rename vercos to coversin

The code to compute 1 - sin(x) belongs to coversin, not vercos.

help/Makefile

@@ -203,33 +203,33 @@ DETAIL_HELP= abs access acos acosh acot acoth acsc acsch address agd \
 	append appr arg argv arrow asec asech asin asinh assign atan atan2 \
 	atanh avg base base2 bernoulli bit blk blkcpy blkfree blocks bround \
 	btrunc calc_tty calclevel calcpath catalan ceil cfappr cfsim char \
-	cmdbuf cmp comb conj cos cosh cot coth count cp csc csch ctime d2dm \
-	d2dms d2g d2r delete den dereference det digit digits display dms2d dp \
-	epsilon errcount errmax errno error estr euler eval exp fact factor \
-	fclose fcnt feof ferror fflush fgetc fgetfield fgetfile fgetline fgets \
-	fgetstr fib files floor fopen forall fpathopen fprintf fputc fputs \
-	fputstr frac free freebernoulli freeeuler freeglobals freeredc \
-	freestatics frem freopen fscan fscanf fseek fsize ftell g2d g2gm g2gms \
-	g2r gcd gcdrem gd getenv gms2g h2hm h2hms hash head highbit hmean \
-	hms2h hnrmod hypot ilog ilog10 ilog2 im indices inputlevel insert int \
-	inverse iroot isalnum isalpha isassoc isatty isblk iscntrl isconfig \
-	isdefined isdigit iserror iseven isfile isgraph ishash isident isint \
-	islist islower ismat ismult isnull isnum isobj isobjtype isodd isprime \
-	isprint isptr ispunct isqrt isrand israndom isreal isrel issimple \
-	isspace issq isstr istype isupper isxdigit jacobi join lcm lcmfact \
-	lfactor ln log log2 logn lowbit ltol makelist matdim matfill matmax \
-	matmin matsum mattrace mattrans max memsize meq min minv mmin mne mod \
-	modify name near newerror nextcand nextprime norm null num oldvalue \
-	ord param perm pfact pi pix places pmod polar poly pop popcnt pound \
-	power prevcand prevprime printf prompt protect ptest push putenv quo \
-	quomod r2d r2g rand randbit random randombit randperm rcin rcmul rcout \
-	rcpow rcsq re remove reverse rewind rm root round rsearch runtime \
-	saveval scale scan scanf search sec sech seed segment select sgn sha1 \
-	sin sinh size sizeof sleep sort sqrt srand srandom ssq stoponerror str \
-	strcasecmp strcat strcmp strcpy strerror strlen strncasecmp strncmp \
-	strncpy strpos strprintf strscan strscanf strtolower strtoupper substr \
-	sum swap system systime tail tan tanh test time trunc usertime vercos \
-	versin version xor
+	cmdbuf cmp comb conj cos cosh cot coth count coversin cp csc csch \
+	ctime d2dm d2dms d2g d2r delete den dereference det digit digits \
+	display dms2d dp epsilon errcount errmax errno error estr euler eval \
+	exp fact factor fclose fcnt feof ferror fflush fgetc fgetfield \
+	fgetfile fgetline fgets fgetstr fib files floor fopen forall fpathopen \
+	fprintf fputc fputs fputstr frac free freebernoulli freeeuler \
+	freeglobals freeredc freestatics frem freopen fscan fscanf fseek fsize \
+	ftell g2d g2gm g2gms g2r gcd gcdrem gd getenv gms2g h2hm h2hms hash \
+	head highbit hmean hms2h hnrmod hypot ilog ilog10 ilog2 im indices \
+	inputlevel insert int inverse iroot isalnum isalpha isassoc isatty \
+	isblk iscntrl isconfig isdefined isdigit iserror iseven isfile isgraph \
+	ishash isident isint islist islower ismat ismult isnull isnum isobj \
+	isobjtype isodd isprime isprint isptr ispunct isqrt isrand israndom \
+	isreal isrel issimple isspace issq isstr istype isupper isxdigit \
+	jacobi join lcm lcmfact lfactor ln log log2 logn lowbit ltol makelist \
+	matdim matfill matmax matmin matsum mattrace mattrans max memsize meq \
+	min minv mmin mne mod modify name near newerror nextcand nextprime \
+	norm null num oldvalue ord param perm pfact pi pix places pmod polar \
+	poly pop popcnt pound power prevcand prevprime printf prompt protect \
+	ptest push putenv quo quomod r2d r2g rand randbit random randombit \
+	randperm rcin rcmul rcout rcpow rcsq re remove reverse rewind rm root \
+	round rsearch runtime saveval scale scan scanf search sec sech seed \
+	segment select sgn sha1 sin sinh size sizeof sleep sort sqrt srand \
+	srandom ssq stoponerror str strcasecmp strcat strcmp strcpy strerror \
+	strlen strncasecmp strncmp strncpy strpos strprintf strscan strscanf \
+	strtolower strtoupper substr sum swap system systime tail tan tanh \
+	test time trunc usertime versin version xor
 
 # This list is of files that are clones of DETAIL_HELP files.  They are
 # built from DETAIL_HELP files.

help/cos

@@ -34,7 +34,7 @@ LINK LIBRARY
 
 SEE ALSO
     sin, tan, sec, csc, cot, epsilon
-    versin, vercos
+    versin, coversin
 
 ## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##

help/cot

@@ -27,7 +27,7 @@ LINK LIBRARY
 
 SEE ALSO
     sin, cos, tan, sec, csc, epsilon
-    versin, vercos
+    versin, coversin
 
 ## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##

help/coversin

@@ -1,8 +1,8 @@
 NAME
-    vercos - versed cosine
+    coversin - coversed sine
 
 SYNOPSIS
-    vercos(x [,eps])
+    coversin(x [,eps])
 
 TYPES
     x		number (real or complex)
@@ -14,31 +14,31 @@ DESCRIPTION
     Calculate the versed cosine of x to a multiple of eps with error less in
     absolute value than .75 * eps.
 
-    The versed cosine function is sometimes called coversin, sometimes called cvs,
+    The coversed sine function is sometimes called covers, or cosiv, or cvs,
     may be defined as:
 
-    	vercos(x) = 1 - sin(x)
+	coversin(x) = 1 - sin(x)
 
 EXAMPLE
-    ; print vercos(0.2), vercos(3/7), vercos(-31)
+    ; print coversin(0.2), coversin(3/7), coversin(-31)
     0.80133066920493878454 0.58442814500694799193 0.59596235467693499395
 
-    ; print vercos(1, 1e-5), vercos(1, 1e-10), vercos(1, 1e-15), vercos(1, 1e-20)
+    ; print coversin(1, 1e-5), coversin(1, 1e-10), coversin(1, 1e-15), coversin(1, 1e-20)
     0.15853 0.1585290152 0.158529015192104 0.15852901519210349335
 
-    ; print vercos(2 + 3i, 1e-5), vercos(2 + 3i, 1e-10)
+    ; print coversin(2 + 3i, 1e-5), coversin(2 + 3i, 1e-10)
     -8.1545+4.16891i -8.1544991469+4.16890696i
 
     ; pi = pi(1e-20)
-    ; print vercos(pi/6, 1e-10), vercos(pi/2, 1e-10), vercos(pi, 1e-10), vercos(3*pi/2, 1e-10)
+    ; print coversin(pi/6, 1e-10), coversin(pi/2, 1e-10), coversin(pi, 1e-10), coversin(3*pi/2, 1e-10)
     0.5 0 1 2
 
 LIMITS
     0 < eps < 1
 
 LINK LIBRARY
-    NUMBER *qvercos(NUMBER *x, NUMBER *eps)
-    COMPLEX *c_vercos(COMPLEX *x, NUMBER *eps)
+    NUMBER *qcoversin(NUMBER *x, NUMBER *eps)
+    COMPLEX *c_coversin(COMPLEX *x, NUMBER *eps)
 
 SEE ALSO
     sin, cos, tan, sec, csc, cot, epsilon

help/csc

@@ -26,7 +26,7 @@ LINK LIBRARY
 
 SEE ALSO
     sin, cos, tan, sec, cot, epsilon
-    versin, vercos
+    versin, coversin
 
 ## Copyright (C) 1999,2023  Landon Curt Noll
 ##

help/sec

@@ -27,7 +27,7 @@ LINK LIBRARY
 
 SEE ALSO
     sin, cos, tan, csc, cot, epsilon
-    versin, vercos
+    versin, coversin
 
 ## Copyright (C) 1999,2023  Landon Curt Noll
 ##

help/sin

@@ -34,7 +34,7 @@ LINK LIBRARY
 
 SEE ALSO
     cos, tan, sec, csc, cot, epsilon
-    versin, vercos
+    versin, coversin
 
 ## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##

help/tan

@@ -28,7 +28,7 @@ LINK LIBRARY
 
 SEE ALSO
     sin, cos, sec, csc, cot, epsilon
-    versin, vercos
+    versin, coversin
 
 ## Copyright (C) 1999,2023  Landon Curt Noll
 ##

help/versin

@@ -17,7 +17,7 @@ DESCRIPTION
     The versed sine function is sometimes called vers, sometimes called ver,
     may be defined as:
 
-    	versin(x) = 1 - cos(x)
+	versin(x) = 1 - cos(x)
 
 EXAMPLE
     ; print versin(0.2), versin(3/7), versin(-31)
@@ -42,7 +42,7 @@ LINK LIBRARY
 
 SEE ALSO
     sin, cos, tan, sec, csc, cot, epsilon
-    vercos
+    coversin
 
 ## Copyright (C) 2023  Landon Curt Noll
 ##