diff options
| -rw-r--r-- | ChangeLog | 2 | ||||
| -rw-r--r-- | sysdeps/ieee754/dbl-64/s_sin.c | 2116 |
2 files changed, 1214 insertions, 904 deletions
@@ -1,5 +1,7 @@ 2013-04-30 Siddhesh Poyarekar <siddhesh@redhat.com> + * sysdeps/ieee754/dbl-64/s_sin.c: Format code. + * benchtests/Makefile (bench): Remove slow benchmarks. * benchtests/atan-inputs: Add slow benchmark inputs. * benchtests/bench-modf.c (NUM_VARIANTS): Define. 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 |