function.ref

任意精度的数学库

Example:    M_APM  apmresult, apm_num1, apm_num2;
	    int    decimal_places;
            m_apm_divide(apmresult, decimal_places, apm_num1, apm_num2);

            This function will divide apm_num1 by apm_num2 and put the 
	    result in 'apmresult'.  The 'apmresult' parameter cannot be 
	    one of the other MAPM parameters.

            Unlike the other three basic operations, division cannot be 
	    counted on to produce non-repeating decimals, so the 
	    'decimal_places' variable is used to tell this routine how many
            digits are to be calculated before stopping.  

	    Note that the number of decimal places is referenced to the 
	    value as if the number was in fixed point notation. m_apm_divide
	    is the only function where decimal places is referenced to 
	    fixed point notation, all other functions are referenced to 
	    scientific notation. This was an intentional design decision 
	    so 'm_apm_integer_divide' and 'm_apm_integer_div_rem' would 
	    work as expected.
	    
            Division by zero creates a zero result and a warning on stderr.

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Prototype:  void  m_apm_integer_divide(M_APM, M_APM, M_APM);

Example:    M_APM  apmresult, apm_num1, apm_num2;
            m_apm_integer_divide(apmresult, apm_num1, apm_num2);

            This function will divide apm_num1 by apm_num2, truncating the
	    result to an integer and put the result in 'apmresult'.  The 
	    'apmresult' parameter cannot be one of the other MAPM parameters.

            Division by zero creates a zero result and a warning on stderr.

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Prototype:  void  m_apm_integer_div_rem(M_APM, M_APM, M_APM, M_APM);

Example:    M_APM  quotient, remainder, num1, num2;
            m_apm_integer_div_rem(quotient, remainder, num1, num2);

            This function will divide num1 by num2, truncating the
	    result to an integer and put the result in 'quotient' and it
	    will put the remainder in 'remainder'. So, 173 / 26 will yield
	    a quotient of 6 and a remainder of 17.

	    Note that the input numbers do not necessarily have to be 
	    integers. This function can be used to split up the integer
	    portion and fractional portion of a floating point number 
	    by calling the function with num2 set to 'MM_One'. So, 
	    32.17042 can be split up into '32' and '0.17042'.
	    
	    The 'quotient' and 'remainder' parameters cannot be one of the 
	    other MAPM parameters.

            Division by zero creates a zero result and a warning on stderr.

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Prototype:  void  m_apm_factorial(M_APM, M_APM);

Example:    M_APM  apmresult, apm_num;
            m_apm_factorial(apmresult, apm_num);

            This function will compute the factorial of 'apm_num' and put 
	    the result in 'apmresult'.

	    A non-integer input will yield nonsense. Actually, the algorithm 
	    simply multiplies : (though 0! and 1! return 1)

	    N * (N - 1) * (N - 2) ... until N < 2.
	    
	    The 'apmresult' parameter cannot be the other MAPM parameter.

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Prototype:  void  m_apm_sqrt(M_APM, int, M_APM);

Example:    M_APM  apmresult, apm_num;
	    int    decimal_places;
            m_apm_sqrt(apmresult, decimal_places, apm_num);

            This function will take the square root of 'apm_num' and it 
	    will put the result in 'apmresult'. The result will be accurate
	    to the number of decimal places specified.

	    The 'apmresult' parameter cannot be the other MAPM parameter.

            An input < zero creates a zero result and a warning on stderr.

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Prototype:  void  m_apm_log(M_APM, int, M_APM);

Example:    M_APM  apmresult, apm_num;
	    int    decimal_places;
            m_apm_log(apmresult, decimal_places, apm_num);

            This function will take the natural log (base 2.718 ...) of 
	    'apm_num' and it will put the result in 'apmresult'. The result 
	    will be accurate to the number of decimal places specified.

	    The 'apmresult' parameter cannot be the other MAPM parameter.

            An input <= zero creates a zero result and a warning on stderr.

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Prototype:  void  m_apm_log10(M_APM, int, M_APM);

Example:    M_APM  apmresult, apm_num;
	    int    decimal_places;
            m_apm_log10(apmresult, decimal_places, apm_num);

            This function will take the common log (base 10) of 'apm_num' 
	    and it will put the result in 'apmresult'. The result will be 
	    accurate to the number of decimal places specified.

	    The 'apmresult' parameter cannot be the other MAPM parameter.

            An input <= zero creates a zero result and a warning on stderr.

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Prototype:  void  m_apm_exp(M_APM, int, M_APM);

Example:    M_APM  apmresult, apm_num;
	    int    decimal_places;
            m_apm_exp(apmresult, decimal_places, apm_num);

            This function will perform E ^ apm_num where 'E' is 2.718...
	    (the exponential function) and it will put the result in 
	    'apmresult'. The result will be accurate to the number of 
	    decimal places specified.

	    The 'apmresult' parameter cannot be the other MAPM parameter.

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Prototype:  void  m_apm_pow(M_APM, int, M_APM, M_APM);

Example:    M_APM  apmresult, apm_x, apm_y;
	    int    decimal_places;
            m_apm_pow(apmresult, decimal_places, apm_x, apm_y);

            This function will raise 'apm_x' to the 'apm_y' power and it 
	    will put the result in 'apmresult'. The result will be accurate 
	    to the number of decimal places specified.

	    The 'apmresult' parameter cannot be one of the other MAPM 
	    parameters.

            'apm_x' must be >= zero.
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Prototype:  void  m_apm_integer_pow(M_APM, int, M_APM, int);

Example:    M_APM  apmresult, apm_x;
	    int    decimal_places, ipower;
            m_apm_integer_pow(apmresult, decimal_places, apm_x, ipower);

            This function will raise 'apm_x' to the 'ipower' power and it 
	    will put the result in 'apmresult'. The result will be accurate 
	    to the number of decimal places specified.

	    If calculating X^Y, this function should be used when 'Y'
	    is an integer. This function is considerably faster than the
	    generic 'm_apm_pow' function (when 'ipower' is not excessively
	    large). 'apm_x' and/or 'ipower' may be negative.

	    Note that 'ipower' is an integer and not a MAPM number. 

	    The 'apmresult' parameter cannot be the other MAPM parameter.

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Prototype:  void  m_apm_sin(M_APM, int, M_APM);

Example:    M_APM  apmresult, apm_num;
	    int    decimal_places;
            m_apm_sin(apmresult, decimal_places, apm_num);

            This function will take the sine of 'apm_num' and it will put 
	    the result in 'apmresult'. The input angle is assumed to be in 
	    radians. The result will be accurate to the number of decimal 
	    places specified.

	    The 'apmresult' parameter cannot be the other MAPM parameter.

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Prototype:  void  m_apm_cos(M_APM, int, M_APM);

Example:    M_APM  apmresult, apm_num;
	    int    decimal_places;
            m_apm_cos(apmresult, decimal_places, apm_num);

            This function will take the cosine of 'apm_num' and it will put 
	    the result in 'apmresult'. The input angle is assumed to be in 
	    radians. The result will be accurate to the number of decimal 
	    places specified.

	    The 'apmresult' parameter cannot be the other MAPM parameter.

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Prototype:  void  m_apm_sin_cos(M_APM, M_APM, int, M_APM);

Example:    M_APM  sin_val, cos_val, apm_num;
	    int    decimal_places;
            m_apm_sin_cos(sin_val, cos_val, decimal_places, apm_num);

            This function computes the sin and cos of apm_num and it will
	    be more efficient than calling each function separately.
	    The input angle is assumed to be in radians. The results will 
	    be accurate to the number of decimal places specified.

	    The 'sin_val' and 'cos_val' parameter cannot be the input 
	    MAPM parameter.

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Prototype:  void  m_apm_tan(M_APM, int, M_APM);

Example:    M_APM  apmresult, apm_num;
	    int    decimal_places;
            m_apm_tan(apmresult, decimal_places, apm_num);

            This function will take the tangent of 'apm_num' and it will put 
	    the result in 'apmresult'. The input angle is assumed to be in 
	    radians. The result will be accurate to the number of decimal 
	    places specified.

	    The 'apmresult' parameter cannot be the other MAPM parameter.

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Prototype:  void  m_apm_arcsin(M_APM, int, M_APM);

Example:    M_APM  apmresult, apm_num;
	    int    decimal_places;
            m_apm_arcsin(apmresult, decimal_places, apm_num);

            This function will take the arc sine of 'apm_num' and it will put 
	    the result in 'apmresult'. The angle returned is in the range 
	    -PI / 2 to +PI / 2. The result will be accurate to the number of 
	    decimal places specified.

	    The 'apmresult' parameter cannot be the other MAPM parameter.

            |Input| > 1 creates a zero result and a warning on stderr.

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Prototype:  void  m_apm_arccos(M_APM, int, M_APM);

Example:    M_APM  apmresult, apm_num;
	    int    decimal_places;
            m_apm_arccos(apmresult, decimal_places, apm_num);

            This function will take the arc cosine of 'apm_num' and it will 
	    put the result in 'apmresult'. The angle returned is in the range 
	    0 to +PI. The result will be accurate to the number of decimal 
	    places specified.

	    The 'apmresult' parameter cannot be the other MAPM parameter.

            |Input| > 1 creates a zero result and a warning on stderr.

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Prototype:  void  m_apm_arctan(M_APM, int, M_APM);

Example:    M_APM  apmresult, apm_num;
	    int    decimal_places;
            m_apm_arctan(apmresult, decimal_places, apm_num);

            This function will take the arc tangent of 'apm_num' and it will 
	    put the result in 'apmresult'. The angle returned is in the range 
	    -PI / 2 to +PI / 2. The result will be accurate to the number of 
	    decimal places specified.

	    The 'apmresult' parameter cannot be the other MAPM parameter.

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Prototype:  void  m_apm_arctan2(M_APM, int, M_APM, M_APM);

Example:    M_APM  apmresult, apm_x, apm_y;
	    int    decimal_places;
            m_apm_arctan2(apmresult, decimal_places, apm_y, apm_x);

            This function will perform the 4 quadrant arc tangent of 'apm_y' 
	    and 'apm_x' and it will put the result in 'apmresult'. The angle 
	    returned is in the range -PI to +PI. The function will determine 
	    the quadrant based on the signs of the 2 inputs.  The result will 
	    be accurate to the number of decimal places specified.

	    The 'apmresult' parameter cannot be one of the other MAPM 
	    parameters.

            x, y both = zero yields a zero result and a warning on stderr.

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