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Diffstat (limited to 'lib/Math/Trig.pm')
| -rw-r--r-- | lib/Math/Trig.pm | 242 |
1 files changed, 242 insertions, 0 deletions
diff --git a/lib/Math/Trig.pm b/lib/Math/Trig.pm new file mode 100644 index 0000000000..7c3570c840 --- /dev/null +++ b/lib/Math/Trig.pm @@ -0,0 +1,242 @@ +# +# Trigonometric functions, mostly inherited from Math::Complex. +# -- Jarkko Hietaniemi, April 1997 +# + +require Exporter; +package Math::Trig; + +use strict; + +use Math::Complex qw(:trig); + +use vars qw($VERSION $PACKAGE + @ISA + @EXPORT + $pi2 $DR $RD $DG $GD $RG $GR); + +@ISA = qw(Exporter); + +$VERSION = 1.00; + +my @angcnv = qw(rad_to_deg rad_to_grad + deg_to_rad deg_to_grad + grad_to_rad grad_to_dec); + +@EXPORT = (@{$Math::Complex::EXPORT_TAGS{'trig'}}, + @angcnv); + +sub pi2 () { + $pi2 = 2 * pi unless ($pi2); + $pi2; +} + +sub DR () { + $DR = pi2/360 unless ($DR); + $DR; +} + +sub RD () { + $RD = 360/pi2 unless ($RD); + $RD; +} + +sub DG () { + $DG = 400/360 unless ($DG); + $DG; +} + +sub GD () { + $GD = 360/400 unless ($GD); + $GD; +} + +sub RG () { + $RG = 400/pi2 unless ($RG); + $RG; +} + +sub GR () { + $GR = pi2/400 unless ($GR); + $GR; +} + +# +# Truncating remainder. +# + +sub remt ($$) { + # Oh yes, POSIX::fmod() would be faster. Possibly. If it is available. + $_[0] - $_[1] * int($_[0] / $_[1]); +} + +# +# Angle conversions. +# + +sub rad_to_deg ($) { + remt(RD * $_[0], 360); +} + +sub deg_to_rad ($) { + remt(DR * $_[0], pi2); +} + +sub grad_to_deg ($) { + remt(GD * $_[0], 360); +} + +sub deg_to_grad ($) { + remt(DG * $_[0], 400); +} + +sub rad_to_grad ($) { + remt(RG * $_[0], 400); +} + +sub grad_to_rad ($) { + remt(GR * $_[0], pi2); +} + +=head1 NAME + +Math::Trig - trigonometric functions + +=head1 SYNOPSIS + + use Math::Trig; + + $x = tan(0.9); + $y = acos(3.7); + $z = asin(2.4); + + $halfpi = pi/2; + + $rad = deg_to_rad(120); + +=head1 DESCRIPTION + +C<Math::Trig> defines many trigonometric functions not defined by the +core Perl (which defines only the C<sin()> and C<cos()>. The constant +B<pi> is also defined as are a few convenience functions for angle +conversions. + +=head1 TRIGONOMETRIC FUNCTIONS + +The tangent + + tan + +The cofunctions of the sine, cosine, and tangent (cosec/csc and cotan/cot +are aliases) + + csc cosec sec cot cotan + +The arcus (also known as the inverse) functions of the sine, cosine, +and tangent + + asin acos atan + +The principal value of the arc tangent of y/x + + atan2(y, x) + +The arcus cofunctions of the sine, cosine, and tangent (acosec/acsc +and acotan/acot are aliases) + + acsc acosec asec acot acotan + +The hyperbolic sine, cosine, and tangent + + sinh cosh tanh + +The cofunctions of the hyperbolic sine, cosine, and tangent (cosech/csch +and cotanh/coth are aliases) + + csch cosech sech coth cotanh + +The arcus (also known as the inverse) functions of the hyperbolic +sine, cosine, and tangent + + asinh acosh atanh + +The arcus cofunctions of the hyperbolic sine, cosine, and tangent +(acsch/acosech and acoth/acotanh are aliases) + + acsch acosech asech acoth acotanh + +The trigonometric constant B<pi> is also defined. + + $pi2 = 2 * pi; + +=head2 SIMPLE ARGUMENTS, COMPLEX RESULTS + +Please note that some of the trigonometric functions can break out +from the B<real axis> into the B<complex plane>. For example +C<asin(2)> has no definition for plain real numbers but it has +definition for complex numbers. + +In Perl terms this means that supplying the usual Perl numbers (also +known as scalars, please see L<perldata>) as input for the +trigonometric functions might produce as output results that no more +are simple real numbers: instead they are complex numbers. + +The C<Math::Trig> handles this by using the C<Math::Complex> package +which knows how to handle complex numbers, please see L<Math::Complex> +for more information. In practice you need not to worry about getting +complex numbers as results because the C<Math::Complex> takes care of +details like for example how to display complex numbers. For example: + + print asin(2), "\n"; + +should produce something like this (take or leave few last decimals): + + 1.5707963267949-1.31695789692482i + +That is, a complex number with the real part of approximately E<1.571> +and the imaginary part of approximately E<-1.317>. + +=head1 ANGLE CONVERSIONS + +(Plane, 2-dimensional) angles may be converted with the following functions. + + $radians = deg_to_rad($degrees); + $radians = grad_to_rad($gradians); + + $degrees = rad_to_deg($radians); + $degrees = grad_to_deg($gradians); + + $gradians = deg_to_grad($degrees); + $gradians = rad_to_grad($radians); + +The full circle is 2 B<pi> radians or E<360> degrees or E<400> gradians. + +=head1 + +The following functions + + tan + sec + csc + cot + atan + acot + tanh + sech + csch + coth + atanh + asech + acsch + acoth + +cannot be computed for all arguments because that would mean dividing +by zero. These situations cause fatal runtime errors looking like this + + cot(0): Division by zero. + (Because in the definition of cot(0), sin(0) is 0) + Died at ... + +=cut + +# eof |