diff --git a/library/GNUmakefile.68k b/library/GNUmakefile.68k index dcf3160..34cc29c 100644 --- a/library/GNUmakefile.68k +++ b/library/GNUmakefile.68k @@ -1,5 +1,5 @@ # -# $Id: GNUmakefile.68k,v 1.57 2005-05-30 08:10:36 obarthel Exp $ +# $Id: GNUmakefile.68k,v 1.58 2005-05-30 08:47:25 obarthel Exp $ # # :ts=8 # @@ -519,13 +519,14 @@ MATH_LIB = \ complex_creal.o \ complex_crealf.o \ complex_creall.o \ - math_coshf.o \ - math_sinhf.o \ - math_tanhf.o \ math_acos.o \ math_acosf.o \ + math_acosh.o \ + math_acoshf.o \ math_asin.o \ math_asinf.o \ + math_asinh.o \ + math_asinhf.o \ math_atan.o \ math_atan2.o \ math_atan2f.o \ @@ -539,6 +540,7 @@ MATH_LIB = \ math_cos.o \ math_cosf.o \ math_cosh.o \ + math_coshf.o \ math_erf.o \ math_erfc.o \ math_erfcf.o \ @@ -572,6 +574,8 @@ MATH_LIB = \ math_kernel_tanf.o \ math_ldexp.o \ math_ldexpf.o \ + math_lgamma.o \ + math_lgammaf.o \ math_log.o \ math_log10.o \ math_log10f.o \ @@ -588,6 +592,8 @@ MATH_LIB = \ math_nextafterf.o \ math_pow.o \ math_powf.o \ + math_remainder.o \ + math_remainderf.o \ math_rem_pio2f.o \ math_rint.o \ math_rintf.o \ @@ -597,11 +603,13 @@ MATH_LIB = \ math_sin.o \ math_sinf.o \ math_sinh.o \ + math_sinhf.o \ math_sqrt.o \ math_sqrtf.o \ math_tan.o \ math_tanf.o \ math_tanh.o \ + math_tanhf.o \ stdio_asprintf.o \ stdio_flush.o \ stdio_flush_all_files.o \ diff --git a/library/GNUmakefile.os4 b/library/GNUmakefile.os4 index d0773c4..69a927d 100644 --- a/library/GNUmakefile.os4 +++ b/library/GNUmakefile.os4 @@ -1,5 +1,5 @@ # -# $Id: GNUmakefile.os4,v 1.61 2005-05-30 08:10:37 obarthel Exp $ +# $Id: GNUmakefile.os4,v 1.62 2005-05-30 08:47:26 obarthel Exp $ # # :ts=8 # @@ -519,13 +519,14 @@ MATH_LIB = \ complex_creal.o \ complex_crealf.o \ complex_creall.o \ - math_coshf.o \ - math_sinhf.o \ - math_tanhf.o \ math_acos.o \ math_acosf.o \ + math_acosh.o \ + math_acoshf.o \ math_asin.o \ math_asinf.o \ + math_asinh.o \ + math_asinhf.o \ math_atan.o \ math_atan2.o \ math_atan2f.o \ @@ -539,6 +540,7 @@ MATH_LIB = \ math_cos.o \ math_cosf.o \ math_cosh.o \ + math_coshf.o \ math_erf.o \ math_erfc.o \ math_erfcf.o \ @@ -578,6 +580,8 @@ MATH_LIB = \ math_kernel_tanf.o \ math_ldexp.o \ math_ldexpf.o \ + math_lgamma.o \ + math_lgammaf.o \ math_log.o \ math_log10.o \ math_log10f.o \ @@ -594,6 +598,8 @@ MATH_LIB = \ math_nextafterf.o \ math_pow.o \ math_powf.o \ + math_remainder.o \ + math_remainderf.o \ math_rem_pio2f.o \ math_rint.o \ math_rintf.o \ @@ -603,11 +609,13 @@ MATH_LIB = \ math_sin.o \ math_sinf.o \ math_sinh.o \ + math_sinhf.o \ math_sqrt.o \ math_sqrtf.o \ math_tan.o \ math_tanf.o \ math_tanh.o \ + math_tanhf.o \ stdio_asprintf.o \ stdio_flush.o \ stdio_flush_all_files.o \ diff --git a/library/TODO b/library/TODO index 7ac4ea8..a1a65d9 100755 --- a/library/TODO +++ b/library/TODO @@ -1,16 +1,10 @@ C99 math functions: (functions generally missing, including their "float" counterparts) - acosh - acoshf - asinh - asinhf exp2 exp2f fma fmaf - lgamma - lgammaf log2 log2f lrint @@ -19,10 +13,6 @@ C99 math functions: lroundf nearbyint nearbyintf - nexttoward - nexttowardf - remainder - remainderf remquo remquof round diff --git a/library/changes b/library/changes index fd7e0c4..51c07f4 100644 --- a/library/changes +++ b/library/changes @@ -73,6 +73,9 @@ - Ported cosf(), coshf(), sinf(), sinhf(), tanf(), tanhf() and hypotf() for C99. +- Ported acosh(), acoshf(), asinh(), asinhf(), lgamma(), lgammaf(), + remainder() and remainderf() for C99. + c.lib 1.192 (12.5.2005) diff --git a/library/include/math.h b/library/include/math.h index d8c6b68..13f8e03 100644 --- a/library/include/math.h +++ b/library/include/math.h @@ -1,5 +1,5 @@ /* - * $Id: math.h,v 1.14 2005-05-30 08:10:41 obarthel Exp $ + * $Id: math.h,v 1.15 2005-05-30 08:47:41 obarthel Exp $ * * :ts=4 * @@ -242,53 +242,49 @@ extern float tanhf(float x); /****************************************************************************/ -extern float logbf(float x); -extern double logb(double x); - -extern float hypotf(float x, float y); -extern double hypot(double x,double y); - -extern float nanf(const char *tagp); -extern double nan(const char *tagp); - -extern float nextafterf(float x,float y); -extern double nextafter(double x,double y); - -extern float copysignf(float x, float y); -extern double copysign(double x, double y); - -extern float fdimf(float x,float y); -extern double fdim(double x,double y); - -extern float fminf(float x,float y); -extern double fmin(double x,double y); - -extern float fmaxf(float x,float y); -extern double fmax(double x,double y); - -extern float scalbnf (float x, int n); -extern double scalbn (double x, int n); - +extern float acoshf(float x); +extern float asinhf(float x); extern float cbrtf(float x); -extern double cbrt(double x); - -extern float erff(float x); -extern double erf(double x); - +extern float copysignf(float x, float y); extern float erfcf(float x); -extern double erfc(double x); - +extern float erff(float x); extern float expm1f(float x); -extern double expm1(double x); - -extern int ilogbf(float x); -extern int ilogb(double x); - +extern float fdimf(float x,float y); +extern float fmaxf(float x,float y); +extern float fminf(float x,float y); +extern float hypotf(float x, float y); +extern float lgammaf(float x); extern float log1pf(float x); -extern double log1p(double x); - +extern float logbf(float x); +extern float nanf(const char *tagp); +extern float nextafterf(float x,float y); +extern float remainderf(float x, float p); extern float rintf(float x); +extern float scalbnf (float x, int n); +extern int ilogbf(float x); + +/****************************************************************************/ + +extern double acosh(double x); +extern double asinh(double x); +extern double cbrt(double x); +extern double copysign(double x, double y); +extern double erf(double x); +extern double erfc(double x); +extern double expm1(double x); +extern double fdim(double x,double y); +extern double fmax(double x,double y); +extern double fmin(double x,double y); +extern double hypot(double x,double y); +extern double lgamma(double x); +extern double log1p(double x); +extern double logb(double x); +extern double nan(const char *tagp); +extern double nextafter(double x,double y); +extern double remainder(double x, double p); extern double rint(double x); +extern double scalbn (double x, int n); +extern int ilogb(double x); /****************************************************************************/ diff --git a/library/math_acosh.c b/library/math_acosh.c index 86cb9d9..4d5e883 100644 --- a/library/math_acosh.c +++ b/library/math_acosh.c @@ -1,5 +1,5 @@ /* - * $Id: math_acosh.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $ + * $Id: math_acosh.c,v 1.2 2005-05-30 08:47:26 obarthel Exp $ * * :ts=4 * @@ -29,6 +29,15 @@ * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE * POSSIBILITY OF SUCH DAMAGE. + * + * + * PowerPC math library based in part on work by Sun Microsystems + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. */ #ifndef _MATH_HEADERS_H @@ -41,11 +50,33 @@ /****************************************************************************/ +static const double +one = 1.0, +ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + double acosh(double x) -{ - /* ZZZ unimplemented */ - return(0); +{ + double t; + LONG hx; + ULONG lx; + EXTRACT_WORDS(hx,lx,x); + if(hx<0x3ff00000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x41b00000) { /* x > 2**28 */ + if(hx >=0x7ff00000) { /* x is inf of NaN */ + return x+x; + } else + return log(x)+ln2; /* acosh(huge)=log(2x) */ + } else if(((hx-0x3ff00000)|lx)==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return log(2.0*x-one/(x+sqrt(t-one))); + } else { /* 1=0x4d800000) { /* x > 2**28 */ + if(hx >=0x7f800000) { /* x is inf of NaN */ + return x+x; + } else + return logf(x)+ln2; /* acosh(huge)=log(2x) */ + } else if (hx==0x3f800000) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return logf((float)2.0*x-one/(x+sqrtf(t-one))); + } else { /* 1=0x7ff00000) return x+x; /* x is inf or NaN */ + if(ix< 0x3e300000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x41b00000) { /* |x| > 2**28 */ + w = log(fabs(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabs(x); + w = log(2.0*t+one/(sqrt(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1p(fabs(x)+t/(one+sqrt(one+t))); + } + if(hx>0) return w; else return -w; } /****************************************************************************/ diff --git a/library/math_asinhf.c b/library/math_asinhf.c index 1e9b8d8..56152ec 100644 --- a/library/math_asinhf.c +++ b/library/math_asinhf.c @@ -1,5 +1,5 @@ /* - * $Id: math_asinhf.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $ + * $Id: math_asinhf.c,v 1.2 2005-05-30 08:47:26 obarthel Exp $ * * :ts=4 * @@ -29,6 +29,18 @@ * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE * POSSIBILITY OF SUCH DAMAGE. + * + * + * PowerPC math library based in part on work by Sun Microsystems + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * + * + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ #ifndef _MATH_HEADERS_H @@ -41,11 +53,32 @@ /****************************************************************************/ +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +ln2 = 6.9314718246e-01, /* 0x3f317218 */ +huge= 1.0000000000e+30; + float asinhf(float x) -{ - /* ZZZ unimplemented */ - return(0); +{ + float t,w; + LONG hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return x+x; /* x is inf or NaN */ + if(ix< 0x31800000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x4d800000) { /* |x| > 2**28 */ + w = logf(fabsf(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabsf(x); + w = logf((float)2.0*t+one/(sqrtf(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1pf(fabsf(x)+t/(one+sqrtf(one+t))); + } + if(hx>0) return w; else return -w; } /****************************************************************************/ diff --git a/library/math_lgamma.c b/library/math_lgamma.c index 5b60f24..4bcd182 100644 --- a/library/math_lgamma.c +++ b/library/math_lgamma.c @@ -1,5 +1,5 @@ /* - * $Id: math_lgamma.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $ + * $Id: math_lgamma.c,v 1.2 2005-05-30 08:47:26 obarthel Exp $ * * :ts=4 * @@ -41,11 +41,211 @@ /****************************************************************************/ +static const double +two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */ +a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */ +a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */ +a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */ +a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */ +a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */ +a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */ +a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */ +a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */ +a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */ +a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */ +a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */ +tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */ +tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */ +/* tt = -(tail of tf) */ +tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */ +t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */ +t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */ +t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */ +t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */ +t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */ +t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */ +t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */ +t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */ +t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */ +t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */ +t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */ +t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */ +t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */ +t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */ +t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */ +u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */ +u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */ +u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */ +u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */ +u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */ +v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */ +v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */ +v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */ +v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */ +v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */ +s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */ +s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */ +s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */ +s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */ +s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */ +s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */ +r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */ +r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */ +r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */ +r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */ +r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */ +r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */ +w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */ +w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */ +w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */ +w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */ +w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */ +w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */ +w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */ + +static const double zero= 0.00000000000000000000e+00; + +static double +sin_pi(double x) +{ + double y,z; + LONG n,ix; + + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = floor(y); + if(z!=y) { /* inexact anyway */ + y *= 0.5; + y = 2.0*(y - floor(y)); /* y = |x| mod 2.0 */ + n = (LONG) (y*4.0); + } else { + if(ix>=0x43400000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x43300000) z = y+two52; /* exact */ + GET_LOW_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __kernel_sin(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cos(pi*(0.5-y),zero); break; + case 3: + case 4: y = __kernel_sin(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cos(pi*(y-1.5),zero); break; + default: y = __kernel_sin(pi*(y-2.0),zero,0); break; + } + return -y; +} + double lgamma(double x) { - /* ZZZ unimplemented */ - return(0); + double t,y,z,nadj=0.0,p,p1,p2,p3,q,r,w; + LONG i,hx,lx,ix; + + EXTRACT_WORDS(hx,lx,x); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x*x; + if((ix|lx)==0) return one/zero; + if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */ + if(hx<0) { + return -log(-x); + } else return -log(x); + } + if(hx<0) { + if(ix>=0x43300000) /* |x|>=2**52, must be -integer */ + return one/zero; + t = sin_pi(x); + if(t==zero) return one/zero; /* -integer */ + nadj = log(pi/fabs(t*x)); + x = -x; + } + + /* purge off 1 and 2 */ + if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0; + /* for x < 2.0 */ + else if(ix<0x40000000) { + if(ix<=0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */ + r = -log(x); + if(ix>=0x3FE76944) {y = one-x; i= 0;} + else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-0.5*y + p1/p2); + } + } + else if(ix<0x40200000) { /* x < 8.0 */ + i = (LONG)x; + t = zero; + y = x-(double)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+6.0); /* FALLTHRU */ + case 6: z *= (y+5.0); /* FALLTHRU */ + case 5: z *= (y+4.0); /* FALLTHRU */ + case 4: z *= (y+3.0); /* FALLTHRU */ + case 3: z *= (y+2.0); /* FALLTHRU */ + r += log(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x43900000) { + t = log(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = x*(log(x)-one); + if(hx<0) r = nadj - r; + return r; } /****************************************************************************/ diff --git a/library/math_lgammaf.c b/library/math_lgammaf.c index 4406dfd..f73bd17 100644 --- a/library/math_lgammaf.c +++ b/library/math_lgammaf.c @@ -1,5 +1,5 @@ /* - * $Id: math_lgammaf.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $ + * $Id: math_lgammaf.c,v 1.2 2005-05-30 08:47:26 obarthel Exp $ * * :ts=4 * @@ -29,6 +29,18 @@ * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE * POSSIBILITY OF SUCH DAMAGE. + * + * + * PowerPC math library based in part on work by Sun Microsystems + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * + * + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ #ifndef _MATH_HEADERS_H @@ -41,11 +53,212 @@ /****************************************************************************/ +static const float +two23= 8.3886080000e+06, /* 0x4b000000 */ +half= 5.0000000000e-01, /* 0x3f000000 */ +one = 1.0000000000e+00, /* 0x3f800000 */ +pi = 3.1415927410e+00, /* 0x40490fdb */ +a0 = 7.7215664089e-02, /* 0x3d9e233f */ +a1 = 3.2246702909e-01, /* 0x3ea51a66 */ +a2 = 6.7352302372e-02, /* 0x3d89f001 */ +a3 = 2.0580807701e-02, /* 0x3ca89915 */ +a4 = 7.3855509982e-03, /* 0x3bf2027e */ +a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ +a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ +a7 = 5.1006977446e-04, /* 0x3a05b634 */ +a8 = 2.2086278477e-04, /* 0x39679767 */ +a9 = 1.0801156895e-04, /* 0x38e28445 */ +a10 = 2.5214456400e-05, /* 0x37d383a2 */ +a11 = 4.4864096708e-05, /* 0x383c2c75 */ +tc = 1.4616321325e+00, /* 0x3fbb16c3 */ +tf = -1.2148628384e-01, /* 0xbdf8cdcd */ +/* tt = -(tail of tf) */ +tt = 6.6971006518e-09, /* 0x31e61c52 */ +t0 = 4.8383611441e-01, /* 0x3ef7b95e */ +t1 = -1.4758771658e-01, /* 0xbe17213c */ +t2 = 6.4624942839e-02, /* 0x3d845a15 */ +t3 = -3.2788541168e-02, /* 0xbd064d47 */ +t4 = 1.7970675603e-02, /* 0x3c93373d */ +t5 = -1.0314224288e-02, /* 0xbc28fcfe */ +t6 = 6.1005386524e-03, /* 0x3bc7e707 */ +t7 = -3.6845202558e-03, /* 0xbb7177fe */ +t8 = 2.2596477065e-03, /* 0x3b141699 */ +t9 = -1.4034647029e-03, /* 0xbab7f476 */ +t10 = 8.8108185446e-04, /* 0x3a66f867 */ +t11 = -5.3859531181e-04, /* 0xba0d3085 */ +t12 = 3.1563205994e-04, /* 0x39a57b6b */ +t13 = -3.1275415677e-04, /* 0xb9a3f927 */ +t14 = 3.3552918467e-04, /* 0x39afe9f7 */ +u0 = -7.7215664089e-02, /* 0xbd9e233f */ +u1 = 6.3282704353e-01, /* 0x3f2200f4 */ +u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ +u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ +u4 = 2.2896373272e-01, /* 0x3e6a7578 */ +u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ +v1 = 2.4559779167e+00, /* 0x401d2ebe */ +v2 = 2.1284897327e+00, /* 0x4008392d */ +v3 = 7.6928514242e-01, /* 0x3f44efdf */ +v4 = 1.0422264785e-01, /* 0x3dd572af */ +v5 = 3.2170924824e-03, /* 0x3b52d5db */ +s0 = -7.7215664089e-02, /* 0xbd9e233f */ +s1 = 2.1498242021e-01, /* 0x3e5c245a */ +s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ +s3 = 1.4635047317e-01, /* 0x3e15dce6 */ +s4 = 2.6642270386e-02, /* 0x3cda40e4 */ +s5 = 1.8402845599e-03, /* 0x3af135b4 */ +s6 = 3.1947532989e-05, /* 0x3805ff67 */ +r1 = 1.3920053244e+00, /* 0x3fb22d3b */ +r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ +r3 = 1.7193385959e-01, /* 0x3e300f6e */ +r4 = 1.8645919859e-02, /* 0x3c98bf54 */ +r5 = 7.7794247773e-04, /* 0x3a4beed6 */ +r6 = 7.3266842264e-06, /* 0x36f5d7bd */ +w0 = 4.1893854737e-01, /* 0x3ed67f1d */ +w1 = 8.3333335817e-02, /* 0x3daaaaab */ +w2 = -2.7777778450e-03, /* 0xbb360b61 */ +w3 = 7.9365057172e-04, /* 0x3a500cfd */ +w4 = -5.9518753551e-04, /* 0xba1c065c */ +w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ +w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ + +static const float zero= 0.0000000000e+00; + +static float +sin_pif(float x) +{ + float y,z; + LONG n,ix; + + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = floorf(y); + if(z!=y) { /* inexact anyway */ + y *= (float)0.5; + y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */ + n = (LONG) (y*(float)4.0); + } else { + if(ix>=0x4b800000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x4b000000) z = y+two23; /* exact */ + GET_FLOAT_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __kernel_sinf(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break; + case 3: + case 4: y = __kernel_sinf(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break; + default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break; + } + return -y; +} + + float lgammaf(float x) { - /* ZZZ unimplemented */ - return(0); + float t,y,z,nadj=0.0,p,p1,p2,p3,q,r,w; + LONG i,hx,ix; + + GET_FLOAT_WORD(hx,x); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return x*x; + if(ix==0) return one/zero; + if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */ + if(hx<0) { + return -logf(-x); + } else return -logf(x); + } + if(hx<0) { + if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ + return one/zero; + t = sin_pif(x); + if(t==zero) return one/zero; /* -integer */ + nadj = logf(pi/fabsf(t*x)); + x = -x; + } + + /* purge off 1 and 2 */ + if (ix==0x3f800000||ix==0x40000000) r = 0; + /* for x < 2.0 */ + else if(ix<0x40000000) { + if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ + r = -logf(x); + if(ix>=0x3f3b4a20) {y = one-x; i= 0;} + else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-(float)0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-(float)0.5*y + p1/p2); + } + } + else if(ix<0x41000000) { /* x < 8.0 */ + i = (LONG)x; + t = zero; + y = x-(float)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+(float)6.0); /* FALLTHRU */ + case 6: z *= (y+(float)5.0); /* FALLTHRU */ + case 5: z *= (y+(float)4.0); /* FALLTHRU */ + case 4: z *= (y+(float)3.0); /* FALLTHRU */ + case 3: z *= (y+(float)2.0); /* FALLTHRU */ + r += logf(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x5c800000) { + t = logf(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = x*(logf(x)-one); + if(hx<0) r = nadj - r; + return r; } /****************************************************************************/ diff --git a/library/math_remainder.c b/library/math_remainder.c index 69c790b..f92251b 100644 --- a/library/math_remainder.c +++ b/library/math_remainder.c @@ -1,5 +1,5 @@ /* - * $Id: math_remainder.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $ + * $Id: math_remainder.c,v 1.2 2005-05-30 08:47:26 obarthel Exp $ * * :ts=4 * @@ -29,6 +29,15 @@ * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE * POSSIBILITY OF SUCH DAMAGE. + * + * + * PowerPC math library based in part on work by Sun Microsystems + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. */ #ifndef _MATH_HEADERS_H @@ -41,11 +50,48 @@ /****************************************************************************/ +static const double zero = 0.0; + double -remainder(double x,double y) +remainder(double x, double p) { - /* ZZZ unimplemented */ - return(0); + LONG hx,hp; + ULONG sx,lx,lp; + double p_half; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hp,lp,p); + sx = hx&0x80000000U; + hp &= 0x7fffffff; + hx &= 0x7fffffff; + + /* purge off exception values */ + if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7ff00000)|| /* x not finite */ + ((hp>=0x7ff00000)&& /* p is NaN */ + (((hp-0x7ff00000)|lp)!=0))) + return (x*p)/(x*p); + + + if (hp<=0x7fdfffff) x = fmod(x,p+p); /* now x < 2p */ + if (((hx-hp)|(lx-lp))==0) return zero*x; + x = fabs(x); + p = fabs(p); + if (hp<0x00200000) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = 0.5*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_HIGH_WORD(hx,x); + SET_HIGH_WORD(x,hx^sx); + return x; } /****************************************************************************/ diff --git a/library/math_remainderf.c b/library/math_remainderf.c index b8d8735..e7b9e34 100644 --- a/library/math_remainderf.c +++ b/library/math_remainderf.c @@ -1,5 +1,5 @@ /* - * $Id: math_remainderf.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $ + * $Id: math_remainderf.c,v 1.2 2005-05-30 08:47:26 obarthel Exp $ * * :ts=4 * @@ -29,6 +29,18 @@ * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE * POSSIBILITY OF SUCH DAMAGE. + * + * + * PowerPC math library based in part on work by Sun Microsystems + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * + * + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ #ifndef _MATH_HEADERS_H @@ -41,11 +53,47 @@ /****************************************************************************/ +static const float zero = 0.0; + float -remainderf(float x,float y) +remainderf(float x, float p) { - /* ZZZ unimplemented */ - return(0); + LONG hx,hp; + ULONG sx; + float p_half; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hp,p); + sx = hx&0x80000000U; + hp &= 0x7fffffff; + hx &= 0x7fffffff; + + /* purge off exception values */ + if(hp==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7f800000)|| /* x not finite */ + ((hp>0x7f800000))) /* p is NaN */ + return (x*p)/(x*p); + + + if (hp<=0x7effffff) x = fmodf(x,p+p); /* now x < 2p */ + if ((hx-hp)==0) return zero*x; + x = fabsf(x); + p = fabsf(p); + if (hp<0x01000000) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = (float)0.5*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_FLOAT_WORD(hx,x); + SET_FLOAT_WORD(x,hx^sx); + return x; } /****************************************************************************/