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| 1906 | serge | 1 | /* __powil.c |
| 2 | * |
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| 3 | * Real raised to integer power, long double precision |
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| 4 | * |
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| 5 | * |
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| 6 | * |
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| 7 | * SYNOPSIS: |
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| 8 | * |
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| 9 | * long double x, y, __powil(); |
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| 10 | * int n; |
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| 11 | * |
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| 12 | * y = __powil( x, n ); |
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| 13 | * |
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| 14 | * |
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| 15 | * |
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| 16 | * DESCRIPTION: |
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| 17 | * |
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| 18 | * Returns argument x raised to the nth power. |
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| 19 | * The routine efficiently decomposes n as a sum of powers of |
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| 20 | * two. The desired power is a product of two-to-the-kth |
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| 21 | * powers of x. Thus to compute the 32767 power of x requires |
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| 22 | * 28 multiplications instead of 32767 multiplications. |
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| 23 | * |
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| 24 | * |
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| 25 | * |
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| 26 | * ACCURACY: |
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| 27 | * |
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| 28 | * |
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| 29 | * Relative error: |
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| 30 | * arithmetic x domain n domain # trials peak rms |
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| 31 | * IEEE .001,1000 -1022,1023 50000 4.3e-17 7.8e-18 |
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| 32 | * IEEE 1,2 -1022,1023 20000 3.9e-17 7.6e-18 |
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| 33 | * IEEE .99,1.01 0,8700 10000 3.6e-16 7.2e-17 |
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| 34 | * |
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| 35 | * Returns INFINITY on overflow, zero on underflow. |
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| 36 | * |
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| 37 | */ |
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| 38 | |||
| 39 | /* __powil.c */ |
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| 40 | |||
| 41 | /* |
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| 42 | Cephes Math Library Release 2.2: December, 1990 |
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| 43 | Copyright 1984, 1990 by Stephen L. Moshier |
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| 44 | Direct inquiries to 30 Frost Street, Cambridge, MA 02140 |
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| 45 | */ |
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| 46 | |||
| 47 | /* |
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| 48 | Modified for mingw |
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| 49 | 2002-07-22 Danny Smith |
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| 50 | */ |
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| 51 | |||
| 52 | #ifdef __MINGW32__ |
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| 53 | #include "cephes_mconf.h" |
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| 54 | #else |
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| 55 | #include "mconf.h" |
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| 56 | extern long double MAXNUML, MAXLOGL, MINLOGL; |
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| 57 | extern long double LOGE2L; |
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| 58 | #ifdef ANSIPROT |
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| 59 | extern long double frexpl ( long double, int * ); |
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| 60 | #else |
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| 61 | long double frexpl(); |
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| 62 | #endif |
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| 63 | #endif /* __MINGW32__ */ |
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| 64 | |||
| 65 | #ifndef _SET_ERRNO |
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| 66 | #define _SET_ERRNO(x) |
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| 67 | #endif |
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| 68 | |||
| 69 | long double __powil( x, nn ) |
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| 70 | long double x; |
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| 71 | int nn; |
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| 72 | { |
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| 73 | long double w, y; |
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| 74 | long double s; |
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| 75 | int n, e, sign, asign, lx; |
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| 76 | |||
| 77 | if( x == 0.0L ) |
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| 78 | { |
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| 79 | if( nn == 0 ) |
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| 80 | return( 1.0L ); |
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| 81 | else if( nn < 0 ) |
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| 82 | return( INFINITYL ); |
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| 83 | else |
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| 84 | return( 0.0L ); |
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| 85 | } |
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| 86 | |||
| 87 | if( nn == 0 ) |
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| 88 | return( 1.0L ); |
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| 89 | |||
| 90 | |||
| 91 | if( x < 0.0L ) |
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| 92 | { |
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| 93 | asign = -1; |
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| 94 | x = -x; |
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| 95 | } |
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| 96 | else |
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| 97 | asign = 0; |
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| 98 | |||
| 99 | |||
| 100 | if( nn < 0 ) |
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| 101 | { |
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| 102 | sign = -1; |
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| 103 | n = -nn; |
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| 104 | } |
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| 105 | else |
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| 106 | { |
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| 107 | sign = 1; |
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| 108 | n = nn; |
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| 109 | } |
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| 110 | |||
| 111 | /* Overflow detection */ |
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| 112 | |||
| 113 | /* Calculate approximate logarithm of answer */ |
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| 114 | s = x; |
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| 115 | s = frexpl( s, &lx ); |
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| 116 | e = (lx - 1)*n; |
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| 117 | if( (e == 0) || (e > 64) || (e < -64) ) |
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| 118 | { |
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| 119 | s = (s - 7.0710678118654752e-1L) / (s + 7.0710678118654752e-1L); |
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| 120 | s = (2.9142135623730950L * s - 0.5L + lx) * nn * LOGE2L; |
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| 121 | } |
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| 122 | else |
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| 123 | { |
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| 124 | s = LOGE2L * e; |
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| 125 | } |
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| 126 | |||
| 127 | if( s > MAXLOGL ) |
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| 128 | { |
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| 129 | mtherr( "__powil", OVERFLOW ); |
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| 130 | _SET_ERRNO(ERANGE); |
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| 131 | y = INFINITYL; |
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| 132 | goto done; |
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| 133 | } |
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| 134 | |||
| 135 | if( s < MINLOGL ) |
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| 136 | { |
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| 137 | mtherr( "__powil", UNDERFLOW ); |
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| 138 | _SET_ERRNO(ERANGE); |
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| 139 | return(0.0L); |
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| 140 | } |
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| 141 | /* Handle tiny denormal answer, but with less accuracy |
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| 142 | * since roundoff error in 1.0/x will be amplified. |
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| 143 | * The precise demarcation should be the gradual underflow threshold. |
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| 144 | */ |
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| 145 | if( s < (-MAXLOGL+2.0L) ) |
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| 146 | { |
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| 147 | x = 1.0L/x; |
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| 148 | sign = -sign; |
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| 149 | } |
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| 150 | |||
| 151 | /* First bit of the power */ |
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| 152 | if( n & 1 ) |
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| 153 | y = x; |
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| 154 | |||
| 155 | else |
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| 156 | { |
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| 157 | y = 1.0L; |
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| 158 | asign = 0; |
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| 159 | } |
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| 160 | |||
| 161 | w = x; |
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| 162 | n >>= 1; |
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| 163 | while( n ) |
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| 164 | { |
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| 165 | w = w * w; /* arg to the 2-to-the-kth power */ |
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| 166 | if( n & 1 ) /* if that bit is set, then include in product */ |
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| 167 | y *= w; |
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| 168 | n >>= 1; |
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| 169 | } |
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| 170 | |||
| 171 | |||
| 172 | done: |
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| 173 | |||
| 174 | if( asign ) |
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| 175 | y = -y; /* odd power of negative number */ |
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| 176 | if( sign < 0 ) |
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| 177 | y = 1.0L/y; |
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| 178 | return(y); |
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| 179 | } |