diff options
| -rw-r--r-- | ChangeLog | 2 | ||||
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_pow.c | 573 |
2 files changed, 315 insertions, 260 deletions
diff --git a/ChangeLog b/ChangeLog index 14f12d6c66..297ff42b39 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,5 +1,7 @@ 2013-10-08 Siddhesh Poyarekar <siddhesh@redhat.com> + * sysdeps/ieee754/dbl-64/e_pow.c: Fix code formatting. + * sysdeps/ieee754/dbl-64/e_exp.c: Fix code formatting. * sysdeps/generic/math_private.h (__mpsin1): Remove diff --git a/sysdeps/ieee754/dbl-64/e_pow.c b/sysdeps/ieee754/dbl-64/e_pow.c index 9a766e7224..9cf2309174 100644 --- a/sysdeps/ieee754/dbl-64/e_pow.c +++ b/sysdeps/ieee754/dbl-64/e_pow.c @@ -49,354 +49,407 @@ static const double huge = 1.0e300, tiny = 1.0e-300; -double __exp1(double x, double xx, double error); -static double log1(double x, double *delta, double *error); -static double my_log2(double x, double *delta, double *error); -double __slowpow(double x, double y,double z); -static double power1(double x, double y); -static int checkint(double x); +double __exp1 (double x, double xx, double error); +static double log1 (double x, double *delta, double *error); +static double my_log2 (double x, double *delta, double *error); +double __slowpow (double x, double y, double z); +static double power1 (double x, double y); +static int checkint (double x); -/***************************************************************************/ -/* An ultimate power routine. Given two IEEE double machine numbers y,x */ -/* it computes the correctly rounded (to nearest) value of X^y. */ -/***************************************************************************/ +/* An ultimate power routine. Given two IEEE double machine numbers y, x it + computes the correctly rounded (to nearest) value of X^y. */ double SECTION -__ieee754_pow(double x, double y) { - double z,a,aa,error, t,a1,a2,y1,y2; - mynumber u,v; +__ieee754_pow (double x, double y) +{ + double z, a, aa, error, t, a1, a2, y1, y2; + mynumber u, v; int k; - int4 qx,qy; - v.x=y; - u.x=x; - if (v.i[LOW_HALF] == 0) { /* of y */ - qx = u.i[HIGH_HALF]&0x7fffffff; - /* Is x a NaN? */ - if (((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000)) - return x; - if (y == 1.0) return x; - if (y == 2.0) return x*x; - if (y == -1.0) return 1.0/x; - if (y == 0) return 1.0; - } + int4 qx, qy; + v.x = y; + u.x = x; + if (v.i[LOW_HALF] == 0) + { /* of y */ + qx = u.i[HIGH_HALF] & 0x7fffffff; + /* Is x a NaN? */ + if (((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000)) + return x; + if (y == 1.0) + return x; + if (y == 2.0) + return x * x; + if (y == -1.0) + return 1.0 / x; + if (y == 0) + return 1.0; + } /* else */ - if(((u.i[HIGH_HALF]>0 && u.i[HIGH_HALF]<0x7ff00000)|| /* x>0 and not x->0 */ - (u.i[HIGH_HALF]==0 && u.i[LOW_HALF]!=0)) && - /* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */ - (v.i[HIGH_HALF]&0x7fffffff) < 0x4ff00000) { /* if y<-1 or y>1 */ - double retval; + if (((u.i[HIGH_HALF] > 0 && u.i[HIGH_HALF] < 0x7ff00000) || /* x>0 and not x->0 */ + (u.i[HIGH_HALF] == 0 && u.i[LOW_HALF] != 0)) && + /* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */ + (v.i[HIGH_HALF] & 0x7fffffff) < 0x4ff00000) + { /* if y<-1 or y>1 */ + double retval; - SET_RESTORE_ROUND (FE_TONEAREST); + SET_RESTORE_ROUND (FE_TONEAREST); - /* Avoid internal underflow for tiny y. The exact value of y does - not matter if |y| <= 2**-64. */ - if (ABS (y) < 0x1p-64) - y = y < 0 ? -0x1p-64 : 0x1p-64; - z = log1(x,&aa,&error); /* x^y =e^(y log (X)) */ - t = y*CN; - y1 = t - (t-y); - y2 = y - y1; - t = z*CN; - a1 = t - (t-z); - a2 = (z - a1)+aa; - a = y1*a1; - aa = y2*a1 + y*a2; - a1 = a+aa; - a2 = (a-a1)+aa; - error = error*ABS(y); - t = __exp1(a1,a2,1.9e16*error); /* return -10 or 0 if wasn't computed exactly */ - retval = (t>0)?t:power1(x,y); + /* Avoid internal underflow for tiny y. The exact value of y does + not matter if |y| <= 2**-64. */ + if (ABS (y) < 0x1p-64) + y = y < 0 ? -0x1p-64 : 0x1p-64; + z = log1 (x, &aa, &error); /* x^y =e^(y log (X)) */ + t = y * CN; + y1 = t - (t - y); + y2 = y - y1; + t = z * CN; + a1 = t - (t - z); + a2 = (z - a1) + aa; + a = y1 * a1; + aa = y2 * a1 + y * a2; + a1 = a + aa; + a2 = (a - a1) + aa; + error = error * ABS (y); + t = __exp1 (a1, a2, 1.9e16 * error); /* return -10 or 0 if wasn't computed exactly */ + retval = (t > 0) ? t : power1 (x, y); - return retval; - } + return retval; + } - if (x == 0) { - if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0) - || (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */ - return y; - if (ABS(y) > 1.0e20) return (y>0)?0:1.0/0.0; - k = checkint(y); - if (k == -1) - return y < 0 ? 1.0/x : x; - else - return y < 0 ? 1.0/0.0 : 0.0; /* return 0 */ - } + if (x == 0) + { + if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0) + || (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */ + return y; + if (ABS (y) > 1.0e20) + return (y > 0) ? 0 : 1.0 / 0.0; + k = checkint (y); + if (k == -1) + return y < 0 ? 1.0 / x : x; + else + return y < 0 ? 1.0 / 0.0 : 0.0; /* return 0 */ + } - qx = u.i[HIGH_HALF]&0x7fffffff; /* no sign */ - qy = v.i[HIGH_HALF]&0x7fffffff; /* no sign */ + qx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */ + qy = v.i[HIGH_HALF] & 0x7fffffff; /* no sign */ - if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) /* NaN */ + if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) /* NaN */ return x; - if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0)) /* NaN */ + if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0)) /* NaN */ return x == 1.0 ? 1.0 : y; /* if x<0 */ - if (u.i[HIGH_HALF] < 0) { - k = checkint(y); - if (k==0) { - if (qy == 0x7ff00000) { - if (x == -1.0) return 1.0; - else if (x > -1.0) return v.i[HIGH_HALF] < 0 ? INF.x : 0.0; - else return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x; - } + if (u.i[HIGH_HALF] < 0) + { + k = checkint (y); + if (k == 0) + { + if (qy == 0x7ff00000) + { + if (x == -1.0) + return 1.0; + else if (x > -1.0) + return v.i[HIGH_HALF] < 0 ? INF.x : 0.0; + else + return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x; + } + else if (qx == 0x7ff00000) + return y < 0 ? 0.0 : INF.x; + return (x - x) / (x - x); /* y not integer and x<0 */ + } else if (qx == 0x7ff00000) - return y < 0 ? 0.0 : INF.x; - return (x - x) / (x - x); /* y not integer and x<0 */ + { + if (k < 0) + return y < 0 ? nZERO.x : nINF.x; + else + return y < 0 ? 0.0 : INF.x; + } + /* if y even or odd */ + return (k == 1) ? __ieee754_pow (-x, y) : -__ieee754_pow (-x, y); } - else if (qx == 0x7ff00000) - { - if (k < 0) - return y < 0 ? nZERO.x : nINF.x; - else - return y < 0 ? 0.0 : INF.x; - } - return (k==1)?__ieee754_pow(-x,y):-__ieee754_pow(-x,y); /* if y even or odd */ - } /* x>0 */ - if (qx == 0x7ff00000) /* x= 2^-0x3ff */ + if (qx == 0x7ff00000) /* x= 2^-0x3ff */ return y > 0 ? x : 0; - if (qy > 0x45f00000 && qy < 0x7ff00000) { - if (x == 1.0) return 1.0; - if (y>0) return (x>1.0)?huge*huge:tiny*tiny; - if (y<0) return (x<1.0)?huge*huge:tiny*tiny; - } + if (qy > 0x45f00000 && qy < 0x7ff00000) + { + if (x == 1.0) + return 1.0; + if (y > 0) + return (x > 1.0) ? huge * huge : tiny * tiny; + if (y < 0) + return (x < 1.0) ? huge * huge : tiny * tiny; + } - if (x == 1.0) return 1.0; - if (y>0) return (x>1.0)?INF.x:0; - if (y<0) return (x<1.0)?INF.x:0; - return 0; /* unreachable, to make the compiler happy */ + if (x == 1.0) + return 1.0; + if (y > 0) + return (x > 1.0) ? INF.x : 0; + if (y < 0) + return (x < 1.0) ? INF.x : 0; + return 0; /* unreachable, to make the compiler happy */ } + #ifndef __ieee754_pow strong_alias (__ieee754_pow, __pow_finite) #endif -/**************************************************************************/ -/* Computing x^y using more accurate but more slow log routine */ -/**************************************************************************/ +/* Compute x^y using more accurate but more slow log routine. */ static double SECTION -power1(double x, double y) { - double z,a,aa,error, t,a1,a2,y1,y2; - z = my_log2(x,&aa,&error); - t = y*CN; - y1 = t - (t-y); +power1 (double x, double y) +{ + double z, a, aa, error, t, a1, a2, y1, y2; + z = my_log2 (x, &aa, &error); + t = y * CN; + y1 = t - (t - y); y2 = y - y1; - t = z*CN; - a1 = t - (t-z); + t = z * CN; + a1 = t - (t - z); a2 = z - a1; - a = y*z; - aa = ((y1*a1-a)+y1*a2+y2*a1)+y2*a2+aa*y; - a1 = a+aa; - a2 = (a-a1)+aa; - error = error*ABS(y); - t = __exp1(a1,a2,1.9e16*error); - return (t >= 0)?t:__slowpow(x,y,z); + a = y * z; + aa = ((y1 * a1 - a) + y1 * a2 + y2 * a1) + y2 * a2 + aa * y; + a1 = a + aa; + a2 = (a - a1) + aa; + error = error * ABS (y); + t = __exp1 (a1, a2, 1.9e16 * error); + return (t >= 0) ? t : __slowpow (x, y, z); } -/****************************************************************************/ -/* Computing log(x) (x is left argument). The result is the returned double */ -/* + the parameter delta. */ -/* The result is bounded by error (rightmost argument) */ -/****************************************************************************/ +/* Compute log(x) (x is left argument). The result is the returned double + the + parameter DELTA. The result is bounded by ERROR. */ static double SECTION -log1(double x, double *delta, double *error) { - int i,j,m; - double uu,vv,eps,nx,e,e1,e2,t,t1,t2,res,add=0; - mynumber u,v; +log1 (double x, double *delta, double *error) +{ + int i, j, m; + double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0; + mynumber u, v; #ifdef BIG_ENDI - mynumber -/**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */ + mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */ #else -#ifdef LITTLE_ENDI - mynumber -/**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */ -#endif +# ifdef LITTLE_ENDI + mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */ +# endif #endif u.x = x; m = u.i[HIGH_HALF]; *error = 0; *delta = 0; - if (m < 0x00100000) /* 1<x<2^-1007 */ - { x = x*t52.x; add = -52.0; u.x = x; m = u.i[HIGH_HALF];} + if (m < 0x00100000) /* 1<x<2^-1007 */ + { + x = x * t52.x; + add = -52.0; + u.x = x; + m = u.i[HIGH_HALF]; + } - if ((m&0x000fffff) < 0x0006a09e) - {u.i[HIGH_HALF] = (m&0x000fffff)|0x3ff00000; two52.i[LOW_HALF]=(m>>20); } + if ((m & 0x000fffff) < 0x0006a09e) + { + u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000; + two52.i[LOW_HALF] = (m >> 20); + } else - {u.i[HIGH_HALF] = (m&0x000fffff)|0x3fe00000; two52.i[LOW_HALF]=(m>>20)+1; } + { + u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000; + two52.i[LOW_HALF] = (m >> 20) + 1; + } v.x = u.x + bigu.x; uu = v.x - bigu.x; - i = (v.i[LOW_HALF]&0x000003ff)<<2; - if (two52.i[LOW_HALF] == 1023) /* nx = 0 */ - { - if (i > 1192 && i < 1208) /* |x-1| < 1.5*2**-10 */ - { + i = (v.i[LOW_HALF] & 0x000003ff) << 2; + if (two52.i[LOW_HALF] == 1023) /* nx = 0 */ + { + if (i > 1192 && i < 1208) /* |x-1| < 1.5*2**-10 */ + { t = x - 1.0; - t1 = (t+5.0e6)-5.0e6; - t2 = t-t1; - e1 = t - 0.5*t1*t1; - e2 = t*t*t*(r3+t*(r4+t*(r5+t*(r6+t*(r7+t*r8)))))-0.5*t2*(t+t1); - res = e1+e2; - *error = 1.0e-21*ABS(t); - *delta = (e1-res)+e2; + t1 = (t + 5.0e6) - 5.0e6; + t2 = t - t1; + e1 = t - 0.5 * t1 * t1; + e2 = (t * t * t * (r3 + t * (r4 + t * (r5 + t * (r6 + t + * (r7 + t * r8))))) + - 0.5 * t2 * (t + t1)); + res = e1 + e2; + *error = 1.0e-21 * ABS (t); + *delta = (e1 - res) + e2; return res; - } /* |x-1| < 1.5*2**-10 */ + } /* |x-1| < 1.5*2**-10 */ else - { - v.x = u.x*(ui.x[i]+ui.x[i+1])+bigv.x; - vv = v.x-bigv.x; - j = v.i[LOW_HALF]&0x0007ffff; - j = j+j+j; - eps = u.x - uu*vv; - e1 = eps*ui.x[i]; - e2 = eps*(ui.x[i+1]+vj.x[j]*(ui.x[i]+ui.x[i+1])); - e = e1+e2; - e2 = ((e1-e)+e2); - t=ui.x[i+2]+vj.x[j+1]; - t1 = t+e; - t2 = (((t-t1)+e)+(ui.x[i+3]+vj.x[j+2]))+e2+e*e*(p2+e*(p3+e*p4)); - res=t1+t2; + { + v.x = u.x * (ui.x[i] + ui.x[i + 1]) + bigv.x; + vv = v.x - bigv.x; + j = v.i[LOW_HALF] & 0x0007ffff; + j = j + j + j; + eps = u.x - uu * vv; + e1 = eps * ui.x[i]; + e2 = eps * (ui.x[i + 1] + vj.x[j] * (ui.x[i] + ui.x[i + 1])); + e = e1 + e2; + e2 = ((e1 - e) + e2); + t = ui.x[i + 2] + vj.x[j + 1]; + t1 = t + e; + t2 = ((((t - t1) + e) + (ui.x[i + 3] + vj.x[j + 2])) + e2 + e * e + * (p2 + e * (p3 + e * p4))); + res = t1 + t2; *error = 1.0e-24; - *delta = (t1-res)+t2; + *delta = (t1 - res) + t2; return res; - } - } /* nx = 0 */ - else /* nx != 0 */ - { + } + } /* nx = 0 */ + else /* nx != 0 */ + { eps = u.x - uu; - nx = (two52.x - two52e.x)+add; - e1 = eps*ui.x[i]; - e2 = eps*ui.x[i+1]; - e=e1+e2; - e2 = (e1-e)+e2; - t=nx*ln2a.x+ui.x[i+2]; - t1=t+e; - t2=(((t-t1)+e)+nx*ln2b.x+ui.x[i+3]+e2)+e*e*(q2+e*(q3+e*(q4+e*(q5+e*q6)))); - res = t1+t2; + nx = (two52.x - two52e.x) + add; + e1 = eps * ui.x[i]; + e2 = eps * ui.x[i + 1]; + e = e1 + e2; + e2 = (e1 - e) + e2; + t = nx * ln2a.x + ui.x[i + 2]; + t1 = t + e; + t2 = ((((t - t1) + e) + nx * ln2b.x + ui.x[i + 3] + e2) + e * e + * (q2 + e * (q3 + e * (q4 + e * (q5 + e * q6))))); + res = t1 + t2; *error = 1.0e-21; - *delta = (t1-res)+t2; + *delta = (t1 - res) + t2; return res; - } /* nx != 0 */ + } /* nx != 0 */ } -/****************************************************************************/ -/* More slow but more accurate routine of log */ -/* Computing log(x)(x is left argument).The result is return double + delta.*/ -/* The result is bounded by error (right argument) */ -/****************************************************************************/ +/* Slower but more accurate routine of log. The returned result is double + + DELTA. The result is bounded by ERROR. */ static double SECTION -my_log2(double x, double *delta, double *error) { - int i,j,m; - double uu,vv,eps,nx,e,e1,e2,t,t1,t2,res,add=0; - double ou1,ou2,lu1,lu2,ov,lv1,lv2,a,a1,a2; - double y,yy,z,zz,j1,j2,j7,j8; +my_log2 (double x, double *delta, double *error) +{ + int i, j, m; + double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0; + double ou1, ou2, lu1, lu2, ov, lv1, lv2, a, a1, a2; + double y, yy, z, zz, j1, j2, j7, j8; #ifndef DLA_FMS - double j3,j4,j5,j6; + double j3, j4, j5, j6; #endif - mynumber u,v; + mynumber u, v; #ifdef BIG_ENDI - mynumber -/**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */ + mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */ #else -#ifdef LITTLE_ENDI - mynumber -/**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */ -#endif +# ifdef LITTLE_ENDI + mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */ +# endif #endif u.x = x; m = u.i[HIGH_HALF]; *error = 0; *delta = 0; - add=0; - if (m<0x00100000) { /* x < 2^-1022 */ - x = x*t52.x; add = -52.0; u.x = x; m = u.i[HIGH_HALF]; } + add = 0; + if (m < 0x00100000) + { /* x < 2^-1022 */ + x = x * t52.x; + add = -52.0; + u.x = x; + m = u.i[HIGH_HALF]; + } - if ((m&0x000fffff) < 0x0006a09e) - {u.i[HIGH_HALF] = (m&0x000fffff)|0x3ff00000; two52.i[LOW_HALF]=(m>>20); } + if ((m & 0x000fffff) < 0x0006a09e) + { + u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000; + two52.i[LOW_HALF] = (m >> 20); + } else - {u.i[HIGH_HALF] = (m&0x000fffff)|0x3fe00000; two52.i[LOW_HALF]=(m>>20)+1; } + { + u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000; + two52.i[LOW_HALF] = (m >> 20) + 1; + } v.x = u.x + bigu.x; uu = v.x - bigu.x; - i = (v.i[LOW_HALF]&0x000003ff)<<2; + i = (v.i[LOW_HALF] & 0x000003ff) << 2; /*------------------------------------- |x-1| < 2**-11------------------------------- */ - if ((two52.i[LOW_HALF] == 1023) && (i == 1200)) - { + if ((two52.i[LOW_HALF] == 1023) && (i == 1200)) + { t = x - 1.0; - EMULV(t,s3,y,yy,j1,j2,j3,j4,j5); - ADD2(-0.5,0,y,yy,z,zz,j1,j2); - MUL2(t,0,z,zz,y,yy,j1,j2,j3,j4,j5,j6,j7,j8); - MUL2(t,0,y,yy,z,zz,j1,j2,j3,j4,j5,j6,j7,j8); + EMULV (t, s3, y, yy, j1, j2, j3, j4, j5); + ADD2 (-0.5, 0, y, yy, z, zz, j1, j2); + MUL2 (t, 0, z, zz, y, yy, j1, j2, j3, j4, j5, j6, j7, j8); + MUL2 (t, 0, y, yy, z, zz, j1, j2, j3, j4, j5, j6, j7, j8); - e1 = t+z; - e2 = (((t-e1)+z)+zz)+t*t*t*(ss3+t*(s4+t*(s5+t*(s6+t*(s7+t*s8))))); - res = e1+e2; - *error = 1.0e-25*ABS(t); - *delta = (e1-res)+e2; + e1 = t + z; + e2 = ((((t - e1) + z) + zz) + t * t * t + * (ss3 + t * (s4 + t * (s5 + t * (s6 + t * (s7 + t * s8)))))); + res = e1 + e2; + *error = 1.0e-25 * ABS (t); + *delta = (e1 - res) + e2; return res; - } + } /*----------------------------- |x-1| > 2**-11 -------------------------- */ else - { /*Computing log(x) according to log table */ - nx = (two52.x - two52e.x)+add; + { /*Computing log(x) according to log table */ + nx = (two52.x - two52e.x) + add; ou1 = ui.x[i]; - ou2 = ui.x[i+1]; - lu1 = ui.x[i+2]; - lu2 = ui.x[i+3]; - v.x = u.x*(ou1+ou2)+bigv.x; - vv = v.x-bigv.x; - j = v.i[LOW_HALF]&0x0007ffff; - j = j+j+j; - eps = u.x - uu*vv; - ov = vj.x[j]; - lv1 = vj.x[j+1]; - lv2 = vj.x[j+2]; - a = (ou1+ou2)*(1.0+ov); - a1 = (a+1.0e10)-1.0e10; - a2 = a*(1.0-a1*uu*vv); - e1 = eps*a1; - e2 = eps*a2; - e = e1+e2; - e2 = (e1-e)+e2; - t=nx*ln2a.x+lu1+lv1; - t1 = t+e; - t2 = (((t-t1)+e)+(lu2+lv2+nx*ln2b.x+e2))+e*e*(p2+e*(p3+e*p4)); - res=t1+t2; + ou2 = ui.x[i + 1]; + lu1 = ui.x[i + 2]; + lu2 = ui.x[i + 3]; + v.x = u.x * (ou1 + ou2) + bigv.x; + vv = v.x - bigv.x; + j = v.i[LOW_HALF] & 0x0007ffff; + j = j + j + j; + eps = u.x - uu * vv; + ov = vj.x[j]; + lv1 = vj.x[j + 1]; + lv2 = vj.x[j + 2]; + a = (ou1 + ou2) * (1.0 + ov); + a1 = (a + 1.0e10) - 1.0e10; + a2 = a * (1.0 - a1 * uu * vv); + e1 = eps * a1; + e2 = eps * a2; + e = e1 + e2; + e2 = (e1 - e) + e2; + t = nx * ln2a.x + lu1 + lv1; + t1 = t + e; + t2 = ((((t - t1) + e) + (lu2 + lv2 + nx * ln2b.x + e2)) + e * e + * (p2 + e * (p3 + e * p4))); + res = t1 + t2; *error = 1.0e-27; - *delta = (t1-res)+t2; + *delta = (t1 - res) + t2; return res; - } + } } -/**********************************************************************/ -/* Routine receives a double x and checks if it is an integer. If not */ -/* it returns 0, else it returns 1 if even or -1 if odd. */ -/**********************************************************************/ +/* This function receives a double x and checks if it is an integer. If not, + it returns 0, else it returns 1 if even or -1 if odd. */ static int SECTION -checkint(double x) { - union {int4 i[2]; double x;} u; - int k,m,n; +checkint (double x) +{ + union + { + int4 i[2]; + double x; + } u; + int k, m, n; u.x = x; - m = u.i[HIGH_HALF]&0x7fffffff; /* no sign */ - if (m >= 0x7ff00000) return 0; /* x is +/-inf or NaN */ - if (m >= 0x43400000) return 1; /* |x| >= 2**53 */ - if (m < 0x40000000) return 0; /* |x| < 2, can not be 0 or 1 */ + m = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */ + if (m >= 0x7ff00000) + return 0; /* x is +/-inf or NaN */ + if (m >= 0x43400000) + return 1; /* |x| >= 2**53 */ + if (m < 0x40000000) + return 0; /* |x| < 2, can not be 0 or 1 */ n = u.i[LOW_HALF]; - k = (m>>20)-1023; /* 1 <= k <= 52 */ - if (k == 52) return (n&1)? -1:1; /* odd or even*/ - if (k>20) { - if (n<<(k-20)) return 0; /* if not integer */ - return (n<<(k-21))?-1:1; - } - if (n) return 0; /*if not integer*/ - if (k == 20) return (m&1)? -1:1; - if (m<<(k+12)) return 0; - return (m<<(k+11))?-1:1; + k = (m >> 20) - 1023; /* 1 <= k <= 52 */ + if (k == 52) + return (n & 1) ? -1 : 1; /* odd or even */ + if (k > 20) + { + if (n << (k - 20)) + return 0; /* if not integer */ + return (n << (k - 21)) ? -1 : 1; + } + if (n) + return 0; /*if not integer */ + if (k == 20) + return (m & 1) ? -1 : 1; + if (m << (k + 12)) + return 0; + return (m << (k + 11)) ? -1 : 1; } |