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-rw-r--r--sysdeps/ieee754/dbl-64/s_sin.c2116
1 files changed, 1212 insertions, 904 deletions
diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c
index 5038b72612..5c388c8b93 100644
--- a/sysdeps/ieee754/dbl-64/s_sin.c
+++ b/sysdeps/ieee754/dbl-64/s_sin.c
@@ -66,299 +66,359 @@ extern const union
} __sincostab attribute_hidden;
static const double
- sn3 = -1.66666666666664880952546298448555E-01,
- sn5 = 8.33333214285722277379541354343671E-03,
- cs2 = 4.99999999999999999999950396842453E-01,
- cs4 = -4.16666666666664434524222570944589E-02,
- cs6 = 1.38888874007937613028114285595617E-03;
-
-void __dubsin(double x, double dx, double w[]);
-void __docos(double x, double dx, double w[]);
-double __mpsin(double x, double dx);
-double __mpcos(double x, double dx);
-double __mpsin1(double x);
-double __mpcos1(double x);
-static double slow(double x);
-static double slow1(double x);
-static double slow2(double x);
-static double sloww(double x, double dx, double orig);
-static double sloww1(double x, double dx, double orig);
-static double sloww2(double x, double dx, double orig, int n);
-static double bsloww(double x, double dx, double orig, int n);
-static double bsloww1(double x, double dx, double orig, int n);
-static double bsloww2(double x, double dx, double orig, int n);
-int __branred(double x, double *a, double *aa);
-static double cslow2(double x);
-static double csloww(double x, double dx, double orig);
-static double csloww1(double x, double dx, double orig);
-static double csloww2(double x, double dx, double orig, int n);
+ sn3 = -1.66666666666664880952546298448555E-01,
+ sn5 = 8.33333214285722277379541354343671E-03,
+ cs2 = 4.99999999999999999999950396842453E-01,
+ cs4 = -4.16666666666664434524222570944589E-02,
+ cs6 = 1.38888874007937613028114285595617E-03;
+
+void __dubsin (double x, double dx, double w[]);
+void __docos (double x, double dx, double w[]);
+double __mpsin (double x, double dx);
+double __mpcos (double x, double dx);
+double __mpsin1 (double x);
+double __mpcos1 (double x);
+static double slow (double x);
+static double slow1 (double x);
+static double slow2 (double x);
+static double sloww (double x, double dx, double orig);
+static double sloww1 (double x, double dx, double orig);
+static double sloww2 (double x, double dx, double orig, int n);
+static double bsloww (double x, double dx, double orig, int n);
+static double bsloww1 (double x, double dx, double orig, int n);
+static double bsloww2 (double x, double dx, double orig, int n);
+int __branred (double x, double *a, double *aa);
+static double cslow2 (double x);
+static double csloww (double x, double dx, double orig);
+static double csloww1 (double x, double dx, double orig);
+static double csloww2 (double x, double dx, double orig, int n);
+
/*******************************************************************/
/* An ultimate sin routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of sin(x) */
/*******************************************************************/
double
SECTION
-__sin(double x){
- double xx,res,t,cor,y,s,c,sn,ssn,cs,ccs,xn,a,da,db,eps,xn1,xn2;
- mynumber u,v;
- int4 k,m,n;
- double retval = 0;
-
- SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
-
- u.x = x;
- m = u.i[HIGH_HALF];
- k = 0x7fffffff&m; /* no sign */
- if (k < 0x3e500000) /* if x->0 =>sin(x)=x */
- { retval = x; goto ret; }
+__sin (double x)
+{
+ double xx, res, t, cor, y, s, c, sn, ssn, cs, ccs, xn, a, da, db, eps, xn1,
+ xn2;
+ mynumber u, v;
+ int4 k, m, n;
+ double retval = 0;
+
+ SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
+
+ u.x = x;
+ m = u.i[HIGH_HALF];
+ k = 0x7fffffff & m; /* no sign */
+ if (k < 0x3e500000) /* if x->0 =>sin(x)=x */
+ {
+ retval = x;
+ goto ret;
+ }
/*---------------------------- 2^-26 < |x|< 0.25 ----------------------*/
- else if (k < 0x3fd00000){
- xx = x*x;
- /*Taylor series */
- t = ((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*(xx*x);
- res = x+t;
- cor = (x-res)+t;
- retval = (res == res + 1.07*cor)? res : slow(x);
- goto ret;
- } /* else if (k < 0x3fd00000) */
+ else if (k < 0x3fd00000)
+ {
+ xx = x * x;
+ /*Taylor series. */
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + s1.x)
+ * (xx * x));
+ res = x + t;
+ cor = (x - res) + t;
+ retval = (res == res + 1.07 * cor) ? res : slow (x);
+ goto ret;
+ } /* else if (k < 0x3fd00000) */
/*---------------------------- 0.25<|x|< 0.855469---------------------- */
- else if (k < 0x3feb6000) {
- u.x=(m>0)?big.x+x:big.x-x;
- y=(m>0)?x-(u.x-big.x):x+(u.x-big.x);
- xx=y*y;
- s = y + y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=(m>0)?__sincostab.x[k]:-__sincostab.x[k];
- ssn=(m>0)?__sincostab.x[k+1]:-__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ssn+s*ccs-sn*c)+cs*s;
- res=sn+cor;
- cor=(sn-res)+cor;
- retval = (res==res+1.096*cor)? res : slow1(x);
- goto ret;
- } /* else if (k < 0x3feb6000) */
+ else if (k < 0x3feb6000)
+ {
+ u.x = (m > 0) ? big.x + x : big.x - x;
+ y = (m > 0) ? x - (u.x - big.x) : x + (u.x - big.x);
+ xx = y * y;
+ s = y + y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = (m > 0) ? __sincostab.x[k] : -__sincostab.x[k];
+ ssn = (m > 0) ? __sincostab.x[k + 1] : -__sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ssn + s * ccs - sn * c) + cs * s;
+ res = sn + cor;
+ cor = (sn - res) + cor;
+ retval = (res == res + 1.096 * cor) ? res : slow1 (x);
+ goto ret;
+ } /* else if (k < 0x3feb6000) */
/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/
- else if (k < 0x400368fd ) {
-
- y = (m>0)? hp0.x-x:hp0.x+x;
- if (y>=0) {
- u.x = big.x+y;
- y = (y-(u.x-big.x))+hp1.x;
- }
- else {
- u.x = big.x-y;
- y = (-hp1.x) - (y+(u.x-big.x));
- }
- xx=y*y;
- s = y + y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ccs-s*ssn-cs*c)-sn*s;
- res=cs+cor;
- cor=(cs-res)+cor;
- retval = (res==res+1.020*cor)? ((m>0)?res:-res) : slow2(x);
- goto ret;
- } /* else if (k < 0x400368fd) */
+ else if (k < 0x400368fd)
+ {
+
+ y = (m > 0) ? hp0.x - x : hp0.x + x;
+ if (y >= 0)
+ {
+ u.x = big.x + y;
+ y = (y - (u.x - big.x)) + hp1.x;
+ }
+ else
+ {
+ u.x = big.x - y;
+ y = (-hp1.x) - (y + (u.x - big.x));
+ }
+ xx = y * y;
+ s = y + y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ccs - s * ssn - cs * c) - sn * s;
+ res = cs + cor;
+ cor = (cs - res) + cor;
+ retval = (res == res + 1.020 * cor) ? ((m > 0) ? res : -res) : slow2 (x);
+ goto ret;
+ } /* else if (k < 0x400368fd) */
/*-------------------------- 2.426265<|x|< 105414350 ----------------------*/
- else if (k < 0x419921FB ) {
- t = (x*hpinv.x + toint.x);
- xn = t - toint.x;
- v.x = t;
- y = (x - xn*mp1.x) - xn*mp2.x;
- n =v.i[LOW_HALF]&3;
- da = xn*mp3.x;
- a=y-da;
- da = (y-a)-da;
- eps = ABS(x)*1.2e-30;
-
- switch (n) { /* quarter of unit circle */
- case 0:
- case 2:
- xx = a*a;
- if (n) {a=-a;da=-da;}
- if (xx < 0.01588) {
- /*Taylor series */
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
- res = a+t;
- cor = (a-res)+t;
- cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
- retval = (res == res + cor)? res : sloww(a,da,x);
+ else if (k < 0x419921FB)
+ {
+ t = (x * hpinv.x + toint.x);
+ xn = t - toint.x;
+ v.x = t;
+ y = (x - xn * mp1.x) - xn * mp2.x;
+ n = v.i[LOW_HALF] & 3;
+ da = xn * mp3.x;
+ a = y - da;
+ da = (y - a) - da;
+ eps = ABS (x) * 1.2e-30;
+
+ switch (n)
+ { /* quarter of unit circle */
+ case 0:
+ case 2:
+ xx = a * a;
+ if (n)
+ {
+ a = -a;
+ da = -da;
+ }
+ if (xx < 0.01588)
+ {
+ /*Taylor series */
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
+ + s1.x) * a - 0.5 * da) * xx + da;
+ res = a + t;
+ cor = (a - res) + t;
+ cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
+ retval = (res == res + cor) ? res : sloww (a, da, x);
goto ret;
}
- else {
- if (a>0)
- {m=1;t=a;db=da;}
+ else
+ {
+ if (a > 0)
+ {
+ m = 1;
+ t = a;
+ db = da;
+ }
else
- {m=0;t=-a;db=-da;}
- u.x=big.x+t;
- y=t-(u.x-big.x);
- xx=y*y;
- s = y + (db+y*xx*(sn3 +xx*sn5));
- c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ssn+s*ccs-sn*c)+cs*s;
- res=sn+cor;
- cor=(sn-res)+cor;
- cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
- retval = (res==res+cor)? ((m)?res:-res) : sloww1(a,da,x);
+ {
+ m = 0;
+ t = -a;
+ db = -da;
+ }
+ u.x = big.x + t;
+ y = t - (u.x - big.x);
+ xx = y * y;
+ s = y + (db + y * xx * (sn3 + xx * sn5));
+ c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ssn + s * ccs - sn * c) + cs * s;
+ res = sn + cor;
+ cor = (sn - res) + cor;
+ cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
+ retval = ((res == res + cor) ? ((m) ? res : -res)
+ : sloww1 (a, da, x));
goto ret;
}
- break;
-
- case 1:
- case 3:
- if (a<0)
- {a=-a;da=-da;}
- u.x=big.x+a;
- y=a-(u.x-big.x)+da;
- xx=y*y;
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- s = y + y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- cor=(ccs-s*ssn-cs*c)-sn*s;
- res=cs+cor;
- cor=(cs-res)+cor;
- cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
- retval = (res==res+cor)? ((n&2)?-res:res) : sloww2(a,da,x,n);
- goto ret;
-
- break;
-
- }
-
- } /* else if (k < 0x419921FB ) */
+ break;
+
+ case 1:
+ case 3:
+ if (a < 0)
+ {
+ a = -a;
+ da = -da;
+ }
+ u.x = big.x + a;
+ y = a - (u.x - big.x) + da;
+ xx = y * y;
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ s = y + y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ cor = (ccs - s * ssn - cs * c) - sn * s;
+ res = cs + cor;
+ cor = (cs - res) + cor;
+ cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
+ retval = ((res == res + cor) ? ((n & 2) ? -res : res)
+ : sloww2 (a, da, x, n));
+ goto ret;
+
+ break;
+ }
+
+ } /* else if (k < 0x419921FB ) */
/*---------------------105414350 <|x|< 281474976710656 --------------------*/
- else if (k < 0x42F00000 ) {
- t = (x*hpinv.x + toint.x);
- xn = t - toint.x;
- v.x = t;
- xn1 = (xn+8.0e22)-8.0e22;
- xn2 = xn - xn1;
- y = ((((x - xn1*mp1.x) - xn1*mp2.x)-xn2*mp1.x)-xn2*mp2.x);
- n =v.i[LOW_HALF]&3;
- da = xn1*pp3.x;
- t=y-da;
- da = (y-t)-da;
- da = (da - xn2*pp3.x) -xn*pp4.x;
- a = t+da;
- da = (t-a)+da;
- eps = 1.0e-24;
-
- switch (n) {
- case 0:
- case 2:
- xx = a*a;
- if (n) {a=-a;da=-da;}
- if (xx < 0.01588) {
+ else if (k < 0x42F00000)
+ {
+ t = (x * hpinv.x + toint.x);
+ xn = t - toint.x;
+ v.x = t;
+ xn1 = (xn + 8.0e22) - 8.0e22;
+ xn2 = xn - xn1;
+ y = ((((x - xn1 * mp1.x) - xn1 * mp2.x) - xn2 * mp1.x) - xn2 * mp2.x);
+ n = v.i[LOW_HALF] & 3;
+ da = xn1 * pp3.x;
+ t = y - da;
+ da = (y - t) - da;
+ da = (da - xn2 * pp3.x) - xn * pp4.x;
+ a = t + da;
+ da = (t - a) + da;
+ eps = 1.0e-24;
+
+ switch (n)
+ {
+ case 0:
+ case 2:
+ xx = a * a;
+ if (n)
+ {
+ a = -a;
+ da = -da;
+ }
+ if (xx < 0.01588)
+ {
/* Taylor series */
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
- res = a+t;
- cor = (a-res)+t;
- cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
- retval = (res == res + cor)? res : bsloww(a,da,x,n);
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
+ + s1.x) * a - 0.5 * da) * xx + da;
+ res = a + t;
+ cor = (a - res) + t;
+ cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
+ retval = (res == res + cor) ? res : bsloww (a, da, x, n);
goto ret;
}
- else {
- if (a>0) {m=1;t=a;db=da;}
- else {m=0;t=-a;db=-da;}
- u.x=big.x+t;
- y=t-(u.x-big.x);
- xx=y*y;
- s = y + (db+y*xx*(sn3 +xx*sn5));
- c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ssn+s*ccs-sn*c)+cs*s;
- res=sn+cor;
- cor=(sn-res)+cor;
- cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
- retval = (res==res+cor)? ((m)?res:-res) : bsloww1(a,da,x,n);
+ else
+ {
+ if (a > 0)
+ {
+ m = 1;
+ t = a;
+ db = da;
+ }
+ else
+ {
+ m = 0;
+ t = -a;
+ db = -da;
+ }
+ u.x = big.x + t;
+ y = t - (u.x - big.x);
+ xx = y * y;
+ s = y + (db + y * xx * (sn3 + xx * sn5));
+ c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ssn + s * ccs - sn * c) + cs * s;
+ res = sn + cor;
+ cor = (sn - res) + cor;
+ cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
+ retval = ((res == res + cor) ? ((m) ? res : -res)
+ : bsloww1 (a, da, x, n));
goto ret;
- }
- break;
-
- case 1:
- case 3:
- if (a<0)
- {a=-a;da=-da;}
- u.x=big.x+a;
- y=a-(u.x-big.x)+da;
- xx=y*y;
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- s = y + y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- cor=(ccs-s*ssn-cs*c)-sn*s;
- res=cs+cor;
- cor=(cs-res)+cor;
- cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
- retval = (res==res+cor)? ((n&2)?-res:res) : bsloww2(a,da,x,n);
- goto ret;
-
- break;
-
- }
-
- } /* else if (k < 0x42F00000 ) */
+ }
+ break;
+
+ case 1:
+ case 3:
+ if (a < 0)
+ {
+ a = -a;
+ da = -da;
+ }
+ u.x = big.x + a;
+ y = a - (u.x - big.x) + da;
+ xx = y * y;
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ s = y + y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ cor = (ccs - s * ssn - cs * c) - sn * s;
+ res = cs + cor;
+ cor = (cs - res) + cor;
+ cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
+ retval = ((res == res + cor) ? ((n & 2) ? -res : res)
+ : bsloww2 (a, da, x, n));
+ goto ret;
+
+ break;
+ }
+ } /* else if (k < 0x42F00000 ) */
/* -----------------281474976710656 <|x| <2^1024----------------------------*/
- else if (k < 0x7ff00000) {
-
- n = __branred(x,&a,&da);
- switch (n) {
- case 0:
- if (a*a < 0.01588) retval = bsloww(a,da,x,n);
- else retval = bsloww1(a,da,x,n);
- goto ret;
- break;
- case 2:
- if (a*a < 0.01588) retval = bsloww(-a,-da,x,n);
- else retval = bsloww1(-a,-da,x,n);
- goto ret;
- break;
-
- case 1:
- case 3:
- retval = bsloww2(a,da,x,n);
- goto ret;
- break;
- }
-
- } /* else if (k < 0x7ff00000 ) */
+ else if (k < 0x7ff00000)
+ {
+ n = __branred (x, &a, &da);
+ switch (n)
+ {
+ case 0:
+ if (a * a < 0.01588)
+ retval = bsloww (a, da, x, n);
+ else
+ retval = bsloww1 (a, da, x, n);
+ goto ret;
+ break;
+ case 2:
+ if (a * a < 0.01588)
+ retval = bsloww (-a, -da, x, n);
+ else
+ retval = bsloww1 (-a, -da, x, n);
+ goto ret;
+ break;
-/*--------------------- |x| > 2^1024 ----------------------------------*/
- else {
- if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
- __set_errno (EDOM);
- retval = x / x;
+ case 1:
+ case 3:
+ retval = bsloww2 (a, da, x, n);
goto ret;
+ break;
}
+ } /* else if (k < 0x7ff00000 ) */
+
+/*--------------------- |x| > 2^1024 ----------------------------------*/
+ else
+ {
+ if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
+ __set_errno (EDOM);
+ retval = x / x;
+ goto ret;
+ }
- ret:
- return retval;
+ret:
+ return retval;
}
@@ -369,11 +429,12 @@ __sin(double x){
double
SECTION
-__cos(double x)
+__cos (double x)
{
- double y,xx,res,t,cor,s,c,sn,ssn,cs,ccs,xn,a,da,db,eps,xn1,xn2;
- mynumber u,v;
- int4 k,m,n;
+ double y, xx, res, t, cor, s, c, sn, ssn, cs, ccs, xn, a, da, db, eps, xn1,
+ xn2;
+ mynumber u, v;
+ int4 k, m, n;
double retval = 0;
@@ -381,251 +442,318 @@ __cos(double x)
u.x = x;
m = u.i[HIGH_HALF];
- k = 0x7fffffff&m;
-
- if (k < 0x3e400000 ) { retval = 1.0; goto ret; } /* |x|<2^-27 => cos(x)=1 */
-
- else if (k < 0x3feb6000 ) {/* 2^-27 < |x| < 0.855469 */
- y=ABS(x);
- u.x = big.x+y;
- y = y-(u.x-big.x);
- xx=y*y;
- s = y + y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ccs-s*ssn-cs*c)-sn*s;
- res=cs+cor;
- cor=(cs-res)+cor;
- retval = (res==res+1.020*cor)? res : cslow2(x);
- goto ret;
-
-} /* else if (k < 0x3feb6000) */
-
- else if (k < 0x400368fd ) {/* 0.855469 <|x|<2.426265 */;
- y=hp0.x-ABS(x);
- a=y+hp1.x;
- da=(y-a)+hp1.x;
- xx=a*a;
- if (xx < 0.01588) {
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
- res = a+t;
- cor = (a-res)+t;
- cor = (cor>0)? 1.02*cor+1.0e-31 : 1.02*cor -1.0e-31;
- retval = (res == res + cor)? res : csloww(a,da,x);
- goto ret;
- }
- else {
- if (a>0) {m=1;t=a;db=da;}
- else {m=0;t=-a;db=-da;}
- u.x=big.x+t;
- y=t-(u.x-big.x);
- xx=y*y;
- s = y + (db+y*xx*(sn3 +xx*sn5));
- c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ssn+s*ccs-sn*c)+cs*s;
- res=sn+cor;
- cor=(sn-res)+cor;
- cor = (cor>0)? 1.035*cor+1.0e-31 : 1.035*cor-1.0e-31;
- retval = (res==res+cor)? ((m)?res:-res) : csloww1(a,da,x);
- goto ret;
-}
+ k = 0x7fffffff & m;
-} /* else if (k < 0x400368fd) */
-
-
- else if (k < 0x419921FB ) {/* 2.426265<|x|< 105414350 */
- t = (x*hpinv.x + toint.x);
- xn = t - toint.x;
- v.x = t;
- y = (x - xn*mp1.x) - xn*mp2.x;
- n =v.i[LOW_HALF]&3;
- da = xn*mp3.x;
- a=y-da;
- da = (y-a)-da;
- eps = ABS(x)*1.2e-30;
-
- switch (n) {
- case 1:
- case 3:
- xx = a*a;
- if (n == 1) {a=-a;da=-da;}
- if (xx < 0.01588) {
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
- res = a+t;
- cor = (a-res)+t;
- cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
- retval = (res == res + cor)? res : csloww(a,da,x);
- goto ret;
- }
- else {
- if (a>0) {m=1;t=a;db=da;}
- else {m=0;t=-a;db=-da;}
- u.x=big.x+t;
- y=t-(u.x-big.x);
- xx=y*y;
- s = y + (db+y*xx*(sn3 +xx*sn5));
- c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ssn+s*ccs-sn*c)+cs*s;
- res=sn+cor;
- cor=(sn-res)+cor;
- cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
- retval = (res==res+cor)? ((m)?res:-res) : csloww1(a,da,x);
- goto ret;
- }
- break;
-
- case 0:
- case 2:
- if (a<0) {a=-a;da=-da;}
- u.x=big.x+a;
- y=a-(u.x-big.x)+da;
- xx=y*y;
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- s = y + y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- cor=(ccs-s*ssn-cs*c)-sn*s;
- res=cs+cor;
- cor=(cs-res)+cor;
- cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
- retval = (res==res+cor)? ((n)?-res:res) : csloww2(a,da,x,n);
+ if (k < 0x3e400000)
+ {
+ retval = 1.0;
+ goto ret;
+ } /* |x|<2^-27 => cos(x)=1 */
+
+ else if (k < 0x3feb6000)
+ { /* 2^-27 < |x| < 0.855469 */
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ xx = y * y;
+ s = y + y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ccs - s * ssn - cs * c) - sn * s;
+ res = cs + cor;
+ cor = (cs - res) + cor;
+ retval = (res == res + 1.020 * cor) ? res : cslow2 (x);
goto ret;
+ } /* else if (k < 0x3feb6000) */
+
+ else if (k < 0x400368fd)
+ { /* 0.855469 <|x|<2.426265 */ ;
+ y = hp0.x - ABS (x);
+ a = y + hp1.x;
+ da = (y - a) + hp1.x;
+ xx = a * a;
+ if (xx < 0.01588)
+ {
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + s1.x)
+ * a - 0.5 * da) * xx + da;
+ res = a + t;
+ cor = (a - res) + t;
+ cor = (cor > 0) ? 1.02 * cor + 1.0e-31 : 1.02 * cor - 1.0e-31;
+ retval = (res == res + cor) ? res : csloww (a, da, x);
+ goto ret;
+ }
+ else
+ {
+ if (a > 0)
+ {
+ m = 1;
+ t = a;
+ db = da;
+ }
+ else
+ {
+ m = 0;
+ t = -a;
+ db = -da;
+ }
+ u.x = big.x + t;
+ y = t - (u.x - big.x);
+ xx = y * y;
+ s = y + (db + y * xx * (sn3 + xx * sn5));
+ c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ssn + s * ccs - sn * c) + cs * s;
+ res = sn + cor;
+ cor = (sn - res) + cor;
+ cor = (cor > 0) ? 1.035 * cor + 1.0e-31 : 1.035 * cor - 1.0e-31;
+ retval = ((res == res + cor) ? ((m) ? res : -res)
+ : csloww1 (a, da, x));
+ goto ret;
+ }
- break;
+ } /* else if (k < 0x400368fd) */
- }
- } /* else if (k < 0x419921FB ) */
-
-
- else if (k < 0x42F00000 ) {
- t = (x*hpinv.x + toint.x);
- xn = t - toint.x;
- v.x = t;
- xn1 = (xn+8.0e22)-8.0e22;
- xn2 = xn - xn1;
- y = ((((x - xn1*mp1.x) - xn1*mp2.x)-xn2*mp1.x)-xn2*mp2.x);
- n =v.i[LOW_HALF]&3;
- da = xn1*pp3.x;
- t=y-da;
- da = (y-t)-da;
- da = (da - xn2*pp3.x) -xn*pp4.x;
- a = t+da;
- da = (t-a)+da;
- eps = 1.0e-24;
-
- switch (n) {
- case 1:
- case 3:
- xx = a*a;
- if (n==1) {a=-a;da=-da;}
- if (xx < 0.01588) {
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
- res = a+t;
- cor = (a-res)+t;
- cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps;
- retval = (res == res + cor)? res : bsloww(a,da,x,n);
- goto ret;
- }
- else {
- if (a>0) {m=1;t=a;db=da;}
- else {m=0;t=-a;db=-da;}
- u.x=big.x+t;
- y=t-(u.x-big.x);
- xx=y*y;
- s = y + (db+y*xx*(sn3 +xx*sn5));
- c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- cor=(ssn+s*ccs-sn*c)+cs*s;
- res=sn+cor;
- cor=(sn-res)+cor;
- cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps;
- retval = (res==res+cor)? ((m)?res:-res) : bsloww1(a,da,x,n);
- goto ret;
- }
- break;
-
- case 0:
- case 2:
- if (a<0) {a=-a;da=-da;}
- u.x=big.x+a;
- y=a-(u.x-big.x)+da;
- xx=y*y;
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- s = y + y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- cor=(ccs-s*ssn-cs*c)-sn*s;
- res=cs+cor;
- cor=(cs-res)+cor;
- cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
- retval = (res==res+cor)? ((n)?-res:res) : bsloww2(a,da,x,n);
- goto ret;
- break;
+ else if (k < 0x419921FB)
+ { /* 2.426265<|x|< 105414350 */
+ t = (x * hpinv.x + toint.x);
+ xn = t - toint.x;
+ v.x = t;
+ y = (x - xn * mp1.x) - xn * mp2.x;
+ n = v.i[LOW_HALF] & 3;
+ da = xn * mp3.x;
+ a = y - da;
+ da = (y - a) - da;
+ eps = ABS (x) * 1.2e-30;
+
+ switch (n)
+ {
+ case 1:
+ case 3:
+ xx = a * a;
+ if (n == 1)
+ {
+ a = -a;
+ da = -da;
+ }
+ if (xx < 0.01588)
+ {
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
+ + s1.x) * a - 0.5 * da) * xx + da;
+ res = a + t;
+ cor = (a - res) + t;
+ cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
+ retval = (res == res + cor) ? res : csloww (a, da, x);
+ goto ret;
+ }
+ else
+ {
+ if (a > 0)
+ {
+ m = 1;
+ t = a;
+ db = da;
+ }
+ else
+ {
+ m = 0;
+ t = -a;
+ db = -da;
+ }
+ u.x = big.x + t;
+ y = t - (u.x - big.x);
+ xx = y * y;
+ s = y + (db + y * xx * (sn3 + xx * sn5));
+ c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ssn + s * ccs - sn * c) + cs * s;
+ res = sn + cor;
+ cor = (sn - res) + cor;
+ cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
+ retval = ((res == res + cor) ? ((m) ? res : -res)
+ : csloww1 (a, da, x));
+ goto ret;
+ }
+ break;
+
+ case 0:
+ case 2:
+ if (a < 0)
+ {
+ a = -a;
+ da = -da;
+ }
+ u.x = big.x + a;
+ y = a - (u.x - big.x) + da;
+ xx = y * y;
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ s = y + y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ cor = (ccs - s * ssn - cs * c) - sn * s;
+ res = cs + cor;
+ cor = (cs - res) + cor;
+ cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
+ retval = ((res == res + cor) ? ((n) ? -res : res)
+ : csloww2 (a, da, x, n));
+ goto ret;
- }
+ break;
+ }
+ } /* else if (k < 0x419921FB ) */
- } /* else if (k < 0x42F00000 ) */
+ else if (k < 0x42F00000)
+ {
+ t = (x * hpinv.x + toint.x);
+ xn = t - toint.x;
+ v.x = t;
+ xn1 = (xn + 8.0e22) - 8.0e22;
+ xn2 = xn - xn1;
+ y = ((((x - xn1 * mp1.x) - xn1 * mp2.x) - xn2 * mp1.x) - xn2 * mp2.x);
+ n = v.i[LOW_HALF] & 3;
+ da = xn1 * pp3.x;
+ t = y - da;
+ da = (y - t) - da;
+ da = (da - xn2 * pp3.x) - xn * pp4.x;
+ a = t + da;
+ da = (t - a) + da;
+ eps = 1.0e-24;
+
+ switch (n)
+ {
+ case 1:
+ case 3:
+ xx = a * a;
+ if (n == 1)
+ {
+ a = -a;
+ da = -da;
+ }
+ if (xx < 0.01588)
+ {
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx
+ + s1.x) * a - 0.5 * da) * xx + da;
+ res = a + t;
+ cor = (a - res) + t;
+ cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
+ retval = (res == res + cor) ? res : bsloww (a, da, x, n);
+ goto ret;
+ }
+ else
+ {
+ if (a > 0)
+ {
+ m = 1;
+ t = a;
+ db = da;
+ }
+ else
+ {
+ m = 0;
+ t = -a;
+ db = -da;
+ }
+ u.x = big.x + t;
+ y = t - (u.x - big.x);
+ xx = y * y;
+ s = y + (db + y * xx * (sn3 + xx * sn5));
+ c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ cor = (ssn + s * ccs - sn * c) + cs * s;
+ res = sn + cor;
+ cor = (sn - res) + cor;
+ cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
+ retval = ((res == res + cor) ? ((m) ? res : -res)
+ : bsloww1 (a, da, x, n));
+ goto ret;
+ }
+ break;
+
+ case 0:
+ case 2:
+ if (a < 0)
+ {
+ a = -a;
+ da = -da;
+ }
+ u.x = big.x + a;
+ y = a - (u.x - big.x) + da;
+ xx = y * y;
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ s = y + y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ cor = (ccs - s * ssn - cs * c) - sn * s;
+ res = cs + cor;
+ cor = (cs - res) + cor;
+ cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
+ retval = ((res == res + cor) ? ((n) ? -res : res)
+ : bsloww2 (a, da, x, n));
+ goto ret;
+ break;
+ }
+ } /* else if (k < 0x42F00000 ) */
+
+ else if (k < 0x7ff00000)
+ { /* 281474976710656 <|x| <2^1024 */
+
+ n = __branred (x, &a, &da);
+ switch (n)
+ {
+ case 1:
+ if (a * a < 0.01588)
+ retval = bsloww (-a, -da, x, n);
+ else
+ retval = bsloww1 (-a, -da, x, n);
+ goto ret;
+ break;
+ case 3:
+ if (a * a < 0.01588)
+ retval = bsloww (a, da, x, n);
+ else
+ retval = bsloww1 (a, da, x, n);
+ goto ret;
+ break;
- else if (k < 0x7ff00000) {/* 281474976710656 <|x| <2^1024 */
+ case 0:
+ case 2:
+ retval = bsloww2 (a, da, x, n);
+ goto ret;
+ break;
+ }
+ } /* else if (k < 0x7ff00000 ) */
- n = __branred(x,&a,&da);
- switch (n) {
- case 1:
- if (a*a < 0.01588) retval = bsloww(-a,-da,x,n);
- else retval = bsloww1(-a,-da,x,n);
+ else
+ {
+ if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
+ __set_errno (EDOM);
+ retval = x / x; /* |x| > 2^1024 */
goto ret;
- break;
- case 3:
- if (a*a < 0.01588) retval = bsloww(a,da,x,n);
- else retval = bsloww1(a,da,x,n);
- goto ret;
- break;
-
- case 0:
- case 2:
- retval = bsloww2(a,da,x,n);
- goto ret;
- break;
}
- } /* else if (k < 0x7ff00000 ) */
-
-
-
-
- else {
- if (k == 0x7ff00000 && u.i[LOW_HALF] == 0)
- __set_errno (EDOM);
- retval = x / x; /* |x| > 2^1024 */
- goto ret;
- }
-
- ret:
+ret:
return retval;
}
@@ -636,25 +764,32 @@ __cos(double x)
static double
SECTION
-slow(double x) {
-static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
- double y,x1,x2,xx,r,t,res,cor,w[2];
- x1=(x+th2_36)-th2_36;
- y = aa.x*x1*x1*x1;
- r=x+y;
- x2=x-x1;
- xx=x*x;
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2;
- t=((x-r)+y)+t;
- res=r+t;
- cor = (r-res)+t;
- if (res == res + 1.0007*cor) return res;
- else {
- __dubsin(ABS(x),0,w);
- if (w[0] == w[0]+1.000000001*w[1]) return (x>0)?w[0]:-w[0];
- else return (x>0)?__mpsin(x,0):-__mpsin(-x,0);
- }
+slow (double x)
+{
+ static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
+ double y, x1, x2, xx, r, t, res, cor, w[2];
+ x1 = (x + th2_36) - th2_36;
+ y = aa.x * x1 * x1 * x1;
+ r = x + y;
+ x2 = x - x1;
+ xx = x * x;
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
+ + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2;
+ t = ((x - r) + y) + t;
+ res = r + t;
+ cor = (r - res) + t;
+ if (res == res + 1.0007 * cor)
+ return res;
+ else
+ {
+ __dubsin (ABS (x), 0, w);
+ if (w[0] == w[0] + 1.000000001 * w[1])
+ return (x > 0) ? w[0] : -w[0];
+ else
+ return (x > 0) ? __mpsin (x, 0) : -__mpsin (-x, 0);
+ }
}
+
/*******************************************************************************/
/* Routine compute sin(x) for 0.25<|x|< 0.855469 by __sincostab.tbl and Taylor */
/* and if result still doesn't accurate enough by mpsin or dubsin */
@@ -662,88 +797,102 @@ static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
static double
SECTION
-slow1(double x) {
+slow1 (double x)
+{
mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
static const double t22 = 6291456.0;
int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k]; /* Data */
- ssn=__sincostab.x[k+1]; /* from */
- cs=__sincostab.x[k+2]; /* tables */
- ccs=__sincostab.x[k+3]; /* __sincostab.tbl */
- y1 = (y+t22)-t22;
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k]; /* Data */
+ ssn = __sincostab.x[k + 1]; /* from */
+ cs = __sincostab.x[k + 2]; /* tables */
+ ccs = __sincostab.x[k + 3]; /* __sincostab.tbl */
+ y1 = (y + t22) - t22;
y2 = y - y1;
- c1 = (cs+t22)-t22;
- c2=(cs-c1)+ccs;
- cor=(ssn+s*ccs+cs*s+c2*y+c1*y2)-sn*c;
- y=sn+c1*y1;
- cor = cor+((sn-y)+c1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- if (res == res+1.0005*cor) return (x>0)?res:-res;
- else {
- __dubsin(ABS(x),0,w);
- if (w[0] == w[0]+1.000000005*w[1]) return (x>0)?w[0]:-w[0];
- else return (x>0)?__mpsin(x,0):-__mpsin(-x,0);
- }
+ c1 = (cs + t22) - t22;
+ c2 = (cs - c1) + ccs;
+ cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2) - sn * c;
+ y = sn + c1 * y1;
+ cor = cor + ((sn - y) + c1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+ if (res == res + 1.0005 * cor)
+ return (x > 0) ? res : -res;
+ else
+ {
+ __dubsin (ABS (x), 0, w);
+ if (w[0] == w[0] + 1.000000005 * w[1])
+ return (x > 0) ? w[0] : -w[0];
+ else
+ return (x > 0) ? __mpsin (x, 0) : -__mpsin (-x, 0);
+ }
}
+
/**************************************************************************/
/* Routine compute sin(x) for 0.855469 <|x|<2.426265 by __sincostab.tbl */
/* and if result still doesn't accurate enough by mpsin or dubsin */
/**************************************************************************/
static double
SECTION
-slow2(double x) {
+slow2 (double x)
+{
mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res,del;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res, del;
static const double t22 = 6291456.0;
int4 k;
- y=ABS(x);
- y = hp0.x-y;
- if (y>=0) {
- u.x = big.x+y;
- y = y-(u.x-big.x);
- del = hp1.x;
- }
- else {
- u.x = big.x-y;
- y = -(y+(u.x-big.x));
- del = -hp1.x;
- }
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = y*del+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- y1 = (y+t22)-t22;
- y2 = (y - y1)+del;
- e1 = (sn+t22)-t22;
- e2=(sn-e1)+ssn;
- cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
- y=cs-e1*y1;
- cor = cor+((cs-y)-e1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- if (res == res+1.0005*cor) return (x>0)?res:-res;
- else {
- y=ABS(x)-hp0.x;
- y1=y-hp1.x;
- y2=(y-y1)-hp1.x;
- __docos(y1,y2,w);
- if (w[0] == w[0]+1.000000005*w[1]) return (x>0)?w[0]:-w[0];
- else return (x>0)?__mpsin(x,0):-__mpsin(-x,0);
- }
+ y = ABS (x);
+ y = hp0.x - y;
+ if (y >= 0)
+ {
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ del = hp1.x;
+ }
+ else
+ {
+ u.x = big.x - y;
+ y = -(y + (u.x - big.x));
+ del = -hp1.x;
+ }
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = y * del + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ y1 = (y + t22) - t22;
+ y2 = (y - y1) + del;
+ e1 = (sn + t22) - t22;
+ e2 = (sn - e1) + ssn;
+ cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+ y = cs - e1 * y1;
+ cor = cor + ((cs - y) - e1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+ if (res == res + 1.0005 * cor)
+ return (x > 0) ? res : -res;
+ else
+ {
+ y = ABS (x) - hp0.x;
+ y1 = y - hp1.x;
+ y2 = (y - y1) - hp1.x;
+ __docos (y1, y2, w);
+ if (w[0] == w[0] + 1.000000005 * w[1])
+ return (x > 0) ? w[0] : -w[0];
+ else
+ return (x > 0) ? __mpsin (x, 0) : -__mpsin (-x, 0);
+ }
}
+
/***************************************************************************/
/* Routine compute sin(x+dx) (Double-Length number) where x is small enough*/
/* to use Taylor series around zero and (x+dx) */
@@ -754,46 +903,74 @@ slow2(double x) {
static double
SECTION
-sloww(double x,double dx, double orig) {
- static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
- double y,x1,x2,xx,r,t,res,cor,w[2],a,da,xn;
- union {int4 i[2]; double x;} v;
+sloww (double x, double dx, double orig)
+{
+ static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
+ double y, x1, x2, xx, r, t, res, cor, w[2], a, da, xn;
+ union
+ {
+ int4 i[2];
+ double x;
+ } v;
int4 n;
- x1=(x+th2_36)-th2_36;
- y = aa.x*x1*x1*x1;
- r=x+y;
- x2=(x-x1)+dx;
- xx=x*x;
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx;
- t=((x-r)+y)+t;
- res=r+t;
- cor = (r-res)+t;
- cor = (cor>0)? 1.0005*cor+ABS(orig)*3.1e-30 : 1.0005*cor-ABS(orig)*3.1e-30;
- if (res == res + cor) return res;
- else {
- (x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w);
- cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-30 : 1.000000001*w[1] - ABS(orig)*1.1e-30;
- if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
- else {
- t = (orig*hpinv.x + toint.x);
- xn = t - toint.x;
- v.x = t;
- y = (orig - xn*mp1.x) - xn*mp2.x;
- n =v.i[LOW_HALF]&3;
- da = xn*pp3.x;
- t=y-da;
- da = (y-t)-da;
- y = xn*pp4.x;
- a = t - y;
- da = ((t-a)-y)+da;
- if (n&2) {a=-a; da=-da;}
- (a>0)? __dubsin(a,da,w) : __dubsin(-a,-da,w);
- cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-40 : 1.000000001*w[1] - ABS(orig)*1.1e-40;
- if (w[0] == w[0]+cor) return (a>0)?w[0]:-w[0];
- else return __mpsin1(orig);
+ x1 = (x + th2_36) - th2_36;
+ y = aa.x * x1 * x1 * x1;
+ r = x + y;
+ x2 = (x - x1) + dx;
+ xx = x * x;
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
+ + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
+ t = ((x - r) + y) + t;
+ res = r + t;
+ cor = (r - res) + t;
+ cor =
+ (cor >
+ 0) ? 1.0005 * cor + ABS (orig) * 3.1e-30 : 1.0005 * cor -
+ ABS (orig) * 3.1e-30;
+ if (res == res + cor)
+ return res;
+ else
+ {
+ (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
+ if (w[1] > 0)
+ cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-30;
+ else
+ cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-30;
+
+ if (w[0] == w[0] + cor)
+ return (x > 0) ? w[0] : -w[0];
+ else
+ {
+ t = (orig * hpinv.x + toint.x);
+ xn = t - toint.x;
+ v.x = t;
+ y = (orig - xn * mp1.x) - xn * mp2.x;
+ n = v.i[LOW_HALF] & 3;
+ da = xn * pp3.x;
+ t = y - da;
+ da = (y - t) - da;
+ y = xn * pp4.x;
+ a = t - y;
+ da = ((t - a) - y) + da;
+ if (n & 2)
+ {
+ a = -a;
+ da = -da;
+ }
+ (a > 0) ? __dubsin (a, da, w) : __dubsin (-a, -da, w);
+ if (w[1] > 0)
+ cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-40;
+ else
+ cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-40;
+
+ if (w[0] == w[0] + cor)
+ return (a > 0) ? w[0] : -w[0];
+ else
+ return __mpsin1 (orig);
+ }
}
- }
}
+
/***************************************************************************/
/* Routine compute sin(x+dx) (Double-Length number) where x in first or */
/* third quarter of unit circle.Routine receive also (right argument) the */
@@ -803,41 +980,58 @@ sloww(double x,double dx, double orig) {
static double
SECTION
-sloww1(double x, double dx, double orig) {
+sloww1 (double x, double dx, double orig)
+{
mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
static const double t22 = 6291456.0;
int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- dx=(x>0)?dx:-dx;
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- y1 = (y+t22)-t22;
- y2 = (y - y1)+dx;
- c1 = (cs+t22)-t22;
- c2=(cs-c1)+ccs;
- cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c;
- y=sn+c1*y1;
- cor = cor+((sn-y)+c1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
- if (res == res + cor) return (x>0)?res:-res;
- else {
- __dubsin(ABS(x),dx,w);
- cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
- if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
- else return __mpsin1(orig);
- }
+
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ dx = (x > 0) ? dx : -dx;
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ y1 = (y + t22) - t22;
+ y2 = (y - y1) + dx;
+ c1 = (cs + t22) - t22;
+ c2 = (cs - c1) + ccs;
+ cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2 - sn * y * dx) - sn * c;
+ y = sn + c1 * y1;
+ cor = cor + ((sn - y) + c1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+
+ if (cor > 0)
+ cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
+ else
+ cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+
+ if (res == res + cor)
+ return (x > 0) ? res : -res;
+ else
+ {
+ __dubsin (ABS (x), dx, w);
+
+ if (w[1] > 0)
+ cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
+ else
+ cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
+
+ if (w[0] == w[0] + cor)
+ return (x > 0) ? w[0] : -w[0];
+ else
+ return __mpsin1 (orig);
+ }
}
+
/***************************************************************************/
/* Routine compute sin(x+dx) (Double-Length number) where x in second or */
/* fourth quarter of unit circle.Routine receive also the original value */
@@ -847,42 +1041,59 @@ sloww1(double x, double dx, double orig) {
static double
SECTION
-sloww2(double x, double dx, double orig, int n) {
+sloww2 (double x, double dx, double orig, int n)
+{
mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
static const double t22 = 6291456.0;
int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- dx=(x>0)?dx:-dx;
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
-
- y1 = (y+t22)-t22;
- y2 = (y - y1)+dx;
- e1 = (sn+t22)-t22;
- e2=(sn-e1)+ssn;
- cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
- y=cs-e1*y1;
- cor = cor+((cs-y)-e1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
- if (res == res + cor) return (n&2)?-res:res;
- else {
- __docos(ABS(x),dx,w);
- cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
- if (w[0] == w[0]+cor) return (n&2)?-w[0]:w[0];
- else return __mpsin1(orig);
- }
+
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ dx = (x > 0) ? dx : -dx;
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = y * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+
+ y1 = (y + t22) - t22;
+ y2 = (y - y1) + dx;
+ e1 = (sn + t22) - t22;
+ e2 = (sn - e1) + ssn;
+ cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+ y = cs - e1 * y1;
+ cor = cor + ((cs - y) - e1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+
+ if (cor > 0)
+ cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
+ else
+ cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+
+ if (res == res + cor)
+ return (n & 2) ? -res : res;
+ else
+ {
+ __docos (ABS (x), dx, w);
+
+ if (w[1] > 0)
+ cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
+ else
+ cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
+
+ if (w[0] == w[0] + cor)
+ return (n & 2) ? -w[0] : w[0];
+ else
+ return __mpsin1 (orig);
+ }
}
+
/***************************************************************************/
/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */
/* is small enough to use Taylor series around zero and (x+dx) */
@@ -893,26 +1104,36 @@ sloww2(double x, double dx, double orig, int n) {
static double
SECTION
-bsloww(double x,double dx, double orig,int n) {
- static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
- double y,x1,x2,xx,r,t,res,cor,w[2];
- x1=(x+th2_36)-th2_36;
- y = aa.x*x1*x1*x1;
- r=x+y;
- x2=(x-x1)+dx;
- xx=x*x;
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx;
- t=((x-r)+y)+t;
- res=r+t;
- cor = (r-res)+t;
- cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24;
- if (res == res + cor) return res;
- else {
- (x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w);
- cor = (w[1]>0)? 1.000000001*w[1] + 1.1e-24 : 1.000000001*w[1] - 1.1e-24;
- if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
- else return (n&1)?__mpcos1(orig):__mpsin1(orig);
- }
+bsloww (double x, double dx, double orig, int n)
+{
+ static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
+ double y, x1, x2, xx, r, t, res, cor, w[2];
+
+ x1 = (x + th2_36) - th2_36;
+ y = aa.x * x1 * x1 * x1;
+ r = x + y;
+ x2 = (x - x1) + dx;
+ xx = x * x;
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
+ + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
+ t = ((x - r) + y) + t;
+ res = r + t;
+ cor = (r - res) + t;
+ cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
+ if (res == res + cor)
+ return res;
+ else
+ {
+ (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
+ if (w[1] > 0)
+ cor = 1.000000001 * w[1] + 1.1e-24;
+ else
+ cor = 1.000000001 * w[1] - 1.1e-24;
+ if (w[0] == w[0] + cor)
+ return (x > 0) ? w[0] : -w[0];
+ else
+ return (n & 1) ? __mpcos1 (orig) : __mpsin1 (orig);
+ }
}
/***************************************************************************/
@@ -924,40 +1145,51 @@ bsloww(double x,double dx, double orig,int n) {
static double
SECTION
-bsloww1(double x, double dx, double orig,int n) {
-mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
- static const double t22 = 6291456.0;
- int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- dx=(x>0)?dx:-dx;
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- y1 = (y+t22)-t22;
- y2 = (y - y1)+dx;
- c1 = (cs+t22)-t22;
- c2=(cs-c1)+ccs;
- cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c;
- y=sn+c1*y1;
- cor = cor+((sn-y)+c1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24;
- if (res == res + cor) return (x>0)?res:-res;
- else {
- __dubsin(ABS(x),dx,w);
- cor = (w[1]>0)? 1.000000005*w[1]+1.1e-24: 1.000000005*w[1]-1.1e-24;
- if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
- else return (n&1)?__mpcos1(orig):__mpsin1(orig);
- }
+bsloww1 (double x, double dx, double orig, int n)
+{
+ mynumber u;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
+ static const double t22 = 6291456.0;
+ int4 k;
+
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ dx = (x > 0) ? dx : -dx;
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ y1 = (y + t22) - t22;
+ y2 = (y - y1) + dx;
+ c1 = (cs + t22) - t22;
+ c2 = (cs - c1) + ccs;
+ cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2 - sn * y * dx) - sn * c;
+ y = sn + c1 * y1;
+ cor = cor + ((sn - y) + c1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+ cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
+ if (res == res + cor)
+ return (x > 0) ? res : -res;
+ else
+ {
+ __dubsin (ABS (x), dx, w);
+
+ if (w[1] > 0)
+ cor = 1.000000005 * w[1] + 1.1e-24;
+ else
+ cor = 1.000000005 * w[1] - 1.1e-24;
+
+ if (w[0] == w[0] + cor)
+ return (x > 0) ? w[0] : -w[0];
+ else
+ return (n & 1) ? __mpcos1 (orig) : __mpsin1 (orig);
+ }
}
/***************************************************************************/
@@ -969,41 +1201,52 @@ mynumber u;
static double
SECTION
-bsloww2(double x, double dx, double orig, int n) {
-mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
- static const double t22 = 6291456.0;
- int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- dx=(x>0)?dx:-dx;
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
-
- y1 = (y+t22)-t22;
- y2 = (y - y1)+dx;
- e1 = (sn+t22)-t22;
- e2=(sn-e1)+ssn;
- cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
- y=cs-e1*y1;
- cor = cor+((cs-y)-e1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24;
- if (res == res + cor) return (n&2)?-res:res;
- else {
- __docos(ABS(x),dx,w);
- cor = (w[1]>0)? 1.000000005*w[1]+1.1e-24 : 1.000000005*w[1]-1.1e-24;
- if (w[0] == w[0]+cor) return (n&2)?-w[0]:w[0];
- else return (n&1)?__mpsin1(orig):__mpcos1(orig);
- }
+bsloww2 (double x, double dx, double orig, int n)
+{
+ mynumber u;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
+ static const double t22 = 6291456.0;
+ int4 k;
+
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ dx = (x > 0) ? dx : -dx;
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = y * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+
+ y1 = (y + t22) - t22;
+ y2 = (y - y1) + dx;
+ e1 = (sn + t22) - t22;
+ e2 = (sn - e1) + ssn;
+ cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+ y = cs - e1 * y1;
+ cor = cor + ((cs - y) - e1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+ cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
+ if (res == res + cor)
+ return (n & 2) ? -res : res;
+ else
+ {
+ __docos (ABS (x), dx, w);
+
+ if (w[1] > 0)
+ cor = 1.000000005 * w[1] + 1.1e-24;
+ else
+ cor = 1.000000005 * w[1] - 1.1e-24;
+
+ if (w[0] == w[0] + cor)
+ return (n & 2) ? -w[0] : w[0];
+ else
+ return (n & 1) ? __mpsin1 (orig) : __mpcos1 (orig);
+ }
}
/************************************************************************/
@@ -1013,39 +1256,44 @@ mynumber u;
static double
SECTION
-cslow2(double x) {
+cslow2 (double x)
+{
mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
static const double t22 = 6291456.0;
int4 k;
- y=ABS(x);
- u.x = big.x+y;
- y = y-(u.x-big.x);
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- y1 = (y+t22)-t22;
+
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ y1 = (y + t22) - t22;
y2 = y - y1;
- e1 = (sn+t22)-t22;
- e2=(sn-e1)+ssn;
- cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
- y=cs-e1*y1;
- cor = cor+((cs-y)-e1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- if (res == res+1.0005*cor)
+ e1 = (sn + t22) - t22;
+ e2 = (sn - e1) + ssn;
+ cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+ y = cs - e1 * y1;
+ cor = cor + ((cs - y) - e1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+ if (res == res + 1.0005 * cor)
return res;
- else {
- y=ABS(x);
- __docos(y,0,w);
- if (w[0] == w[0]+1.000000005*w[1]) return w[0];
- else return __mpcos(x,0);
- }
+ else
+ {
+ y = ABS (x);
+ __docos (y, 0, w);
+ if (w[0] == w[0] + 1.000000005 * w[1])
+ return w[0];
+ else
+ return __mpcos (x, 0);
+ }
}
/***************************************************************************/
@@ -1058,46 +1306,78 @@ cslow2(double x) {
static double
SECTION
-csloww(double x,double dx, double orig) {
- static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
- double y,x1,x2,xx,r,t,res,cor,w[2],a,da,xn;
- union {int4 i[2]; double x;} v;
+csloww (double x, double dx, double orig)
+{
+ static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
+ double y, x1, x2, xx, r, t, res, cor, w[2], a, da, xn;
+ union
+ {
+ int4 i[2];
+ double x;
+ } v;
int4 n;
- x1=(x+th2_36)-th2_36;
- y = aa.x*x1*x1*x1;
- r=x+y;
- x2=(x-x1)+dx;
- xx=x*x;
- /* Taylor series */
- t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx;
- t=((x-r)+y)+t;
- res=r+t;
- cor = (r-res)+t;
- cor = (cor>0)? 1.0005*cor+ABS(orig)*3.1e-30 : 1.0005*cor-ABS(orig)*3.1e-30;
- if (res == res + cor) return res;
- else {
- (x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w);
- cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-30 : 1.000000001*w[1] - ABS(orig)*1.1e-30;
- if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
- else {
- t = (orig*hpinv.x + toint.x);
- xn = t - toint.x;
- v.x = t;
- y = (orig - xn*mp1.x) - xn*mp2.x;
- n =v.i[LOW_HALF]&3;
- da = xn*pp3.x;
- t=y-da;
- da = (y-t)-da;
- y = xn*pp4.x;
- a = t - y;
- da = ((t-a)-y)+da;
- if (n==1) {a=-a; da=-da;}
- (a>0)? __dubsin(a,da,w) : __dubsin(-a,-da,w);
- cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-40 : 1.000000001*w[1] - ABS(orig)*1.1e-40;
- if (w[0] == w[0]+cor) return (a>0)?w[0]:-w[0];
- else return __mpcos1(orig);
+
+ x1 = (x + th2_36) - th2_36;
+ y = aa.x * x1 * x1 * x1;
+ r = x + y;
+ x2 = (x - x1) + dx;
+ xx = x * x;
+ /* Taylor series */
+ t = (((((s5.x * xx + s4.x) * xx + s3.x) * xx + s2.x) * xx + bb.x) * xx
+ + 3.0 * aa.x * x1 * x2) * x + aa.x * x2 * x2 * x2 + dx;
+ t = ((x - r) + y) + t;
+ res = r + t;
+ cor = (r - res) + t;
+
+ if (cor > 0)
+ cor = 1.0005 * cor + ABS (orig) * 3.1e-30;
+ else
+ cor = 1.0005 * cor - ABS (orig) * 3.1e-30;
+
+ if (res == res + cor)
+ return res;
+ else
+ {
+ (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
+
+ if (w[1] > 0)
+ cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-30;
+ else
+ cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-30;
+
+ if (w[0] == w[0] + cor)
+ return (x > 0) ? w[0] : -w[0];
+ else
+ {
+ t = (orig * hpinv.x + toint.x);
+ xn = t - toint.x;
+ v.x = t;
+ y = (orig - xn * mp1.x) - xn * mp2.x;
+ n = v.i[LOW_HALF] & 3;
+ da = xn * pp3.x;
+ t = y - da;
+ da = (y - t) - da;
+ y = xn * pp4.x;
+ a = t - y;
+ da = ((t - a) - y) + da;
+ if (n == 1)
+ {
+ a = -a;
+ da = -da;
+ }
+ (a > 0) ? __dubsin (a, da, w) : __dubsin (-a, -da, w);
+
+ if (w[1] > 0)
+ cor = 1.000000001 * w[1] + ABS (orig) * 1.1e-40;
+ else
+ cor = 1.000000001 * w[1] - ABS (orig) * 1.1e-40;
+
+ if (w[0] == w[0] + cor)
+ return (a > 0) ? w[0] : -w[0];
+ else
+ return __mpcos1 (orig);
+ }
}
- }
}
/***************************************************************************/
@@ -1109,40 +1389,54 @@ csloww(double x,double dx, double orig) {
static double
SECTION
-csloww1(double x, double dx, double orig) {
+csloww1 (double x, double dx, double orig)
+{
mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
static const double t22 = 6291456.0;
int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- dx=(x>0)?dx:-dx;
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
- y1 = (y+t22)-t22;
- y2 = (y - y1)+dx;
- c1 = (cs+t22)-t22;
- c2=(cs-c1)+ccs;
- cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c;
- y=sn+c1*y1;
- cor = cor+((sn-y)+c1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
- if (res == res + cor) return (x>0)?res:-res;
- else {
- __dubsin(ABS(x),dx,w);
- cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
- if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0];
- else return __mpcos1(orig);
- }
+
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ dx = (x > 0) ? dx : -dx;
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+ y1 = (y + t22) - t22;
+ y2 = (y - y1) + dx;
+ c1 = (cs + t22) - t22;
+ c2 = (cs - c1) + ccs;
+ cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2 - sn * y * dx) - sn * c;
+ y = sn + c1 * y1;
+ cor = cor + ((sn - y) + c1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+
+ if (cor > 0)
+ cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
+ else
+ cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+
+ if (res == res + cor)
+ return (x > 0) ? res : -res;
+ else
+ {
+ __dubsin (ABS (x), dx, w);
+ if (w[1] > 0)
+ cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
+ else
+ cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
+ if (w[0] == w[0] + cor)
+ return (x > 0) ? w[0] : -w[0];
+ else
+ return __mpcos1 (orig);
+ }
}
@@ -1155,41 +1449,55 @@ csloww1(double x, double dx, double orig) {
static double
SECTION
-csloww2(double x, double dx, double orig, int n) {
+csloww2 (double x, double dx, double orig, int n)
+{
mynumber u;
- double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res;
+ double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
static const double t22 = 6291456.0;
int4 k;
- y=ABS(x);
- u.x=big.x+y;
- y=y-(u.x-big.x);
- dx=(x>0)?dx:-dx;
- xx=y*y;
- s = y*xx*(sn3 +xx*sn5);
- c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
- k=u.i[LOW_HALF]<<2;
- sn=__sincostab.x[k];
- ssn=__sincostab.x[k+1];
- cs=__sincostab.x[k+2];
- ccs=__sincostab.x[k+3];
-
- y1 = (y+t22)-t22;
- y2 = (y - y1)+dx;
- e1 = (sn+t22)-t22;
- e2=(sn-e1)+ssn;
- cor=(ccs-cs*c-e1*y2-e2*y)-sn*s;
- y=cs-e1*y1;
- cor = cor+((cs-y)-e1*y1);
- res=y+cor;
- cor=(y-res)+cor;
- cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig);
- if (res == res + cor) return (n)?-res:res;
- else {
- __docos(ABS(x),dx,w);
- cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig);
- if (w[0] == w[0]+cor) return (n)?-w[0]:w[0];
- else return __mpcos1(orig);
- }
+
+ y = ABS (x);
+ u.x = big.x + y;
+ y = y - (u.x - big.x);
+ dx = (x > 0) ? dx : -dx;
+ xx = y * y;
+ s = y * xx * (sn3 + xx * sn5);
+ c = y * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
+ k = u.i[LOW_HALF] << 2;
+ sn = __sincostab.x[k];
+ ssn = __sincostab.x[k + 1];
+ cs = __sincostab.x[k + 2];
+ ccs = __sincostab.x[k + 3];
+
+ y1 = (y + t22) - t22;
+ y2 = (y - y1) + dx;
+ e1 = (sn + t22) - t22;
+ e2 = (sn - e1) + ssn;
+ cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
+ y = cs - e1 * y1;
+ cor = cor + ((cs - y) - e1 * y1);
+ res = y + cor;
+ cor = (y - res) + cor;
+
+ if (cor > 0)
+ cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
+ else
+ cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+
+ if (res == res + cor)
+ return (n) ? -res : res;
+ else
+ {
+ __docos (ABS (x), dx, w);
+ if (w[1] > 0)
+ cor = 1.000000005 * w[1] + 1.1e-30 * ABS (orig);
+ else
+ cor = 1.000000005 * w[1] - 1.1e-30 * ABS (orig);
+ if (w[0] == w[0] + cor)
+ return (n) ? -w[0] : w[0];
+ else
+ return __mpcos1 (orig);
+ }
}
#ifndef __cos
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-18 18:31:05 +0000