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-rw-r--r--lib/libm/common_source/acosh.c10
-rw-r--r--lib/libm/common_source/asincos.c38
-rw-r--r--lib/libm/common_source/asinh.c12
-rw-r--r--lib/libm/common_source/atan.c18
-rw-r--r--lib/libm/common_source/atanh.c4
-rw-r--r--lib/libm/common_source/cosh.c26
-rw-r--r--lib/libm/common_source/erf.c16
-rw-r--r--lib/libm/common_source/exp.c20
-rw-r--r--lib/libm/common_source/exp__E.c10
-rw-r--r--lib/libm/common_source/expm1.c32
-rw-r--r--lib/libm/common_source/j0.c28
-rw-r--r--lib/libm/common_source/j1.c32
-rw-r--r--lib/libm/common_source/jn.c44
-rw-r--r--lib/libm/common_source/log.c2
-rw-r--r--lib/libm/common_source/log10.c10
-rw-r--r--lib/libm/common_source/log1p.c30
-rw-r--r--lib/libm/common_source/log__L.c12
-rw-r--r--lib/libm/common_source/pow.c20
-rw-r--r--lib/libm/common_source/sinh.c8
-rw-r--r--lib/libm/common_source/tanh.c4
20 files changed, 188 insertions, 188 deletions
diff --git a/lib/libm/common_source/acosh.c b/lib/libm/common_source/acosh.c
index bc16cc7b46a8..149e5deec1e0 100644
--- a/lib/libm/common_source/acosh.c
+++ b/lib/libm/common_source/acosh.c
@@ -48,10 +48,10 @@ static char sccsid[] = "@(#)acosh.c 8.1 (Berkeley) 6/4/93";
* log1p(x) ...return log(1+x)
*
* Method :
- * Based on
+ * Based on
* acosh(x) = log [ x + sqrt(x*x-1) ]
* we have
- * acosh(x) := log1p(x)+ln2, if (x > 1.0E20); else
+ * acosh(x) := log1p(x)+ln2, if (x > 1.0E20); else
* acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
* These formulae avoid the over/underflow complication.
*
@@ -60,7 +60,7 @@ static char sccsid[] = "@(#)acosh.c 8.1 (Berkeley) 6/4/93";
* acosh(NaN) is NaN without signal.
*
* Accuracy:
- * acosh(x) returns the exact inverse hyperbolic cosine of x nearly
+ * acosh(x) returns the exact inverse hyperbolic cosine of x nearly
* rounded. In a test run with 512,000 random arguments on a VAX, the
* maximum observed error was 3.30 ulps (units of the last place) at
* x=1.0070493753568216 .
@@ -87,7 +87,7 @@ ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)
double acosh(x)
double x;
-{
+{
double t,big=1.E20; /* big+1==big */
#if !defined(vax)&&!defined(tahoe)
@@ -95,7 +95,7 @@ double x;
#endif /* !defined(vax)&&!defined(tahoe) */
/* return log1p(x) + log(2) if x is large */
- if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);}
+ if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);}
t=sqrt(x-1.0);
return(log1p(t*(t+sqrt(x+1.0))));
diff --git a/lib/libm/common_source/asincos.c b/lib/libm/common_source/asincos.c
index c746b1652ac2..12d0e14e1ae3 100644
--- a/lib/libm/common_source/asincos.c
+++ b/lib/libm/common_source/asincos.c
@@ -45,12 +45,12 @@ static char sccsid[] = "@(#)asincos.c 8.1 (Berkeley) 6/4/93";
* sqrt(x)
*
* Required kernel function:
- * atan2(y,x)
+ * atan2(y,x)
*
- * Method :
- * asin(x) = atan2(x,sqrt(1-x*x)); for better accuracy, 1-x*x is
+ * Method :
+ * asin(x) = atan2(x,sqrt(1-x*x)); for better accuracy, 1-x*x is
* computed as follows
- * 1-x*x if x < 0.5,
+ * 1-x*x if x < 0.5,
* 2*(1-|x|)-(1-|x|)*(1-|x|) if x >= 0.5.
*
* Special cases:
@@ -59,22 +59,22 @@ static char sccsid[] = "@(#)asincos.c 8.1 (Berkeley) 6/4/93";
*
* Accuracy:
* 1) If atan2() uses machine PI, then
- *
+ *
* asin(x) returns (PI/pi) * (the exact arc sine of x) nearly rounded;
* and PI is the exact pi rounded to machine precision (see atan2 for
* details):
*
* in decimal:
- * pi = 3.141592653589793 23846264338327 .....
+ * pi = 3.141592653589793 23846264338327 .....
* 53 bits PI = 3.141592653589793 115997963 ..... ,
- * 56 bits PI = 3.141592653589793 227020265 ..... ,
+ * 56 bits PI = 3.141592653589793 227020265 ..... ,
*
* in hexadecimal:
* pi = 3.243F6A8885A308D313198A2E....
* 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps
* 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps
- *
- * In a test run with more than 200,000 random arguments on a VAX, the
+ *
+ * In a test run with more than 200,000 random arguments on a VAX, the
* maximum observed error in ulps (units in the last place) was
* 2.06 ulps. (comparing against (PI/pi)*(exact asin(x)));
*
@@ -82,7 +82,7 @@ static char sccsid[] = "@(#)asincos.c 8.1 (Berkeley) 6/4/93";
*
* asin(x) returns the exact asin(x) with error below about 2 ulps.
*
- * In a test run with more than 1,024,000 random arguments on a VAX, the
+ * In a test run with more than 1,024,000 random arguments on a VAX, the
* maximum observed error in ulps (units in the last place) was
* 1.99 ulps.
*/
@@ -97,7 +97,7 @@ double x;
s=copysign(x,one);
if(s <= 0.5)
return(atan2(x,sqrt(one-x*x)));
- else
+ else
{ t=one-s; s=t+t; return(atan2(x,sqrt(s-t*t))); }
}
@@ -112,9 +112,9 @@ double x;
* sqrt(x)
*
* Required kernel function:
- * atan2(y,x)
+ * atan2(y,x)
*
- * Method :
+ * Method :
* ________
* / 1 - x
* acos(x) = 2*atan2( / -------- , 1 ) .
@@ -126,22 +126,22 @@ double x;
*
* Accuracy:
* 1) If atan2() uses machine PI, then
- *
+ *
* acos(x) returns (PI/pi) * (the exact arc cosine of x) nearly rounded;
* and PI is the exact pi rounded to machine precision (see atan2 for
* details):
*
* in decimal:
- * pi = 3.141592653589793 23846264338327 .....
+ * pi = 3.141592653589793 23846264338327 .....
* 53 bits PI = 3.141592653589793 115997963 ..... ,
- * 56 bits PI = 3.141592653589793 227020265 ..... ,
+ * 56 bits PI = 3.141592653589793 227020265 ..... ,
*
* in hexadecimal:
* pi = 3.243F6A8885A308D313198A2E....
* 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps
* 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps
- *
- * In a test run with more than 200,000 random arguments on a VAX, the
+ *
+ * In a test run with more than 200,000 random arguments on a VAX, the
* maximum observed error in ulps (units in the last place) was
* 2.07 ulps. (comparing against (PI/pi)*(exact acos(x)));
*
@@ -149,7 +149,7 @@ double x;
*
* acos(x) returns the exact acos(x) with error below about 2 ulps.
*
- * In a test run with more than 1,024,000 random arguments on a VAX, the
+ * In a test run with more than 1,024,000 random arguments on a VAX, the
* maximum observed error in ulps (units in the last place) was
* 2.15 ulps.
*/
diff --git a/lib/libm/common_source/asinh.c b/lib/libm/common_source/asinh.c
index 5db8d2ddf7f8..1804145e3a93 100644
--- a/lib/libm/common_source/asinh.c
+++ b/lib/libm/common_source/asinh.c
@@ -49,16 +49,16 @@ static char sccsid[] = "@(#)asinh.c 8.1 (Berkeley) 6/4/93";
* log1p(x) ...return log(1+x)
*
* Method :
- * Based on
+ * Based on
* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
* we have
* asinh(x) := x if 1+x*x=1,
* := sign(x)*(log1p(x)+ln2)) if sqrt(1+x*x)=x, else
- * := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )
+ * := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )
*
* Accuracy:
* asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded.
- * In a test run with 52,000 random arguments on a VAX, the maximum
+ * In a test run with 52,000 random arguments on a VAX, the maximum
* observed error was 1.58 ulps (units in the last place).
*
* Constants:
@@ -82,16 +82,16 @@ ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
double asinh(x)
double x;
-{
+{
double t,s;
const static double small=1.0E-10, /* fl(1+small*small) == 1 */
big =1.0E20, /* fl(1+big) == big */
- one =1.0 ;
+ one =1.0 ;
#if !defined(vax)&&!defined(tahoe)
if(x!=x) return(x); /* x is NaN */
#endif /* !defined(vax)&&!defined(tahoe) */
- if((t=copysign(x,one))>small)
+ if((t=copysign(x,one))>small)
if(t<big) {
s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); }
else /* if |x| > big */
diff --git a/lib/libm/common_source/atan.c b/lib/libm/common_source/atan.c
index 272c7f1cdc48..f29c7d4d3483 100644
--- a/lib/libm/common_source/atan.c
+++ b/lib/libm/common_source/atan.c
@@ -41,32 +41,32 @@ static char sccsid[] = "@(#)atan.c 8.1 (Berkeley) 6/4/93";
* CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
*
* Required kernel function:
- * atan2(y,x)
+ * atan2(y,x)
*
- * Method:
- * atan(x) = atan2(x,1.0).
+ * Method:
+ * atan(x) = atan2(x,1.0).
*
* Special case:
* if x is NaN, return x itself.
*
* Accuracy:
* 1) If atan2() uses machine PI, then
- *
+ *
* atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded;
* and PI is the exact pi rounded to machine precision (see atan2 for
* details):
*
* in decimal:
- * pi = 3.141592653589793 23846264338327 .....
+ * pi = 3.141592653589793 23846264338327 .....
* 53 bits PI = 3.141592653589793 115997963 ..... ,
- * 56 bits PI = 3.141592653589793 227020265 ..... ,
+ * 56 bits PI = 3.141592653589793 227020265 ..... ,
*
* in hexadecimal:
* pi = 3.243F6A8885A308D313198A2E....
* 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps
* 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps
- *
- * In a test run with more than 200,000 random arguments on a VAX, the
+ *
+ * In a test run with more than 200,000 random arguments on a VAX, the
* maximum observed error in ulps (units in the last place) was
* 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))).
*
@@ -74,7 +74,7 @@ static char sccsid[] = "@(#)atan.c 8.1 (Berkeley) 6/4/93";
*
* atan(x) returns the exact atan(x) with error below about 2 ulps.
*
- * In a test run with more than 1,024,000 random arguments on a VAX, the
+ * In a test run with more than 1,024,000 random arguments on a VAX, the
* maximum observed error in ulps (units in the last place) was
* 0.85 ulps.
*/
diff --git a/lib/libm/common_source/atanh.c b/lib/libm/common_source/atanh.c
index 89cb61cca25e..e5cdadde9052 100644
--- a/lib/libm/common_source/atanh.c
+++ b/lib/libm/common_source/atanh.c
@@ -38,14 +38,14 @@ static char sccsid[] = "@(#)atanh.c 8.1 (Berkeley) 6/4/93";
/* ATANH(X)
* RETURN THE HYPERBOLIC ARC TANGENT OF X
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
- * CODED IN C BY K.C. NG, 1/8/85;
+ * CODED IN C BY K.C. NG, 1/8/85;
* REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85.
*
* Required kernel function:
* log1p(x) ...return log(1+x)
*
* Method :
- * Return
+ * Return
* 1 2x x
* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
* 2 1 - x 1 - x
diff --git a/lib/libm/common_source/cosh.c b/lib/libm/common_source/cosh.c
index e2b30731b8c1..e8d35195eb05 100644
--- a/lib/libm/common_source/cosh.c
+++ b/lib/libm/common_source/cosh.c
@@ -38,7 +38,7 @@ static char sccsid[] = "@(#)cosh.c 8.1 (Berkeley) 6/4/93";
/* COSH(X)
* RETURN THE HYPERBOLIC COSINE OF X
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
- * CODED IN C BY K.C. NG, 1/8/85;
+ * CODED IN C BY K.C. NG, 1/8/85;
* REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
*
* Required system supported functions :
@@ -46,20 +46,20 @@ static char sccsid[] = "@(#)cosh.c 8.1 (Berkeley) 6/4/93";
* scalb(x,N)
*
* Required kernel function:
- * exp(x)
+ * exp(x)
* exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465
*
* Method :
- * 1. Replace x by |x|.
- * 2.
- * [ exp(x) - 1 ]^2
+ * 1. Replace x by |x|.
+ * 2.
+ * [ exp(x) - 1 ]^2
* 0 <= x <= 0.3465 : cosh(x) := 1 + -------------------
* 2*exp(x)
*
* exp(x) + 1/exp(x)
* 0.3465 <= x <= 22 : cosh(x) := -------------------
* 2
- * 22 <= x <= lnovfl : cosh(x) := exp(x)/2
+ * 22 <= x <= lnovfl : cosh(x) := exp(x)/2
* lnovfl <= x <= lnovfl+log(2)
* : cosh(x) := exp(x)/2 (avoid overflow)
* log(2)+lnovfl < x < INF: overflow to INF
@@ -106,7 +106,7 @@ static max = 1023 ;
double cosh(x)
double x;
-{
+{
static const double half=1.0/2.0,
one=1.0, small=1.0E-18; /* fl(1+small)==1 */
double t;
@@ -115,19 +115,19 @@ double x;
if(x!=x) return(x); /* x is NaN */
#endif /* !defined(vax)&&!defined(tahoe) */
if((x=copysign(x,one)) <= 22)
- if(x<0.3465)
+ if(x<0.3465)
if(x<small) return(one+x);
else {t=x+__exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
else /* for x lies in [0.3465,22] */
{ t=exp(x); return((t+one/t)*half); }
- if( lnovfl <= x && x <= (lnovfl+0.7))
- /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1))
- * and return 2^max*exp(x) to avoid unnecessary overflow
+ if( lnovfl <= x && x <= (lnovfl+0.7))
+ /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1))
+ * and return 2^max*exp(x) to avoid unnecessary overflow
*/
- return(scalb(exp((x-mln2hi)-mln2lo), max));
+ return(scalb(exp((x-mln2hi)-mln2lo), max));
- else
+ else
return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */
}
diff --git a/lib/libm/common_source/erf.c b/lib/libm/common_source/erf.c
index 308f1a952d73..ba0c006eea5f 100644
--- a/lib/libm/common_source/erf.c
+++ b/lib/libm/common_source/erf.c
@@ -68,13 +68,13 @@ static char sccsid[] = "@(#)erf.c 8.1 (Berkeley) 6/4/93";
* erfc(x) = 1 - erf(x) if x<=0.25
* = 0.5 + ((0.5-x)-x*P) if x in [0.25,0.84375]
* where
- * 2 2 4 20
+ * 2 2 4 20
* P = P(x ) = (p0 + p1 * x + p2 * x + ... + p10 * x )
* is an approximation to (erf(x)-x)/x with precision
*
* -56.45
* | P - (erf(x)-x)/x | <= 2
- *
+ *
*
* Remark. The formula is derived by noting
* erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
@@ -96,7 +96,7 @@ static char sccsid[] = "@(#)erf.c 8.1 (Berkeley) 6/4/93";
* That is, we use rational approximation to approximate
* erf(1+s) - (c = (single)0.84506291151)
* Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
- * where
+ * where
* P1(s) = degree 6 poly in s
* Q1(s) = degree 6 poly in s
*
@@ -105,7 +105,7 @@ static char sccsid[] = "@(#)erf.c 8.1 (Berkeley) 6/4/93";
* erfc(x) = (1/x)exp(-x*x-(.5*log(pi) -.5z + R(z)/S(z))
*
* Where z = 1/(x*x), R is degree 9, and S is degree 3;
- *
+ *
* 5. For x in [4,28]
* erf(x) = 1.0 - tiny
* erfc(x) = (1/x)exp(-x*x-(.5*log(pi)+eps + zP(z))
@@ -139,7 +139,7 @@ static char sccsid[] = "@(#)erf.c 8.1 (Berkeley) 6/4/93";
*
* 7. Special cases:
* erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
- * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
+ * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
* erfc/erf(NaN) is NaN
*/
@@ -181,7 +181,7 @@ p8 = 1.640186161764254363152286358441771740838e-0006,
p9 = -1.571599331700515057841960987689515895479e-0007,
p10= 1.073087585213621540635426191486561494058e-0008;
/*
- * Coefficients for approximation to erf in [0.84375,1.25]
+ * Coefficients for approximation to erf in [0.84375,1.25]
*/
static double
pa0 = -2.362118560752659485957248365514511540287e-0003,
@@ -319,7 +319,7 @@ double erf(x)
return (z-one);
}
-double erfc(x)
+double erfc(x)
double x;
{
double R,S,P,Q,s,ax,y,z,r,fabs(),__exp__D();
@@ -352,7 +352,7 @@ double erfc(x)
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if (x>=0) {
- z = one-c; return z - P/Q;
+ z = one-c; return z - P/Q;
} else {
z = c+P/Q; return one+z;
}
diff --git a/lib/libm/common_source/exp.c b/lib/libm/common_source/exp.c
index 9b4f045f82e4..fa6ea75735c5 100644
--- a/lib/libm/common_source/exp.c
+++ b/lib/libm/common_source/exp.c
@@ -38,21 +38,21 @@ static char sccsid[] = "@(#)exp.c 8.1 (Berkeley) 6/4/93";
/* EXP(X)
* RETURN THE EXPONENTIAL OF X
* DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
- * CODED IN C BY K.C. NG, 1/19/85;
+ * CODED IN C BY K.C. NG, 1/19/85;
* REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
*
* Required system supported functions:
- * scalb(x,n)
- * copysign(x,y)
+ * scalb(x,n)
+ * copysign(x,y)
* finite(x)
*
* Method:
- * 1. Argument Reduction: given the input x, find r and integer k such
+ * 1. Argument Reduction: given the input x, find r and integer k such
* that
- * x = k*ln2 + r, |r| <= 0.5*ln2 .
+ * x = k*ln2 + r, |r| <= 0.5*ln2 .
* r will be represented as r := z+c for better accuracy.
*
- * 2. Compute exp(r) by
+ * 2. Compute exp(r) by
*
* exp(r) = 1 + r + r*R1/(2-R1),
* where
@@ -143,7 +143,7 @@ double x;
}
/* end of x > lntiny */
- else
+ else
/* exp(-big#) underflows to zero */
if(finite(x)) return(scalb(1.0,-5000));
@@ -152,7 +152,7 @@ double x;
}
/* end of x < lnhuge */
- else
+ else
/* exp(INF) is INF, exp(+big#) overflows to INF */
return( finite(x) ? scalb(1.0,5000) : x);
}
@@ -188,7 +188,7 @@ double x, c;
}
/* end of x > lntiny */
- else
+ else
/* exp(-big#) underflows to zero */
if(finite(x)) return(scalb(1.0,-5000));
@@ -197,7 +197,7 @@ double x, c;
}
/* end of x < lnhuge */
- else
+ else
/* exp(INF) is INF, exp(+big#) overflows to INF */
return( finite(x) ? scalb(1.0,5000) : x);
}
diff --git a/lib/libm/common_source/exp__E.c b/lib/libm/common_source/exp__E.c
index ab972477a04b..16ec4cbb2179 100644
--- a/lib/libm/common_source/exp__E.c
+++ b/lib/libm/common_source/exp__E.c
@@ -41,7 +41,7 @@ static char sccsid[] = "@(#)exp__E.c 8.1 (Berkeley) 6/4/93";
* exp__E RETURNS
*
* / exp(x+c) - 1 - x , 1E-19 < |x| < .3465736
- * exp__E(x,c) = |
+ * exp__E(x,c) = |
* \ 0 , |x| < 1E-19.
*
* DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
@@ -50,12 +50,12 @@ static char sccsid[] = "@(#)exp__E.c 8.1 (Berkeley) 6/4/93";
* REVISED BY K.C. NG on 3/16/85, 4/16/85.
*
* Required system supported function:
- * copysign(x,y)
+ * copysign(x,y)
*
* Method:
* 1. Rational approximation. Let r=x+c.
* Based on
- * 2 * sinh(r/2)
+ * 2 * sinh(r/2)
* exp(r) - 1 = ---------------------- ,
* cosh(r/2) - sinh(r/2)
* exp__E(r) is computed using
@@ -76,7 +76,7 @@ static char sccsid[] = "@(#)exp__E.c 8.1 (Berkeley) 6/4/93";
* Approximation error:
*
* | exp(x) - 1 | 2**(-57), (IEEE double)
- * | ------------ - (exp__E(x,0)+x)/x | <=
+ * | ------------ - (exp__E(x,0)+x)/x | <=
* | x | 2**(-69). (VAX D)
*
* Constants:
@@ -120,7 +120,7 @@ double x,c;
#else /* defined(vax)||defined(tahoe) */
q = z*( q1 +z* q2 );
#endif /* defined(vax)||defined(tahoe) */
- xp= x*p ;
+ xp= x*p ;
xh= x*half ;
w = xh-(q-xp) ;
p = p+p;
diff --git a/lib/libm/common_source/expm1.c b/lib/libm/common_source/expm1.c
index 760d2bed677d..8a84f14c4da2 100644
--- a/lib/libm/common_source/expm1.c
+++ b/lib/libm/common_source/expm1.c
@@ -38,36 +38,36 @@ static char sccsid[] = "@(#)expm1.c 8.1 (Berkeley) 6/4/93";
/* EXPM1(X)
* RETURN THE EXPONENTIAL OF X MINUS ONE
* DOUBLE PRECISION (IEEE 53 BITS, VAX D FORMAT 56 BITS)
- * CODED IN C BY K.C. NG, 1/19/85;
+ * CODED IN C BY K.C. NG, 1/19/85;
* REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/21/85, 4/16/85.
*
* Required system supported functions:
- * scalb(x,n)
- * copysign(x,y)
+ * scalb(x,n)
+ * copysign(x,y)
* finite(x)
*
* Kernel function:
* exp__E(x,c)
*
* Method:
- * 1. Argument Reduction: given the input x, find r and integer k such
+ * 1. Argument Reduction: given the input x, find r and integer k such
* that
- * x = k*ln2 + r, |r| <= 0.5*ln2 .
+ * x = k*ln2 + r, |r| <= 0.5*ln2 .
* r will be represented as r := z+c for better accuracy.
*
- * 2. Compute EXPM1(r)=exp(r)-1 by
+ * 2. Compute EXPM1(r)=exp(r)-1 by
*
* EXPM1(r=z+c) := z + exp__E(z,c)
*
* 3. EXPM1(x) = 2^k * ( EXPM1(r) + 1-2^-k ).
*
- * Remarks:
+ * Remarks:
* 1. When k=1 and z < -0.25, we use the following formula for
* better accuracy:
* EXPM1(x) = 2 * ( (z+0.5) + exp__E(z,c) )
* 2. To avoid rounding error in 1-2^-k where k is large, we use
* EXPM1(x) = 2^k * { [z+(exp__E(z,c)-2^-k )] + 1 }
- * when k>56.
+ * when k>56.
*
* Special cases:
* EXPM1(INF) is INF, EXPM1(NaN) is NaN;
@@ -108,7 +108,7 @@ ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE)
double expm1(x)
double x;
{
- const static double one=1.0, half=1.0/2.0;
+ const static double one=1.0, half=1.0/2.0;
double z,hi,lo,c;
int k;
#if defined(vax)||defined(tahoe)
@@ -126,13 +126,13 @@ double x;
/* argument reduction : x - k*ln2 */
k= invln2 *x+copysign(0.5,x); /* k=NINT(x/ln2) */
- hi=x-k*ln2hi ;
+ hi=x-k*ln2hi ;
z=hi-(lo=k*ln2lo);
c=(hi-z)-lo;
if(k==0) return(z+__exp__E(z,c));
if(k==1)
- if(z< -0.25)
+ if(z< -0.25)
{x=z+half;x +=__exp__E(z,c); return(x+x);}
else
{z+=__exp__E(z,c); x=half+z; return(x+x);}
@@ -143,17 +143,17 @@ double x;
{ x=one-scalb(one,-k); z += __exp__E(z,c);}
else if(k<100)
{ x = __exp__E(z,c)-scalb(one,-k); x+=z; z=one;}
- else
+ else
{ x = __exp__E(z,c)+z; z=one;}
- return (scalb(x+z,k));
+ return (scalb(x+z,k));
}
}
/* end of x > lnunfl */
- else
+ else
/* expm1(-big#) rounded to -1 (inexact) */
- if(finite(x))
+ if(finite(x))
{ ln2hi+ln2lo; return(-one);}
/* expm1(-INF) is -1 */
@@ -161,7 +161,7 @@ double x;
}
/* end of x < lnhuge */
- else
+ else
/* expm1(INF) is INF, expm1(+big#) overflows to INF */
return( finite(x) ? scalb(one,5000) : x);
}
diff --git a/lib/libm/common_source/j0.c b/lib/libm/common_source/j0.c
index a9b28b38caea..684fb4d42c3e 100644
--- a/lib/libm/common_source/j0.c
+++ b/lib/libm/common_source/j0.c
@@ -46,18 +46,18 @@ static char sccsid[] = "@(#)j0.c 8.2 (Berkeley) 11/30/93";
*
* 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.
* ====================================================
*
* ******************* WARNING ********************
* This is an alpha version of SunPro's FDLIBM (Freely
- * Distributable Math Library) for IEEE double precision
+ * Distributable Math Library) for IEEE double precision
* arithmetic. FDLIBM is a basic math library written
- * in C that runs on machines that conform to IEEE
- * Standard 754/854. This alpha version is distributed
- * for testing purpose. Those who use this software
- * should report any bugs to
+ * in C that runs on machines that conform to IEEE
+ * Standard 754/854. This alpha version is distributed
+ * for testing purpose. Those who use this software
+ * should report any bugs to
*
* fdlibm-comments@sunpro.eng.sun.com
*
@@ -84,20 +84,20 @@ static char sccsid[] = "@(#)j0.c 8.2 (Berkeley) 11/30/93";
* (To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.)
- *
+ *
* 3 Special cases
* j0(nan)= nan
* j0(0) = 1
* j0(inf) = 0
- *
+ *
* Method -- y0(x):
* 1. For x<2.
- * Since
+ * Since
* y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
* therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
* We use the following function to approximate y0,
* y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
- * where
+ * where
* U(z) = u0 + u1*z + ... + u6*z^6
* V(z) = 1 + v1*z + ... + v4*z^4
* with absolute approximation error bounded by 2**-72.
@@ -121,7 +121,7 @@ static char sccsid[] = "@(#)j0.c 8.2 (Berkeley) 11/30/93";
static double pzero __P((double)), qzero __P((double));
-static double
+static double
huge = 1e300,
zero = 0.0,
one = 1.0,
@@ -138,7 +138,7 @@ s03 = 5.135465502073181376284426245689510134134e-0007,
s04 = 1.166140033337900097836930825478674320464e-0009;
double
-j0(x)
+j0(x)
double x;
{
double z, s,c,ss,cc,r,u,v;
@@ -201,7 +201,7 @@ v03 = 2.591508518404578033173189144579208685163e-0007,
v04 = 4.411103113326754838596529339004302243157e-0010;
double
-y0(x)
+y0(x)
double x;
{
double z, s, c, ss, cc, u, v;
@@ -345,7 +345,7 @@ static double pzero(x)
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return one+ r/s;
}
-
+
/* For x >= 8, the asymptotic expansions of qzero is
* -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
diff --git a/lib/libm/common_source/j1.c b/lib/libm/common_source/j1.c
index 71602aac1381..e8ca43ad83b8 100644
--- a/lib/libm/common_source/j1.c
+++ b/lib/libm/common_source/j1.c
@@ -46,18 +46,18 @@ static char sccsid[] = "@(#)j1.c 8.2 (Berkeley) 11/30/93";
*
* 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.
* ====================================================
*
* ******************* WARNING ********************
* This is an alpha version of SunPro's FDLIBM (Freely
- * Distributable Math Library) for IEEE double precision
+ * Distributable Math Library) for IEEE double precision
* arithmetic. FDLIBM is a basic math library written
- * in C that runs on machines that conform to IEEE
- * Standard 754/854. This alpha version is distributed
- * for testing purpose. Those who use this software
- * should report any bugs to
+ * in C that runs on machines that conform to IEEE
+ * Standard 754/854. This alpha version is distributed
+ * for testing purpose. Those who use this software
+ * should report any bugs to
*
* fdlibm-comments@sunpro.eng.sun.com
*
@@ -85,16 +85,16 @@ static char sccsid[] = "@(#)j1.c 8.2 (Berkeley) 11/30/93";
* (To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.)
- *
+ *
* 3 Special cases
* j1(nan)= nan
* j1(0) = 0
* j1(inf) = 0
- *
+ *
* Method -- y1(x):
- * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
+ * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
* 2. For x<2.
- * Since
+ * Since
* y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
* therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
* We use the following function to approximate y1,
@@ -122,7 +122,7 @@ static char sccsid[] = "@(#)j1.c 8.2 (Berkeley) 11/30/93";
static double pone(), qone();
-static double
+static double
huge = 1e300,
zero = 0.0,
one = 1.0,
@@ -142,7 +142,7 @@ s05 = 1.235422744261379203512624973117299248281e-0011;
#define two_129 6.80564733841876926e+038 /* 2^129 */
#define two_m54 5.55111512312578270e-017 /* 2^-54 */
-double j1(x)
+double j1(x)
double x;
{
double z, s,c,ss,cc,r,u,v,y;
@@ -205,7 +205,7 @@ static double v0[5] = {
1.665592462079920695971450872592458916421e-0011,
};
-double y1(x)
+double y1(x)
double x;
{
double z, s, c, ss, cc, u, v;
@@ -254,10 +254,10 @@ double y1(x)
z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
}
return z;
- }
+ }
if (x <= two_m54) { /* x < 2**-54 */
return (-tpi/x);
- }
+ }
z = x*x;
u = u0[0]+z*(u0[1]+z*(u0[2]+z*(u0[3]+z*u0[4])));
v = one+z*(v0[0]+z*(v0[1]+z*(v0[2]+z*(v0[3]+z*v0[4]))));
@@ -351,7 +351,7 @@ static double pone(x)
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return (one + r/s);
}
-
+
/* For x >= 8, the asymptotic expansions of qone is
* 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
diff --git a/lib/libm/common_source/jn.c b/lib/libm/common_source/jn.c
index 85a54012ecae..28d9687a51b1 100644
--- a/lib/libm/common_source/jn.c
+++ b/lib/libm/common_source/jn.c
@@ -46,18 +46,18 @@ static char sccsid[] = "@(#)jn.c 8.2 (Berkeley) 11/30/93";
*
* 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.
* ====================================================
*
* ******************* WARNING ********************
* This is an alpha version of SunPro's FDLIBM (Freely
- * Distributable Math Library) for IEEE double precision
+ * Distributable Math Library) for IEEE double precision
* arithmetic. FDLIBM is a basic math library written
- * in C that runs on machines that conform to IEEE
- * Standard 754/854. This alpha version is distributed
- * for testing purpose. Those who use this software
- * should report any bugs to
+ * in C that runs on machines that conform to IEEE
+ * Standard 754/854. This alpha version is distributed
+ * for testing purpose. Those who use this software
+ * should report any bugs to
*
* fdlibm-comments@sunpro.eng.sun.com
*
@@ -69,7 +69,7 @@ static char sccsid[] = "@(#)jn.c 8.2 (Berkeley) 11/30/93";
* jn(int n, double x), yn(int n, double x)
* floating point Bessel's function of the 1st and 2nd kind
* of order n
- *
+ *
* Special cases:
* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
@@ -88,7 +88,7 @@ static char sccsid[] = "@(#)jn.c 8.2 (Berkeley) 11/30/93";
* yn(n,x) is similar in all respects, except
* that forward recursion is used for all
* values of n>1.
- *
+ *
*/
#include <math.h>
@@ -120,7 +120,7 @@ double jn(n,x)
*/
/* if J(n,NaN) is NaN */
if (_IEEE && isnan(x)) return x+x;
- if (n<0){
+ if (n<0){
n = -n;
x = -x;
}
@@ -134,10 +134,10 @@ double jn(n,x)
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
if (_IEEE && x >= 8.148143905337944345e+090) {
/* x >= 2**302 */
- /* (x >> n**2)
+ /* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Let s=sin(x), c=cos(x),
+ * Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
@@ -154,7 +154,7 @@ double jn(n,x)
case 3: temp = cos(x)-sin(x); break;
}
b = invsqrtpi*temp/sqrt(x);
- } else {
+ } else {
a = j0(x);
b = j1(x);
for(i=1;i<n;i++){
@@ -165,7 +165,7 @@ double jn(n,x)
}
} else {
if (x < 1.86264514923095703125e-009) { /* x < 2**-29 */
- /* x is tiny, return the first Taylor expansion of J(n,x)
+ /* x is tiny, return the first Taylor expansion of J(n,x)
* J(n,x) = 1/n!*(x/2)^n - ...
*/
if (n > 33) /* underflow */
@@ -180,14 +180,14 @@ double jn(n,x)
}
} else {
/* use backward recurrence */
- /* x x^2 x^2
+ /* x x^2 x^2
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
* 2n - 2(n+1) - 2(n+2)
*
- * 1 1 1
+ * 1 1 1
* (for large x) = ---- ------ ------ .....
* 2n 2(n+1) 2(n+2)
- * -- - ------ - ------ -
+ * -- - ------ - ------ -
* x x x
*
* Let w = 2n/x and h=2/x, then the above quotient
@@ -203,9 +203,9 @@ double jn(n,x)
* To determine how many terms needed, let
* Q(0) = w, Q(1) = w(w+h) - 1,
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
- * When Q(k) > 1e4 good for single
- * When Q(k) > 1e9 good for double
- * When Q(k) > 1e17 good for quadruple
+ * When Q(k) > 1e4 good for single
+ * When Q(k) > 1e9 good for double
+ * When Q(k) > 1e17 good for quadruple
*/
/* determine k */
double t,v;
@@ -254,7 +254,7 @@ double jn(n,x)
}
return ((sgn == 1) ? -b : b);
}
-double yn(n,x)
+double yn(n,x)
int n; double x;
{
int i, sign;
@@ -275,10 +275,10 @@ double yn(n,x)
if (n == 0) return(y0(x));
if (n == 1) return(sign*y1(x));
if(_IEEE && x >= 8.148143905337944345e+090) { /* x > 2**302 */
- /* (x >> n**2)
+ /* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
- * Let s=sin(x), c=cos(x),
+ * Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
diff --git a/lib/libm/common_source/log.c b/lib/libm/common_source/log.c
index ae186722f8df..908b8544f93c 100644
--- a/lib/libm/common_source/log.c
+++ b/lib/libm/common_source/log.c
@@ -391,7 +391,7 @@ log(x) double x;
return (x+x);
else
return (infnan(ERANGE));
-
+
/* Argument reduction: 1 <= g < 2; x/2^m = g; */
/* y = F*(1 + f/F) for |f| <= 2^-8 */
diff --git a/lib/libm/common_source/log10.c b/lib/libm/common_source/log10.c
index d2617ccebb9e..75205cd5ee15 100644
--- a/lib/libm/common_source/log10.c
+++ b/lib/libm/common_source/log10.c
@@ -38,9 +38,9 @@ static char sccsid[] = "@(#)log10.c 8.1 (Berkeley) 6/4/93";
/* LOG10(X)
* RETURN THE BASE 10 LOGARITHM OF x
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
- * CODED IN C BY K.C. NG, 1/20/85;
+ * CODED IN C BY K.C. NG, 1/20/85;
* REVISED BY K.C. NG on 1/23/85, 3/7/85, 4/16/85.
- *
+ *
* Required kernel function:
* log(x)
*
@@ -52,12 +52,12 @@ static char sccsid[] = "@(#)log10.c 8.1 (Berkeley) 6/4/93";
* Note:
* [log(10)] rounded to 56 bits has error .0895 ulps,
* [1/log(10)] rounded to 53 bits has error .198 ulps;
- * therefore, for better accuracy, in VAX D format, we divide
- * log(x) by log(10), but in IEEE Double format, we multiply
+ * therefore, for better accuracy, in VAX D format, we divide
+ * log(x) by log(10), but in IEEE Double format, we multiply
* log(x) by [1/log(10)].
*
* Special cases:
- * log10(x) is NaN with signal if x < 0;
+ * log10(x) is NaN with signal if x < 0;
* log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
* log10(NaN) is that NaN with no signal.
*
diff --git a/lib/libm/common_source/log1p.c b/lib/libm/common_source/log1p.c
index cbf9fcd895e2..020266721ed6 100644
--- a/lib/libm/common_source/log1p.c
+++ b/lib/libm/common_source/log1p.c
@@ -35,24 +35,24 @@
static char sccsid[] = "@(#)log1p.c 8.1 (Berkeley) 6/4/93";
#endif /* not lint */
-/* LOG1P(x)
+/* LOG1P(x)
* RETURN THE LOGARITHM OF 1+x
* DOUBLE PRECISION (VAX D FORMAT 56 bits, IEEE DOUBLE 53 BITS)
- * CODED IN C BY K.C. NG, 1/19/85;
+ * CODED IN C BY K.C. NG, 1/19/85;
* REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/24/85, 4/16/85.
- *
+ *
* Required system supported functions:
- * scalb(x,n)
+ * scalb(x,n)
* copysign(x,y)
- * logb(x)
+ * logb(x)
* finite(x)
*
* Required kernel function:
* log__L(z)
*
* Method :
- * 1. Argument Reduction: find k and f such that
- * 1+x = 2^k * (1+f),
+ * 1. Argument Reduction: find k and f such that
+ * 1+x = 2^k * (1+f),
* where sqrt(2)/2 < 1+f < sqrt(2) .
*
* 2. Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
@@ -65,11 +65,11 @@ static char sccsid[] = "@(#)log1p.c 8.1 (Berkeley) 6/4/93";
*
* See log__L() for the values of the coefficients.
*
- * 3. Finally, log(1+x) = k*ln2 + log(1+f).
+ * 3. Finally, log(1+x) = k*ln2 + log(1+f).
*
* Remarks 1. In step 3 n*ln2 will be stored in two floating point numbers
- * n*ln2hi + n*ln2lo, where ln2hi is chosen such that the last
- * 20 bits (for VAX D format), or the last 21 bits ( for IEEE
+ * n*ln2hi + n*ln2lo, where ln2hi is chosen such that the last
+ * 20 bits (for VAX D format), or the last 21 bits ( for IEEE
* double) is 0. This ensures n*ln2hi is exactly representable.
* 2. In step 1, f may not be representable. A correction term c
* for f is computed. It follows that the correction term for
@@ -83,7 +83,7 @@ static char sccsid[] = "@(#)log1p.c 8.1 (Berkeley) 6/4/93";
* only log1p(0)=0 is exact for finite argument.
*
* Accuracy:
- * log1p(x) returns the exact log(1+x) nearly rounded. In a test run
+ * log1p(x) returns the exact log(1+x) nearly rounded. In a test run
* with 1,536,000 random arguments on a VAX, the maximum observed
* error was .846 ulps (units in the last place).
*
@@ -114,7 +114,7 @@ ic(sqrt2, 1.4142135623730951455E0, 0, 1.6A09E667F3BCD)
double log1p(x)
double x;
{
- const static double zero=0.0, negone= -1.0, one=1.0,
+ const static double zero=0.0, negone= -1.0, one=1.0,
half=1.0/2.0, small=1.0E-20; /* 1+small == 1 */
double z,s,t,c;
int k;
@@ -129,7 +129,7 @@ double x;
/* argument reduction */
if(copysign(x,one)<small) return(x);
k=logb(one+x); z=scalb(x,-k); t=scalb(one,-k);
- if(z+t >= sqrt2 )
+ if(z+t >= sqrt2 )
{ k += 1 ; z *= half; t *= half; }
t += negone; x = z + t;
c = (t-x)+z ; /* correction term for x */
@@ -162,9 +162,9 @@ double x;
/* end of if (finite(x)) */
/* log(-INF) is NaN */
- else if(x<0)
+ else if(x<0)
return(zero/zero);
/* log(+INF) is INF */
- else return(x);
+ else return(x);
}
diff --git a/lib/libm/common_source/log__L.c b/lib/libm/common_source/log__L.c
index c00158fa5172..207cb0d9e5d8 100644
--- a/lib/libm/common_source/log__L.c
+++ b/lib/libm/common_source/log__L.c
@@ -39,14 +39,14 @@ static char sccsid[] = "@(#)log__L.c 8.1 (Berkeley) 6/4/93";
* LOG(1+X) - 2S X
* RETURN --------------- WHERE Z = S*S, S = ------- , 0 <= Z <= .0294...
* S 2 + X
- *
+ *
* DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
* KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS
- * CODED IN C BY K.C. NG, 1/19/85;
+ * CODED IN C BY K.C. NG, 1/19/85;
* REVISED BY K.C. Ng, 2/3/85, 4/16/85.
*
* Method :
- * 1. Polynomial approximation: let s = x/(2+x).
+ * 1. Polynomial approximation: let s = x/(2+x).
* Based on log(1+x) = log(1+s) - log(1-s)
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
*
@@ -54,11 +54,11 @@ static char sccsid[] = "@(#)log__L.c 8.1 (Berkeley) 6/4/93";
*
* z*(L1 + z*(L2 + z*(... (L7 + z*L8)...)))
*
- * where z=s*s. (See the listing below for Lk's values.) The
- * coefficients are obtained by a special Remez algorithm.
+ * where z=s*s. (See the listing below for Lk's values.) The
+ * coefficients are obtained by a special Remez algorithm.
*
* Accuracy:
- * Assuming no rounding error, the maximum magnitude of the approximation
+ * Assuming no rounding error, the maximum magnitude of the approximation
* error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63)
* for VAX D format.
*
diff --git a/lib/libm/common_source/pow.c b/lib/libm/common_source/pow.c
index cb4fc5029f4d..9e92985f8f97 100644
--- a/lib/libm/common_source/pow.c
+++ b/lib/libm/common_source/pow.c
@@ -35,17 +35,17 @@
static char sccsid[] = "@(#)pow.c 8.1 (Berkeley) 6/4/93";
#endif /* not lint */
-/* POW(X,Y)
- * RETURN X**Y
+/* POW(X,Y)
+ * RETURN X**Y
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
- * CODED IN C BY K.C. NG, 1/8/85;
+ * CODED IN C BY K.C. NG, 1/8/85;
* REVISED BY K.C. NG on 7/10/85.
* KERNEL pow_P() REPLACED BY P. McILROY 7/22/92.
* Required system supported functions:
- * scalb(x,n)
- * logb(x)
- * copysign(x,y)
- * finite(x)
+ * scalb(x,n)
+ * logb(x)
+ * copysign(x,y)
+ * finite(x)
* drem(x,y)
*
* Required kernel functions:
@@ -56,7 +56,7 @@ static char sccsid[] = "@(#)pow.c 8.1 (Berkeley) 6/4/93";
* 1. Compute and return log(x) in three pieces:
* log(x) = n*ln2 + hi + lo,
* where n is an integer.
- * 2. Perform y*log(x) by simulating muti-precision arithmetic and
+ * 2. Perform y*log(x) by simulating muti-precision arithmetic and
* return the answer in three pieces:
* y*log(x) = m*ln2 + hi + lo,
* where m is an integer.
@@ -94,7 +94,7 @@ static char sccsid[] = "@(#)pow.c 8.1 (Berkeley) 6/4/93";
* pow(integer,integer)
* always returns the correct integer provided it is representable.
* In a test run with 100,000 random arguments with 0 < x, y < 20.0
- * on a VAX, the maximum observed error was 1.79 ulps (units in the
+ * on a VAX, the maximum observed error was 1.79 ulps (units in the
* last place).
*
* Constants :
@@ -123,7 +123,7 @@ const static double zero=0.0, one=1.0, two=2.0, negone= -1.0;
static double pow_P __P((double, double));
-double pow(x,y)
+double pow(x,y)
double x,y;
{
double t;
diff --git a/lib/libm/common_source/sinh.c b/lib/libm/common_source/sinh.c
index 0516849cff13..075172c074e1 100644
--- a/lib/libm/common_source/sinh.c
+++ b/lib/libm/common_source/sinh.c
@@ -38,7 +38,7 @@ static char sccsid[] = "@(#)sinh.c 8.1 (Berkeley) 6/4/93";
/* SINH(X)
* RETURN THE HYPERBOLIC SINE OF X
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
- * CODED IN C BY K.C. NG, 1/8/85;
+ * CODED IN C BY K.C. NG, 1/8/85;
* REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85.
*
* Required system supported functions :
@@ -50,14 +50,14 @@ static char sccsid[] = "@(#)sinh.c 8.1 (Berkeley) 6/4/93";
*
* Method :
* 1. reduce x to non-negative by sinh(-x) = - sinh(x).
- * 2.
+ * 2.
*
* expm1(x) + expm1(x)/(expm1(x)+1)
* 0 <= x <= lnovfl : sinh(x) := --------------------------------
* 2
* lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
* lnovfl+ln2 < x < INF : overflow to INF
- *
+ *
*
* Special cases:
* sinh(x) is x if x is +INF, -INF, or NaN.
@@ -112,7 +112,7 @@ double x;
{t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}
else if(x <= lnovfl+0.7)
- /* subtract x by ln(2^(max+1)) and return 2^max*exp(x)
+ /* subtract x by ln(2^(max+1)) and return 2^max*exp(x)
to avoid unnecessary overflow */
return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));
diff --git a/lib/libm/common_source/tanh.c b/lib/libm/common_source/tanh.c
index d4923b3418bd..6813b55a3a70 100644
--- a/lib/libm/common_source/tanh.c
+++ b/lib/libm/common_source/tanh.c
@@ -38,7 +38,7 @@ static char sccsid[] = "@(#)tanh.c 8.1 (Berkeley) 6/4/93";
/* TANH(X)
* RETURN THE HYPERBOLIC TANGENT OF X
* DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
- * CODED IN C BY K.C. NG, 1/8/85;
+ * CODED IN C BY K.C. NG, 1/8/85;
* REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85.
*
* Required system supported functions :
@@ -85,7 +85,7 @@ double x;
sign=copysign(one,x);
x=copysign(x,one);
- if(x < 22.0)
+ if(x < 22.0)
if( x > one )
return(copysign(one-two/(expm1(x+x)+two),sign));
else if ( x > small )
generated by cgit v1.2.3 (git 2.25.1) at 2025-10-31 06:29:51 +0000