[fusl] clang-format fusl

fusl/src/math/jn.c

 /* origin: FreeBSD /usr/src/lib/msun/src/e_jn.c */
 /*
  * ====================================================
  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  *
  * Developed at SunSoft, a Sun Microsystems, Inc. business.
  * Permission to use, copy, modify, and distribute this
  * software is freely granted, provided that this notice
  * is preserved.
  * ====================================================
@@ skipping 18 matching lines @@
  *      compared with the actual value to correct the
  *      supposed value of j(n,x).
  *
  *      yn(n,x) is similar in all respects, except
  *      that forward recursion is used for all
  *      values of n>1.
  */
 
 #include "libm.h"
 
-static const double invsqrtpi = 5.64189583547756279280e-01; /* 0x3FE20DD7, 0x50429B6D */
-
-double jn(int n, double x)
-{
-        uint32_t ix, lx;
-        int nm1, i, sign;
-        double a, b, temp;
-
-        EXTRACT_WORDS(ix, lx, x);
-        sign = ix>>31;
-        ix &= 0x7fffffff;
-
-        if ((ix | (lx|-lx)>>31) > 0x7ff00000) /* nan */
-                return x;
-
-        /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
-         * Thus, J(-n,x) = J(n,-x)
-         */
-        /* nm1 = |n|-1 is used instead of |n| to handle n==INT_MIN */
-        if (n == 0)
-                return j0(x);
-        if (n < 0) {
-                nm1 = -(n+1);
-                x = -x;
-                sign ^= 1;
-        } else
-                nm1 = n-1;
-        if (nm1 == 0)
-                return j1(x);
-
-        sign &= n;  /* even n: 0, odd n: signbit(x) */
-        x = fabs(x);
-        if ((ix|lx) == 0 || ix == 0x7ff00000)  /* if x is 0 or inf */
-                b = 0.0;
-        else if (nm1 < x) {
-                /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
-                if (ix >= 0x52d00000) { /* x > 2**302 */
-                        /* (x >> n**2)
-                         *      Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
-                         *      Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
-                         *      Let s=sin(x), c=cos(x),
-                         *          xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
-                         *
-                         *             n    sin(xn)*sqt2    cos(xn)*sqt2
-                         *          ----------------------------------
-                         *             0     s-c             c+s
-                         *             1    -s-c            -c+s
-                         *             2    -s+c            -c-s
-                         *             3     s+c             c-s
-                         */
-                        switch(nm1&3) {
-                        case 0: temp = -cos(x)+sin(x); break;
-                        case 1: temp = -cos(x)-sin(x); break;
-                        case 2: temp =  cos(x)-sin(x); break;
-                        default:
-                        case 3: temp =  cos(x)+sin(x); break;
-                        }
-                        b = invsqrtpi*temp/sqrt(x);
-                } else {
-                        a = j0(x);
-                        b = j1(x);
-                        for (i=0; i<nm1; ) {
-                                i++;
-                                temp = b;
-                                b = b*(2.0*i/x) - a; /* avoid underflow */
-                                a = temp;
-                        }
-                }
-        } else {
-                if (ix < 0x3e100000) { /* x < 2**-29 */
-                        /* x is tiny, return the first Taylor expansion of J(n,x)
-                         * J(n,x) = 1/n!*(x/2)^n  - ...
-                         */
-                        if (nm1 > 32)  /* underflow */
-                                b = 0.0;
-                        else {
-                                temp = x*0.5;
-                                b = temp;
-                                a = 1.0;
-                                for (i=2; i<=nm1+1; i++) {
-                                        a *= (double)i; /* a = n! */
-                                        b *= temp;      /* b = (x/2)^n */
-                                }
-                                b = b/a;
-                        }
-                } else {
-                        /* use backward recurrence */
-                        /*                      x      x^2      x^2
-                         *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
-                         *                      2n  - 2(n+1) - 2(n+2)
-                         *
-                         *                      1      1        1
-                         *  (for large x)   =  ----  ------   ------   .....
-                         *                      2n   2(n+1)   2(n+2)
-                         *                      -- - ------ - ------ -
-                         *                       x     x         x
-                         *
-                         * Let w = 2n/x and h=2/x, then the above quotient
-                         * is equal to the continued fraction:
-                         *                  1
-                         *      = -----------------------
-                         *                     1
-                         *         w - -----------------
-                         *                        1
-                         *              w+h - ---------
-                         *                     w+2h - ...
-                         *
-                         * To determine how many terms needed, let
-                         * Q(0) = w, Q(1) = w(w+h) - 1,
-                         * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
-                         * When Q(k) > 1e4      good for single
-                         * When Q(k) > 1e9      good for double
-                         * When Q(k) > 1e17     good for quadruple
-                         */
-                        /* determine k */
-                        double t,q0,q1,w,h,z,tmp,nf;
-                        int k;
-
-                        nf = nm1 + 1.0;
-                        w = 2*nf/x;
-                        h = 2/x;
-                        z = w+h;
-                        q0 = w;
-                        q1 = w*z - 1.0;
-                        k = 1;
-                        while (q1 < 1.0e9) {
-                                k += 1;
-                                z += h;
-                                tmp = z*q1 - q0;
-                                q0 = q1;
-                                q1 = tmp;
-                        }
-                        for (t=0.0, i=k; i>=0; i--)
-                                t = 1/(2*(i+nf)/x - t);
-                        a = t;
-                        b = 1.0;
-                        /*  estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
-                         *  Hence, if n*(log(2n/x)) > ...
-                         *  single 8.8722839355e+01
-                         *  double 7.09782712893383973096e+02
-                         *  long double 1.1356523406294143949491931077970765006170e+04
-                         *  then recurrent value may overflow and the result is
-                         *  likely underflow to zero
-                         */
-                        tmp = nf*log(fabs(w));
-                        if (tmp < 7.09782712893383973096e+02) {
-                                for (i=nm1; i>0; i--) {
-                                        temp = b;
-                                        b = b*(2.0*i)/x - a;
-                                        a = temp;
-                                }
-                        } else {
-                                for (i=nm1; i>0; i--) {
-                                        temp = b;
-                                        b = b*(2.0*i)/x - a;
-                                        a = temp;
-                                        /* scale b to avoid spurious overflow */
-                                        if (b > 0x1p500) {
-                                                a /= b;
-                                                t /= b;
-                                                b  = 1.0;
-                                        }
-                                }
-                        }
-                        z = j0(x);
-                        w = j1(x);
-                        if (fabs(z) >= fabs(w))
-                                b = t*z/b;
-                        else
-                                b = t*w/a;
-                }
-        }
-        return sign ? -b : b;
+static const double invsqrtpi =
+    5.64189583547756279280e-01; /* 0x3FE20DD7, 0x50429B6D */
+
+double jn(int n, double x) {
+  uint32_t ix, lx;
+  int nm1, i, sign;
+  double a, b, temp;
+
+  EXTRACT_WORDS(ix, lx, x);
+  sign = ix >> 31;
+  ix &= 0x7fffffff;
+
+  if ((ix | (lx | -lx) >> 31) > 0x7ff00000) /* nan */
+    return x;
+
+  /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
+   * Thus, J(-n,x) = J(n,-x)
+   */
+  /* nm1 = |n|-1 is used instead of |n| to handle n==INT_MIN */
+  if (n == 0)
+    return j0(x);
+  if (n < 0) {
+    nm1 = -(n + 1);
+    x = -x;
+    sign ^= 1;
+  } else
+    nm1 = n - 1;
+  if (nm1 == 0)
+    return j1(x);
+
+  sign &= n; /* even n: 0, odd n: signbit(x) */
+  x = fabs(x);
+  if ((ix | lx) == 0 || ix == 0x7ff00000) /* if x is 0 or inf */
+    b = 0.0;
+  else if (nm1 < x) {
+    /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
+    if (ix >= 0x52d00000) { /* x > 2**302 */
+                            /* (x >> n**2)
+                             *      Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+                             *      Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+                             *      Let s=sin(x), c=cos(x),
+                             *          xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+                             *
+                             *             n    sin(xn)*sqt2    cos(xn)*sqt2
+                             *          ----------------------------------
+                             *             0     s-c             c+s
+                             *             1    -s-c            -c+s
+                             *             2    -s+c            -c-s
+                             *             3     s+c             c-s
+                             */
+      switch (nm1 & 3) {
+        case 0:
+          temp = -cos(x) + sin(x);
+          break;
+        case 1:
+          temp = -cos(x) - sin(x);
+          break;
+        case 2:
+          temp = cos(x) - sin(x);
+          break;
+        default:
+        case 3:
+          temp = cos(x) + sin(x);
+          break;
+      }
+      b = invsqrtpi * temp / sqrt(x);
+    } else {
+      a = j0(x);
+      b = j1(x);
+      for (i = 0; i < nm1;) {
+        i++;
+        temp = b;
+        b = b * (2.0 * i / x) - a; /* avoid underflow */
+        a = temp;
+      }
+    }
+  } else {
+    if (ix < 0x3e100000) { /* x < 2**-29 */
+      /* x is tiny, return the first Taylor expansion of J(n,x)
+       * J(n,x) = 1/n!*(x/2)^n  - ...
+       */
+      if (nm1 > 32) /* underflow */
+        b = 0.0;
+      else {
+        temp = x * 0.5;
+        b = temp;
+        a = 1.0;
+        for (i = 2; i <= nm1 + 1; i++) {
+          a *= (double)i; /* a = n! */
+          b *= temp;      /* b = (x/2)^n */
+        }
+        b = b / a;
+      }
+    } else {
+      /* use backward recurrence */
+      /*                      x      x^2      x^2
+       *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
+       *                      2n  - 2(n+1) - 2(n+2)
+       *
+       *                      1      1        1
+       *  (for large x)   =  ----  ------   ------   .....
+       *                      2n   2(n+1)   2(n+2)
+       *                      -- - ------ - ------ -
+       *                       x     x         x
+       *
+       * Let w = 2n/x and h=2/x, then the above quotient
+       * is equal to the continued fraction:
+       *                  1
+       *      = -----------------------
+       *                     1
+       *         w - -----------------
+       *                        1
+       *              w+h - ---------
+       *                     w+2h - ...
+       *
+       * To determine how many terms needed, let
+       * Q(0) = w, Q(1) = w(w+h) - 1,
+       * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
+       * When Q(k) > 1e4      good for single
+       * When Q(k) > 1e9      good for double
+       * When Q(k) > 1e17     good for quadruple
+       */
+      /* determine k */
+      double t, q0, q1, w, h, z, tmp, nf;
+      int k;
+
+      nf = nm1 + 1.0;
+      w = 2 * nf / x;
+      h = 2 / x;
+      z = w + h;
+      q0 = w;
+      q1 = w * z - 1.0;
+      k = 1;
+      while (q1 < 1.0e9) {
+        k += 1;
+        z += h;
+        tmp = z * q1 - q0;
+        q0 = q1;
+        q1 = tmp;
+      }
+      for (t = 0.0, i = k; i >= 0; i--)
+        t = 1 / (2 * (i + nf) / x - t);
+      a = t;
+      b = 1.0;
+      /*  estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
+       *  Hence, if n*(log(2n/x)) > ...
+       *  single 8.8722839355e+01
+       *  double 7.09782712893383973096e+02
+       *  long double 1.1356523406294143949491931077970765006170e+04
+       *  then recurrent value may overflow and the result is
+       *  likely underflow to zero
+       */
+      tmp = nf * log(fabs(w));
+      if (tmp < 7.09782712893383973096e+02) {
+        for (i = nm1; i > 0; i--) {
+          temp = b;
+          b = b * (2.0 * i) / x - a;
+          a = temp;
+        }
+      } else {
+        for (i = nm1; i > 0; i--) {
+          temp = b;
+          b = b * (2.0 * i) / x - a;
+          a = temp;
+          /* scale b to avoid spurious overflow */
+          if (b > 0x1p500) {
+            a /= b;
+            t /= b;
+            b = 1.0;
+          }
+        }
+      }
+      z = j0(x);
+      w = j1(x);
+      if (fabs(z) >= fabs(w))
+        b = t * z / b;
+      else
+        b = t * w / a;
+    }
+  }
+  return sign ? -b : b;
 }
 
-
-double yn(int n, double x)
-{
-        uint32_t ix, lx, ib;
-        int nm1, sign, i;
-        double a, b, temp;
-
-        EXTRACT_WORDS(ix, lx, x);
-        sign = ix>>31;
-        ix &= 0x7fffffff;
-
-        if ((ix | (lx|-lx)>>31) > 0x7ff00000) /* nan */
-                return x;
-        if (sign && (ix|lx)!=0) /* x < 0 */
-                return 0/0.0;
-        if (ix == 0x7ff00000)
-                return 0.0;
-
-        if (n == 0)
-                return y0(x);
-        if (n < 0) {
-                nm1 = -(n+1);
-                sign = n&1;
-        } else {
-                nm1 = n-1;
-                sign = 0;
-        }
-        if (nm1 == 0)
-                return sign ? -y1(x) : y1(x);
-
-        if (ix >= 0x52d00000) { /* x > 2**302 */
-                /* (x >> n**2)
-                 *      Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
-                 *      Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
-                 *      Let s=sin(x), c=cos(x),
-                 *          xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
-                 *
-                 *             n    sin(xn)*sqt2    cos(xn)*sqt2
-                 *          ----------------------------------
-                 *             0     s-c             c+s
-                 *             1    -s-c            -c+s
-                 *             2    -s+c            -c-s
-                 *             3     s+c             c-s
-                 */
-                switch(nm1&3) {
-                case 0: temp = -sin(x)-cos(x); break;
-                case 1: temp = -sin(x)+cos(x); break;
-                case 2: temp =  sin(x)+cos(x); break;
-                default:
-                case 3: temp =  sin(x)-cos(x); break;
-                }
-                b = invsqrtpi*temp/sqrt(x);
-        } else {
-                a = y0(x);
-                b = y1(x);
-                /* quit if b is -inf */
-                GET_HIGH_WORD(ib, b);
-                for (i=0; i<nm1 && ib!=0xfff00000; ){
-                        i++;
-                        temp = b;
-                        b = (2.0*i/x)*b - a;
-                        GET_HIGH_WORD(ib, b);
-                        a = temp;
-                }
-        }
-        return sign ? -b : b;
+double yn(int n, double x) {
+  uint32_t ix, lx, ib;
+  int nm1, sign, i;
+  double a, b, temp;
+
+  EXTRACT_WORDS(ix, lx, x);
+  sign = ix >> 31;
+  ix &= 0x7fffffff;
+
+  if ((ix | (lx | -lx) >> 31) > 0x7ff00000) /* nan */
+    return x;
+  if (sign && (ix | lx) != 0) /* x < 0 */
+    return 0 / 0.0;
+  if (ix == 0x7ff00000)
+    return 0.0;
+
+  if (n == 0)
+    return y0(x);
+  if (n < 0) {
+    nm1 = -(n + 1);
+    sign = n & 1;
+  } else {
+    nm1 = n - 1;
+    sign = 0;
+  }
+  if (nm1 == 0)
+    return sign ? -y1(x) : y1(x);
+
+  if (ix >= 0x52d00000) { /* x > 2**302 */
+                          /* (x >> n**2)
+                           *      Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+                           *      Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+                           *      Let s=sin(x), c=cos(x),
+                           *          xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+                           *
+                           *             n    sin(xn)*sqt2    cos(xn)*sqt2
+                           *          ----------------------------------
+                           *             0     s-c             c+s
+                           *             1    -s-c            -c+s
+                           *             2    -s+c            -c-s
+                           *             3     s+c             c-s
+                           */
+    switch (nm1 & 3) {
+      case 0:
+        temp = -sin(x) - cos(x);
+        break;
+      case 1:
+        temp = -sin(x) + cos(x);
+        break;
+      case 2:
+        temp = sin(x) + cos(x);
+        break;
+      default:
+      case 3:
+        temp = sin(x) - cos(x);
+        break;
+    }
+    b = invsqrtpi * temp / sqrt(x);
+  } else {
+    a = y0(x);
+    b = y1(x);
+    /* quit if b is -inf */
+    GET_HIGH_WORD(ib, b);
+    for (i = 0; i < nm1 && ib != 0xfff00000;) {
+      i++;
+      temp = b;
+      b = (2.0 * i / x) * b - a;
+      GET_HIGH_WORD(ib, b);
+      a = temp;
+    }
+  }
+  return sign ? -b : b;
 }