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6.6 Mathematics

A binding for each of the following constants is exported by (vicare platform constants): 

     M_E         M_LOG2E     M_LOG10E
     M_LN2       M_LN10      M_PI
     M_PI_2      M_PI_4      M_1_PI
     M_2_PI      M_2_SQRTPI  M_SQRT2
     M_SQRT1_2

The following bindings are exported by the (vicare glibc) library. The functions are implemented by the GNU C library and are probably faster than the ones implemented by the R6RS libraries. All the arguments fl must be flonums, all the arguments cfl must be complex flonums.

Trigonometric functions
— Function: csin cfl
— Function: ccos cfl
— Function: ctan cfl

Trigonometric functions for complex flonums.

— Function: casin cfl
— Function: cacos cfl
— Function: catan cfl

Inverse trigonometric functions for complex flonums.

Exponents and logarithms
— Function: cexp cfl

Return the base of the natural logarithms raised to the power of the operand.

— Function: clog cfl

Return the natural logarithm of the operand.

— Function: clog10 cfl

Return the base 10 logarithm of the operand.

— Function: csqrt cfl

Return the square root of the operand.

— Function: cpow cfl1 cfl2

Return cfl1 raised to the power of cfl2.

Hyperbolic functions
— Function: sinh fl
— Function: cosh fl
— Function: tanh fl

Hyperbolic functions for flonums.

— Function: asinh fl
— Function: acosh fl
— Function: atanh fl

Inverse hyperbolic functions for flonums.

— Function: csinh cfl
— Function: ccosh cfl
— Function: ctanh cfl

Hyperbolic functions for complex flonums.

— Function: casinh cfl
— Function: cacosh cfl
— Function: catanh cfl

Inverse hyperbolic functions for complex flonums.

Special functions
— Function: erf fl
— Function: erfc fl

Interfaces to the C functions erf() and erfc(), erf. Compute the error function.

— Function: lgamma fl

Interface to the C function lgamma(), lgamma. Compute the natural logarithm of the absolute value of the gamma function of the operand. Return two values: a flonum being the result of the function and a fixnum representing the sign of the intermediate result.

— Function: tgamma fl

Interface to the C function tgamma(), lgamma. Compute the gamma function of the operand.

— Function: j0 fl
— Function: j1 fl
— Function: jn fx fl

Interfaces to the C functions j0(), j1() and jn(); j0. Compute the Bessel functions of the first kind. fx must be a fixnum.

— Function: y0 fl
— Function: y1 fl
— Function: yn fx fl

Interfaces to the C functions y0(), y1() and yn(); y0. Compute the Bessel functions of the second kind. fx must be a fixnum.