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author | Ondřej Bílka <neleai@seznam.cz> | 2013-10-17 16:03:24 +0200 |
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committer | Ondřej Bílka <neleai@seznam.cz> | 2013-10-17 16:03:24 +0200 |
commit | c5d5d574cbfa96d0f6c1db24d1e072c472627e41 (patch) | |
tree | 83b97e29ee65636dfe1247ea8d2344ca3f0b04b4 /sysdeps/ieee754/dbl-64/dosincos.c | |
parent | e5c2c2d0c0315ca24cc9cd638cdb1a2d8dcc4b0d (diff) | |
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Format floating routines.
Diffstat (limited to 'sysdeps/ieee754/dbl-64/dosincos.c')
-rw-r--r-- | sysdeps/ieee754/dbl-64/dosincos.c | 254 |
1 files changed, 137 insertions, 117 deletions
diff --git a/sysdeps/ieee754/dbl-64/dosincos.c b/sysdeps/ieee754/dbl-64/dosincos.c index 00726285a9..e1c8836b72 100644 --- a/sysdeps/ieee754/dbl-64/dosincos.c +++ b/sysdeps/ieee754/dbl-64/dosincos.c @@ -57,49 +57,52 @@ extern const union void SECTION -__dubsin(double x, double dx, double v[]) { - double r,s,c,cc,d,dd,d2,dd2,e,ee, - sn,ssn,cs,ccs,ds,dss,dc,dcc; +__dubsin (double x, double dx, double v[]) +{ + double r, s, c, cc, d, dd, d2, dd2, e, ee, + sn, ssn, cs, ccs, ds, dss, dc, dcc; #ifndef DLA_FMS - double p,hx,tx,hy,ty,q; + double p, hx, tx, hy, ty, q; #endif mynumber u; int4 k; - u.x=x+big.x; - k = u.i[LOW_HALF]<<2; - x=x-(u.x-big.x); - d=x+dx; - dd=(x-d)+dx; - /* sin(x+dx)=sin(Xi+t)=sin(Xi)*cos(t) + cos(Xi)sin(t) where t ->0 */ - MUL2(d,dd,d,dd,d2,dd2,p,hx,tx,hy,ty,q,c,cc); - sn=__sincostab.x[k]; /* */ - ssn=__sincostab.x[k+1]; /* sin(Xi) and cos(Xi) */ - cs=__sincostab.x[k+2]; /* */ - ccs=__sincostab.x[k+3]; /* */ - MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc); /* Taylor */ - ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s); - MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); /* series */ - ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s); - MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); /* for sin */ - MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); - ADD2(ds,dss,d,dd,ds,dss,r,s); /* ds=sin(t) */ - - MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc); ;/* Taylor */ - ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s); - MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); /* series */ - ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s); - MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); /* for cos */ - ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s); - MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); /* dc=cos(t) */ - - MUL2(cs,ccs,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc); - MUL2(dc,dcc,sn,ssn,dc,dcc,p,hx,tx,hy,ty,q,c,cc); - SUB2(e,ee,dc,dcc,e,ee,r,s); - ADD2(e,ee,sn,ssn,e,ee,r,s); /* e+ee=sin(x+dx) */ - - v[0]=e; - v[1]=ee; + u.x = x + big.x; + k = u.i[LOW_HALF] << 2; + x = x - (u.x - big.x); + d = x + dx; + dd = (x - d) + dx; + /* sin(x+dx)=sin(Xi+t)=sin(Xi)*cos(t) + cos(Xi)sin(t) where t ->0 */ + MUL2 (d, dd, d, dd, d2, dd2, p, hx, tx, hy, ty, q, c, cc); + sn = __sincostab.x[k]; /* */ + ssn = __sincostab.x[k + 1]; /* sin(Xi) and cos(Xi) */ + cs = __sincostab.x[k + 2]; /* */ + ccs = __sincostab.x[k + 3]; /* */ + /* Taylor series for sin ds=sin(t) */ + MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, d, dd, ds, dss, r, s); + + /* Taylor series for cos dc=cos(t) */ + MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + + MUL2 (cs, ccs, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc); + MUL2 (dc, dcc, sn, ssn, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + SUB2 (e, ee, dc, dcc, e, ee, r, s); + ADD2 (e, ee, sn, ssn, e, ee, r, s); /* e+ee=sin(x+dx) */ + + v[0] = e; + v[1] = ee; } /**********************************************************************/ /* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */ @@ -110,64 +113,65 @@ __dubsin(double x, double dx, double v[]) { void SECTION -__dubcos(double x, double dx, double v[]) { - double r,s,c,cc,d,dd,d2,dd2,e,ee, - sn,ssn,cs,ccs,ds,dss,dc,dcc; +__dubcos (double x, double dx, double v[]) +{ + double r, s, c, cc, d, dd, d2, dd2, e, ee, + sn, ssn, cs, ccs, ds, dss, dc, dcc; #ifndef DLA_FMS - double p,hx,tx,hy,ty,q; + double p, hx, tx, hy, ty, q; #endif mynumber u; int4 k; - u.x=x+big.x; - k = u.i[LOW_HALF]<<2; - x=x-(u.x-big.x); - d=x+dx; - dd=(x-d)+dx; /* cos(x+dx)=cos(Xi+t)=cos(Xi)cos(t) - sin(Xi)sin(t) */ - MUL2(d,dd,d,dd,d2,dd2,p,hx,tx,hy,ty,q,c,cc); - sn=__sincostab.x[k]; /* */ - ssn=__sincostab.x[k+1]; /* sin(Xi) and cos(Xi) */ - cs=__sincostab.x[k+2]; /* */ - ccs=__sincostab.x[k+3]; /* */ - MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc); - ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s); - MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); - ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s); - MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); - MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); - ADD2(ds,dss,d,dd,ds,dss,r,s); - - MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc); - ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s); - MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); - ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s); - MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); - ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s); - MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); - - MUL2(cs,ccs,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc); - MUL2(dc,dcc,sn,ssn,dc,dcc,p,hx,tx,hy,ty,q,c,cc); - - MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc); - ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s); - MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); - ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s); - MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); - MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); - ADD2(ds,dss,d,dd,ds,dss,r,s); - MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc); - ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s); - MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); - ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s); - MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); - ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s); - MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); - MUL2(sn,ssn,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc); - MUL2(dc,dcc,cs,ccs,dc,dcc,p,hx,tx,hy,ty,q,c,cc); - ADD2(e,ee,dc,dcc,e,ee,r,s); - SUB2(cs,ccs,e,ee,e,ee,r,s); - - v[0]=e; - v[1]=ee; + u.x = x + big.x; + k = u.i[LOW_HALF] << 2; + x = x - (u.x - big.x); + d = x + dx; + dd = (x - d) + dx; /* cos(x+dx)=cos(Xi+t)=cos(Xi)cos(t) - sin(Xi)sin(t) */ + MUL2 (d, dd, d, dd, d2, dd2, p, hx, tx, hy, ty, q, c, cc); + sn = __sincostab.x[k]; /* */ + ssn = __sincostab.x[k + 1]; /* sin(Xi) and cos(Xi) */ + cs = __sincostab.x[k + 2]; /* */ + ccs = __sincostab.x[k + 3]; /* */ + MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, d, dd, ds, dss, r, s); + + MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + + MUL2 (cs, ccs, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc); + MUL2 (dc, dcc, sn, ssn, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + + MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s); + MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc); + ADD2 (ds, dss, d, dd, ds, dss, r, s); + MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s); + MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + MUL2 (sn, ssn, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc); + MUL2 (dc, dcc, cs, ccs, dc, dcc, p, hx, tx, hy, ty, q, c, cc); + ADD2 (e, ee, dc, dcc, e, ee, r, s); + SUB2 (cs, ccs, e, ee, e, ee, r, s); + + v[0] = e; + v[1] = ee; } /**********************************************************************/ /* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */ @@ -175,29 +179,45 @@ __dubcos(double x, double dx, double v[]) { /**********************************************************************/ void SECTION -__docos(double x, double dx, double v[]) { - double y,yy,p,w[2]; - if (x>0) {y=x; yy=dx;} - else {y=-x; yy=-dx;} - if (y<0.5*hp0.x) /* y< PI/4 */ - {__dubcos(y,yy,w); v[0]=w[0]; v[1]=w[1];} - else if (y<1.5*hp0.x) { /* y< 3/4 * PI */ - p=hp0.x-y; /* p = PI/2 - y */ - yy=hp1.x-yy; - y=p+yy; - yy=(p-y)+yy; - if (y>0) {__dubsin(y,yy,w); v[0]=w[0]; v[1]=w[1];} - /* cos(x) = sin ( 90 - x ) */ - else {__dubsin(-y,-yy,w); v[0]=-w[0]; v[1]=-w[1]; - } - } - else { /* y>= 3/4 * PI */ - p=2.0*hp0.x-y; /* p = PI- y */ - yy=2.0*hp1.x-yy; - y=p+yy; - yy=(p-y)+yy; - __dubcos(y,yy,w); - v[0]=-w[0]; - v[1]=-w[1]; - } +__docos (double x, double dx, double v[]) +{ + double y, yy, p, w[2]; + if (x > 0) + { + y = x; yy = dx; + } + else + { + y = -x; yy = -dx; + } + if (y < 0.5 * hp0.x) /* y< PI/4 */ + { + __dubcos (y, yy, w); v[0] = w[0]; v[1] = w[1]; + } + else if (y < 1.5 * hp0.x) /* y< 3/4 * PI */ + { + p = hp0.x - y; /* p = PI/2 - y */ + yy = hp1.x - yy; + y = p + yy; + yy = (p - y) + yy; + if (y > 0) + { + __dubsin (y, yy, w); v[0] = w[0]; v[1] = w[1]; + } + /* cos(x) = sin ( 90 - x ) */ + else + { + __dubsin (-y, -yy, w); v[0] = -w[0]; v[1] = -w[1]; + } + } + else /* y>= 3/4 * PI */ + { + p = 2.0 * hp0.x - y; /* p = PI- y */ + yy = 2.0 * hp1.x - yy; + y = p + yy; + yy = (p - y) + yy; + __dubcos (y, yy, w); + v[0] = -w[0]; + v[1] = -w[1]; + } } |