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.
........

5 files changed, 245 insertions, 11 deletions

diff --git a/Modules/Setup.dist b/Modules/Setup.dist
index e1cb235..45bf531 100644
--- a/Modules/Setup.dist
+++ b/Modules/Setup.dist
@@ -157,7 +157,7 @@ _symtable symtablemodule.c
 # Modules that should always be present (non UNIX dependent):
 
 #array arraymodule.c	# array objects
-#cmath cmathmodule.c # -lm # complex math library functions
+#cmath cmathmodule.c _math.c # -lm # complex math library functions
 #math mathmodule.c _math.c # -lm # math library functions, e.g. sin()
 #_struct _struct.c	# binary structure packing/unpacking
 #time timemodule.c # -lm # time operations and variables
diff --git a/Modules/_math.c b/Modules/_math.c
index 9d330aa..e27c100 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);
+    }
+}
diff --git a/Modules/_math.h b/Modules/_math.h
index 69c96b5..c0ceece 100644
--- a/Modules/_math.h
+++ b/Modules/_math.h
@@ -1,4 +1,32 @@
+double _Py_acosh(double x);
+double _Py_asinh(double x);
+double _Py_atanh(double x);
 double _Py_expm1(double x);
+double _Py_log1p(double x);
+
+#ifdef HAVE_ACOSH
+#define m_acosh acosh
+#else
+/* if the system doesn't have acosh, use the substitute
+   function defined in Modules/_math.c. */
+#define m_acosh _Py_acosh
+#endif
+
+#ifdef HAVE_ASINH
+#define m_asinh asinh
+#else
+/* if the system doesn't have asinh, use the substitute
+   function defined in Modules/_math.c. */
+#define m_asinh _Py_asinh
+#endif
+
+#ifdef HAVE_ATANH
+#define m_atanh atanh
+#else
+/* if the system doesn't have atanh, use the substitute
+   function defined in Modules/_math.c. */
+#define m_atanh _Py_atanh
+#endif
 
 #ifdef HAVE_EXPM1
 #define m_expm1 expm1
@@ -7,3 +35,11 @@ double _Py_expm1(double x);
    function defined in Modules/_math.c. */
 #define m_expm1 _Py_expm1
 #endif
+
+#ifdef HAVE_LOG1P
+#define m_log1p log1p
+#else
+/* if the system doesn't have log1p, use the substitute
+   function defined in Modules/_math.c. */
+#define m_log1p _Py_log1p
+#endif
diff --git a/Modules/cmathmodule.c b/Modules/cmathmodule.c
index fbf6ece..4d13e58 100644
--- a/Modules/cmathmodule.c
+++ b/Modules/cmathmodule.c
@@ -3,6 +3,7 @@
 /* much code borrowed from mathmodule.c */
 
 #include "Python.h"
+#include "_math.h"
 /* we need DBL_MAX, DBL_MIN, DBL_EPSILON, DBL_MANT_DIG and FLT_RADIX from
    float.h.  We assume that FLT_RADIX is either 2 or 16. */
 #include <float.h>
@@ -149,7 +150,7 @@ c_acos(Py_complex z)
 		s2.imag = z.imag;
 		s2 = c_sqrt(s2);
 		r.real = 2.*atan2(s1.real, s2.real);
-		r.imag = asinh(s2.real*s1.imag - s2.imag*s1.real);
+		r.imag = m_asinh(s2.real*s1.imag - s2.imag*s1.real);
 	}
 	errno = 0;
 	return r;
@@ -181,7 +182,7 @@ c_acosh(Py_complex z)
 		s2.real = z.real + 1.;
 		s2.imag = z.imag;
 		s2 = c_sqrt(s2);
-		r.real = asinh(s1.real*s2.real + s1.imag*s2.imag);
+		r.real = m_asinh(s1.real*s2.real + s1.imag*s2.imag);
 		r.imag = 2.*atan2(s1.imag, s2.real);
 	}
 	errno = 0;
@@ -238,7 +239,7 @@ c_asinh(Py_complex z)
 		s2.real = 1.-z.imag;
 		s2.imag = z.real;
 		s2 = c_sqrt(s2);
-		r.real = asinh(s1.real*s2.imag-s2.real*s1.imag);
+		r.real = m_asinh(s1.real*s2.imag-s2.real*s1.imag);
 		r.imag = atan2(z.imag, s1.real*s2.real-s1.imag*s2.imag);
 	}
 	errno = 0;
@@ -342,7 +343,7 @@ c_atanh(Py_complex z)
 			errno = 0;
 		}
 	} else {
-		r.real = log1p(4.*z.real/((1-z.real)*(1-z.real) + ay*ay))/4.;
+		r.real = m_log1p(4.*z.real/((1-z.real)*(1-z.real) + ay*ay))/4.;
 		r.imag = -atan2(-2.*z.imag, (1-z.real)*(1+z.real) - ay*ay)/2.;
 		errno = 0;
 	}
@@ -552,7 +553,7 @@ c_log(Py_complex z)
 		if (0.71 <= h && h <= 1.73) {
 			am = ax > ay ? ax : ay;  /* max(ax, ay) */
 			an = ax > ay ? ay : ax;  /* min(ax, ay) */
-			r.real = log1p((am-1)*(am+1)+an*an)/2.;
+			r.real = m_log1p((am-1)*(am+1)+an*an)/2.;
 		} else {
 			r.real = log(h);
 		}
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 92f5f42..a057cac 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -816,18 +816,18 @@ math_2(PyObject *args, double (*func) (double, double), char *funcname)
 
 FUNC1(acos, acos, 0,
       "acos(x)\n\nReturn the arc cosine (measured in radians) of x.")
-FUNC1(acosh, acosh, 0,
+FUNC1(acosh, m_acosh, 0,
       "acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x.")
 FUNC1(asin, asin, 0,
       "asin(x)\n\nReturn the arc sine (measured in radians) of x.")
-FUNC1(asinh, asinh, 0,
+FUNC1(asinh, m_asinh, 0,
       "asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x.")
 FUNC1(atan, atan, 0,
       "atan(x)\n\nReturn the arc tangent (measured in radians) of x.")
 FUNC2(atan2, m_atan2,
       "atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n"
       "Unlike atan(y/x), the signs of both x and y are considered.")
-FUNC1(atanh, atanh, 0,
+FUNC1(atanh, m_atanh, 0,
       "atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x.")
 
 static PyObject * math_ceil(PyObject *self, PyObject *number) {
@@ -895,7 +895,7 @@ FUNC1A(gamma, m_tgamma,
       "gamma(x)\n\nGamma function at x.")
 FUNC1A(lgamma, m_lgamma,
       "lgamma(x)\n\nNatural logarithm of absolute value of Gamma function at x.")
-FUNC1(log1p, log1p, 1,
+FUNC1(log1p, m_log1p, 1,
       "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n"
       "The result is computed in a way which is accurate for x near zero.")
 FUNC1(sin, sin, 0,