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  1. /*                                                      powi.c
  2.  *
  3.  *      Real raised to integer power
  4.  *
  5.  *
  6.  *
  7.  * SYNOPSIS:
  8.  *
  9.  * double x, y, __powi();
  10.  * int n;
  11.  *
  12.  * y = __powi( x, n );
  13.  *
  14.  *
  15.  *
  16.  * DESCRIPTION:
  17.  *
  18.  * Returns argument x raised to the nth power.
  19.  * The routine efficiently decomposes n as a sum of powers of
  20.  * two. The desired power is a product of two-to-the-kth
  21.  * powers of x.  Thus to compute the 32767 power of x requires
  22.  * 28 multiplications instead of 32767 multiplications.
  23.  *
  24.  *
  25.  *
  26.  * ACCURACY:
  27.  *
  28.  *
  29.  *                      Relative error:
  30.  * arithmetic   x domain   n domain  # trials      peak         rms
  31.  *    DEC       .04,26     -26,26    100000       2.7e-16     4.3e-17
  32.  *    IEEE      .04,26     -26,26     50000       2.0e-15     3.8e-16
  33.  *    IEEE        1,2    -1022,1023   50000       8.6e-14     1.6e-14
  34.  *
  35.  * Returns MAXNUM on overflow, zero on underflow.
  36.  *
  37.  */
  39. /*                                                      powi.c  */
  40.  
  41. /*
  42. Cephes Math Library Release 2.8:  June, 2000
  43. Copyright 1984, 1995, 2000 by Stephen L. Moshier
  44. */
  45.  
  46. /*
  47. Modified for mingw
  48. 2002-07-22 Danny Smith <dannysmith@users.sourceforge.net>
  49. */
  50.  
  51. #ifdef __MINGW32__
  52. #include "cephes_mconf.h"
  53. #else
  54. #include "mconf.h"
  55. #ifdef ANSIPROT
  56. extern double log ( double );
  57. extern double frexp ( double, int * );
  58. extern int signbit ( double );
  59. #else
  60. double log(), frexp();
  61. int signbit();
  62. #endif
  63. extern double NEGZERO, INFINITY, MAXNUM, MAXLOG, MINLOG, LOGE2;
  64. #endif /* __MINGW32__ */
  65.  
  66. #ifndef _SET_ERRNO
  67. #define _SET_ERRNO(x)
  68. #endif
  69.  
  70. double __powi( x, nn )
  71. double x;
  72. int nn;
  73. {
  74. int n, e, sign, asign, lx;
  75. double w, y, s;
  76.  
  77. /* See pow.c for these tests.  */
  78. if( x == 0.0 )
  79.         {
  80.         if( nn == 0 )
  81.                 return( 1.0 );
  82.         else if( nn < 0 )
  83.             return( INFINITY );
  84.         else
  85.           {
  86.             if( nn & 1 )
  87.               return( x );
  88.             else
  89.               return( 0.0 );
  90.           }
  91.         }
  92.  
  93. if( nn == 0 )
  94.         return( 1.0 );
  95.  
  96. if( nn == -1 )
  97.         return( 1.0/x );
  98.  
  99. if( x < 0.0 )
  100.         {
  101.         asign = -1;
  102.         x = -x;
  103.         }
  104. else
  105.         asign = 0;
  106.  
  107.  
  108. if( nn < 0 )
  109.         {
  110.         sign = -1;
  111.         n = -nn;
  112.         }
  113. else
  114.         {
  115.         sign = 1;
  116.         n = nn;
  117.         }
  118.  
  119. /* Even power will be positive. */
  120. if( (n & 1) == 0 )
  121.         asign = 0;
  122.  
  123. /* Overflow detection */
  124.  
  125. /* Calculate approximate logarithm of answer */
  126. s = frexp( x, &lx );
  127. e = (lx - 1)*n;
  128. if( (e == 0) || (e > 64) || (e < -64) )
  129.         {
  130.         s = (s - 7.0710678118654752e-1) / (s +  7.0710678118654752e-1);
  131.         s = (2.9142135623730950 * s - 0.5 + lx) * nn * LOGE2;
  132.         }
  133. else
  134.         {
  135.         s = LOGE2 * e;
  136.         }
  137.  
  138. if( s > MAXLOG )
  139.         {
  140.         mtherr( "powi", OVERFLOW );
  141.         _SET_ERRNO(ERANGE);
  142.         y = INFINITY;
  143.         goto done;
  144.         }
  145.  
  146. #if DENORMAL
  147. if( s < MINLOG )
  148.         {
  149.         y = 0.0;
  150.         goto done;
  151.         }
  152.  
  153. /* Handle tiny denormal answer, but with less accuracy
  154.  * since roundoff error in 1.0/x will be amplified.
  155.  * The precise demarcation should be the gradual underflow threshold.
  156.  */
  157. if( (s < (-MAXLOG+2.0)) && (sign < 0) )
  158.         {
  159.         x = 1.0/x;
  160.         sign = -sign;
  161.         }
  162. #else
  163. /* do not produce denormal answer */
  164. if( s < -MAXLOG )
  165.         return(0.0);
  166. #endif
  167.  
  168.  
  169. /* First bit of the power */
  170. if( n & 1 )
  171.         y = x;
  172.                
  173. else
  174.         y = 1.0;
  175.  
  176. w = x;
  177. n >>= 1;
  178. while( n )
  179.         {
  180.         w = w * w;      /* arg to the 2-to-the-kth power */
  181.         if( n & 1 )     /* if that bit is set, then include in product */
  182.                 y *= w;
  183.         n >>= 1;
  184.         }
  185.  
  186. if( sign < 0 )
  187.         y = 1.0/y;
  188.  
  189. done:
  190.  
  191. if( asign )
  192.         {
  193.         /* odd power of negative number */
  194.         if( y == 0.0 )
  195.                 y = NEGZERO;
  196.         else
  197.                 y = -y;
  198.         }
  199. return(y);
  200. }
  201.