diff options
Diffstat (limited to 'Modules/mathmodule.c')
| -rw-r--r-- | Modules/mathmodule.c | 2004 |
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; } |