Add some more functions to the math library

uspace/lib/math/generic/internal.h

@@ -30,6 +30,120 @@
 #ifndef MATH_INTERNAL_H_
 #define MATH_INTERNAL_H_
 
+#include <stdint.h>
+
+#if __BE__
+
+typedef union
+{
+	double value;
+	struct
+	{
+		uint32_t msw;
+		uint32_t lsw;
+	} parts;
+	uint64_t word;
+} ieee_double_shape_type;
+
+#endif
+
+#if __LE__
+
+typedef union
+{
+	double value;
+	struct
+	{
+		uint32_t lsw;
+		uint32_t msw;
+	} parts;
+	uint64_t word;
+} ieee_double_shape_type;
+
+#endif
+
+#define EXTRACT_WORDS(ix0,ix1,d)                                \
+do {                                                                \
+  ieee_double_shape_type ew_u;                                        \
+  ew_u.value = (d);                                                \
+  (ix0) = ew_u.parts.msw;                                        \
+  (ix1) = ew_u.parts.lsw;                                        \
+} while (0)
+
+/* Get the more significant 32 bit int from a double.  */
+#ifndef GET_HIGH_WORD
+# define GET_HIGH_WORD(i,d)                                        \
+do {                                                                \
+  ieee_double_shape_type gh_u;                                        \
+  gh_u.value = (d);                                                \
+  (i) = gh_u.parts.msw;                                                \
+} while (0)
+#endif
+
+/* Get the less significant 32 bit int from a double.  */
+#ifndef GET_LOW_WORD
+# define GET_LOW_WORD(i,d)                                        \
+do {                                                                \
+  ieee_double_shape_type gl_u;                                        \
+  gl_u.value = (d);                                                \
+  (i) = gl_u.parts.lsw;                                                \
+} while (0)
+#endif
+
+/* Get all in one, efficient on 64-bit machines.  */
+#ifndef EXTRACT_WORDS64
+# define EXTRACT_WORDS64(i,d)                                        \
+do {                                                                \
+  ieee_double_shape_type gh_u;                                        \
+  gh_u.value = (d);                                                \
+  (i) = gh_u.word;                                                \
+} while (0)
+#endif
+
+/* Set a double from two 32 bit ints.  */
+#ifndef INSERT_WORDS
+# define INSERT_WORDS(d,ix0,ix1)                                \
+do {                                                                \
+  ieee_double_shape_type iw_u;                                        \
+  iw_u.parts.msw = (ix0);                                        \
+  iw_u.parts.lsw = (ix1);                                        \
+  (d) = iw_u.value;                                                \
+} while (0)
+#endif
+
+/* Get all in one, efficient on 64-bit machines.  */
+#ifndef INSERT_WORDS64
+# define INSERT_WORDS64(d,i)                                        \
+do {                                                                \
+  ieee_double_shape_type iw_u;                                        \
+  iw_u.word = (i);                                                \
+  (d) = iw_u.value;                                                \
+} while (0)
+#endif
+
+/* Set the more significant 32 bits of a double from an int.  */
+#ifndef SET_HIGH_WORD
+#define SET_HIGH_WORD(d,v)                                        \
+do {                                                                \
+  ieee_double_shape_type sh_u;                                        \
+  sh_u.value = (d);                                                \
+  sh_u.parts.msw = (v);                                                \
+  (d) = sh_u.value;                                                \
+} while (0)
+#endif
+
+/* Set the less significant 32 bits of a double from an int.  */
+#ifndef SET_LOW_WORD
+# define SET_LOW_WORD(d,v)                                        \
+do {                                                                \
+  ieee_double_shape_type sl_u;                                        \
+  sl_u.value = (d);                                                \
+  sl_u.parts.lsw = (v);                                                \
+  (d) = sl_u.value;                                                \
+} while (0)
+#endif
+
+
 float __math_base_sin_32(float);
 float __math_base_cos_32(float);
 double __math_base_sin_64(double);

uspace/lib/math/generic/log.c

@@ -0,0 +1,147 @@
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/** @addtogroup libmath
+ * @{
+ */
+/** @file log mathematical function
+ */
+
+/* log(x)
+ * Return the logarithm of x
+ *
+ * Method :
+ *   1. Argument Reduction: find k and f such that
+ *                      x = 2^k * (1+f),
+ *         where  sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ *   2. Approximation of log(1+f).
+ *      Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
+ *               = 2s + 2/3 s**3 + 2/5 s**5 + .....,
+ *               = 2s + s*R
+ *      We use a special Remez algorithm on [0,0.1716] to generate
+ *      a polynomial of degree 14 to approximate R The maximum error
+ *      of this polynomial approximation is bounded by 2**-58.45. In
+ *      other words,
+ *                      2      4      6      8      10      12      14
+ *          R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s
+ *      (the values of Lg1 to Lg7 are listed in the program)
+ *      and
+ *          |      2          14          |     -58.45
+ *          | Lg1*s +...+Lg7*s    -  R(z) | <= 2
+ *          |                             |
+ *      Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
+ *      In order to guarantee error in log below 1ulp, we compute log
+ *      by
+ *              log(1+f) = f - s*(f - R)        (if f is not too large)
+ *              log(1+f) = f - (hfsq - s*(hfsq+R)).     (better accuracy)
+ *
+ *      3. Finally,  log(x) = k*ln2 + log(1+f).
+ *                          = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
+ *         Here ln2 is split into two floating point number:
+ *                      ln2_hi + ln2_lo,
+ *         where n*ln2_hi is always exact for |n| < 2000.
+ *
+ * Special cases:
+ *      log(x) is NaN with signal if x < 0 (including -INF) ;
+ *      log(+INF) is +INF; log(0) is -INF with signal;
+ *      log(NaN) is that NaN with no signal.
+ *
+ * Accuracy:
+ *      according to an error analysis, the error is always less than
+ *      1 ulp (unit in the last place).
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include <math.h>
+#include <stdint.h>
+
+#include "internal.h"
+
+static const double
+ln2_hi  =  6.93147180369123816490e-01,	/* 3fe62e42 fee00000 */
+ln2_lo  =  1.90821492927058770002e-10,	/* 3dea39ef 35793c76 */
+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;
+static volatile double vzero = 0.0;
+
+
+double log(double x)
+{
+	double hfsq,f,s,z,R,w,t1,t2,dk;
+	int32_t k,hx,i,j;
+	uint32_t lx;
+
+	EXTRACT_WORDS(hx,lx,x);
+
+	k=0;
+	if (hx < 0x00100000) {			/* x < 2**-1022  */
+	    if (((hx&0x7fffffff)|lx)==0) 
+		return -two54/vzero;		/* 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;
+	if((0x000fffff&(2+hx))<3) {	/* -2**-20 <= f < 2**-20 */
+	    if(f==zero) {
+		if(k==0) {
+		    return zero;
+		} else {
+		    dk=(double)k;
+		    return dk*ln2_hi+dk*ln2_lo;
+		}
+	    }
+	    R = f*f*(0.5-0.33333333333333333*f);
+	    if(k==0) return f-R; else {dk=(double)k;
+	    	     return dk*ln2_hi-((R-dk*ln2_lo)-f);}
+	}
+ 	s = f/(2.0+f); 
+	dk = (double)k;
+	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;
+	    if(k==0) return f-(hfsq-s*(hfsq+R)); else
+		     return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
+	} else {
+	    if(k==0) return f-s*(f-R); else
+		     return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
+	}
+}
+
+/** @}
+ */