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author | Antoine Pitrou <solipsis@pitrou.net> | 2010-05-09 15:52:27 (GMT) |
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committer | Antoine Pitrou <solipsis@pitrou.net> | 2010-05-09 15:52:27 (GMT) |
commit | f95a1b3c53bdd678b64aa608d4375660033460c3 (patch) | |
tree | a8bee40b1b14e28ff5978ea519f3035a3c399912 /Modules/_math.c | |
parent | bd250300191133d276a71b395b6428081bf825b8 (diff) | |
download | cpython-f95a1b3c53bdd678b64aa608d4375660033460c3.zip cpython-f95a1b3c53bdd678b64aa608d4375660033460c3.tar.gz cpython-f95a1b3c53bdd678b64aa608d4375660033460c3.tar.bz2 |
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.c | 206 |
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); } } |