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-rw-r--r--libm/s_expm1.c48
1 files changed, 24 insertions, 24 deletions
diff --git a/libm/s_expm1.c b/libm/s_expm1.c
index 5e7e9d84f..aee70835b 100644
--- a/libm/s_expm1.c
+++ b/libm/s_expm1.c
@@ -5,7 +5,7 @@
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
+ * software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
@@ -21,9 +21,9 @@ static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $";
* 1. Argument reduction:
* Given x, find r and integer k such that
*
- * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658
+ * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658
*
- * Here a correction term c will be computed to compensate
+ * Here a correction term c will be computed to compensate
* the error in r when rounded to a floating-point number.
*
* 2. Approximating expm1(r) by a special rational function on
@@ -36,9 +36,9 @@ static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $";
* R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
* = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
* = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
- * We use a special Reme algorithm on [0,0.347] to generate
- * a polynomial of degree 5 in r*r to approximate R1. The
- * maximum error of this polynomial approximation is bounded
+ * We use a special Reme algorithm on [0,0.347] to generate
+ * a polynomial of degree 5 in r*r to approximate R1. The
+ * maximum error of this polynomial approximation is bounded
* by 2**-61. In other words,
* R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
* where Q1 = -1.6666666666666567384E-2,
@@ -49,28 +49,28 @@ static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $";
* (where z=r*r, and the values of Q1 to Q5 are listed below)
* with error bounded by
* | 5 | -61
- * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
+ * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
* | |
- *
- * expm1(r) = exp(r)-1 is then computed by the following
- * specific way which minimize the accumulation rounding error:
+ *
+ * expm1(r) = exp(r)-1 is then computed by the following
+ * specific way which minimize the accumulation rounding error:
* 2 3
* r r [ 3 - (R1 + R1*r/2) ]
* expm1(r) = r + --- + --- * [--------------------]
* 2 2 [ 6 - r*(3 - R1*r/2) ]
- *
+ *
* To compensate the error in the argument reduction, we use
- * expm1(r+c) = expm1(r) + c + expm1(r)*c
- * ~ expm1(r) + c + r*c
+ * expm1(r+c) = expm1(r) + c + expm1(r)*c
+ * ~ expm1(r) + c + r*c
* Thus c+r*c will be added in as the correction terms for
- * expm1(r+c). Now rearrange the term to avoid optimization
+ * expm1(r+c). Now rearrange the term to avoid optimization
* screw up:
* ( 2 2 )
* ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
* expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
* ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
* ( )
- *
+ *
* = r - E
* 3. Scale back to obtain expm1(x):
* From step 1, we have
@@ -87,7 +87,7 @@ static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $";
* else return 1.0+2.0*(r-E);
* (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
* (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
- * (vii) return 2^k(1-((E+2^-k)-r))
+ * (vii) return 2^k(1-((E+2^-k)-r))
*
* Special cases:
* expm1(INF) is INF, expm1(NaN) is NaN;
@@ -99,12 +99,12 @@ static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $";
* 1 ulp (unit in the last place).
*
* Misc. info.
- * For IEEE double
+ * For IEEE double
* if x > 7.09782712893383973096e+02 then expm1(x) overflow
*
* Constants:
- * The hexadecimal values are the intended ones for the following
- * constants. The decimal values may be used, provided that the
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
@@ -153,7 +153,7 @@ Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
if(hx>=0x7ff00000) {
u_int32_t low;
GET_LOW_WORD(low,x);
- if(((hx&0xfffff)|low)!=0)
+ if(((hx&0xfffff)|low)!=0)
return x+x; /* NaN */
else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
}
@@ -166,7 +166,7 @@ Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
}
/* argument reduction */
- if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
+ 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;}
@@ -180,10 +180,10 @@ Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
}
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));
+ return x - (t-(huge+x));
}
else k = 0;
@@ -198,7 +198,7 @@ Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
e = (x*(e-c)-c);
e -= hxs;
if(k== -1) return 0.5*(x-e)-0.5;
- if(k==1) {
+ if(k==1) {
if(x < -0.25) return -2.0*(e-(x+0.5));
else return one+2.0*(x-e);
}