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add config("triground") to trigonometric function rounding

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The config("triground") controls rounding for the following
trigonometric and hyperbolic functions:

    sin, cos, tan, cot, sec, csc
    asin, acos, atan, acot, asec, acsc
    versin, coversin, vercos, covercos
    aversin, acoversin, avercos, acovercos
    haversin, hacoversin, havercos, hacovercos
    ahaversin, hacoversin, havercos, ahacovercos
    exsec, aexsec, excsc, aexcsc
    crd, acrd
    cas, cis
    sinh, cosh, tanh, coth, sech, csch
    asinh, acosh, atanh, acoth, asech, acsch

In addition to taking a complex root (such as via the power
function on a complex value), "triground" is used for:

    exp, polar

For the above mentioned functions, the rounding mode used to
round the result to the nearest epsilon value is controlled by,
and defaults to:

    config("triground", 24)

As with other config options, the call returns the previous mode,
without a 2nd argument, returns the current mode without changing it:

    config("triground")

Improved "SEE ALSO" for the hyperbolic function help files.
This commit is contained in:
Landon Curt Noll
2023-10-03 20:31:13 -07:00
parent fec9712b9a
commit db582d6e34
22 changed files with 177 additions and 63 deletions
Download Patch File Download Diff File Expand all files Collapse all files

75
qtrans.c
View File

@@ -32,6 +32,7 @@
#include "qmath.h"
#include "config.h"
#include "errtbl.h"
@@ -126,7 +127,7 @@ qsincos(NUMBER *q, long bitnum, NUMBER **vs, NUMBER **vc)
m++;
} /* m is working number of bits */
qtmp1 = qscale(q, m - n);
zquo(qtmp1->num, qtmp1->den, &X, 24);
zquo(qtmp1->num, qtmp1->den, &X, conf->triground);
qfree(qtmp1);
if (ziszero(X)) {
zfree(X);
@@ -224,7 +225,7 @@ qcos(NUMBER *q, NUMBER *epsilon)
return qlink(&_qzero_);
qsincos(q, n + 2, &sin, &cos);
qfree(sin);
res = qmappr(cos, epsilon, 24);
res = qmappr(cos, epsilon, conf->triground);
qfree(cos);
return res;
}
@@ -248,7 +249,7 @@ qsin(NUMBER *q, NUMBER *epsilon)
return qlink(&_qzero_);
qsincos(q, n + 2, &sin, &cos);
qfree(cos);
res = qmappr(sin, epsilon, 24);
res = qmappr(sin, epsilon, conf->triground);
qfree(sin);
return res;
}
@@ -289,7 +290,7 @@ qtan(NUMBER *q, NUMBER *epsilon)
tan = qqdiv(sin, cos);
qfree(sin);
qfree(cos);
res = qmappr(tan, epsilon, 24);
res = qmappr(tan, epsilon, conf->triground);
qfree(tan);
return res;
}
@@ -335,7 +336,7 @@ qcot(NUMBER *q, NUMBER *epsilon)
cot = qqdiv(cos, sin);
qfree(sin);
qfree(cos);
res = qmappr(cot, epsilon, 24);
res = qmappr(cot, epsilon, conf->triground);
qfree(cot);
return res;
}
@@ -374,7 +375,7 @@ qsec(NUMBER *q, NUMBER *epsilon)
}
sec = qinv(cos);
qfree(cos);
res = qmappr(sec, epsilon, 24);
res = qmappr(sec, epsilon, conf->triground);
qfree(sec);
return res;
}
@@ -418,7 +419,7 @@ qcsc(NUMBER *q, NUMBER *epsilon)
}
csc = qinv(sin);
qfree(sin);
res = qmappr(csc, epsilon, 24);
res = qmappr(csc, epsilon, conf->triground);
qfree(csc);
return res;
}
@@ -461,7 +462,7 @@ qasin(NUMBER *q, NUMBER *epsilon)
zsquare(q->den, &ztmp);
zsub(ztmp, qtmp1->num, &qtmp1->den);
zfree(ztmp);
qtmp2 = qsqrt(qtmp1, epsilon1, 24);
qtmp2 = qsqrt(qtmp1, epsilon1, conf->triground);
qfree(qtmp1);
qtmp1 = qatan(qtmp2, epsilon);
}
@@ -504,7 +505,7 @@ qacos(NUMBER *q, NUMBER *epsilon)
q1 = qalloc();
zsub(q->den, q->num, &q1->num);
zadd(q->den, q->num, &q1->den);
q2 = qsqrt(q1, epsilon1, 24L);
q2 = qsqrt(q1, epsilon1, conf->triground);
qfree(q1);
qfree(epsilon1);
epsilon1 = qscale(epsilon, -1L);
@@ -544,7 +545,7 @@ qatan(NUMBER *q, NUMBER *epsilon)
if (m < 8)
m = 8; /* m is number of working binary digits */
qtmp = qscale(q, m);
zquo(qtmp->num, qtmp->den, &X, 24);
zquo(qtmp->num, qtmp->den, &X, conf->triground);
qfree(qtmp);
zbitvalue(m, &D); /* q has become X/D */
zsquare(D, &DD);
@@ -553,13 +554,13 @@ qatan(NUMBER *q, NUMBER *epsilon)
zsquare(X, &ztmp1);
zadd(ztmp1, DD, &ztmp2);
zfree(ztmp1);
zsqrt(ztmp2, &ztmp1, 24L);
zsqrt(ztmp2, &ztmp1, conf->triground);
zfree(ztmp2);
zadd(ztmp1, D, &ztmp2);
zfree(ztmp1);
zshift(X, m, &ztmp1);
zfree(X);
zquo(ztmp1, ztmp2, &X, 24L);
zquo(ztmp1, ztmp2, &X, conf->triground);
zfree(ztmp1);
zfree(ztmp2);
}
@@ -608,7 +609,7 @@ qatan(NUMBER *q, NUMBER *epsilon)
qtmp->num = sum;
}
zbitvalue(m - 4 - k, &qtmp->den);
res = qmappr(qtmp, epsilon, 24L);
res = qmappr(qtmp, epsilon, conf->triground);
qfree(qtmp);
return res;
}
@@ -677,7 +678,7 @@ qacot(NUMBER *q, NUMBER *epsilon)
tmp3 = qqadd(tmp1, tmp2);
qfree(tmp1);
qfree(tmp2);
tmp1 = qmappr(tmp3, epsilon, 24L);
tmp1 = qmappr(tmp3, epsilon, conf->triground);
qfree(tmp3);
return tmp1;
}
@@ -817,7 +818,7 @@ qpi(NUMBER *epsilon)
qtmp.den = sum;
t1 = qscale(&qtmp, shift);
zfree(sum);
r = qmappr(t1, epsilon, 24L);
r = qmappr(t1, epsilon, conf->triground);
qfree(t1);
pivalue[LAST_PI_EPSILON] = qlink(epsilon);
pivalue[LAST_PI_VALUE] = qlink(r);
@@ -949,7 +950,7 @@ qexp(NUMBER *q, NUMBER *epsilon)
qfree(tmp2);
tmp2 = tmp1;
}
tmp1 = qmappr(tmp2, epsilon, 24L);
tmp1 = qmappr(tmp2, epsilon, conf->triground);
qfree(tmp2);
return tmp1;
}
@@ -992,7 +993,7 @@ qexprel(NUMBER *q, long bitnum)
m++;
} /* m is working number of bits */
qtmp1 = qscale(q, m - n);
zquo(qtmp1->num, qtmp1->den, &X, 24);
zquo(qtmp1->num, qtmp1->den, &X, conf->triground);
qfree(qtmp1);
if (ziszero(X)) {
zfree(X);
@@ -1083,7 +1084,7 @@ qln(NUMBER *q, NUMBER *epsilon)
}
m += 18; /* 8 more sqrts, 8 for rounding, 2 for epsilon/4 */
qtmp = qscale(q, m - k);
zquo(qtmp->num, qtmp->den, &X, 24L);
zquo(qtmp->num, qtmp->den, &X, conf->triground);
qfree(q);
qfree(qtmp);
@@ -1098,7 +1099,7 @@ qln(NUMBER *q, NUMBER *epsilon)
n++;
zshift(X, m + (k & 1), &ztmp);
zfree(X);
zsqrt(ztmp, &X, 24);
zsqrt(ztmp, &X, conf->triground);
zfree(ztmp)
k /= 2;
}
@@ -1109,7 +1110,7 @@ qln(NUMBER *q, NUMBER *epsilon)
zfree(D);
zshift(pow, m, &ztmp);
zfree(pow);
zquo(ztmp, mul, &pow, 24); /* pow now (X - D)/(X + D) */
zquo(ztmp, mul, &pow, conf->triground); /* pow now (X - D)/(X + D) */
zfree(ztmp);
zfree(mul);
@@ -1152,7 +1153,7 @@ qln(NUMBER *q, NUMBER *epsilon)
}
zbitvalue(m - k - n, &qtmp->den);
}
res = qmappr(qtmp, epsilon, 24L);
res = qmappr(qtmp, epsilon, conf->triground);
qfree(qtmp);
return res;
}
@@ -1425,7 +1426,7 @@ qpower(NUMBER *q1, NUMBER *q2, NUMBER *epsilon)
not_reached();
}
if (qisone(q2))
return qmappr(q1, epsilon, 24);
return qmappr(q1, epsilon, conf->triground);
if (zrel(q1->num, q1->den) < 0) {
q1tmp = qinv(q1);
q2tmp = qneg(q2);
@@ -1435,7 +1436,7 @@ qpower(NUMBER *q1, NUMBER *q2, NUMBER *epsilon)
}
if (qisone(q2tmp)) {
qfree(q2tmp);
q2tmp = qmappr(q1tmp, epsilon, 24);
q2tmp = qmappr(q1tmp, epsilon, conf->triground);
qfree(q1tmp);
return q2tmp;
}
@@ -1510,7 +1511,7 @@ qpower(NUMBER *q1, NUMBER *q2, NUMBER *epsilon)
}
}
qfree(tmp2);
tmp2 = qmappr(tmp1, epsilon, 24L);
tmp2 = qmappr(tmp1, epsilon, conf->triground);
qfree(tmp1);
return tmp2;
}
@@ -1536,7 +1537,7 @@ qroot(NUMBER *q1, NUMBER *q2, NUMBER *epsilon)
if (qiszero(q1) || qisone(q1) || qisone(q2))
return qlink(q1);
if (qistwo(q2))
return qsqrt(q1, epsilon, 24L);
return qsqrt(q1, epsilon, conf->triground);
neg = qisneg(q1);
if (neg) {
if (ziseven(q2->num)) {
@@ -1581,7 +1582,7 @@ qcosh(NUMBER *q, NUMBER *epsilon)
qfree(tmp2)
tmp1 = qscale(tmp3, -1);
qfree(tmp3);
tmp2 = qmappr(tmp1, epsilon, 24L);
tmp2 = qmappr(tmp1, epsilon, conf->triground);
qfree(tmp1);
return tmp2;
}
@@ -1612,7 +1613,7 @@ qsinh(NUMBER *q, NUMBER *epsilon)
qfree(tmp2)
tmp1 = qscale(tmp3, -1);
qfree(tmp3);
tmp2 = qmappr(tmp1, epsilon, 24L);
tmp2 = qmappr(tmp1, epsilon, conf->triground);
qfree(tmp1);
return tmp2;
}
@@ -1661,7 +1662,7 @@ qtanh(NUMBER *q, NUMBER *epsilon)
qfree(tmp2);
qfree(tmp3);
}
tmp2 = qmappr(tmp1, epsilon, 24L);
tmp2 = qmappr(tmp1, epsilon, conf->triground);
qfree(tmp1);
if (qisneg(q)) {
tmp1 = qneg(tmp2);
@@ -1724,7 +1725,7 @@ qcoth(NUMBER *q, NUMBER *epsilon)
qfree(tmp1);
tmp1 = tmp2;
}
res = qmappr(tmp1, epsilon, 24L);
res = qmappr(tmp1, epsilon, conf->triground);
qfree(tmp1);
return res;
}
@@ -1765,7 +1766,7 @@ qsech(NUMBER *q, NUMBER *epsilon)
qfree(tmp3);
tmp2 = qscale(tmp1, 1);
qfree(tmp1);
res = qmappr(tmp2, epsilon, 24L);
res = qmappr(tmp2, epsilon, conf->triground);
qfree(tmp2);
return res;
}
@@ -1812,7 +1813,7 @@ qcsch(NUMBER *q, NUMBER *epsilon)
qfree(tmp3)
tmp2 = qscale(tmp1, 1);
qfree(tmp1);
res = qmappr(tmp2, epsilon, 24L);
res = qmappr(tmp2, epsilon, conf->triground);
qfree(tmp2);
return res;
}
@@ -1842,14 +1843,14 @@ qacosh(NUMBER *q, NUMBER *epsilon)
tmp1 = qsquare(q);
tmp2 = qdec(tmp1);
qfree(tmp1);
tmp1 = qsqrt(tmp2, epsilon1, 24L);
tmp1 = qsqrt(tmp2, epsilon1, conf->triground);
qfree(tmp2);
tmp2 = qqadd(tmp1, q);
qfree(tmp1);
tmp1 = qln(tmp2, epsilon1);
qfree(tmp2);
qfree(epsilon1);
tmp2 = qmappr(tmp1, epsilon, 24L);
tmp2 = qmappr(tmp1, epsilon, conf->triground);
qfree(tmp1);
return tmp2;
}
@@ -1880,7 +1881,7 @@ qasinh(NUMBER *q, NUMBER *epsilon)
tmp1 = qsquare(q);
tmp2 = qinc(tmp1);
qfree(tmp1);
tmp1 = qsqrt(tmp2, epsilon1, 24L);
tmp1 = qsqrt(tmp2, epsilon1, conf->triground);
qfree(tmp2);
tmp2 = qqadd(tmp1, q);
qfree(tmp1);
@@ -1888,7 +1889,7 @@ qasinh(NUMBER *q, NUMBER *epsilon)
qfree(tmp2);
qfree(q);
qfree(epsilon1);
tmp2 = qmappr(tmp1, epsilon, 24L);
tmp2 = qmappr(tmp1, epsilon, conf->triground);
if (neg) {
tmp1 = qneg(tmp2);
qfree(tmp2);
@@ -3677,9 +3678,9 @@ qcas(NUMBER *q, NUMBER *epsilon)
* compute cosine and sine
*/
qsincos(q, n + 2, &sin, &cos);
tcos = qmappr(cos, epsilon, 24);
tcos = qmappr(cos, epsilon, conf->triground);
qfree(cos);
tsin = qmappr(sin, epsilon, 24);
tsin = qmappr(sin, epsilon, conf->triground);
qfree(sin);
res = qqadd(tcos, tsin);
qfree(tcos);