else return scm_exact_to_inexact (result); case NO_EXACTNESS: default: if (implicit_x == INEXACT) { if (SCM_INEXACTP (result)) return result; else return scm_exact_to_inexact (result); } else return result; } } SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, (SCM string, SCM radix), "Return 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 radix\n" "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" "supplied, then the default radix is 10. If string is not a\n" "syntactically valid notation for a number, then\n" "@code{string->number} returns @code{#f}.") #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_i_mem2number (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_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_INEXACTP (x)) return SCM_BOOL_F; if (SCM_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_i_big2dbl (x) == SCM_REAL_VALUE (y)); } else if (SCM_COMPLEXP (y)) { return SCM_BOOL ((scm_i_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_i_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_i_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_i_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_i_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, 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_i_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_i_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, 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_i_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_i_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_i_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_i_big2dbl (x) + SCM_REAL_VALUE (y)); } else if (SCM_COMPLEXP (y)) { return scm_make_complex (scm_i_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_i_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_i_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 with one argument @var{z1}, -@var{z1} returned. Otherwise * the sum of all but the first argument are subtracted from the first * argument. */ #define FUNC_NAME s_difference SCM scm_difference (SCM x, SCM y) { if (SCM_UNBNDP (y)) { if (SCM_UNBNDP (x)) { SCM_WTA_DISPATCH_0 (g_difference, s_difference); } else if (SCM_INUMP (x)) { long xx = -SCM_INUM (x); if (SCM_FIXABLE (xx)) { return SCM_MAKINUM (xx); } else { #ifdef SCM_BIGDIG return scm_i_long2big (xx); #else return scm_make_real ((double) xx); #endif } } else if (SCM_BIGP (x)) { SCM z = scm_i_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_i_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_i_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_i_big2dbl (x) - SCM_REAL_VALUE (y)); } else if (SCM_COMPLEXP (y)) { return scm_make_complex (scm_i_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_i_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_i_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); } } #undef FUNC_NAME 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_i_big2dbl (x) * SCM_REAL_VALUE (y)); } else if (SCM_COMPLEXP (y)) { double z = scm_i_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_i_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_i_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_i_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. If called with one argument @var{z1}, 1/@var{z1} is returned. */ #define FUNC_NAME s_divide SCM scm_divide (SCM x, SCM y) { double a; if (SCM_UNBNDP (y)) { if (SCM_UNBNDP (x)) { SCM_WTA_DISPATCH_0 (g_divide, 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_i_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_i_long2big (z); #else return scm_make_real ((double) xx / (double) yy); #endif } } } else if (SCM_BIGP (y)) { return scm_make_real ((double) xx / scm_i_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_i_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_i_big2dbl (x) / (double) yy) : scm_i_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_i_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_i_big2dbl (x) / scm_i_big2dbl (y)); } else if (SCM_REALP (y)) { return scm_make_real (scm_i_big2dbl (x) / SCM_REAL_VALUE (y)); } else if (SCM_COMPLEXP (y)) { a = scm_i_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_i_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_i_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); } } #undef FUNC_NAME 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, "$atanh", scm_tc7_cxr, (SCM (*)()) scm_atanh, g_atanh); /* "Return the inverse hyperbolic tangent of @var{x}." */ double scm_atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } SCM_GPROC1 (s_truncate, "truncate", scm_tc7_cxr, (SCM (*)()) scm_truncate, g_truncate); /* "Round the inexact number @var{x} towards zero." */ double scm_truncate (double x) { if (x < 0.0) return -floor (-x); return floor (x); } SCM_GPROC1 (s_round, "round", scm_tc7_cxr, (SCM (*)()) scm_round, g_round); /* "Round the inexact number @var{x}. If @var{x} is halfway between two\n" * "numbers, round towards even." */ double scm_round (double x) { double plus_half = x + 0.5; double result = floor (plus_half); /* Adjust so that the scm_round is towards even. */ return (plus_half == result && plus_half / 2 != floor (plus_half / 2)) ? result - 1 : result; } SCM_GPROC1 (s_i_floor, "floor", scm_tc7_cxr, (SCM (*)()) floor, g_i_floor); /* "Round the number @var{x} towards minus infinity." */ SCM_GPROC1 (s_i_ceil, "ceiling", scm_tc7_cxr, (SCM (*)()) ceil, g_i_ceil); /* "Round the number @var{x} towards infinity." */ SCM_GPROC1 (s_i_sqrt, "$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_i_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_i_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_i_long2big (-zz); #else scm_num_overflow (s_magnitude); #endif } } else if (SCM_BIGP (z)) { if (!SCM_BIGSIGN (z)) { return z; } else { return scm_i_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_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); /* Convert the number @var{x} to its inexact representation.\n" */ SCM scm_exact_to_inexact (SCM z) { if (SCM_INUMP (z)) return scm_make_real ((double) SCM_INUM (z)); else if (SCM_BIGP (z)) return scm_make_real (scm_i_big2dbl (z)); else if (SCM_INEXACTP (z)) return z; else SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); } SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, (SCM z), "Return 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_i_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_i_dbl2big (double d) { size_t 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_i_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_i_big2dbl (SCM b) { double ans = 0.0; size_t 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 #ifdef HAVE_LONG_LONGS # ifndef LLONG_MAX # define ULLONG_MAX ((unsigned long long) (-1)) # define LLONG_MAX ((long long) (ULLONG_MAX >> 1)) # define LLONG_MIN (~LLONG_MAX) # endif #endif #ifndef SIZE_MAX #define SIZE_MAX ((size_t) (-1)) #endif #ifndef PTRDIFF_MIN /* the below is not really guaranteed to work (I think), but probably does: */ #define PTRDIFF_MIN ((ptrdiff_t) ((ptrdiff_t)1 << (sizeof (ptrdiff_t)*8 - 1))) /* this prevents num2integral.c.i from using PTRDIFF_MIN in preprocessor expressions. */ #define NO_PREPRO_MAGIC #endif #ifndef PTRDIFF_MAX #define PTRDIFF_MAX (~ PTRDIFF_MIN) #endif #define NUM2INTEGRAL scm_num2short #define INTEGRAL2NUM scm_short2num #define INTEGRAL2BIG scm_i_short2big #define ITYPE short #define MIN_VALUE SHRT_MIN #define MAX_VALUE SHRT_MAX #include "libguile/num2integral.i.c" #define NUM2INTEGRAL scm_num2ushort #define INTEGRAL2NUM scm_ushort2num #define INTEGRAL2BIG scm_i_ushort2big #define UNSIGNED #define ITYPE unsigned short #define MAX_VALUE USHRT_MAX #include "libguile/num2integral.i.c" #define NUM2INTEGRAL scm_num2int #define INTEGRAL2NUM scm_int2num #define INTEGRAL2BIG scm_i_int2big #define ITYPE int #define MIN_VALUE INT_MIN #define MAX_VALUE INT_MAX #include "libguile/num2integral.i.c" #define NUM2INTEGRAL scm_num2uint #define INTEGRAL2NUM scm_uint2num #define INTEGRAL2BIG scm_i_uint2big #define UNSIGNED #define ITYPE unsigned int #define MAX_VALUE UINT_MAX #include "libguile/num2integral.i.c" #define NUM2INTEGRAL scm_num2long #define INTEGRAL2NUM scm_long2num #define INTEGRAL2BIG scm_i_long2big #define ITYPE long #define MIN_VALUE LONG_MIN #define MAX_VALUE LONG_MAX #include "libguile/num2integral.i.c" #define NUM2INTEGRAL scm_num2ulong #define INTEGRAL2NUM scm_ulong2num #define INTEGRAL2BIG scm_i_ulong2big #define UNSIGNED #define ITYPE unsigned long #define MAX_VALUE ULONG_MAX #include "libguile/num2integral.i.c" #define NUM2INTEGRAL scm_num2ptrdiff #define INTEGRAL2NUM scm_ptrdiff2num #define INTEGRAL2BIG scm_i_ptrdiff2big #define ITYPE ptrdiff_t #define MIN_VALUE PTRDIFF_MIN #define MAX_VALUE PTRDIFF_MAX #include "libguile/num2integral.i.c" #define NUM2INTEGRAL scm_num2size #define INTEGRAL2NUM scm_size2num #define INTEGRAL2BIG scm_i_size2big #define UNSIGNED #define ITYPE size_t #define MAX_VALUE SIZE_MAX #include "libguile/num2integral.i.c" #ifdef HAVE_LONG_LONGS #ifndef ULONG_LONG_MAX #define ULONG_LONG_MAX (~0ULL) #endif #define NUM2INTEGRAL scm_num2long_long #define INTEGRAL2NUM scm_long_long2num #define INTEGRAL2BIG scm_i_long_long2big #define ITYPE long long #define MIN_VALUE LLONG_MIN #define MAX_VALUE LLONG_MAX #define NO_PREPRO_MAGIC #include "libguile/num2integral.i.c" #define NUM2INTEGRAL scm_num2ulong_long #define INTEGRAL2NUM scm_ulong_long2num #define INTEGRAL2BIG scm_i_ulong_long2big #define UNSIGNED #define ITYPE unsigned long long #define MAX_VALUE ULLONG_MAX #define NO_PREPRO_MAGIC #include "libguile/num2integral.i.c" #endif /* HAVE_LONG_LONGS */ #define NUM2FLOAT scm_num2float #define FLOAT2NUM scm_float2num #define FTYPE float #include "libguile/num2float.i.c" #define NUM2FLOAT scm_num2double #define FLOAT2NUM scm_double2num #define FTYPE double #include "libguile/num2float.i.c" #ifdef GUILE_DEBUG #define CHECK(type, v) \ do { \ if ((v) != scm_num2##type (scm_##type##2num (v), 1, "check_sanity")) \ abort (); \ } while (0); static void check_sanity () { CHECK (short, 0); CHECK (ushort, 0U); CHECK (int, 0); CHECK (uint, 0U); CHECK (long, 0L); CHECK (ulong, 0UL); CHECK (size, 0); CHECK (ptrdiff, 0); CHECK (short, -1); CHECK (int, -1); CHECK (long, -1L); CHECK (ptrdiff, -1); CHECK (short, SHRT_MAX); CHECK (short, SHRT_MIN); CHECK (ushort, USHRT_MAX); CHECK (int, INT_MAX); CHECK (int, INT_MIN); CHECK (uint, UINT_MAX); CHECK (long, LONG_MAX); CHECK (long, LONG_MIN); CHECK (ulong, ULONG_MAX); CHECK (size, SIZE_MAX); CHECK (ptrdiff, PTRDIFF_MAX); CHECK (ptrdiff, PTRDIFF_MIN); #ifdef HAVE_LONG_LONGS CHECK (long_long, 0LL); CHECK (ulong_long, 0ULL); CHECK (long_long, -1LL); CHECK (long_long, LLONG_MAX); CHECK (long_long, LLONG_MIN); CHECK (ulong_long, ULLONG_MAX); #endif } #undef CHECK #define CHECK \ scm_internal_catch (SCM_BOOL_T, check_body, &data, check_handler, &data); \ if (!SCM_FALSEP (data)) abort(); static SCM check_body (void *data) { SCM num = *(SCM *) data; scm_num2ulong (num, 1, NULL); return SCM_UNSPECIFIED; } static SCM check_handler (void *data, SCM tag, SCM throw_args) { SCM *num = (SCM *) data; *num = SCM_BOOL_F; return SCM_UNSPECIFIED; } SCM_DEFINE (scm_sys_check_number_conversions, "%check-number-conversions", 0, 0, 0, (), "Number conversion sanity checking.") #define FUNC_NAME s_scm_sys_check_number_conversions { SCM data = SCM_MAKINUM (-1); CHECK; data = scm_int2num (INT_MIN); CHECK; data = scm_ulong2num (ULONG_MAX); data = scm_difference (SCM_INUM0, data); CHECK; data = scm_ulong2num (ULONG_MAX); data = scm_sum (SCM_MAKINUM (1), data); data = scm_difference (SCM_INUM0, data); CHECK; data = scm_int2num (-10000); data = scm_product (data, data); data = scm_product (data, data); CHECK; return SCM_UNSPECIFIED; } #undef FUNC_NAME #endif void scm_init_numbers () { abs_most_negative_fixnum = scm_i_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_c_define ("most-positive-fixnum", SCM_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); scm_c_define ("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 */ #ifdef GUILE_DEBUG check_sanity (); #endif #ifndef SCM_MAGIC_SNARFER #include "libguile/numbers.x" #endif } /* Local Variables: c-file-style: "gnu" End: */