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.
........

1 files changed, 1002 insertions, 1002 deletions

diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 87afdab..76d7906 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -73,36 +73,36 @@ static const double sqrtpi = 1.772453850905516027298167483341145182798;
 static double
 sinpi(double x)
 {
-	double y, r;
-	int n;
-	/* this function should only ever be called for finite arguments */
-	assert(Py_IS_FINITE(x));
-	y = fmod(fabs(x), 2.0);
-	n = (int)round(2.0*y);
-	assert(0 <= n && n <= 4);
-	switch (n) {
-	case 0:
-		r = sin(pi*y);
-		break;
-	case 1:
-		r = cos(pi*(y-0.5));
-		break;
-	case 2:
-		/* N.B. -sin(pi*(y-1.0)) is *not* equivalent: it would give
-		   -0.0 instead of 0.0 when y == 1.0. */
-		r = sin(pi*(1.0-y));
-		break;
-	case 3:
-		r = -cos(pi*(y-1.5));
-		break;
-	case 4:
-		r = sin(pi*(y-2.0));
-		break;
-	default:
-		assert(0);  /* should never get here */
-		r = -1.23e200; /* silence gcc warning */
-	}
-	return copysign(1.0, x)*r;
+    double y, r;
+    int n;
+    /* this function should only ever be called for finite arguments */
+    assert(Py_IS_FINITE(x));
+    y = fmod(fabs(x), 2.0);
+    n = (int)round(2.0*y);
+    assert(0 <= n && n <= 4);
+    switch (n) {
+    case 0:
+        r = sin(pi*y);
+        break;
+    case 1:
+        r = cos(pi*(y-0.5));
+        break;
+    case 2:
+        /* N.B. -sin(pi*(y-1.0)) is *not* equivalent: it would give
+           -0.0 instead of 0.0 when y == 1.0. */
+        r = sin(pi*(1.0-y));
+        break;
+    case 3:
+        r = -cos(pi*(y-1.5));
+        break;
+    case 4:
+        r = sin(pi*(y-2.0));
+        break;
+    default:
+        assert(0);  /* should never get here */
+        r = -1.23e200; /* silence gcc warning */
+    }
+    return copysign(1.0, x)*r;
 }
 
 /* Implementation of the real gamma function.  In extensive but non-exhaustive
@@ -166,34 +166,34 @@ sinpi(double x)
 static const double lanczos_g = 6.024680040776729583740234375;
 static const double lanczos_g_minus_half = 5.524680040776729583740234375;
 static const double lanczos_num_coeffs[LANCZOS_N] = {
-	23531376880.410759688572007674451636754734846804940,
-	42919803642.649098768957899047001988850926355848959,
-	35711959237.355668049440185451547166705960488635843,
-	17921034426.037209699919755754458931112671403265390,
-	6039542586.3520280050642916443072979210699388420708,
-	1439720407.3117216736632230727949123939715485786772,
-	248874557.86205415651146038641322942321632125127801,
-	31426415.585400194380614231628318205362874684987640,
-	2876370.6289353724412254090516208496135991145378768,
-	186056.26539522349504029498971604569928220784236328,
-	8071.6720023658162106380029022722506138218516325024,
-	210.82427775157934587250973392071336271166969580291,
-	2.5066282746310002701649081771338373386264310793408
+    23531376880.410759688572007674451636754734846804940,
+    42919803642.649098768957899047001988850926355848959,
+    35711959237.355668049440185451547166705960488635843,
+    17921034426.037209699919755754458931112671403265390,
+    6039542586.3520280050642916443072979210699388420708,
+    1439720407.3117216736632230727949123939715485786772,
+    248874557.86205415651146038641322942321632125127801,
+    31426415.585400194380614231628318205362874684987640,
+    2876370.6289353724412254090516208496135991145378768,
+    186056.26539522349504029498971604569928220784236328,
+    8071.6720023658162106380029022722506138218516325024,
+    210.82427775157934587250973392071336271166969580291,
+    2.5066282746310002701649081771338373386264310793408
 };
 
 /* denominator is x*(x+1)*...*(x+LANCZOS_N-2) */
 static const double lanczos_den_coeffs[LANCZOS_N] = {
-	0.0, 39916800.0, 120543840.0, 150917976.0, 105258076.0, 45995730.0,
-	13339535.0, 2637558.0, 357423.0, 32670.0, 1925.0, 66.0, 1.0};
+    0.0, 39916800.0, 120543840.0, 150917976.0, 105258076.0, 45995730.0,
+    13339535.0, 2637558.0, 357423.0, 32670.0, 1925.0, 66.0, 1.0};
 
 /* gamma values for small positive integers, 1 though NGAMMA_INTEGRAL */
 #define NGAMMA_INTEGRAL 23
 static const double gamma_integral[NGAMMA_INTEGRAL] = {
-	1.0, 1.0, 2.0, 6.0, 24.0, 120.0, 720.0, 5040.0, 40320.0, 362880.0,
-	3628800.0, 39916800.0, 479001600.0, 6227020800.0, 87178291200.0,
-	1307674368000.0, 20922789888000.0, 355687428096000.0,
-	6402373705728000.0, 121645100408832000.0, 2432902008176640000.0,
-	51090942171709440000.0, 1124000727777607680000.0,
+    1.0, 1.0, 2.0, 6.0, 24.0, 120.0, 720.0, 5040.0, 40320.0, 362880.0,
+    3628800.0, 39916800.0, 479001600.0, 6227020800.0, 87178291200.0,
+    1307674368000.0, 20922789888000.0, 355687428096000.0,
+    6402373705728000.0, 121645100408832000.0, 2432902008176640000.0,
+    51090942171709440000.0, 1124000727777607680000.0,
 };
 
 /* Lanczos' sum L_g(x), for positive x */
@@ -201,125 +201,125 @@ static const double gamma_integral[NGAMMA_INTEGRAL] = {
 static double
 lanczos_sum(double x)
 {
-	double num = 0.0, den = 0.0;
-	int i;
-	assert(x > 0.0);
-	/* evaluate the rational function lanczos_sum(x).  For large
-	   x, the obvious algorithm risks overflow, so we instead
-	   rescale the denominator and numerator of the rational
-	   function by x**(1-LANCZOS_N) and treat this as a
-	   rational function in 1/x.  This also reduces the error for
-	   larger x values.  The choice of cutoff point (5.0 below) is
-	   somewhat arbitrary; in tests, smaller cutoff values than
-	   this resulted in lower accuracy. */
-	if (x < 5.0) {
-		for (i = LANCZOS_N; --i >= 0; ) {
-			num = num * x + lanczos_num_coeffs[i];
-			den = den * x + lanczos_den_coeffs[i];
-		}
-	}
-	else {
-		for (i = 0; i < LANCZOS_N; i++) {
-			num = num / x + lanczos_num_coeffs[i];
-			den = den / x + lanczos_den_coeffs[i];
-		}
-	}
-	return num/den;
+    double num = 0.0, den = 0.0;
+    int i;
+    assert(x > 0.0);
+    /* evaluate the rational function lanczos_sum(x).  For large
+       x, the obvious algorithm risks overflow, so we instead
+       rescale the denominator and numerator of the rational
+       function by x**(1-LANCZOS_N) and treat this as a
+       rational function in 1/x.  This also reduces the error for
+       larger x values.  The choice of cutoff point (5.0 below) is
+       somewhat arbitrary; in tests, smaller cutoff values than
+       this resulted in lower accuracy. */
+    if (x < 5.0) {
+        for (i = LANCZOS_N; --i >= 0; ) {
+            num = num * x + lanczos_num_coeffs[i];
+            den = den * x + lanczos_den_coeffs[i];
+        }
+    }
+    else {
+        for (i = 0; i < LANCZOS_N; i++) {
+            num = num / x + lanczos_num_coeffs[i];
+            den = den / x + lanczos_den_coeffs[i];
+        }
+    }
+    return num/den;
 }
 
 static double
 m_tgamma(double x)
 {
-	double absx, r, y, z, sqrtpow;
-
-	/* special cases */
-	if (!Py_IS_FINITE(x)) {
-		if (Py_IS_NAN(x) || x > 0.0)
-			return x;  /* tgamma(nan) = nan, tgamma(inf) = inf */
-		else {
-			errno = EDOM;
-			return Py_NAN;  /* tgamma(-inf) = nan, invalid */
-		}
-	}
-	if (x == 0.0) {
-		errno = EDOM;
-		return 1.0/x; /* tgamma(+-0.0) = +-inf, divide-by-zero */
-	}
-
-	/* integer arguments */
-	if (x == floor(x)) {
-		if (x < 0.0) {
-			errno = EDOM;  /* tgamma(n) = nan, invalid for */
-			return Py_NAN; /* negative integers n */
-		}
-		if (x <= NGAMMA_INTEGRAL)
-			return gamma_integral[(int)x - 1];
-	}
-	absx = fabs(x);
-
-	/* tiny arguments:  tgamma(x) ~ 1/x for x near 0 */
-	if (absx < 1e-20) {
-		r = 1.0/x;
-		if (Py_IS_INFINITY(r))
-			errno = ERANGE;
-		return r;
-	}
-
-	/* large arguments: assuming IEEE 754 doubles, tgamma(x) overflows for
-	   x > 200, and underflows to +-0.0 for x < -200, not a negative
-	   integer. */
-	if (absx > 200.0) {
-		if (x < 0.0) {
-			return 0.0/sinpi(x);
-		}
-		else {
-			errno = ERANGE;
-			return Py_HUGE_VAL;
-		}
-	}
-
-	y = absx + lanczos_g_minus_half;
-	/* compute error in sum */
-	if (absx > lanczos_g_minus_half) {
-		/* note: the correction can be foiled by an optimizing
-		   compiler that (incorrectly) thinks that an expression like
-		   a + b - a - b can be optimized to 0.0.  This shouldn't
-		   happen in a standards-conforming compiler. */
-		double q = y - absx;
-		z = q - lanczos_g_minus_half;
-	}
-	else {
-		double q = y - lanczos_g_minus_half;
-		z = q - absx;
-	}
-	z = z * lanczos_g / y;
-	if (x < 0.0) {
-		r = -pi / sinpi(absx) / absx * exp(y) / lanczos_sum(absx);
-		r -= z * r;
-		if (absx < 140.0) {
-			r /= pow(y, absx - 0.5);
-		}
-		else {
-			sqrtpow = pow(y, absx / 2.0 - 0.25);
-			r /= sqrtpow;
-			r /= sqrtpow;
-		}
-	}
-	else {
-		r = lanczos_sum(absx) / exp(y);
-		r += z * r;
-		if (absx < 140.0) {
-			r *= pow(y, absx - 0.5);
-		}
-		else {
-			sqrtpow = pow(y, absx / 2.0 - 0.25);
-			r *= sqrtpow;
-			r *= sqrtpow;
-		}
-	}
-	if (Py_IS_INFINITY(r))
-		errno = ERANGE;
-	return r;
+    double absx, r, y, z, sqrtpow;
+
+    /* special cases */
+    if (!Py_IS_FINITE(x)) {
+        if (Py_IS_NAN(x) || x > 0.0)
+            return x;  /* tgamma(nan) = nan, tgamma(inf) = inf */
+        else {
+            errno = EDOM;
+            return Py_NAN;  /* tgamma(-inf) = nan, invalid */
+        }
+    }
+    if (x == 0.0) {
+        errno = EDOM;
+        return 1.0/x; /* tgamma(+-0.0) = +-inf, divide-by-zero */
+    }
+
+    /* integer arguments */
+    if (x == floor(x)) {
+        if (x < 0.0) {
+            errno = EDOM;  /* tgamma(n) = nan, invalid for */
+            return Py_NAN; /* negative integers n */
+        }
+        if (x <= NGAMMA_INTEGRAL)
+            return gamma_integral[(int)x - 1];
+    }
+    absx = fabs(x);
+
+    /* tiny arguments:  tgamma(x) ~ 1/x for x near 0 */
+    if (absx < 1e-20) {
+        r = 1.0/x;
+        if (Py_IS_INFINITY(r))
+            errno = ERANGE;
+        return r;
+    }
+
+    /* large arguments: assuming IEEE 754 doubles, tgamma(x) overflows for
+       x > 200, and underflows to +-0.0 for x < -200, not a negative
+       integer. */
+    if (absx > 200.0) {
+        if (x < 0.0) {
+            return 0.0/sinpi(x);
+        }
+        else {
+            errno = ERANGE;
+            return Py_HUGE_VAL;
+        }
+    }
+
+    y = absx + lanczos_g_minus_half;
+    /* compute error in sum */
+    if (absx > lanczos_g_minus_half) {
+        /* note: the correction can be foiled by an optimizing
+           compiler that (incorrectly) thinks that an expression like
+           a + b - a - b can be optimized to 0.0.  This shouldn't
+           happen in a standards-conforming compiler. */
+        double q = y - absx;
+        z = q - lanczos_g_minus_half;
+    }
+    else {
+        double q = y - lanczos_g_minus_half;
+        z = q - absx;
+    }
+    z = z * lanczos_g / y;
+    if (x < 0.0) {
+        r = -pi / sinpi(absx) / absx * exp(y) / lanczos_sum(absx);
+        r -= z * r;
+        if (absx < 140.0) {
+            r /= pow(y, absx - 0.5);
+        }
+        else {
+            sqrtpow = pow(y, absx / 2.0 - 0.25);
+            r /= sqrtpow;
+            r /= sqrtpow;
+        }
+    }
+    else {
+        r = lanczos_sum(absx) / exp(y);
+        r += z * r;
+        if (absx < 140.0) {
+            r *= pow(y, absx - 0.5);
+        }
+        else {
+            sqrtpow = pow(y, absx / 2.0 - 0.25);
+            r *= sqrtpow;
+            r *= sqrtpow;
+        }
+    }
+    if (Py_IS_INFINITY(r))
+        errno = ERANGE;
+    return r;
 }
 
 /*
@@ -330,49 +330,49 @@ m_tgamma(double x)
 static double
 m_lgamma(double x)
 {
-	double r, absx;
-
-	/* special cases */
-	if (!Py_IS_FINITE(x)) {
-		if (Py_IS_NAN(x))
-			return x;  /* lgamma(nan) = nan */
-		else
-			return Py_HUGE_VAL; /* lgamma(+-inf) = +inf */
-	}
-
-	/* integer arguments */
-	if (x == floor(x) && x <= 2.0) {
-		if (x <= 0.0) {
-			errno = EDOM;  /* lgamma(n) = inf, divide-by-zero for */
-			return Py_HUGE_VAL; /* integers n <= 0 */
-		}
-		else {
-			return 0.0; /* lgamma(1) = lgamma(2) = 0.0 */
-		}
-	}
-
-	absx = fabs(x);
-	/* tiny arguments: lgamma(x) ~ -log(fabs(x)) for small x */
-	if (absx < 1e-20)
-		return -log(absx);
-
-	/* Lanczos' formula */
-	if (x > 0.0) {
-		/* we could save a fraction of a ulp in accuracy by having a
-		   second set of numerator coefficients for lanczos_sum that
-		   absorbed the exp(-lanczos_g) term, and throwing out the
-		   lanczos_g subtraction below; it's probably not worth it. */
-		r = log(lanczos_sum(x)) - lanczos_g +
-			(x-0.5)*(log(x+lanczos_g-0.5)-1);
-	}
-	else {
-		r = log(pi) - log(fabs(sinpi(absx))) - log(absx) -
-			(log(lanczos_sum(absx)) - lanczos_g +
-			 (absx-0.5)*(log(absx+lanczos_g-0.5)-1));
-	}
-	if (Py_IS_INFINITY(r))
-		errno = ERANGE;
-	return r;
+    double r, absx;
+
+    /* special cases */
+    if (!Py_IS_FINITE(x)) {
+        if (Py_IS_NAN(x))
+            return x;  /* lgamma(nan) = nan */
+        else
+            return Py_HUGE_VAL; /* lgamma(+-inf) = +inf */
+    }
+
+    /* integer arguments */
+    if (x == floor(x) && x <= 2.0) {
+        if (x <= 0.0) {
+            errno = EDOM;  /* lgamma(n) = inf, divide-by-zero for */
+            return Py_HUGE_VAL; /* integers n <= 0 */
+        }
+        else {
+            return 0.0; /* lgamma(1) = lgamma(2) = 0.0 */
+        }
+    }
+
+    absx = fabs(x);
+    /* tiny arguments: lgamma(x) ~ -log(fabs(x)) for small x */
+    if (absx < 1e-20)
+        return -log(absx);
+
+    /* Lanczos' formula */
+    if (x > 0.0) {
+        /* we could save a fraction of a ulp in accuracy by having a
+           second set of numerator coefficients for lanczos_sum that
+           absorbed the exp(-lanczos_g) term, and throwing out the
+           lanczos_g subtraction below; it's probably not worth it. */
+        r = log(lanczos_sum(x)) - lanczos_g +
+            (x-0.5)*(log(x+lanczos_g-0.5)-1);
+    }
+    else {
+        r = log(pi) - log(fabs(sinpi(absx))) - log(absx) -
+            (log(lanczos_sum(absx)) - lanczos_g +
+             (absx-0.5)*(log(absx+lanczos_g-0.5)-1));
+    }
+    if (Py_IS_INFINITY(r))
+        errno = ERANGE;
+    return r;
 }
 
 /*
@@ -428,17 +428,17 @@ m_lgamma(double x)
 static double
 m_erf_series(double x)
 {
-	double x2, acc, fk;
-	int i;
-
-	x2 = x * x;
-	acc = 0.0;
-	fk = (double)ERF_SERIES_TERMS + 0.5;
-	for (i = 0; i < ERF_SERIES_TERMS; i++) {
-		acc = 2.0 + x2 * acc / fk;
-		fk -= 1.0;
-	}
-	return acc * x * exp(-x2) / sqrtpi;
+    double x2, acc, fk;
+    int i;
+
+    x2 = x * x;
+    acc = 0.0;
+    fk = (double)ERF_SERIES_TERMS + 0.5;
+    for (i = 0; i < ERF_SERIES_TERMS; i++) {
+        acc = 2.0 + x2 * acc / fk;
+        fk -= 1.0;
+    }
+    return acc * x * exp(-x2) / sqrtpi;
 }
 
 /*
@@ -453,26 +453,26 @@ m_erf_series(double x)
 static double
 m_erfc_contfrac(double x)
 {
-	double x2, a, da, p, p_last, q, q_last, b;
-	int i;
-
-	if (x >= ERFC_CONTFRAC_CUTOFF)
-		return 0.0;
-
-	x2 = x*x;
-	a = 0.0;
-	da = 0.5;
-	p = 1.0; p_last = 0.0;
-	q = da + x2; q_last = 1.0;
-	for (i = 0; i < ERFC_CONTFRAC_TERMS; i++) {
-		double temp;
-		a += da;
-		da += 2.0;
-		b = da + x2;
-		temp = p; p = b*p - a*p_last; p_last = temp;
-		temp = q; q = b*q - a*q_last; q_last = temp;
-	}
-	return p / q * x * exp(-x2) / sqrtpi;
+    double x2, a, da, p, p_last, q, q_last, b;
+    int i;
+
+    if (x >= ERFC_CONTFRAC_CUTOFF)
+        return 0.0;
+
+    x2 = x*x;
+    a = 0.0;
+    da = 0.5;
+    p = 1.0; p_last = 0.0;
+    q = da + x2; q_last = 1.0;
+    for (i = 0; i < ERFC_CONTFRAC_TERMS; i++) {
+        double temp;
+        a += da;
+        da += 2.0;
+        b = da + x2;
+        temp = p; p = b*p - a*p_last; p_last = temp;
+        temp = q; q = b*q - a*q_last; q_last = temp;
+    }
+    return p / q * x * exp(-x2) / sqrtpi;
 }
 
 /* Error function erf(x), for general x */
@@ -480,17 +480,17 @@ m_erfc_contfrac(double x)
 static double
 m_erf(double x)
 {
-	double absx, cf;
-
-	if (Py_IS_NAN(x))
-		return x;
-	absx = fabs(x);
-	if (absx < ERF_SERIES_CUTOFF)
-		return m_erf_series(x);
-	else {
-		cf = m_erfc_contfrac(absx);
-		return x > 0.0 ? 1.0 - cf : cf - 1.0;
-	}
+    double absx, cf;
+
+    if (Py_IS_NAN(x))
+        return x;
+    absx = fabs(x);
+    if (absx < ERF_SERIES_CUTOFF)
+        return m_erf_series(x);
+    else {
+        cf = m_erfc_contfrac(absx);
+        return x > 0.0 ? 1.0 - cf : cf - 1.0;
+    }
 }
 
 /* Complementary error function erfc(x), for general x. */
@@ -498,17 +498,17 @@ m_erf(double x)
 static double
 m_erfc(double x)
 {
-	double absx, cf;
-
-	if (Py_IS_NAN(x))
-		return x;
-	absx = fabs(x);
-	if (absx < ERF_SERIES_CUTOFF)
-		return 1.0 - m_erf_series(x);
-	else {
-		cf = m_erfc_contfrac(absx);
-		return x > 0.0 ? cf : 2.0 - cf;
-	}
+    double absx, cf;
+
+    if (Py_IS_NAN(x))
+        return x;
+    absx = fabs(x);
+    if (absx < ERF_SERIES_CUTOFF)
+        return 1.0 - m_erf_series(x);
+    else {
+        cf = m_erfc_contfrac(absx);
+        return x > 0.0 ? cf : 2.0 - cf;
+    }
 }
 
 /*
@@ -522,29 +522,29 @@ m_erfc(double x)
 static double
 m_atan2(double y, double x)
 {
-	if (Py_IS_NAN(x) || Py_IS_NAN(y))
-		return Py_NAN;
-	if (Py_IS_INFINITY(y)) {
-		if (Py_IS_INFINITY(x)) {
-			if (copysign(1., x) == 1.)
-				/* atan2(+-inf, +inf) == +-pi/4 */
-				return copysign(0.25*Py_MATH_PI, y);
-			else
-				/* atan2(+-inf, -inf) == +-pi*3/4 */
-				return copysign(0.75*Py_MATH_PI, y);
-		}
-		/* atan2(+-inf, x) == +-pi/2 for finite x */
-		return copysign(0.5*Py_MATH_PI, y);
-	}
-	if (Py_IS_INFINITY(x) || y == 0.) {
-		if (copysign(1., x) == 1.)
-			/* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
-			return copysign(0., y);
-		else
-			/* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
-			return copysign(Py_MATH_PI, y);
-	}
-	return atan2(y, x);
+    if (Py_IS_NAN(x) || Py_IS_NAN(y))
+        return Py_NAN;
+    if (Py_IS_INFINITY(y)) {
+        if (Py_IS_INFINITY(x)) {
+            if (copysign(1., x) == 1.)
+                /* atan2(+-inf, +inf) == +-pi/4 */
+                return copysign(0.25*Py_MATH_PI, y);
+            else
+                /* atan2(+-inf, -inf) == +-pi*3/4 */
+                return copysign(0.75*Py_MATH_PI, y);
+        }
+        /* atan2(+-inf, x) == +-pi/2 for finite x */
+        return copysign(0.5*Py_MATH_PI, y);
+    }
+    if (Py_IS_INFINITY(x) || y == 0.) {
+        if (copysign(1., x) == 1.)
+            /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
+            return copysign(0., y);
+        else
+            /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
+            return copysign(Py_MATH_PI, y);
+    }
+    return atan2(y, x);
 }
 
 /*
@@ -557,45 +557,45 @@ m_atan2(double y, double x)
 static double
 m_log(double x)
 {
-	if (Py_IS_FINITE(x)) {
-		if (x > 0.0)
-			return log(x);
-		errno = EDOM;
-		if (x == 0.0)
-			return -Py_HUGE_VAL; /* log(0) = -inf */
-		else
-			return Py_NAN; /* log(-ve) = nan */
-	}
-	else if (Py_IS_NAN(x))
-		return x; /* log(nan) = nan */
-	else if (x > 0.0)
-		return x; /* log(inf) = inf */
-	else {
-		errno = EDOM;
-		return Py_NAN; /* log(-inf) = nan */
-	}
+    if (Py_IS_FINITE(x)) {
+        if (x > 0.0)
+            return log(x);
+        errno = EDOM;
+        if (x == 0.0)
+            return -Py_HUGE_VAL; /* log(0) = -inf */
+        else
+            return Py_NAN; /* log(-ve) = nan */
+    }
+    else if (Py_IS_NAN(x))
+        return x; /* log(nan) = nan */
+    else if (x > 0.0)
+        return x; /* log(inf) = inf */
+    else {
+        errno = EDOM;
+        return Py_NAN; /* log(-inf) = nan */
+    }
 }
 
 static double
 m_log10(double x)
 {
-	if (Py_IS_FINITE(x)) {
-		if (x > 0.0)
-			return log10(x);
-		errno = EDOM;
-		if (x == 0.0)
-			return -Py_HUGE_VAL; /* log10(0) = -inf */
-		else
-			return Py_NAN; /* log10(-ve) = nan */
-	}
-	else if (Py_IS_NAN(x))
-		return x; /* log10(nan) = nan */
-	else if (x > 0.0)
-		return x; /* log10(inf) = inf */
-	else {
-		errno = EDOM;
-		return Py_NAN; /* log10(-inf) = nan */
-	}
+    if (Py_IS_FINITE(x)) {
+        if (x > 0.0)
+            return log10(x);
+        errno = EDOM;
+        if (x == 0.0)
+            return -Py_HUGE_VAL; /* log10(0) = -inf */
+        else
+            return Py_NAN; /* log10(-ve) = nan */
+    }
+    else if (Py_IS_NAN(x))
+        return x; /* log10(nan) = nan */
+    else if (x > 0.0)
+        return x; /* log10(inf) = inf */
+    else {
+        errno = EDOM;
+        return Py_NAN; /* log10(-inf) = nan */
+    }
 }
 
 
@@ -606,37 +606,37 @@ m_log10(double x)
 static int
 is_error(double x)
 {
-	int result = 1;	/* presumption of guilt */
-	assert(errno);	/* non-zero errno is a precondition for calling */
-	if (errno == EDOM)
-		PyErr_SetString(PyExc_ValueError, "math domain error");
-
-	else if (errno == ERANGE) {
-		/* ANSI C generally requires libm functions to set ERANGE
-		 * on overflow, but also generally *allows* them to set
-		 * ERANGE on underflow too.  There's no consistency about
-		 * the latter across platforms.
-		 * Alas, C99 never requires that errno be set.
-		 * Here we suppress the underflow errors (libm functions
-		 * should return a zero on underflow, and +- HUGE_VAL on
-		 * overflow, so testing the result for zero suffices to
-		 * distinguish the cases).
-		 *
-		 * On some platforms (Ubuntu/ia64) it seems that errno can be
-		 * set to ERANGE for subnormal results that do *not* underflow
-		 * to zero.  So to be safe, we'll ignore ERANGE whenever the
-		 * function result is less than one in absolute value.
-		 */
-		if (fabs(x) < 1.0)
-			result = 0;
-		else
-			PyErr_SetString(PyExc_OverflowError,
-					"math range error");
-	}
-	else
-                /* Unexpected math error */
-		PyErr_SetFromErrno(PyExc_ValueError);
-	return result;
+    int result = 1;     /* presumption of guilt */
+    assert(errno);      /* non-zero errno is a precondition for calling */
+    if (errno == EDOM)
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+
+    else if (errno == ERANGE) {
+        /* ANSI C generally requires libm functions to set ERANGE
+         * on overflow, but also generally *allows* them to set
+         * ERANGE on underflow too.  There's no consistency about
+         * the latter across platforms.
+         * Alas, C99 never requires that errno be set.
+         * Here we suppress the underflow errors (libm functions
+         * should return a zero on underflow, and +- HUGE_VAL on
+         * overflow, so testing the result for zero suffices to
+         * distinguish the cases).
+         *
+         * On some platforms (Ubuntu/ia64) it seems that errno can be
+         * set to ERANGE for subnormal results that do *not* underflow
+         * to zero.  So to be safe, we'll ignore ERANGE whenever the
+         * function result is less than one in absolute value.
+         */
+        if (fabs(x) < 1.0)
+            result = 0;
+        else
+            PyErr_SetString(PyExc_OverflowError,
+                            "math range error");
+    }
+    else
+        /* Unexpected math error */
+        PyErr_SetFromErrno(PyExc_ValueError);
+    return result;
 }
 
 /*
@@ -674,33 +674,33 @@ math_1_to_whatever(PyObject *arg, double (*func) (double),
                    PyObject *(*from_double_func) (double),
                    int can_overflow)
 {
-	double x, r;
-	x = PyFloat_AsDouble(arg);
-	if (x == -1.0 && PyErr_Occurred())
-		return NULL;
-	errno = 0;
-	PyFPE_START_PROTECT("in math_1", return 0);
-	r = (*func)(x);
-	PyFPE_END_PROTECT(r);
-	if (Py_IS_NAN(r) && !Py_IS_NAN(x)) {
-		PyErr_SetString(PyExc_ValueError,
-				"math domain error"); /* invalid arg */
-		return NULL;
-	}
-	if (Py_IS_INFINITY(r) && Py_IS_FINITE(x)) {
-			if (can_overflow)
-				PyErr_SetString(PyExc_OverflowError,
-					"math range error"); /* overflow */
-			else
-				PyErr_SetString(PyExc_ValueError,
-					"math domain error"); /* singularity */
-			return NULL;
-	}
-	if (Py_IS_FINITE(r) && errno && is_error(r))
-		/* this branch unnecessary on most platforms */
-		return NULL;
-
-	return (*from_double_func)(r);
+    double x, r;
+    x = PyFloat_AsDouble(arg);
+    if (x == -1.0 && PyErr_Occurred())
+        return NULL;
+    errno = 0;
+    PyFPE_START_PROTECT("in math_1", return 0);
+    r = (*func)(x);
+    PyFPE_END_PROTECT(r);
+    if (Py_IS_NAN(r) && !Py_IS_NAN(x)) {
+        PyErr_SetString(PyExc_ValueError,
+                        "math domain error"); /* invalid arg */
+        return NULL;
+    }
+    if (Py_IS_INFINITY(r) && Py_IS_FINITE(x)) {
+                    if (can_overflow)
+                            PyErr_SetString(PyExc_OverflowError,
+                                    "math range error"); /* overflow */
+            else
+                PyErr_SetString(PyExc_ValueError,
+                    "math domain error"); /* singularity */
+            return NULL;
+    }
+    if (Py_IS_FINITE(r) && errno && is_error(r))
+        /* this branch unnecessary on most platforms */
+        return NULL;
+
+    return (*from_double_func)(r);
 }
 
 /* variant of math_1, to be used when the function being wrapped is known to
@@ -710,17 +710,17 @@ math_1_to_whatever(PyObject *arg, double (*func) (double),
 static PyObject *
 math_1a(PyObject *arg, double (*func) (double))
 {
-	double x, r;
-	x = PyFloat_AsDouble(arg);
-	if (x == -1.0 && PyErr_Occurred())
-		return NULL;
-	errno = 0;
-	PyFPE_START_PROTECT("in math_1a", return 0);
-	r = (*func)(x);
-	PyFPE_END_PROTECT(r);
-	if (errno && is_error(r))
-		return NULL;
-	return PyFloat_FromDouble(r);
+    double x, r;
+    x = PyFloat_AsDouble(arg);
+    if (x == -1.0 && PyErr_Occurred())
+        return NULL;
+    errno = 0;
+    PyFPE_START_PROTECT("in math_1a", return 0);
+    r = (*func)(x);
+    PyFPE_END_PROTECT(r);
+    if (errno && is_error(r))
+        return NULL;
+    return PyFloat_FromDouble(r);
 }
 
 /*
@@ -753,65 +753,65 @@ math_1a(PyObject *arg, double (*func) (double))
 static PyObject *
 math_1(PyObject *arg, double (*func) (double), int can_overflow)
 {
-	return math_1_to_whatever(arg, func, PyFloat_FromDouble, can_overflow);
+    return math_1_to_whatever(arg, func, PyFloat_FromDouble, can_overflow);
 }
 
 static PyObject *
 math_1_to_int(PyObject *arg, double (*func) (double), int can_overflow)
 {
-	return math_1_to_whatever(arg, func, PyLong_FromDouble, can_overflow);
+    return math_1_to_whatever(arg, func, PyLong_FromDouble, can_overflow);
 }
 
 static PyObject *
 math_2(PyObject *args, double (*func) (double, double), char *funcname)
 {
-	PyObject *ox, *oy;
-	double x, y, r;
-	if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
-		return NULL;
-	x = PyFloat_AsDouble(ox);
-	y = PyFloat_AsDouble(oy);
-	if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
-		return NULL;
-	errno = 0;
-	PyFPE_START_PROTECT("in math_2", return 0);
-	r = (*func)(x, y);
-	PyFPE_END_PROTECT(r);
-	if (Py_IS_NAN(r)) {
-		if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
-			errno = EDOM;
-		else
-			errno = 0;
-	}
-	else if (Py_IS_INFINITY(r)) {
-		if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
-			errno = ERANGE;
-		else
-			errno = 0;
-	}
-	if (errno && is_error(r))
-		return NULL;
-	else
-		return PyFloat_FromDouble(r);
+    PyObject *ox, *oy;
+    double x, y, r;
+    if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
+        return NULL;
+    x = PyFloat_AsDouble(ox);
+    y = PyFloat_AsDouble(oy);
+    if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
+        return NULL;
+    errno = 0;
+    PyFPE_START_PROTECT("in math_2", return 0);
+    r = (*func)(x, y);
+    PyFPE_END_PROTECT(r);
+    if (Py_IS_NAN(r)) {
+        if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
+            errno = EDOM;
+        else
+            errno = 0;
+    }
+    else if (Py_IS_INFINITY(r)) {
+        if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
+            errno = ERANGE;
+        else
+            errno = 0;
+    }
+    if (errno && is_error(r))
+        return NULL;
+    else
+        return PyFloat_FromDouble(r);
 }
 
-#define FUNC1(funcname, func, can_overflow, docstring)			\
-	static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
-		return math_1(args, func, can_overflow);		    \
-	}\
-        PyDoc_STRVAR(math_##funcname##_doc, docstring);
+#define FUNC1(funcname, func, can_overflow, docstring)                  \
+    static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
+        return math_1(args, func, can_overflow);                            \
+    }\
+    PyDoc_STRVAR(math_##funcname##_doc, docstring);
 
-#define FUNC1A(funcname, func, docstring)				\
-	static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
-		return math_1a(args, func);				\
-	}\
-        PyDoc_STRVAR(math_##funcname##_doc, docstring);
+#define FUNC1A(funcname, func, docstring)                               \
+    static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
+        return math_1a(args, func);                                     \
+    }\
+    PyDoc_STRVAR(math_##funcname##_doc, docstring);
 
 #define FUNC2(funcname, func, docstring) \
-	static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
-		return math_2(args, func, #funcname); \
-	}\
-        PyDoc_STRVAR(math_##funcname##_doc, docstring);
+    static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
+        return math_2(args, func, #funcname); \
+    }\
+    PyDoc_STRVAR(math_##funcname##_doc, docstring);
 
 FUNC1(acos, acos, 0,
       "acos(x)\n\nReturn the arc cosine (measured in radians) of x.")
@@ -830,25 +830,25 @@ 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) {
-	static PyObject *ceil_str = NULL;
-	PyObject *method;
-
-	if (ceil_str == NULL) {
-		ceil_str = PyUnicode_InternFromString("__ceil__");
-		if (ceil_str == NULL)
-			return NULL;
-	}
-
-	method = _PyType_Lookup(Py_TYPE(number), ceil_str);
-	if (method == NULL)
-		return math_1_to_int(number, ceil, 0);
-	else
-		return PyObject_CallFunction(method, "O", number);
+    static PyObject *ceil_str = NULL;
+    PyObject *method;
+
+    if (ceil_str == NULL) {
+        ceil_str = PyUnicode_InternFromString("__ceil__");
+        if (ceil_str == NULL)
+            return NULL;
+    }
+
+    method = _PyType_Lookup(Py_TYPE(number), ceil_str);
+    if (method == NULL)
+        return math_1_to_int(number, ceil, 0);
+    else
+        return PyObject_CallFunction(method, "O", number);
 }
 
 PyDoc_STRVAR(math_ceil_doc,
-	     "ceil(x)\n\nReturn the ceiling of x as an int.\n"
-	     "This is the smallest integral value >= x.");
+             "ceil(x)\n\nReturn the ceiling of x as an int.\n"
+             "This is the smallest integral value >= x.");
 
 FUNC2(copysign, copysign,
       "copysign(x, y)\n\nReturn x with the sign of y.")
@@ -870,25 +870,25 @@ FUNC1(fabs, fabs, 0,
       "fabs(x)\n\nReturn the absolute value of the float x.")
 
 static PyObject * math_floor(PyObject *self, PyObject *number) {
-	static PyObject *floor_str = NULL;
-	PyObject *method;
-
-	if (floor_str == NULL) {
-		floor_str = PyUnicode_InternFromString("__floor__");
-		if (floor_str == NULL)
-			return NULL;
-	}
-
-	method = _PyType_Lookup(Py_TYPE(number), floor_str);
-	if (method == NULL)
-        	return math_1_to_int(number, floor, 0);
-	else
-		return PyObject_CallFunction(method, "O", number);
+    static PyObject *floor_str = NULL;
+    PyObject *method;
+
+    if (floor_str == NULL) {
+        floor_str = PyUnicode_InternFromString("__floor__");
+        if (floor_str == NULL)
+            return NULL;
+    }
+
+    method = _PyType_Lookup(Py_TYPE(number), floor_str);
+    if (method == NULL)
+        return math_1_to_int(number, floor, 0);
+    else
+        return PyObject_CallFunction(method, "O", number);
 }
 
 PyDoc_STRVAR(math_floor_doc,
-	     "floor(x)\n\nReturn the floor of x as an int.\n"
-	     "This is the largest integral value <= x.");
+             "floor(x)\n\nReturn the floor of x as an int.\n"
+             "This is the largest integral value <= x.");
 
 FUNC1A(gamma, m_tgamma,
       "gamma(x)\n\nGamma function at x.")
@@ -928,7 +928,7 @@ FUNC1(tanh, tanh, 0,
    Also, the volatile declaration forces the values to be stored in memory as
    regular doubles instead of extended long precision (80-bit) values.  This
    prevents double rounding because any addition or subtraction of two doubles
-   can be resolved exactly into double-sized hi and lo values.  As long as the 
+   can be resolved exactly into double-sized hi and lo values.  As long as the
    hi value gets forced into a double before yr and lo are computed, the extra
    bits in downstream extended precision operations (x87 for example) will be
    exactly zero and therefore can be losslessly stored back into a double,
@@ -951,27 +951,27 @@ static int                          /* non-zero on error */
 _fsum_realloc(double **p_ptr, Py_ssize_t  n,
              double  *ps,    Py_ssize_t *m_ptr)
 {
-	void *v = NULL;
-	Py_ssize_t m = *m_ptr;
-
-	m += m;  /* double */
-	if (n < m && m < (PY_SSIZE_T_MAX / sizeof(double))) {
-		double *p = *p_ptr;
-		if (p == ps) {
-			v = PyMem_Malloc(sizeof(double) * m);
-			if (v != NULL)
-				memcpy(v, ps, sizeof(double) * n);
-		}
-		else
-			v = PyMem_Realloc(p, sizeof(double) * m);
-	}
-	if (v == NULL) {        /* size overflow or no memory */
-		PyErr_SetString(PyExc_MemoryError, "math.fsum partials");
-		return 1;
-	}
-	*p_ptr = (double*) v;
-	*m_ptr = m;
-	return 0;
+    void *v = NULL;
+    Py_ssize_t m = *m_ptr;
+
+    m += m;  /* double */
+    if (n < m && m < (PY_SSIZE_T_MAX / sizeof(double))) {
+        double *p = *p_ptr;
+        if (p == ps) {
+            v = PyMem_Malloc(sizeof(double) * m);
+            if (v != NULL)
+                memcpy(v, ps, sizeof(double) * n);
+        }
+        else
+            v = PyMem_Realloc(p, sizeof(double) * m);
+    }
+    if (v == NULL) {        /* size overflow or no memory */
+        PyErr_SetString(PyExc_MemoryError, "math.fsum partials");
+        return 1;
+    }
+    *p_ptr = (double*) v;
+    *m_ptr = m;
+    return 0;
 }
 
 /* Full precision summation of a sequence of floats.
@@ -979,17 +979,17 @@ _fsum_realloc(double **p_ptr, Py_ssize_t  n,
    def msum(iterable):
        partials = []  # sorted, non-overlapping partial sums
        for x in iterable:
-           i = 0
-           for y in partials:
-               if abs(x) < abs(y):
-                   x, y = y, x
-               hi = x + y
-               lo = y - (hi - x)
-               if lo:
-                   partials[i] = lo
-                   i += 1
-               x = hi
-           partials[i:] = [x]
+       i = 0
+       for y in partials:
+           if abs(x) < abs(y):
+           x, y = y, x
+           hi = x + y
+           lo = y - (hi - x)
+           if lo:
+           partials[i] = lo
+           i += 1
+           x = hi
+       partials[i:] = [x]
        return sum_exact(partials)
 
    Rounded x+y stored in hi with the roundoff stored in lo.  Together hi+lo
@@ -1007,119 +1007,119 @@ _fsum_realloc(double **p_ptr, Py_ssize_t  n,
 static PyObject*
 math_fsum(PyObject *self, PyObject *seq)
 {
-	PyObject *item, *iter, *sum = NULL;
-	Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
-	double x, y, t, ps[NUM_PARTIALS], *p = ps;
-	double xsave, special_sum = 0.0, inf_sum = 0.0;
-	volatile double hi, yr, lo;
-
-	iter = PyObject_GetIter(seq);
-	if (iter == NULL)
-		return NULL;
-
-	PyFPE_START_PROTECT("fsum", Py_DECREF(iter); return NULL)
-
-	for(;;) {           /* for x in iterable */
-		assert(0 <= n && n <= m);
-		assert((m == NUM_PARTIALS && p == ps) ||
-		       (m >  NUM_PARTIALS && p != NULL));
-
-		item = PyIter_Next(iter);
-		if (item == NULL) {
-			if (PyErr_Occurred())
-				goto _fsum_error;
-			break;
-		}
-		x = PyFloat_AsDouble(item);
-		Py_DECREF(item);
-		if (PyErr_Occurred())
-			goto _fsum_error;
-
-		xsave = x;
-		for (i = j = 0; j < n; j++) {       /* for y in partials */
-			y = p[j];
-			if (fabs(x) < fabs(y)) {
-				t = x; x = y; y = t;
-			}
-			hi = x + y;
-			yr = hi - x;
-			lo = y - yr;
-			if (lo != 0.0)
-				p[i++] = lo;
-			x = hi;
-		}
-
-		n = i;                              /* ps[i:] = [x] */
-		if (x != 0.0) {
-			if (! Py_IS_FINITE(x)) {
-				/* a nonfinite x could arise either as
-				   a result of intermediate overflow, or
-				   as a result of a nan or inf in the
-				   summands */
-				if (Py_IS_FINITE(xsave)) {
-					PyErr_SetString(PyExc_OverflowError,
-					      "intermediate overflow in fsum");
-					goto _fsum_error;
-				}
-				if (Py_IS_INFINITY(xsave))
-					inf_sum += xsave;
-				special_sum += xsave;
-				/* reset partials */
-				n = 0;
-			}
-			else if (n >= m && _fsum_realloc(&p, n, ps, &m))
-				goto _fsum_error;
-			else
-				p[n++] = x;
-		}
-	}
-
-	if (special_sum != 0.0) {
-		if (Py_IS_NAN(inf_sum))
-			PyErr_SetString(PyExc_ValueError,
-					"-inf + inf in fsum");
-		else
-			sum = PyFloat_FromDouble(special_sum);
-		goto _fsum_error;
-	}
-
-	hi = 0.0;
-	if (n > 0) {
-		hi = p[--n];
-		/* sum_exact(ps, hi) from the top, stop when the sum becomes
-		   inexact. */
-		while (n > 0) {
-			x = hi;
-			y = p[--n];
-			assert(fabs(y) < fabs(x));
-			hi = x + y;
-			yr = hi - x;
-			lo = y - yr;
-			if (lo != 0.0)
-				break;
-		}
-		/* Make half-even rounding work across multiple partials.
-		   Needed so that sum([1e-16, 1, 1e16]) will round-up the last
-		   digit to two instead of down to zero (the 1e-16 makes the 1
-		   slightly closer to two).  With a potential 1 ULP rounding
-		   error fixed-up, math.fsum() can guarantee commutativity. */
-		if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) ||
-			      (lo > 0.0 && p[n-1] > 0.0))) {
-			y = lo * 2.0;
-			x = hi + y;
-			yr = x - hi;
-			if (y == yr)
-				hi = x;
-		}
-	}
-	sum = PyFloat_FromDouble(hi);
+    PyObject *item, *iter, *sum = NULL;
+    Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
+    double x, y, t, ps[NUM_PARTIALS], *p = ps;
+    double xsave, special_sum = 0.0, inf_sum = 0.0;
+    volatile double hi, yr, lo;
+
+    iter = PyObject_GetIter(seq);
+    if (iter == NULL)
+        return NULL;
+
+    PyFPE_START_PROTECT("fsum", Py_DECREF(iter); return NULL)
+
+    for(;;) {           /* for x in iterable */
+        assert(0 <= n && n <= m);
+        assert((m == NUM_PARTIALS && p == ps) ||
+               (m >  NUM_PARTIALS && p != NULL));
+
+        item = PyIter_Next(iter);
+        if (item == NULL) {
+            if (PyErr_Occurred())
+                goto _fsum_error;
+            break;
+        }
+        x = PyFloat_AsDouble(item);
+        Py_DECREF(item);
+        if (PyErr_Occurred())
+            goto _fsum_error;
+
+        xsave = x;
+        for (i = j = 0; j < n; j++) {       /* for y in partials */
+            y = p[j];
+            if (fabs(x) < fabs(y)) {
+                t = x; x = y; y = t;
+            }
+            hi = x + y;
+            yr = hi - x;
+            lo = y - yr;
+            if (lo != 0.0)
+                p[i++] = lo;
+            x = hi;
+        }
+
+        n = i;                              /* ps[i:] = [x] */
+        if (x != 0.0) {
+            if (! Py_IS_FINITE(x)) {
+                /* a nonfinite x could arise either as
+                   a result of intermediate overflow, or
+                   as a result of a nan or inf in the
+                   summands */
+                if (Py_IS_FINITE(xsave)) {
+                    PyErr_SetString(PyExc_OverflowError,
+                          "intermediate overflow in fsum");
+                    goto _fsum_error;
+                }
+                if (Py_IS_INFINITY(xsave))
+                    inf_sum += xsave;
+                special_sum += xsave;
+                /* reset partials */
+                n = 0;
+            }
+            else if (n >= m && _fsum_realloc(&p, n, ps, &m))
+                goto _fsum_error;
+            else
+                p[n++] = x;
+        }
+    }
+
+    if (special_sum != 0.0) {
+        if (Py_IS_NAN(inf_sum))
+            PyErr_SetString(PyExc_ValueError,
+                            "-inf + inf in fsum");
+        else
+            sum = PyFloat_FromDouble(special_sum);
+        goto _fsum_error;
+    }
+
+    hi = 0.0;
+    if (n > 0) {
+        hi = p[--n];
+        /* sum_exact(ps, hi) from the top, stop when the sum becomes
+           inexact. */
+        while (n > 0) {
+            x = hi;
+            y = p[--n];
+            assert(fabs(y) < fabs(x));
+            hi = x + y;
+            yr = hi - x;
+            lo = y - yr;
+            if (lo != 0.0)
+                break;
+        }
+        /* Make half-even rounding work across multiple partials.
+           Needed so that sum([1e-16, 1, 1e16]) will round-up the last
+           digit to two instead of down to zero (the 1e-16 makes the 1
+           slightly closer to two).  With a potential 1 ULP rounding
+           error fixed-up, math.fsum() can guarantee commutativity. */
+        if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) ||
+                      (lo > 0.0 && p[n-1] > 0.0))) {
+            y = lo * 2.0;
+            x = hi + y;
+            yr = x - hi;
+            if (y == yr)
+                hi = x;
+        }
+    }
+    sum = PyFloat_FromDouble(hi);
 
 _fsum_error:
-	PyFPE_END_PROTECT(hi)
-	Py_DECREF(iter);
-	if (p != ps)
-		PyMem_Free(p);
-	return sum;
+    PyFPE_END_PROTECT(hi)
+    Py_DECREF(iter);
+    if (p != ps)
+        PyMem_Free(p);
+    return sum;
 }
 
 #undef NUM_PARTIALS
@@ -1132,53 +1132,53 @@ Assumes IEEE-754 floating point arithmetic.");
 static PyObject *
 math_factorial(PyObject *self, PyObject *arg)
 {
-	long i, x;
-	PyObject *result, *iobj, *newresult;
-
-	if (PyFloat_Check(arg)) {
-		PyObject *lx;
-		double dx = PyFloat_AS_DOUBLE((PyFloatObject *)arg);
-		if (!(Py_IS_FINITE(dx) && dx == floor(dx))) {
-			PyErr_SetString(PyExc_ValueError, 
-				"factorial() only accepts integral values");
-			return NULL;
-		}
-		lx = PyLong_FromDouble(dx);
-		if (lx == NULL)
-			return NULL;
-		x = PyLong_AsLong(lx);
-		Py_DECREF(lx);
-	}
-	else
-		x = PyLong_AsLong(arg);
-
-	if (x == -1 && PyErr_Occurred())
-		return NULL;
-	if (x < 0) {
-		PyErr_SetString(PyExc_ValueError, 
-			"factorial() not defined for negative values");
-		return NULL;
-	}
-
-	result = (PyObject *)PyLong_FromLong(1);
-	if (result == NULL)
-		return NULL;
-	for (i=1 ; i<=x ; i++) {
-		iobj = (PyObject *)PyLong_FromLong(i);
-		if (iobj == NULL)
-			goto error;
-		newresult = PyNumber_Multiply(result, iobj);
-		Py_DECREF(iobj);
-		if (newresult == NULL)
-			goto error;
-		Py_DECREF(result);
-		result = newresult;
-	}
-	return result;
+    long i, x;
+    PyObject *result, *iobj, *newresult;
+
+    if (PyFloat_Check(arg)) {
+        PyObject *lx;
+        double dx = PyFloat_AS_DOUBLE((PyFloatObject *)arg);
+        if (!(Py_IS_FINITE(dx) && dx == floor(dx))) {
+            PyErr_SetString(PyExc_ValueError,
+                "factorial() only accepts integral values");
+            return NULL;
+        }
+        lx = PyLong_FromDouble(dx);
+        if (lx == NULL)
+            return NULL;
+        x = PyLong_AsLong(lx);
+        Py_DECREF(lx);
+    }
+    else
+        x = PyLong_AsLong(arg);
+
+    if (x == -1 && PyErr_Occurred())
+        return NULL;
+    if (x < 0) {
+        PyErr_SetString(PyExc_ValueError,
+            "factorial() not defined for negative values");
+        return NULL;
+    }
+
+    result = (PyObject *)PyLong_FromLong(1);
+    if (result == NULL)
+        return NULL;
+    for (i=1 ; i<=x ; i++) {
+        iobj = (PyObject *)PyLong_FromLong(i);
+        if (iobj == NULL)
+            goto error;
+        newresult = PyNumber_Multiply(result, iobj);
+        Py_DECREF(iobj);
+        if (newresult == NULL)
+            goto error;
+        Py_DECREF(result);
+        result = newresult;
+    }
+    return result;
 
 error:
-	Py_DECREF(result);
-	return NULL;
+    Py_DECREF(result);
+    return NULL;
 }
 
 PyDoc_STRVAR(math_factorial_doc,
@@ -1189,28 +1189,28 @@ PyDoc_STRVAR(math_factorial_doc,
 static PyObject *
 math_trunc(PyObject *self, PyObject *number)
 {
-	static PyObject *trunc_str = NULL;
-	PyObject *trunc;
-
-	if (Py_TYPE(number)->tp_dict == NULL) {
-		if (PyType_Ready(Py_TYPE(number)) < 0)
-			return NULL;
-	}
-
-	if (trunc_str == NULL) {
-		trunc_str = PyUnicode_InternFromString("__trunc__");
-		if (trunc_str == NULL)
-			return NULL;
-	}
-
-	trunc = _PyType_Lookup(Py_TYPE(number), trunc_str);
-	if (trunc == NULL) {
-		PyErr_Format(PyExc_TypeError,
-			     "type %.100s doesn't define __trunc__ method",
-			     Py_TYPE(number)->tp_name);
-		return NULL;
-	}
-	return PyObject_CallFunctionObjArgs(trunc, number, NULL);
+    static PyObject *trunc_str = NULL;
+    PyObject *trunc;
+
+    if (Py_TYPE(number)->tp_dict == NULL) {
+        if (PyType_Ready(Py_TYPE(number)) < 0)
+            return NULL;
+    }
+
+    if (trunc_str == NULL) {
+        trunc_str = PyUnicode_InternFromString("__trunc__");
+        if (trunc_str == NULL)
+            return NULL;
+    }
+
+    trunc = _PyType_Lookup(Py_TYPE(number), trunc_str);
+    if (trunc == NULL) {
+        PyErr_Format(PyExc_TypeError,
+                     "type %.100s doesn't define __trunc__ method",
+                     Py_TYPE(number)->tp_name);
+        return NULL;
+    }
+    return PyObject_CallFunctionObjArgs(trunc, number, NULL);
 }
 
 PyDoc_STRVAR(math_trunc_doc,
@@ -1221,21 +1221,21 @@ PyDoc_STRVAR(math_trunc_doc,
 static PyObject *
 math_frexp(PyObject *self, PyObject *arg)
 {
-	int i;
-	double x = PyFloat_AsDouble(arg);
-	if (x == -1.0 && PyErr_Occurred())
-		return NULL;
-	/* deal with special cases directly, to sidestep platform
-	   differences */
-	if (Py_IS_NAN(x) || Py_IS_INFINITY(x) || !x) {
-		i = 0;
-	}
-	else {
-		PyFPE_START_PROTECT("in math_frexp", return 0);
-		x = frexp(x, &i);
-		PyFPE_END_PROTECT(x);
-	}
-	return Py_BuildValue("(di)", x, i);
+    int i;
+    double x = PyFloat_AsDouble(arg);
+    if (x == -1.0 && PyErr_Occurred())
+        return NULL;
+    /* deal with special cases directly, to sidestep platform
+       differences */
+    if (Py_IS_NAN(x) || Py_IS_INFINITY(x) || !x) {
+        i = 0;
+    }
+    else {
+        PyFPE_START_PROTECT("in math_frexp", return 0);
+        x = frexp(x, &i);
+        PyFPE_END_PROTECT(x);
+    }
+    return Py_BuildValue("(di)", x, i);
 }
 
 PyDoc_STRVAR(math_frexp_doc,
@@ -1248,53 +1248,53 @@ PyDoc_STRVAR(math_frexp_doc,
 static PyObject *
 math_ldexp(PyObject *self, PyObject *args)
 {
-	double x, r;
-	PyObject *oexp;
-	long exp;
-	int overflow;
-	if (! PyArg_ParseTuple(args, "dO:ldexp", &x, &oexp))
-		return NULL;
-
-	if (PyLong_Check(oexp)) {
-		/* on overflow, replace exponent with either LONG_MAX
-		   or LONG_MIN, depending on the sign. */
-		exp = PyLong_AsLongAndOverflow(oexp, &overflow);
-		if (exp == -1 && PyErr_Occurred())
-			return NULL;
-		if (overflow)
-			exp = overflow < 0 ? LONG_MIN : LONG_MAX;
-	}
-	else {
-		PyErr_SetString(PyExc_TypeError,
-				"Expected an int or long as second argument "
-				"to ldexp.");
-		return NULL;
-	}
-
-	if (x == 0. || !Py_IS_FINITE(x)) {
-		/* NaNs, zeros and infinities are returned unchanged */
-		r = x;
-		errno = 0;
-	} else if (exp > INT_MAX) {
-		/* overflow */
-		r = copysign(Py_HUGE_VAL, x);
-		errno = ERANGE;
-	} else if (exp < INT_MIN) {
-		/* underflow to +-0 */
-		r = copysign(0., x);
-		errno = 0;
-	} else {
-		errno = 0;
-		PyFPE_START_PROTECT("in math_ldexp", return 0);
-		r = ldexp(x, (int)exp);
-		PyFPE_END_PROTECT(r);
-		if (Py_IS_INFINITY(r))
-			errno = ERANGE;
-	}
-
-	if (errno && is_error(r))
-		return NULL;
-	return PyFloat_FromDouble(r);
+    double x, r;
+    PyObject *oexp;
+    long exp;
+    int overflow;
+    if (! PyArg_ParseTuple(args, "dO:ldexp", &x, &oexp))
+        return NULL;
+
+    if (PyLong_Check(oexp)) {
+        /* on overflow, replace exponent with either LONG_MAX
+           or LONG_MIN, depending on the sign. */
+        exp = PyLong_AsLongAndOverflow(oexp, &overflow);
+        if (exp == -1 && PyErr_Occurred())
+            return NULL;
+        if (overflow)
+            exp = overflow < 0 ? LONG_MIN : LONG_MAX;
+    }
+    else {
+        PyErr_SetString(PyExc_TypeError,
+                        "Expected an int or long as second argument "
+                        "to ldexp.");
+        return NULL;
+    }
+
+    if (x == 0. || !Py_IS_FINITE(x)) {
+        /* NaNs, zeros and infinities are returned unchanged */
+        r = x;
+        errno = 0;
+    } else if (exp > INT_MAX) {
+        /* overflow */
+        r = copysign(Py_HUGE_VAL, x);
+        errno = ERANGE;
+    } else if (exp < INT_MIN) {
+        /* underflow to +-0 */
+        r = copysign(0., x);
+        errno = 0;
+    } else {
+        errno = 0;
+        PyFPE_START_PROTECT("in math_ldexp", return 0);
+        r = ldexp(x, (int)exp);
+        PyFPE_END_PROTECT(r);
+        if (Py_IS_INFINITY(r))
+            errno = ERANGE;
+    }
+
+    if (errno && is_error(r))
+        return NULL;
+    return PyFloat_FromDouble(r);
 }
 
 PyDoc_STRVAR(math_ldexp_doc,
@@ -1304,23 +1304,23 @@ Return x * (2**i).");
 static PyObject *
 math_modf(PyObject *self, PyObject *arg)
 {
-	double y, x = PyFloat_AsDouble(arg);
-	if (x == -1.0 && PyErr_Occurred())
-		return NULL;
-	/* some platforms don't do the right thing for NaNs and
-	   infinities, so we take care of special cases directly. */
-	if (!Py_IS_FINITE(x)) {
-		if (Py_IS_INFINITY(x))
-			return Py_BuildValue("(dd)", copysign(0., x), x);
-		else if (Py_IS_NAN(x))
-			return Py_BuildValue("(dd)", x, x);
-	}          
-
-	errno = 0;
-	PyFPE_START_PROTECT("in math_modf", return 0);
-	x = modf(x, &y);
-	PyFPE_END_PROTECT(x);
-	return Py_BuildValue("(dd)", x, y);
+    double y, x = PyFloat_AsDouble(arg);
+    if (x == -1.0 && PyErr_Occurred())
+        return NULL;
+    /* some platforms don't do the right thing for NaNs and
+       infinities, so we take care of special cases directly. */
+    if (!Py_IS_FINITE(x)) {
+        if (Py_IS_INFINITY(x))
+            return Py_BuildValue("(dd)", copysign(0., x), x);
+        else if (Py_IS_NAN(x))
+            return Py_BuildValue("(dd)", x, x);
+    }
+
+    errno = 0;
+    PyFPE_START_PROTECT("in math_modf", return 0);
+    x = modf(x, &y);
+    PyFPE_END_PROTECT(x);
+    return Py_BuildValue("(dd)", x, y);
 }
 
 PyDoc_STRVAR(math_modf_doc,
@@ -1341,56 +1341,56 @@ PyDoc_STRVAR(math_modf_doc,
 static PyObject*
 loghelper(PyObject* arg, double (*func)(double), char *funcname)
 {
-	/* If it is long, do it ourselves. */
-	if (PyLong_Check(arg)) {
-		double x;
-		Py_ssize_t e;
-		x = _PyLong_Frexp((PyLongObject *)arg, &e);
-		if (x == -1.0 && PyErr_Occurred())
-			return NULL;
-		if (x <= 0.0) {
-			PyErr_SetString(PyExc_ValueError,
-					"math domain error");
-			return NULL;
-		}
-		/* Special case for log(1), to make sure we get an
-		   exact result there. */
-		if (e == 1 && x == 0.5)
-			return PyFloat_FromDouble(0.0);
-		/* Value is ~= x * 2**e, so the log ~= log(x) + log(2) * e. */
-		x = func(x) + func(2.0) * e;
-		return PyFloat_FromDouble(x);
-	}
-
-	/* Else let libm handle it by itself. */
-	return math_1(arg, func, 0);
+    /* If it is long, do it ourselves. */
+    if (PyLong_Check(arg)) {
+        double x;
+        Py_ssize_t e;
+        x = _PyLong_Frexp((PyLongObject *)arg, &e);
+        if (x == -1.0 && PyErr_Occurred())
+            return NULL;
+        if (x <= 0.0) {
+            PyErr_SetString(PyExc_ValueError,
+                            "math domain error");
+            return NULL;
+        }
+        /* Special case for log(1), to make sure we get an
+           exact result there. */
+        if (e == 1 && x == 0.5)
+            return PyFloat_FromDouble(0.0);
+        /* Value is ~= x * 2**e, so the log ~= log(x) + log(2) * e. */
+        x = func(x) + func(2.0) * e;
+        return PyFloat_FromDouble(x);
+    }
+
+    /* Else let libm handle it by itself. */
+    return math_1(arg, func, 0);
 }
 
 static PyObject *
 math_log(PyObject *self, PyObject *args)
 {
-	PyObject *arg;
-	PyObject *base = NULL;
-	PyObject *num, *den;
-	PyObject *ans;
-
-	if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
-		return NULL;
-
-	num = loghelper(arg, m_log, "log");
-	if (num == NULL || base == NULL)
-		return num;
-
-	den = loghelper(base, m_log, "log");
-	if (den == NULL) {
-		Py_DECREF(num);
-		return NULL;
-	}
-
-	ans = PyNumber_TrueDivide(num, den);
-	Py_DECREF(num);
-	Py_DECREF(den);
-	return ans;
+    PyObject *arg;
+    PyObject *base = NULL;
+    PyObject *num, *den;
+    PyObject *ans;
+
+    if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
+        return NULL;
+
+    num = loghelper(arg, m_log, "log");
+    if (num == NULL || base == NULL)
+        return num;
+
+    den = loghelper(base, m_log, "log");
+    if (den == NULL) {
+        Py_DECREF(num);
+        return NULL;
+    }
+
+    ans = PyNumber_TrueDivide(num, den);
+    Py_DECREF(num);
+    Py_DECREF(den);
+    return ans;
 }
 
 PyDoc_STRVAR(math_log_doc,
@@ -1401,7 +1401,7 @@ If the base not specified, returns the natural logarithm (base e) of x.");
 static PyObject *
 math_log10(PyObject *self, PyObject *arg)
 {
-	return loghelper(arg, m_log10, "log10");
+    return loghelper(arg, m_log10, "log10");
 }
 
 PyDoc_STRVAR(math_log10_doc,
@@ -1410,31 +1410,31 @@ PyDoc_STRVAR(math_log10_doc,
 static PyObject *
 math_fmod(PyObject *self, PyObject *args)
 {
-	PyObject *ox, *oy;
-	double r, x, y;
-	if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
-		return NULL;
-	x = PyFloat_AsDouble(ox);
-	y = PyFloat_AsDouble(oy);
-	if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
-		return NULL;
-	/* fmod(x, +/-Inf) returns x for finite x. */
-	if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
-		return PyFloat_FromDouble(x);
-	errno = 0;
-	PyFPE_START_PROTECT("in math_fmod", return 0);
-	r = fmod(x, y);
-	PyFPE_END_PROTECT(r);
-	if (Py_IS_NAN(r)) {
-		if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
-			errno = EDOM;
-		else
-			errno = 0;
-	}
-	if (errno && is_error(r))
-		return NULL;
-	else
-		return PyFloat_FromDouble(r);
+    PyObject *ox, *oy;
+    double r, x, y;
+    if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
+        return NULL;
+    x = PyFloat_AsDouble(ox);
+    y = PyFloat_AsDouble(oy);
+    if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
+        return NULL;
+    /* fmod(x, +/-Inf) returns x for finite x. */
+    if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
+        return PyFloat_FromDouble(x);
+    errno = 0;
+    PyFPE_START_PROTECT("in math_fmod", return 0);
+    r = fmod(x, y);
+    PyFPE_END_PROTECT(r);
+    if (Py_IS_NAN(r)) {
+        if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
+            errno = EDOM;
+        else
+            errno = 0;
+    }
+    if (errno && is_error(r))
+        return NULL;
+    else
+        return PyFloat_FromDouble(r);
 }
 
 PyDoc_STRVAR(math_fmod_doc,
@@ -1444,39 +1444,39 @@ PyDoc_STRVAR(math_fmod_doc,
 static PyObject *
 math_hypot(PyObject *self, PyObject *args)
 {
-	PyObject *ox, *oy;
-	double r, x, y;
-	if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
-		return NULL;
-	x = PyFloat_AsDouble(ox);
-	y = PyFloat_AsDouble(oy);
-	if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
-		return NULL;
-	/* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
-	if (Py_IS_INFINITY(x))
-		return PyFloat_FromDouble(fabs(x));
-	if (Py_IS_INFINITY(y))
-		return PyFloat_FromDouble(fabs(y));
-	errno = 0;
-	PyFPE_START_PROTECT("in math_hypot", return 0);
-	r = hypot(x, y);
-	PyFPE_END_PROTECT(r);
-	if (Py_IS_NAN(r)) {
-		if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
-			errno = EDOM;
-		else
-			errno = 0;
-	}
-	else if (Py_IS_INFINITY(r)) {
-		if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
-			errno = ERANGE;
-		else
-			errno = 0;
-	}
-	if (errno && is_error(r))
-		return NULL;
-	else
-		return PyFloat_FromDouble(r);
+    PyObject *ox, *oy;
+    double r, x, y;
+    if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
+        return NULL;
+    x = PyFloat_AsDouble(ox);
+    y = PyFloat_AsDouble(oy);
+    if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
+        return NULL;
+    /* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
+    if (Py_IS_INFINITY(x))
+        return PyFloat_FromDouble(fabs(x));
+    if (Py_IS_INFINITY(y))
+        return PyFloat_FromDouble(fabs(y));
+    errno = 0;
+    PyFPE_START_PROTECT("in math_hypot", return 0);
+    r = hypot(x, y);
+    PyFPE_END_PROTECT(r);
+    if (Py_IS_NAN(r)) {
+        if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
+            errno = EDOM;
+        else
+            errno = 0;
+    }
+    else if (Py_IS_INFINITY(r)) {
+        if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
+            errno = ERANGE;
+        else
+            errno = 0;
+    }
+    if (errno && is_error(r))
+        return NULL;
+    else
+        return PyFloat_FromDouble(r);
 }
 
 PyDoc_STRVAR(math_hypot_doc,
@@ -1491,79 +1491,79 @@ PyDoc_STRVAR(math_hypot_doc,
 static PyObject *
 math_pow(PyObject *self, PyObject *args)
 {
-	PyObject *ox, *oy;
-	double r, x, y;
-	int odd_y;
-
-	if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
-		return NULL;
-	x = PyFloat_AsDouble(ox);
-	y = PyFloat_AsDouble(oy);
-	if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
-		return NULL;
-
-	/* deal directly with IEEE specials, to cope with problems on various
-	   platforms whose semantics don't exactly match C99 */
-	r = 0.; /* silence compiler warning */
-	if (!Py_IS_FINITE(x) || !Py_IS_FINITE(y)) {
-		errno = 0;
-		if (Py_IS_NAN(x))
-			r = y == 0. ? 1. : x; /* NaN**0 = 1 */
-		else if (Py_IS_NAN(y))
-			r = x == 1. ? 1. : y; /* 1**NaN = 1 */
-		else if (Py_IS_INFINITY(x)) {
-			odd_y = Py_IS_FINITE(y) && fmod(fabs(y), 2.0) == 1.0;
-			if (y > 0.)
-				r = odd_y ? x : fabs(x);
-			else if (y == 0.)
-				r = 1.;
-			else /* y < 0. */
-				r = odd_y ? copysign(0., x) : 0.;
-		}
-		else if (Py_IS_INFINITY(y)) {
-			if (fabs(x) == 1.0)
-				r = 1.;
-			else if (y > 0. && fabs(x) > 1.0)
-				r = y;
-			else if (y < 0. && fabs(x) < 1.0) {
-				r = -y; /* result is +inf */
-				if (x == 0.) /* 0**-inf: divide-by-zero */
-					errno = EDOM;
-			}
-			else
-				r = 0.;
-		}
-	}
-	else {
-		/* let libm handle finite**finite */
-		errno = 0;
-		PyFPE_START_PROTECT("in math_pow", return 0);
-		r = pow(x, y);
-		PyFPE_END_PROTECT(r);
-		/* a NaN result should arise only from (-ve)**(finite
-		   non-integer); in this case we want to raise ValueError. */
-		if (!Py_IS_FINITE(r)) {
-			if (Py_IS_NAN(r)) {
-				errno = EDOM;
-			}
-			/* 
-			   an infinite result here arises either from:
-			   (A) (+/-0.)**negative (-> divide-by-zero)
-			   (B) overflow of x**y with x and y finite
-			*/
-			else if (Py_IS_INFINITY(r)) {
-				if (x == 0.)
-					errno = EDOM;
-				else
-					errno = ERANGE;
-			}
-		}
-	}
-
-	if (errno && is_error(r))
-		return NULL;
-	else
-		return PyFloat_FromDouble(r);
+    PyObject *ox, *oy;
+    double r, x, y;
+    int odd_y;
+
+    if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
+        return NULL;
+    x = PyFloat_AsDouble(ox);
+    y = PyFloat_AsDouble(oy);
+    if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
+        return NULL;
+
+    /* deal directly with IEEE specials, to cope with problems on various
+       platforms whose semantics don't exactly match C99 */
+    r = 0.; /* silence compiler warning */
+    if (!Py_IS_FINITE(x) || !Py_IS_FINITE(y)) {
+        errno = 0;
+        if (Py_IS_NAN(x))
+            r = y == 0. ? 1. : x; /* NaN**0 = 1 */
+        else if (Py_IS_NAN(y))
+            r = x == 1. ? 1. : y; /* 1**NaN = 1 */
+        else if (Py_IS_INFINITY(x)) {
+            odd_y = Py_IS_FINITE(y) && fmod(fabs(y), 2.0) == 1.0;
+            if (y > 0.)
+                r = odd_y ? x : fabs(x);
+            else if (y == 0.)
+                r = 1.;
+            else /* y < 0. */
+                r = odd_y ? copysign(0., x) : 0.;
+        }
+        else if (Py_IS_INFINITY(y)) {
+            if (fabs(x) == 1.0)
+                r = 1.;
+            else if (y > 0. && fabs(x) > 1.0)
+                r = y;
+            else if (y < 0. && fabs(x) < 1.0) {
+                r = -y; /* result is +inf */
+                if (x == 0.) /* 0**-inf: divide-by-zero */
+                    errno = EDOM;
+            }
+            else
+                r = 0.;
+        }
+    }
+    else {
+        /* let libm handle finite**finite */
+        errno = 0;
+        PyFPE_START_PROTECT("in math_pow", return 0);
+        r = pow(x, y);
+        PyFPE_END_PROTECT(r);
+        /* a NaN result should arise only from (-ve)**(finite
+           non-integer); in this case we want to raise ValueError. */
+        if (!Py_IS_FINITE(r)) {
+            if (Py_IS_NAN(r)) {
+                errno = EDOM;
+            }
+            /*
+               an infinite result here arises either from:
+               (A) (+/-0.)**negative (-> divide-by-zero)
+               (B) overflow of x**y with x and y finite
+            */
+            else if (Py_IS_INFINITY(r)) {
+                if (x == 0.)
+                    errno = EDOM;
+                else
+                    errno = ERANGE;
+            }
+        }
+    }
+
+    if (errno && is_error(r))
+        return NULL;
+    else
+        return PyFloat_FromDouble(r);
 }
 
 PyDoc_STRVAR(math_pow_doc,
@@ -1575,10 +1575,10 @@ static const double radToDeg = 180.0 / Py_MATH_PI;
 static PyObject *
 math_degrees(PyObject *self, PyObject *arg)
 {
-	double x = PyFloat_AsDouble(arg);
-	if (x == -1.0 && PyErr_Occurred())
-		return NULL;
-	return PyFloat_FromDouble(x * radToDeg);
+    double x = PyFloat_AsDouble(arg);
+    if (x == -1.0 && PyErr_Occurred())
+        return NULL;
+    return PyFloat_FromDouble(x * radToDeg);
 }
 
 PyDoc_STRVAR(math_degrees_doc,
@@ -1588,10 +1588,10 @@ Convert angle x from radians to degrees.");
 static PyObject *
 math_radians(PyObject *self, PyObject *arg)
 {
-	double x = PyFloat_AsDouble(arg);
-	if (x == -1.0 && PyErr_Occurred())
-		return NULL;
-	return PyFloat_FromDouble(x * degToRad);
+    double x = PyFloat_AsDouble(arg);
+    if (x == -1.0 && PyErr_Occurred())
+        return NULL;
+    return PyFloat_FromDouble(x * degToRad);
 }
 
 PyDoc_STRVAR(math_radians_doc,
@@ -1601,10 +1601,10 @@ Convert angle x from degrees to radians.");
 static PyObject *
 math_isnan(PyObject *self, PyObject *arg)
 {
-	double x = PyFloat_AsDouble(arg);
-	if (x == -1.0 && PyErr_Occurred())
-		return NULL;
-	return PyBool_FromLong((long)Py_IS_NAN(x));
+    double x = PyFloat_AsDouble(arg);
+    if (x == -1.0 && PyErr_Occurred())
+        return NULL;
+    return PyBool_FromLong((long)Py_IS_NAN(x));
 }
 
 PyDoc_STRVAR(math_isnan_doc,
@@ -1614,10 +1614,10 @@ Check if float x is not a number (NaN).");
 static PyObject *
 math_isinf(PyObject *self, PyObject *arg)
 {
-	double x = PyFloat_AsDouble(arg);
-	if (x == -1.0 && PyErr_Occurred())
-		return NULL;
-	return PyBool_FromLong((long)Py_IS_INFINITY(x));
+    double x = PyFloat_AsDouble(arg);
+    if (x == -1.0 && PyErr_Occurred())
+        return NULL;
+    return PyBool_FromLong((long)Py_IS_INFINITY(x));
 }
 
 PyDoc_STRVAR(math_isinf_doc,
@@ -1625,47 +1625,47 @@ PyDoc_STRVAR(math_isinf_doc,
 Check if float x is infinite (positive or negative).");
 
 static PyMethodDef math_methods[] = {
-	{"acos",	math_acos,	METH_O,		math_acos_doc},
-	{"acosh",	math_acosh,	METH_O,		math_acosh_doc},
-	{"asin",	math_asin,	METH_O,		math_asin_doc},
-	{"asinh",	math_asinh,	METH_O,		math_asinh_doc},
-	{"atan",	math_atan,	METH_O,		math_atan_doc},
-	{"atan2",	math_atan2,	METH_VARARGS,	math_atan2_doc},
-	{"atanh",	math_atanh,	METH_O,		math_atanh_doc},
-	{"ceil",	math_ceil,	METH_O,		math_ceil_doc},
-	{"copysign",	math_copysign,	METH_VARARGS,	math_copysign_doc},
-	{"cos",		math_cos,	METH_O,		math_cos_doc},
-	{"cosh",	math_cosh,	METH_O,		math_cosh_doc},
-	{"degrees",	math_degrees,	METH_O,		math_degrees_doc},
-	{"erf",		math_erf,	METH_O,		math_erf_doc},
-	{"erfc",	math_erfc,	METH_O,		math_erfc_doc},
-	{"exp",		math_exp,	METH_O,		math_exp_doc},
-	{"expm1",	math_expm1,	METH_O,		math_expm1_doc},
-	{"fabs",	math_fabs,	METH_O,		math_fabs_doc},
-	{"factorial",	math_factorial,	METH_O,		math_factorial_doc},
-	{"floor",	math_floor,	METH_O,		math_floor_doc},
-	{"fmod",	math_fmod,	METH_VARARGS,	math_fmod_doc},
-	{"frexp",	math_frexp,	METH_O,		math_frexp_doc},
-	{"fsum",	math_fsum,	METH_O,		math_fsum_doc},
-	{"gamma",	math_gamma,	METH_O,		math_gamma_doc},
-	{"hypot",	math_hypot,	METH_VARARGS,	math_hypot_doc},
-	{"isinf",	math_isinf,	METH_O,		math_isinf_doc},
-	{"isnan",	math_isnan,	METH_O,		math_isnan_doc},
-	{"ldexp",	math_ldexp,	METH_VARARGS,	math_ldexp_doc},
-	{"lgamma",	math_lgamma,	METH_O,		math_lgamma_doc},
-	{"log",		math_log,	METH_VARARGS,	math_log_doc},
-	{"log1p",	math_log1p,	METH_O,		math_log1p_doc},
-	{"log10",	math_log10,	METH_O,		math_log10_doc},
-	{"modf",	math_modf,	METH_O,		math_modf_doc},
-	{"pow",		math_pow,	METH_VARARGS,	math_pow_doc},
-	{"radians",	math_radians,	METH_O,		math_radians_doc},
-	{"sin",		math_sin,	METH_O,		math_sin_doc},
-	{"sinh",	math_sinh,	METH_O,		math_sinh_doc},
-	{"sqrt",	math_sqrt,	METH_O,		math_sqrt_doc},
-	{"tan",		math_tan,	METH_O,		math_tan_doc},
-	{"tanh",	math_tanh,	METH_O,		math_tanh_doc},
-	{"trunc",	math_trunc,	METH_O,		math_trunc_doc},
-	{NULL,		NULL}		/* sentinel */
+    {"acos",            math_acos,      METH_O,         math_acos_doc},
+    {"acosh",           math_acosh,     METH_O,         math_acosh_doc},
+    {"asin",            math_asin,      METH_O,         math_asin_doc},
+    {"asinh",           math_asinh,     METH_O,         math_asinh_doc},
+    {"atan",            math_atan,      METH_O,         math_atan_doc},
+    {"atan2",           math_atan2,     METH_VARARGS,   math_atan2_doc},
+    {"atanh",           math_atanh,     METH_O,         math_atanh_doc},
+    {"ceil",            math_ceil,      METH_O,         math_ceil_doc},
+    {"copysign",        math_copysign,  METH_VARARGS,   math_copysign_doc},
+    {"cos",             math_cos,       METH_O,         math_cos_doc},
+    {"cosh",            math_cosh,      METH_O,         math_cosh_doc},
+    {"degrees",         math_degrees,   METH_O,         math_degrees_doc},
+    {"erf",             math_erf,       METH_O,         math_erf_doc},
+    {"erfc",            math_erfc,      METH_O,         math_erfc_doc},
+    {"exp",             math_exp,       METH_O,         math_exp_doc},
+    {"expm1",           math_expm1,     METH_O,         math_expm1_doc},
+    {"fabs",            math_fabs,      METH_O,         math_fabs_doc},
+    {"factorial",       math_factorial, METH_O,         math_factorial_doc},
+    {"floor",           math_floor,     METH_O,         math_floor_doc},
+    {"fmod",            math_fmod,      METH_VARARGS,   math_fmod_doc},
+    {"frexp",           math_frexp,     METH_O,         math_frexp_doc},
+    {"fsum",            math_fsum,      METH_O,         math_fsum_doc},
+    {"gamma",           math_gamma,     METH_O,         math_gamma_doc},
+    {"hypot",           math_hypot,     METH_VARARGS,   math_hypot_doc},
+    {"isinf",           math_isinf,     METH_O,         math_isinf_doc},
+    {"isnan",           math_isnan,     METH_O,         math_isnan_doc},
+    {"ldexp",           math_ldexp,     METH_VARARGS,   math_ldexp_doc},
+    {"lgamma",          math_lgamma,    METH_O,         math_lgamma_doc},
+    {"log",             math_log,       METH_VARARGS,   math_log_doc},
+    {"log1p",           math_log1p,     METH_O,         math_log1p_doc},
+    {"log10",           math_log10,     METH_O,         math_log10_doc},
+    {"modf",            math_modf,      METH_O,         math_modf_doc},
+    {"pow",             math_pow,       METH_VARARGS,   math_pow_doc},
+    {"radians",         math_radians,   METH_O,         math_radians_doc},
+    {"sin",             math_sin,       METH_O,         math_sin_doc},
+    {"sinh",            math_sinh,      METH_O,         math_sinh_doc},
+    {"sqrt",            math_sqrt,      METH_O,         math_sqrt_doc},
+    {"tan",             math_tan,       METH_O,         math_tan_doc},
+    {"tanh",            math_tanh,      METH_O,         math_tanh_doc},
+    {"trunc",           math_trunc,     METH_O,         math_trunc_doc},
+    {NULL,              NULL}           /* sentinel */
 };
 
 
@@ -1675,29 +1675,29 @@ PyDoc_STRVAR(module_doc,
 
 
 static struct PyModuleDef mathmodule = {
-	PyModuleDef_HEAD_INIT,
-	"math",
-	module_doc,
-	-1,
-	math_methods,
-	NULL,
-	NULL,
-	NULL,
-	NULL
+    PyModuleDef_HEAD_INIT,
+    "math",
+    module_doc,
+    -1,
+    math_methods,
+    NULL,
+    NULL,
+    NULL,
+    NULL
 };
 
 PyMODINIT_FUNC
 PyInit_math(void)
 {
-	PyObject *m;
+    PyObject *m;
 
-	m = PyModule_Create(&mathmodule);
-	if (m == NULL)
-		goto finally;
+    m = PyModule_Create(&mathmodule);
+    if (m == NULL)
+        goto finally;
 
-	PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
-	PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
+    PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
+    PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
 
     finally:
-	return m;
+    return m;
 }