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/* Copyright (C) 1995,1996,1998,2000,2001,2002,2003,2004,2005, 2006 Free Software Foundation, Inc.
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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#include "libguile/__scm.h"
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#include "libguile/print.h"
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#if SCM_HAVE_FLOATINGPOINT_H
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# include <floatingpoint.h>
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#endif /* SCM_HAVE_NAN_H */
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/* Immediate Numbers, also known as fixnums
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* Inums are exact integer data that fits within an SCM word. */
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/* SCM_T_SIGNED_MAX is (- (expt 2 n) 1),
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* SCM_MOST_POSITIVE_FIXNUM should be (- (expt 2 (- n 2)) 1)
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* which is the same as (/ (- (expt 2 n) 4) 4)
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#define SCM_I_FIXNUM_BIT (SCM_LONG_BIT - 2)
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#define SCM_MOST_POSITIVE_FIXNUM ((SCM_T_SIGNED_BITS_MAX-3)/4)
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#define SCM_MOST_NEGATIVE_FIXNUM (-SCM_MOST_POSITIVE_FIXNUM-1)
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/* SCM_SRS is signed right shift */
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#if (-1 == (((-1) << 2) + 2) >> 2)
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# define SCM_SRS(x, y) ((x) >> (y))
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# define SCM_SRS(x, y) ((x) < 0 ? ~((~(x)) >> (y)) : ((x) >> (y)))
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#endif /* (-1 == (((-1) << 2) + 2) >> 2) */
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#define SCM_I_INUMP(x) (2 & SCM_UNPACK (x))
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#define SCM_I_NINUMP(x) (!SCM_I_INUMP (x))
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#define SCM_I_MAKINUM(x) \
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(SCM_PACK ((((scm_t_signed_bits) (x)) << 2) + scm_tc2_int))
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#define SCM_I_INUM(x) (SCM_SRS ((scm_t_signed_bits) SCM_UNPACK (x), 2))
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/* SCM_FIXABLE is true if its long argument can be encoded in an SCM_INUM. */
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#define SCM_POSFIXABLE(n) ((n) <= SCM_MOST_POSITIVE_FIXNUM)
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#define SCM_NEGFIXABLE(n) ((n) >= SCM_MOST_NEGATIVE_FIXNUM)
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#define SCM_FIXABLE(n) (SCM_POSFIXABLE (n) && SCM_NEGFIXABLE (n))
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#define SCM_INUM0 (SCM_I_MAKINUM (0))
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/* SCM_MAXEXP is the maximum double precision exponent
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* SCM_FLTMAX is less than or scm_equal the largest single precision float
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#if SCM_HAVE_STDC_HEADERS
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# define copysign _copysign
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# define finite _finite
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# endif /* __MINGW32__ */
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# endif /* ndef GO32 */
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#endif /* def STDC_HEADERS */
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#ifdef DBL_MAX_10_EXP
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# define SCM_MAXEXP DBL_MAX_10_EXP
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# define SCM_MAXEXP 308 /* IEEE doubles */
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#endif /* def DBL_MAX_10_EXP */
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# define SCM_FLTMAX FLT_MAX
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# define SCM_FLTMAX 1e+23
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#endif /* def FLT_MAX */
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/* SCM_INTBUFLEN is the maximum number of characters neccessary for
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* the printed or scm_string representation of an scm_t_intmax in
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* radix 2. The buffer passed to scm_iint2str and scm_iuint2str must
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* be of this size, for example.
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#define SCM_INTBUFLEN (5 + SCM_CHAR_BIT*sizeof(scm_t_intmax))
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/* Note that scm_tc16_real and scm_tc16_complex are given tc16-codes that only
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* differ in one bit: This way, checking if an object is an inexact number can
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* be done quickly (using the TYP16S macro). */
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/* Number subtype 1 to 3 (note the dependency on the predicates SCM_INEXACTP
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#define scm_tc16_big (scm_tc7_number + 1 * 256L)
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#define scm_tc16_real (scm_tc7_number + 2 * 256L)
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#define scm_tc16_complex (scm_tc7_number + 3 * 256L)
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#define scm_tc16_fraction (scm_tc7_number + 4 * 256L)
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#define SCM_INEXACTP(x) \
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(!SCM_IMP (x) && (0xfeff & SCM_CELL_TYPE (x)) == scm_tc16_real)
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#define SCM_REALP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_real)
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#define SCM_COMPLEXP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_complex)
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#define SCM_REAL_VALUE(x) (((scm_t_double *) SCM2PTR (x))->real)
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#define SCM_COMPLEX_MEM(x) ((scm_t_complex *) SCM_CELL_WORD_1 (x))
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#define SCM_COMPLEX_REAL(x) (SCM_COMPLEX_MEM (x)->real)
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#define SCM_COMPLEX_IMAG(x) (SCM_COMPLEX_MEM (x)->imag)
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/* Each bignum is just an mpz_t stored in a double cell starting at word 1. */
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#define SCM_I_BIG_MPZ(x) (*((mpz_t *) (SCM_CELL_OBJECT_LOC((x),1))))
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#define SCM_BIGP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_big)
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#define SCM_NUMBERP(x) (SCM_I_INUMP(x) || SCM_NUMP(x))
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#define SCM_NUMP(x) (!SCM_IMP(x) \
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&& (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) \
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|| ((0xfbff & SCM_CELL_TYPE (x)) == scm_tc7_number)))
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/* 0xfcff (#b1100) for 0 free, 1 big, 2 real, 3 complex, then 0xfbff (#b1011) for 4 fraction */
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#define SCM_FRACTIONP(x) (!SCM_IMP (x) && SCM_TYP16 (x) == scm_tc16_fraction)
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#define SCM_FRACTION_NUMERATOR(x) (SCM_CELL_OBJECT_1 (x))
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#define SCM_FRACTION_DENOMINATOR(x) (SCM_CELL_OBJECT_2 (x))
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#define SCM_FRACTION_SET_NUMERATOR(x, v) (SCM_SET_CELL_OBJECT_1 ((x), (v)))
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#define SCM_FRACTION_SET_DENOMINATOR(x, v) (SCM_SET_CELL_OBJECT_2 ((x), (v)))
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/* I think the left half word is free in the type, so I'll use bit 17 */
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#define SCM_FRACTION_REDUCED_BIT 0x10000
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#define SCM_FRACTION_REDUCED_SET(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) | SCM_FRACTION_REDUCED_BIT)))
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#define SCM_FRACTION_REDUCED_CLEAR(x) (SCM_SET_CELL_TYPE((x), (SCM_CELL_TYPE (x) & ~SCM_FRACTION_REDUCED_BIT)))
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#define SCM_FRACTION_REDUCED(x) (0x10000 & SCM_CELL_TYPE (x))
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typedef struct scm_t_double
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typedef struct scm_t_complex
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SCM_API SCM scm_exact_p (SCM x);
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SCM_API SCM scm_odd_p (SCM n);
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SCM_API SCM scm_even_p (SCM n);
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SCM_API SCM scm_inf_p (SCM n);
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SCM_API SCM scm_nan_p (SCM n);
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SCM_API SCM scm_inf (void);
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SCM_API SCM scm_nan (void);
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SCM_API SCM scm_abs (SCM x);
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SCM_API SCM scm_quotient (SCM x, SCM y);
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SCM_API SCM scm_remainder (SCM x, SCM y);
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SCM_API SCM scm_modulo (SCM x, SCM y);
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SCM_API SCM scm_gcd (SCM x, SCM y);
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SCM_API SCM scm_lcm (SCM n1, SCM n2);
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SCM_API SCM scm_logand (SCM n1, SCM n2);
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SCM_API SCM scm_logior (SCM n1, SCM n2);
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SCM_API SCM scm_logxor (SCM n1, SCM n2);
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SCM_API SCM scm_logtest (SCM n1, SCM n2);
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SCM_API SCM scm_logbit_p (SCM n1, SCM n2);
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SCM_API SCM scm_lognot (SCM n);
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SCM_API SCM scm_modulo_expt (SCM n, SCM k, SCM m);
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SCM_API SCM scm_integer_expt (SCM z1, SCM z2);
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SCM_API SCM scm_ash (SCM n, SCM cnt);
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SCM_API SCM scm_bit_extract (SCM n, SCM start, SCM end);
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SCM_API SCM scm_logcount (SCM n);
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SCM_API SCM scm_integer_length (SCM n);
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SCM_API size_t scm_iint2str (scm_t_intmax num, int rad, char *p);
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SCM_API size_t scm_iuint2str (scm_t_uintmax num, int rad, char *p);
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SCM_API SCM scm_number_to_string (SCM x, SCM radix);
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SCM_API int scm_print_real (SCM sexp, SCM port, scm_print_state *pstate);
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SCM_API int scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate);
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SCM_API int scm_bigprint (SCM exp, SCM port, scm_print_state *pstate);
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SCM_API SCM scm_c_locale_stringn_to_number (const char *mem, size_t len,
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SCM_API SCM scm_string_to_number (SCM str, SCM radix);
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SCM_API SCM scm_bigequal (SCM x, SCM y);
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SCM_API SCM scm_real_equalp (SCM x, SCM y);
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SCM_API SCM scm_complex_equalp (SCM x, SCM y);
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SCM_API SCM scm_number_p (SCM x);
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SCM_API SCM scm_complex_p (SCM x);
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SCM_API SCM scm_real_p (SCM x);
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SCM_API SCM scm_rational_p (SCM z);
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SCM_API SCM scm_integer_p (SCM x);
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SCM_API SCM scm_inexact_p (SCM x);
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SCM_API SCM scm_num_eq_p (SCM x, SCM y);
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SCM_API SCM scm_less_p (SCM x, SCM y);
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SCM_API SCM scm_gr_p (SCM x, SCM y);
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SCM_API SCM scm_leq_p (SCM x, SCM y);
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SCM_API SCM scm_geq_p (SCM x, SCM y);
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SCM_API SCM scm_zero_p (SCM z);
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SCM_API SCM scm_positive_p (SCM x);
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SCM_API SCM scm_negative_p (SCM x);
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SCM_API SCM scm_max (SCM x, SCM y);
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SCM_API SCM scm_min (SCM x, SCM y);
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SCM_API SCM scm_sum (SCM x, SCM y);
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SCM_API SCM scm_oneplus (SCM x);
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SCM_API SCM scm_difference (SCM x, SCM y);
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SCM_API SCM scm_oneminus (SCM x);
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SCM_API SCM scm_product (SCM x, SCM y);
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SCM_API SCM scm_divide (SCM x, SCM y);
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SCM_API SCM scm_floor (SCM x);
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SCM_API SCM scm_ceiling (SCM x);
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SCM_API double scm_asinh (double x);
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SCM_API double scm_acosh (double x);
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SCM_API double scm_atanh (double x);
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SCM_API double scm_c_truncate (double x);
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SCM_API double scm_c_round (double x);
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SCM_API SCM scm_truncate_number (SCM x);
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SCM_API SCM scm_round_number (SCM x);
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SCM_API SCM scm_sys_expt (SCM z1, SCM z2);
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SCM_API SCM scm_sys_atan2 (SCM z1, SCM z2);
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SCM_API SCM scm_make_rectangular (SCM z1, SCM z2);
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SCM_API SCM scm_make_polar (SCM z1, SCM z2);
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SCM_API SCM scm_real_part (SCM z);
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SCM_API SCM scm_imag_part (SCM z);
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SCM_API SCM scm_magnitude (SCM z);
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SCM_API SCM scm_angle (SCM z);
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SCM_API SCM scm_exact_to_inexact (SCM z);
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SCM_API SCM scm_inexact_to_exact (SCM z);
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SCM_API SCM scm_trunc (SCM x);
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SCM_API SCM scm_log (SCM z);
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SCM_API SCM scm_log10 (SCM z);
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SCM_API SCM scm_exp (SCM z);
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SCM_API SCM scm_sqrt (SCM z);
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/* bignum internal functions */
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SCM_API SCM scm_i_mkbig (void);
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SCM_API SCM scm_i_normbig (SCM x);
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SCM_API int scm_i_bigcmp (SCM a, SCM b);
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SCM_API SCM scm_i_dbl2big (double d);
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SCM_API SCM scm_i_dbl2num (double d);
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SCM_API double scm_i_big2dbl (SCM b);
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SCM_API SCM scm_i_long2big (long n);
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SCM_API SCM scm_i_ulong2big (unsigned long n);
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SCM_API SCM scm_i_clonebig (SCM src_big, int same_sign_p);
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/* ratio functions */
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SCM_API SCM scm_rationalize (SCM x, SCM err);
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SCM_API SCM scm_numerator (SCM z);
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SCM_API SCM scm_denominator (SCM z);
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/* fraction internal functions */
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SCM_API double scm_i_fraction2double (SCM z);
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SCM_API SCM scm_i_fraction_equalp (SCM x, SCM y);
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SCM_API int scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate);
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/* general internal functions */
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SCM_API void scm_i_print_double (double val, SCM port);
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SCM_API void scm_i_print_complex (double real, double imag, SCM port);
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/* conversion functions for integers */
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SCM_API int scm_is_integer (SCM val);
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SCM_API int scm_is_signed_integer (SCM val,
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scm_t_intmax min, scm_t_intmax max);
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SCM_API int scm_is_unsigned_integer (SCM val,
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scm_t_uintmax min, scm_t_uintmax max);
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SCM_API SCM scm_from_signed_integer (scm_t_intmax val);
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SCM_API SCM scm_from_unsigned_integer (scm_t_uintmax val);
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SCM_API scm_t_intmax scm_to_signed_integer (SCM val,
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SCM_API scm_t_uintmax scm_to_unsigned_integer (SCM val,
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SCM_API scm_t_int8 scm_to_int8 (SCM x);
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SCM_API SCM scm_from_int8 (scm_t_int8 x);
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SCM_API scm_t_uint8 scm_to_uint8 (SCM x);
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SCM_API SCM scm_from_uint8 (scm_t_uint8 x);
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SCM_API scm_t_int16 scm_to_int16 (SCM x);
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SCM_API SCM scm_from_int16 (scm_t_int16 x);
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SCM_API scm_t_uint16 scm_to_uint16 (SCM x);
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SCM_API SCM scm_from_uint16 (scm_t_uint16 x);
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SCM_API scm_t_int32 scm_to_int32 (SCM x);
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SCM_API SCM scm_from_int32 (scm_t_int32 x);
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SCM_API scm_t_uint32 scm_to_uint32 (SCM x);
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SCM_API SCM scm_from_uint32 (scm_t_uint32 x);
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SCM_API scm_t_int64 scm_to_int64 (SCM x);
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SCM_API SCM scm_from_int64 (scm_t_int64 x);
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SCM_API scm_t_uint64 scm_to_uint64 (SCM x);
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SCM_API SCM scm_from_uint64 (scm_t_uint64 x);
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SCM_API void scm_to_mpz (SCM x, mpz_t rop);
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SCM_API SCM scm_from_mpz (mpz_t rop);
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/* The conversion functions for other types are aliased to the
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appropriate ones from above. We pick the right one based on the
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Not each and every possibility is covered by the code below, and
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while it is trivial to complete the tests, it might be better to
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just test for the 'sane' possibilities. When one of the tests
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below fails, chances are good that some silent assumption somewhere
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#if SCM_SIZEOF_CHAR == 1
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#define scm_to_schar scm_to_int8
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#define scm_from_schar scm_from_int8
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#define scm_to_uchar scm_to_uint8
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#define scm_from_uchar scm_from_uint8
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#define scm_to_char scm_to_uint8
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#define scm_from_char scm_from_uint8
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#define scm_to_char scm_to_int8
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#define scm_from_char scm_from_int8
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#error sizeof(char) is not 1.
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#if SCM_SIZEOF_SHORT == 1
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#define scm_to_short scm_to_int8
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#define scm_from_short scm_from_int8
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#define scm_to_ushort scm_to_uint8
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#define scm_from_ushort scm_from_uint8
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#if SCM_SIZEOF_SHORT == 2
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#define scm_to_short scm_to_int16
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#define scm_from_short scm_from_int16
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#define scm_to_ushort scm_to_uint16
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#define scm_from_ushort scm_from_uint16
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#if SCM_SIZEOF_SHORT == 4
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#define scm_to_short scm_to_int32
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#define scm_from_short scm_from_int32
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#define scm_to_ushort scm_to_uint32
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#define scm_from_ushort scm_from_uint32
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#error sizeof(short) is not 1, 2, or 4.
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#if SCM_SIZEOF_INT == 4
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#define scm_to_int scm_to_int32
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#define scm_from_int scm_from_int32
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#define scm_to_uint scm_to_uint32
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#define scm_from_uint scm_from_uint32
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#if SCM_SIZEOF_INT == 8
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#define scm_to_int scm_to_int64
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#define scm_from_int scm_from_int64
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#define scm_to_uint scm_to_uint64
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#define scm_from_uint scm_from_uint64
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#error sizeof(int) is not 4 or 8.
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#if SCM_SIZEOF_LONG == 4
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#define scm_to_long scm_to_int32
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#define scm_from_long scm_from_int32
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#define scm_to_ulong scm_to_uint32
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#define scm_from_ulong scm_from_uint32
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#if SCM_SIZEOF_LONG == 8
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#define scm_to_long scm_to_int64
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#define scm_from_long scm_from_int64
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#define scm_to_ulong scm_to_uint64
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#define scm_from_ulong scm_from_uint64
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#error sizeof(long) is not 4 or 8.
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#if SCM_SIZEOF_INTMAX == 4
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#define scm_to_intmax scm_to_int32
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#define scm_from_intmax scm_from_int32
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#define scm_to_uintmax scm_to_uint32
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#define scm_from_uintmax scm_from_uint32
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#if SCM_SIZEOF_INTMAX == 8
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#define scm_to_intmax scm_to_int64
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#define scm_from_intmax scm_from_int64
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#define scm_to_uintmax scm_to_uint64
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#define scm_from_uintmax scm_from_uint64
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#error sizeof(scm_t_intmax) is not 4 or 8.
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#if SCM_SIZEOF_LONG_LONG == 0
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#if SCM_SIZEOF_LONG_LONG == 8
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#define scm_to_long_long scm_to_int64
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#define scm_from_long_long scm_from_int64
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#define scm_to_ulong_long scm_to_uint64
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#define scm_from_ulong_long scm_from_uint64
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#error sizeof(long long) is not 8.
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#if SCM_SIZEOF_SIZE_T == 4
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#define scm_to_ssize_t scm_to_int32
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#define scm_from_ssize_t scm_from_int32
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#define scm_to_size_t scm_to_uint32
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#define scm_from_size_t scm_from_uint32
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#if SCM_SIZEOF_SIZE_T == 8
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#define scm_to_ssize_t scm_to_int64
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#define scm_from_ssize_t scm_from_int64
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#define scm_to_size_t scm_to_uint64
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#define scm_from_size_t scm_from_uint64
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#error sizeof(size_t) is not 4 or 8.
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/* conversion functions for double */
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SCM_API int scm_is_real (SCM val);
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SCM_API int scm_is_rational (SCM val);
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SCM_API double scm_to_double (SCM val);
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SCM_API SCM scm_from_double (double val);
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/* conversion functions for complex */
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SCM_API int scm_is_complex (SCM val);
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SCM_API SCM scm_c_make_rectangular (double re, double im);
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SCM_API SCM scm_c_make_polar (double mag, double ang);
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SCM_API double scm_c_real_part (SCM z);
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SCM_API double scm_c_imag_part (SCM z);
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SCM_API double scm_c_magnitude (SCM z);
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SCM_API double scm_c_angle (SCM z);
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SCM_API int scm_is_number (SCM val);
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SCM_API void scm_init_numbers (void);
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#endif /* SCM_NUMBERS_H */
added
removed
libguile/numbers.h
