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Diffstat (limited to 'libm/float/powf.c')
-rw-r--r-- | libm/float/powf.c | 338 |
1 files changed, 0 insertions, 338 deletions
diff --git a/libm/float/powf.c b/libm/float/powf.c deleted file mode 100644 index 367a39ad4..000000000 --- a/libm/float/powf.c +++ /dev/null @@ -1,338 +0,0 @@ -/* 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 ); -} |