math: add freebsd trascendentals as they are a bit faster than gcc

Change-Id: Icf82721e3bf2da21be3fb859a054dd4f47bbdcea

4 files changed, 1054 insertions, 0 deletions

diff --git a/firmware/external/freebsd/lib/msun/src/e_atan2f.c b/firmware/external/freebsd/lib/msun/src/e_atan2f.c
new file mode 100644
index 00000000..fc77bffa
--- /dev/null
+++ b/firmware/external/freebsd/lib/msun/src/e_atan2f.c
@@ -0,0 +1,96 @@
+/* e_atan2f.c -- float version of e_atan2.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include "math.h"
+#include "math_private.h"
+
+static volatile float
+tiny  = 1.0e-30;
+static const float
+zero  = 0.0,
+pi_o_4  = 7.8539818525e-01, /* 0x3f490fdb */
+pi_o_2  = 1.5707963705e+00, /* 0x3fc90fdb */
+pi      = 3.1415927410e+00; /* 0x40490fdb */
+static volatile float
+pi_lo   = -8.7422776573e-08; /* 0xb3bbbd2e */
+
+float
+__ieee754_atan2f(float y, float x)
+{
+	float z;
+	int32_t k,m,hx,hy,ix,iy;
+
+	GET_FLOAT_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	GET_FLOAT_WORD(hy,y);
+	iy = hy&0x7fffffff;
+	if((ix>0x7f800000)||
+	   (iy>0x7f800000))	/* x or y is NaN */
+	   return x+y;
+	if(hx==0x3f800000) return atanf(y);   /* x=1.0 */
+	m = ((hy>>31)&1)|((hx>>30)&2);	/* 2*sign(x)+sign(y) */
+
+    /* when y = 0 */
+	if(iy==0) {
+	    switch(m) {
+		case 0:
+		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
+		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
+		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
+	    }
+	}
+    /* when x = 0 */
+	if(ix==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
+
+    /* when x is INF */
+	if(ix==0x7f800000) {
+	    if(iy==0x7f800000) {
+		switch(m) {
+		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
+		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
+		    case 2: return  (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
+		    case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
+		}
+	    } else {
+		switch(m) {
+		    case 0: return  zero  ;	/* atan(+...,+INF) */
+		    case 1: return -zero  ;	/* atan(-...,+INF) */
+		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
+		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
+		}
+	    }
+	}
+    /* when y is INF */
+	if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
+
+    /* compute y/x */
+	k = (iy-ix)>>23;
+	if(k > 26) {			/* |y/x| >  2**26 */
+	    z=pi_o_2+(float)0.5*pi_lo;
+	    m&=1;
+	}
+	else if(k<-26&&hx<0) z=0.0; 	/* 0 > |y|/x > -2**-26 */
+	else z=atanf(fabsf(y/x));	/* safe to do y/x */
+	switch (m) {
+	    case 0: return       z  ;	/* atan(+,+) */
+	    case 1: return      -z  ;	/* atan(-,+) */
+	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
+	    default: /* case 3 */
+	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
+	}
+}
diff --git a/firmware/external/freebsd/lib/msun/src/e_expf.c b/firmware/external/freebsd/lib/msun/src/e_expf.c
new file mode 100644
index 00000000..b1fe2c53
--- /dev/null
+++ b/firmware/external/freebsd/lib/msun/src/e_expf.c
@@ -0,0 +1,98 @@
+/* e_expf.c -- float version of e_exp.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <float.h>
+
+#include "math.h"
+#include "math_private.h"
+
+static const float
+one	= 1.0,
+halF[2]	= {0.5,-0.5,},
+o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
+u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
+ln2HI[2]   ={ 6.9314575195e-01,		/* 0x3f317200 */
+	     -6.9314575195e-01,},	/* 0xbf317200 */
+ln2LO[2]   ={ 1.4286067653e-06,  	/* 0x35bfbe8e */
+	     -1.4286067653e-06,},	/* 0xb5bfbe8e */
+invln2 =  1.4426950216e+00, 		/* 0x3fb8aa3b */
+/*
+ * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
+ * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
+ */
+P1 =  1.6666625440e-1,		/*  0xaaaa8f.0p-26 */
+P2 = -2.7667332906e-3;		/* -0xb55215.0p-32 */
+
+static volatile float
+huge	= 1.0e+30,
+twom100 = 7.8886090522e-31;      /* 2**-100=0x0d800000 */
+
+float
+__ieee754_expf(float x)
+{
+	float y,hi=0.0,lo=0.0,c,t,twopk;
+	int32_t k=0,xsb;
+	u_int32_t hx;
+
+	GET_FLOAT_WORD(hx,x);
+	xsb = (hx>>31)&1;		/* sign bit of x */
+	hx &= 0x7fffffff;		/* high word of |x| */
+
+    /* filter out non-finite argument */
+	if(hx >= 0x42b17218) {			/* if |x|>=88.721... */
+	    if(hx>0x7f800000)
+		 return x+x;	 		/* NaN */
+            if(hx==0x7f800000)
+		return (xsb==0)? x:0.0;		/* exp(+-inf)={inf,0} */
+	    if(x > o_threshold) return huge*huge; /* overflow */
+	    if(x < u_threshold) return twom100*twom100; /* underflow */
+	}
+
+    /* argument reduction */
+	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */
+	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
+		hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
+	    } else {
+		k  = invln2*x+halF[xsb];
+		t  = k;
+		hi = x - t*ln2HI[0];	/* t*ln2HI is exact here */
+		lo = t*ln2LO[0];
+	    }
+	    STRICT_ASSIGN(float, x, hi - lo);
+	}
+	else if(hx < 0x39000000)  {	/* when |x|<2**-14 */
+	    if(huge+x>one) return one+x;/* trigger inexact */
+	}
+	else k = 0;
+
+    /* x is now in primary range */
+	t  = x*x;
+	if(k >= -125)
+	    SET_FLOAT_WORD(twopk,0x3f800000+(k<<23));
+	else
+	    SET_FLOAT_WORD(twopk,0x3f800000+((k+100)<<23));
+	c  = x - t*(P1+t*P2);
+	if(k==0) 	return one-((x*c)/(c-(float)2.0)-x);
+	else 		y = one-((lo-(x*c)/((float)2.0-c))-hi);
+	if(k >= -125) {
+	    if(k==128) return y*2.0F*0x1p127F;
+	    return y*twopk;
+	} else {
+	    return y*twopk*twom100;
+	}
+}
diff --git a/firmware/external/freebsd/lib/msun/src/math_private.h b/firmware/external/freebsd/lib/msun/src/math_private.h
new file mode 100644
index 00000000..5bcd62e6
--- /dev/null
+++ b/firmware/external/freebsd/lib/msun/src/math_private.h
@@ -0,0 +1,768 @@
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/*
+ * from: @(#)fdlibm.h 5.1 93/09/24
+ * $FreeBSD$
+ */
+
+#ifndef _MATH_PRIVATE_H_
+#define	_MATH_PRIVATE_H_
+
+#include <sys/types.h>
+#include <machine/endian.h>
+
+#include <stdint.h>
+typedef uint32_t u_int32_t;
+typedef uint64_t u_int64_t;
+
+/*
+ * The original fdlibm code used statements like:
+ *	n0 = ((*(int*)&one)>>29)^1;		* index of high word *
+ *	ix0 = *(n0+(int*)&x);			* high word of x *
+ *	ix1 = *((1-n0)+(int*)&x);		* low word of x *
+ * to dig two 32 bit words out of the 64 bit IEEE floating point
+ * value.  That is non-ANSI, and, moreover, the gcc instruction
+ * scheduler gets it wrong.  We instead use the following macros.
+ * Unlike the original code, we determine the endianness at compile
+ * time, not at run time; I don't see much benefit to selecting
+ * endianness at run time.
+ */
+
+/*
+ * A union which permits us to convert between a double and two 32 bit
+ * ints.
+ */
+
+#ifdef __arm__
+#if defined(__VFP_FP__) || defined(__ARM_EABI__)
+#define	IEEE_WORD_ORDER	BYTE_ORDER
+#else
+#define	IEEE_WORD_ORDER	BIG_ENDIAN
+#endif
+#else /* __arm__ */
+#define	IEEE_WORD_ORDER	BYTE_ORDER
+#endif
+
+#if IEEE_WORD_ORDER == BIG_ENDIAN
+
+typedef union
+{
+  double value;
+  struct
+  {
+    u_int32_t msw;
+    u_int32_t lsw;
+  } parts;
+  struct
+  {
+    u_int64_t w;
+  } xparts;
+} ieee_double_shape_type;
+
+#endif
+
+#if IEEE_WORD_ORDER == LITTLE_ENDIAN
+
+typedef union
+{
+  double value;
+  struct
+  {
+    u_int32_t lsw;
+    u_int32_t msw;
+  } parts;
+  struct
+  {
+    u_int64_t w;
+  } xparts;
+} ieee_double_shape_type;
+
+#endif
+
+/* Get two 32 bit ints from a double.  */
+
+#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 a 64-bit int from a double. */
+#define EXTRACT_WORD64(ix,d)					\
+do {								\
+  ieee_double_shape_type ew_u;					\
+  ew_u.value = (d);						\
+  (ix) = ew_u.xparts.w;						\
+} while (0)
+
+/* Get the more significant 32 bit int from a double.  */
+
+#define GET_HIGH_WORD(i,d)					\
+do {								\
+  ieee_double_shape_type gh_u;					\
+  gh_u.value = (d);						\
+  (i) = gh_u.parts.msw;						\
+} while (0)
+
+/* Get the less significant 32 bit int from a double.  */
+
+#define GET_LOW_WORD(i,d)					\
+do {								\
+  ieee_double_shape_type gl_u;					\
+  gl_u.value = (d);						\
+  (i) = gl_u.parts.lsw;						\
+} while (0)
+
+/* Set a double from two 32 bit ints.  */
+
+#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)
+
+/* Set a double from a 64-bit int. */
+#define INSERT_WORD64(d,ix)					\
+do {								\
+  ieee_double_shape_type iw_u;					\
+  iw_u.xparts.w = (ix);						\
+  (d) = iw_u.value;						\
+} while (0)
+
+/* Set the more significant 32 bits of a double from an int.  */
+
+#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)
+
+/* Set the less significant 32 bits of a double from an int.  */
+
+#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)
+
+/*
+ * A union which permits us to convert between a float and a 32 bit
+ * int.
+ */
+
+typedef union
+{
+  float value;
+  /* FIXME: Assumes 32 bit int.  */
+  unsigned int word;
+} ieee_float_shape_type;
+
+/* Get a 32 bit int from a float.  */
+
+#define GET_FLOAT_WORD(i,d)					\
+do {								\
+  ieee_float_shape_type gf_u;					\
+  gf_u.value = (d);						\
+  (i) = gf_u.word;						\
+} while (0)
+
+/* Set a float from a 32 bit int.  */
+
+#define SET_FLOAT_WORD(d,i)					\
+do {								\
+  ieee_float_shape_type sf_u;					\
+  sf_u.word = (i);						\
+  (d) = sf_u.value;						\
+} while (0)
+
+/*
+ * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long
+ * double.
+ */
+
+#define	EXTRACT_LDBL80_WORDS(ix0,ix1,d)				\
+do {								\
+  union IEEEl2bits ew_u;					\
+  ew_u.e = (d);							\
+  (ix0) = ew_u.xbits.expsign;					\
+  (ix1) = ew_u.xbits.man;					\
+} while (0)
+
+/*
+ * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit
+ * long double.
+ */
+
+#define	EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d)			\
+do {								\
+  union IEEEl2bits ew_u;					\
+  ew_u.e = (d);							\
+  (ix0) = ew_u.xbits.expsign;					\
+  (ix1) = ew_u.xbits.manh;					\
+  (ix2) = ew_u.xbits.manl;					\
+} while (0)
+
+/* Get expsign as a 16 bit int from a long double.  */
+
+#define	GET_LDBL_EXPSIGN(i,d)					\
+do {								\
+  union IEEEl2bits ge_u;					\
+  ge_u.e = (d);							\
+  (i) = ge_u.xbits.expsign;					\
+} while (0)
+
+/*
+ * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int
+ * mantissa.
+ */
+
+#define	INSERT_LDBL80_WORDS(d,ix0,ix1)				\
+do {								\
+  union IEEEl2bits iw_u;					\
+  iw_u.xbits.expsign = (ix0);					\
+  iw_u.xbits.man = (ix1);					\
+  (d) = iw_u.e;							\
+} while (0)
+
+/*
+ * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints
+ * comprising the mantissa.
+ */
+
+#define	INSERT_LDBL128_WORDS(d,ix0,ix1,ix2)			\
+do {								\
+  union IEEEl2bits iw_u;					\
+  iw_u.xbits.expsign = (ix0);					\
+  iw_u.xbits.manh = (ix1);					\
+  iw_u.xbits.manl = (ix2);					\
+  (d) = iw_u.e;							\
+} while (0)
+
+/* Set expsign of a long double from a 16 bit int.  */
+
+#define	SET_LDBL_EXPSIGN(d,v)					\
+do {								\
+  union IEEEl2bits se_u;					\
+  se_u.e = (d);							\
+  se_u.xbits.expsign = (v);					\
+  (d) = se_u.e;							\
+} while (0)
+
+#ifdef __i386__
+/* Long double constants are broken on i386. */
+#define	LD80C(m, ex, v) {						\
+	.xbits.man = __CONCAT(m, ULL),					\
+	.xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0),	\
+}
+#else
+/* The above works on non-i386 too, but we use this to check v. */
+#define	LD80C(m, ex, v)	{ .e = (v), }
+#endif
+
+#ifdef FLT_EVAL_METHOD
+/*
+ * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
+ */
+#if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
+#define	STRICT_ASSIGN(type, lval, rval)	((lval) = (rval))
+#else
+#define	STRICT_ASSIGN(type, lval, rval) do {	\
+	volatile type __lval;			\
+						\
+	if (sizeof(type) >= sizeof(long double))	\
+		(lval) = (rval);		\
+	else {					\
+		__lval = (rval);		\
+		(lval) = __lval;		\
+	}					\
+} while (0)
+#endif
+#endif /* FLT_EVAL_METHOD */
+
+/* Support switching the mode to FP_PE if necessary. */
+#if defined(__i386__) && !defined(NO_FPSETPREC)
+#define	ENTERI()				\
+	long double __retval;			\
+	fp_prec_t __oprec;			\
+						\
+	if ((__oprec = fpgetprec()) != FP_PE)	\
+		fpsetprec(FP_PE)
+#define	RETURNI(x) do {				\
+	__retval = (x);				\
+	if (__oprec != FP_PE)			\
+		fpsetprec(__oprec);		\
+	RETURNF(__retval);			\
+} while (0)
+#else
+#define	ENTERI(x)
+#define	RETURNI(x)	RETURNF(x)
+#endif
+
+/* Default return statement if hack*_t() is not used. */
+#define      RETURNF(v)      return (v)
+
+/*
+ * 2sum gives the same result as 2sumF without requiring |a| >= |b| or
+ * a == 0, but is slower.
+ */
+#define	_2sum(a, b) do {	\
+	__typeof(a) __s, __w;	\
+				\
+	__w = (a) + (b);	\
+	__s = __w - (a);	\
+	(b) = ((a) - (__w - __s)) + ((b) - __s); \
+	(a) = __w;		\
+} while (0)
+
+/*
+ * 2sumF algorithm.
+ *
+ * "Normalize" the terms in the infinite-precision expression a + b for
+ * the sum of 2 floating point values so that b is as small as possible
+ * relative to 'a'.  (The resulting 'a' is the value of the expression in
+ * the same precision as 'a' and the resulting b is the rounding error.)
+ * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and
+ * exponent overflow or underflow must not occur.  This uses a Theorem of
+ * Dekker (1971).  See Knuth (1981) 4.2.2 Theorem C.  The name "TwoSum"
+ * is apparently due to Skewchuk (1997).
+ *
+ * For this to always work, assignment of a + b to 'a' must not retain any
+ * extra precision in a + b.  This is required by C standards but broken
+ * in many compilers.  The brokenness cannot be worked around using
+ * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this
+ * algorithm would be destroyed by non-null strict assignments.  (The
+ * compilers are correct to be broken -- the efficiency of all floating
+ * point code calculations would be destroyed similarly if they forced the
+ * conversions.)
+ *
+ * Fortunately, a case that works well can usually be arranged by building
+ * any extra precision into the type of 'a' -- 'a' should have type float_t,
+ * double_t or long double.  b's type should be no larger than 'a's type.
+ * Callers should use these types with scopes as large as possible, to
+ * reduce their own extra-precision and efficiciency problems.  In
+ * particular, they shouldn't convert back and forth just to call here.
+ */
+#ifdef DEBUG
+#define	_2sumF(a, b) do {				\
+	__typeof(a) __w;				\
+	volatile __typeof(a) __ia, __ib, __r, __vw;	\
+							\
+	__ia = (a);					\
+	__ib = (b);					\
+	assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib));	\
+							\
+	__w = (a) + (b);				\
+	(b) = ((a) - __w) + (b);			\
+	(a) = __w;					\
+							\
+	/* The next 2 assertions are weak if (a) is already long double. */ \
+	assert((long double)__ia + __ib == (long double)(a) + (b));	\
+	__vw = __ia + __ib;				\
+	__r = __ia - __vw;				\
+	__r += __ib;					\
+	assert(__vw == (a) && __r == (b));		\
+} while (0)
+#else /* !DEBUG */
+#define	_2sumF(a, b) do {	\
+	__typeof(a) __w;	\
+				\
+	__w = (a) + (b);	\
+	(b) = ((a) - __w) + (b); \
+	(a) = __w;		\
+} while (0)
+#endif /* DEBUG */
+
+/*
+ * Set x += c, where x is represented in extra precision as a + b.
+ * x must be sufficiently normalized and sufficiently larger than c,
+ * and the result is then sufficiently normalized.
+ *
+ * The details of ordering are that |a| must be >= |c| (so that (a, c)
+ * can be normalized without extra work to swap 'a' with c).  The details of
+ * the normalization are that b must be small relative to the normalized 'a'.
+ * Normalization of (a, c) makes the normalized c tiny relative to the
+ * normalized a, so b remains small relative to 'a' in the result.  However,
+ * b need not ever be tiny relative to 'a'.  For example, b might be about
+ * 2**20 times smaller than 'a' to give about 20 extra bits of precision.
+ * That is usually enough, and adding c (which by normalization is about
+ * 2**53 times smaller than a) cannot change b significantly.  However,
+ * cancellation of 'a' with c in normalization of (a, c) may reduce 'a'
+ * significantly relative to b.  The caller must ensure that significant
+ * cancellation doesn't occur, either by having c of the same sign as 'a',
+ * or by having |c| a few percent smaller than |a|.  Pre-normalization of
+ * (a, b) may help.
+ *
+ * This is is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2
+ * exercise 19).  We gain considerable efficiency by requiring the terms to
+ * be sufficiently normalized and sufficiently increasing.
+ */
+#define	_3sumF(a, b, c) do {	\
+	__typeof(a) __tmp;	\
+				\
+	__tmp = (c);		\
+	_2sumF(__tmp, (a));	\
+	(b) += (a);		\
+	(a) = __tmp;		\
+} while (0)
+
+/*
+ * Common routine to process the arguments to nan(), nanf(), and nanl().
+ */
+void _scan_nan(uint32_t *__words, int __num_words, const char *__s);
+
+#ifdef _COMPLEX_H
+
+/*
+ * C99 specifies that complex numbers have the same representation as
+ * an array of two elements, where the first element is the real part
+ * and the second element is the imaginary part.
+ */
+typedef union {
+	float complex f;
+	float a[2];
+} float_complex;
+typedef union {
+	double complex f;
+	double a[2];
+} double_complex;
+typedef union {
+	long double complex f;
+	long double a[2];
+} long_double_complex;
+#define	REALPART(z)	((z).a[0])
+#define	IMAGPART(z)	((z).a[1])
+
+/*
+ * Inline functions that can be used to construct complex values.
+ *
+ * The C99 standard intends x+I*y to be used for this, but x+I*y is
+ * currently unusable in general since gcc introduces many overflow,
+ * underflow, sign and efficiency bugs by rewriting I*y as
+ * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
+ * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
+ * to -0.0+I*0.0.
+ */
+static __inline float complex
+cpackf(float x, float y)
+{
+	float_complex z;
+
+	REALPART(z) = x;
+	IMAGPART(z) = y;
+	return (z.f);
+}
+
+static __inline double complex
+cpack(double x, double y)
+{
+	double_complex z;
+
+	REALPART(z) = x;
+	IMAGPART(z) = y;
+	return (z.f);
+}
+
+static __inline long double complex
+cpackl(long double x, long double y)
+{
+	long_double_complex z;
+
+	REALPART(z) = x;
+	IMAGPART(z) = y;
+	return (z.f);
+}
+#endif /* _COMPLEX_H */
+ 
+#ifdef __GNUCLIKE_ASM
+
+/* Asm versions of some functions. */
+
+#ifdef __amd64__
+static __inline int
+irint(double x)
+{
+	int n;
+
+	asm("cvtsd2si %1,%0" : "=r" (n) : "x" (x));
+	return (n);
+}
+#define	HAVE_EFFICIENT_IRINT
+#endif
+
+#ifdef __i386__
+static __inline int
+irint(double x)
+{
+	int n;
+
+	asm("fistl %0" : "=m" (n) : "t" (x));
+	return (n);
+}
+#define	HAVE_EFFICIENT_IRINT
+#endif
+
+#if defined(__amd64__) || defined(__i386__)
+static __inline int
+irintl(long double x)
+{
+	int n;
+
+	asm("fistl %0" : "=m" (n) : "t" (x));
+	return (n);
+}
+#define	HAVE_EFFICIENT_IRINTL
+#endif
+
+#endif /* __GNUCLIKE_ASM */
+
+#ifdef DEBUG
+#if defined(__amd64__) || defined(__i386__)
+#define	breakpoint()	asm("int $3")
+#else
+#include <signal.h>
+
+#define	breakpoint()	raise(SIGTRAP)
+#endif
+#endif
+
+/* Write a pari script to test things externally. */
+#ifdef DOPRINT
+#include <stdio.h>
+
+#ifndef DOPRINT_SWIZZLE
+#define	DOPRINT_SWIZZLE		0
+#endif
+
+#ifdef DOPRINT_LD80
+
+#define	DOPRINT_START(xp) do {						\
+	uint64_t __lx;							\
+	uint16_t __hx;							\
+									\
+	/* Hack to give more-problematic args. */			\
+	EXTRACT_LDBL80_WORDS(__hx, __lx, *xp);				\
+	__lx ^= DOPRINT_SWIZZLE;					\
+	INSERT_LDBL80_WORDS(*xp, __hx, __lx);				\
+	printf("x = %.21Lg; ", (long double)*xp);			\
+} while (0)
+#define	DOPRINT_END1(v)							\
+	printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
+#define	DOPRINT_END2(hi, lo)						\
+	printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",		\
+	    (long double)(hi), (long double)(lo))
+
+#elif defined(DOPRINT_D64)
+
+#define	DOPRINT_START(xp) do {						\
+	uint32_t __hx, __lx;						\
+									\
+	EXTRACT_WORDS(__hx, __lx, *xp);					\
+	__lx ^= DOPRINT_SWIZZLE;					\
+	INSERT_WORDS(*xp, __hx, __lx);					\
+	printf("x = %.21Lg; ", (long double)*xp);			\
+} while (0)
+#define	DOPRINT_END1(v)							\
+	printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
+#define	DOPRINT_END2(hi, lo)						\
+	printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",		\
+	    (long double)(hi), (long double)(lo))
+
+#elif defined(DOPRINT_F32)
+
+#define	DOPRINT_START(xp) do {						\
+	uint32_t __hx;							\
+									\
+	GET_FLOAT_WORD(__hx, *xp);					\
+	__hx ^= DOPRINT_SWIZZLE;					\
+	SET_FLOAT_WORD(*xp, __hx);					\
+	printf("x = %.21Lg; ", (long double)*xp);			\
+} while (0)
+#define	DOPRINT_END1(v)							\
+	printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
+#define	DOPRINT_END2(hi, lo)						\
+	printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",		\
+	    (long double)(hi), (long double)(lo))
+
+#else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */
+
+#ifndef DOPRINT_SWIZZLE_HIGH
+#define	DOPRINT_SWIZZLE_HIGH	0
+#endif
+
+#define	DOPRINT_START(xp) do {						\
+	uint64_t __lx, __llx;						\
+	uint16_t __hx;							\
+									\
+	EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp);			\
+	__llx ^= DOPRINT_SWIZZLE;					\
+	__lx ^= DOPRINT_SWIZZLE_HIGH;					\
+	INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx);			\
+	printf("x = %.36Lg; ", (long double)*xp);					\
+} while (0)
+#define	DOPRINT_END1(v)							\
+	printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v))
+#define	DOPRINT_END2(hi, lo)						\
+	printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n",		\
+	    (long double)(hi), (long double)(lo))
+
+#endif /* DOPRINT_LD80 */
+
+#else /* !DOPRINT */
+#define	DOPRINT_START(xp)
+#define	DOPRINT_END1(v)
+#define	DOPRINT_END2(hi, lo)
+#endif /* DOPRINT */
+
+#define	RETURNP(x) do {			\
+	DOPRINT_END1(x);		\
+	RETURNF(x);			\
+} while (0)
+#define	RETURNPI(x) do {		\
+	DOPRINT_END1(x);		\
+	RETURNI(x);			\
+} while (0)
+#define	RETURN2P(x, y) do {		\
+	DOPRINT_END2((x), (y));		\
+	RETURNF((x) + (y));		\
+} while (0)
+#define	RETURN2PI(x, y) do {		\
+	DOPRINT_END2((x), (y));		\
+	RETURNI((x) + (y));		\
+} while (0)
+#ifdef STRUCT_RETURN
+#define	RETURNSP(rp) do {		\
+	if (!(rp)->lo_set)		\
+		RETURNP((rp)->hi);	\
+	RETURN2P((rp)->hi, (rp)->lo);	\
+} while (0)
+#define	RETURNSPI(rp) do {		\
+	if (!(rp)->lo_set)		\
+		RETURNPI((rp)->hi);	\
+	RETURN2PI((rp)->hi, (rp)->lo);	\
+} while (0)
+#endif
+#define	SUM2P(x, y) ({			\
+	const __typeof (x) __x = (x);	\
+	const __typeof (y) __y = (y);	\
+					\
+	DOPRINT_END2(__x, __y);		\
+	__x + __y;			\
+})
+
+/*
+ * ieee style elementary functions
+ *
+ * We rename functions here to improve other sources' diffability
+ * against fdlibm.
+ */
+#define	__ieee754_sqrt	sqrt
+#define	__ieee754_acos	acos
+#define	__ieee754_acosh	acosh
+#define	__ieee754_log	log
+#define	__ieee754_log2	log2
+#define	__ieee754_atanh	atanh
+#define	__ieee754_asin	asin
+#define	__ieee754_atan2	atan2
+#define	__ieee754_exp	exp
+#define	__ieee754_cosh	cosh
+#define	__ieee754_fmod	fmod
+#define	__ieee754_pow	pow
+#define	__ieee754_lgamma lgamma
+#define	__ieee754_gamma	gamma
+#define	__ieee754_lgamma_r lgamma_r
+#define	__ieee754_gamma_r gamma_r
+#define	__ieee754_log10	log10
+#define	__ieee754_sinh	sinh
+#define	__ieee754_hypot	hypot
+#define	__ieee754_j0	j0
+#define	__ieee754_j1	j1
+#define	__ieee754_y0	y0
+#define	__ieee754_y1	y1
+#define	__ieee754_jn	jn
+#define	__ieee754_yn	yn
+#define	__ieee754_remainder remainder
+#define	__ieee754_scalb	scalb
+#define	__ieee754_sqrtf	sqrtf
+#define	__ieee754_acosf	acosf
+#define	__ieee754_acoshf acoshf
+#define	__ieee754_logf	logf
+#define	__ieee754_atanhf atanhf
+#define	__ieee754_asinf	asinf
+#define	__ieee754_atan2f atan2f
+#define	__ieee754_expf	expf
+#define	__ieee754_coshf	coshf
+#define	__ieee754_fmodf	fmodf
+#define	__ieee754_powf	powf
+#define	__ieee754_lgammaf lgammaf
+#define	__ieee754_gammaf gammaf
+#define	__ieee754_lgammaf_r lgammaf_r
+#define	__ieee754_gammaf_r gammaf_r
+#define	__ieee754_log10f log10f
+#define	__ieee754_log2f log2f
+#define	__ieee754_sinhf	sinhf
+#define	__ieee754_hypotf hypotf
+#define	__ieee754_j0f	j0f
+#define	__ieee754_j1f	j1f
+#define	__ieee754_y0f	y0f
+#define	__ieee754_y1f	y1f
+#define	__ieee754_jnf	jnf
+#define	__ieee754_ynf	ynf
+#define	__ieee754_remainderf remainderf
+#define	__ieee754_scalbf scalbf
+
+/* fdlibm kernel function */
+int	__kernel_rem_pio2(double*,double*,int,int,int);
+
+/* double precision kernel functions */
+#ifndef INLINE_REM_PIO2
+int	__ieee754_rem_pio2(double,double*);
+#endif
+double	__kernel_sin(double,double,int);
+double	__kernel_cos(double,double);
+double	__kernel_tan(double,double,int);
+double	__ldexp_exp(double,int);
+#ifdef _COMPLEX_H
+double complex __ldexp_cexp(double complex,int);
+#endif
+
+/* float precision kernel functions */
+#ifndef INLINE_REM_PIO2F
+int	__ieee754_rem_pio2f(float,double*);
+#endif
+#ifndef INLINE_KERNEL_SINDF
+float	__kernel_sindf(double);
+#endif
+#ifndef INLINE_KERNEL_COSDF
+float	__kernel_cosdf(double);
+#endif
+#ifndef INLINE_KERNEL_TANDF
+float	__kernel_tandf(double,int);
+#endif
+float	__ldexp_expf(float,int);
+#ifdef _COMPLEX_H
+float complex __ldexp_cexpf(float complex,int);
+#endif
+
+/* long double precision kernel functions */
+long double __kernel_sinl(long double, long double, int);
+long double __kernel_cosl(long double, long double);
+long double __kernel_tanl(long double, long double, int);
+
+#endif /* !_MATH_PRIVATE_H_ */
diff --git a/firmware/external/freebsd/lib/msun/src/s_atanf.c b/firmware/external/freebsd/lib/msun/src/s_atanf.c
new file mode 100644
index 00000000..b3a371f3
--- /dev/null
+++ b/firmware/external/freebsd/lib/msun/src/s_atanf.c
@@ -0,0 +1,92 @@
+/* s_atanf.c -- float version of s_atan.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include "math.h"
+#include "math_private.h"
+
+static const float atanhi[] = {
+  4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
+  7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
+  9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
+  1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
+};
+
+static const float atanlo[] = {
+  5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
+  3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
+  3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
+  7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
+};
+
+static const float aT[] = {
+  3.3333328366e-01,
+ -1.9999158382e-01,
+  1.4253635705e-01,
+ -1.0648017377e-01,
+  6.1687607318e-02,
+};
+
+static const float
+one   = 1.0,
+huge   = 1.0e30;
+
+float
+atanf(float x)
+{
+	float w,s1,s2,z;
+	int32_t ix,hx,id;
+
+	GET_FLOAT_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix>=0x4c800000) {	/* if |x| >= 2**26 */
+	    if(ix>0x7f800000)
+		return x+x;		/* NaN */
+	    if(hx>0) return  atanhi[3]+*(volatile float *)&atanlo[3];
+	    else     return -atanhi[3]-*(volatile float *)&atanlo[3];
+	} if (ix < 0x3ee00000) {	/* |x| < 0.4375 */
+	    if (ix < 0x39800000) {	/* |x| < 2**-12 */
+		if(huge+x>one) return x;	/* raise inexact */
+	    }
+	    id = -1;
+	} else {
+	x = fabsf(x);
+	if (ix < 0x3f980000) {		/* |x| < 1.1875 */
+	    if (ix < 0x3f300000) {	/* 7/16 <=|x|<11/16 */
+		id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
+	    } else {			/* 11/16<=|x|< 19/16 */
+		id = 1; x  = (x-one)/(x+one);
+	    }
+	} else {
+	    if (ix < 0x401c0000) {	/* |x| < 2.4375 */
+		id = 2; x  = (x-(float)1.5)/(one+(float)1.5*x);
+	    } else {			/* 2.4375 <= |x| < 2**26 */
+		id = 3; x  = -(float)1.0/x;
+	    }
+	}}
+    /* end of argument reduction */
+	z = x*x;
+	w = z*z;
+    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
+	s1 = z*(aT[0]+w*(aT[2]+w*aT[4]));
+	s2 = w*(aT[1]+w*aT[3]);
+	if (id<0) return x - x*(s1+s2);
+	else {
+	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
+	    return (hx<0)? -z:z;
+	}
+}