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Diffstat (limited to 'src/mp.h')
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1 files changed, 357 insertions, 0 deletions
diff --git a/src/mp.h b/src/mp.h new file mode 100644 index 0000000..d71111d --- /dev/null +++ b/src/mp.h @@ -0,0 +1,357 @@ + +/* Copyright (c) 1987-2008 Sun Microsystems, Inc. All Rights Reserved. + * Copyright (c) 2008-2009 Robert Ancell + * + * 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 program; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA + * 02111-1307, USA. + */ + +/* This maths library is based on the MP multi-precision floating-point + * arithmetic package originally written in FORTRAN by Richard Brent, + * Computer Centre, Australian National University in the 1970's. + * + * It has been converted from FORTRAN into C using the freely available + * f2c translator, available via netlib on research.att.com. + * + * The subsequently converted C code has then been tidied up, mainly to + * remove any dependencies on the libI77 and libF77 support libraries. + * + * FOR A GENERAL DESCRIPTION OF THE PHILOSOPHY AND DESIGN OF MP, + * SEE - R. P. BRENT, A FORTRAN MULTIPLE-PRECISION ARITHMETIC + * PACKAGE, ACM TRANS. MATH. SOFTWARE 4 (MARCH 1978), 57-70. + * SOME ADDITIONAL DETAILS ARE GIVEN IN THE SAME ISSUE, 71-81. + * FOR DETAILS OF THE IMPLEMENTATION, CALLING SEQUENCES ETC. SEE + * THE MP USERS GUIDE. + */ + +#ifndef MP_H +#define MP_H + +#include <stdbool.h> +#include <stdint.h> +#include <glib.h> + +/* Size of the multiple precision values */ +#define MP_SIZE 1000 + +/* Base for numbers */ +#define MP_BASE 10000 + +/* Object for a high precision floating point number representation + * + * x = sign * (MP_BASE^(exponent-1) + MP_BASE^(exponent-2) + ...) + */ +typedef struct +{ + /* Sign (+1, -1) or 0 for the value zero */ + int sign, im_sign; + + /* Exponent (to base MP_BASE) */ + int exponent, im_exponent; + + /* Normalized fraction */ + int fraction[MP_SIZE], im_fraction[MP_SIZE]; +} MPNumber; + +typedef enum +{ + MP_RADIANS, + MP_DEGREES, + MP_GRADIANS +} MPAngleUnit; + +/* Returns error string or NULL if no error */ +// FIXME: Global variable +const char *mp_get_error(void); + +/* Clear any current error */ +void mp_clear_error(void); + +/* Returns: + * 0 if x == y + * <0 if x < y + * >0 if x > y + */ +int mp_compare_mp_to_mp(const MPNumber *x, const MPNumber *y); + +/* Return true if the value is x == 0 */ +bool mp_is_zero(const MPNumber *x); + +/* Return true if x < 0 */ +bool mp_is_negative(const MPNumber *x); + +/* Return true if x is integer */ +bool mp_is_integer(const MPNumber *x); + +/* Return true if x is a positive integer */ +bool mp_is_positive_integer(const MPNumber *x); + +/* Return true if x is a natural number (an integer ≥ 0) */ +bool mp_is_natural(const MPNumber *x); + +/* Return true if x has an imaginary component */ +bool mp_is_complex(const MPNumber *x); + +/* Return true if x == y */ +bool mp_is_equal(const MPNumber *x, const MPNumber *y); + +/* Return true if x ≥ y */ +bool mp_is_greater_equal(const MPNumber *x, const MPNumber *y); + +/* Return true if x > y */ +bool mp_is_greater_than(const MPNumber *x, const MPNumber *y); + +/* Return true if x ≤ y */ +bool mp_is_less_equal(const MPNumber *x, const MPNumber *y); + +/* Return true if x < y */ +bool mp_is_less_than(const MPNumber *x, const MPNumber *y); + +/* Sets z = |x| */ +void mp_abs(const MPNumber *x, MPNumber *z); + +/* Sets z = Arg(x) */ +void mp_arg(const MPNumber *x, MPAngleUnit unit, MPNumber *z); + +/* Sets z = ‾̅x */ +void mp_conjugate(const MPNumber *x, MPNumber *z); + +/* Sets z = Re(x) */ +void mp_real_component(const MPNumber *x, MPNumber *z); + +/* Sets z = Im(x) */ +void mp_imaginary_component(const MPNumber *x, MPNumber *z); + +/* Sets z = −x */ +void mp_invert_sign(const MPNumber *x, MPNumber *z); + +/* Sets z = x + y */ +void mp_add(const MPNumber *x, const MPNumber *y, MPNumber *z); + +/* Sets z = x + y */ +void mp_add_integer(const MPNumber *x, int64_t y, MPNumber *z); + +/* Sets z = x + numerator ÷ denominator */ +void mp_add_fraction(const MPNumber *x, int64_t numerator, int64_t denominator, MPNumber *z); + +/* Sets z = x − y */ +void mp_subtract(const MPNumber *x, const MPNumber *y, MPNumber *z); + +/* Sets z = x × y */ +void mp_multiply(const MPNumber *x, const MPNumber *y, MPNumber *z); + +/* Sets z = x × y */ +void mp_multiply_integer(const MPNumber *x, int64_t y, MPNumber *z); + +/* Sets z = x × numerator ÷ denominator */ +void mp_multiply_fraction(const MPNumber *x, int64_t numerator, int64_t denominator, MPNumber *z); + +/* Sets z = x ÷ y */ +void mp_divide(const MPNumber *x, const MPNumber *y, MPNumber *z); + +/* Sets z = x ÷ y */ +void mp_divide_integer(const MPNumber *x, int64_t y, MPNumber *z); + +/* Sets z = 1 ÷ x */ +void mp_reciprocal(const MPNumber *, MPNumber *); + +/* Sets z = sgn(x) */ +void mp_sgn(const MPNumber *x, MPNumber *z); + +void mp_integer_component(const MPNumber *x, MPNumber *z); + +/* Sets z = x mod 1 */ +void mp_fractional_component(const MPNumber *x, MPNumber *z); + +/* Sets z = {x} */ +void mp_fractional_part(const MPNumber *x, MPNumber *z); + +/* Sets z = ⌊x⌋ */ +void mp_floor(const MPNumber *x, MPNumber *z); + +/* Sets z = ⌈x⌉ */ +void mp_ceiling(const MPNumber *x, MPNumber *z); + +/* Sets z = [x] */ +void mp_round(const MPNumber *x, MPNumber *z); + +/* Sets z = ln x */ +void mp_ln(const MPNumber *x, MPNumber *z); + +/* Sets z = log_n x */ +void mp_logarithm(int64_t n, const MPNumber *x, MPNumber *z); + +/* Sets z = π */ +void mp_get_pi(MPNumber *z); + +/* Sets z = e */ +void mp_get_eulers(MPNumber *z); + +/* Sets z = i (√−1) */ +void mp_get_i(MPNumber *z); + +/* Sets z = n√x */ +void mp_root(const MPNumber *x, int64_t n, MPNumber *z); + +/* Sets z = √x */ +void mp_sqrt(const MPNumber *x, MPNumber *z); + +/* Sets z = x! */ +void mp_factorial(const MPNumber *x, MPNumber *z); + +/* Sets z = x mod y */ +void mp_modulus_divide(const MPNumber *x, const MPNumber *y, MPNumber *z); + +/* Sets z = x^y */ +void mp_xpowy(const MPNumber *x, const MPNumber *y, MPNumber *z); + +/* Sets z = x^y */ +void mp_xpowy_integer(const MPNumber *x, int64_t y, MPNumber *z); + +/* Sets z = e^x */ +void mp_epowy(const MPNumber *x, MPNumber *z); + +/* Returns a list of all prime factors in x as MPNumbers */ +GList* mp_factorize(const MPNumber *x); + +/* Sets z = x */ +void mp_set_from_mp(const MPNumber *x, MPNumber *z); + +/* Sets z = x */ +void mp_set_from_float(float x, MPNumber *z); + +/* Sets z = x */ +void mp_set_from_double(double x, MPNumber *z); + +/* Sets z = x */ +void mp_set_from_integer(int64_t x, MPNumber *z); + +/* Sets z = x */ +void mp_set_from_unsigned_integer(uint64_t x, MPNumber *z); + +/* Sets z = numerator ÷ denominator */ +void mp_set_from_fraction(int64_t numerator, int64_t denominator, MPNumber *z); + +/* Sets z = r(cos theta + i sin theta) */ +void mp_set_from_polar(const MPNumber *r, MPAngleUnit unit, const MPNumber *theta, MPNumber *z); + +/* Sets z = x + iy */ +void mp_set_from_complex(const MPNumber *x, const MPNumber *y, MPNumber *z); + +/* Sets z to be a uniform random number in the range [0, 1] */ +void mp_set_from_random(MPNumber *z); + +/* Sets z from a string representation in 'text'. + * Returns true on success. + */ +bool mp_set_from_string(const char *text, int default_base, MPNumber *z); + +/* Returns x as a native single-precision floating point number */ +float mp_cast_to_float(const MPNumber *x); + +/* Returns x as a native double-precision floating point number */ +double mp_cast_to_double(const MPNumber *x); + +/* Returns x as a native integer */ +int64_t mp_cast_to_int(const MPNumber *x); + +/* Returns x as a native unsigned integer */ +uint64_t mp_cast_to_unsigned_int(const MPNumber *x); + +/* Converts x to a string representation. + * The string is written into 'buffer' which is guaranteed to be at least 'buffer_length' octets in size. + * If not enough space is available the string is truncated. + * The numbers are written in 'base' (e.g. 10). + * If 'trim_zeroes' is non-zero then strip off trailing zeroes. + * Fractional components are truncated at 'max_digits' digits. + */ +void mp_cast_to_string(const MPNumber *x, int default_base, int base, int max_digits, bool trim_zeroes, char *buffer, int buffer_length); + +/* Converts x to a string representation in exponential form. + * The string is written into 'buffer' which is guaranteed to be at least 'buffer_length' octets in size. + * If not enough space is available the string is truncated. + * The numbers are written in 'base' (e.g. 10). + * If 'trim_zeroes' is non-zero then strip off trailing zeroes. + * Fractional components are truncated at 'max_digits' digits. + */ +void mp_cast_to_exponential_string(const MPNumber *x, int default_base, int base, int max_digits, bool trim_zeroes, bool eng_format, char *buffer, int buffer_length); + +/* Sets z = sin x */ +void mp_sin(const MPNumber *x, MPAngleUnit unit, MPNumber *z); + +/* Sets z = cos x */ +void mp_cos(const MPNumber *x, MPAngleUnit unit, MPNumber *z); + +/* Sets z = tan x */ +void mp_tan(const MPNumber *x, MPAngleUnit unit, MPNumber *z); + +/* Sets z = sin⁻¹ x */ +void mp_asin(const MPNumber *x, MPAngleUnit unit, MPNumber *z); + +/* Sets z = cos⁻¹ x */ +void mp_acos(const MPNumber *x, MPAngleUnit unit, MPNumber *z); + +/* Sets z = tan⁻¹ x */ +void mp_atan(const MPNumber *x, MPAngleUnit unit, MPNumber *z); + +/* Sets z = sinh x */ +void mp_sinh(const MPNumber *x, MPNumber *z); + +/* Sets z = cosh x */ +void mp_cosh(const MPNumber *x, MPNumber *z); + +/* Sets z = tanh x */ +void mp_tanh(const MPNumber *x, MPNumber *z); + +/* Sets z = sinh⁻¹ x */ +void mp_asinh(const MPNumber *x, MPNumber *z); + +/* Sets z = cosh⁻¹ x */ +void mp_acosh(const MPNumber *x, MPNumber *z); + +/* Sets z = tanh⁻¹ x */ +void mp_atanh(const MPNumber *x, MPNumber *z); + +/* Returns true if x is cannot be represented in a binary word of length 'wordlen' */ +bool mp_is_overflow(const MPNumber *x, int wordlen); + +/* Sets z = boolean AND for each bit in x and z */ +void mp_and(const MPNumber *x, const MPNumber *y, MPNumber *z); + +/* Sets z = boolean OR for each bit in x and z */ +void mp_or(const MPNumber *x, const MPNumber *y, MPNumber *z); + +/* Sets z = boolean XOR for each bit in x and z */ +void mp_xor(const MPNumber *x, const MPNumber *y, MPNumber *z); + +/* Sets z = boolean XNOR for each bit in x and z for word of length 'wordlen' */ +void mp_xnor(const MPNumber *x, const MPNumber *y, int wordlen, MPNumber *z); + +/* Sets z = boolean NOT for each bit in x and z for word of length 'wordlen' */ +void mp_not(const MPNumber *x, int wordlen, MPNumber *z); + +/* Sets z = x masked to 'wordlen' bits */ +void mp_mask(const MPNumber *x, int wordlen, MPNumber *z); + +/* Sets z = x shifted by 'count' bits. Positive shift increases the value, negative decreases */ +void mp_shift(const MPNumber *x, int count, MPNumber *z); + +/* Sets z to be the ones complement of x for word of length 'wordlen' */ +void mp_ones_complement(const MPNumber *x, int wordlen, MPNumber *z); + +/* Sets z to be the twos complement of x for word of length 'wordlen' */ +void mp_twos_complement(const MPNumber *x, int wordlen, MPNumber *z); + +#endif /* MP_H */ |