/* * Copyright (C) 1987-2008 Sun Microsystems, Inc. All Rights Reserved. * Copyright (C) 2008-2011 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 of the License, or (at your option) any later * version. See http://www.gnu.org/copyleft/gpl.html the full text of the * license. */ /* 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 #include #include /* 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); /* 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 */