- replace dtoa w/ David's gdtoa, version 2008-03-15

- provide proper dtoa locks
- use the real strtof implementation
- add strtold, __hdtoa, __hldtoa
- add %a/%A support
- don't lose precision in printf, don't round to double anymore
- implement extended-precision versions of libc functions: fpclassify,
isnan, isinf, signbit, isnormal, isfinite, now that the ieee.h is
fixed
- separate vax versions of strtof, and __hdtoa
- add complex math support.  added functions: cacos, casin, catan,
ccos, csin, ctan, cacosh, casinh, catanh, ccosh, csinh, ctanh, cexp,
clog, cabs, cpow, csqrt, carg, cimag, conj, cproj, creal, cacosf,
casinf, catanf, ccosf, csinf, ctanf, cacoshf, casinhf, catanhf,
ccoshf, csinhf, ctanhf, cexpf, clogf, cabsf, cpowf, csqrtf, cargf,
cimagf, conjf, cprojf, crealf
- add fdim, fmax, fmin
- add log2. (adapted implementation e_log.c.  could be more acruate
& faster, but it's good enough for now)
- remove wrappers & cruft in libm, supposed to work-around mistakes
in SVID, etc.;  use ieee versions.  fixes issues in python 2.6 for
djm@
- make _digittoint static
- proper definitions for i386, and amd64 in ieee.h
- sh, powerpc don't really have extended-precision
- add missing definitions for mips64 (quad), m{6,8}k (96-bit) float.h
for LDBL_*
- merge lead to frac for m{6,8}k, for gdtoa to work properly
- add FRAC*BITS & EXT_TO_ARRAY32 definitions in ieee.h, for hdtoa&ldtoa
to use
- add EXT_IMPLICIT_NBIT definition, which indicates implicit
normalization bit
- add regression tests for libc: fpclassify and printf
- arith.h & gd_qnan.h definitions
- update ieee.h: hppa doesn't have quad-precision, hppa64 does
- add missing prototypes to gdtoaimp
- on 64-bit platforms make sure gdtoa doesn't use a long when it
really wants an int
- etc., what i may have forgotten...
- bump libm major, due to removed&changed symbols
- no libc bump, since this is riding on djm's libc major crank from
a day ago

discussed with / requested by / testing theo, sthen@, djm@, jsg@,
merdely@, jsing@, tedu@, brad@, jakemsr@, and others.
looks good to millert@
parts of the diff ok kettenis@

this commit does not include:
- man page changes

1 files changed, 74 insertions, 0 deletions

diff --git a/lib/libm/src/e_log2.c b/lib/libm/src/e_log2.c
new file mode 100644
index 00000000000..aed716670dc
--- /dev/null
+++ b/lib/libm/src/e_log2.c
@@ -0,0 +1,74 @@
+/* @(#)e_log.c 1.3 95/01/18 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+ln2 = 0.6931471805599452862268,
+two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
+Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
+Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
+Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
+Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
+Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
+Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
+Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
+
+static const double zero   =  0.0;
+
+double
+log2(double x)
+{
+	double hfsq,f,s,z,R,w,t1,t2,dk;
+	int32_t k,hx,i,j;
+	u_int32_t lx;
+
+	EXTRACT_WORDS(hx,lx,x);
+
+	k=0;
+	if (hx < 0x00100000) {			/* x < 2**-1022  */
+	    if (((hx&0x7fffffff)|lx)==0) 
+		return -two54/zero;		/* log(+-0)=-inf */
+	    if (hx<0) return (x-x)/zero;	/* log(-#) = NaN */
+	    k -= 54; x *= two54; /* subnormal number, scale up x */
+	    GET_HIGH_WORD(hx,x);
+	} 
+	if (hx >= 0x7ff00000) return x+x;
+	k += (hx>>20)-1023;
+	hx &= 0x000fffff;
+	i = (hx+0x95f64)&0x100000;
+	SET_HIGH_WORD(x,hx|(i^0x3ff00000));	/* normalize x or x/2 */
+	k += (i>>20);
+	f = x-1.0;
+	dk = (double)k;
+	if((0x000fffff&(2+hx))<3) {	/* |f| < 2**-20 */
+	    if (f==zero) 
+		    return (dk);
+	    R = f*f*(0.5-0.33333333333333333*f);
+	    return (dk-(R-f)/ln2);
+	}
+ 	s = f/(2.0+f); 
+	z = s*s;
+	i = hx-0x6147a;
+	w = z*z;
+	j = 0x6b851-hx;
+	t1= w*(Lg2+w*(Lg4+w*Lg6)); 
+	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 
+	i |= j;
+	R = t2+t1;
+	if(i>0) {
+	    hfsq=0.5*f*f;
+	    return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
+	} else
+		return (dk-((s*(f-R))-f)/ln2);
+}