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ieee754/dbl-64: Reduce the scope of temporary storage variables

Browse Source 
This came to light when adding hard-flaot support to ARC glibc port
without hardware sqrt support causing glibc build to fail:

| ../sysdeps/ieee754/dbl-64/e_sqrt.c: In function '__ieee754_sqrt':
| ../sysdeps/ieee754/dbl-64/e_sqrt.c:58:54: error: unused variable 'ty' [-Werror=unused-variable]
|   double y, t, del, res, res1, hy, z, zz, p, hx, tx, ty, s;

The reason being EMULV() macro uses the hardware provided
__builtin_fma() variant, leaving temporary variables 'p, hx, tx, hy, ty'
unused hence compiler warning and ensuing error.

The intent of the patch was to fix that error, but EMULV is pervasive
and used fair bit indirectly via othe rmacros, hence this patch.
Functionally it should not result in code gen changes and if at all
those would be better since the scope of those temporaries is greatly
reduced now

Built tested with aarch64-linux-gnu arm-linux-gnueabi arm-linux-gnueabihf hppa-linux-gnu x86_64-linux-gnu arm-linux-gnueabihf riscv64-linux-gnu-rv64imac-lp64 riscv64-linux-gnu-rv64imafdc-lp64 powerpc-linux-gnu microblaze-linux-gnu nios2-linux-gnu hppa-linux-gnu

Also as suggested by Joseph [1] used --strip and compared the libs with
and w/o patch and they are byte-for-byte unchanged (with gcc 9).

| for i in `find . -name libm-2.31.9000.so`;
| do
|    echo $i; diff $i /SCRATCH/vgupta/gnu2/install/glibcs/$i ; echo $?;
| done

| ./aarch64-linux-gnu/lib64/libm-2.31.9000.so
| 0
| ./arm-linux-gnueabi/lib/libm-2.31.9000.so
| 0
| ./x86_64-linux-gnu/lib64/libm-2.31.9000.so
| 0
| ./arm-linux-gnueabihf/lib/libm-2.31.9000.so
| 0
| ./riscv64-linux-gnu-rv64imac-lp64/lib64/lp64/libm-2.31.9000.so
| 0
| ./riscv64-linux-gnu-rv64imafdc-lp64/lib64/lp64/libm-2.31.9000.so
| 0
| ./powerpc-linux-gnu/lib/libm-2.31.9000.so
| 0
| ./microblaze-linux-gnu/lib/libm-2.31.9000.so
| 0
| ./nios2-linux-gnu/lib/libm-2.31.9000.so
| 0
| ./hppa-linux-gnu/lib/libm-2.31.9000.so
| 0
| ./s390x-linux-gnu/lib64/libm-2.31.9000.so

[1] https://sourceware.org/pipermail/libc-alpha/2019-November/108267.html
This commit is contained in:
Vineet Gupta 2019-11-08 11:32:00 -08:00
parent 27bf5e9506
commit e93c264336
7 changed files with 193 additions and 223 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

34
sysdeps/ieee754/dbl-64/dla.h
View File

@ -67,13 +67,15 @@
/* storage variables of type double. */
#ifdef DLA_FMS
# define EMULV(x, y, z, zz, p, hx, tx, hy, ty) \
# define EMULV(x, y, z, zz) \
z = x * y; zz = DLA_FMS (x, y, z);
#else
# define EMULV(x, y, z, zz, p, hx, tx, hy, ty) \
p = CN * (x); hx = ((x) - p) + p; tx = (x) - hx; \
p = CN * (y); hy = ((y) - p) + p; ty = (y) - hy; \
z = (x) * (y); zz = (((hx * hy - z) + hx * ty) + tx * hy) + tx * ty;
# define EMULV(x, y, z, zz) \
({ __typeof__ (x) __p, hx, tx, hy, ty; \
__p = CN * (x); hx = ((x) - __p) + __p; tx = (x) - hx; \
__p = CN * (y); hy = ((y) - __p) + __p; ty = (y) - hy; \
z = (x) * (y); zz = (((hx * hy - z) + hx * ty) + tx * hy) + tx * ty; \
})
#endif
@ -83,13 +85,15 @@
/* storage variables of type double. */
#ifdef DLA_FMS
# define MUL12(x,y,z,zz,p,hx,tx,hy,ty,q) \
EMULV(x,y,z,zz,p,hx,tx,hy,ty)
# define MUL12(x, y, z, zz) \
EMULV(x, y, z, zz)
#else
# define MUL12(x,y,z,zz,p,hx,tx,hy,ty,q) \
p=CN*(x); hx=((x)-p)+p; tx=(x)-hx; \
p=CN*(y); hy=((y)-p)+p; ty=(y)-hy; \
p=hx*hy; q=hx*ty+tx*hy; z=p+q; zz=((p-z)+q)+tx*ty;
# define MUL12(x, y, z, zz) \
({ __typeof__ (x) __p, hx, tx, hy, ty, __q; \
__p=CN*(x); hx=((x)-__p)+__p; tx=(x)-hx; \
__p=CN*(y); hy=((y)-__p)+__p; ty=(y)-hy; \
__p=hx*hy; __q=hx*ty+tx*hy; z=__p+__q; zz=((__p-z)+__q)+tx*ty; \
})
#endif
@ -125,8 +129,8 @@
/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc are */
/* temporary storage variables of type double. */
#define MUL2(x, xx, y, yy, z, zz, p, hx, tx, hy, ty, q, c, cc) \
MUL12 (x, y, c, cc, p, hx, tx, hy, ty, q) \
#define MUL2(x, xx, y, yy, z, zz, c, cc) \
MUL12 (x, y, c, cc); \
cc = ((x) * (yy) + (xx) * (y)) + cc; z = c + cc; zz = (c - z) + cc;
@ -136,8 +140,8 @@
/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc,u,uu */
/* are temporary storage variables of type double. */
#define DIV2(x,xx,y,yy,z,zz,p,hx,tx,hy,ty,q,c,cc,u,uu) \
c=(x)/(y); MUL12(c,y,u,uu,p,hx,tx,hy,ty,q) \
#define DIV2(x, xx, y, yy, z, zz, c, cc, u, uu) \
c=(x)/(y); MUL12(c,y,u,uu); \
cc=(((((x)-u)-uu)+(xx))-c*(yy))/(y); z=c+cc; zz=(c-z)+cc;

15
sysdeps/ieee754/dbl-64/doasin.c
View File

@ -58,9 +58,6 @@ __doasin(double x, double dx, double v[]) {
double xx,p,pp,u,uu,r,s;
double tc,tcc;
#ifndef DLA_FMS
double hx,tx,hy,ty,tp,tq;
#endif
/* Taylor series for arcsin for Double-Length numbers */
@ -68,16 +65,16 @@ __doasin(double x, double dx, double v[]) {
p = ((((((d11*xx+d10)*xx+d9)*xx+d8)*xx+d7)*xx+d6)*xx+d5)*xx;
pp = 0;
MUL2(x,dx,x,dx,u,uu,tp,hx,tx,hy,ty,tq,tc,tcc);
MUL2(x,dx,x,dx,u,uu,tc,tcc);
ADD2(p,pp,c4.x,cc4.x,p,pp,r,s);
MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
MUL2(p,pp,u,uu,p,pp,tc,tcc);
ADD2(p,pp,c3.x,cc3.x,p,pp,r,s);
MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
MUL2(p,pp,u,uu,p,pp,tc,tcc);
ADD2(p,pp,c2.x,cc2.x,p,pp,r,s);
MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
MUL2(p,pp,u,uu,p,pp,tc,tcc);
ADD2(p,pp,c1.x,cc1.x,p,pp,r,s);
MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
MUL2(p,pp,x,dx,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
MUL2(p,pp,u,uu,p,pp,tc,tcc);
MUL2(p,pp,x,dx,p,pp,tc,tcc);
ADD2(p,pp,x,dx,p,pp,r,s);
v[0]=p;
v[1]=pp; /* arcsin(x+dx)=v[0]+v[1] */

70
sysdeps/ieee754/dbl-64/dosincos.c
View File

@ -61,9 +61,6 @@ __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;
#endif
mynumber u;
int4 k;
@ -73,31 +70,31 @@ __dubsin (double x, double dx, double v[])
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);
MUL2 (d, dd, d, dd, d2, dd2, 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);
MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, 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);
MUL2 (d2, dd2, ds, dss, ds, dss, 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);
MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
MUL2 (d, dd, ds, dss, ds, dss, 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);
MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, 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);
MUL2 (d2, dd2, dc, dcc, dc, dcc, 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);
MUL2 (d2, dd2, dc, dcc, dc, dcc, 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 (d2, dd2, dc, dcc, dc, dcc, 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 (cs, ccs, ds, dss, e, ee, c, cc);
MUL2 (dc, dcc, sn, ssn, dc, dcc, 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) */
@ -117,9 +114,6 @@ __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;
#endif
mynumber u;
int4 k;
u.x = x + big.x;
@ -127,46 +121,46 @@ __dubcos (double x, double dx, double v[])
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);
MUL2 (d, dd, d, dd, d2, dd2, 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);
MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, 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);
MUL2 (d2, dd2, ds, dss, ds, dss, 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);
MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
MUL2 (d, dd, ds, dss, ds, dss, 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);
MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, 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);
MUL2 (d2, dd2, dc, dcc, dc, dcc, 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);
MUL2 (d2, dd2, dc, dcc, dc, dcc, 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 (d2, dd2, dc, dcc, dc, dcc, 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 (cs, ccs, ds, dss, e, ee, c, cc);
MUL2 (dc, dcc, sn, ssn, dc, dcc, c, cc);
MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc);
MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, 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);
MUL2 (d2, dd2, ds, dss, ds, dss, 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);
MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
MUL2 (d, dd, ds, dss, ds, dss, 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);
MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, 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);
MUL2 (d2, dd2, dc, dcc, dc, dcc, 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);
MUL2 (d2, dd2, dc, dcc, dc, dcc, 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);
MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
MUL2 (sn, ssn, ds, dss, e, ee, c, cc);
MUL2 (dc, dcc, cs, ccs, dc, dcc, c, cc);
ADD2 (e, ee, dc, dcc, e, ee, r, s);
SUB2 (cs, ccs, e, ee, e, ee, r, s);

89
sysdeps/ieee754/dbl-64/e_atan2.c
View File

@ -77,11 +77,8 @@ __ieee754_atan2 (double y, double x)
{
int i, de, ux, dx, uy, dy;
static const int pr[MM] = { 6, 8, 10, 20, 32 };
double ax, ay, u, du, u9, ua, v, vv, dv, t1, t2, t3, t7, t8,
double ax, ay, u, du, u9, ua, v, vv, dv, t1, t2, t3,
z, zz, cor, s1, ss1, s2, ss2;
#ifndef DLA_FMS
double t4, t5, t6;
#endif
number num;
static const int ep = 59768832, /* 57*16**5 */
@ -246,13 +243,13 @@ __ieee754_atan2 (double y, double x)
if (ay < ax)
{
u = ay / ax;
EMULV (ax, u, v, vv, t1, t2, t3, t4, t5);
EMULV (ax, u, v, vv);
du = ((ay - v) - vv) / ax;
}
else
{
u = ax / ay;
EMULV (ay, u, v, vv, t1, t2, t3, t4, t5);
EMULV (ay, u, v, vv);
du = ((ax - v) - vv) / ay;
}
@ -275,18 +272,18 @@ __ieee754_atan2 (double y, double x)
if ((z = u + (zz - u1.d * u)) == u + (zz + u1.d * u))
return signArctan2 (y, z);
MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (u, du, u, du, v, vv, t1, t2);
s1 = v * (f11.d + v * (f13.d
+ v * (f15.d + v * (f17.d + v * f19.d))));
ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
MUL2 (u, du, s1, ss1, s2, ss2, t1, t2);
ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
if ((z = s1 + (ss1 - u5.d * s1)) == s1 + (ss1 + u5.d * s1))
@ -331,13 +328,13 @@ __ieee754_atan2 (double y, double x)
+ v * (hij[i][14].d
+ v * hij[i][15].d))));
ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
if ((z = s2 + (ss2 - ub.d * s2)) == s2 + (ss2 + ub.d * s2))
@ -360,19 +357,19 @@ __ieee754_atan2 (double y, double x)
if ((z = t2 + (t3 - u2.d)) == t2 + (t3 + u2.d))
return signArctan2 (y, z);
MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (u, du, u, du, v, vv, t1, t2);
s1 = v * (f11.d
+ v * (f13.d
+ v * (f15.d + v * (f17.d + v * f19.d))));
ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
MUL2 (u, du, s1, ss1, s2, ss2, t1, t2);
ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
SUB2 (hpi.d, hpi1.d, s1, ss1, s2, ss2, t1, t2);
@ -408,13 +405,13 @@ __ieee754_atan2 (double y, double x)
+ v * hij[i][15].d))));
ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
SUB2 (hpi.d, hpi1.d, s2, ss2, s1, ss1, t1, t2);
@ -439,18 +436,18 @@ __ieee754_atan2 (double y, double x)
if ((z = t2 + (t3 - u3.d)) == t2 + (t3 + u3.d))
return signArctan2 (y, z);
MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (u, du, u, du, v, vv, t1, t2);
s1 = v * (f11.d
+ v * (f13.d + v * (f15.d + v * (f17.d + v * f19.d))));
ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
MUL2 (u, du, s1, ss1, s2, ss2, t1, t2);
ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
ADD2 (hpi.d, hpi1.d, s1, ss1, s2, ss2, t1, t2);
@ -483,13 +480,13 @@ __ieee754_atan2 (double y, double x)
+ v * (hij[i][14].d
+ v * hij[i][15].d))));
ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
ADD2 (hpi.d, hpi1.d, s2, ss2, s1, ss1, t1, t2);
@ -511,17 +508,17 @@ __ieee754_atan2 (double y, double x)
if ((z = t2 + (t3 - u4.d)) == t2 + (t3 + u4.d))
return signArctan2 (y, z);
MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (u, du, u, du, v, vv, t1, t2);
s1 = v * (f11.d + v * (f13.d + v * (f15.d + v * (f17.d + v * f19.d))));
ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
MUL2 (u, du, s1, ss1, s2, ss2, t1, t2);
ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
SUB2 (opi.d, opi1.d, s1, ss1, s2, ss2, t1, t2);
@ -555,13 +552,13 @@ __ieee754_atan2 (double y, double x)
+ v * (hij[i][14].d + v * hij[i][15].d))));
ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
SUB2 (opi.d, opi1.d, s2, ss2, s1, ss1, t1, t2);

4
sysdeps/ieee754/dbl-64/e_sqrt.c
View File

@ -61,7 +61,7 @@ __ieee754_sqrt (double x)
rt2 = 3.75017500867345182581453026130850E-01,
rt3 = 3.12523626554518656309172508769531E-01;
static const double big = 134217728.0;
double y, t, del, res, res1, hy, z, zz, p, hx, tx, ty, s;
double y, t, del, res, res1, hy, z, zz, s;
mynumber a, c = { { 0, 0 } };
int4 k;
@ -89,7 +89,7 @@ __ieee754_sqrt (double x)
else
{
res1 = res + 1.5 * ((y - res) + del);
EMULV (res, res1, z, zz, p, hx, tx, hy, ty); /* (z+zz)=res*res1 */
EMULV (res, res1, z, zz); /* (z+zz)=res*res1 */
res = ((((z - s) + zz) < 0) ? max (res, res1) :
min (res, res1));
ret = res * c.x;

56
sysdeps/ieee754/dbl-64/s_atan.c
View File

@ -65,11 +65,8 @@ __signArctan (double x, double y)
double
__atan (double x)
{
double cor, s1, ss1, s2, ss2, t1, t2, t3, t7, t8, t9, t10, u, u2, u3,
double cor, s1, ss1, s2, ss2, t1, t2, t3, t4, u, u2, u3,
v, vv, w, ww, y, yy, z, zz;
#ifndef DLA_FMS
double t4, t5, t6;
#endif
int i, ux, dx;
static const int pr[M] = { 6, 8, 10, 32 };
number num;
@ -108,7 +105,7 @@ __atan (double x)
if ((y = x + (yy - U1 * x)) == x + (yy + U1 * x))
return y;
EMULV (x, x, v, vv, t1, t2, t3, t4, t5); /* v+vv=x^2 */
EMULV (x, x, v, vv); /* v+vv=x^2 */
s1 = f17.d + v * f19.d;
s1 = f15.d + v * s1;
@ -117,15 +114,14 @@ __atan (double x)
s1 *= v;
ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (x, 0, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7,
t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
MUL2 (x, 0, s1, ss1, s2, ss2, t1, t2);
ADD2 (x, 0, s2, ss2, s1, ss1, t1, t2);
if ((y = s1 + (ss1 - U5 * s1)) == s1 + (ss1 + U5 * s1))
return y;
@ -171,13 +167,13 @@ __atan (double x)
s1 *= z;
ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
if ((y = s2 + (ss2 - U6 * s2)) == s2 + (ss2 + U6 * s2))
return __signArctan (x, y);
@ -190,7 +186,7 @@ __atan (double x)
if (u < D)
{ /* C <= u < D */
w = 1 / u;
EMULV (w, u, t1, t2, t3, t4, t5, t6, t7);
EMULV (w, u, t1, t2);
ww = w * ((1 - t1) - t2);
i = (TWO52 + TWO8 * w) - TWO52;
i -= 16;
@ -210,8 +206,7 @@ __atan (double x)
if ((y = t1 + (yy - u3)) == t1 + (yy + u3))
return __signArctan (x, y);
DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, t9,
t10);
DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4);
t1 = w - hij[i][0].d;
EADD (t1, ww, z, zz);
@ -222,13 +217,13 @@ __atan (double x)
s1 *= z;
ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2);
ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
SUB2 (HPI, HPI1, s2, ss2, s1, ss1, t1, t2);
if ((y = s1 + (ss1 - U7)) == s1 + (ss1 + U7))
@ -242,7 +237,7 @@ __atan (double x)
{ /* D <= u < E */
w = 1 / u;
v = w * w;
EMULV (w, u, t1, t2, t3, t4, t5, t6, t7);
EMULV (w, u, t1, t2);
yy = d11.d + v * d13.d;
yy = d9.d + v * yy;
@ -257,9 +252,8 @@ __atan (double x)
if ((y = t3 + (yy - U4)) == t3 + (yy + U4))
return __signArctan (x, y);
DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8,
t9, t10);
MUL2 (w, ww, w, ww, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4);
MUL2 (w, ww, w, ww, v, vv, t1, t2);
s1 = f17.d + v * f19.d;
s1 = f15.d + v * s1;
@ -268,14 +262,14 @@ __atan (double x)
s1 *= v;
ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2);
MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2);
ADD2 (w, ww, s2, ss2, s1, ss1, t1, t2);
SUB2 (HPI, HPI1, s1, ss1, s2, ss2, t1, t2);

148
sysdeps/ieee754/dbl-64/s_tan.c
View File

@ -63,11 +63,8 @@ __tan (double x)
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, t7, t8, t9, t10, w, x2, xn, xx2, y, ya,
s, sy, t, t1, t2, t3, t4, w, x2, xn, xx2, y, ya,
yya, z0, z, zz, z2, zz2;
#ifndef DLA_FMS
double t5, t6;
#endif
int p;
number num, v;
mp_no mpa, mpt1, mpt2;
@ -127,20 +124,20 @@ __tan (double x)
c1 = a15.d + x2 * c1;
c1 *= x2;
EMULV (x, x, x2, xx2, t1, t2, t3, t4, t5);
EMULV (x, x, x2, xx2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
MUL2 (x, 0.0, c1, cc1, c2, cc2, t1, t2);
ADD2 (x, 0.0, c2, cc2, c1, cc1, t1, t2);
if ((y = c1 + (cc1 - u2.d * c1)) == c1 + (cc1 + u2.d * c1))
{
@ -179,19 +176,18 @@ __tan (double x)
/* 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);
EMULV (z, z, z2, zz2);
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);
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, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
MUL2 (z, 0.0, c1, cc1, c2, cc2, t1, t2);
ADD2 (z, 0.0, 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);
MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2);
SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2);
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);
if ((y = c3 + (cc3 - u4.d * c3)) == c3 + (cc3 + u4.d * c3))
{
@ -248,8 +244,7 @@ __tan (double x)
{
/* First stage -cot */
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);
if ((y = c + (dc - u6.d * c)) == c + (dc + u6.d * c))
{
retval = (-y);
@ -283,7 +278,7 @@ __tan (double x)
EADD (a, da, t1, t2);
a = t1;
da = t2;
MUL2 (a, da, a, da, x2, xx2, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (a, da, a, da, x2, xx2, t1, t2);
c1 = a25.d + x2 * a27.d;
c1 = a23.d + x2 * c1;
@ -294,25 +289,24 @@ __tan (double x)
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
MUL2 (a, da, c1, cc1, c2, cc2, t1, t2);
ADD2 (a, da, c2, cc2, c1, cc1, t1, t2);
if (n)
{
/* 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);
if ((y = c2 + (cc2 - u8.d * c2)) == c2 + (cc2 + u8.d * c2))
{
retval = (-y);
@ -380,24 +374,23 @@ __tan (double x)
/* 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);
MUL2 (z, zz, z, zz, z2, zz2, t1, t2);
c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
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);
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);
MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2);
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);
MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2);
SUB2 (1.0, 0.0, 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);
DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4);
if ((y = c3 + (cc3 - u12.d * c3)) == c3 + (cc3 + u12.d * c3))
{
retval = (-sy * y);
@ -407,8 +400,7 @@ __tan (double x)
else
{
/* 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);
if ((y = c3 + (cc3 - u11.d * c3)) == c3 + (cc3 + u11.d * c3))
{
retval = (sy * y);
@ -472,8 +464,7 @@ __tan (double x)
{
/* First stage -cot */
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);
if ((y = c + (dc - u14.d * c)) == c + (dc + u14.d * c))
{
retval = (-y);
@ -491,7 +482,7 @@ __tan (double x)
}
/* 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);
c1 = a25.d + x2 * a27.d;
c1 = a23.d + x2 * c1;
c1 = a21.d + x2 * c1;
@ -501,25 +492,24 @@ __tan (double x)
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
MUL2 (a, da, c1, cc1, c2, cc2, t1, t2);
ADD2 (a, da, c2, cc2, c1, cc1, t1, t2);
if (n)
{
/* 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);
if ((y = c2 + (cc2 - u16.d * c2)) == c2 + (cc2 + u16.d * c2))
{
retval = (-y);
@ -586,24 +576,23 @@ __tan (double x)
/* 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);
MUL2 (z, zz, z, zz, z2, zz2, t1, t2);
c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
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);
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);
MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2);
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);
MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2);
SUB2 (1.0, 0.0, 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);
DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4);
if ((y = c3 + (cc3 - u20.d * c3)) == c3 + (cc3 + u20.d * c3))
{
retval = (-sy * y);
@ -613,8 +602,7 @@ __tan (double x)
else
{
/* 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);
if ((y = c3 + (cc3 - u19.d * c3)) == c3 + (cc3 + u19.d * c3))
{
retval = (sy * y);
@ -664,8 +652,7 @@ __tan (double x)
{
/* First stage -cot */
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);
if ((y = c + (dc - u22.d * c)) == c + (dc + u22.d * c))
{
retval = (-y);
@ -691,7 +678,7 @@ __tan (double x)
__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);
c1 = a25.d + x2 * a27.d;
c1 = a23.d + x2 * c1;
@ -702,25 +689,24 @@ __tan (double x)
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
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);
MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
MUL2 (a, da, c1, cc1, c2, cc2, t1, t2);
ADD2 (a, da, c2, cc2, c1, cc1, t1, t2);
if (n)
{
/* 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);
if ((y = c2 + (cc2 - u24.d * c2)) == c2 + (cc2 + u24.d * c2))
{
retval = (-y);
@ -787,24 +773,23 @@ __tan (double x)
/* 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);
MUL2 (z, zz, z, zz, z2, zz2, t1, t2);
c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
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);
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);
MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2);
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);
MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2);
SUB2 (1.0, 0.0, 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);
DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4);
if ((y = c3 + (cc3 - u28.d * c3)) == c3 + (cc3 + u28.d * c3))
{
retval = (-sy * y);
@ -814,8 +799,7 @@ __tan (double x)
else
{
/* 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);
if ((y = c3 + (cc3 - u27.d * c3)) == c3 + (cc3 + u27.d * c3))
{
retval = (sy * y);