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Release calc version 2.10.3t5.45

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This commit is contained in:
Landon Curt Noll
1997-10-04 20:06:29 -07:00
parent 4618313a82
commit 6e10e97592
300 changed files with 38279 additions and 8584 deletions
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415
comfunc.c
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@@ -125,10 +125,12 @@ csqrt(COMPLEX *c, NUMBER *epsilon, long R)
if (cisreal(c)) {
r = comalloc();
if (!qisneg(c->real)) {
qfree(r->real);
r->real = qsqrt(c->real, epsilon, R);
return r;
}
ntmp = qneg(c->real);
qfree(r->imag);
r->imag = qsqrt(ntmp, epsilon, R);
qfree(ntmp);
return r;
@@ -160,7 +162,7 @@ csqrt(COMPLEX *c, NUMBER *epsilon, long R)
return clink(&_czero_);
}
aes = qscale(c->imag, -1);
v = qdiv(aes, u);
v = qqdiv(aes, u);
qfree(aes);
r = comalloc();
r->real = u;
@@ -170,8 +172,8 @@ csqrt(COMPLEX *c, NUMBER *epsilon, long R)
#endif
imsign = c->imag->num.sign;
es = qsquare(epsilon);
aes = qdiv(c->real, es);
bes = qdiv(c->imag, es);
aes = qqdiv(c->real, es);
bes = qqdiv(c->imag, es);
qfree(es);
zgcd(aes->den, bes->den, &g);
zequo(bes->den, g, &tmp1);
@@ -217,12 +219,14 @@ csqrt(COMPLEX *c, NUMBER *epsilon, long R)
r = comalloc();
qtemp = *aes;
qtemp.num.sign = sign;
qfree(r->real);
r->real = qmul(&qtemp, epsilon);
qfree(aes);
bes = qscale(r->real, 1);
qtemp = *bes;
qtemp.num.sign = sign ^ imsign;
r->imag = qdiv(c->imag, &qtemp);
qfree(r->imag);
r->imag = qqdiv(c->imag, &qtemp);
qfree(bes);
return r;
}
@@ -272,12 +276,14 @@ csqrt(COMPLEX *c, NUMBER *epsilon, long R)
r = comalloc();
qtemp = *aes;
qtemp.num.sign = sign;
qfree(r->real);
r->real = qmul(&qtemp, epsilon);
qfree(aes);
bes = qscale(r->real, 1);
qtemp = *bes;
qtemp.num.sign = sign ^ imsign;
r->imag = qdiv(c->imag, &qtemp);
qfree(r->imag);
r->imag = qqdiv(c->imag, &qtemp);
qfree(bes);
return r;
}
@@ -355,10 +361,10 @@ csqrt(COMPLEX *c, NUMBER *epsilon, long R)
return clink(&_czero_);
}
r = comalloc();
if (!qiszero(u))
r->real = u;
if (!qiszero(v))
r->imag = v;
qfree(r->real);
qfree(r->imag);
r->real = u;
r->imag = v;
return r;
}
@@ -384,6 +390,7 @@ croot(COMPLEX *c, NUMBER *q, NUMBER *epsilon)
return csqrt(c, epsilon, 24L);
if (cisreal(c) && !qisneg(c->real)) {
r = comalloc();
qfree(r->real);
r->real = qroot(c->real, q, epsilon);
return r;
}
@@ -412,7 +419,7 @@ croot(COMPLEX *c, NUMBER *q, NUMBER *epsilon)
epsilon2 = qbitvalue(n - m - 4);
tmp1 = qatan2(c->imag, c->real, epsilon2);
qfree(epsilon2);
tmp2 = qdiv(tmp1, q);
tmp2 = qqdiv(tmp1, q);
qfree(tmp1);
r = cpolar(root, tmp2, epsilon);
qfree(root);
@@ -437,8 +444,9 @@ cexp(COMPLEX *c, NUMBER *epsilon)
math_error("Zero epsilon for cexp");
/*NOTREACHED*/
}
r = comalloc();
if (cisreal(c)) {
r = comalloc();
qfree(r->real);
r->real = qexp(c->real, epsilon);
return r;
}
@@ -458,11 +466,14 @@ cexp(COMPLEX *c, NUMBER *epsilon)
qsincos(c->imag, k - n + 2, &sin, &cos);
tmp2 = qmul(tmp1, cos);
qfree(cos);
r = comalloc();
qfree(r->real);
r->real = qmappr(tmp2, epsilon, 24L);
qfree(tmp2);
tmp2 = qmul(tmp1, sin);
qfree(tmp1);
qfree(sin);
qfree(r->imag);
r->imag = qmappr(tmp2, epsilon, 24L);
qfree(tmp2);
return r;
@@ -488,6 +499,7 @@ cln(COMPLEX *c, NUMBER *epsilon)
return clink(&_czero_);
r = comalloc();
if (cisreal(c) && !qisneg(c->real)) {
qfree(r->real);
r->real = qln(c->real, epsilon);
return r;
}
@@ -500,8 +512,10 @@ cln(COMPLEX *c, NUMBER *epsilon)
tmp1 = qln(a2b2, epsilon1);
qfree(a2b2);
qfree(epsilon1);
qfree(r->real);
r->real = qscale(tmp1, -1L);
qfree(tmp1);
qfree(r->imag);
r->imag = qatan2(c->imag, c->real, epsilon);
return r;
}
@@ -526,6 +540,8 @@ ccos(COMPLEX *c, NUMBER *epsilon)
}
n = qilog2(epsilon);
ctmp1 = comalloc();
qfree(ctmp1->real);
qfree(ctmp1->imag);
neg = qisneg(c->imag);
ctmp1->real = neg ? qneg(c->imag) : qlink(c->imag);
ctmp1->imag = neg ? qlink(c->real) : qneg(c->real);
@@ -544,7 +560,9 @@ ccos(COMPLEX *c, NUMBER *epsilon)
ctmp1 = cscale(ctmp3, -1);
comfree(ctmp3);
r = comalloc();
qfree(r->real);
r->real = qmappr(ctmp1->real, epsilon, 24L);
qfree(r->imag);
r->imag = qmappr(ctmp1->imag, epsilon, 24L);
comfree(ctmp1);
return r;
@@ -573,6 +591,8 @@ csin(COMPLEX *c, NUMBER *epsilon)
n = qilog2(epsilon);
ctmp1 = comalloc();
neg = qisneg(c->imag);
qfree(ctmp1->real);
qfree(ctmp1->imag);
ctmp1->real = neg ? qneg(c->imag) : qlink(c->imag);
ctmp1->imag = neg ? qlink(c->real) : qneg(c->real);
epsilon1 = qbitvalue(n - 2);
@@ -591,9 +611,11 @@ csin(COMPLEX *c, NUMBER *epsilon)
comfree(ctmp3);
r = comalloc();
qtmp = neg ? qlink(ctmp1->imag) : qneg(ctmp1->imag);
qfree(r->real);
r->real = qmappr(qtmp, epsilon, 24L);
qfree(qtmp);
qtmp = neg ? qneg(ctmp1->real) : qlink(ctmp1->real);
qfree(r->imag);
r->imag = qmappr(qtmp, epsilon, 24L);
qfree(qtmp);
comfree(ctmp1);
@@ -601,6 +623,364 @@ csin(COMPLEX *c, NUMBER *epsilon)
}
COMPLEX *
ccosh(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2, *tmp3;
tmp1 = cexp(c, epsilon);
tmp2 = cneg(c);
tmp3 = cexp(tmp2, epsilon);
comfree(tmp2);
tmp2 = cadd(tmp1, tmp3);
comfree(tmp1);
comfree(tmp3);
tmp1 = cscale(tmp2, -1);
comfree(tmp2);
return tmp1;
}
COMPLEX *
csinh(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2, *tmp3;
tmp1 = cexp(c, epsilon);
tmp2 = cneg(c);
tmp3 = cexp(tmp2, epsilon);
comfree(tmp2);
tmp2 = csub(tmp1, tmp3);
comfree(tmp1);
comfree(tmp3);
tmp1 = cscale(tmp2, -1);
comfree(tmp2);
return tmp1;
}
COMPLEX *
casin(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2;
tmp1 = cmul(&_conei_, c);
tmp2 = casinh(tmp1, epsilon);
comfree(tmp1);
tmp1 = cdiv(tmp2, &_conei_);
comfree(tmp2);
return tmp1;
}
COMPLEX *
cacos(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2;
tmp1 = csquare(c);
tmp2 = csub(&_cone_, tmp1);
comfree(tmp1);
tmp1 = csqrt(tmp2, epsilon, 24);
comfree(tmp2);
tmp2 = cmul(&_conei_, tmp1);
comfree(tmp1);
tmp1 = cadd(c, tmp2);
comfree(tmp2);
tmp2 = cln(tmp1, epsilon);
comfree(tmp1);
tmp1 = cdiv(tmp2, &_conei_);
comfree(tmp2);
return tmp1;
}
COMPLEX *
casinh(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2, *tmp3;
BOOL neg;
neg = qisneg(c->real);
tmp1 = neg ? cneg(c) : clink(c);
tmp2 = csquare(tmp1);
tmp3 = cadd(&_cone_, tmp2);
comfree(tmp2);
tmp2 = csqrt(tmp3, epsilon, 24);
comfree(tmp3);
tmp3 = cadd(tmp2, tmp1);
comfree(tmp1);
comfree(tmp2);
tmp1 = cln(tmp3, epsilon);
comfree(tmp3);
if (neg) {
tmp2 = cneg(tmp1);
comfree(tmp1);
return tmp2;
}
return tmp1;
}
COMPLEX *
cacosh(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2;
tmp1 = csquare(c);
tmp2 = csub(tmp1, &_cone_);
comfree(tmp1);
tmp1 = csqrt(tmp2, epsilon, 24);
comfree(tmp2);
tmp2 = cadd(c, tmp1);
comfree(tmp1);
tmp1 = cln(tmp2, epsilon);
comfree(tmp2);
return tmp1;
}
COMPLEX *
catan(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2, *tmp3;
if (qiszero(c->real) && qisunit(c->imag))
return NULL;
tmp1 = csub(&_conei_, c);
tmp2 = cadd(&_conei_, c);
tmp3 = cdiv(tmp1, tmp2);
comfree(tmp1);
comfree(tmp2);
tmp1 = cln(tmp3, epsilon);
comfree(tmp3);
tmp2 = cscale(tmp1, -1);
comfree(tmp1);
tmp1 = cdiv(tmp2, &_conei_);
comfree(tmp2);
return tmp1;
}
COMPLEX *
cacot(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2, *tmp3;
if (qiszero(c->real) && qisunit(c->imag))
return NULL;
tmp1 = cadd(c, &_conei_);
tmp2 = csub(c, &_conei_);
tmp3 = cdiv(tmp1, tmp2);
comfree(tmp1);
comfree(tmp2);
tmp1 = cln(tmp3, epsilon);
comfree(tmp3);
tmp2 = cscale(tmp1, -1);
comfree(tmp1);
tmp1 = cdiv(tmp2, &_conei_);
comfree(tmp2);
return tmp1;
}
COMPLEX *
casec(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2;
tmp1 = cinv(c);
tmp2 = cacos(tmp1, epsilon);
comfree(tmp1);
return tmp2;
}
COMPLEX *
cacsc(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2;
tmp1 = cinv(c);
tmp2 = casin(tmp1, epsilon);
comfree(tmp1);
return tmp2;
}
COMPLEX *
catanh(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2, *tmp3;
if (qiszero(c->imag) && qisunit(c->real))
return NULL;
tmp1 = cadd(&_cone_, c);
tmp2 = csub(&_cone_, c);
tmp3 = cdiv(tmp1, tmp2);
comfree(tmp1);
comfree(tmp2);
tmp1 = cln(tmp3, epsilon);
comfree(tmp3);
tmp2 = cscale(tmp1, -1);
comfree(tmp1);
return tmp2;
}
COMPLEX *
cacoth(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2, *tmp3;
if (qiszero(c->imag) && qisunit(c->real))
return NULL;
tmp1 = cadd(c, &_cone_);
tmp2 = csub(c, &_cone_);
tmp3 = cdiv(tmp1, tmp2);
comfree(tmp1);
comfree(tmp2);
tmp1 = cln(tmp3, epsilon);
comfree(tmp3);
tmp2 = cscale(tmp1, -1);
comfree(tmp1);
return tmp2;
}
COMPLEX *
casech(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2;
tmp1 = cinv(c);
tmp2 = cacosh(tmp1, epsilon);
comfree(tmp1);
return tmp2;
}
COMPLEX *
cacsch(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2;
tmp1 = cinv(c);
tmp2 = casinh(tmp1, epsilon);
comfree(tmp1);
return tmp2;
}
COMPLEX *
cgd(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2, *tmp3;
NUMBER *q1, *q2;
NUMBER *sin, *cos;
NUMBER *eps;
int n, n1;
BOOL neg;
if (cisreal(c)) {
q1 = qscale(c->real, -1);
eps = qscale(epsilon, -1);
q2 = qtanh(q1, eps);
qfree(q1);
q1 = qatan(q2, eps);
qfree(eps);
qfree(q2);
tmp1 = comalloc();
qfree(tmp1->real);
tmp1->real = qscale(q1, 1);
qfree(q1);
return tmp1;
}
if (qiszero(c->real)) {
n = - qilog2(epsilon);
qsincos(c->imag, n + 8, &sin, &cos);
if (qiszero(cos) || (n1 = -qilog2(cos)) > n) {
qfree(sin);
qfree(cos);
return NULL;
}
neg = qisneg(sin);
q1 = neg ? qsub(&_qone_, sin) : qqadd(&_qone_, sin);
qfree(sin);
if (n1 > 8) {
qfree(q1);
qfree(cos);
qsincos(c->imag, n + n1, &sin, &cos);
q1 = neg ? qsub(&_qone_, sin) : qqadd(&_qone_, sin);
qfree(sin);
}
q2 = qqdiv(q1, cos);
qfree(q1);
q1 = qln(q2, epsilon);
qfree(q2);
if (neg) {
q2 = qneg(q1);
qfree(q1);
q1 = q2;
}
tmp1 = comalloc();
qfree(tmp1->imag);
tmp1->imag = q1;
if (qisneg(cos)) {
qfree(tmp1->real);
q1 = qpi(epsilon);
if (qisneg(c->imag)) {
q2 = qneg(q1);
qfree(q1);
q1 = q2;
}
tmp1->real = q1;
}
qfree(cos);
return tmp1;
}
neg = qisneg(c->real);
tmp1 = neg ? cneg(c) : clink(c);
tmp2 = cexp(tmp1, epsilon);
comfree(tmp1);
tmp1 = cmul(&_conei_, tmp2);
tmp3 = cadd(&_conei_, tmp2);
comfree(tmp2);
tmp2 = cadd(tmp1, &_cone_);
comfree(tmp1);
if (ciszero(tmp2) || ciszero(tmp3)) {
comfree(tmp2);
comfree(tmp3);
return NULL;
}
tmp1 = cdiv(tmp2, tmp3);
comfree(tmp2);
comfree(tmp3);
tmp2 = cln(tmp1, epsilon);
comfree(tmp1);
tmp1 = cdiv(tmp2, &_conei_);
comfree(tmp2);
if (neg) {
tmp2 = cneg(tmp1);
comfree(tmp1);
return tmp2;
}
return tmp1;
}
COMPLEX *
cagd(COMPLEX *c, NUMBER *epsilon)
{
COMPLEX *tmp1, *tmp2;
tmp1 = cmul(&_conei_, c);
tmp2 = cgd(tmp1, epsilon);
comfree(tmp1);
if (tmp2 == NULL)
return NULL;
tmp1 = cdiv(tmp2, &_conei_);
comfree(tmp2);
return tmp1;
}
/*
* Convert a number from polar coordinates to normal complex number form
* within the specified accuracy. This produces the value:
@@ -625,16 +1005,19 @@ cpolar(NUMBER *q1, NUMBER *q2, NUMBER *epsilon)
return qlink(&_czero_);
r = comalloc();
if (qiszero(q2)) {
qfree(r->real);
r->real = qlink(q1);
return r;
}
qsincos(q2, m - n + 2, &sin, &cos);
tmp = qmul(q1, cos);
qfree(cos);
qfree(r->real);
r->real = qmappr(tmp, epsilon, 24L);
qfree(tmp);
tmp = qmul(q1, sin);
qfree(sin);
qfree(r->imag);
r->imag = qmappr(tmp, epsilon, 24L);
qfree(tmp);
return r;
@@ -666,12 +1049,12 @@ cpower(COMPLEX *c1, COMPLEX *c2, NUMBER *epsilon)
n = qilog2(epsilon);
m1 = m2 = -1000000;
k1 = k2 = 0;
qtmp1 = qsquare(c1->real);
qtmp2 = qsquare(c1->imag);
a2b2 = qqadd(qtmp1, qtmp2);
qfree(qtmp1);
qfree(qtmp2);
if (!qiszero(c2->real)) {
qtmp1 = qsquare(c1->real);
qtmp2 = qsquare(c1->imag);
a2b2 = qqadd(qtmp1, qtmp2);
qfree(qtmp1);
qfree(qtmp2);
m1 = qilog2(c2->real);
epsilon1 = qbitvalue(-m1 - 1);
qtmp1 = qln(a2b2, epsilon1);