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authorOndřej Bílka <neleai@seznam.cz>2013-10-17 16:03:24 +0200
committerOndřej Bílka <neleai@seznam.cz>2013-10-17 16:03:24 +0200
commitc5d5d574cbfa96d0f6c1db24d1e072c472627e41 (patch)
tree83b97e29ee65636dfe1247ea8d2344ca3f0b04b4 /sysdeps/ieee754/dbl-64/dosincos.c
parente5c2c2d0c0315ca24cc9cd638cdb1a2d8dcc4b0d (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.c254
1 files changed, 137 insertions, 117 deletions
diff --git a/sysdeps/ieee754/dbl-64/dosincos.c b/sysdeps/ieee754/dbl-64/dosincos.c
index 0072628..e1c8836 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];
+ }
}