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guile/libguile/numbers.c
Dirk Herrmann dee01b012c * Removed deprecated stuff. 
* Some more renamings to SCM_<filename>_H.
2001-08-31 12:13:50 +00:00

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/* 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 <math.h>
#include <ctype.h>
#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 {
int k = 1;
long t;
/* Determine a common factor 2^k */
while (!(1 & (u | v))) {
k <<= 1;
u >>= 1;
v >>= 1;
}
/* Now, any factor 2^n can be eliminated */
if (u & 1) {
t = -v;
} else {
t = u;
b3:
t = SCM_SRS (t, 1);
}
if (!(1 & t))
goto b3;
if (t > 0)
u = t;
else
v = -t;
t = u - v;
if (t != 0)
goto b3;
result = u * k;
}
if (SCM_POSFIXABLE (result)) {
return SCM_MAKINUM (result);
} else {
#ifdef SCM_BIGDIG
return scm_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
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 (<ureal R>,
* <uinteger R>, ...) 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: <uinteger R>. */
/* 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)
return SCM_BOOL_F;
digit_value = XDIGIT2UINT (c);
if (digit_value >= radix)
return SCM_BOOL_F;
}
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: <decimal 10>. 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 prepoint. 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 prepoint, 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;
SCM big_shift = SCM_MAKINUM (1);
SCM big_add = SCM_MAKINUM (0);
SCM result;
if (idx == len)
return prepoint;
if (mem[idx] == '.')
{
scm_t_bits shift = 1;
scm_t_bits add = 0;
unsigned int digit_value;
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));
big_add = scm_product (big_add, SCM_MAKINUM (shift));
if (add > 0)
big_add = scm_sum (big_add, 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));
big_add = scm_product (big_add, SCM_MAKINUM (shift));
big_add = scm_sum (big_add, SCM_MAKINUM (add));
}
/* We've seen a decimal point, thus the value is implicitly inexact. */
x = INEXACT;
}
big_add = scm_divide (big_add, big_shift);
result = scm_sum (prepoint, big_add);
if (idx != len)
{
int sign = 1;
unsigned int start;
char c;
int exponent;
SCM e;
/* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */
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: <ureal R> */
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: <complex R> */
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 +<ureal>i or -<ureal>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: <real>@<real>. */
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 <real>[+-]<ureal>?i */
idx++;
if (idx == len)
return SCM_BOOL_F;
else
{
int sign = (c == '+') ? 1 : -1;
SCM imag = mem2ureal (mem, len, &idx, radix, p_exactness);
SCM result;
if (SCM_FALSEP (imag))
imag = SCM_MAKINUM (sign);
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;
if (sign == -1)
imag = scm_difference (imag, SCM_UNDEFINED);
result = scm_make_rectangular (ureal, imag);
return result;
}
default:
return SCM_BOOL_F;
}
}
}
/* R5RS, section 7.1.1, lexical structure of numbers: <number> */
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: <prefix R> */
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: <complex R> */
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)))
#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
#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
#include "libguile/num2integral.i.c"
#endif /* HAVE_LONG_LONGS */
#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
}
#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:
*/
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