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-rw-r--r--libm/float/powf.c338
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diff --git a/libm/float/powf.c b/libm/float/powf.c
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-/* powf.c
- *
- * Power function
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, z, powf();
- *
- * z = powf( x, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes x raised to the yth power. Analytically,
- *
- * x**y = exp( y log(x) ).
- *
- * Following Cody and Waite, this program uses a lookup table
- * of 2**-i/16 and pseudo extended precision arithmetic to
- * obtain an extra three bits of accuracy in both the logarithm
- * and the exponential.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,10 100,000 1.4e-7 3.6e-8
- * 1/10 < x < 10, x uniformly distributed.
- * -10 < y < 10, y uniformly distributed.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * powf overflow x**y > MAXNUMF MAXNUMF
- * powf underflow x**y < 1/MAXNUMF 0.0
- * powf domain x<0 and y noninteger 0.0
- *
- */
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1988 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-static char fname[] = {"powf"};
-
-
-/* 2^(-i/16)
- * The decimal values are rounded to 24-bit precision
- */
-static float A[] = {
- 1.00000000000000000000E0,
- 9.57603275775909423828125E-1,
- 9.17004048824310302734375E-1,
- 8.78126084804534912109375E-1,
- 8.40896427631378173828125E-1,
- 8.05245161056518554687500E-1,
- 7.71105408668518066406250E-1,
- 7.38413095474243164062500E-1,
- 7.07106769084930419921875E-1,
- 6.77127778530120849609375E-1,
- 6.48419797420501708984375E-1,
- 6.20928883552551269531250E-1,
- 5.94603538513183593750000E-1,
- 5.69394290447235107421875E-1,
- 5.45253872871398925781250E-1,
- 5.22136867046356201171875E-1,
- 5.00000000000000000000E-1
-};
-/* continuation, for even i only
- * 2^(i/16) = A[i] + B[i/2]
- */
-static float B[] = {
- 0.00000000000000000000E0,
--5.61963907099083340520586E-9,
--1.23776636307969995237668E-8,
- 4.03545234539989593104537E-9,
- 1.21016171044789693621048E-8,
--2.00949968760174979411038E-8,
- 1.89881769396087499852802E-8,
--6.53877009617774467211965E-9,
- 0.00000000000000000000E0
-};
-
-/* 1 / A[i]
- * The decimal values are full precision
- */
-static float Ainv[] = {
- 1.00000000000000000000000E0,
- 1.04427378242741384032197E0,
- 1.09050773266525765920701E0,
- 1.13878863475669165370383E0,
- 1.18920711500272106671750E0,
- 1.24185781207348404859368E0,
- 1.29683955465100966593375E0,
- 1.35425554693689272829801E0,
- 1.41421356237309504880169E0,
- 1.47682614593949931138691E0,
- 1.54221082540794082361229E0,
- 1.61049033194925430817952E0,
- 1.68179283050742908606225E0,
- 1.75625216037329948311216E0,
- 1.83400808640934246348708E0,
- 1.91520656139714729387261E0,
- 2.00000000000000000000000E0
-};
-
-#ifdef DEC
-#define MEXP 2032.0
-#define MNEXP -2032.0
-#else
-#define MEXP 2048.0
-#define MNEXP -2400.0
-#endif
-
-/* log2(e) - 1 */
-#define LOG2EA 0.44269504088896340736F
-extern float MAXNUMF;
-
-#define F W
-#define Fa Wa
-#define Fb Wb
-#define G W
-#define Ga Wa
-#define Gb u
-#define H W
-#define Ha Wb
-#define Hb Wb
-
-
-#ifdef ANSIC
-float floorf( float );
-float frexpf( float, int *);
-float ldexpf( float, int );
-float powif( float, int );
-#else
-float floorf(), frexpf(), ldexpf(), powif();
-#endif
-
-/* Find a multiple of 1/16 that is within 1/16 of x. */
-#define reduc(x) 0.0625 * floorf( 16 * (x) )
-
-#ifdef ANSIC
-float powf( float x, float y )
-#else
-float powf( x, y )
-float x, y;
-#endif
-{
-float u, w, z, W, Wa, Wb, ya, yb;
-/* float F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
-int e, i, nflg;
-
-
-nflg = 0; /* flag = 1 if x<0 raised to integer power */
-w = floorf(y);
-if( w < 0 )
- z = -w;
-else
- z = w;
-if( (w == y) && (z < 32768.0) )
- {
- i = w;
- w = powif( x, i );
- return( w );
- }
-
-
-if( x <= 0.0F )
- {
- if( x == 0.0 )
- {
- if( y == 0.0 )
- return( 1.0 ); /* 0**0 */
- else
- return( 0.0 ); /* 0**y */
- }
- else
- {
- if( w != y )
- { /* noninteger power of negative number */
- mtherr( fname, DOMAIN );
- return(0.0);
- }
- nflg = 1;
- if( x < 0 )
- x = -x;
- }
- }
-
-/* separate significand from exponent */
-x = frexpf( x, &e );
-
-/* find significand in antilog table A[] */
-i = 1;
-if( x <= A[9] )
- i = 9;
-if( x <= A[i+4] )
- i += 4;
-if( x <= A[i+2] )
- i += 2;
-if( x >= A[1] )
- i = -1;
-i += 1;
-
-
-/* Find (x - A[i])/A[i]
- * in order to compute log(x/A[i]):
- *
- * log(x) = log( a x/a ) = log(a) + log(x/a)
- *
- * log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a
- */
-x -= A[i];
-x -= B[ i >> 1 ];
-x *= Ainv[i];
-
-
-/* rational approximation for log(1+v):
- *
- * log(1+v) = v - 0.5 v^2 + v^3 P(v)
- * Theoretical relative error of the approximation is 3.5e-11
- * on the interval 2^(1/16) - 1 > v > 2^(-1/16) - 1
- */
-z = x*x;
-w = (((-0.1663883081054895 * x
- + 0.2003770364206271) * x
- - 0.2500006373383951) * x
- + 0.3333331095506474) * x * z;
-w -= 0.5 * z;
-
-/* Convert to base 2 logarithm:
- * multiply by log2(e)
- */
-w = w + LOG2EA * w;
-/* Note x was not yet added in
- * to above rational approximation,
- * so do it now, while multiplying
- * by log2(e).
- */
-z = w + LOG2EA * x;
-z = z + x;
-
-/* Compute exponent term of the base 2 logarithm. */
-w = -i;
-w *= 0.0625; /* divide by 16 */
-w += e;
-/* Now base 2 log of x is w + z. */
-
-/* Multiply base 2 log by y, in extended precision. */
-
-/* separate y into large part ya
- * and small part yb less than 1/16
- */
-ya = reduc(y);
-yb = y - ya;
-
-
-F = z * y + w * yb;
-Fa = reduc(F);
-Fb = F - Fa;
-
-G = Fa + w * ya;
-Ga = reduc(G);
-Gb = G - Ga;
-
-H = Fb + Gb;
-Ha = reduc(H);
-w = 16 * (Ga + Ha);
-
-/* Test the power of 2 for overflow */
-if( w > MEXP )
- {
- mtherr( fname, OVERFLOW );
- return( MAXNUMF );
- }
-
-if( w < MNEXP )
- {
- mtherr( fname, UNDERFLOW );
- return( 0.0 );
- }
-
-e = w;
-Hb = H - Ha;
-
-if( Hb > 0.0 )
- {
- e += 1;
- Hb -= 0.0625;
- }
-
-/* Now the product y * log2(x) = Hb + e/16.0.
- *
- * Compute base 2 exponential of Hb,
- * where -0.0625 <= Hb <= 0.
- * Theoretical relative error of the approximation is 2.8e-12.
- */
-/* z = 2**Hb - 1 */
-z = ((( 9.416993633606397E-003 * Hb
- + 5.549356188719141E-002) * Hb
- + 2.402262883964191E-001) * Hb
- + 6.931471791490764E-001) * Hb;
-
-/* Express e/16 as an integer plus a negative number of 16ths.
- * Find lookup table entry for the fractional power of 2.
- */
-if( e < 0 )
- i = -( -e >> 4 );
-else
- i = (e >> 4) + 1;
-e = (i << 4) - e;
-w = A[e];
-z = w + w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */
-z = ldexpf( z, i ); /* multiply by integer power of 2 */
-
-if( nflg )
- {
-/* For negative x,
- * find out if the integer exponent
- * is odd or even.
- */
- w = 2 * floorf( (float) 0.5 * w );
- if( w != y )
- z = -z; /* odd exponent */
- }
-
-return( z );
-}