mirror of git://sourceware.org/git/glibc.git
Format s_tan.c
This commit is contained in:
Siddhesh Poyarekar
parent
a64d7e0efb
commit
27ec37f185
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@ -1,5 +1,7 @@
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2013-03-29 Siddhesh Poyarekar <siddhesh@redhat.com>
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2013-03-29 Siddhesh Poyarekar <siddhesh@redhat.com>
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* sysdeps/ieee754/dbl-64/s_tan.c: Fix formatting.
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* sysdeps/ieee754/dbl-64/mpa.h (ZERO, MZERO): Remove defines.
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* sysdeps/ieee754/dbl-64/mpa.h (ZERO, MZERO): Remove defines.
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(__pow_mp): Replace ZERO and MZERO with their values.
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(__pow_mp): Replace ZERO and MZERO with their values.
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* sysdeps/ieee754/dbl-64/e_atan2.c (__ieee754_atan2): Likewise.
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* sysdeps/ieee754/dbl-64/e_atan2.c (__ieee754_atan2): Likewise.
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@ -51,13 +51,15 @@ void __mptan(double, mp_no *, int);
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double
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double
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SECTION
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SECTION
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tan(double x) {
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tan (double x)
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{
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#include "utan.h"
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#include "utan.h"
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#include "utan.tbl"
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#include "utan.tbl"
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int ux, i, n;
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int ux, i, n;
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double a,da,a2,b,db,c,dc,c1,cc1,c2,cc2,c3,cc3,fi,ffi,gi,pz,s,sy,
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double a, da, a2, b, db, c, dc, c1, cc1, c2, cc2, c3, cc3, fi, ffi, gi, pz,
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t,t1,t2,t3,t4,t7,t8,t9,t10,w,x2,xn,xx2,y,ya,yya,z0,z,zz,z2,zz2;
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s, sy, t, t1, t2, t3, t4, t7, t8, t9, t10, w, x2, xn, xx2, y, ya, yya, z0,
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z, zz, z2, zz2;
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#ifndef DLA_FMS
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#ifndef DLA_FMS
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double t5, t6;
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double t5, t6;
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#endif
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#endif
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@ -73,8 +75,10 @@ tan(double x) {
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SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
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SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
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/* x=+-INF, x=NaN */
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/* x=+-INF, x=NaN */
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num.d = x; ux = num.i[HIGH_HALF];
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num.d = x;
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if ((ux&0x7ff00000)==0x7ff00000) {
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ux = num.i[HIGH_HALF];
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if ((ux & 0x7ff00000) == 0x7ff00000)
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{
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if ((ux & 0x7fffffff) == 0x7ff00000)
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if ((ux & 0x7fffffff) == 0x7ff00000)
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__set_errno (EDOM);
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__set_errno (EDOM);
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retval = x - x;
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retval = x - x;
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@ -84,75 +88,119 @@ tan(double x) {
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w = (x < 0.0) ? -x : x;
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w = (x < 0.0) ? -x : x;
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/* (I) The case abs(x) <= 1.259e-8 */
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/* (I) The case abs(x) <= 1.259e-8 */
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if (w<=g1.d) { retval = x; goto ret; }
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if (w <= g1.d)
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{
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retval = x;
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goto ret;
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}
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/* (II) The case 1.259e-8 < abs(x) <= 0.0608 */
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/* (II) The case 1.259e-8 < abs(x) <= 0.0608 */
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if (w<=g2.d) {
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if (w <= g2.d)
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{
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/* First stage */
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/* First stage */
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x2 = x * x;
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x2 = x * x;
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t2 = x*x2*(d3.d+x2*(d5.d+x2*(d7.d+x2*(d9.d+x2*d11.d))));
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if ((y=x+(t2-u1.d*t2)) == x+(t2+u1.d*t2)) { retval = y; goto ret; }
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t2 = d9.d + x2 * d11.d;
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t2 = d7.d + x2 * t2;
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t2 = d5.d + x2 * t2;
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t2 = d3.d + x2 * t2;
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t2 *= x * x2;
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if ((y = x + (t2 - u1.d * t2)) == x + (t2 + u1.d * t2))
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{
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retval = y;
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goto ret;
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}
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/* Second stage */
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/* Second stage */
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c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
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c1 = a25.d + x2 * a27.d;
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x2*a27.d))))));
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c1 = a23.d + x2 * c1;
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EMULV(x,x,x2,xx2,t1,t2,t3,t4,t5)
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c1 = a21.d + x2 * c1;
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ADD2(a13.d,aa13.d,c1,0.0,c2,cc2,t1,t2)
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c1 = a19.d + x2 * c1;
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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c1 = a17.d + x2 * c1;
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ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
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c1 = a15.d + x2 * c1;
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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c1 *= x2;
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ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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EMULV (x, x, x2, xx2, t1, t2, t3, t4, t5);
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ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
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ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2);
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
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ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2);
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
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ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2);
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MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
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MUL2(x ,0.0,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
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ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2);
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ADD2(x ,0.0,c2,cc2,c1,cc1,t1,t2)
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
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if ((y=c1+(cc1-u2.d*c1)) == c1+(cc1+u2.d*c1)) { retval = y; goto ret; }
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ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2);
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
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MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
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MUL2 (x, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (x, 0.0, c2, cc2, c1, cc1, t1, t2);
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if ((y = c1 + (cc1 - u2.d * c1)) == c1 + (cc1 + u2.d * c1))
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{
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retval = y;
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goto ret;
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}
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retval = tanMp (x);
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retval = tanMp (x);
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goto ret;
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goto ret;
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}
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}
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/* (III) The case 0.0608 < abs(x) <= 0.787 */
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/* (III) The case 0.0608 < abs(x) <= 0.787 */
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if (w<=g3.d) {
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if (w <= g3.d)
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{
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/* First stage */
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/* First stage */
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i = ((int) (mfftnhf.d + TWO8 * w));
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i = ((int) (mfftnhf.d + TWO8 * w));
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z = w-xfg[i][0].d; z2 = z*z; s = (x<0.0) ? MONE : ONE;
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z = w - xfg[i][0].d;
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z2 = z * z;
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s = (x < 0.0) ? MONE : ONE;
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pz = z + z * z2 * (e0.d + z2 * e1.d);
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pz = z + z * z2 * (e0.d + z2 * e1.d);
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fi = xfg[i][1].d; gi = xfg[i][2].d; t2 = pz*(gi+fi)/(gi-pz);
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fi = xfg[i][1].d;
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if ((y=fi+(t2-fi*u3.d))==fi+(t2+fi*u3.d)) { retval = (s*y); goto ret; }
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gi = xfg[i][2].d;
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t2 = pz * (gi + fi) / (gi - pz);
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if ((y = fi + (t2 - fi * u3.d)) == fi + (t2 + fi * u3.d))
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{
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retval = (s * y);
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goto ret;
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}
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t3 = (t2 < 0.0) ? -t2 : t2;
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t3 = (t2 < 0.0) ? -t2 : t2;
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t4 = fi * ua3.d + t3 * ub3.d;
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t4 = fi * ua3.d + t3 * ub3.d;
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if ((y=fi+(t2-t4))==fi+(t2+t4)) { retval = (s*y); goto ret; }
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if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
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{
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retval = (s * y);
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goto ret;
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}
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/* Second stage */
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/* Second stage */
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ffi = xfg[i][3].d;
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ffi = xfg[i][3].d;
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c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
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c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
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EMULV(z,z,z2,zz2,t1,t2,t3,t4,t5)
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EMULV (z, z, z2, zz2, t1, t2, t3, t4, t5);
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ADD2(a5.d,aa5.d,c1,0.0,c2,cc2,t1,t2)
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ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2);
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MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2(a3.d,aa3.d,c1,cc1,c2,cc2,t1,t2)
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ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
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MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
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MUL2(z ,0.0,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2 (z, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2(z ,0.0,c2,cc2,c1,cc1,t1,t2)
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ADD2 (z, 0.0, c2, cc2, c1, cc1, t1, t2);
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ADD2(fi ,ffi,c1,cc1,c2,cc2,t1,t2)
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ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2);
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MUL2(fi ,ffi,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8)
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MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8);
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SUB2(1.0,0.0,c3,cc3,c1,cc1,t1,t2)
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SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2);
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DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
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DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9,
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t10);
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if ((y=c3+(cc3-u4.d*c3))==c3+(cc3+u4.d*c3)) { retval = (s*y); goto ret; }
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if ((y = c3 + (cc3 - u4.d * c3)) == c3 + (cc3 + u4.d * c3))
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{
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retval = (s * y);
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goto ret;
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}
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retval = tanMp (x);
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retval = tanMp (x);
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goto ret;
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goto ret;
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}
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}
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/* (---) The case 0.787 < abs(x) <= 25 */
|
/* (---) The case 0.787 < abs(x) <= 25 */
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if (w<=g4.d) {
|
if (w <= g4.d)
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{
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/* Range reduction by algorithm i */
|
/* Range reduction by algorithm i */
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t = (x * hpinv.d + toint.d);
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t = (x * hpinv.d + toint.d);
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xn = t - toint.d;
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xn = t - toint.d;
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|
|
@ -162,24 +210,57 @@ tan(double x) {
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da = xn * mp3.d;
|
da = xn * mp3.d;
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a = t1 - da;
|
a = t1 - da;
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da = (t1 - a) - da;
|
da = (t1 - a) - da;
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if (a<0.0) {ya=-a; yya=-da; sy=MONE;}
|
if (a < 0.0)
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else {ya= a; yya= da; sy= ONE;}
|
{
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|
ya = -a;
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|
yya = -da;
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|
sy = MONE;
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|
}
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|
else
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|
{
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|
ya = a;
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|
yya = da;
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|
sy = ONE;
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|
}
|
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|
|
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/* (IV),(V) The case 0.787 < abs(x) <= 25, abs(y) <= 1e-7 */
|
/* (IV),(V) The case 0.787 < abs(x) <= 25, abs(y) <= 1e-7 */
|
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if (ya<=gy1.d) { retval = tanMp(x); goto ret; }
|
if (ya <= gy1.d)
|
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|
{
|
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|
retval = tanMp (x);
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|
goto ret;
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|
}
|
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|
|
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/* (VI) The case 0.787 < abs(x) <= 25, 1e-7 < abs(y) <= 0.0608 */
|
/* (VI) The case 0.787 < abs(x) <= 25, 1e-7 < abs(y) <= 0.0608 */
|
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if (ya<=gy2.d) {
|
if (ya <= gy2.d)
|
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|
{
|
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a2 = a * a;
|
a2 = a * a;
|
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t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d))));
|
t2 = d9.d + a2 * d11.d;
|
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if (n) {
|
t2 = d7.d + a2 * t2;
|
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|
t2 = d5.d + a2 * t2;
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|
t2 = d3.d + a2 * t2;
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|
t2 = da + a * a2 * t2;
|
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|
|
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|
if (n)
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|
{
|
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/* First stage -cot */
|
/* First stage -cot */
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EADD(a,t2,b,db)
|
EADD (a, t2, b, db);
|
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DIV2(1.0,0.0,b,db,c,dc,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
|
DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8,
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if ((y=c+(dc-u6.d*c))==c+(dc+u6.d*c)) { retval = (-y); goto ret; } }
|
t9, t10);
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else {
|
if ((y = c + (dc - u6.d * c)) == c + (dc + u6.d * c))
|
||||||
|
{
|
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|
retval = (-y);
|
||||||
|
goto ret;
|
||||||
|
}
|
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|
}
|
||||||
|
else
|
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|
{
|
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/* First stage tan */
|
/* First stage tan */
|
||||||
if ((y=a+(t2-u5.d*a))==a+(t2+u5.d*a)) { retval = y; goto ret; } }
|
if ((y = a + (t2 - u5.d * a)) == a + (t2 + u5.d * a))
|
||||||
|
{
|
||||||
|
retval = y;
|
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|
goto ret;
|
||||||
|
}
|
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|
}
|
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/* Second stage */
|
/* Second stage */
|
||||||
/* Range reduction by algorithm ii */
|
/* Range reduction by algorithm ii */
|
||||||
t = (x * hpinv.d + toint.d);
|
t = (x * hpinv.d + toint.d);
|
||||||
|
|
@ -195,32 +276,54 @@ tan(double x) {
|
||||||
da = ((t - a) - t1) + da;
|
da = ((t - a) - t1) + da;
|
||||||
|
|
||||||
/* Second stage */
|
/* Second stage */
|
||||||
EADD(a,da,t1,t2) a=t1; da=t2;
|
EADD (a, da, t1, t2);
|
||||||
MUL2(a,da,a,da,x2,xx2,t1,t2,t3,t4,t5,t6,t7,t8)
|
a = t1;
|
||||||
c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
|
da = t2;
|
||||||
x2*a27.d))))));
|
MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
ADD2(a13.d,aa13.d,c1,0.0,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
MUL2(a ,da ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a ,da ,c2,cc2,c1,cc1,t1,t2)
|
|
||||||
|
|
||||||
if (n) {
|
c1 = a25.d + x2 * a27.d;
|
||||||
|
c1 = a23.d + x2 * c1;
|
||||||
|
c1 = a21.d + x2 * c1;
|
||||||
|
c1 = a19.d + x2 * c1;
|
||||||
|
c1 = a17.d + x2 * c1;
|
||||||
|
c1 = a15.d + x2 * c1;
|
||||||
|
c1 *= x2;
|
||||||
|
|
||||||
|
ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a, da, c2, cc2, c1, cc1, t1, t2);
|
||||||
|
|
||||||
|
if (n)
|
||||||
|
{
|
||||||
/* Second stage -cot */
|
/* Second stage -cot */
|
||||||
DIV2(1.0,0.0,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
|
DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7,
|
||||||
if ((y=c2+(cc2-u8.d*c2)) == c2+(cc2+u8.d*c2)) { retval = (-y); goto ret; } }
|
t8, t9, t10);
|
||||||
else {
|
if ((y = c2 + (cc2 - u8.d * c2)) == c2 + (cc2 + u8.d * c2))
|
||||||
|
{
|
||||||
|
retval = (-y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
/* Second stage tan */
|
/* Second stage tan */
|
||||||
if ((y=c1+(cc1-u7.d*c1)) == c1+(cc1+u7.d*c1)) { retval = y; goto ret; } }
|
if ((y = c1 + (cc1 - u7.d * c1)) == c1 + (cc1 + u7.d * c1))
|
||||||
|
{
|
||||||
|
retval = y;
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
retval = tanMp (x);
|
retval = tanMp (x);
|
||||||
goto ret;
|
goto ret;
|
||||||
}
|
}
|
||||||
|
|
@ -229,56 +332,93 @@ tan(double x) {
|
||||||
|
|
||||||
/* First stage */
|
/* First stage */
|
||||||
i = ((int) (mfftnhf.d + TWO8 * ya));
|
i = ((int) (mfftnhf.d + TWO8 * ya));
|
||||||
z = (z0=(ya-xfg[i][0].d))+yya; z2 = z*z;
|
z = (z0 = (ya - xfg[i][0].d)) + yya;
|
||||||
|
z2 = z * z;
|
||||||
pz = z + z * z2 * (e0.d + z2 * e1.d);
|
pz = z + z * z2 * (e0.d + z2 * e1.d);
|
||||||
fi = xfg[i][1].d; gi = xfg[i][2].d;
|
fi = xfg[i][1].d;
|
||||||
|
gi = xfg[i][2].d;
|
||||||
|
|
||||||
if (n) {
|
if (n)
|
||||||
|
{
|
||||||
/* -cot */
|
/* -cot */
|
||||||
t2 = pz * (fi + gi) / (fi + pz);
|
t2 = pz * (fi + gi) / (fi + pz);
|
||||||
if ((y=gi-(t2-gi*u10.d))==gi-(t2+gi*u10.d)) { retval = (-sy*y); goto ret; }
|
if ((y = gi - (t2 - gi * u10.d)) == gi - (t2 + gi * u10.d))
|
||||||
|
{
|
||||||
|
retval = (-sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
t3 = (t2 < 0.0) ? -t2 : t2;
|
t3 = (t2 < 0.0) ? -t2 : t2;
|
||||||
t4 = gi * ua10.d + t3 * ub10.d;
|
t4 = gi * ua10.d + t3 * ub10.d;
|
||||||
if ((y=gi-(t2-t4))==gi-(t2+t4)) { retval = (-sy*y); goto ret; } }
|
if ((y = gi - (t2 - t4)) == gi - (t2 + t4))
|
||||||
else {
|
{
|
||||||
|
retval = (-sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
/* tan */
|
/* tan */
|
||||||
t2 = pz * (gi + fi) / (gi - pz);
|
t2 = pz * (gi + fi) / (gi - pz);
|
||||||
if ((y=fi+(t2-fi*u9.d))==fi+(t2+fi*u9.d)) { retval = (sy*y); goto ret; }
|
if ((y = fi + (t2 - fi * u9.d)) == fi + (t2 + fi * u9.d))
|
||||||
|
{
|
||||||
|
retval = (sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
t3 = (t2 < 0.0) ? -t2 : t2;
|
t3 = (t2 < 0.0) ? -t2 : t2;
|
||||||
t4 = fi * ua9.d + t3 * ub9.d;
|
t4 = fi * ua9.d + t3 * ub9.d;
|
||||||
if ((y=fi+(t2-t4))==fi+(t2+t4)) { retval = (sy*y); goto ret; } }
|
if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
|
||||||
|
{
|
||||||
|
retval = (sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
/* Second stage */
|
/* Second stage */
|
||||||
ffi = xfg[i][3].d;
|
ffi = xfg[i][3].d;
|
||||||
EADD (z0, yya, z, zz)
|
EADD (z0, yya, z, zz)
|
||||||
MUL2(z,zz,z,zz,z2,zz2,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
|
c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
|
||||||
ADD2(a5.d,aa5.d,c1,0.0,c2,cc2,t1,t2)
|
ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2);
|
||||||
MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
ADD2(a3.d,aa3.d,c1,cc1,c2,cc2,t1,t2)
|
ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
MUL2(z ,zz ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
ADD2(z ,zz ,c2,cc2,c1,cc1,t1,t2)
|
ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2);
|
||||||
|
|
||||||
ADD2(fi ,ffi,c1,cc1,c2,cc2,t1,t2)
|
ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2);
|
||||||
MUL2(fi ,ffi,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
SUB2(1.0,0.0,c3,cc3,c1,cc1,t1,t2)
|
SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2);
|
||||||
|
|
||||||
if (n) {
|
if (n)
|
||||||
|
{
|
||||||
/* -cot */
|
/* -cot */
|
||||||
DIV2(c1,cc1,c2,cc2,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
|
DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9,
|
||||||
if ((y=c3+(cc3-u12.d*c3))==c3+(cc3+u12.d*c3)) { retval = (-sy*y); goto ret; } }
|
t10);
|
||||||
else {
|
if ((y = c3 + (cc3 - u12.d * c3)) == c3 + (cc3 + u12.d * c3))
|
||||||
|
{
|
||||||
|
retval = (-sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
/* tan */
|
/* tan */
|
||||||
DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
|
DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9,
|
||||||
if ((y=c3+(cc3-u11.d*c3))==c3+(cc3+u11.d*c3)) { retval = (sy*y); goto ret; } }
|
t10);
|
||||||
|
if ((y = c3 + (cc3 - u11.d * c3)) == c3 + (cc3 + u11.d * c3))
|
||||||
|
{
|
||||||
|
retval = (sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
retval = tanMp (x);
|
retval = tanMp (x);
|
||||||
goto ret;
|
goto ret;
|
||||||
}
|
}
|
||||||
|
|
||||||
/* (---) The case 25 < abs(x) <= 1e8 */
|
/* (---) The case 25 < abs(x) <= 1e8 */
|
||||||
if (w<=g5.d) {
|
if (w <= g5.d)
|
||||||
|
{
|
||||||
/* Range reduction by algorithm ii */
|
/* Range reduction by algorithm ii */
|
||||||
t = (x * hpinv.d + toint.d);
|
t = (x * hpinv.d + toint.d);
|
||||||
xn = t - toint.d;
|
xn = t - toint.d;
|
||||||
|
|
@ -291,52 +431,106 @@ tan(double x) {
|
||||||
t1 = xn * pp4.d;
|
t1 = xn * pp4.d;
|
||||||
a = t - t1;
|
a = t - t1;
|
||||||
da = ((t - a) - t1) + da;
|
da = ((t - a) - t1) + da;
|
||||||
EADD(a,da,t1,t2) a=t1; da=t2;
|
EADD (a, da, t1, t2);
|
||||||
if (a<0.0) {ya=-a; yya=-da; sy=MONE;}
|
a = t1;
|
||||||
else {ya= a; yya= da; sy= ONE;}
|
da = t2;
|
||||||
|
if (a < 0.0)
|
||||||
|
{
|
||||||
|
ya = -a;
|
||||||
|
yya = -da;
|
||||||
|
sy = MONE;
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
ya = a;
|
||||||
|
yya = da;
|
||||||
|
sy = ONE;
|
||||||
|
}
|
||||||
|
|
||||||
/* (+++) The case 25 < abs(x) <= 1e8, abs(y) <= 1e-7 */
|
/* (+++) The case 25 < abs(x) <= 1e8, abs(y) <= 1e-7 */
|
||||||
if (ya<=gy1.d) { retval = tanMp(x); goto ret; }
|
if (ya <= gy1.d)
|
||||||
|
{
|
||||||
|
retval = tanMp (x);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
|
||||||
/* (VIII) The case 25 < abs(x) <= 1e8, 1e-7 < abs(y) <= 0.0608 */
|
/* (VIII) The case 25 < abs(x) <= 1e8, 1e-7 < abs(y) <= 0.0608 */
|
||||||
if (ya<=gy2.d) {
|
if (ya <= gy2.d)
|
||||||
|
{
|
||||||
a2 = a * a;
|
a2 = a * a;
|
||||||
t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d))));
|
t2 = d9.d + a2 * d11.d;
|
||||||
if (n) {
|
t2 = d7.d + a2 * t2;
|
||||||
|
t2 = d5.d + a2 * t2;
|
||||||
|
t2 = d3.d + a2 * t2;
|
||||||
|
t2 = da + a * a2 * t2;
|
||||||
|
|
||||||
|
if (n)
|
||||||
|
{
|
||||||
/* First stage -cot */
|
/* First stage -cot */
|
||||||
EADD(a,t2,b,db)
|
EADD (a, t2, b, db);
|
||||||
DIV2(1.0,0.0,b,db,c,dc,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
|
DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8,
|
||||||
if ((y=c+(dc-u14.d*c))==c+(dc+u14.d*c)) { retval = (-y); goto ret; } }
|
t9, t10);
|
||||||
else {
|
if ((y = c + (dc - u14.d * c)) == c + (dc + u14.d * c))
|
||||||
|
{
|
||||||
|
retval = (-y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
/* First stage tan */
|
/* First stage tan */
|
||||||
if ((y=a+(t2-u13.d*a))==a+(t2+u13.d*a)) { retval = y; goto ret; } }
|
if ((y = a + (t2 - u13.d * a)) == a + (t2 + u13.d * a))
|
||||||
|
{
|
||||||
|
retval = y;
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
/* Second stage */
|
/* Second stage */
|
||||||
MUL2(a,da,a,da,x2,xx2,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
|
c1 = a25.d + x2 * a27.d;
|
||||||
x2*a27.d))))));
|
c1 = a23.d + x2 * c1;
|
||||||
ADD2(a13.d,aa13.d,c1,0.0,c2,cc2,t1,t2)
|
c1 = a21.d + x2 * c1;
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
c1 = a19.d + x2 * c1;
|
||||||
ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
|
c1 = a17.d + x2 * c1;
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
c1 = a15.d + x2 * c1;
|
||||||
ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
|
c1 *= x2;
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
MUL2(a ,da ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a ,da ,c2,cc2,c1,cc1,t1,t2)
|
|
||||||
|
|
||||||
if (n) {
|
ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a, da, c2, cc2, c1, cc1, t1, t2);
|
||||||
|
|
||||||
|
if (n)
|
||||||
|
{
|
||||||
/* Second stage -cot */
|
/* Second stage -cot */
|
||||||
DIV2(1.0,0.0,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
|
DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7,
|
||||||
if ((y=c2+(cc2-u16.d*c2)) == c2+(cc2+u16.d*c2)) { retval = (-y); goto ret; } }
|
t8, t9, t10);
|
||||||
else {
|
if ((y = c2 + (cc2 - u16.d * c2)) == c2 + (cc2 + u16.d * c2))
|
||||||
|
{
|
||||||
|
retval = (-y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
/* Second stage tan */
|
/* Second stage tan */
|
||||||
if ((y=c1+(cc1-u15.d*c1)) == c1+(cc1+u15.d*c1)) { retval = (y); goto ret; } }
|
if ((y = c1 + (cc1 - u15.d * c1)) == c1 + (cc1 + u15.d * c1))
|
||||||
|
{
|
||||||
|
retval = (y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
retval = tanMp (x);
|
retval = tanMp (x);
|
||||||
goto ret;
|
goto ret;
|
||||||
}
|
}
|
||||||
|
|
@ -344,49 +538,85 @@ tan(double x) {
|
||||||
/* (IX) The case 25 < abs(x) <= 1e8, 0.0608 < abs(y) <= 0.787 */
|
/* (IX) The case 25 < abs(x) <= 1e8, 0.0608 < abs(y) <= 0.787 */
|
||||||
/* First stage */
|
/* First stage */
|
||||||
i = ((int) (mfftnhf.d + TWO8 * ya));
|
i = ((int) (mfftnhf.d + TWO8 * ya));
|
||||||
z = (z0=(ya-xfg[i][0].d))+yya; z2 = z*z;
|
z = (z0 = (ya - xfg[i][0].d)) + yya;
|
||||||
|
z2 = z * z;
|
||||||
pz = z + z * z2 * (e0.d + z2 * e1.d);
|
pz = z + z * z2 * (e0.d + z2 * e1.d);
|
||||||
fi = xfg[i][1].d; gi = xfg[i][2].d;
|
fi = xfg[i][1].d;
|
||||||
|
gi = xfg[i][2].d;
|
||||||
|
|
||||||
if (n) {
|
if (n)
|
||||||
|
{
|
||||||
/* -cot */
|
/* -cot */
|
||||||
t2 = pz * (fi + gi) / (fi + pz);
|
t2 = pz * (fi + gi) / (fi + pz);
|
||||||
if ((y=gi-(t2-gi*u18.d))==gi-(t2+gi*u18.d)) { retval = (-sy*y); goto ret; }
|
if ((y = gi - (t2 - gi * u18.d)) == gi - (t2 + gi * u18.d))
|
||||||
|
{
|
||||||
|
retval = (-sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
t3 = (t2 < 0.0) ? -t2 : t2;
|
t3 = (t2 < 0.0) ? -t2 : t2;
|
||||||
t4 = gi * ua18.d + t3 * ub18.d;
|
t4 = gi * ua18.d + t3 * ub18.d;
|
||||||
if ((y=gi-(t2-t4))==gi-(t2+t4)) { retval = (-sy*y); goto ret; } }
|
if ((y = gi - (t2 - t4)) == gi - (t2 + t4))
|
||||||
else {
|
{
|
||||||
|
retval = (-sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
/* tan */
|
/* tan */
|
||||||
t2 = pz * (gi + fi) / (gi - pz);
|
t2 = pz * (gi + fi) / (gi - pz);
|
||||||
if ((y=fi+(t2-fi*u17.d))==fi+(t2+fi*u17.d)) { retval = (sy*y); goto ret; }
|
if ((y = fi + (t2 - fi * u17.d)) == fi + (t2 + fi * u17.d))
|
||||||
|
{
|
||||||
|
retval = (sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
t3 = (t2 < 0.0) ? -t2 : t2;
|
t3 = (t2 < 0.0) ? -t2 : t2;
|
||||||
t4 = fi * ua17.d + t3 * ub17.d;
|
t4 = fi * ua17.d + t3 * ub17.d;
|
||||||
if ((y=fi+(t2-t4))==fi+(t2+t4)) { retval = (sy*y); goto ret; } }
|
if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
|
||||||
|
{
|
||||||
|
retval = (sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
/* Second stage */
|
/* Second stage */
|
||||||
ffi = xfg[i][3].d;
|
ffi = xfg[i][3].d;
|
||||||
EADD(z0,yya,z,zz)
|
EADD (z0, yya, z, zz);
|
||||||
MUL2(z,zz,z,zz,z2,zz2,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
|
c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
|
||||||
ADD2(a5.d,aa5.d,c1,0.0,c2,cc2,t1,t2)
|
ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2);
|
||||||
MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
ADD2(a3.d,aa3.d,c1,cc1,c2,cc2,t1,t2)
|
ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
MUL2(z ,zz ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
ADD2(z ,zz ,c2,cc2,c1,cc1,t1,t2)
|
ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2);
|
||||||
|
|
||||||
ADD2(fi ,ffi,c1,cc1,c2,cc2,t1,t2)
|
ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2);
|
||||||
MUL2(fi ,ffi,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
SUB2(1.0,0.0,c3,cc3,c1,cc1,t1,t2)
|
SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2);
|
||||||
|
|
||||||
if (n) {
|
if (n)
|
||||||
|
{
|
||||||
/* -cot */
|
/* -cot */
|
||||||
DIV2(c1,cc1,c2,cc2,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
|
DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9,
|
||||||
if ((y=c3+(cc3-u20.d*c3))==c3+(cc3+u20.d*c3)) { retval = (-sy*y); goto ret; } }
|
t10);
|
||||||
else {
|
if ((y = c3 + (cc3 - u20.d * c3)) == c3 + (cc3 + u20.d * c3))
|
||||||
|
{
|
||||||
|
retval = (-sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
/* tan */
|
/* tan */
|
||||||
DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
|
DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9,
|
||||||
if ((y=c3+(cc3-u19.d*c3))==c3+(cc3+u19.d*c3)) { retval = (sy*y); goto ret; } }
|
t10);
|
||||||
|
if ((y = c3 + (cc3 - u19.d * c3)) == c3 + (cc3 + u19.d * c3))
|
||||||
|
{
|
||||||
|
retval = (sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
retval = tanMp (x);
|
retval = tanMp (x);
|
||||||
goto ret;
|
goto ret;
|
||||||
}
|
}
|
||||||
|
|
@ -394,57 +624,114 @@ tan(double x) {
|
||||||
/* (---) The case 1e8 < abs(x) < 2**1024 */
|
/* (---) The case 1e8 < abs(x) < 2**1024 */
|
||||||
/* Range reduction by algorithm iii */
|
/* Range reduction by algorithm iii */
|
||||||
n = (__branred (x, &a, &da)) & 0x00000001;
|
n = (__branred (x, &a, &da)) & 0x00000001;
|
||||||
EADD(a,da,t1,t2) a=t1; da=t2;
|
EADD (a, da, t1, t2);
|
||||||
if (a<0.0) {ya=-a; yya=-da; sy=MONE;}
|
a = t1;
|
||||||
else {ya= a; yya= da; sy= ONE;}
|
da = t2;
|
||||||
|
if (a < 0.0)
|
||||||
|
{
|
||||||
|
ya = -a;
|
||||||
|
yya = -da;
|
||||||
|
sy = MONE;
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
ya = a;
|
||||||
|
yya = da;
|
||||||
|
sy = ONE;
|
||||||
|
}
|
||||||
|
|
||||||
/* (+++) The case 1e8 < abs(x) < 2**1024, abs(y) <= 1e-7 */
|
/* (+++) The case 1e8 < abs(x) < 2**1024, abs(y) <= 1e-7 */
|
||||||
if (ya<=gy1.d) { retval = tanMp(x); goto ret; }
|
if (ya <= gy1.d)
|
||||||
|
{
|
||||||
|
retval = tanMp (x);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
|
||||||
/* (X) The case 1e8 < abs(x) < 2**1024, 1e-7 < abs(y) <= 0.0608 */
|
/* (X) The case 1e8 < abs(x) < 2**1024, 1e-7 < abs(y) <= 0.0608 */
|
||||||
if (ya<=gy2.d) {
|
if (ya <= gy2.d)
|
||||||
|
{
|
||||||
a2 = a * a;
|
a2 = a * a;
|
||||||
t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d))));
|
t2 = d9.d + a2 * d11.d;
|
||||||
if (n) {
|
t2 = d7.d + a2 * t2;
|
||||||
|
t2 = d5.d + a2 * t2;
|
||||||
|
t2 = d3.d + a2 * t2;
|
||||||
|
t2 = da + a * a2 * t2;
|
||||||
|
if (n)
|
||||||
|
{
|
||||||
/* First stage -cot */
|
/* First stage -cot */
|
||||||
EADD(a,t2,b,db)
|
EADD (a, t2, b, db);
|
||||||
DIV2(1.0,0.0,b,db,c,dc,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
|
DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4, t5, t6, t7, t8, t9,
|
||||||
if ((y=c+(dc-u22.d*c))==c+(dc+u22.d*c)) { retval = (-y); goto ret; } }
|
t10);
|
||||||
else {
|
if ((y = c + (dc - u22.d * c)) == c + (dc + u22.d * c))
|
||||||
|
{
|
||||||
|
retval = (-y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
/* First stage tan */
|
/* First stage tan */
|
||||||
if ((y=a+(t2-u21.d*a))==a+(t2+u21.d*a)) { retval = y; goto ret; } }
|
if ((y = a + (t2 - u21.d * a)) == a + (t2 + u21.d * a))
|
||||||
|
{
|
||||||
|
retval = y;
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
/* Second stage */
|
/* Second stage */
|
||||||
/* Reduction by algorithm iv */
|
/* Reduction by algorithm iv */
|
||||||
p=10; n = (__mpranred(x,&mpa,p)) & 0x00000001;
|
p = 10;
|
||||||
__mp_dbl(&mpa,&a,p); __dbl_mp(a,&mpt1,p);
|
n = (__mpranred (x, &mpa, p)) & 0x00000001;
|
||||||
__sub(&mpa,&mpt1,&mpt2,p); __mp_dbl(&mpt2,&da,p);
|
__mp_dbl (&mpa, &a, p);
|
||||||
|
__dbl_mp (a, &mpt1, p);
|
||||||
|
__sub (&mpa, &mpt1, &mpt2, p);
|
||||||
|
__mp_dbl (&mpt2, &da, p);
|
||||||
|
|
||||||
MUL2(a,da,a,da,x2,xx2,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
|
|
||||||
x2*a27.d))))));
|
|
||||||
ADD2(a13.d,aa13.d,c1,0.0,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
|
|
||||||
MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
MUL2(a ,da ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
|
|
||||||
ADD2(a ,da ,c2,cc2,c1,cc1,t1,t2)
|
|
||||||
|
|
||||||
if (n) {
|
c1 = a25.d + x2 * a27.d;
|
||||||
|
c1 = a23.d + x2 * c1;
|
||||||
|
c1 = a21.d + x2 * c1;
|
||||||
|
c1 = a19.d + x2 * c1;
|
||||||
|
c1 = a17.d + x2 * c1;
|
||||||
|
c1 = a15.d + x2 * c1;
|
||||||
|
c1 *= x2;
|
||||||
|
|
||||||
|
ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
|
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
MUL2 (a, da, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
|
ADD2 (a, da, c2, cc2, c1, cc1, t1, t2);
|
||||||
|
|
||||||
|
if (n)
|
||||||
|
{
|
||||||
/* Second stage -cot */
|
/* Second stage -cot */
|
||||||
DIV2(1.0,0.0,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
|
DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8,
|
||||||
if ((y=c2+(cc2-u24.d*c2)) == c2+(cc2+u24.d*c2)) { retval = (-y); goto ret; } }
|
t9, t10);
|
||||||
else {
|
if ((y = c2 + (cc2 - u24.d * c2)) == c2 + (cc2 + u24.d * c2))
|
||||||
|
{
|
||||||
|
retval = (-y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
/* Second stage tan */
|
/* Second stage tan */
|
||||||
if ((y=c1+(cc1-u23.d*c1)) == c1+(cc1+u23.d*c1)) { retval = y; goto ret; } }
|
if ((y = c1 + (cc1 - u23.d * c1)) == c1 + (cc1 + u23.d * c1))
|
||||||
|
{
|
||||||
|
retval = y;
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
retval = tanMp (x);
|
retval = tanMp (x);
|
||||||
goto ret;
|
goto ret;
|
||||||
}
|
}
|
||||||
|
|
@ -452,49 +739,85 @@ tan(double x) {
|
||||||
/* (XI) The case 1e8 < abs(x) < 2**1024, 0.0608 < abs(y) <= 0.787 */
|
/* (XI) The case 1e8 < abs(x) < 2**1024, 0.0608 < abs(y) <= 0.787 */
|
||||||
/* First stage */
|
/* First stage */
|
||||||
i = ((int) (mfftnhf.d + TWO8 * ya));
|
i = ((int) (mfftnhf.d + TWO8 * ya));
|
||||||
z = (z0=(ya-xfg[i][0].d))+yya; z2 = z*z;
|
z = (z0 = (ya - xfg[i][0].d)) + yya;
|
||||||
|
z2 = z * z;
|
||||||
pz = z + z * z2 * (e0.d + z2 * e1.d);
|
pz = z + z * z2 * (e0.d + z2 * e1.d);
|
||||||
fi = xfg[i][1].d; gi = xfg[i][2].d;
|
fi = xfg[i][1].d;
|
||||||
|
gi = xfg[i][2].d;
|
||||||
|
|
||||||
if (n) {
|
if (n)
|
||||||
|
{
|
||||||
/* -cot */
|
/* -cot */
|
||||||
t2 = pz * (fi + gi) / (fi + pz);
|
t2 = pz * (fi + gi) / (fi + pz);
|
||||||
if ((y=gi-(t2-gi*u26.d))==gi-(t2+gi*u26.d)) { retval = (-sy*y); goto ret; }
|
if ((y = gi - (t2 - gi * u26.d)) == gi - (t2 + gi * u26.d))
|
||||||
|
{
|
||||||
|
retval = (-sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
t3 = (t2 < 0.0) ? -t2 : t2;
|
t3 = (t2 < 0.0) ? -t2 : t2;
|
||||||
t4 = gi * ua26.d + t3 * ub26.d;
|
t4 = gi * ua26.d + t3 * ub26.d;
|
||||||
if ((y=gi-(t2-t4))==gi-(t2+t4)) { retval = (-sy*y); goto ret; } }
|
if ((y = gi - (t2 - t4)) == gi - (t2 + t4))
|
||||||
else {
|
{
|
||||||
|
retval = (-sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
/* tan */
|
/* tan */
|
||||||
t2 = pz * (gi + fi) / (gi - pz);
|
t2 = pz * (gi + fi) / (gi - pz);
|
||||||
if ((y=fi+(t2-fi*u25.d))==fi+(t2+fi*u25.d)) { retval = (sy*y); goto ret; }
|
if ((y = fi + (t2 - fi * u25.d)) == fi + (t2 + fi * u25.d))
|
||||||
|
{
|
||||||
|
retval = (sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
t3 = (t2 < 0.0) ? -t2 : t2;
|
t3 = (t2 < 0.0) ? -t2 : t2;
|
||||||
t4 = fi * ua25.d + t3 * ub25.d;
|
t4 = fi * ua25.d + t3 * ub25.d;
|
||||||
if ((y=fi+(t2-t4))==fi+(t2+t4)) { retval = (sy*y); goto ret; } }
|
if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
|
||||||
|
{
|
||||||
|
retval = (sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
/* Second stage */
|
/* Second stage */
|
||||||
ffi = xfg[i][3].d;
|
ffi = xfg[i][3].d;
|
||||||
EADD(z0,yya,z,zz)
|
EADD (z0, yya, z, zz);
|
||||||
MUL2(z,zz,z,zz,z2,zz2,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (z, zz, z, zz, z2, zz2, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
|
c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
|
||||||
ADD2(a5.d,aa5.d,c1,0.0,c2,cc2,t1,t2)
|
ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2);
|
||||||
MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
ADD2(a3.d,aa3.d,c1,cc1,c2,cc2,t1,t2)
|
ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
|
||||||
MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
MUL2(z ,zz ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
ADD2(z ,zz ,c2,cc2,c1,cc1,t1,t2)
|
ADD2 (z, zz, c2, cc2, c1, cc1, t1, t2);
|
||||||
|
|
||||||
ADD2(fi ,ffi,c1,cc1,c2,cc2,t1,t2)
|
ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2);
|
||||||
MUL2(fi ,ffi,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8)
|
MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8);
|
||||||
SUB2(1.0,0.0,c3,cc3,c1,cc1,t1,t2)
|
SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2);
|
||||||
|
|
||||||
if (n) {
|
if (n)
|
||||||
|
{
|
||||||
/* -cot */
|
/* -cot */
|
||||||
DIV2(c1,cc1,c2,cc2,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
|
DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9,
|
||||||
if ((y=c3+(cc3-u28.d*c3))==c3+(cc3+u28.d*c3)) { retval = (-sy*y); goto ret; } }
|
t10);
|
||||||
else {
|
if ((y = c3 + (cc3 - u28.d * c3)) == c3 + (cc3 + u28.d * c3))
|
||||||
|
{
|
||||||
|
retval = (-sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
/* tan */
|
/* tan */
|
||||||
DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
|
DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4, t5, t6, t7, t8, t9,
|
||||||
if ((y=c3+(cc3-u27.d*c3))==c3+(cc3+u27.d*c3)) { retval = (sy*y); goto ret; } }
|
t10);
|
||||||
|
if ((y = c3 + (cc3 - u27.d * c3)) == c3 + (cc3 + u27.d * c3))
|
||||||
|
{
|
||||||
|
retval = (sy * y);
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
retval = tanMp (x);
|
retval = tanMp (x);
|
||||||
goto ret;
|
goto ret;
|
||||||
|
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue