update major trigonometric help files and regression tests

Improved help files for sin, cos, tan, cot, sec, csc.  In case
of tan, cot, sec, csc corrected help file was corrected to
indicate that complex arguments are allowed.  This was a help
file oversight from long ago when those trigonometric functions

Expanded the calc regression test suite test 34dd to test various
real and complex values for sin, cos, tan, cot, sec, csc.

CHANGES

@@ -176,6 +176,15 @@ The following are the changes from calc version 2.14.3.5 to date:
     number generator in place of the additive 55 generator for a
     while now.
 
+    Improved help files for sin, cos, tan, cot, sec, csc.  In case
+    of tan, cot, sec, csc corrected help file was corrected to
+    indicate that complex arguments are allowed.  This was a help
+    file oversight from long ago when those trigonometric functions
+    were expanded to include complex arguments.
+
+    Expanded the calc regression test suite test 34dd to test various
+    real and complex values for sin, cos, tan, cot, sec, csc.
+
 
 The following are the changes from calc version 2.14.3.4 to 2.14.3.5:
 

cal/regress.cal

@@ -2959,6 +2959,14 @@ define test_2600()
 	local tnum;	/* test number */
 	local i;
 
+	/*
+	 * NOTE: The various functions test in this are often accurate to
+	 *	 eps (epsilon) or better, which defaults to about 20 decimal
+	 *	 digits.  We test a number of functions to 10 digits using
+	 *	 round(..., 10) because we do not want to have to put lots
+	 *	 of digits in the verify identities.
+	 */
+
 	print '2600: Beginning extensive numeric function test';
 
 	i = config("sqrt");
@@ -3529,6 +3537,7 @@ print '049: parsed test_det()';
 /*
  * test 050-051: define test_trig and read test3400.trig for test 34dd
  *
+ *
  * This function tests common trig functions.
  */
 read -once "test3400.trig";
@@ -3540,6 +3549,14 @@ define test_trig()
 	local pi;       /* pi to 1e-20 precision */
 	local i;
 
+	/*
+	 * NOTE: The various functions test in this are often accurate to
+	 *	 eps (epsilon) or better, which defaults to about 20 decimal
+	 *	 digits.  We test a number of functions to 10 digits using
+	 *	 round(..., 10) because we do not want to have to put lots
+	 *	 of digits in the verify identities.
+	 */
+
 	print '3400: Beginning test_trig';
 
 	/* test 3401-3407 */
@@ -3550,8 +3567,146 @@ define test_trig()
 	/* test trigonometric sine */
 	vrfy(sin(0, 1e-10) == 0,
 				strcat(str(tnum++), ': sin(0, 1e-10) == 0'));
+	vrfy(round(sin(1, 1e-10), 10) == 0.8414709848,
+	    strcat(str(tnum++),
+		   ': round(sin(1, 1e-10), 10) == 0.8414709848'));
+	vrfy(round(sin(2 + 3i, 1e-10), 10) == 9.1544991469-4.16890696i,
+	    strcat(str(tnum++),
+		   ': round(sin(2 + 3i, 1e-10), 10) == 9.1544991469-4.16890696i'));
 	vrfy(sin(pi/6, 1e-10) == 0.5,
 				strcat(str(tnum++), ': sin(pi/6, 1e-10) == 0.5'));
+	vrfy(sin(pi/2, 1e-10) == 1,
+				strcat(str(tnum++), ': sin(pi/2, 1e-10) == 1'));
+	vrfy(sin(pi, 1e-10) == 0,
+				strcat(str(tnum++), ': sin(pi, 1e-10) == 1'));
+	vrfy(round(sin(1/2, 1e-10), 10) == 0.4794255386,
+	    strcat(str(tnum++),
+		   ': round(sin(1/2, 1e-10), 10) == 0.4794255386'));
+	vrfy(round(sin(5/7, 1e-10), 10) == 0.6550778972,
+	    strcat(str(tnum++),
+		   ': round(sin(5/7, 1e-10), 10) == 0.6550778972'));
+	vrfy(round(sin(42/7, 1e-10), 10) == -0.2794154982,
+	    strcat(str(tnum++),
+		   ': round(sin(42/7, 1e-10), 10) == -0.2794154982'));
+
+	/* test trigonometric cosine */
+	vrfy(cos(0, 1e-10) == 1,
+				strcat(str(tnum++), ': cos(0, 1e-10) == 1'));
+	vrfy(round(cos(1, 1e-10), 10) == 0.5403023059,
+	    strcat(str(tnum++),
+		   ': round(cos(0.2, 1e-10), 10) == 0.5403023059'));
+	vrfy(cos(pi/3, 1e-10) == 0.5,
+				strcat(str(tnum++), ': cos(pi/3, 1e-10) == 0.5'));
+	vrfy(cos(pi/2, 1e-10) == 0,
+				strcat(str(tnum++), ': cos(pi/2, 1e-10) == 0'));
+	vrfy(cos(pi, 1e-10) == -1,
+				strcat(str(tnum++), ': cos(pi, 1e-10) == -1'));
+	vrfy(round(cos(2 + 3i, 1e-10), 10) == -4.189625691-9.1092278938i,
+	    strcat(str(tnum++),
+		   ': round(cos(2 + 3i, 1e-10), 10) == -4.189625691-9.1092278938i'));
+	vrfy(round(cos(1/2, 1e-10), 10) == 0.8775825619,
+	    strcat(str(tnum++),
+		   ': round(cos(1/2, 1e-10), 10) == 0.8775825619'));
+	vrfy(round(cos(5/7, 1e-10), 10) == 0.7555613467,
+	    strcat(str(tnum++),
+		   ': round(cos(5/7, 1e-10), 10) == 0.7555613467'));
+	vrfy(round(cos(42/7, 1e-10), 10) == 0.9601702866,
+	    strcat(str(tnum++),
+		   ': round(cos(42/7, 1e-10), 10) == 0.9601702866'));
+
+	/* test trigonometric tangent */
+	vrfy(tan(0, 1e-10) == 0,
+				strcat(str(tnum++), ': tan(0, 1e-10) == 0'));
+	vrfy(round(tan(1, 1e-10), 10) == 1.5574077247,
+	    strcat(str(tnum++),
+		   ': round(tan(0.2, 1e-10), 10) == 1.5574077247'));
+	vrfy(round(tan(pi/6, 1e-10), 10) == 0.5773502692,
+	    strcat(str(tnum++),
+		   ': round(tan(pi/6, 1e-10), 10) == 0.5773502692'));
+	vrfy(round(tan(pi/3, 1e-10), 10) == 1.7320508076,
+	    strcat(str(tnum++),
+		   ': round(tan(pi/3, 1e-10), 10) == 1.7320508076'));
+	vrfy(tan(pi, 1e-10) == 0,
+				strcat(str(tnum++), ': tan(pi, 1e-10) == 0'));
+	vrfy(round(tan(1/2, 1e-10), 10) == 0.5463024898,
+	    strcat(str(tnum++),
+		   ': round(tan(1/2, 1e-10), 10) == 0.5463024898'));
+	vrfy(round(tan(5/7, 1e-10), 10) == 0.8670082185,
+	    strcat(str(tnum++),
+		   ': round(tan(5/7, 1e-10), 10) == 0.8670082185'));
+	vrfy(round(tan(42/7, 1e-10), 10) == -0.2910061914,
+	    strcat(str(tnum++),
+		   ': round(tan(42/7, 1e-10), 10) == -0.2910061914'));
+
+	/* test trigonometric cotangent */
+	vrfy(round(cot(1, 1e-10), 10) == 0.6420926159,
+	    strcat(str(tnum++),
+		   ': round(cot(0.2, 1e-10), 10) == 0.6420926159'));
+	vrfy(round(cot(pi/12, 1e-10), 10) == 3.7320508076,
+	    strcat(str(tnum++),
+		   ': round(cot(pi/12, 1e-10), 10) == 3.7320508076'));
+	vrfy(round(cot(pi/6, 1e-10), 10) == 1.7320508076,
+	    strcat(str(tnum++),
+		   ': round(cot(pi/6, 1e-10), 10) == 1.7320508076'));
+	vrfy(round(cot(pi/3, 1e-10), 10) == 0.5773502692,
+	    strcat(str(tnum++),
+		   ': round(cot(pi/3, 1e-10), 10) == 0.5773502692'));
+	vrfy(cot(pi/2, 1e-10) == 0,
+				strcat(str(tnum++), ': cot(pi/2, 1e-10) == 0'));
+	vrfy(round(cot(1/2, 1e-10), 10) == 1.8304877217,
+	    strcat(str(tnum++),
+		   ': round(cot(1/2, 1e-10), 10) == 1.8304877217'));
+	vrfy(round(cot(5/7, 1e-10), 10) == 1.1533916042,
+	    strcat(str(tnum++),
+		   ': round(cot(5/7, 1e-10), 10) == 1.1533916042'));
+	vrfy(round(cot(42/7, 1e-10), 10) == -3.4363530042,
+	    strcat(str(tnum++),
+		   ': round(cot(42/7, 1e-10), 10) == -3.4363530042'));
+
+	/* test trigonometric cosecant */
+	vrfy(round(csc(1, 1e-10), 10) == 1.1883951058,
+	    strcat(str(tnum++),
+		   ': round(csc(0.2, 1e-10), 10) == 1.1883951058'));
+	vrfy(csc(pi/6, 1e-10) == 2,
+				strcat(str(tnum++), ': csc(pi/6, 1e-10) == 2'));
+	vrfy(round(csc(pi/3, 1e-10), 10) == 1.1547005384,
+	    strcat(str(tnum++),
+		   ': round(csc(pi/3, 1e-10), 10) == 1.1547005384'));
+	vrfy(round(csc(4*pi/3, 1e-10), 10) == -1.1547005384,
+	    strcat(str(tnum++),
+		   ': round(csc(4*pi/3, 1e-10), 10) == -1.1547005384'));
+	vrfy(round(csc(1/2, 1e-10), 10) == 2.0858296429,
+	    strcat(str(tnum++),
+		   ': round(csc(1/2, 1e-10), 10) == 2.0858296429'));
+	vrfy(round(csc(5/7, 1e-10), 10) == 1.5265360109,
+	    strcat(str(tnum++),
+		   ': round(csc(5/7, 1e-10), 10) == 1.5265360109'));
+	vrfy(round(csc(42/7, 1e-10), 10) == -3.5788995473,
+	    strcat(str(tnum++),
+		   ': round(csc(42/7, 1e-10), 10) == -3.5788995473'));
+
+	/* test trigonometric secant */
+	vrfy(sec(0, 1e-10) == 1,
+				strcat(str(tnum++), ': sec(0, 1e-10) == 1'));
+	vrfy(round(sec(1, 1e-10), 10) == 1.8508157177,
+	    strcat(str(tnum++),
+		   ': round(sec(0.2, 1e-10), 10) == 1.8508157177'));
+	vrfy(round(sec(pi/6, 1e-10), 10) == 1.1547005384,
+	    strcat(str(tnum++),
+		   ': round(sec(pi/6, 1e-10), 10) == 1.1547005384'));
+	vrfy(sec(pi/3, 1e-10) == 2,
+				strcat(str(tnum++), ': sec(pi/2, 1e-10) == 2'));
+	vrfy(sec(pi, 1e-10) == -1,
+				strcat(str(tnum++), ': sec(pi, 1e-10) == -1'));
+	vrfy(round(sec(1/2, 1e-10), 10) == 1.1394939273,
+	    strcat(str(tnum++),
+		   ': round(sec(1/2, 1e-10), 10) == 1.1394939273'));
+	vrfy(round(sec(5/7, 1e-10), 10) == 1.3235192673,
+	    strcat(str(tnum++),
+		   ': round(sec(5/7, 1e-10), 10) == 1.3235192673'));
+	vrfy(round(sec(42/7, 1e-10), 10) == 1.0414819266,
+	    strcat(str(tnum++),
+		   ': round(sec(42/7, 1e-10), 10) == 1.0414819266'));
 
 	/* test versed trigonometric sine */
 	vrfy(versin(0, 1e-10) == 0,

help/cos

@@ -25,6 +25,9 @@ EXAMPLE
     ; print cos(pi/3, 1e-10), cos(pi/2, 1e-10), cos(pi, 1e-10)
     0.5 0 -1
 
+    ; print cos(1/2), cos(5/7), cos(42/7)
+    0.87758256189037271612 0.75556134670069659847 0.96017028665036602055
+
 LIMITS
     0 < eps < 1
 

help/cot

@@ -5,7 +5,7 @@ SYNOPSIS
     cot(x [,eps])
 
 TYPES
-    x		nonzero real
+    x		number (real or complex)
     eps		0 < real < 1, defaults to epsilon()
 
     return	real
@@ -18,12 +18,21 @@ EXAMPLE
     ; print cot(1, 1e-5), cot(1, 1e-10), cot(1, 1e-15), cot(1, 1e-20)
     0.64209 0.6420926159 0.642092615934331 0.64209261593433070301
 
+    ; print cot(2 + 3i, 1e-5), cot(2 + 3i, 1e-10)
+    ~-0.00373977357605613583-~0.99675796378381737782i ~-0.00373971037383300017-~0.99675779657435500069i
+
+    ; pi = pi(1e-20)
+    ; print cot(pi/12, 1e-10), cot(pi/6, 1e-10), cot(pi/3, 1e-10), cot(pi/2, 1e-10)
+    3.7320508076 1.7320508076 0.5773502692 0
+
+    ; print cot(1/2), cot(5/7), cot(42/7)
+    1.83048772171245191927 1.15339160419695060142 -3.43635300418012783207
+
 LIMITS
     0 < eps < 1
 
 LINK LIBRARY
     NUMBER *qcot(NUMBER *x, NUMBER *eps)
-    COMPLEX *c_acot(COMPLEX *c, NUMBER *eps);
 
 SEE ALSO
     sin, cos, tan, sec, csc

help/csc

@@ -5,7 +5,7 @@ SYNOPSIS
     csc(x [,eps])
 
 TYPES
-    x		real
+    x		number (real or complex)
     eps		0 < real < 1, defaults to epsilon()
 
     return	real
@@ -18,6 +18,16 @@ EXAMPLE
     ; print csc(1, 1e-5), csc(1, 1e-10), csc(1, 1e-15), csc(1, 1e-20)
     1.1884 1.1883951058 1.188395105778121 1.18839510577812121626
 
+    ; print csc(2 + 3i, 1e-5), csc(2 + 3i, 1e-10)
+    ~0.09047318155450436310+~0.04120099965201690801i ~0.09047320975303232503+~0.04120098628887626238i
+
+    ; pi = pi(1e-20)
+    ; print csc(pi/6, 1e-10), csc(pi/3, 1e-10), csc(4*pi/3, 1e-10)
+    2 1.1547005384 -1.1547005384
+
+    ; print csc(1/2), csc(5/7), csc(42/7)
+    2.08582964293348818577 1.52653601091884339347 -3.57889954725440563736
+
 LIMITS
     0 < eps < 1
 

help/sec

@@ -5,7 +5,7 @@ SYNOPSIS
     sec(x [,eps])
 
 TYPES
-    x		real
+    x		number (real or complex)
     eps		0 < real < 1, defaults to epsilon()
 
     return	real
@@ -18,8 +18,17 @@ EXAMPLE
     ; print sec(1, 1e-5), sec(1, 1e-10), sec(1, 1e-15), sec(1, 1e-20)
     1.85082 1.8508157177 1.850815717680926 1.85081571768092561791
 
+    ; print sec(2 + 3i, 1e-5), sec(2 + 3i, 1e-10)
+    ~-0.04167497639869547021+~0.09061109101765280898i ~-0.04167496441100888150+~0.09061113719571288336i
+
+    ; pi = pi(1e-20)
+    ; print 1e-10), sec(pi/6, 1e-10), sec(pi/3, 1e-10), sec(pi, 1e-10)
+    1.1547005384 2 -1
+
+    ; print sec(1/2), sec(5/7), sec(42/7)
+    1.13949392732454912231 1.3235192673191814545 1.04148192659510767648
+
 LIMITS
-    unlike sin and cos, x must be real
     0 < eps < 1
 
 LINK LIBRARY

help/sin

@@ -25,6 +25,9 @@ EXAMPLE
     ; print sin(pi/6, 1e-10), sin(pi/2, 1e-10), sin(pi, 1e-10)
     0.5 1 0
 
+    ; print sin(1/2), sin(5/7), sin(42/7)
+    0.47942553860420300027 0.6550778971785185742 -0.27941549819892587281
+
 LIMITS
     0 < eps < 1
 

help/tan

@@ -5,7 +5,7 @@ SYNOPSIS
     tan(x [,eps])
 
 TYPES
-    x		real
+    x		number (real or complex)
     eps		0 < real < 1, defaults to epsilon()
 
     return	real
@@ -18,13 +18,21 @@ EXAMPLE
     ; print tan(1, 1e-5), tan(1, 1e-10), tan(1, 1e-15), tan(1, 1e-20)
     1.55741 1.5574077247 1.557407724654902 1.55740772465490223051
 
+    ; print tan(2 + 3i, 1e-5), tan(2 + 3i, 1e-10)
+    ~-0.00376408798745471014+~1.00323845857938817252i ~-0.00376402563894634508+~1.00323862734859967572i
+
+    ; pi = pi(1e-20)
+    ; print tan(0, 1e-10), tan(pi/6, 1e-10), tan(pi/3, 1e-10), tan(pi, 1e-10)
+    0 0.5773502692 1.7320508076 0
+
+    ; print tan(1/2), tan(5/7), tan(42/7)
+    0.54630248984379051326 0.8670082185107029875 -0.29100619138474915705
+
 LIMITS
-    unlike sin and cos, x must be real
     0 < eps < 1
 
 LINK LIBRARY
     NUMBER *qtan(NUMBER *x, NUMBER *eps)
-    COMPLEX *c_atan(COMPLEX *c, NUMBER *eps);
 
 SEE ALSO
     sin, cos, cot, sec, csc