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Format e_pow.c
This commit is contained in:
Siddhesh Poyarekar
parent
e7b2d1dd62
commit
885766357d
@ -1,5 +1,7 @@
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2013-10-08 Siddhesh Poyarekar <siddhesh@redhat.com>
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* sysdeps/ieee754/dbl-64/e_pow.c: Fix code formatting.
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* sysdeps/ieee754/dbl-64/e_exp.c: Fix code formatting.
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* sysdeps/generic/math_private.h (__mpsin1): Remove
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@ -49,354 +49,407 @@
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static const double huge = 1.0e300, tiny = 1.0e-300;
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double __exp1(double x, double xx, double error);
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static double log1(double x, double *delta, double *error);
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static double my_log2(double x, double *delta, double *error);
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double __slowpow(double x, double y,double z);
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static double power1(double x, double y);
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static int checkint(double x);
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double __exp1 (double x, double xx, double error);
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static double log1 (double x, double *delta, double *error);
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static double my_log2 (double x, double *delta, double *error);
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double __slowpow (double x, double y, double z);
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static double power1 (double x, double y);
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static int checkint (double x);
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/***************************************************************************/
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/* An ultimate power routine. Given two IEEE double machine numbers y,x */
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/* it computes the correctly rounded (to nearest) value of X^y. */
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/***************************************************************************/
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/* An ultimate power routine. Given two IEEE double machine numbers y, x it
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computes the correctly rounded (to nearest) value of X^y. */
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double
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SECTION
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__ieee754_pow(double x, double y) {
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double z,a,aa,error, t,a1,a2,y1,y2;
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mynumber u,v;
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__ieee754_pow (double x, double y)
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{
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double z, a, aa, error, t, a1, a2, y1, y2;
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mynumber u, v;
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int k;
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int4 qx,qy;
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v.x=y;
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u.x=x;
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if (v.i[LOW_HALF] == 0) { /* of y */
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qx = u.i[HIGH_HALF]&0x7fffffff;
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/* Is x a NaN? */
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if (((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000))
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return x;
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if (y == 1.0) return x;
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if (y == 2.0) return x*x;
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if (y == -1.0) return 1.0/x;
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if (y == 0) return 1.0;
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}
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int4 qx, qy;
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v.x = y;
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u.x = x;
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if (v.i[LOW_HALF] == 0)
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{ /* of y */
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qx = u.i[HIGH_HALF] & 0x7fffffff;
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/* Is x a NaN? */
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if (((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000))
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return x;
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if (y == 1.0)
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return x;
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if (y == 2.0)
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return x * x;
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if (y == -1.0)
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return 1.0 / x;
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if (y == 0)
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return 1.0;
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}
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/* else */
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if(((u.i[HIGH_HALF]>0 && u.i[HIGH_HALF]<0x7ff00000)|| /* x>0 and not x->0 */
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(u.i[HIGH_HALF]==0 && u.i[LOW_HALF]!=0)) &&
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/* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */
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(v.i[HIGH_HALF]&0x7fffffff) < 0x4ff00000) { /* if y<-1 or y>1 */
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double retval;
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if (((u.i[HIGH_HALF] > 0 && u.i[HIGH_HALF] < 0x7ff00000) || /* x>0 and not x->0 */
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(u.i[HIGH_HALF] == 0 && u.i[LOW_HALF] != 0)) &&
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/* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */
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(v.i[HIGH_HALF] & 0x7fffffff) < 0x4ff00000)
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{ /* if y<-1 or y>1 */
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double retval;
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SET_RESTORE_ROUND (FE_TONEAREST);
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SET_RESTORE_ROUND (FE_TONEAREST);
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/* Avoid internal underflow for tiny y. The exact value of y does
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not matter if |y| <= 2**-64. */
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if (ABS (y) < 0x1p-64)
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y = y < 0 ? -0x1p-64 : 0x1p-64;
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z = log1(x,&aa,&error); /* x^y =e^(y log (X)) */
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t = y*CN;
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y1 = t - (t-y);
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y2 = y - y1;
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t = z*CN;
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a1 = t - (t-z);
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a2 = (z - a1)+aa;
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a = y1*a1;
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aa = y2*a1 + y*a2;
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a1 = a+aa;
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a2 = (a-a1)+aa;
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error = error*ABS(y);
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t = __exp1(a1,a2,1.9e16*error); /* return -10 or 0 if wasn't computed exactly */
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retval = (t>0)?t:power1(x,y);
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/* Avoid internal underflow for tiny y. The exact value of y does
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not matter if |y| <= 2**-64. */
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if (ABS (y) < 0x1p-64)
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y = y < 0 ? -0x1p-64 : 0x1p-64;
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z = log1 (x, &aa, &error); /* x^y =e^(y log (X)) */
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t = y * CN;
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y1 = t - (t - y);
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y2 = y - y1;
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t = z * CN;
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a1 = t - (t - z);
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a2 = (z - a1) + aa;
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a = y1 * a1;
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aa = y2 * a1 + y * a2;
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a1 = a + aa;
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a2 = (a - a1) + aa;
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error = error * ABS (y);
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t = __exp1 (a1, a2, 1.9e16 * error); /* return -10 or 0 if wasn't computed exactly */
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retval = (t > 0) ? t : power1 (x, y);
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return retval;
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}
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return retval;
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}
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if (x == 0) {
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if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0)
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|| (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */
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return y;
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if (ABS(y) > 1.0e20) return (y>0)?0:1.0/0.0;
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k = checkint(y);
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if (k == -1)
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return y < 0 ? 1.0/x : x;
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else
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return y < 0 ? 1.0/0.0 : 0.0; /* return 0 */
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}
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if (x == 0)
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{
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if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0)
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|| (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */
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return y;
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if (ABS (y) > 1.0e20)
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return (y > 0) ? 0 : 1.0 / 0.0;
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k = checkint (y);
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if (k == -1)
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return y < 0 ? 1.0 / x : x;
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else
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return y < 0 ? 1.0 / 0.0 : 0.0; /* return 0 */
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}
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qx = u.i[HIGH_HALF]&0x7fffffff; /* no sign */
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qy = v.i[HIGH_HALF]&0x7fffffff; /* no sign */
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qx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */
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qy = v.i[HIGH_HALF] & 0x7fffffff; /* no sign */
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if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) /* NaN */
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if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) /* NaN */
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return x;
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if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0)) /* NaN */
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if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0)) /* NaN */
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return x == 1.0 ? 1.0 : y;
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/* if x<0 */
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if (u.i[HIGH_HALF] < 0) {
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k = checkint(y);
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if (k==0) {
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if (qy == 0x7ff00000) {
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if (x == -1.0) return 1.0;
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else if (x > -1.0) return v.i[HIGH_HALF] < 0 ? INF.x : 0.0;
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else return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x;
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}
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if (u.i[HIGH_HALF] < 0)
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{
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k = checkint (y);
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if (k == 0)
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{
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if (qy == 0x7ff00000)
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{
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if (x == -1.0)
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return 1.0;
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else if (x > -1.0)
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return v.i[HIGH_HALF] < 0 ? INF.x : 0.0;
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else
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return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x;
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}
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else if (qx == 0x7ff00000)
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return y < 0 ? 0.0 : INF.x;
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return (x - x) / (x - x); /* y not integer and x<0 */
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}
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else if (qx == 0x7ff00000)
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return y < 0 ? 0.0 : INF.x;
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return (x - x) / (x - x); /* y not integer and x<0 */
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{
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if (k < 0)
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return y < 0 ? nZERO.x : nINF.x;
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else
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return y < 0 ? 0.0 : INF.x;
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}
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/* if y even or odd */
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return (k == 1) ? __ieee754_pow (-x, y) : -__ieee754_pow (-x, y);
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}
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else if (qx == 0x7ff00000)
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{
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if (k < 0)
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return y < 0 ? nZERO.x : nINF.x;
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else
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return y < 0 ? 0.0 : INF.x;
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}
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return (k==1)?__ieee754_pow(-x,y):-__ieee754_pow(-x,y); /* if y even or odd */
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}
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/* x>0 */
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if (qx == 0x7ff00000) /* x= 2^-0x3ff */
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if (qx == 0x7ff00000) /* x= 2^-0x3ff */
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return y > 0 ? x : 0;
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if (qy > 0x45f00000 && qy < 0x7ff00000) {
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if (x == 1.0) return 1.0;
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if (y>0) return (x>1.0)?huge*huge:tiny*tiny;
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if (y<0) return (x<1.0)?huge*huge:tiny*tiny;
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}
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if (qy > 0x45f00000 && qy < 0x7ff00000)
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{
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if (x == 1.0)
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return 1.0;
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if (y > 0)
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return (x > 1.0) ? huge * huge : tiny * tiny;
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if (y < 0)
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return (x < 1.0) ? huge * huge : tiny * tiny;
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}
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if (x == 1.0) return 1.0;
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if (y>0) return (x>1.0)?INF.x:0;
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if (y<0) return (x<1.0)?INF.x:0;
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return 0; /* unreachable, to make the compiler happy */
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if (x == 1.0)
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return 1.0;
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if (y > 0)
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return (x > 1.0) ? INF.x : 0;
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if (y < 0)
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return (x < 1.0) ? INF.x : 0;
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return 0; /* unreachable, to make the compiler happy */
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}
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#ifndef __ieee754_pow
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strong_alias (__ieee754_pow, __pow_finite)
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#endif
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/**************************************************************************/
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/* Computing x^y using more accurate but more slow log routine */
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/**************************************************************************/
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/* Compute x^y using more accurate but more slow log routine. */
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static double
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SECTION
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power1(double x, double y) {
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double z,a,aa,error, t,a1,a2,y1,y2;
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z = my_log2(x,&aa,&error);
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t = y*CN;
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y1 = t - (t-y);
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power1 (double x, double y)
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{
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double z, a, aa, error, t, a1, a2, y1, y2;
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z = my_log2 (x, &aa, &error);
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t = y * CN;
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y1 = t - (t - y);
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y2 = y - y1;
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t = z*CN;
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a1 = t - (t-z);
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t = z * CN;
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a1 = t - (t - z);
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a2 = z - a1;
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a = y*z;
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aa = ((y1*a1-a)+y1*a2+y2*a1)+y2*a2+aa*y;
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a1 = a+aa;
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a2 = (a-a1)+aa;
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error = error*ABS(y);
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t = __exp1(a1,a2,1.9e16*error);
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return (t >= 0)?t:__slowpow(x,y,z);
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a = y * z;
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aa = ((y1 * a1 - a) + y1 * a2 + y2 * a1) + y2 * a2 + aa * y;
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a1 = a + aa;
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a2 = (a - a1) + aa;
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error = error * ABS (y);
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t = __exp1 (a1, a2, 1.9e16 * error);
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return (t >= 0) ? t : __slowpow (x, y, z);
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}
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/****************************************************************************/
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/* Computing log(x) (x is left argument). The result is the returned double */
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/* + the parameter delta. */
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/* The result is bounded by error (rightmost argument) */
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/****************************************************************************/
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/* Compute log(x) (x is left argument). The result is the returned double + the
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parameter DELTA. The result is bounded by ERROR. */
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static double
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SECTION
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log1(double x, double *delta, double *error) {
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int i,j,m;
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double uu,vv,eps,nx,e,e1,e2,t,t1,t2,res,add=0;
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mynumber u,v;
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log1 (double x, double *delta, double *error)
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{
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int i, j, m;
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double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0;
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mynumber u, v;
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#ifdef BIG_ENDI
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mynumber
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/**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */
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mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */
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#else
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#ifdef LITTLE_ENDI
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mynumber
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/**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */
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#endif
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# ifdef LITTLE_ENDI
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mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */
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# endif
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#endif
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u.x = x;
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m = u.i[HIGH_HALF];
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*error = 0;
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*delta = 0;
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if (m < 0x00100000) /* 1<x<2^-1007 */
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{ x = x*t52.x; add = -52.0; u.x = x; m = u.i[HIGH_HALF];}
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if (m < 0x00100000) /* 1<x<2^-1007 */
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{
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x = x * t52.x;
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add = -52.0;
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u.x = x;
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m = u.i[HIGH_HALF];
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}
|
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if ((m&0x000fffff) < 0x0006a09e)
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{u.i[HIGH_HALF] = (m&0x000fffff)|0x3ff00000; two52.i[LOW_HALF]=(m>>20); }
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if ((m & 0x000fffff) < 0x0006a09e)
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{
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u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000;
|
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two52.i[LOW_HALF] = (m >> 20);
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}
|
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else
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{u.i[HIGH_HALF] = (m&0x000fffff)|0x3fe00000; two52.i[LOW_HALF]=(m>>20)+1; }
|
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{
|
||||
u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000;
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two52.i[LOW_HALF] = (m >> 20) + 1;
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}
|
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v.x = u.x + bigu.x;
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uu = v.x - bigu.x;
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i = (v.i[LOW_HALF]&0x000003ff)<<2;
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if (two52.i[LOW_HALF] == 1023) /* nx = 0 */
|
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{
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if (i > 1192 && i < 1208) /* |x-1| < 1.5*2**-10 */
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||||
{
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i = (v.i[LOW_HALF] & 0x000003ff) << 2;
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if (two52.i[LOW_HALF] == 1023) /* nx = 0 */
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{
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if (i > 1192 && i < 1208) /* |x-1| < 1.5*2**-10 */
|
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{
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t = x - 1.0;
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t1 = (t+5.0e6)-5.0e6;
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t2 = t-t1;
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e1 = t - 0.5*t1*t1;
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e2 = t*t*t*(r3+t*(r4+t*(r5+t*(r6+t*(r7+t*r8)))))-0.5*t2*(t+t1);
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res = e1+e2;
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*error = 1.0e-21*ABS(t);
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*delta = (e1-res)+e2;
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t1 = (t + 5.0e6) - 5.0e6;
|
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t2 = t - t1;
|
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e1 = t - 0.5 * t1 * t1;
|
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e2 = (t * t * t * (r3 + t * (r4 + t * (r5 + t * (r6 + t
|
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* (r7 + t * r8)))))
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- 0.5 * t2 * (t + t1));
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res = e1 + e2;
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*error = 1.0e-21 * ABS (t);
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*delta = (e1 - res) + e2;
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return res;
|
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} /* |x-1| < 1.5*2**-10 */
|
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} /* |x-1| < 1.5*2**-10 */
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else
|
||||
{
|
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v.x = u.x*(ui.x[i]+ui.x[i+1])+bigv.x;
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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;
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user