| /* |
| * IBM Accurate Mathematical Library |
| * written by International Business Machines Corp. |
| * Copyright (C) 2001, 2009 Free Software Foundation |
| * |
| * This program is free software; you can redistribute it and/or modify |
| * it under the terms of the GNU Lesser General Public License as published by |
| * the Free Software Foundation; either version 2.1 of the License, or |
| * (at your option) any later version. |
| * |
| * This program is distributed in the hope that it will be useful, |
| * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| * GNU Lesser General Public License for more details. |
| * |
| * You should have received a copy of the GNU Lesser General Public License |
| * along with this program; if not, write to the Free Software |
| * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
| */ |
| /*********************************************************************/ |
| /* MODULE_NAME: utan.c */ |
| /* */ |
| /* FUNCTIONS: utan */ |
| /* tanMp */ |
| /* */ |
| /* FILES NEEDED:dla.h endian.h mpa.h mydefs.h utan.h */ |
| /* branred.c sincos32.c mptan.c */ |
| /* utan.tbl */ |
| /* */ |
| /* An ultimate tan routine. Given an IEEE double machine number x */ |
| /* it computes the correctly rounded (to nearest) value of tan(x). */ |
| /* Assumption: Machine arithmetic operations are performed in */ |
| /* round to nearest mode of IEEE 754 standard. */ |
| /* */ |
| /*********************************************************************/ |
| |
| #include <errno.h> |
| #include "endian.h" |
| #include "dla.h" |
| #include "mpa.h" |
| #include "MathLib.h" |
| #include "math.h" |
| |
| static double tanMp(double); |
| void __mptan(double, mp_no *, int); |
| |
| double tan(double x) { |
| #include "utan.h" |
| #include "utan.tbl" |
| |
| int ux,i,n; |
| double a,da,a2,b,db,c,dc,c1,cc1,c2,cc2,c3,cc3,fi,ffi,gi,pz,s,sy, |
| t,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,w,x2,xn,xx2,y,ya,yya,z0,z,zz,z2,zz2; |
| int p; |
| number num,v; |
| mp_no mpa,mpt1,mpt2; |
| #if 0 |
| mp_no mpy; |
| #endif |
| |
| int __branred(double, double *, double *); |
| int __mpranred(double, mp_no *, int); |
| |
| /* x=+-INF, x=NaN */ |
| num.d = x; ux = num.i[HIGH_HALF]; |
| if ((ux&0x7ff00000)==0x7ff00000) { |
| if ((ux&0x7fffffff)==0x7ff00000) |
| __set_errno (EDOM); |
| return x-x; |
| } |
| |
| w=(x<ZERO) ? -x : x; |
| |
| /* (I) The case abs(x) <= 1.259e-8 */ |
| if (w<=g1.d) return x; |
| |
| /* (II) The case 1.259e-8 < abs(x) <= 0.0608 */ |
| if (w<=g2.d) { |
| |
| /* First stage */ |
| x2 = x*x; |
| t2 = x*x2*(d3.d+x2*(d5.d+x2*(d7.d+x2*(d9.d+x2*d11.d)))); |
| if ((y=x+(t2-u1.d*t2)) == x+(t2+u1.d*t2)) return y; |
| |
| /* Second stage */ |
| c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+ |
| x2*a27.d)))))); |
| EMULV(x,x,x2,xx2,t1,t2,t3,t4,t5) |
| ADD2(a13.d,aa13.d,c1,zero.d,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(x ,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8) |
| ADD2(x ,zero.d,c2,cc2,c1,cc1,t1,t2) |
| if ((y=c1+(cc1-u2.d*c1)) == c1+(cc1+u2.d*c1)) return y; |
| return tanMp(x); |
| } |
| |
| /* (III) The case 0.0608 < abs(x) <= 0.787 */ |
| if (w<=g3.d) { |
| |
| /* First stage */ |
| i = ((int) (mfftnhf.d+TWO8*w)); |
| z = w-xfg[i][0].d; z2 = z*z; s = (x<ZERO) ? MONE : ONE; |
| pz = z+z*z2*(e0.d+z2*e1.d); |
| fi = xfg[i][1].d; gi = xfg[i][2].d; t2 = pz*(gi+fi)/(gi-pz); |
| if ((y=fi+(t2-fi*u3.d))==fi+(t2+fi*u3.d)) return (s*y); |
| t3 = (t2<ZERO) ? -t2 : t2; |
| t4 = fi*ua3.d+t3*ub3.d; |
| if ((y=fi+(t2-t4))==fi+(t2+t4)) return (s*y); |
| |
| /* Second stage */ |
| ffi = xfg[i][3].d; |
| c1 = z2*(a7.d+z2*(a9.d+z2*a11.d)); |
| EMULV(z,z,z2,zz2,t1,t2,t3,t4,t5) |
| ADD2(a5.d,aa5.d,c1,zero.d,c2,cc2,t1,t2) |
| 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) |
| MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8) |
| MUL2(z ,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8) |
| ADD2(z ,zero.d,c2,cc2,c1,cc1,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) |
| SUB2(one.d,zero.d,c3,cc3,c1,cc1,t1,t2) |
| DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) |
| |
| if ((y=c3+(cc3-u4.d*c3))==c3+(cc3+u4.d*c3)) return (s*y); |
| return tanMp(x); |
| } |
| |
| /* (---) The case 0.787 < abs(x) <= 25 */ |
| if (w<=g4.d) { |
| /* Range reduction by algorithm i */ |
| t = (x*hpinv.d + toint.d); |
| xn = t - toint.d; |
| v.d = t; |
| t1 = (x - xn*mp1.d) - xn*mp2.d; |
| n =v.i[LOW_HALF] & 0x00000001; |
| da = xn*mp3.d; |
| a=t1-da; |
| da = (t1-a)-da; |
| if (a<ZERO) {ya=-a; yya=-da; sy=MONE;} |
| else {ya= a; yya= da; sy= ONE;} |
| |
| /* (IV),(V) The case 0.787 < abs(x) <= 25, abs(y) <= 1e-7 */ |
| if (ya<=gy1.d) return tanMp(x); |
| |
| /* (VI) The case 0.787 < abs(x) <= 25, 1e-7 < abs(y) <= 0.0608 */ |
| if (ya<=gy2.d) { |
| a2 = a*a; |
| t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d)))); |
| if (n) { |
| /* First stage -cot */ |
| EADD(a,t2,b,db) |
| DIV2(one.d,zero.d,b,db,c,dc,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) |
| if ((y=c+(dc-u6.d*c))==c+(dc+u6.d*c)) return (-y); } |
| else { |
| /* First stage tan */ |
| if ((y=a+(t2-u5.d*a))==a+(t2+u5.d*a)) return y; } |
| /* Second stage */ |
| /* Range reduction by algorithm ii */ |
| t = (x*hpinv.d + toint.d); |
| xn = t - toint.d; |
| v.d = t; |
| t1 = (x - xn*mp1.d) - xn*mp2.d; |
| n =v.i[LOW_HALF] & 0x00000001; |
| da = xn*pp3.d; |
| t=t1-da; |
| da = (t1-t)-da; |
| t1 = xn*pp4.d; |
| a = t - t1; |
| da = ((t-a)-t1)+da; |
| |
| /* Second stage */ |
| EADD(a,da,t1,t2) a=t1; da=t2; |
| 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,zero.d,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 */ |
| DIV2(one.d,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) |
| if ((y=c2+(cc2-u8.d*c2)) == c2+(cc2+u8.d*c2)) return (-y); } |
| else { |
| /* Second stage tan */ |
| if ((y=c1+(cc1-u7.d*c1)) == c1+(cc1+u7.d*c1)) return y; } |
| return tanMp(x); |
| } |
| |
| /* (VII) The case 0.787 < abs(x) <= 25, 0.0608 < abs(y) <= 0.787 */ |
| |
| /* First stage */ |
| i = ((int) (mfftnhf.d+TWO8*ya)); |
| z = (z0=(ya-xfg[i][0].d))+yya; z2 = z*z; |
| pz = z+z*z2*(e0.d+z2*e1.d); |
| fi = xfg[i][1].d; gi = xfg[i][2].d; |
| |
| if (n) { |
| /* -cot */ |
| t2 = pz*(fi+gi)/(fi+pz); |
| if ((y=gi-(t2-gi*u10.d))==gi-(t2+gi*u10.d)) return (-sy*y); |
| t3 = (t2<ZERO) ? -t2 : t2; |
| t4 = gi*ua10.d+t3*ub10.d; |
| if ((y=gi-(t2-t4))==gi-(t2+t4)) return (-sy*y); } |
| else { |
| /* tan */ |
| t2 = pz*(gi+fi)/(gi-pz); |
| if ((y=fi+(t2-fi*u9.d))==fi+(t2+fi*u9.d)) return (sy*y); |
| t3 = (t2<ZERO) ? -t2 : t2; |
| t4 = fi*ua9.d+t3*ub9.d; |
| if ((y=fi+(t2-t4))==fi+(t2+t4)) return (sy*y); } |
| |
| /* Second stage */ |
| ffi = xfg[i][3].d; |
| EADD(z0,yya,z,zz) |
| 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)); |
| ADD2(a5.d,aa5.d,c1,zero.d,c2,cc2,t1,t2) |
| 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) |
| 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) |
| ADD2(z ,zz ,c2,cc2,c1,cc1,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) |
| SUB2(one.d,zero.d,c3,cc3,c1,cc1,t1,t2) |
| |
| if (n) { |
| /* -cot */ |
| DIV2(c1,cc1,c2,cc2,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) |
| if ((y=c3+(cc3-u12.d*c3))==c3+(cc3+u12.d*c3)) return (-sy*y); } |
| else { |
| /* tan */ |
| DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) |
| if ((y=c3+(cc3-u11.d*c3))==c3+(cc3+u11.d*c3)) return (sy*y); } |
| |
| return tanMp(x); |
| } |
| |
| /* (---) The case 25 < abs(x) <= 1e8 */ |
| if (w<=g5.d) { |
| /* Range reduction by algorithm ii */ |
| t = (x*hpinv.d + toint.d); |
| xn = t - toint.d; |
| v.d = t; |
| t1 = (x - xn*mp1.d) - xn*mp2.d; |
| n =v.i[LOW_HALF] & 0x00000001; |
| da = xn*pp3.d; |
| t=t1-da; |
| da = (t1-t)-da; |
| t1 = xn*pp4.d; |
| a = t - t1; |
| da = ((t-a)-t1)+da; |
| EADD(a,da,t1,t2) a=t1; da=t2; |
| if (a<ZERO) {ya=-a; yya=-da; sy=MONE;} |
| else {ya= a; yya= da; sy= ONE;} |
| |
| /* (+++) The case 25 < abs(x) <= 1e8, abs(y) <= 1e-7 */ |
| if (ya<=gy1.d) return tanMp(x); |
| |
| /* (VIII) The case 25 < abs(x) <= 1e8, 1e-7 < abs(y) <= 0.0608 */ |
| if (ya<=gy2.d) { |
| a2 = a*a; |
| t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d)))); |
| if (n) { |
| /* First stage -cot */ |
| EADD(a,t2,b,db) |
| DIV2(one.d,zero.d,b,db,c,dc,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) |
| if ((y=c+(dc-u14.d*c))==c+(dc+u14.d*c)) return (-y); } |
| else { |
| /* First stage tan */ |
| if ((y=a+(t2-u13.d*a))==a+(t2+u13.d*a)) return y; } |
| |
| /* Second stage */ |
| 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,zero.d,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 */ |
| DIV2(one.d,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) |
| if ((y=c2+(cc2-u16.d*c2)) == c2+(cc2+u16.d*c2)) return (-y); } |
| else { |
| /* Second stage tan */ |
| if ((y=c1+(cc1-u15.d*c1)) == c1+(cc1+u15.d*c1)) return (y); } |
| return tanMp(x); |
| } |
| |
| /* (IX) The case 25 < abs(x) <= 1e8, 0.0608 < abs(y) <= 0.787 */ |
| /* First stage */ |
| i = ((int) (mfftnhf.d+TWO8*ya)); |
| z = (z0=(ya-xfg[i][0].d))+yya; z2 = z*z; |
| pz = z+z*z2*(e0.d+z2*e1.d); |
| fi = xfg[i][1].d; gi = xfg[i][2].d; |
| |
| if (n) { |
| /* -cot */ |
| t2 = pz*(fi+gi)/(fi+pz); |
| if ((y=gi-(t2-gi*u18.d))==gi-(t2+gi*u18.d)) return (-sy*y); |
| t3 = (t2<ZERO) ? -t2 : t2; |
| t4 = gi*ua18.d+t3*ub18.d; |
| if ((y=gi-(t2-t4))==gi-(t2+t4)) return (-sy*y); } |
| else { |
| /* tan */ |
| t2 = pz*(gi+fi)/(gi-pz); |
| if ((y=fi+(t2-fi*u17.d))==fi+(t2+fi*u17.d)) return (sy*y); |
| t3 = (t2<ZERO) ? -t2 : t2; |
| t4 = fi*ua17.d+t3*ub17.d; |
| if ((y=fi+(t2-t4))==fi+(t2+t4)) return (sy*y); } |
| |
| /* Second stage */ |
| ffi = xfg[i][3].d; |
| EADD(z0,yya,z,zz) |
| 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)); |
| ADD2(a5.d,aa5.d,c1,zero.d,c2,cc2,t1,t2) |
| 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) |
| 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) |
| ADD2(z ,zz ,c2,cc2,c1,cc1,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) |
| SUB2(one.d,zero.d,c3,cc3,c1,cc1,t1,t2) |
| |
| if (n) { |
| /* -cot */ |
| DIV2(c1,cc1,c2,cc2,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) |
| if ((y=c3+(cc3-u20.d*c3))==c3+(cc3+u20.d*c3)) return (-sy*y); } |
| else { |
| /* tan */ |
| DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) |
| if ((y=c3+(cc3-u19.d*c3))==c3+(cc3+u19.d*c3)) return (sy*y); } |
| return tanMp(x); |
| } |
| |
| /* (---) The case 1e8 < abs(x) < 2**1024 */ |
| /* Range reduction by algorithm iii */ |
| n = (__branred(x,&a,&da)) & 0x00000001; |
| EADD(a,da,t1,t2) a=t1; da=t2; |
| if (a<ZERO) {ya=-a; yya=-da; sy=MONE;} |
| else {ya= a; yya= da; sy= ONE;} |
| |
| /* (+++) The case 1e8 < abs(x) < 2**1024, abs(y) <= 1e-7 */ |
| if (ya<=gy1.d) return tanMp(x); |
| |
| /* (X) The case 1e8 < abs(x) < 2**1024, 1e-7 < abs(y) <= 0.0608 */ |
| if (ya<=gy2.d) { |
| a2 = a*a; |
| t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d)))); |
| if (n) { |
| /* First stage -cot */ |
| EADD(a,t2,b,db) |
| DIV2(one.d,zero.d,b,db,c,dc,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) |
| if ((y=c+(dc-u22.d*c))==c+(dc+u22.d*c)) return (-y); } |
| else { |
| /* First stage tan */ |
| if ((y=a+(t2-u21.d*a))==a+(t2+u21.d*a)) return y; } |
| |
| /* Second stage */ |
| /* Reduction by algorithm iv */ |
| p=10; n = (__mpranred(x,&mpa,p)) & 0x00000001; |
| __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) |
| 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,zero.d,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 */ |
| DIV2(one.d,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) |
| if ((y=c2+(cc2-u24.d*c2)) == c2+(cc2+u24.d*c2)) return (-y); } |
| else { |
| /* Second stage tan */ |
| if ((y=c1+(cc1-u23.d*c1)) == c1+(cc1+u23.d*c1)) return y; } |
| return tanMp(x); |
| } |
| |
| /* (XI) The case 1e8 < abs(x) < 2**1024, 0.0608 < abs(y) <= 0.787 */ |
| /* First stage */ |
| i = ((int) (mfftnhf.d+TWO8*ya)); |
| z = (z0=(ya-xfg[i][0].d))+yya; z2 = z*z; |
| pz = z+z*z2*(e0.d+z2*e1.d); |
| fi = xfg[i][1].d; gi = xfg[i][2].d; |
| |
| if (n) { |
| /* -cot */ |
| t2 = pz*(fi+gi)/(fi+pz); |
| if ((y=gi-(t2-gi*u26.d))==gi-(t2+gi*u26.d)) return (-sy*y); |
| t3 = (t2<ZERO) ? -t2 : t2; |
| t4 = gi*ua26.d+t3*ub26.d; |
| if ((y=gi-(t2-t4))==gi-(t2+t4)) return (-sy*y); } |
| else { |
| /* tan */ |
| t2 = pz*(gi+fi)/(gi-pz); |
| if ((y=fi+(t2-fi*u25.d))==fi+(t2+fi*u25.d)) return (sy*y); |
| t3 = (t2<ZERO) ? -t2 : t2; |
| t4 = fi*ua25.d+t3*ub25.d; |
| if ((y=fi+(t2-t4))==fi+(t2+t4)) return (sy*y); } |
| |
| /* Second stage */ |
| ffi = xfg[i][3].d; |
| EADD(z0,yya,z,zz) |
| 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)); |
| ADD2(a5.d,aa5.d,c1,zero.d,c2,cc2,t1,t2) |
| 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) |
| 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) |
| ADD2(z ,zz ,c2,cc2,c1,cc1,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) |
| SUB2(one.d,zero.d,c3,cc3,c1,cc1,t1,t2) |
| |
| if (n) { |
| /* -cot */ |
| DIV2(c1,cc1,c2,cc2,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) |
| if ((y=c3+(cc3-u28.d*c3))==c3+(cc3+u28.d*c3)) return (-sy*y); } |
| else { |
| /* tan */ |
| DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10) |
| if ((y=c3+(cc3-u27.d*c3))==c3+(cc3+u27.d*c3)) return (sy*y); } |
| return tanMp(x); |
| } |
| |
| |
| /* multiple precision stage */ |
| /* Convert x to multi precision number,compute tan(x) by mptan() routine */ |
| /* and converts result back to double */ |
| static double tanMp(double x) |
| { |
| int p; |
| double y; |
| mp_no mpy; |
| p=32; |
| __mptan(x, &mpy, p); |
| __mp_dbl(&mpy,&y,p); |
| return y; |
| } |
| |
| #ifdef NO_LONG_DOUBLE |
| weak_alias (tan, tanl) |
| #endif |
