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authorAntoine Pitrou <solipsis@pitrou.net>2010-05-09 15:52:27 (GMT)
committerAntoine Pitrou <solipsis@pitrou.net>2010-05-09 15:52:27 (GMT)
commitf95a1b3c53bdd678b64aa608d4375660033460c3 (patch)
treea8bee40b1b14e28ff5978ea519f3035a3c399912 /Modules/_math.c
parentbd250300191133d276a71b395b6428081bf825b8 (diff)
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Recorded merge of revisions 81029 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk ........ r81029 | antoine.pitrou | 2010-05-09 16:46:46 +0200 (dim., 09 mai 2010) | 3 lines Untabify C files. Will watch buildbots. ........
Diffstat (limited to 'Modules/_math.c')
-rw-r--r--Modules/_math.c206
1 files changed, 103 insertions, 103 deletions
diff --git a/Modules/_math.c b/Modules/_math.c
index 995d1c0..b5d8b45 100644
--- a/Modules/_math.c
+++ b/Modules/_math.c
@@ -14,7 +14,7 @@
*
* 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.
* ====================================================
*/
@@ -27,11 +27,11 @@ static const double zero = 0.0;
/* acosh(x)
* Method :
* Based on
- * acosh(x) = log [ x + sqrt(x*x-1) ]
+ * acosh(x) = log [ x + sqrt(x*x-1) ]
* we have
- * acosh(x) := log(x)+ln2, if x is large; else
- * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
- * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
+ * acosh(x) := log(x)+ln2, if x is large; else
+ * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
+ * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
*
* Special cases:
* acosh(x) is NaN with signal if x<1.
@@ -41,82 +41,82 @@ static const double zero = 0.0;
double
_Py_acosh(double x)
{
- if (Py_IS_NAN(x)) {
- return x+x;
- }
- if (x < 1.) { /* x < 1; return a signaling NaN */
- errno = EDOM;
+ if (Py_IS_NAN(x)) {
+ return x+x;
+ }
+ if (x < 1.) { /* x < 1; return a signaling NaN */
+ errno = EDOM;
#ifdef Py_NAN
- return Py_NAN;
+ return Py_NAN;
#else
- return (x-x)/(x-x);
+ return (x-x)/(x-x);
#endif
- }
- else if (x >= two_pow_p28) { /* x > 2**28 */
- if (Py_IS_INFINITY(x)) {
- return x+x;
- } else {
- return log(x)+ln2; /* acosh(huge)=log(2x) */
- }
- }
- else if (x == 1.) {
- return 0.0; /* acosh(1) = 0 */
- }
- else if (x > 2.) { /* 2 < x < 2**28 */
- double t = x*x;
- return log(2.0*x - 1.0 / (x + sqrt(t - 1.0)));
- }
- else { /* 1 < x <= 2 */
- double t = x - 1.0;
- return m_log1p(t + sqrt(2.0*t + t*t));
- }
+ }
+ else if (x >= two_pow_p28) { /* x > 2**28 */
+ if (Py_IS_INFINITY(x)) {
+ return x+x;
+ } else {
+ return log(x)+ln2; /* acosh(huge)=log(2x) */
+ }
+ }
+ else if (x == 1.) {
+ return 0.0; /* acosh(1) = 0 */
+ }
+ else if (x > 2.) { /* 2 < x < 2**28 */
+ double t = x*x;
+ return log(2.0*x - 1.0 / (x + sqrt(t - 1.0)));
+ }
+ else { /* 1 < x <= 2 */
+ double t = x - 1.0;
+ return m_log1p(t + sqrt(2.0*t + t*t));
+ }
}
/* asinh(x)
* Method :
- * Based on
- * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
- * we have
- * asinh(x) := x if 1+x*x=1,
- * := sign(x)*(log(x)+ln2)) for large |x|, else
- * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
- * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
+ * Based on
+ * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
+ * we have
+ * asinh(x) := x if 1+x*x=1,
+ * := sign(x)*(log(x)+ln2)) for large |x|, else
+ * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
+ * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
*/
double
_Py_asinh(double x)
-{
- double w;
- double absx = fabs(x);
-
- if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) {
- return x+x;
- }
- if (absx < two_pow_m28) { /* |x| < 2**-28 */
- return x; /* return x inexact except 0 */
- }
- if (absx > two_pow_p28) { /* |x| > 2**28 */
- w = log(absx)+ln2;
- }
- else if (absx > 2.0) { /* 2 < |x| < 2**28 */
- w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx));
- }
- else { /* 2**-28 <= |x| < 2= */
- double t = x*x;
- w = m_log1p(absx + t / (1.0 + sqrt(1.0 + t)));
- }
- return copysign(w, x);
-
+{
+ double w;
+ double absx = fabs(x);
+
+ if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) {
+ return x+x;
+ }
+ if (absx < two_pow_m28) { /* |x| < 2**-28 */
+ return x; /* return x inexact except 0 */
+ }
+ if (absx > two_pow_p28) { /* |x| > 2**28 */
+ w = log(absx)+ln2;
+ }
+ else if (absx > 2.0) { /* 2 < |x| < 2**28 */
+ w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx));
+ }
+ else { /* 2**-28 <= |x| < 2= */
+ double t = x*x;
+ w = m_log1p(absx + t / (1.0 + sqrt(1.0 + t)));
+ }
+ return copysign(w, x);
+
}
/* atanh(x)
* Method :
* 1.Reduced x to positive by atanh(-x) = -atanh(x)
* 2.For x>=0.5
- * 1 2x x
+ * 1 2x x
* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
- * 2 1 - x 1 - x
+ * 2 1 - x 1 - x
*
* For x<0.5
* atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
@@ -130,32 +130,32 @@ _Py_asinh(double x)
double
_Py_atanh(double x)
{
- double absx;
- double t;
-
- if (Py_IS_NAN(x)) {
- return x+x;
- }
- absx = fabs(x);
- if (absx >= 1.) { /* |x| >= 1 */
- errno = EDOM;
+ double absx;
+ double t;
+
+ if (Py_IS_NAN(x)) {
+ return x+x;
+ }
+ absx = fabs(x);
+ if (absx >= 1.) { /* |x| >= 1 */
+ errno = EDOM;
#ifdef Py_NAN
- return Py_NAN;
+ return Py_NAN;
#else
- return x/zero;
+ return x/zero;
#endif
- }
- if (absx < two_pow_m28) { /* |x| < 2**-28 */
- return x;
- }
- if (absx < 0.5) { /* |x| < 0.5 */
- t = absx+absx;
- t = 0.5 * m_log1p(t + t*absx / (1.0 - absx));
- }
- else { /* 0.5 <= |x| <= 1.0 */
- t = 0.5 * m_log1p((absx + absx) / (1.0 - absx));
- }
- return copysign(t, x);
+ }
+ if (absx < two_pow_m28) { /* |x| < 2**-28 */
+ return x;
+ }
+ if (absx < 0.5) { /* |x| < 0.5 */
+ t = absx+absx;
+ t = 0.5 * m_log1p(t + t*absx / (1.0 - absx));
+ }
+ else { /* 0.5 <= |x| <= 1.0 */
+ t = 0.5 * m_log1p((absx + absx) / (1.0 - absx));
+ }
+ return copysign(t, x);
}
/* Mathematically, expm1(x) = exp(x) - 1. The expm1 function is designed
@@ -173,15 +173,15 @@ _Py_expm1(double x)
*/
if (fabs(x) < 0.7) {
- double u;
- u = exp(x);
- if (u == 1.0)
- return x;
- else
- return (u - 1.0) * x / log(u);
+ double u;
+ u = exp(x);
+ if (u == 1.0)
+ return x;
+ else
+ return (u - 1.0) * x / log(u);
}
else
- return exp(x) - 1.0;
+ return exp(x) - 1.0;
}
/* log1p(x) = log(1+x). The log1p function is designed to avoid the
@@ -194,7 +194,7 @@ _Py_log1p(double x)
/* For x small, we use the following approach. Let y be the nearest float
to 1+x, then
- 1+x = y * (1 - (y-1-x)/y)
+ 1+x = y * (1 - (y-1-x)/y)
so log(1+x) = log(y) + log(1-(y-1-x)/y). Since (y-1-x)/y is tiny, the
second term is well approximated by (y-1-x)/y. If abs(x) >=
@@ -213,17 +213,17 @@ _Py_log1p(double x)
double y;
if (fabs(x) < DBL_EPSILON/2.) {
- return x;
+ return x;
} else if (-0.5 <= x && x <= 1.) {
- /* WARNING: it's possible than an overeager compiler
- will incorrectly optimize the following two lines
- to the equivalent of "return log(1.+x)". If this
- happens, then results from log1p will be inaccurate
- for small x. */
- y = 1.+x;
- return log(y)-((y-1.)-x)/y;
+ /* WARNING: it's possible than an overeager compiler
+ will incorrectly optimize the following two lines
+ to the equivalent of "return log(1.+x)". If this
+ happens, then results from log1p will be inaccurate
+ for small x. */
+ y = 1.+x;
+ return log(y)-((y-1.)-x)/y;
} else {
- /* NaNs and infinities should end up here */
- return log(1.+x);
+ /* NaNs and infinities should end up here */
+ return log(1.+x);
}
}