Merged revisions 76978 via svnmerge from

svn+ssh://pythondev@svn.python.org/python/trunk

........
  r76978 | mark.dickinson | 2009-12-21 15:22:00 +0000 (Mon, 21 Dec 2009) | 3 lines

  Issue #7518:  Move substitute definitions of C99 math functions from
  pymath.c to Modules/_math.c.
........

1 files changed, 198 insertions, 1 deletions

diff --git a/Modules/_math.c b/Modules/_math.c
index 9d330aa0d5..e27c10092b 100644
--- a/Modules/_math.c
+++ b/Modules/_math.c
@@ -1,8 +1,161 @@
 /* Definitions of some C99 math library functions, for those platforms
    that don't implement these functions already. */
 
+#include "Python.h"
 #include <float.h>
-#include <math.h>
+
+/* The following copyright notice applies to the original
+   implementations of acosh, asinh and atanh. */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+static const double ln2 = 6.93147180559945286227E-01;
+static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */
+static const double two_pow_p28 = 268435456.0; /* 2**28 */
+static const double zero = 0.0;
+
+/* acosh(x)
+ * Method :
+ *      Based on
+ *	      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.
+ *
+ * Special cases:
+ *      acosh(x) is NaN with signal if x<1.
+ *      acosh(NaN) is NaN without signal.
+ */
+
+double
+_Py_acosh(double x)
+{
+	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;
+#else
+		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 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)))  
+ */
+
+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 = 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
+ *      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
+ *		  2	     1 - x		      1 - x
+ *
+ *      For x<0.5
+ *      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
+ *
+ * Special cases:
+ *      atanh(x) is NaN if |x| >= 1 with signal;
+ *      atanh(NaN) is that NaN with no signal;
+ *
+ */
+
+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;
+#ifdef Py_NAN
+		return Py_NAN;
+#else
+		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 * log1p(t + t*absx / (1.0 - absx));
+	} 
+	else {				/* 0.5 <= |x| <= 1.0 */
+		t = 0.5 * log1p((absx + absx) / (1.0 - absx));
+	}
+	return copysign(t, x);
+}
 
 /* Mathematically, expm1(x) = exp(x) - 1.  The expm1 function is designed
    to avoid the significant loss of precision that arises from direct
@@ -29,3 +182,47 @@ _Py_expm1(double x)
     else
         return exp(x) - 1.0;
 }
+
+/* log1p(x) = log(1+x).  The log1p function is designed to avoid the
+   significant loss of precision that arises from direct evaluation when x is
+   small. */
+
+double
+_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)
+
+       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) >=
+       DBL_EPSILON/2 or the rounding-mode is some form of round-to-nearest
+       then y-1-x will be exactly representable, and is computed exactly by
+       (y-1)-x.
+
+       If abs(x) < DBL_EPSILON/2 and the rounding mode is not known to be
+       round-to-nearest then this method is slightly dangerous: 1+x could be
+       rounded up to 1+DBL_EPSILON instead of down to 1, and in that case
+       y-1-x will not be exactly representable any more and the result can be
+       off by many ulps.  But this is easily fixed: for a floating-point
+       number |x| < DBL_EPSILON/2., the closest floating-point number to
+       log(1+x) is exactly x.
+    */
+
+    double y;
+    if (fabs(x) < DBL_EPSILON/2.) {
+        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;
+    } else {
+        /* NaNs and infinities should end up here */
+        return log(1.+x);
+    }
+}