<HEAD><TITLE>discuss@charon: [1096] in "Coldmud discussion meeting"</TITLE>
<H1>[1096] in Coldmud discussion meeting</H1></HEAD>
<A HREF="/"><IMG SRC="/i-d.gif" ALT="root"></A>
<A HREF="?1096"><IMG SRC="/i-back.gif" ALT="meeting"></A>
<A HREF="/help.html"><IMG SRC="/i-help.gif" ALT="help"></A>
<A HREF="1"><IMG SRC="/i-first.gif" ALT="first"></A>
<IMG SRC="/n-fref.gif" ALT="">
<IMG SRC="/n-pref.gif" ALT="">
<A HREF="1095"><IMG SRC="/i-prev.gif" ALT="previous"></A>
<A HREF="1097"><IMG SRC="/i-next.gif" ALT="next"></A>
<IMG SRC="/n-nref.gif" ALT="">
<IMG SRC="/n-lref.gif" ALT="">
<A HREF="1641"><IMG SRC="/i-last.gif" ALT="last"></A>
<HR><H2>[COLD] Math library</H2>
<H3>daemon@ATHENA.MIT.EDU (Wed Oct  2 15:14:14 1996
)</H3>
<PRE>
Date: Wed, 2 Oct 1996 20:37:11 +0200 (MET DST)
From: Miroslav Silovic &lt;silovic@public.srce.hr&gt;
To: coldstuff@cold.org


I had some extra energy to burn. So... here are $math natives and
$math object with quite extensive math library (and hopefully clean
enough to use as standard). Enjoy!

Comments appreciated, as always. :)

-------------------------------------------------- cdc_math.c


#define NATIVE_MODULE "$math"

#include &lt;math.h&gt;
#include "cdc_math.h"
#include "list.h"

module_t cdc_math_module = {init_math, uninit_math};

void init_math(Int argc, char ** argv)
{
}

void uninit_math(void)
{
}

static int check_one_vector(cList *l1, Int *len_ret)
{
    Int i,len;

    len=list_length(l1);
    for (i=0; i&lt;len; i++) {
	if (list_elem(l1,i)-&gt;type != FLOAT)
	    THROW((type_id, "Arguments must be lists of floats."))
    }
    *len_ret=len;
    RETURN_TRUE;
}

static int check_vectors(cList *l1, cList *l2, Int *len_ret)
{
    Int i,len;

    len=list_length(l1);
    if (list_length(l2)!=len)
	THROW((range_id, "Arguments are not of the same length."))
    for (i=0; i&lt;len; i++) {
	if (list_elem(l1,i)-&gt;type != FLOAT)
	    THROW((type_id, "Arguments must be lists of floats."))
	if (list_elem(l2,i)-&gt;type != FLOAT)
	    THROW((type_id, "Arguments must be lists of floats."))
    }
    *len_ret=len;
    RETURN_TRUE;
}


NATIVE_METHOD(minor) {
    Int i,len;
    cList *l,*l1,*l2;

    INIT_2_ARGS(LIST,LIST);
    l1=LIST1;
    l2=LIST2;
    if (!check_vectors (l1,l2,&amp;len))
	RETURN_FALSE;
    l=list_new(len);
    l-&gt;len=len;
    for (i=0; i&lt;len; i++) {
	Float p,q;

	p=list_elem(l1,i)-&gt;u.fval;
	q=list_elem(l2,i)-&gt;u.fval;
	list_elem(l,i)-&gt;type=FLOAT;
	list_elem(l,i)-&gt;u.fval=p&lt;q ? p : q;
    }
    CLEAN_RETURN_LIST(l);
}

NATIVE_METHOD(major) {
    Int i,len;
    cList *l,*l1,*l2;

    INIT_2_ARGS(LIST,LIST);
    l1=LIST1;
    l2=LIST2;
    if (!check_vectors (l1,l2,&amp;len))
	RETURN_FALSE;
    l=list_new(len);
    l-&gt;len=len;
    for (i=0; i&lt;len; i++) {
	Float p,q;

	p=list_elem(l1,i)-&gt;u.fval;
	q=list_elem(l2,i)-&gt;u.fval;
	list_elem(l,i)-&gt;type=FLOAT;
	list_elem(l,i)-&gt;u.fval=p&gt;q ? p : q;
    }
    CLEAN_RETURN_LIST(l);
}

NATIVE_METHOD(add) {
    Int i,len;
    cList *l,*l1,*l2;

    INIT_2_ARGS(LIST,LIST);
    l1=LIST1;
    l2=LIST2;
    if (!check_vectors (l1,l2,&amp;len))
	RETURN_FALSE;
    l=list_new(len);
    l-&gt;len=len;
    for (i=0; i&lt;len; i++) {
	Float p,q;

	p=list_elem(l1,i)-&gt;u.fval;
	q=list_elem(l2,i)-&gt;u.fval;
	list_elem(l,i)-&gt;type=FLOAT;
	list_elem(l,i)-&gt;u.fval=p+q;
    }
    CLEAN_RETURN_LIST(l);
}

NATIVE_METHOD(sub) {
    Int i,len;
    cList *l,*l1,*l2;

    INIT_2_ARGS(LIST,LIST);
    l1=LIST1;
    l2=LIST2;
    if (!check_vectors (l1,l2,&amp;len))
	RETURN_FALSE;
    l=list_new(len);
    l-&gt;len=len;
    for (i=0; i&lt;len; i++) {
	Float p,q;

	p=list_elem(l1,i)-&gt;u.fval;
	q=list_elem(l2,i)-&gt;u.fval;
	list_elem(l,i)-&gt;type=FLOAT;
	list_elem(l,i)-&gt;u.fval=p-q;
    }
    CLEAN_RETURN_LIST(l);
}

NATIVE_METHOD(dot) {
    Int i,len;
    cList *l1,*l2;
    Float s;

    INIT_2_ARGS(LIST,LIST);
    l1=LIST1;
    l2=LIST2;
    if (!check_vectors (l1,l2,&amp;len))
	RETURN_FALSE;
    for (s=0.0,i=0; i&lt;len; i++) {
	Float p,q;

	p=list_elem(l1,i)-&gt;u.fval;
	q=list_elem(l2,i)-&gt;u.fval;
	s+=p*q;
    }
    CLEAN_RETURN_FLOAT(s);
}

NATIVE_METHOD(distance) {
    Int i,len;
    cList *l1,*l2;
    Float s;

    INIT_2_ARGS(LIST,LIST);
    l1=LIST1;
    l2=LIST2;
    if (!check_vectors (l1,l2,&amp;len))
	RETURN_FALSE;
    for (s=0.0,i=0; i&lt;len; i++) {
	Float p,q,d;

	p=list_elem(l1,i)-&gt;u.fval;
	q=list_elem(l2,i)-&gt;u.fval;
	d=p-q;
	s+=d*d;
    }
    CLEAN_RETURN_FLOAT(sqrt(s));
}

NATIVE_METHOD(cross) {
    Int i,len;
    cList *l,*l1,*l2;
    cData *f,*f1,*f2;

    INIT_2_ARGS(LIST,LIST);
    l1=LIST1;
    l2=LIST2;
    if (!check_vectors (l1,l2,&amp;len))
	RETURN_FALSE;
    if (len!=3)
	THROW((~range_id,"The vectors are not of length 3."))
    l=list_new(len);
    l-&gt;len=len;
    f=list_elem(l,0);
    f1=list_elem(l1,0);
    f2=list_elem(l2,0);
    f[0].type=f[1].type=f[2].type=FLOAT;
    f[0].u.fval=f1[1].u.fval*f2[2].u.fval-f1[2].u.fval*f2[1].u.fval;
    f[1].u.fval=f1[2].u.fval*f2[0].u.fval-f1[0].u.fval*f2[2].u.fval;
    f[2].u.fval=f1[0].u.fval*f2[1].u.fval-f1[1].u.fval*f2[0].u.fval;
    CLEAN_RETURN_LIST(l);
}

NATIVE_METHOD(scale) {
    Int i,len;
    cList *l,*l1;
    Float f;

    INIT_2_ARGS(FLOAT,LIST);
    l1=LIST2;
    f=FLOAT1;
    if (!check_one_vector (l1,&amp;len))
	RETURN_FALSE;
    l=list_new(len);
    l-&gt;len=len;
    for (i=0; i&lt;len; i++) {
	Float p;

	p=list_elem(l1,i)-&gt;u.fval;
	list_elem(l,i)-&gt;type=FLOAT;
	list_elem(l,i)-&gt;u.fval=p*f;
    }
    CLEAN_RETURN_LIST(l);
}

NATIVE_METHOD(is_lower) {
    Int i,len;
    cList *l1,*l2;
    
    INIT_2_ARGS(LIST,LIST);
    l1=LIST1;
    l2=LIST2;
    if (!check_vectors (l1,l2,&amp;len))
	RETURN_FALSE;
    for (i=0; i&lt;len; i++) {
	Float p,q;

	p=list_elem(l1,i)-&gt;u.fval;
	q=list_elem(l2,i)-&gt;u.fval;
	if (p&gt;=q)
	    CLEAN_RETURN_INTEGER(0);
    }
    CLEAN_RETURN_INTEGER(1);
}

NATIVE_METHOD(transpose) {
    Int i,len,len1;
    cList *l,*l1;
    cData *e,*o;

    INIT_1_ARG(LIST);
    l1=LIST1;
    len=list_length(l1);
    if (!len) {
	CLEAN_RETURN_LIST(l1);
    }
    e=list_elem(l1,0);
    for (i=0; i&lt;len; i++) {
	if (e[i].type!=LIST)
	    THROW((type_id,"The argument must be a list of lists."))
    }
    len1=list_length(e[1].u.list);
    for (i=1; i&lt;len; i++) {
	if (list_length(e[i].u.list)!=len1)
	    THROW((range_id,"All sublists must be of the same length"))
    }
    l=list_new(len1);
    l-&gt;len=len1;
    o=list_elem(l,0);
    for (i=0; i&lt;len1; i++) {
	cList *l2;
	cData *k;
	Int j;

	l2=list_new(len);
	l2-&gt;len=len;
	o[i].type=LIST;
	o[i].u.list=l2;
	k=list_elem(l2,0);
	for (j=0; j&lt;len; j++)
	    data_dup(&amp;k[j],list_elem(e[j].u.list,i));
    }
    CLEAN_RETURN_LIST(l);
}

-------------------------------------------------- cdc_math.h

#ifndef _math_mod_h_
#define _math_mod_h_

#include "defs.h"
#include "cdc_pcode.h"

void init_math(Int argc, char ** argv);
void uninit_math(void);

#ifndef _cdc_math_
extern module_t cdc_math_module;
#endif


extern NATIVE_METHOD(minor);
extern NATIVE_METHOD(major);
extern NATIVE_METHOD(add);
extern NATIVE_METHOD(sub);
extern NATIVE_METHOD(dot);
extern NATIVE_METHOD(distance);
extern NATIVE_METHOD(cross);
extern NATIVE_METHOD(scale);
extern NATIVE_METHOD(is_lower);
extern NATIVE_METHOD(transpose);

#endif

-------------------------------------------------- cdc_math.mod

##  object.method_name           function                 
native $math.minor()              minor
native $math.major()              major
native $math.add()                add
native $math.sub()            	  sub
native $math.dot()                dot
native $math.distance()           distance
native $math.cross()              cross
native $math.scale()              scale
native $math.is_lower()           is_lower
native $math.transpose()          transpose
objs cdc_math.o

-------------------------------------------------- math.coldc

object $math: $libraries;
var $root manager = $jenner;
var $root flags = ['variables, 'methods, 'code];
var $root created_on = 844267864;
var $root owners = [$jenner];
var $root inited = 1;
var $math pi = 3.14159;
var $math pi2 = 6.28318;
var $math origin_2d = [0.0, 0.0];
var $math origin_3d = [0.0, 0.0, 0.0];
var $math transmat_2d = [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0]];
var $math transmat_3d = [[1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0,
   1.0, 0.0]];
public method $math.minor(): native {
};
public method $math.major(): native {
};
public method $math.add(): native {
};
public method $math.sub(): native {
};
public method $math.dot(): native {
};
public method $math.distance(): native {
};
public method $math.cross(): native {
};
public method $math.scale(): native {
};
public method $math.is_lower(): native {
};
public method $math.transpose(): native {
};
public method $math.polar_rectangular() {
    arg coords;
    
    return [coords[1] * cos(coords[2]), coords[1] * sin(coords[2])];
};
public method $math.rectangular_polar() {
    arg coords;
    var a;
    
    a = atan2(coords[2], coords[1]);
    if (a &lt; 0)
        a += pi2;
    return [.distance(coords, origin_2d), a];
};
public method $math.pi() {
    return pi;
};
public method $math.pi2() {
    return pi2;
};
public method $math.deg_rad() {
    arg angle;
    
    return angle / 57.2958;
};
public method $math.rad_deg() {
    arg angle;
    
    return angle * 57.2958;
};
public method $math.matrix_add() {
    arg m1, m2;
    var i;
    
    return map i in [1 .. m1.length()] to (.add(m1[i], m2[i]));
};
public method $math.matrix_sub() {
    arg m1, m2;
    var i;
    
    return map i in [1 .. m2.length()] to (.sub(m1[i], m2[i]));
};
public method $math.matrix_mul() {
    arg m1, m2;
    var x, y;
    
    m2 = .transpose(m2);
    return map x in (m1) to (map y in (m2) to (.dot(x, y)));
};
public method $math.spherical_rectangular() {
    arg coords;
    var r, phi, theta, r1;
    
    r = coords[1];
    phi = coords[2];
    theta = coords[3];
    r1 = r * cos(theta);
    return [r1 * cos(phi), r1 * sin(phi), r * sin(theta)];
};
public method $math.rectangular_spherical() {
    arg coords;
    var a, d;
    
    a = atan2(coords[2], coords[1]);
    if (a &lt; 0)
        a += pi2;
    return [(d = .distance(coords, origin_3d)), a, atan2(coords[3],
   .distance(coords.subrange(1, 2), origin_2d))];
};
public method $math.ident_mat() {
    arg n;
    var x, y;
    
    return map x in [1 .. n] to (map y in [1 .. n] to (x == y ? 1.0 : 0.0));
};
public method $math.translation_mat() {
    arg vector;
    var x, y;
    
    if (vector.length() == 2)
        return [@transmat_2d, [@vector, 1.0]];
    else
        return [@transmat_3d, [@vector, 1.0]];
};
public method $math.rectangular_cylindrical() {
    arg coords;
    var a;
    
    a = atan2(coords[2], coords[1]);
    if (a &lt; 0)
        a += pi2;
    return [.distance(coords, origin_2d), a, coords[3]];
};
public method $math.cylindrical_rectangular() {
    arg coords;
    
    return [coords[1] * cos(coords[2]), coords[1] * sin(coords[2]), coords[3]];
};
public method $math.matrix_scale() {
    arg s, m;
    var x;
    
    return map x in (m) to (.scale(s, x));
};
public method $math.tensor() {
    arg v1, v2;
    var x, y;
    
    return map x in (v1) to (map y in (v2) to (x * y));
};
public method $math.skew() {
    arg v;
    
    return [[0.0, v[3], -v[2]], [-v[3], 0.0, v[1]], [v[2], -v[1], 0.0]];
};
public method $math.rotation_mat_3d() {
    arg axis, angle;
    var s, c, m, tens;
    
    s = sin(angle);
    c = cos(angle);
    if (type(axis) == 'list) {
        axis = .scale(1.0 / .distance(axis, origin_3d), axis);
        tens = .tensor(axis, axis);
        m = .matrix_add(tens, .matrix_add(.matrix_scale(s, .skew(axis)),
   .matrix_scale(c, .matrix_sub(.ident_mat(3), tens))));
        return [[@m[1], 0.0], [@m[2], 0.0], [@m[3], 0.0], [0.0, 0.0, 0.0,
   1.0]];
    } else {
        switch (axis) {
            case 'z:
                return [[c, s, 0.0, 0.0], [-s, c, 0.0, 0.0], [0.0, 0.0, 1.0,
   0.0], [0.0, 0.0, 0.0, 1.0]];
            case 'y:
                return [[c, 0.0, -s, 0.0], [0.0, 1.0, 0.0, 0.0], [s, 0.0, c,
   0.0], [0.0, 0.0, 0.0, 1.0]];
            case 'x:
                return [[1.0, 0.0, 0.0, 0.0], [0.0, c, s, 0.0], [0.0, -s, c,
   0.0], [0.0, 0.0, 0.0, 1.0]];
        }
    }
};
public method $math.transform_vect() {
    arg m, v;
    var x, outvect, flag;
    
    if (m.length() == v.length() + 1) {
        v = [@v, 1.0];
        flag = 1;
    }
    outvect = map x in (m) to (.dot(x, v));
    return flag ? outvect.subrange(1, outvect.length() - 1) : outvect;
};
public method $math.rotation_mat_2d() {
    arg angle;
    var s, c;
    
    s = sin(angle);
    c = cos(angle);
    return [[c, s, 0.0], [-s, c, 0.0], [0.0, 0.0, 1.0]];
};
public method $math.scale_mat() {
    arg scale;
    
    if (scale.length() == 2)
        return [[scale[1], 0.0, 0.0], [0, scale[2], 0.0], [0.0, 0.0, 1.0]];
    else
        return [[scale[1], 0.0, 0.0, 0.0], [0.0, scale[2], 0.0, 0.0], [0.0,
   0.0, scale[3], 0.0], [0.0, 0.0, 0.0, 1]];
};
</PRE>
