[fusl] clang-format fusl

fusl/src/math/tgamma.c

 /*
 "A Precision Approximation of the Gamma Function" - Cornelius Lanczos (1964)
 "Lanczos Implementation of the Gamma Function" - Paul Godfrey (2001)
 "An Analysis of the Lanczos Gamma Approximation" - Glendon Ralph Pugh (2004)
 
 approximation method:
 
                         (x - 0.5)         S(x)
 Gamma(x) = (x + g - 0.5)         *  ----------------
                                     exp(x + g - 0.5)
 
 with
                  a1      a2      a3            aN
 S(x) ~= [ a0 + ----- + ----- + ----- + ... + ----- ]
                x + 1   x + 2   x + 3         x + N
 
 with a0, a1, a2, a3,.. aN constants which depend on g.
 
 for x < 0 the following reflection formula is used:
 
 Gamma(x)*Gamma(-x) = -pi/(x sin(pi x))
 
 most ideas and constants are from boost and python
 */
 #include "libm.h"
 
 static const double pi = 3.141592653589793238462643383279502884;
 
 /* sin(pi x) with x > 0x1p-100, if sin(pi*x)==0 the sign is arbitrary */
-static double sinpi(double x)
-{
-        int n;
+static double sinpi(double x) {
+  int n;
 
-        /* argument reduction: x = |x| mod 2 */
-        /* spurious inexact when x is odd int */
-        x = x * 0.5;
-        x = 2 * (x - floor(x));
+  /* argument reduction: x = |x| mod 2 */
+  /* spurious inexact when x is odd int */
+  x = x * 0.5;
+  x = 2 * (x - floor(x));
 
-        /* reduce x into [-.25,.25] */
-        n = 4 * x;
-        n = (n+1)/2;
-        x -= n * 0.5;
+  /* reduce x into [-.25,.25] */
+  n = 4 * x;
+  n = (n + 1) / 2;
+  x -= n * 0.5;
 
-        x *= pi;
-        switch (n) {
-        default: /* case 4 */
-        case 0:
-                return __sin(x, 0, 0);
-        case 1:
-                return __cos(x, 0);
-        case 2:
-                return __sin(-x, 0, 0);
-        case 3:
-                return -__cos(x, 0);
-        }
+  x *= pi;
+  switch (n) {
+    default: /* case 4 */
+    case 0:
+      return __sin(x, 0, 0);
+    case 1:
+      return __cos(x, 0);
+    case 2:
+      return __sin(-x, 0, 0);
+    case 3:
+      return -__cos(x, 0);
+  }
 }
 
 #define N 12
-//static const double g = 6.024680040776729583740234375;
+// static const double g = 6.024680040776729583740234375;
 static const double gmhalf = 5.524680040776729583740234375;
-static const double Snum[N+1] = {
-        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,
+static const double Snum[N + 1] = {
+    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,
 };
-static const double Sden[N+1] = {
-        0, 39916800, 120543840, 150917976, 105258076, 45995730, 13339535,
-        2637558, 357423, 32670, 1925, 66, 1,
+static const double Sden[N + 1] = {
+    0,       39916800, 120543840, 150917976, 105258076, 45995730, 13339535,
+    2637558, 357423,   32670,     1925,      66,        1,
 };
 /* n! for small integer n */
 static const double fact[] = {
-        1, 1, 2, 6, 24, 120, 720, 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,
+    1,
+    2,
+    6,
+    24,
+    120,
+    720,
+    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,
 };
 
 /* S(x) rational function for positive x */
-static double S(double x)
-{
-        double_t num = 0, den = 0;
-        int i;
+static double S(double x) {
+  double_t num = 0, den = 0;
+  int i;
 
-        /* to avoid overflow handle large x differently */
-        if (x < 8)
-                for (i = N; i >= 0; i--) {
-                        num = num * x + Snum[i];
-                        den = den * x + Sden[i];
-                }
-        else
-                for (i = 0; i <= N; i++) {
-                        num = num / x + Snum[i];
-                        den = den / x + Sden[i];
-                }
-        return num/den;
+  /* to avoid overflow handle large x differently */
+  if (x < 8)
+    for (i = N; i >= 0; i--) {
+      num = num * x + Snum[i];
+      den = den * x + Sden[i];
+    }
+  else
+    for (i = 0; i <= N; i++) {
+      num = num / x + Snum[i];
+      den = den / x + Sden[i];
+    }
+  return num / den;
 }
 
-double tgamma(double x)
-{
-        union {double f; uint64_t i;} u = {x};
-        double absx, y;
-        double_t dy, z, r;
-        uint32_t ix = u.i>>32 & 0x7fffffff;
-        int sign = u.i>>63;
+double tgamma(double x) {
+  union {
+    double f;
+    uint64_t i;
+  } u = {x};
+  double absx, y;
+  double_t dy, z, r;
+  uint32_t ix = u.i >> 32 & 0x7fffffff;
+  int sign = u.i >> 63;
 
-        /* special cases */
-        if (ix >= 0x7ff00000)
-                /* tgamma(nan)=nan, tgamma(inf)=inf, tgamma(-inf)=nan with invalid */
-                return x + INFINITY;
-        if (ix < (0x3ff-54)<<20)
-                /* |x| < 2^-54: tgamma(x) ~ 1/x, +-0 raises div-by-zero */
-                return 1/x;
+  /* special cases */
+  if (ix >= 0x7ff00000)
+    /* tgamma(nan)=nan, tgamma(inf)=inf, tgamma(-inf)=nan with invalid */
+    return x + INFINITY;
+  if (ix < (0x3ff - 54) << 20)
+    /* |x| < 2^-54: tgamma(x) ~ 1/x, +-0 raises div-by-zero */
+    return 1 / x;
 
-        /* integer arguments */
-        /* raise inexact when non-integer */
-        if (x == floor(x)) {
-                if (sign)
-                        return 0/0.0;
-                if (x <= sizeof fact/sizeof *fact)
-                        return fact[(int)x - 1];
-        }
+  /* integer arguments */
+  /* raise inexact when non-integer */
+  if (x == floor(x)) {
+    if (sign)
+      return 0 / 0.0;
+    if (x <= sizeof fact / sizeof *fact)
+      return fact[(int)x - 1];
+  }
 
-        /* x >= 172: tgamma(x)=inf with overflow */
-        /* x =< -184: tgamma(x)=+-0 with underflow */
-        if (ix >= 0x40670000) { /* |x| >= 184 */
-                if (sign) {
-                        FORCE_EVAL((float)(0x1p-126/x));
-                        if (floor(x) * 0.5 == floor(x * 0.5))
-                                return 0;
-                        return -0.0;
-                }
-                x *= 0x1p1023;
-                return x;
-        }
+  /* x >= 172: tgamma(x)=inf with overflow */
+  /* x =< -184: tgamma(x)=+-0 with underflow */
+  if (ix >= 0x40670000) { /* |x| >= 184 */
+    if (sign) {
+      FORCE_EVAL((float)(0x1p-126 / x));
+      if (floor(x) * 0.5 == floor(x * 0.5))
+        return 0;
+      return -0.0;
+    }
+    x *= 0x1p1023;
+    return x;
+  }
 
-        absx = sign ? -x : x;
+  absx = sign ? -x : x;
 
-        /* handle the error of x + g - 0.5 */
-        y = absx + gmhalf;
-        if (absx > gmhalf) {
-                dy = y - absx;
-                dy -= gmhalf;
-        } else {
-                dy = y - gmhalf;
-                dy -= absx;
-        }
+  /* handle the error of x + g - 0.5 */
+  y = absx + gmhalf;
+  if (absx > gmhalf) {
+    dy = y - absx;
+    dy -= gmhalf;
+  } else {
+    dy = y - gmhalf;
+    dy -= absx;
+  }
 
-        z = absx - 0.5;
-        r = S(absx) * exp(-y);
-        if (x < 0) {
-                /* reflection formula for negative x */
-                /* sinpi(absx) is not 0, integers are already handled */
-                r = -pi / (sinpi(absx) * absx * r);
-                dy = -dy;
-                z = -z;
-        }
-        r += dy * (gmhalf+0.5) * r / y;
-        z = pow(y, 0.5*z);
-        y = r * z * z;
-        return y;
+  z = absx - 0.5;
+  r = S(absx) * exp(-y);
+  if (x < 0) {
+    /* reflection formula for negative x */
+    /* sinpi(absx) is not 0, integers are already handled */
+    r = -pi / (sinpi(absx) * absx * r);
+    dy = -dy;
+    z = -z;
+  }
+  r += dy * (gmhalf + 0.5) * r / y;
+  z = pow(y, 0.5 * z);
+  y = r * z * z;
+  return y;
 }
 
 #if 0
 double __lgamma_r(double x, int *sign)
 {
         double r, absx;
 
         *sign = 1;
 
         /* special cases */
@@ skipping 32 matching lines @@
                 /* reflection formula for negative x */
                 x = sinpi(absx);
                 *sign = 2*!!signbit(x) - 1;
                 r = log(pi/(fabs(x)*absx)) - r;
         }
         return r;
 }
 
 weak_alias(__lgamma_r, lgamma_r);
 #endif