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Source for wiki CompnumsCowan version 1
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cowan
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127.11.51.1
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CompnumsCowan
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A ''compnum'' is a general complex number whose `real-part` and `imag-part` are both flonums. The following procedures should be in a different library from the flonum procedures.
== Compnum operations paralleling R6RS flonum library ==
The R6RS-specific integer division procedures have been removed, as have the condition types.
{{{
#!html
<p>
This section uses <i>cx</i>, <i>cx<sub>1</sub></i>, <i>cx<sub>2</sub></i>, etc., as
parameter names for compnum arguments, and <i>icx</i>
as a name for integer-valued compnum arguments, i.e., compnums for which the
<tt>integer?</tt> predicate returns true.</p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_950"></a>compnum?<i> obj</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<p>
Returns <tt>#t</tt> if <i>obj</i> is a compnum, <tt>#f</tt> otherwise.
</p>
<p></p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_952"></a>compnum<i> x</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<p>
Returns the best compnum representation of
<i>x</i>.</p>
<p>
The value returned is a compnum that is numerically closest to the
argument.</p>
<p>
</p>
<blockquote><em>Note:<span style="margin-left: .5em">‌</span></em>
If compnums are represented in binary floating point, then
implementations should break ties by preferring
the floating-point representation whose least significant bit is
zero.
</blockquote>
<p></p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_982"></a>cxmake-rectangular<i> <i>fl<sub>1</sub></i> <i>fl<sub>2</sub></i> </i>)</tt><span style="margin-left: .5em">‌</span>
<span style="margin-left: .5em">‌</span>procedure </div>
<p>
The value returned is a compnum whose real part is the flonum <i>fl<sub>1</sub></i> and whose imaginary part is the flonum <i>fl<sub>2</sub></i></p>
<p></p>
<p></p>
<div align=left><tt>(<a name="node_idx_982"></a>cxmake-polar<i> <i>fl<sub>1</sub></i> <i>fl
<sub>2</sub></i> </i>)</tt><span style="margin-left: .5em">‌</span>
<span style="margin-left: .5em">‌</span>procedure </div>
<p>
The value returned is a compnum whose magnitude is the flonum <i>fl<sub>1</sub></i>
and whose angle is the flonum <i>fl<sub>2</sub></i></p>
<p></p>
<div align=left><tt>(<a name="node_idx_954"></a>cx=?<i> <i>cx<sub>1</sub></i> <i>cx<sub>2</sub></i> <i>cx<sub>3</sub></i> <tt>...</tt></i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<p>
This procedure returns <tt>#t</tt> if its arguments are equal.</p>
<p>
</p>
<div align=left><tt>(<a name="node_idx_966"></a>cxzero?<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_976"></a>cxfinite?<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_978"></a>cxinfinite?<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_980"></a>cxnan?<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<p>
These numerical predicates test a compnum for a particular property,
returning <tt>#t</tt> or <tt>#f</tt>.
The <tt>cxzero?</tt> procedure tests whether
it is <tt>cx=?</tt> to <tt>0.0+0.0i</i>,
<tt>cxfinite?</tt> tests whether both the real and the imaginary parts
are not an infinity and not a NaN,
<tt>cxinfinite?</tt> tests whether either the real or the imaginary parts or both is an infinity, and
<tt>cxnan?</tt> tests whether either the real part or the imaginary part or both is a NaN.</p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_986"></a>cx+<i> <i>cx<sub>1</sub></i> <tt>...</tt></i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_988"></a>cx*<i> <i>cx<sub>1</sub></i> <tt>...</tt></i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<p>
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.)</p>
<p>
</p>
<div align=left><tt>(<a name="node_idx_994"></a>cx/<i> <i>cx<sub>1</sub></i> <i>cx<sub>2</sub></i> <tt>...</tt></i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_996"></a>cx/<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<p>
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.)</p>
<p>
</p>
<tt>(cx- +inf.0 +inf.0) <span style="margin-left: 2em">‌</span>⇒ +nan.0<p></tt></p>
<p>
For undefined quotients, <tt>cx/</tt> behaves as specified by the
IEEE standards</p>
<p>
</p>
<div align=left><tt>(<a name="node_idx_998"></a>cxreal-part<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<p>
This procedure returns the real part of <i>cx</i>.
</p>
<p>
</p>
<div align=left><tt>(<a name="node_idx_998"></a>cximag-part<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<p>
This procedure returns the imaginary part of <i>cx</i>.
</p>
<p>
</p>
<div align=left><tt>(<a name="node_idx_998"></a>cxangle<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<p>
This procedure returns the angle of <i>cx</i>.
</p>
<p>
</p>
<div align=left><tt>(<a name="node_idx_998"></a>cxabs<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_998"></a>cxmagnitude<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<p>
These procedures return the absolute value (magnitude) of <i>cx</i>.
</p>
<p></p>
<p></p>
<div align=left><tt>(<a name="node_idx_1024"></a>cxexp<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_1026"></a>cxlog<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_1028"></a>cxlog<i> <i>cx<sub>1</sub></i> <i>cx<sub>2</sub></i></i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_1030"></a>cxsin<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_1032"></a>cxcos<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_1034"></a>cxtan<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_1036"></a>cxasin<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_1038"></a>cxacos<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_1040"></a>cxatan<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_1030h"></a>cxsinh<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_1032h"></a>cxcosh<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_1034h"></a>cxtanh<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_1036h"></a>cxasinh<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_1038h"></a>cxacosh<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<div align=left><tt>(<a name="node_idx_1040h"></a>cxatanh<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
These procedures compute the usual transcendental functions.
The <tt>cxexp</tt> procedure computes the base-<em>e</em> exponential of <i>cx</i>.
The <tt>cxlog</tt> procedure with a single argument computes the natural logarithm of
<i>cx</i> (not the base ten logarithm); <tt>(cxlog <i>cx<sub>1</sub></i>
<i>cx<sub>2</sub></i>)</tt> computes the base-<i>cx<sub>2</sub></i> logarithm of <i>cx<sub>1</sub></i>.
The <tt>cxsin</tt>, <tt>cxcos</tt>, <tt>cxtan</tt>,
<tt>cxasin</tt>, <tt>cxacos</tt>, <tt>cxatan</tt>,
The <tt>cxsin</tt>, <tt>cxcosh</tt>, <tt>cxtanh</tt>,
<tt>cxasinh</tt>, <tt>cxacosh</tt>, and <tt>cxatanh</tt> procedures compute
the sine, cosine, tangent, arcsine,
arccosine, arctangent, and their hyperbolic analogues respectively. <tt>(cxatan[h] <i>cx<sub>1</sub></i>
<i>cx<sub>2</sub></i>)</tt> computes the (hyperbolic) arc tangent of <i>cx<sub>1</sub></i>/<i>cx<sub>2</sub></i>.</p>
<p>
See report
section on “Transcendental functions” for the underlying
mathematical operations. In the event that these operations do not
yield a real result for the given arguments, the result may be a NaN,
or may be some unspecified compnum.</p>
<p>
Implementations that use IEEE binary floating-point arithmetic
should follow the relevant standards for these procedures.</p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_1044"></a>cxsqrt<i> cx</i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<p>
Returns the principal square root of <i>cx</i>. For negative arguments,
the result may be a NaN or some unspecified compnum.</p>
<p>
</p>
<p></p>
<div align=left><tt>(<a name="node_idx_1046"></a>cxexpt<i> <i>cx<sub>1</sub></i> <i>cx<sub>2</sub></i></i>)</tt><span style="margin-left: .5em">‌</span><span style="margin-left: .5em">‌</span>procedure </div>
<p>
Either <i>cx<sub>1</sub></i> should be non-negative, or, if <i>cx<sub>1</sub></i> is
negative, <i>cx<sub>2</sub></i> should be an integer object.
The <tt>cxexpt</tt> procedure returns <i>cx<sub>1</sub></i> raised to the power <i>cx<sub>2</sub></i>. If <i>cx<sub>1</sub></i> is
negative and <i>cx<sub>2</sub></i> is not an integer object, the result may be a
NaN, or may be some unspecified compnum. If <i>cx<sub>1</sub></i> is zero, then
the result is zero.
</p>
<p></p>
<p>
</p>
}}}
== C99 <complex.h> constants ==
The following constants are defined in terms of the constants of the <math.h> header of ISO/IEC 9899:1999 (C language).
||Scheme name||C name||Comments||
||cx:i||I||0+1i as a compnum||
== Compnum procedures from <complex.h> ==
||Scheme name||C signature||Comments||
||`cxconjugate`||`double complex conj(double complex)`||complex conjugate||
||`cxexp`||`double complex cexp(double complex)`||-||
||`cxprojection`||`double complex cproj(double complex)`||projects to Riemann sphere
The following are general complex number functions, not just for compnums.
`(cis `''z''`)`
Returns e^i''z''^, a complex number whose real part is cos ''z'' and whose imaginary part is sin ''z''.
`(signum `''z''`)`
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''. As a consequence of this definition, negative real numbers return -1, positive real numbers return 1, and zero returns zero.
time
2016-06-19 07:12:17
version
1