new versions, mostly from Cody and Waite
This commit is contained in:
ceriel
parent
03d44703a2
commit
9f7ee118f7
10 changed files with 369 additions and 358 deletions
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@ -3,7 +3,6 @@ asin.c
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atan2.c
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atan.c
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ceil.c
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cosh.c
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fabs.c
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gamma.c
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hypot.c
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@ -12,30 +12,58 @@
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extern int errno;
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static double
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asin_acos(x, cosfl)
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double x;
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{
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int negative = x < 0;
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extern double sqrt(), atan();
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int negative = x < 0;
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int i;
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double g;
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extern double sqrt();
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static double p[] = {
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-0.27368494524164255994e+2,
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0.57208227877891731407e+2,
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-0.39688862997540877339e+2,
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0.10152522233806463645e+2,
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-0.69674573447350646411e+0
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};
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static double q[] = {
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-0.16421096714498560795e+3,
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0.41714430248260412556e+3,
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-0.38186303361750149284e+3,
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0.15095270841030604719e+3,
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-0.23823859153670238830e+2,
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1.0
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};
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if (negative) {
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x = -x;
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}
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if (x > 1) {
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errno = EDOM;
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return 0;
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if (x > 0.5) {
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i = 1 - cosfl;
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if (x > 1) {
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errno = EDOM;
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return 0;
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}
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g = 0.5 - 0.5 * y;
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y = - sqrt(g);
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y += y;
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}
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if (x == 1) {
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x = M_PI_2;
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else {
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/* ??? avoid underflow ??? */
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g = y * y;
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}
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else x = atan(x/sqrt(1-x*x));
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if (negative) x = -x;
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if (cosfl) {
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return M_PI_2 - x;
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y += y * g * POLYNOM4(g, x) / POLYNOM5(g, y);
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if (i == 1) {
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if (cosfl == 0 || ! negative) {
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y = (y + M_PI_4) + M_PI_4;
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}
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else if (cosfl && negative) {
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y = (y + M_PI_2) + M_PI_2;
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}
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}
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return x;
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if (! cosfl && negative) y = -y;
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return y;
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}
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double
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@ -10,94 +10,61 @@
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#include <math.h>
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#include <errno.h>
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extern int errno;
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double
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atan(x)
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double x;
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{
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/* The interval [0, infinity) is treated as follows:
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Define partition points Xi
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X0 = 0
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X1 = tan(pi/16)
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X2 = tan(3pi/16)
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X3 = tan(5pi/16)
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X4 = tan(7pi/16)
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X5 = infinity
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and evaluation nodes xi
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x2 = tan(2pi/16)
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x3 = tan(4pi/16)
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x4 = tan(6pi/16)
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x5 = infinity
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An argument x in [Xn-1, Xn] is now reduced to an argument
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t in [-X1, X1] by the following formulas:
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t = 1/xn - (1/(xn*xn) + 1)/((1/xn) + x)
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arctan(x) = arctan(xi) + arctan(t)
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For the interval [0, p/16] an approximation is used:
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arctan(x) = x * P(x*x)/Q(x*x)
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/* Algorithm and coefficients from:
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"Software manual for the elementary functions"
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by W.J. Cody and W. Waite, Prentice-Hall, 1980
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*/
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static struct precomputed {
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double X; /* partition point */
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double arctan; /* arctan of evaluation node */
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double one_o_x; /* 1 / xn */
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double one_o_xsq_p_1; /* 1 / (xn*xn) + 1 */
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} prec[5] = {
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{ 0.19891236737965800691159762264467622,
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0.0,
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0.0, /* these don't matter */
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0.0 } ,
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{ 0.66817863791929891999775768652308076, /* tan(3pi/16) */
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M_PI_8,
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2.41421356237309504880168872420969808,
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6.82842712474619009760337744841939616 },
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{ 1.49660576266548901760113513494247691, /* tan(5pi/16) */
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M_PI_4,
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1.0,
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2.0 },
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{ 5.02733949212584810451497507106407238, /* tan(7pi/16) */
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M_3PI_8,
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0.41421356237309504880168872420969808,
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1.17157287525380998659662255158060384 },
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{ MAXDOUBLE,
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M_PI_2,
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0.0,
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1.0 }};
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/* Hart & Cheney # 5037 */
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static double p[5] = {
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0.7698297257888171026986294745e+03,
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0.1557282793158363491416585283e+04,
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0.1033384651675161628243434662e+04,
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0.2485841954911840502660889866e+03,
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0.1566564964979791769948970100e+02
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static double p[] = {
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-0.13688768894191926929e+2,
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-0.20505855195861651981e+2,
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-0.84946240351320683534e+1,
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-0.83758299368150059274e+0
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};
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static double q[] = {
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0.41066306682575781263e+2,
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0.86157349597130242515e+2,
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0.59578436142597344465e+2,
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0.15024001160028576121e+2,
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1.0
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};
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static double a[] = {
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0.0,
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0.52359877559829887307710723554658381, /* pi/6 */
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M_PI_2,
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1.04719755119659774615421446109316763 /* pi/3 */
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};
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static double q[6] = {
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0.7698297257888171026986294911e+03,
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0.1813892701754635858982709369e+04,
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0.1484049607102276827437401170e+04,
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0.4904645326203706217748848797e+03,
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0.5593479839280348664778328000e+02,
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0.1000000000000000000000000000e+01
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};
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int neg = x < 0;
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int n;
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double g;
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int negative = x < 0.0;
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register struct precomputed *pr = prec;
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if (negative) {
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if (neg) {
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x = -x;
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}
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while (x > pr->X) pr++;
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if (pr != prec) {
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x = pr->arctan +
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atan(pr->one_o_x - pr->one_o_xsq_p_1/(pr->one_o_x + x));
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if (x > 1.0) {
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x = 1.0/x;
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n = 2;
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}
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else {
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double xsq = x*x;
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else n = 0;
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x = x * POLYNOM4(xsq, p)/POLYNOM5(xsq, q);
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if (x > 0.26794919243112270647) { /* 2-sqtr(3) */
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n = n + 1;
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x = (((0.73205080756887729353*x-0.5)-0.5)+x)/
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(1.73205080756887729353+x);
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}
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return negative ? -x : x;
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/* ??? avoid underflow ??? */
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g = x * x;
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x += x * g * POLYNOM3(g, p) / POLYNOM4(g, q);
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if (n > 1) x = -x;
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x += a[n];
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return neg ? -x : x;
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}
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@ -1,5 +1,5 @@
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/*
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* (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
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* (c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
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* See the copyright notice in the ACK home directory, in the file "Copyright".
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*
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* Author: Ceriel J.H. Jacobs
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@ -10,32 +10,33 @@
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#include <math.h>
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#include <errno.h>
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extern int errno;
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extern int errno;
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extern double ldexp();
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double
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exp(x)
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double x;
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double x;
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{
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/* 2**x = (Q(x*x)+x*P(x*x))/(Q(x*x)-x*P(x*x)) for x in [0,0.5] */
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/* Hart & Cheney #1069 */
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/* Algorithm and coefficients from:
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"Software manual for the elementary functions"
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by W.J. Cody and W. Waite, Prentice-Hall, 1980
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*/
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static double p[3] = {
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0.2080384346694663001443843411e+07,
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0.3028697169744036299076048876e+05,
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0.6061485330061080841615584556e+02
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static double p[] = {
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0.25000000000000000000e+0,
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0.75753180159422776666e-2,
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0.31555192765684646356e-4
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};
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static double q[4] = {
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0.6002720360238832528230907598e+07,
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0.3277251518082914423057964422e+06,
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0.1749287689093076403844945335e+04,
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0.1000000000000000000000000000e+01
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static double q[] = {
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0.50000000000000000000e+0,
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0.56817302698551221787e-1,
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0.63121894374398503557e-3,
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0.75104028399870046114e-6
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};
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int negative = x < 0;
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int ipart, large = 0;
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double xsqr, xPxx, Qxx;
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extern double floor(), ldexp();
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double xn, g;
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int n;
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int negative = x < 0;
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if (x <= M_LN_MIN_D) {
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if (x < M_LN_MIN_D) errno = ERANGE;
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@ -46,22 +47,18 @@ exp(x)
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return M_MAX_D;
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}
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if (negative) {
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x = -x;
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/* ??? avoid underflow ??? */
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n = x * M_LOG2E + 0.5; /* 1/ln(2) = log2(e), 0.5 added for rounding */
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xn = n;
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{
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double x1 = (long) x;
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double x2 = x - x1;
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g = ((x1-xn*0.693359375)+x2) - xn*(-2.1219444005469058277e-4);
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}
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x /= M_LN2;
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ipart = floor(x);
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x -= ipart;
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if (x > 0.5) {
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large = 1;
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x -= 0.5;
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}
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xsqr = x * x;
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xPxx = x * POLYNOM2(xsqr, p);
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Qxx = POLYNOM3(xsqr, q);
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x = (Qxx + xPxx) / (Qxx - xPxx);
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if (large) x *= M_SQRT2;
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x = ldexp(x, ipart);
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if (negative) return 1.0/x;
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return x;
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xn = g * g;
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x = g * POLYNOM2(xn, p);
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n += 1;
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return (ldexp(0.5 + x/(POLYNOM3(xn, q) - x), n));
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}
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@ -1,5 +1,5 @@
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/*
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* (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
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* (c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
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* See the copyright notice in the ACK home directory, in the file "Copyright".
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*
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* Author: Ceriel J.H. Jacobs
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@ -10,35 +10,31 @@
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#include <math.h>
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#include <errno.h>
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extern int errno;
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extern int errno;
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extern double frexp();
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double
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log(x)
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double x;
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double x;
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{
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/* log(x) = z*P(z*z)/Q(z*z), z = (x-1)/(x+1), x in [1/sqrt(2), sqrt(2)]
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/* Algorithm and coefficients from:
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"Software manual for the elementary functions"
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by W.J. Cody and W. Waite, Prentice-Hall, 1980
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*/
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/* Hart & Cheney #2707 */
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static double p[5] = {
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0.7504094990777122217455611007e+02,
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-0.1345669115050430235318253537e+03,
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0.7413719213248602512779336470e+02,
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-0.1277249755012330819984385000e+02,
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0.3327108381087686938144000000e+00
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static double a[] = {
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-0.64124943423745581147e2,
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0.16383943563021534222e2,
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-0.78956112887491257267e0
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};
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static double b[] = {
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-0.76949932108494879777e3,
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0.31203222091924532844e3,
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-0.35667977739034646171e2,
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1.0
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};
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static double q[5] = {
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0.3752047495388561108727775374e+02,
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-0.7979028073715004879439951583e+02,
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0.5616126132118257292058560360e+02,
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-0.1450868091858082685362325000e+02,
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0.1000000000000000000000000000e+01
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};
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extern double frexp();
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double z, zsqr;
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int exponent;
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double znum, zden, z, w;
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int exponent;
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if (x <= 0) {
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errno = EDOM;
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@ -46,11 +42,18 @@ log(x)
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}
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x = frexp(x, &exponent);
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while (x < M_1_SQRT2) {
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x += x;
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if (x > M_1_SQRT2) {
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znum = (x - 0.5) - 0.5;
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zden = x * 0.5 + 0.5;
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}
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else {
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znum = x - 0.5;
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zden = znum * 0.5 + 0.5;
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exponent--;
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}
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z = (x-1)/(x+1);
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zsqr = z*z;
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return z * POLYNOM4(zsqr, p) / POLYNOM4(zsqr, q) + exponent * M_LN2;
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z = znum/zden; w = z * z;
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x = z + z * w * (POLYNOM2(w,a)/POLYNOM3(w,b));
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z = exponent;
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x += z * (-2.121944400546905827679e-4);
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return x + z * 0.693359375;
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}
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@ -11,13 +11,19 @@
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#include <errno.h>
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extern int errno;
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extern double modf(), exp(), log();
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double
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pow(x,y)
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double x,y;
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{
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/* Simple version for now. The Cody and Waite book has
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a very complicated, much more precise version, but
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this version has machine-dependant arrays A1 and A2,
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and I don't know yet how to solve this ???
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*/
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double dummy;
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extern double modf(), exp(), log();
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int result_neg = 0;
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if ((x == 0 && y == 0) ||
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(x < 0 && modf(y, &dummy) != 0)) {
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@ -28,13 +34,26 @@ pow(x,y)
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if (x == 0) return x;
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if (x < 0) {
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double val = exp(log(-x) * y);
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if (modf(y/2.0, &dummy) != 0) {
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/* y was odd */
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val = - val;
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result_neg = 1;
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}
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return val;
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x = -x;
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}
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x = log(x);
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if (x < 0) {
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x = -x;
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y = -y;
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}
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if (y > M_LN_MAX_D/x) {
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errno = ERANGE;
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return 0;
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}
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if (y < M_LN_MIN_D/x) {
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errno = ERANGE;
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return 0;
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}
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return exp(log(x) * y);
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x = exp(x * y);
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return result_neg ? -x : x;
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}
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@ -10,93 +10,77 @@
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#include <math.h>
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#include <errno.h>
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extern int errno;
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extern int errno;
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extern double modf();
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static double
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sinus(x, quadrant)
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sinus(x, cos_flag)
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double x;
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{
|
||||
/* sin(0.5*pi*x) = x * P(x*x)/Q(x*x) for x in [0,1] */
|
||||
/* Hart & Cheney # 3374 */
|
||||
/* Algorithm and coefficients from:
|
||||
"Software manual for the elementary functions"
|
||||
by W.J. Cody and W. Waite, Prentice-Hall, 1980
|
||||
*/
|
||||
|
||||
static double p[6] = {
|
||||
0.4857791909822798473837058825e+10,
|
||||
-0.1808816670894030772075877725e+10,
|
||||
0.1724314784722489597789244188e+09,
|
||||
-0.6351331748520454245913645971e+07,
|
||||
0.1002087631419532326179108883e+06,
|
||||
-0.5830988897678192576148973679e+03
|
||||
static double r[] = {
|
||||
-0.16666666666666665052e+0,
|
||||
0.83333333333331650314e-2,
|
||||
-0.19841269841201840457e-3,
|
||||
0.27557319210152756119e-5,
|
||||
-0.25052106798274584544e-7,
|
||||
0.16058936490371589114e-9,
|
||||
-0.76429178068910467734e-12,
|
||||
0.27204790957888846175e-14
|
||||
};
|
||||
|
||||
static double q[6] = {
|
||||
0.3092566379840468199410228418e+10,
|
||||
0.1202384907680254190870913060e+09,
|
||||
0.2321427631602460953669856368e+07,
|
||||
0.2848331644063908832127222835e+05,
|
||||
0.2287602116741682420054505174e+03,
|
||||
0.1000000000000000000000000000e+01
|
||||
};
|
||||
|
||||
double xsqr;
|
||||
int t;
|
||||
double xsqr;
|
||||
double y;
|
||||
int neg = 0;
|
||||
|
||||
if (x < 0) {
|
||||
quadrant += 2;
|
||||
x = -x;
|
||||
neg = 1;
|
||||
}
|
||||
if (M_PI_2 - x == M_PI_2) {
|
||||
switch(quadrant) {
|
||||
case 0:
|
||||
case 2:
|
||||
return 0.0;
|
||||
case 1:
|
||||
return 1.0;
|
||||
case 3:
|
||||
return -1.0;
|
||||
}
|
||||
if (cos_flag) {
|
||||
neg = 0;
|
||||
y = M_PI_2 + x;
|
||||
}
|
||||
if (x >= M_2PI) {
|
||||
if (x <= 0x7fffffff) {
|
||||
/* Use extended precision to calculate reduced argument.
|
||||
Split 2pi in 2 parts a1 and a2, of which the first only
|
||||
uses some bits of the mantissa, so that n * a1 is
|
||||
exactly representable, where n is the integer part of
|
||||
x/pi.
|
||||
Here we used 12 bits of the mantissa for a1.
|
||||
Also split x in integer part x1 and fraction part x2.
|
||||
We then compute x-n*2pi as ((x1 - n*a1) + x2) - n*a2.
|
||||
*/
|
||||
#define A1 6.2822265625
|
||||
#define A2 0.00095874467958647692528676655900576
|
||||
double n = (long) (x / M_2PI);
|
||||
double x1 = (long) x;
|
||||
double x2 = x - x1;
|
||||
x = x1 - n * A1;
|
||||
else y = x;
|
||||
|
||||
/* ??? avoid loss of significance, if y is too large, error ??? */
|
||||
|
||||
y = y * M_1_PI + 0.5;
|
||||
|
||||
/* Use extended precision to calculate reduced argument.
|
||||
Here we used 12 bits of the mantissa for a1.
|
||||
Also split x in integer part x1 and fraction part x2.
|
||||
*/
|
||||
#define A1 3.1416015625
|
||||
#define A2 -8.908910206761537356617e-6
|
||||
{
|
||||
double x1, x2;
|
||||
|
||||
modf(y, &y);
|
||||
if (modf(0.5*y, &x1)) neg = !neg;
|
||||
if (cos_flag) y -= 0.5;
|
||||
x2 = modf(x, &x1);
|
||||
x = x1 - y * A1;
|
||||
x += x2;
|
||||
x -= n * A2;
|
||||
x -= y * A2;
|
||||
#undef A1
|
||||
#undef A2
|
||||
}
|
||||
else {
|
||||
extern double modf();
|
||||
double dummy;
|
||||
}
|
||||
|
||||
x = modf(x/M_2PI, &dummy) * M_2PI;
|
||||
}
|
||||
}
|
||||
x /= M_PI_2;
|
||||
t = x;
|
||||
x -= t;
|
||||
quadrant = (quadrant + (int)(t % 4)) % 4;
|
||||
if (quadrant & 01) {
|
||||
x = 1 - x;
|
||||
}
|
||||
if (quadrant > 1) {
|
||||
if (x < 0) {
|
||||
neg = !neg;
|
||||
x = -x;
|
||||
}
|
||||
xsqr = x * x;
|
||||
x = x * POLYNOM5(xsqr, p) / POLYNOM5(xsqr, q);
|
||||
return x;
|
||||
|
||||
/* ??? avoid underflow ??? */
|
||||
|
||||
y = x * x;
|
||||
x += x * y * POLYNOM7(y, r);
|
||||
return neg ? -x : x;
|
||||
}
|
||||
|
||||
double
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
/*
|
||||
* (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
|
||||
* (c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
|
||||
* See the copyright notice in the ACK home directory, in the file "Copyright".
|
||||
*
|
||||
* Author: Ceriel J.H. Jacobs
|
||||
|
|
@ -10,33 +10,73 @@
|
|||
#include <math.h>
|
||||
#include <errno.h>
|
||||
|
||||
extern int errno;
|
||||
extern int errno;
|
||||
extern double exp();
|
||||
|
||||
static double
|
||||
sinh_cosh(x, cosh_flag)
|
||||
double x;
|
||||
{
|
||||
/* Algorithm and coefficients from:
|
||||
"Software manual for the elementary functions"
|
||||
by W.J. Cody and W. Waite, Prentice-Hall, 1980
|
||||
*/
|
||||
|
||||
static double p[] = {
|
||||
-0.35181283430177117881e+6,
|
||||
-0.11563521196851768270e+5,
|
||||
-0.16375798202630751372e+3,
|
||||
-0.78966127417357099479e+0
|
||||
};
|
||||
static double q[] = {
|
||||
-0.21108770058106271242e+7,
|
||||
0.36162723109421836460e+5,
|
||||
-0.27773523119650701167e+3,
|
||||
1.0
|
||||
};
|
||||
int negative = x < 0;
|
||||
double y = negative ? -x : x;
|
||||
|
||||
if (! cosh_flag && y <= 1.0) {
|
||||
/* ??? check for underflow ??? */
|
||||
y = y * y;
|
||||
return x + x * y * POLYNOM3(y, p)/POLYNOM3(y,q);
|
||||
}
|
||||
|
||||
if (y >= M_LN_MAX_D) {
|
||||
/* exp(y) would cause overflow */
|
||||
#define LNV 0.69316101074218750000e+0
|
||||
#define VD2M1 0.52820835025874852469e-4
|
||||
double w = y - LNV;
|
||||
|
||||
if (w < M_LN_MAX_D+M_LN2-LNV) {
|
||||
x = exp(w);
|
||||
x += VD2M1 * x;
|
||||
}
|
||||
else {
|
||||
errno = ERANGE;
|
||||
x = HUGE;
|
||||
}
|
||||
}
|
||||
else {
|
||||
double z = exp(y);
|
||||
|
||||
x = 0.5 * (z + (cosh_flag ? 1.0 : -1.0)/z);
|
||||
}
|
||||
return negative ? -x : x;
|
||||
}
|
||||
|
||||
double
|
||||
sinh(x)
|
||||
double x;
|
||||
{
|
||||
int negx = x < 0;
|
||||
extern double exp();
|
||||
|
||||
if (negx) {
|
||||
x = -x;
|
||||
}
|
||||
if (x > M_LN_MAX_D) {
|
||||
/* exp(x) would overflow */
|
||||
if (x >= M_LN_MAX_D + M_LN2) {
|
||||
/* not representable */
|
||||
x = HUGE;
|
||||
errno = ERANGE;
|
||||
}
|
||||
else x = exp (x - M_LN2);
|
||||
}
|
||||
else {
|
||||
double expx = exp(x);
|
||||
x = 0.5 * (expx - 1.0/expx);
|
||||
}
|
||||
if (negx) {
|
||||
return -x;
|
||||
}
|
||||
return x;
|
||||
return sinh_cosh(x, 0);
|
||||
}
|
||||
|
||||
double
|
||||
cosh(x)
|
||||
double x;
|
||||
{
|
||||
if (x < 0) x = -x;
|
||||
return sinh_cosh(x, 1);
|
||||
}
|
||||
|
|
|
|||
|
|
@ -10,117 +10,64 @@
|
|||
#include <math.h>
|
||||
#include <errno.h>
|
||||
|
||||
extern int errno;
|
||||
extern int errno;
|
||||
extern double modf();
|
||||
|
||||
double
|
||||
tan(x)
|
||||
double x;
|
||||
{
|
||||
/* First reduce range to [0, pi/4].
|
||||
Then use approximation tan(x*pi/4) = x * P(x*x)/Q(x*x).
|
||||
Hart & Cheney # 4288
|
||||
Use: tan(x) = 1/tan(pi/2 - x)
|
||||
tan(-x) = -tan(x)
|
||||
tan(x+k*pi) = tan(x)
|
||||
/* Algorithm and coefficients from:
|
||||
"Software manual for the elementary functions"
|
||||
by W.J. Cody and W. Waite, Prentice-Hall, 1980
|
||||
*/
|
||||
|
||||
static double p[5] = {
|
||||
-0.5712939549476836914932149599e+10,
|
||||
0.4946855977542506692946040594e+09,
|
||||
-0.9429037070546336747758930844e+07,
|
||||
0.5282725819868891894772108334e+05,
|
||||
-0.6983913274721550913090621370e+02
|
||||
};
|
||||
|
||||
static double q[6] = {
|
||||
-0.7273940551075393257142652672e+10,
|
||||
0.2125497341858248436051062591e+10,
|
||||
-0.8000791217568674135274814656e+08,
|
||||
0.8232855955751828560307269007e+06,
|
||||
-0.2396576810261093558391373322e+04,
|
||||
0.1000000000000000000000000000e+01
|
||||
};
|
||||
|
||||
int negative = x < 0;
|
||||
double tmp, tmp1, tmp2;
|
||||
double xsq;
|
||||
int invert = 0;
|
||||
int ip;
|
||||
double y;
|
||||
static double p[] = {
|
||||
1.0,
|
||||
-0.13338350006421960681e+0,
|
||||
0.34248878235890589960e-2,
|
||||
-0.17861707342254426711e-4
|
||||
};
|
||||
static double q[] = {
|
||||
1.0,
|
||||
-0.46671683339755294240e+0,
|
||||
0.25663832289440112864e-1,
|
||||
-0.31181531907010027307e-3,
|
||||
0.49819433993786512270e-6
|
||||
};
|
||||
|
||||
if (negative) x = -x;
|
||||
|
||||
/* first reduce to [0, pi) */
|
||||
if (x >= M_PI) {
|
||||
if (x <= 0x7fffffff) {
|
||||
/* Use extended precision to calculate reduced argument.
|
||||
Split pi in 2 parts a1 and a2, of which the first only
|
||||
uses some bits of the mantissa, so that n * a1 is
|
||||
exactly representable, where n is the integer part of
|
||||
x/pi.
|
||||
Here we used 12 bits of the mantissa for a1.
|
||||
Also split x in integer part x1 and fraction part x2.
|
||||
We then compute x-n*pi as ((x1 - n*a1) + x2) - n*a2.
|
||||
*/
|
||||
#define A1 3.14111328125
|
||||
#define A2 0.00047937233979323846264338327950288
|
||||
double n = (long) (x / M_PI);
|
||||
double x1 = (long) x;
|
||||
double x2 = x - x1;
|
||||
x = x1 - n * A1;
|
||||
/* ??? avoid loss of significance, error if x is too large ??? */
|
||||
|
||||
y = x * M_2_PI + 0.5;
|
||||
|
||||
/* Use extended precision to calculate reduced argument.
|
||||
Here we used 12 bits of the mantissa for a1.
|
||||
Also split x in integer part x1 and fraction part x2.
|
||||
*/
|
||||
#define A1 1.57080078125
|
||||
#define A2 -4.454455103380768678308e-6
|
||||
{
|
||||
double x1, x2;
|
||||
|
||||
modf(y, &y);
|
||||
if (modf(0.5*y, &x1)) invert = 1;
|
||||
x2 = modf(x, &x1);
|
||||
x = x1 - y * A1;
|
||||
x += x2;
|
||||
x -= n * A2;
|
||||
x -= y * A2;
|
||||
#undef A1
|
||||
#undef A2
|
||||
}
|
||||
else {
|
||||
extern double modf();
|
||||
|
||||
x = modf(x/M_PI, &tmp) * M_PI;
|
||||
}
|
||||
}
|
||||
/* because the approximation uses x*pi/4, we reverse this */
|
||||
x /= M_PI_4;
|
||||
ip = (int) x;
|
||||
x -= ip;
|
||||
|
||||
switch(ip) {
|
||||
case 0:
|
||||
/* [0,pi/4] */
|
||||
break;
|
||||
case 1:
|
||||
/* [pi/4, pi/2]
|
||||
tan(x+pi/4) = 1/tan(pi/2 - (x+pi/4)) = 1/tan(pi/4 - x)
|
||||
*/
|
||||
invert = 1;
|
||||
x = 1.0 - x;
|
||||
break;
|
||||
case 2:
|
||||
/* [pi/2, 3pi/4]
|
||||
tan(x+pi/2) = tan((x+pi/2)-pi) = -tan(pi/2 - x) =
|
||||
-1/tan(x)
|
||||
*/
|
||||
negative = ! negative;
|
||||
invert = 1;
|
||||
break;
|
||||
case 3:
|
||||
/* [3pi/4, pi)
|
||||
tan(x+3pi/4) = tan(x-pi/4) = - tan(pi/4-x)
|
||||
*/
|
||||
x = 1.0 - x;
|
||||
negative = ! negative;
|
||||
break;
|
||||
}
|
||||
xsq = x * x;
|
||||
tmp1 = x*POLYNOM4(xsq, p);
|
||||
tmp2 = POLYNOM5(xsq, q);
|
||||
tmp = tmp1 / tmp2;
|
||||
if (invert) {
|
||||
if (tmp == 0.0) {
|
||||
errno = ERANGE;
|
||||
tmp = HUGE;
|
||||
}
|
||||
else tmp = tmp2 / tmp1;
|
||||
}
|
||||
|
||||
return negative ? -tmp : tmp;
|
||||
/* ??? avoid underflow ??? */
|
||||
y = x * x;
|
||||
x += x * y * POLYNOM2(y, p+1);
|
||||
y = POLYNOM4(y, q);
|
||||
if (neg) x = -x;
|
||||
return invert ? -y/x : x/y;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
/*
|
||||
* (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
|
||||
* (c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
|
||||
* See the copyright notice in the ACK home directory, in the file "Copyright".
|
||||
*
|
||||
* Author: Ceriel J.H. Jacobs
|
||||
|
|
@ -10,18 +10,45 @@
|
|||
#include <math.h>
|
||||
#include <errno.h>
|
||||
|
||||
extern int errno;
|
||||
extern double exp();
|
||||
|
||||
double
|
||||
tanh(x)
|
||||
double x;
|
||||
double x;
|
||||
{
|
||||
extern double exp();
|
||||
/* Algorithm and coefficients from:
|
||||
"Software manual for the elementary functions"
|
||||
by W.J. Cody and W. Waite, Prentice-Hall, 1980
|
||||
*/
|
||||
|
||||
static double p[] = {
|
||||
-0.16134119023996228053e+4,
|
||||
-0.99225929672236083313e+2,
|
||||
-0.96437492777225469787e+0
|
||||
};
|
||||
static double q[] = {
|
||||
0.48402357071988688686e+4,
|
||||
0.22337720718962312926e+4,
|
||||
0.11274474380534949335e+3,
|
||||
1.0
|
||||
};
|
||||
int negative = x < 0;
|
||||
|
||||
if (negative) x = -x;
|
||||
|
||||
if (x <= 0.5*M_LN_MIN_D) {
|
||||
return -1;
|
||||
}
|
||||
if (x >= 0.5*M_LN_MAX_D) {
|
||||
return 1;
|
||||
x = 1.0;
|
||||
}
|
||||
x = exp(x + x);
|
||||
return (x - 1.0)/(x + 1.0);
|
||||
#define LN3D2 0.54930614433405484570e+0 /* ln(3)/2 */
|
||||
else if (x > LN3D2) {
|
||||
x = 0.5 - 1.0/(exp(x+x)+1.0);
|
||||
x += x;
|
||||
}
|
||||
else {
|
||||
/* ??? avoid underflow ??? */
|
||||
double g = x*x;
|
||||
x += x * g * POLYNOM2(g, p)/POLYNOM3(g, q);
|
||||
}
|
||||
return negative ? -x : x;
|
||||
}
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue