Document revision date: 30 March 2001
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Compaq Portable Mathematics Library
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cabs - Complex Absolute Value

Interface

F_TYPE cabs (F_TYPE x, F_TYPE y)

Description

cabs(x,y) is defined as the square root of (x**2 + y**2) and returns the same value as hypot(x,y).

Exceptions

Exceptional Argument Routine Behavior
sqrt(x**2 + y**2) > max_float Overflow

See Also


Appendix A, Critical Floating-Point Values

cbrt - Cube Root

Interface

F_TYPE cbrt (F_TYPE x)

Description

cbrt() returns the cube root of x.

Exceptions

None.

ccos - Cosine of Angle of a Complex Number

Interface

F_COMPLEX ccos (F_TYPE x, F_TYPE y)

Description

ccos() returns the cosine of a complex number, x + iy.

ccos(x,y) is defined as cos (x + iy) = (cos x * cosh y - i * sin x * sinh y).

Exceptions

Exceptional Argument Routine Behavior
|x| = infinity Invalid argument
(sin x sinh y) > max_float Overflow
(cos x cosh y) > max_float Overflow

See Also


Appendix A, Critical Floating-Point Values

cdiv - Complex Division

Interface

F_COMPLEX cdiv (F_TYPE a, F_TYPE b, F_TYPE c, F_TYPE d)

Description

cdiv() returns the quotient of two complex numbers: (a + ib)/(c + id).

Exceptions

Exceptional Argument Routine Behavior
c=d=0 Invalid argument

The quotient may overflow.

ceil - Ceiling

Interface

F_TYPE ceil (F_TYPE x)

Description

ceil() returns the smallest floating-point number of integral value greater than or equal to x.

Exceptions

None.

cexp - Complex Exponential

Interface

F_COMPLEX cexp (F_TYPE x, F_TYPE y)

Description

cexp() returns the exponential of a complex number.

cexp(x,y) is defined as e**(x + iy) = e**x cos y + ie**x sin y.

Exceptions

Exceptional Argument Routine Behavior
|y| = infinity Invalid argument
|e**x cos y| > max_float Overflow
|e**x sin y| > max_float Overflow

See Also

Appendix A, Critical Floating-Point Values

clog - Complex Natural Logarithm

Interface

F_COMPLEX clog (F_TYPE x, F_TYPE y)

Description

clog() returns the natural logarithm of a complex number.

clog(x,y) is defined as ln(x + iy) = 1/2 ln(x**2 + y**2) + i * atan2(y,x).

Exceptions

Exceptional Argument Routine Behavior
y=x=0 Invalid argument
|y|=|x|=infinity Invalid argument

cmul - Complex Multiplication

Interface

F_COMPLEX cmul (F_TYPE a, F_TYPE b, F_TYPE c, F_TYPE d)

Description

cmul() returns the product of two complex numbers.

cmul(a,b,c,d) is defined as (a + ib) * (c + id).

Exceptions

None.

copysign - Copy Sign

Interface

F_TYPE copysign (F_TYPE x, F_TYPE y)

Description

copysign() returns x with the same sign as y. IEEE Std 754 requires copysign(x,NaN) = +x or -x.

Exceptions

None.

cos - Cosine of Angle

Interface

F_TYPE cos (F_TYPE x)

F_TYPE cosd (F_TYPE x)

Description

cos() computes the cosine of x, measured in radians.

cosd() computes the cosine of x, measured in degrees.

Exceptions

Exceptional Argument Routine Behavior
|x| = infinity Invalid argument

cosh - Hyperbolic Cosine of Angle

Interface

F_TYPE cosh (F_TYPE x)

Description

cosh() computes the hyperbolic cosine of x.

cosh(x) is defined as (exp(x) + exp(-x))/2.

Exceptions

Exceptional Argument Routine Behavior
|x| > ln(2 * max_float) Overflow

See Also

Appendix A, Critical Floating-Point Values

cot - Cotangent of Angle

Interface

F_TYPE cot (F_TYPE x)

F_TYPE cotd (F_TYPE x)

Description

cot() computes the cotangent of x, measured in radians.

cotd() computes the cotangent of x, measured in degrees.

Exceptions

Exceptional Argument Routine Behavior
(cot) x=0 Overflow
(cotd) |x| = multiples of 180 degrees Overflow

cpow - Complex Power

Interface

F_COMPLEX cpow (F_TYPE a, F_TYPE b, F_TYPE c, F_TYPE d)

Description

cpow() raises a complex base (a + ib) to a complex exponent (c + id).

cpow(a,b,c,d) is defined as e**((c + id) ln(a + ib)).

Exceptions

Exceptional Argument Routine Behavior
sqrt (a**2 + b**2) > max_float Overflow
c/2 * ln(a**2 + b**2) > max_float Overflow
c/2 * ln(a**2 + b**2) - (d * atan2(b,c)) > max_float Overflow
a=b=c=d=0 Invalid argument

See Also

Appendix A, Critical Floating-Point Values

csin - Sine of Angle of a Complex Number

Interface

F_COMPLEX csin (F_TYPE x, F_TYPE y)

Description

csin() computes the sine of a complex number, x + iy.

csin(x,y) is defined as csin (x + iy) = sin x * cosh y + i * cos x * sinh y.

Exceptions

Exceptional Argument Routine Behavior
|x| = infinity Invalid argument
|sin x * cosh y| > max_float Overflow
|cos x * sinh y| > max_float Overflow

See Also

Appendix A, Critical Floating-Point Values

csqrt - Complex Square Root

Interface

F_COMPLEX csqrt (F_TYPE x, F_TYPE y)

Description

csqrt() computes the square root of a complex number, x + iy. The root is chosen so that the real part of csqrt(x,y) is greater than or equal to zero.

Exceptions

None.

cvt_ftof - Convert Between Supported Floating-Point Data Types

Interface

int cvt_ftof void *x, int x_type, void *y, int y_type, options

Description

Note
This routine does not apply to OpenVMS Alpha. OpenVMS Alpha users should use the CVT$FTOF routine documented in the OpenVMS RTL Library (LIB$) Manual.

cvt_ftof() converts a floating-point value from one data type to another. x points to the input value to be converted, and y points to the converted result. The conversion is subject to the options specified in the options (bit field) argument.

x_type and y_type identify the data type of x and y as follows:
Values for x_type and y_type Floating-Point Data Type
CVT_VAX_F VAX F Floating ( 4 bytes)
CVT_VAX_D VAX D Floating ( 8 bytes)
CVT_VAX_G VAX G Floating ( 8 bytes)
CVT_VAX_H VAX H Floating (16 bytes)
CVT_IEEE_S IEEE Little Endian S Floating ( 4 bytes)
CVT_IEEE_T IEEE Little Endian T Floating ( 8 bytes)
CVT_IEEE_X IEEE Little Endian X Floating (16 bytes)
CVT_BIG_ENDIAN_IEEE_S IEEE Big Endian S Floating ( 4 bytes)
CVT_BIG_ENDIAN_IEEE_T IEEE Big Endian T Floating ( 8 bytes)
CVT_BIG_ENDIAN_IEEE_X IEEE Big Endian X Floating (16 bytes)
CVT_IBM_SHORT IBM_Short_Floating ( 4 bytes)
CVT_IBM_LONG IBM_Long_Floating ( 8 bytes)
CVT_CRAY_SINGLE CRAY_Floating ( 8 bytes)

Provide a zero (0) value to the options argument to select the default behavior or choose one or more options (status condition option, rounding options, "FORCE" options, CRAY and IBM options) from the tables below as the options argument. Specify only the options that apply to your conversion. A conflicting or incompatible options argument will be reported as an error (CVT_INVALID_OPTION).
Applicable Conversion Status Condition Option Description  
All CVT_REPORT_ALL Report all applicable status conditions as the default. The reporting of recoverable status conditions is disabled by default when this option is not used.  
Applicable Conversion Rounding Options Description  
All CVT_ROUND_TO_NEAREST The default rounding option for conversions to IEEE data types. This IEEE Std. 754 rounding mode results in the representable output value nearest to the infinitely precise result. If the two nearest representable values are equally near, the one with its least significant bit zero is the result.  
All CVT_BIASED_ROUNDING The default rounding option for conversions to non-IEEE data types. Performs "traditional" style rounding. This mode results in the representable output value nearest to the infinitely precise result. If the two nearest representable values are equally near, the result is the value with the largest magnitude.  
All CVT_ROUND_TO_ZERO Round the output value toward zero (truncate).  
All CVT_ROUND_TO_POS Round the output value toward positive infinity.  
All CVT_ROUND_TO_NEG Round the output value toward negative infinity.  
Applicable Conversion "FORCE" Options Description  
All CVT_FORCE_ALL_SPECIAL_VALUES Apply all applicable "FORCE" options for the current conversion.  
IEEE CVT_FORCE_DENORM_TO_ZERO 1 Force a denormalized IEEE output value to zero.  
IEEE CVT_FORCE_INF_TO_MAX_FLOAT 1 Force a positive IEEE infinite output value to +max_float and force a negative IEEE infinite output value to -max_float.  
IEEE or VAX CVT_FORCE_INVALID_TO_ZERO 2 Force an invalid IEEE NaN (not a number) output value or a VAX ROP (reserved operand) output value to zero.  

1This option is valid only for conversions to IEEE output values.
2This option is valid only for conversions to IEEE or VAX output values.
Applicable Conversion Options for CRAY Format Conversion Description  
CRAY CVT_ALLOW_OVRFLW_RANGE_VALUES Allow an input/output exponent value > 60000 (8).  
CRAY CVT_ALLOW_UDRFLW_RANGE_VALUES Allow an input/output exponent value < 20000 (8).  
Applicable Conversion Option for IBM Format Conversion Description  
IBM CVT_ALLOW_UNNORMALIZED_VALUES Allow unnormalized input arguments. Allow an unnormalized output value for a small value that would normalize to zero.  

Returns


The return value is a bit field containing the condition codes raised by the function. cvt_ftof() returns CVT_NORMAL; otherwise, it sets one or more of the following recoverable and unrecoverable conditions. Use the following condition names to determine which conditions are set:
Condition Name Condition (Always reported by default)  
CVT_INVALID_INPUT_TYPE Invalid input type code.
CVT_INVALID_OUTPUT_TYPE Invalid output type code.
CVT_INVALID_OPTION Invalid option argument.
Condition Name Condition (Only reported if the CVT_REPORT_ALL option is selected)  
CVT_RESULT_INFINITE Conversion produced an infinite result. 1
CVT_RESULT_DENORMALIZED Conversion produced a denormalized result. 1
CVT_RESULT_OVERFLOW_RANGE Conversion yielded an exponent > 60000 (8). 2
CVT_RESULT_UNDERFLOW_RANGE Conversion yielded an exponent < 20000 (8). 2
CVT_RESULT_UNNORMALIZED Conversion produced an unnormalized result. 3
CVT_RESULT_INVALID Conversion result is either ROP (reserved operand), NaN (not a number), or closest equivalent. CRAY and IBM data types return 0. 4
CVT_RESULT_OVERFLOW Conversion resulted in overflow. 4
CVT_RESULT_UNDERFLOW Conversion resulted in underflow. 4
CVT_RESULT_INEXACT Conversion resulted in a loss of precision. 4

1For IEEE data type conversions.
2For CRAY data type conversions.
3For IBM data type conversions.
4For all data type conversions.

See Also

Appendix A, Critical Floating-Point Values
ANSI/IEEE Std 754-1985, IEEE Standard for Binary Floating-Point Arithmetic

Example


 
      status = cvt_ftof( &big_x, CVT_BIG_ENDIAN_IEEE_T, 
                         &little_x, CVT_IEEE_T, 0 );

This example converts the value pointed to by big_x, which is of type IEEE Big Endian T Floating, to the IEEE Little Endian T Floating data type. It stores the result in the location pointed to by little_x. No conversion options are specified. 


 
      status = cvt_ftof(&x, CVT_VAX_D, &y, CVT_IEEE_T, 
            (CVT_FORCE_ALL_SPECIAL_VALUES | CVT_REPORT_ALL) );

This example converts the value pointed to by x, which is of type VAX D Floating, to the IEEE Little Endian T Floating data type. It stores the result in the location pointed to by y. Any special IEEE values that would normally be generated will be removed. That is, NaN and Denormalized results will be returned as zero and infinite results will go to +- max_float. In addition, all recordable status conditions will be reported.

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