bpo-45548: Remove _math.c workarounds for pre-C99 libm (GH-29179)

The :mod:`math` and :mod:`cmath` implementation now require a C99 compatible
``libm`` and no longer ship with workarounds for missing acosh, asinh,
expm1, and log1p functions.

The changeset also removes ``_math.c`` and moves the last remaining
workaround into ``_math.h``. This simplifies static builds with
``Modules/Setup`` and resolves symbol conflicts.

Co-authored-by: Mark Dickinson <mdickinson@enthought.com>
Co-authored-by: Brett Cannon <brett@python.org>
Signed-off-by: Christian Heimes <christian@python.org>

Makefile.pre.in

@@ -611,10 +611,6 @@ pybuilddir.txt: $(BUILDPYTHON)
 		exit 1 ; \
 	fi
 
-# This is shared by the math and cmath modules
-Modules/_math.o: Modules/_math.c Modules/_math.h
-	$(CC) -c $(CCSHARED) $(PY_CORE_CFLAGS) -o $@ $<
-
 # blake2s is auto-generated from blake2b
 $(srcdir)/Modules/_blake2/blake2s_impl.c: $(srcdir)/Modules/_blake2/blake2b_impl.c $(srcdir)/Modules/_blake2/blake2b2s.py
 	$(PYTHON_FOR_REGEN) $(srcdir)/Modules/_blake2/blake2b2s.py
@@ -625,7 +621,7 @@ $(srcdir)/Modules/_blake2/blake2s_impl.c: $(srcdir)/Modules/_blake2/blake2b_impl
 # -s, --silent or --quiet is always the first char.
 # Under BSD make, MAKEFLAGS might be " -s -v x=y".
 # Ignore macros passed by GNU make, passed after --
-sharedmods: $(BUILDPYTHON) pybuilddir.txt Modules/_math.o
+sharedmods: $(BUILDPYTHON) pybuilddir.txt
 	@case "`echo X $$MAKEFLAGS | sed 's/^X //;s/ -- .*//'`" in \
 	    *\ -s*|s*) quiet="-q";; \
 	    *) quiet="";; \

Misc/NEWS.d/next/Build/2021-10-24-21-49-49.bpo-45548.UWx0UC.rst

@@ -0,0 +1,3 @@
+The :mod:`math` and :mod:`cmath` implementation now require a C99 compatible
+``libm`` and no longer ship with workarounds for missing acosh, asinh, atanh,
+expm1, and log1p functions.

Modules/Setup

@@ -171,8 +171,8 @@ time timemodule.c
 #array arraymodule.c
 #audioop audioop.c
 #binascii binascii.c
-#cmath cmathmodule.c _math.c  # -lm
+#cmath cmathmodule.c  # -lm
-#math mathmodule.c _math.c  # -lm
+#math mathmodule.c  # -lm
 #pyexpat -I$(srcdir)/Modules/expat  expat/xmlparse.c expat/xmlrole.c expat/xmltok.c pyexpat.c
 #unicodedata  unicodedata.c
 

Modules/_math.c

@@ -1,270 +0,0 @@
-/* Definitions of some C99 math library functions, for those platforms
-   that don't implement these functions already. */
-
-#ifndef Py_BUILD_CORE_BUILTIN
-#  define Py_BUILD_CORE_MODULE 1
-#endif
-
-#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.
- * ====================================================
- */
-
-#if !defined(HAVE_ACOSH) || !defined(HAVE_ASINH)
-static const double ln2 = 6.93147180559945286227E-01;
-static const double two_pow_p28 = 268435456.0; /* 2**28 */
-#endif
-#if !defined(HAVE_ASINH) || !defined(HAVE_ATANH)
-static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */
-#endif
-#if !defined(HAVE_ATANH) && !defined(Py_NAN)
-static const double zero = 0.0;
-#endif
-
-
-#ifndef HAVE_ACOSH
-/* 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 m_log1p(t + sqrt(2.0 * t + t * t));
-    }
-}
-#endif   /* HAVE_ACOSH */
-
-
-#ifndef HAVE_ASINH
-/* 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 = m_log1p(absx + t / (1.0 + sqrt(1.0 + t)));
-    }
-    return copysign(w, x);
-
-}
-#endif   /* HAVE_ASINH */
-
-
-#ifndef HAVE_ATANH
-/* 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 * 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);
-}
-#endif   /* HAVE_ATANH */
-
-
-#ifndef HAVE_EXPM1
-/* Mathematically, expm1(x) = exp(x) - 1.  The expm1 function is designed
-   to avoid the significant loss of precision that arises from direct
-   evaluation of the expression exp(x) - 1, for x near 0. */
-
-double
-_Py_expm1(double x)
-{
-    /* For abs(x) >= log(2), it's safe to evaluate exp(x) - 1 directly; this
-       also works fine for infinities and nans.
-
-       For smaller x, we can use a method due to Kahan that achieves close to
-       full accuracy.
-    */
-
-    if (fabs(x) < 0.7) {
-        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;
-}
-#endif   /* HAVE_EXPM1 */
-
-
-/* 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)
-{
-#ifdef HAVE_LOG1P
-    /* Some platforms supply a log1p function but don't respect the sign of
-       zero:  log1p(-0.0) gives 0.0 instead of the correct result of -0.0.
-
-       To save fiddling with configure tests and platform checks, we handle the
-       special case of zero input directly on all platforms.
-    */
-    if (x == 0.0) {
-        return x;
-    }
-    else {
-        return log1p(x);
-    }
-#else
-    /* 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 that 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);
-    }
-#endif /* ifdef HAVE_LOG1P */
-}
-

Modules/_math.h

@@ -1,41 +1,24 @@
-#ifdef HAVE_ACOSH
+/* log1p(x) = log(1+x).  The log1p function is designed to avoid the
-#  define m_acosh acosh
+   significant loss of precision that arises from direct evaluation when x is
-#else
+   small. Use the substitute from _math.h on all platforms: it includes
-/* if the system doesn't have acosh, use the substitute
+   workarounds for buggy handling of zeros.
-   function defined in Modules/_math.c. */
+ */
-double _Py_acosh(double x);
-#  define m_acosh _Py_acosh
-#endif
 
-#ifdef HAVE_ASINH
+static double
-#  define m_asinh asinh
+_Py_log1p(double x)
-#else
+{
-/* if the system doesn't have asinh, use the substitute
+    /* Some platforms supply a log1p function but don't respect the sign of
-   function defined in Modules/_math.c. */
+       zero:  log1p(-0.0) gives 0.0 instead of the correct result of -0.0.
-double _Py_asinh(double x);
-#  define m_asinh _Py_asinh
-#endif
 
-#ifdef HAVE_ATANH
+       To save fiddling with configure tests and platform checks, we handle the
-#  define m_atanh atanh
+       special case of zero input directly on all platforms.
-#else
+    */
-/* if the system doesn't have atanh, use the substitute
+    if (x == 0.0) {
-   function defined in Modules/_math.c. */
+        return x;
-double _Py_atanh(double x);
+    }
-#define m_atanh _Py_atanh
+    else {
-#endif
+        return log1p(x);
+    }
+}
 
-#ifdef HAVE_EXPM1
-#  define m_expm1 expm1
-#else
-/* if the system doesn't have expm1, use the substitute
-   function defined in Modules/_math.c. */
-double _Py_expm1(double x);
-#define m_expm1 _Py_expm1
-#endif
-
-double _Py_log1p(double x);
-
-/* Use the substitute from _math.c on all platforms:
-   it includes workarounds for buggy handling of zeros. */
 #define m_log1p _Py_log1p

Modules/cmathmodule.c

@@ -8,11 +8,13 @@
 
 #include "Python.h"
 #include "pycore_dtoa.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>
 
+/* For _Py_log1p with workarounds for buggy handling of zeros. */
+#include "_math.h"
+
 #include "clinic/cmathmodule.c.h"
 /*[clinic input]
 module cmath
@@ -246,7 +248,7 @@ cmath_acos_impl(PyObject *module, Py_complex z)
         s2.imag = z.imag;
         s2 = cmath_sqrt_impl(module, s2);
         r.real = 2.*atan2(s1.real, s2.real);
-        r.imag = m_asinh(s2.real*s1.imag - s2.imag*s1.real);
+        r.imag = asinh(s2.real*s1.imag - s2.imag*s1.real);
     }
     errno = 0;
     return r;
@@ -280,7 +282,7 @@ cmath_acosh_impl(PyObject *module, Py_complex z)
         s2.real = z.real + 1.;
         s2.imag = z.imag;
         s2 = cmath_sqrt_impl(module, s2);
-        r.real = m_asinh(s1.real*s2.real + s1.imag*s2.imag);
+        r.real = asinh(s1.real*s2.real + s1.imag*s2.imag);
         r.imag = 2.*atan2(s1.imag, s2.real);
     }
     errno = 0;
@@ -340,7 +342,7 @@ cmath_asinh_impl(PyObject *module, Py_complex z)
         s2.real = 1.-z.imag;
         s2.imag = z.real;
         s2 = cmath_sqrt_impl(module, s2);
-        r.real = m_asinh(s1.real*s2.imag-s2.real*s1.imag);
+        r.real = asinh(s1.real*s2.imag-s2.real*s1.imag);
         r.imag = atan2(z.imag, s1.real*s2.real-s1.imag*s2.imag);
     }
     errno = 0;

Modules/mathmodule.c

@@ -61,6 +61,9 @@ raised for division by zero and mod by zero.
 #include "pycore_call.h"          // _PyObject_CallNoArgs()
 #include "pycore_dtoa.h"          // _Py_dg_infinity()
 #include "pycore_long.h"          // _PyLong_GetZero()
+/* For DBL_EPSILON in _math.h */
+#include <float.h>
+/* For _Py_log1p with workarounds for buggy handling of zeros. */
 #include "_math.h"
 
 #include "clinic/mathmodule.c.h"
@@ -1166,14 +1169,14 @@ FUNC1(acos, acos, 0,
       "acos($module, x, /)\n--\n\n"
       "Return the arc cosine (measured in radians) of x.\n\n"
       "The result is between 0 and pi.")
-FUNC1(acosh, m_acosh, 0,
+FUNC1(acosh, acosh, 0,
       "acosh($module, x, /)\n--\n\n"
       "Return the inverse hyperbolic cosine of x.")
 FUNC1(asin, asin, 0,
       "asin($module, x, /)\n--\n\n"
       "Return the arc sine (measured in radians) of x.\n\n"
       "The result is between -pi/2 and pi/2.")
-FUNC1(asinh, m_asinh, 0,
+FUNC1(asinh, asinh, 0,
       "asinh($module, x, /)\n--\n\n"
       "Return the inverse hyperbolic sine of x.")
 FUNC1(atan, atan, 0,
@@ -1184,7 +1187,7 @@ FUNC2(atan2, m_atan2,
       "atan2($module, y, x, /)\n--\n\n"
       "Return the arc tangent (measured in radians) of y/x.\n\n"
       "Unlike atan(y/x), the signs of both x and y are considered.")
-FUNC1(atanh, m_atanh, 0,
+FUNC1(atanh, atanh, 0,
       "atanh($module, x, /)\n--\n\n"
       "Return the inverse hyperbolic tangent of x.")
 FUNC1(cbrt, cbrt, 0,
@@ -1245,7 +1248,7 @@ FUNC1A(erfc, m_erfc,
 FUNC1(exp, exp, 1,
       "exp($module, x, /)\n--\n\n"
       "Return e raised to the power of x.")
-FUNC1(expm1, m_expm1, 1,
+FUNC1(expm1, expm1, 1,
       "expm1($module, x, /)\n--\n\n"
       "Return exp(x)-1.\n\n"
       "This function avoids the loss of precision involved in the direct "

PCbuild/pythoncore.vcxproj

@@ -332,7 +332,6 @@
     <ClCompile Include="..\Modules\_json.c" />
     <ClCompile Include="..\Modules\_localemodule.c" />
     <ClCompile Include="..\Modules\_lsprof.c" />
-    <ClCompile Include="..\Modules\_math.c" />
     <ClCompile Include="..\Modules\_pickle.c" />
     <ClCompile Include="..\Modules\_randommodule.c" />
     <ClCompile Include="..\Modules\_sha3\sha3module.c" />

PCbuild/pythoncore.vcxproj.filters

@@ -689,9 +689,6 @@
     <ClCompile Include="..\Modules\_lsprof.c">
       <Filter>Modules</Filter>
     </ClCompile>
-    <ClCompile Include="..\Modules\_math.c">
-      <Filter>Modules</Filter>
-    </ClCompile>
     <ClCompile Include="..\Modules\_pickle.c">
       <Filter>Modules</Filter>
     </ClCompile>

configure

@@ -15092,7 +15092,7 @@ fi
 LIBS_SAVE=$LIBS
 LIBS="$LIBS $LIBM"
 
-for ac_func in acosh asinh atanh erf erfc expm1 finite gamma
+for ac_func in acosh asinh atanh erf erfc expm1 finite gamma lgamma log1p log2 tgamma
 do :
   as_ac_var=`$as_echo "ac_cv_func_$ac_func" | $as_tr_sh`
 ac_fn_c_check_func "$LINENO" "$ac_func" "$as_ac_var"
@@ -15101,21 +15101,13 @@ if eval test \"x\$"$as_ac_var"\" = x"yes"; then :
 #define `$as_echo "HAVE_$ac_func" | $as_tr_cpp` 1
 _ACEOF
 
-fi
+else
-done
+  as_fn_error $? "Python requires C99 compatible libm" "$LINENO" 5
-
-for ac_func in lgamma log1p log2 tgamma
-do :
-  as_ac_var=`$as_echo "ac_cv_func_$ac_func" | $as_tr_sh`
-ac_fn_c_check_func "$LINENO" "$ac_func" "$as_ac_var"
-if eval test \"x\$"$as_ac_var"\" = x"yes"; then :
-  cat >>confdefs.h <<_ACEOF
-#define `$as_echo "HAVE_$ac_func" | $as_tr_cpp` 1
-_ACEOF
 
 fi
 done
 
+LIBS=$LIBS_SAVE
 
 # For multiprocessing module, check that sem_open
 # actually works.  For FreeBSD versions <= 7.2,

configure.ac

@@ -4692,8 +4692,12 @@ fi
 LIBS_SAVE=$LIBS
 LIBS="$LIBS $LIBM"
 
-AC_CHECK_FUNCS([acosh asinh atanh erf erfc expm1 finite gamma])
+AC_CHECK_FUNCS(
-AC_CHECK_FUNCS([lgamma log1p log2 tgamma])
+  [acosh asinh atanh erf erfc expm1 finite gamma lgamma log1p log2 tgamma],
+  [],
+  [AC_MSG_ERROR([Python requires C99 compatible libm])]
+)
+LIBS=$LIBS_SAVE
 
 # For multiprocessing module, check that sem_open
 # actually works.  For FreeBSD versions <= 7.2,

setup.py

@@ -904,18 +904,14 @@ class PyBuildExt(build_ext):
         # Context Variables
         self.add(Extension('_contextvars', ['_contextvarsmodule.c']))
 
-        shared_math = 'Modules/_math.o'
-
         # math library functions, e.g. sin()
         self.add(Extension('math',  ['mathmodule.c'],
-                           extra_objects=[shared_math],
+                           depends=['_math.h'],
-                           depends=['_math.h', shared_math],
                            libraries=['m']))
 
         # complex math library functions
         self.add(Extension('cmath', ['cmathmodule.c'],
-                           extra_objects=[shared_math],
+                           depends=['_math.h'],
-                           depends=['_math.h', shared_math],
                            libraries=['m']))
 
         # time libraries: librt may be needed for clock_gettime()