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-rw-r--r--sysdeps/ieee754/dbl-64/s_expm1.c227
1 files changed, 126 insertions, 101 deletions
diff --git a/sysdeps/ieee754/dbl-64/s_expm1.c b/sysdeps/ieee754/dbl-64/s_expm1.c
index 1a4bcd979a..9c9bb34559 100644
--- a/sysdeps/ieee754/dbl-64/s_expm1.c
+++ b/sysdeps/ieee754/dbl-64/s_expm1.c
@@ -11,7 +11,7 @@
*/
/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25,
for performance improvement on pipelined processors.
-*/
+ */
/* expm1(x)
* Returns exp(x)-1, the exponential of x minus 1.
@@ -113,120 +113,145 @@
#include <math_private.h>
#define one Q[0]
static const double
-huge = 1.0e+300,
-tiny = 1.0e-300,
-o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
-ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */
-ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */
-invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
- /* scaled coefficients related to expm1 */
-Q[] = {1.0, -3.33333333333331316428e-02, /* BFA11111 111110F4 */
- 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
- -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
- 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
- -2.01099218183624371326e-07}; /* BE8AFDB7 6E09C32D */
+ huge = 1.0e+300,
+ tiny = 1.0e-300,
+ o_threshold = 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
+ ln2_hi = 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
+ ln2_lo = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
+ invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
+/* scaled coefficients related to expm1 */
+ Q[] = { 1.0, -3.33333333333331316428e-02, /* BFA11111 111110F4 */
+ 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
+ -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
+ 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
+ -2.01099218183624371326e-07 }; /* BE8AFDB7 6E09C32D */
double
-__expm1(double x)
+__expm1 (double x)
{
- double y,hi,lo,c,t,e,hxs,hfx,r1,h2,h4,R1,R2,R3;
- int32_t k,xsb;
- u_int32_t hx;
+ double y, hi, lo, c, t, e, hxs, hfx, r1, h2, h4, R1, R2, R3;
+ int32_t k, xsb;
+ u_int32_t hx;
- GET_HIGH_WORD(hx,x);
- xsb = hx&0x80000000; /* sign bit of x */
- if(xsb==0) y=x; else y= -x; /* y = |x| */
- hx &= 0x7fffffff; /* high word of |x| */
+ GET_HIGH_WORD (hx, x);
+ xsb = hx & 0x80000000; /* sign bit of x */
+ if (xsb == 0)
+ y = x;
+ else
+ y = -x; /* y = |x| */
+ hx &= 0x7fffffff; /* high word of |x| */
- /* filter out huge and non-finite argument */
- if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */
- if(hx >= 0x40862E42) { /* if |x|>=709.78... */
- if(hx>=0x7ff00000) {
- u_int32_t low;
- GET_LOW_WORD(low,x);
- if(((hx&0xfffff)|low)!=0)
- return x+x; /* NaN */
- else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
- }
- if(x > o_threshold) {
- __set_errno (ERANGE);
- return huge*huge; /* overflow */
- }
+ /* filter out huge and non-finite argument */
+ if (hx >= 0x4043687A) /* if |x|>=56*ln2 */
+ {
+ if (hx >= 0x40862E42) /* if |x|>=709.78... */
+ {
+ if (hx >= 0x7ff00000)
+ {
+ u_int32_t low;
+ GET_LOW_WORD (low, x);
+ if (((hx & 0xfffff) | low) != 0)
+ return x + x; /* NaN */
+ else
+ return (xsb == 0) ? x : -1.0; /* exp(+-inf)={inf,-1} */
}
- if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
- math_force_eval(x+tiny); /* raise inexact */
- return tiny-one; /* return -1 */
+ if (x > o_threshold)
+ {
+ __set_errno (ERANGE);
+ return huge * huge; /* overflow */
}
}
+ if (xsb != 0) /* x < -56*ln2, return -1.0 with inexact */
+ {
+ math_force_eval (x + tiny); /* raise inexact */
+ return tiny - one; /* return -1 */
+ }
+ }
- /* argument reduction */
- if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
- if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
- if(xsb==0)
- {hi = x - ln2_hi; lo = ln2_lo; k = 1;}
- else
- {hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
- } else {
- k = invln2*x+((xsb==0)?0.5:-0.5);
- t = k;
- hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
- lo = t*ln2_lo;
+ /* argument reduction */
+ if (hx > 0x3fd62e42) /* if |x| > 0.5 ln2 */
+ {
+ if (hx < 0x3FF0A2B2) /* and |x| < 1.5 ln2 */
+ {
+ if (xsb == 0)
+ {
+ hi = x - ln2_hi; lo = ln2_lo; k = 1;
+ }
+ else
+ {
+ hi = x + ln2_hi; lo = -ln2_lo; k = -1;
}
- x = hi - lo;
- c = (hi-x)-lo;
}
- else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */
- t = huge+x; /* return x with inexact flags when x!=0 */
- return x - (t-(huge+x));
+ else
+ {
+ k = invln2 * x + ((xsb == 0) ? 0.5 : -0.5);
+ t = k;
+ hi = x - t * ln2_hi; /* t*ln2_hi is exact here */
+ lo = t * ln2_lo;
}
- else k = 0;
+ x = hi - lo;
+ c = (hi - x) - lo;
+ }
+ else if (hx < 0x3c900000) /* when |x|<2**-54, return x */
+ {
+ t = huge + x; /* return x with inexact flags when x!=0 */
+ return x - (t - (huge + x));
+ }
+ else
+ k = 0;
- /* x is now in primary range */
- hfx = 0.5*x;
- hxs = x*hfx;
-#ifdef DO_NOT_USE_THIS
- r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
-#else
- R1 = one+hxs*Q[1]; h2 = hxs*hxs;
- R2 = Q[2]+hxs*Q[3]; h4 = h2*h2;
- R3 = Q[4]+hxs*Q[5];
- r1 = R1 + h2*R2 + h4*R3;
-#endif
- t = 3.0-r1*hfx;
- e = hxs*((r1-t)/(6.0 - x*t));
- if(k==0) return x - (x*e-hxs); /* c is 0 */
- else {
- e = (x*(e-c)-c);
- e -= hxs;
- if(k== -1) return 0.5*(x-e)-0.5;
- if(k==1) {
- if(x < -0.25) return -2.0*(e-(x+0.5));
- else return one+2.0*(x-e);
- }
- if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
- u_int32_t high;
- y = one-(e-x);
- GET_HIGH_WORD(high,y);
- SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
- return y-one;
- }
- t = one;
- if(k<20) {
- u_int32_t high;
- SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */
- y = t-(e-x);
- GET_HIGH_WORD(high,y);
- SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
- } else {
- u_int32_t high;
- SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */
- y = x-(e+t);
- y += one;
- GET_HIGH_WORD(high,y);
- SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
- }
+ /* x is now in primary range */
+ hfx = 0.5 * x;
+ hxs = x * hfx;
+ R1 = one + hxs * Q[1]; h2 = hxs * hxs;
+ R2 = Q[2] + hxs * Q[3]; h4 = h2 * h2;
+ R3 = Q[4] + hxs * Q[5];
+ r1 = R1 + h2 * R2 + h4 * R3;
+ t = 3.0 - r1 * hfx;
+ e = hxs * ((r1 - t) / (6.0 - x * t));
+ if (k == 0)
+ return x - (x * e - hxs); /* c is 0 */
+ else
+ {
+ e = (x * (e - c) - c);
+ e -= hxs;
+ if (k == -1)
+ return 0.5 * (x - e) - 0.5;
+ if (k == 1)
+ {
+ if (x < -0.25)
+ return -2.0 * (e - (x + 0.5));
+ else
+ return one + 2.0 * (x - e);
+ }
+ if (k <= -2 || k > 56) /* suffice to return exp(x)-1 */
+ {
+ u_int32_t high;
+ y = one - (e - x);
+ GET_HIGH_WORD (high, y);
+ SET_HIGH_WORD (y, high + (k << 20)); /* add k to y's exponent */
+ return y - one;
+ }
+ t = one;
+ if (k < 20)
+ {
+ u_int32_t high;
+ SET_HIGH_WORD (t, 0x3ff00000 - (0x200000 >> k)); /* t=1-2^-k */
+ y = t - (e - x);
+ GET_HIGH_WORD (high, y);
+ SET_HIGH_WORD (y, high + (k << 20)); /* add k to y's exponent */
+ }
+ else
+ {
+ u_int32_t high;
+ SET_HIGH_WORD (t, ((0x3ff - k) << 20)); /* 2^-k */
+ y = x - (e + t);
+ y += one;
+ GET_HIGH_WORD (high, y);
+ SET_HIGH_WORD (y, high + (k << 20)); /* add k to y's exponent */
}
- return y;
+ }
+ return y;
}
weak_alias (__expm1, expm1)
#ifdef NO_LONG_DOUBLE
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