Document revision date: 30 March 2001

## 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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