Compnums­Cowan

The compnums are the subset of the inexact complex numbers whose real part and imaginary part are both flonums. This library is based on the R6RS flonum library lifted to compnums, except that the R6RS-specific integer division procedures have been removed, as have the condition types, and a few procedures have been added from the C99 <complex.h> library.

Specification

This section uses cx, cx₁, cx₂, etc., as parameter names for compnum arguments.

Constructors

The value returned is a compnum that is numerically closest to x. This procedure can be used to transform a flonum to a compnum.

The value returned is a compnum whose real part is the flonum fl₁ and whose imaginary part is the flonum fl₂

The value returned is a compnum whose magnitude is the flonum fl₁ and whose angle is the flonum fl₂

Predicates

Returns #t if obj is a compnum, #f otherwise.

This procedure returns #t if its arguments are numerically equal.

These numerical predicates test a compnum for a particular property, returning #t or #f. The cxzero? procedure tests whether it is cx=? to 0.0+0.0i, cxfinite? tests whether both the real and the imaginary parts are not an infinity and not a NaN, cxinfinite? tests whether either the real or the imaginary parts or both is an infinity, and cxnan? tests whether either the real part or the imaginary part or both is a NaN.

Arithmetic operations

These procedures return the compnum sum or product of their compnum arguments. In general, they should return the compnum that best approximates the mathematical sum or product. (For implementations that represent compnums using IEEE binary floating point, the meaning of “best” is defined by the IEEE standards.)

With two or more arguments, these procedures return the compnum difference or quotient of their compnum arguments, associating to the left. With one argument, however, they return the additive or multiplicative compnum inverse of their argument. In general, they should return the compnum that best approximates the mathematical difference or quotient. (For implementations that represent compnums using IEEE binary floating point, the meaning of “best” is reasonably well-defined by the IEEE standards.)

For undefined quotients, cx/ behaves as specified by the IEEE standards.

This procedure returns the real part of cx as a flonum.

This procedure returns the imaginary part of cx as a flonum.

This procedure returns the nearest approximation to the angle of cx that is a flonum.

These procedures return the nearest approximation to the absolute value (magnitude) of cx that is a compnum.

This procedure returns the complex conjugate of cx. The result has the same as the real part of cx. Its imaginary part is the negation of the imaginary part of cx.

This procedure returns the Riemann projection of cx. This is the same as cx unless cx has an infinite real part or complex part. In this case, the result is a compnum whose real part is 0.0 and whose imaginary part is either 0.0 or -0.0, depending on the sign of the imaginary part of cx.

This procedure returns a complex number whose phase is the same as z but whose magnitude is 1, unless z is zero, in which case it returns z.

Transcendental functions

(cxexp cx)

(cxlog cx)

(cxlog cx₁ cx₂)

(cxsin cx)

(cxcos cx)

(cxcis cx)

(cxtan cx)

(cxasin cx)

(cxacos cx)

(cxatan cx)

(cxsinh cx)

(cxcosh cx)

(cxtanh cx)

(cxasinh cx)

(cxacosh cx)

(cxatanh cx)

These procedures compute the usual transcendental functions. The cxexp procedure computes the base-e exponential of cx. The cxlog procedure with a single argument computes the natural logarithm of cx (not the base ten logarithm); (cxlog cx₁ cx₂) computes the base-cx₂ logarithm of cx₁. The cxsin, cxcos, cxtan, cxasin, cxacos, cxatan, The cxsin, cxcosh, cxtanh, cxasinh, cxacosh, and cxatanh procedures compute the sine, cosine, tangent, arcsine, arccosine, arctangent, and their hyperbolic analogues respectively. (cxatan[h] cx₁ cx₂) computes the (hyperbolic) arc tangent of cx₁/cx₂. Finally, the cxcis function computes the compnum whose real part is the cosine of cx and whose imaginary part is the sine of cx.

See the corresponding section of R⁷RS-small for the underlying mathematical operations.

Implementations that use IEEE binary floating-point arithmetic should follow the relevant standards for these procedures.

(cxsqrt cx)

Returns the principal square root of cx..

(cxexpt cx₁ cx₂)

Either cx₁ should be non-negative, or, if cx₁ is negative, cx₂ should be an integer object. The cxexpt procedure returns cx₁ raised to the power cx₂. If cx₁ is negative and cx₂ is not an integer object, the result may be a NaN, or may be some unspecified compnum. If cx₁ is zero, then the result is zero.