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acos, sin, tanh, exp, log, sqrt - Floating Point Functions

The following table shows the floating point functions that expect a floating point number as an unnamed argument. Floating point functions are overloaded so that the return code can have the type decfloat34 or f. Decimal floating point numbers are still only possible as arguments of exp, log, log10, and sqrt.

Other versions: 7.31 | 7.40 | 7.54

Syntax

... func( arg ) ...

Effect

The argument of a floating point function must be a single data object outside an arithmetic expression and can be an arithmetic expression itself within an arithmetic expression.

Effect of the floating point functions:

Function func	Meaning	Definition Range
acos	arccosine	[-1,1], no decfloat34
asin	arcsine	[-1,1], no decfloat34
atan	arctangent	-, no decfloat34
cos	cosine	-, no decfloat34
sin	sine	-, no decfloat34
tan	tangent	-, no decfloat34
cosh	hyperbolic cosine	-, no decfloat34
sinh	hyperbolic sine	-, no decfloat34
tanh	hyperbolic tangent	-, no decfloat34
exp	Exponential function for base e	[-709, 709] for type f and [-14144, 14149] for type decfloat34
log	Natural logarithm	> 0
log10	Logarithm to base 10	> 0
sqrt	Square root	>= 0

Functions that specify "no decfloat34" cannot currently have the calculation type decfloat34. If one of these functions is specified in an expression with this calculation type, a syntax error occurs or the exception CX_SY_UNSUPPORTED_FUNCTION is raised.

The following applies to the floating point arithmetic in which a floating point function is calculated, and to the data type of the return code:

• If the argument has the type decfloat16 or decfloat34, a floating point function is calculated in decimal floating point arithmetic and the return code has the type decfloat34.

• If a floating point function is used in an arithmetic expression whose calculation type is decfloat34, it also calculates a return code with the type decfloat34 and the argument is first converted to the data type decfloat34, if necessary.

• In all other cases, floating point functions use binary floating point arithmetic to calculate a return code with type f and the argument is first converted to the data type f, if necessary.

Functions with a definition range require the value of arg to be within the specified limits. Arguments within the definition ranges are guaranteed to be error-free for the exponential function exp, since the results are then within the value ranges for binary or decimal floating point numbers in accordance with IEEE-754. For arguments less than -709, the result for binary floating point numbers is (depending on the platform) a subnormal number, 0, or a handleable exception of the class CX_SY_ARITHMETIC_OVERFLOW is raised from a specific value.

The trigonometric functions sin, cos, and tan are defined for any arguments but the results become imprecise if the argument is greater than approximately 100,000,000.

Note

The atan function is undefined for odd-number multiples of pi/2, but the definition range of atan is nevertheless restricted since an argument of this function can never contain the precise value of pi/2.