Accept FS #10244 by Wincent Balin: more pdbox work done for GSoC; also some keyword and line-ending fixes by me

git-svn-id: svn://svn.rockbox.org/rockbox/trunk@21626 a1c6a512-1295-4272-9138-f99709370657

1 files changed, 2428 insertions, 0 deletions

diff --git a/apps/plugins/pdbox/pdbox-func.c b/apps/plugins/pdbox/pdbox-func.c
new file mode 100644
index 0000000000..ee4a8fd166
--- /dev/null
+++ b/apps/plugins/pdbox/pdbox-func.c
@@ -0,0 +1,2428 @@
+/***************************************************************************
+ *             __________               __   ___.
+ *   Open      \______   \ ____   ____ |  | _\_ |__   _______  ___
+ *   Source     |       _//  _ \_/ ___\|  |/ /| __ \ /  _ \  \/  /
+ *   Jukebox    |    |   (  <_> )  \___|    < | \_\ (  <_> > <  <
+ *   Firmware   |____|_  /\____/ \___  >__|_ \|___  /\____/__/\_ \
+ *                     \/            \/     \/    \/            \/
+ * $Id$
+ *
+ * Copyright (C) 2009 Wincent Balin
+ *
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY OF ANY
+ * KIND, either express or implied.
+ *
+ ****************************************************************************/
+
+#include "plugin.h"
+#include "pdbox.h"
+#include "ctype.h"
+
+#include "m_pd.h"
+#include "s_stuff.h"
+
+
+/* This implementation of strncat is taken from lua plug-in. */
+
+/* gcc is broken and has a non-SUSv2 compliant internal prototype.
+ * This causes it to warn about a type mismatch here.  Ignore it. */
+char *rb_strncat(char *s, const char *t, size_t n)
+{
+    char *dest = s;
+    register char *max;
+    s += strlen(s);
+
+    if((max = s + n) == s)
+        goto strncat_fini;
+
+    while(true)
+    {
+        if(!(*s = *t))
+            break;
+        if(++s == max)
+            break;
+        ++t;
+
+#ifndef WANT_SMALL_STRING_ROUTINES
+    if(!(*s = *t))
+        break;
+    if(++s == max)
+        break;
+    ++t;
+    if(!(*s = *t))
+        break;
+    if(++s == max)
+        break;
+    ++t;
+    if(!(*s = *t))
+        break;
+    if(++s == max)
+        break;
+    ++t;
+#endif
+    }
+
+    *s = 0;
+
+strncat_fini:
+    return dest;
+}
+
+
+/* Implementation of floor, original. */
+float rb_floor(float value)
+{
+    /* If value is negative, decrement value to match function's definition. */
+    if(value < 0.0)
+    {
+        value -= 1.0;
+    }
+
+    /* Truncate fractional part (convert to integer)
+       and afterwards convert back to double. */
+    return (float) ((int) value);
+}
+
+
+/* Implementation of strtod() and atof(),
+   taken from SanOS (http://www.jbox.dk/sanos/). */
+static int rb_errno = 0;
+
+double rb_strtod(const char *str, char **endptr)
+{
+  double number;
+  int exponent;
+  int negative;
+  char *p = (char *) str;
+  double p10;
+  int n;
+  int num_digits;
+  int num_decimals;
+
+    /* Reset Rockbox errno -- W.B. */
+#ifdef ROCKBOX
+    rb_errno = 0;
+#endif
+
+  // Skip leading whitespace
+  while (isspace(*p)) p++;
+
+  // Handle optional sign
+  negative = 0;
+  switch (*p) 
+  {
+    case '-': negative = 1; // Fall through to increment position
+    case '+': p++;
+  }
+
+  number = 0.;
+  exponent = 0;
+  num_digits = 0;
+  num_decimals = 0;
+
+  // Process string of digits
+  while (isdigit(*p))
+  {
+    number = number * 10. + (*p - '0');
+    p++;
+    num_digits++;
+  }
+
+  // Process decimal part
+  if (*p == '.') 
+  {
+    p++;
+
+    while (isdigit(*p))
+    {
+      number = number * 10. + (*p - '0');
+      p++;
+      num_digits++;
+      num_decimals++;
+    }
+
+    exponent -= num_decimals;
+  }
+
+  if (num_digits == 0)
+  {
+#ifdef ROCKBOX
+    rb_errno = 1;
+#else
+    errno = ERANGE;
+#endif
+    return 0.0;
+  }
+
+  // Correct for sign
+  if (negative) number = -number;
+
+  // Process an exponent string
+  if (*p == 'e' || *p == 'E') 
+  {
+    // Handle optional sign
+    negative = 0;
+    switch(*++p) 
+    {   
+      case '-': negative = 1;   // Fall through to increment pos
+      case '+': p++;
+    }
+
+    // Process string of digits
+    n = 0;
+    while (isdigit(*p)) 
+    {   
+      n = n * 10 + (*p - '0');
+      p++;
+    }
+
+    if (negative) 
+      exponent -= n;
+    else
+      exponent += n;
+  }
+
+#ifndef ROCKBOX
+  if (exponent < DBL_MIN_EXP  || exponent > DBL_MAX_EXP)
+  {
+    errno = ERANGE;
+    return HUGE_VAL;
+  }
+#endif
+
+  // Scale the result
+  p10 = 10.;
+  n = exponent;
+  if (n < 0) n = -n;
+  while (n) 
+  {
+    if (n & 1) 
+    {
+      if (exponent < 0)
+        number /= p10;
+      else
+        number *= p10;
+    }
+    n >>= 1;
+    p10 *= p10;
+  }
+
+#ifndef ROCKBOX
+  if (number == HUGE_VAL) errno = ERANGE;
+#endif
+  if (endptr) *endptr = p;
+
+  return number;
+}
+
+double rb_atof(const char *str)
+{
+    return rb_strtod(str, NULL);
+}
+
+
+/* Implementation of ftoa(), original. */
+void rb_ftoan(float f, char* out, int size)
+{
+    #define SBUFSIZE 12
+    char sbuf[SBUFSIZE];
+
+    /* Zero out string. */
+    *out = '\0';
+    size--;
+
+    /* Handle negative numbers. */
+    if(f < 0.0)
+    {
+        f = -f;
+        strcat(out, "-");
+        size--;
+    }
+
+    /* Find and convert integer part. */
+    int int_part = (int) f;
+    snprintf(sbuf, SBUFSIZE-1, "%d", int_part);
+    int int_part_len = strlen(sbuf);
+    if(size < int_part_len)
+        return;
+
+    /* Append integral part to output string. */
+    strcat(out, sbuf);
+    size -= int_part_len;
+
+    /* Check whether further content is possible. */
+    if(size <= 0)
+        return;
+
+    /* Append decimal point. */
+    strcat(out, ".");
+    size--;
+
+    /* Calculate first rest and convert it. */
+    float rest1 = (f - (float) int_part) * 1000000000.0;
+    int irest1 = (int) rest1;
+    snprintf(sbuf, SBUFSIZE-1, "%09d", irest1);
+
+    /* Append first rest to output string. */
+    int rest1_len = strlen(sbuf);
+    int rest1_minlen = MIN(size, rest1_len);
+    strncat(out, sbuf, rest1_minlen);
+    size -= rest1_minlen;
+
+    /* Check whether output string still has enough space. */
+    if(size <= 0)
+        return;
+
+    /* Calculate second rest and convert it. */
+    float rest2 = (rest1 - (float) irest1) * 1000000000.0;
+    int irest2 = (int) rest2;
+    snprintf(sbuf, SBUFSIZE-1, "%09d", irest2);
+
+    /* Append second rest to the output string. */
+    int rest2_len = strlen(sbuf);
+    int rest2_minlen = MIN(size, rest2_len);
+    strncat(out, sbuf, rest2_minlen);
+}
+
+
+/* Implementation of atol(), adapted from
+   the atoi() implementation in Rockbox. */
+long rb_atol(const char* str)
+{
+    long value = 0L;
+    long sign = 1L;
+
+    while (isspace(*str))
+    {
+        str++;
+    }
+
+    if ('-' == *str)
+    {
+        sign = -1L;
+        str++;
+    }
+    else if ('+' == *str)
+    {
+        str++;
+    }
+
+    while ('0' == *str)
+    {
+        str++;
+    }
+
+    while (isdigit(*str))
+    {
+        value = (value * 10L) + (*str - '0');
+        str++;
+    }
+
+    return value * sign;
+}
+
+
+/* Implementation of sin() and cos(),
+   adapted from http://lab.polygonal.de/2007/07/18/fast-and-accurate-sinecosine-approximation/
+*/
+
+float rb_sin(float rad)
+{
+    /* Trim input value to -PI..PI interval. */
+    if(rad < -3.14159265)
+        rad += 6.28318531;
+    else if(rad > 3.14159265)
+        rad -= 6.28318531;
+
+    if(rad < 0)
+        return (1.27323954 * rad + 0.405284735 * rad * rad);
+    else
+        return (1.27323954 * rad - 0.405284735 * rad * rad);
+}
+
+float rb_cos(float rad)
+{
+    /* Compute cosine: sin(x + PI/2) = cos(x) */
+    rad += 1.57079632;
+    if(rad > 3.14159265)
+        rad -= 6.28318531;
+
+    return rb_sin(rad);
+}
+
+
+/* Emulation of fscanf(fd, "%f", (float*) xxx);
+   Basically a reimplementation of rb_strtod() above. */
+int rb_fscanf_f(int fd, float* f)
+{
+    #define FSCANF_F_BUFSIZE 64
+    char buf[FSCANF_F_BUFSIZE];
+
+    /* Read line from file. */
+    int bytes_read = rb->read_line(fd, buf, FSCANF_F_BUFSIZE-1);
+
+    /* Terminate string. */
+    if(bytes_read >= FSCANF_F_BUFSIZE)
+        buf[FSCANF_F_BUFSIZE-1] = '\0';
+    else
+        buf[bytes_read-1] = '\0';
+
+    /* Convert buffer to float. */
+    *f = rb_atof(buf);
+
+    /* If there was an error, no float was read. */
+    if(rb_errno)
+        return 0;
+
+    return 1;
+}
+
+/* Emulation of fprintf(fd, "%f\n", (float*) xxx); */
+int rb_fprintf_f(int fd, float f)
+{
+    #define FPRINTF_F_BUFSIZE 64
+    char buf[FPRINTF_F_BUFSIZE];
+    const char* next_line = "\n";
+
+    /* Convert float to string. */
+    rb_ftoan(f, buf, sizeof(buf)-1);
+
+    /* Add next line character. */
+    strcat(buf, next_line);
+
+    /* Write string into file. */
+    return write(fd, buf, strlen(buf));
+}
+
+
+/* Natural logarithm.
+   Taken from glibc-2.8 */
+static const float
+ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
+ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
+two25 =    3.355443200e+07,	/* 0x4c000000 */
+Lg1 = 6.6666668653e-01,	/* 3F2AAAAB */
+Lg2 = 4.0000000596e-01,	/* 3ECCCCCD */
+Lg3 = 2.8571429849e-01, /* 3E924925 */
+Lg4 = 2.2222198546e-01, /* 3E638E29 */
+Lg5 = 1.8183572590e-01, /* 3E3A3325 */
+Lg6 = 1.5313838422e-01, /* 3E1CD04F */
+Lg7 = 1.4798198640e-01; /* 3E178897 */
+
+static const float zero   =  0.0;
+
+/* A union which permits us to convert between a float and a 32 bit
+   int.  */
+
+typedef union
+{
+  float value;
+  uint32_t 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)
+
+
+float rb_log(float x)
+{
+    float hfsq, f, s, z, R, w, t1, t2, dk;
+    int32_t k, ix, i, j;
+
+    GET_FLOAT_WORD(ix,x);
+
+    k=0;
+    if (ix < 0x00800000) {          /* x < 2**-126  */
+        if ((ix&0x7fffffff)==0)
+            return -two25/(x-x);		/* log(+-0)=-inf */
+        if (ix<0) return (x-x)/(x-x);	/* log(-#) = NaN */
+        k -= 25; x *= two25; /* subnormal number, scale up x */
+        GET_FLOAT_WORD(ix,x);
+    }
+    if (ix >= 0x7f800000) return x+x;
+    k += (ix>>23)-127;
+    ix &= 0x007fffff;
+    i = (ix+(0x95f64<<3))&0x800000;
+    SET_FLOAT_WORD(x,ix|(i^0x3f800000));	/* normalize x or x/2 */
+    k += (i>>23);
+    f = x-(float)1.0;
+    if((0x007fffff&(15+ix))<16) {	/* |f| < 2**-20 */
+        if(f==zero) {
+            if(k==0)
+                return zero;
+            else
+            {
+                dk=(float)k;
+                return dk*ln2_hi+dk*ln2_lo;
+            }
+        }
+        R = f*f*((float)0.5-(float)0.33333333333333333*f);
+        if(k==0)
+            return f-R;
+        else
+        {
+            dk=(float)k;
+            return dk*ln2_hi-((R-dk*ln2_lo)-f);
+        }
+    }
+    s = f/((float)2.0+f);
+    dk = (float)k;
+    z = s*s;
+    i = ix-(0x6147a<<3);
+    w = z*z;
+    j = (0x6b851<<3)-ix;
+    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=(float)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);
+    }
+}
+
+
+/* Logarithm for 10th base,
+   taken from glibc-2.8 */
+
+static const float
+ivln10     =  4.3429449201e-01, /* 0x3ede5bd9 */
+log10_2hi  =  3.0102920532e-01, /* 0x3e9a2080 */
+log10_2lo  =  7.9034151668e-07; /* 0x355427db */
+
+float rb_log10(float x)
+{
+	float y,z;
+	int32_t i,k,hx;
+
+	GET_FLOAT_WORD(hx,x);
+
+        k=0;
+        if (hx < 0x00800000) {			/* x < 2**-126  */
+            if ((hx&0x7fffffff)==0)
+                return -two25/(x-x);		/* log(+-0)=-inf */
+            if (hx<0) return (x-x)/(x-x);	/* log(-#) = NaN */
+            k -= 25; x *= two25; /* subnormal number, scale up x */
+	    GET_FLOAT_WORD(hx,x);
+        }
+	if (hx >= 0x7f800000) return x+x;
+	k += (hx>>23)-127;
+	i  = ((uint32_t)k&0x80000000)>>31;
+        hx = (hx&0x007fffff)|((0x7f-i)<<23);
+        y  = (float)(k+i);
+	SET_FLOAT_WORD(x,hx);
+	z  = y*log10_2lo + ivln10*rb_log(x);
+	return  z+y*log10_2hi;
+}
+
+
+/* Power function,
+   Taken from glibc-2.8 */
+
+int rb_isinf(float x)
+{
+    int32_t ix, t;
+    GET_FLOAT_WORD(ix,x);
+    t = ix & 0x7fffffff;
+    t ^= 0x7f800000;
+    t |= -t;
+    return ~(t >> 31) & (ix >> 30);
+}
+
+float rb_copysignf(float x, float y)
+{
+    uint32_t ix, iy;
+    GET_FLOAT_WORD(ix,x);
+    GET_FLOAT_WORD(iy,y);
+    SET_FLOAT_WORD(x,(ix&0x7fffffff)|(iy&0x80000000));
+    return x;
+}
+
+static const float
+huge = 1.0e+30,
+tiny = 1.0e-30,
+twom25  =  2.9802322388e-08;	/* 0x33000000 */
+
+float rb_scalbnf(float x, int n)
+{
+    int32_t k, ix;
+    GET_FLOAT_WORD(ix,x);
+    k = (ix&0x7f800000)>>23;		/* extract exponent */
+    if (k==0) {				/* 0 or subnormal x */
+        if ((ix&0x7fffffff)==0) return x; /* +-0 */
+        x *= two25;
+        GET_FLOAT_WORD(ix,x);
+        k = ((ix&0x7f800000)>>23) - 25;
+    }
+    if (k==0xff) return x+x;		/* NaN or Inf */
+    k = k+n;
+    if (n> 50000 || k >  0xfe)
+        return huge*rb_copysignf(huge,x); /* overflow  */
+    if (n< -50000)
+        return tiny*rb_copysignf(tiny,x);	/*underflow*/
+    if (k > 0) 				/* normal result */
+        {SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); return x;}
+    if (k <= -25)
+        return tiny*rb_copysignf(tiny,x);	/*underflow*/
+    k += 25;				/* subnormal result */
+    SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23));
+    return x*twom25;
+}
+
+
+static const float
+bp[] = {1.0, 1.5,},
+dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
+dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
+one	=  1.0,
+two	=  2.0,
+two24	=  16777216.0,	/* 0x4b800000 */
+	/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
+L1  =  6.0000002384e-01, /* 0x3f19999a */
+L2  =  4.2857143283e-01, /* 0x3edb6db7 */
+L3  =  3.3333334327e-01, /* 0x3eaaaaab */
+L4  =  2.7272811532e-01, /* 0x3e8ba305 */
+L5  =  2.3066075146e-01, /* 0x3e6c3255 */
+L6  =  2.0697501302e-01, /* 0x3e53f142 */
+P1   =  1.6666667163e-01, /* 0x3e2aaaab */
+P2   = -2.7777778450e-03, /* 0xbb360b61 */
+P3   =  6.6137559770e-05, /* 0x388ab355 */
+P4   = -1.6533901999e-06, /* 0xb5ddea0e */
+P5   =  4.1381369442e-08; /* 0x3331bb4c */
+
+static const float
+lg2  =  6.9314718246e-01, /* 0x3f317218 */
+lg2_h  =  6.93145752e-01, /* 0x3f317200 */
+lg2_l  =  1.42860654e-06, /* 0x35bfbe8c */
+ovt =  4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
+cp    =  9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
+cp_h  =  9.6179199219e-01, /* 0x3f763800 =head of cp */
+cp_l  =  4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
+ivln2    =  1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
+ivln2_h  =  1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
+ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
+
+float rb_pow(float x, float y)
+{
+    float z, ax, z_h, z_l, p_h, p_l;
+    float y1, t1, t2, r, s, t, u, v, w;
+    int32_t i, j, k, yisint, n;
+    int32_t hx, hy, ix, iy, is;
+
+    GET_FLOAT_WORD(hx,x);
+    GET_FLOAT_WORD(hy,y);
+    ix = hx&0x7fffffff;
+    iy = hy&0x7fffffff;
+
+    /* y==zero: x**0 = 1 */
+    if(iy==0) return one;
+
+    /* x==+-1 */
+    if(x == 1.0) return one;
+    if(x == -1.0 && rb_isinf(y)) return one;
+
+    /* +-NaN return x+y */
+    if(ix > 0x7f800000 || iy > 0x7f800000)
+        return x+y;
+
+    /* determine if y is an odd int when x < 0
+     * yisint = 0	... y is not an integer
+     * yisint = 1	... y is an odd int
+     * yisint = 2	... y is an even int
+     */
+    yisint = 0;
+    if(hx<0) {
+        if(iy>=0x4b800000) yisint = 2; /* even integer y */
+        else if(iy>=0x3f800000) {
+            k = (iy>>23)-0x7f;	   /* exponent */
+            j = iy>>(23-k);
+            if((j<<(23-k))==iy) yisint = 2-(j&1);
+        }
+    }
+
+    /* special value of y */
+    if (iy==0x7f800000) {	/* y is +-inf */
+        if (ix==0x3f800000)
+            return  y - y;	/* inf**+-1 is NaN */
+        else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
+            return (hy>=0)? y: zero;
+        else			/* (|x|<1)**-,+inf = inf,0 */
+            return (hy<0)?-y: zero;
+    }
+    if(iy==0x3f800000) {	/* y is  +-1 */
+        if(hy<0) return one/x; else return x;
+    }
+    if(hy==0x40000000) return x*x; /* y is  2 */
+    if(hy==0x3f000000) {	/* y is  0.5 */
+        if(hx>=0)	/* x >= +0 */
+            return rb_sqrt(x);
+    }
+
+    ax = rb_fabs(x);
+    /* special value of x */
+    if(ix==0x7f800000||ix==0||ix==0x3f800000){
+        z = ax;			/*x is +-0,+-inf,+-1*/
+        if(hy<0) z = one/z;	/* z = (1/|x|) */
+        if(hx<0) {
+            if(((ix-0x3f800000)|yisint)==0) {
+                z = (z-z)/(z-z); /* (-1)**non-int is NaN */
+            } else if(yisint==1)
+                z = -z;		/* (x<0)**odd = -(|x|**odd) */
+        }
+        return z;
+    }
+
+    /* (x<0)**(non-int) is NaN */
+    if(((((uint32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
+
+    /* |y| is huge */
+    if(iy>0x4d000000) { /* if |y| > 2**27 */
+        /* over/underflow if x is not close to one */
+        if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
+        if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
+	/* now |1-x| is tiny <= 2**-20, suffice to compute
+	   log(x) by x-x^2/2+x^3/3-x^4/4 */
+        t = x-1;		/* t has 20 trailing zeros */
+        w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
+        u = ivln2_h*t;	/* ivln2_h has 16 sig. bits */
+        v = t*ivln2_l-w*ivln2;
+        t1 = u+v;
+        GET_FLOAT_WORD(is,t1);
+        SET_FLOAT_WORD(t1,is&0xfffff000);
+        t2 = v-(t1-u);
+    } else {
+        float s2, s_h, s_l, t_h, t_l;
+        n = 0;
+	/* take care subnormal number */
+        if(ix<0x00800000)
+            {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
+        n  += ((ix)>>23)-0x7f;
+        j  = ix&0x007fffff;
+	/* determine interval */
+        ix = j|0x3f800000;		/* normalize ix */
+        if(j<=0x1cc471) k=0;	/* |x|<sqrt(3/2) */
+        else if(j<0x5db3d7) k=1;	/* |x|<sqrt(3)   */
+        else {k=0;n+=1;ix -= 0x00800000;}
+        SET_FLOAT_WORD(ax,ix);
+
+        /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
+        u = ax-bp[k];		/* bp[0]=1.0, bp[1]=1.5 */
+        v = one/(ax+bp[k]);
+        s = u*v;
+        s_h = s;
+        GET_FLOAT_WORD(is,s_h);
+        SET_FLOAT_WORD(s_h,is&0xfffff000);
+	/* t_h=ax+bp[k] High */
+        SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
+        t_l = ax - (t_h-bp[k]);
+        s_l = v*((u-s_h*t_h)-s_h*t_l);
+	/* compute log(ax) */
+        s2 = s*s;
+        r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
+        r += s_l*(s_h+s);
+        s2  = s_h*s_h;
+        t_h = (float)3.0+s2+r;
+        GET_FLOAT_WORD(is,t_h);
+        SET_FLOAT_WORD(t_h,is&0xfffff000);
+        t_l = r-((t_h-(float)3.0)-s2);
+	/* u+v = s*(1+...) */
+        u = s_h*t_h;
+        v = s_l*t_h+t_l*s;
+	/* 2/(3log2)*(s+...) */
+        p_h = u+v;
+        GET_FLOAT_WORD(is,p_h);
+        SET_FLOAT_WORD(p_h,is&0xfffff000);
+        p_l = v-(p_h-u);
+        z_h = cp_h*p_h;		/* cp_h+cp_l = 2/(3*log2) */
+        z_l = cp_l*p_h+p_l*cp+dp_l[k];
+	/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
+        t = (float)n;
+        t1 = (((z_h+z_l)+dp_h[k])+t);
+        GET_FLOAT_WORD(is,t1);
+        SET_FLOAT_WORD(t1,is&0xfffff000);
+        t2 = z_l-(((t1-t)-dp_h[k])-z_h);
+    }
+
+    s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
+    if(((((uint32_t)hx>>31)-1)|(yisint-1))==0)
+        s = -one;	/* (-ve)**(odd int) */
+
+    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+    GET_FLOAT_WORD(is,y);
+    SET_FLOAT_WORD(y1,is&0xfffff000);
+    p_l = (y-y1)*t1+y*t2;
+    p_h = y1*t1;
+    z = p_l+p_h;
+    GET_FLOAT_WORD(j,z);
+    if (j>0x43000000)				/* if z > 128 */
+        return s*huge*huge;				/* overflow */
+    else if (j==0x43000000) {			/* if z == 128 */
+        if(p_l+ovt>z-p_h) return s*huge*huge;	/* overflow */
+    }
+    else if ((j&0x7fffffff)>0x43160000)		/* z <= -150 */
+        return s*tiny*tiny;				/* underflow */
+    else if ((uint32_t) j==0xc3160000){		/* z == -150 */
+        if(p_l<=z-p_h) return s*tiny*tiny;		/* underflow */
+    }
+    /*
+     * compute 2**(p_h+p_l)
+     */
+    i = j&0x7fffffff;
+    k = (i>>23)-0x7f;
+    n = 0;
+    if(i>0x3f000000) {		/* if |z| > 0.5, set n = [z+0.5] */
+        n = j+(0x00800000>>(k+1));
+        k = ((n&0x7fffffff)>>23)-0x7f;	/* new k for n */
+        SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
+        n = ((n&0x007fffff)|0x00800000)>>(23-k);
+        if(j<0) n = -n;
+        p_h -= t;
+    }
+    t = p_l+p_h;
+    GET_FLOAT_WORD(is,t);
+    SET_FLOAT_WORD(t,is&0xfffff000);
+    u = t*lg2_h;
+    v = (p_l-(t-p_h))*lg2+t*lg2_l;
+    z = u+v;
+    w = v-(z-u);
+    t  = z*z;
+    t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
+    r  = (z*t1)/(t1-two)-(w+z*w);
+    z  = one-(r-z);
+    GET_FLOAT_WORD(j,z);
+    j += (n<<23);
+    if((j>>23)<=0) z = rb_scalbnf(z,n);	/* subnormal output */
+    else SET_FLOAT_WORD(z,j);
+    return s*z;
+}
+
+
+
+/* Square root function, original. */
+float rb_sqrt(float x)
+{
+	float z;
+	int32_t sign = (int)0x80000000; 
+	int32_t ix,s,q,m,t,i;
+	uint32_t r;
+
+	GET_FLOAT_WORD(ix,x);
+
+    /* take care of Inf and NaN */
+	if((ix&0x7f800000)==0x7f800000) {			
+	    return x*x+x;		/* sqrt(NaN)=NaN, sqrt(+inf)=+inf
+					   sqrt(-inf)=sNaN */
+	} 
+    /* take care of zero */
+	if(ix<=0) {
+	    if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */
+	    else if(ix<0)
+		return (x-x)/(x-x);		/* sqrt(-ve) = sNaN */
+	}
+    /* normalize x */
+	m = (ix>>23);
+	if(m==0) {				/* subnormal x */
+	    for(i=0;(ix&0x00800000)==0;i++) ix<<=1;
+	    m -= i-1;
+	}
+	m -= 127;	/* unbias exponent */
+	ix = (ix&0x007fffff)|0x00800000;
+	if(m&1)	/* odd m, double x to make it even */
+	    ix += ix;
+	m >>= 1;	/* m = [m/2] */
+
+    /* generate sqrt(x) bit by bit */
+	ix += ix;
+	q = s = 0;		/* q = sqrt(x) */
+	r = 0x01000000;		/* r = moving bit from right to left */
+
+	while(r!=0) {
+	    t = s+r; 
+	    if(t<=ix) { 
+		s    = t+r; 
+		ix  -= t; 
+		q   += r; 
+	    } 
+	    ix += ix;
+	    r>>=1;
+	}
+
+    /* use floating add to find out rounding direction */
+	if(ix!=0) {
+	    z = one-tiny; /* trigger inexact flag */
+	    if (z>=one) {
+	        z = one+tiny;
+		if (z>one)
+		    q += 2;
+		else
+		    q += (q&1);
+	    }
+	}
+	ix = (q>>1)+0x3f000000;
+	ix += (m <<23);
+	SET_FLOAT_WORD(z,ix);
+	return z;
+}
+
+/* Absolute value,
+   taken from glibc-2.8 */
+float rb_fabs(float x)
+{
+	uint32_t ix;
+	GET_FLOAT_WORD(ix,x);
+	SET_FLOAT_WORD(x,ix&0x7fffffff);
+        return x;
+}
+
+/* Arc tangent,
+   taken from glibc-2.8. */
+
+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[] = {
+  3.3333334327e-01, /* 0x3eaaaaaa */
+ -2.0000000298e-01, /* 0xbe4ccccd */
+  1.4285714924e-01, /* 0x3e124925 */
+ -1.1111110449e-01, /* 0xbde38e38 */
+  9.0908870101e-02, /* 0x3dba2e6e */
+ -7.6918758452e-02, /* 0xbd9d8795 */
+  6.6610731184e-02, /* 0x3d886b35 */
+ -5.8335702866e-02, /* 0xbd6ef16b */
+  4.9768779427e-02, /* 0x3d4bda59 */
+ -3.6531571299e-02, /* 0xbd15a221 */
+  1.6285819933e-02, /* 0x3c8569d7 */
+};
+
+
+float rb_atan(float x)
+{
+	float w,s1,s2,z;
+	int32_t ix,hx,id;
+
+	GET_FLOAT_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix>=0x50800000) {	/* if |x| >= 2^34 */
+	    if(ix>0x7f800000)
+		return x+x;		/* NaN */
+	    if(hx>0) return  atanhi[3]+atanlo[3];
+	    else     return -atanhi[3]-atanlo[3];
+	} if (ix < 0x3ee00000) {	/* |x| < 0.4375 */
+	    if (ix < 0x31000000) {	/* |x| < 2^-29 */
+		if(huge+x>one) return x;	/* raise inexact */
+	    }
+	    id = -1;
+	} else {
+	x = rb_fabs(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| < 2^66 */
+		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]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
+	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
+	if (id<0) return x - x*(s1+s2);
+	else {
+	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
+	    return (hx<0)? -z:z;
+	}
+}
+
+/* Arc tangent from two variables, original. */
+
+static const float
+pi_o_4  = 7.8539818525e-01,  /* 0x3f490fdb */
+pi_o_2  = 1.5707963705e+00,  /* 0x3fc90fdb */
+pi      = 3.1415927410e+00,  /* 0x40490fdb */
+pi_lo   = -8.7422776573e-08; /* 0xb3bbbd2e */
+
+float rb_atan2(float x, float y)
+{
+	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 rb_atan(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 > 60) z=pi_o_2+(float)0.5*pi_lo; 	/* |y/x| >  2**60 */
+	else if(hx<0&&k<-60) z=0.0; 	/* |y|/x < -2**60 */
+	else z=rb_atan(rb_fabs(y/x));	/* safe to do y/x */
+	switch (m) {
+	    case 0: return       z  ;	/* atan(+,+) */
+	    case 1: {
+	    	      uint32_t zh;
+		      GET_FLOAT_WORD(zh,z);
+		      SET_FLOAT_WORD(z,zh ^ 0x80000000);
+		    }
+		    return       z  ;	/* atan(-,+) */
+	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
+	    default: /* case 3 */
+	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
+	}
+}
+
+
+/* Sine hyperbolic,
+   taken from glibc-2.8 */
+
+static const float
+o_threshold	= 8.8721679688e+01,/* 0x42b17180 */
+invln2		= 1.4426950216e+00,/* 0x3fb8aa3b */
+	/* scaled coefficients related to expm1 */
+Q1  =  -3.3333335072e-02, /* 0xbd088889 */
+Q2  =   1.5873016091e-03, /* 0x3ad00d01 */
+Q3  =  -7.9365076090e-05, /* 0xb8a670cd */
+Q4  =   4.0082177293e-06, /* 0x36867e54 */
+Q5  =  -2.0109921195e-07; /* 0xb457edbb */
+
+float rb_expm1(float x)
+{
+	float y,hi,lo,c=0,t,e,hxs,hfx,r1;
+	int32_t k,xsb;
+	uint32_t hx;
+
+	GET_FLOAT_WORD(hx,x);
+	xsb = hx&0x80000000;		/* sign bit of x */
+	if(xsb==0) y=x; else y= -x;	/* y = |x| */
+	hx &= 0x7fffffff;		/* high word of |x| */
+
+    /* filter out huge and non-finite argument */
+	if(hx >= 0x4195b844) {			/* if |x|>=27*ln2 */
+	    if(hx >= 0x42b17218) {		/* if |x|>=88.721... */
+                if(hx>0x7f800000)
+		    return x+x; 	 /* NaN */
+		if(hx==0x7f800000)
+		    return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
+	        if(x > o_threshold) return huge*huge; /* overflow */
+	    }
+	    if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
+		if(x+tiny<(float)0.0)	/* raise inexact */
+		return tiny-one;	/* return -1 */
+	    }
+	}
+
+    /* argument reduction */
+	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */
+	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
+		if(xsb==0)
+		    {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
+		else
+		    {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
+	    } else {
+		k  = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
+		t  = k;
+		hi = x - t*ln2_hi;	/* t*ln2_hi is exact here */
+		lo = t*ln2_lo;
+	    }
+	    x  = hi - lo;
+	    c  = (hi-x)-lo;
+	}
+	else if(hx < 0x33000000) {  	/* when |x|<2**-25, return x */
+	    t = huge+x;	/* return x with inexact flags when x!=0 */
+	    return x - (t-(huge+x));
+	}
+	else k = 0;
+
+    /* x is now in primary range */
+	hfx = (float)0.5*x;
+	hxs = x*hfx;
+	r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
+	t  = (float)3.0-r1*hfx;
+	e  = hxs*((r1-t)/((float)6.0 - x*t));
+	if(k==0) return x - (x*e-hxs);		/* c is 0 */
+	else {
+	    e  = (x*(e-c)-c);
+	    e -= hxs;
+	    if(k== -1) return (float)0.5*(x-e)-(float)0.5;
+	    if(k==1) {
+	       	if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
+	       	else 	      return  one+(float)2.0*(x-e);
+	    }
+	    if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
+	        int32_t i;
+	        y = one-(e-x);
+		GET_FLOAT_WORD(i,y);
+		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */
+	        return y-one;
+	    }
+	    t = one;
+	    if(k<23) {
+	        int32_t i;
+	        SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
+	       	y = t-(e-x);
+		GET_FLOAT_WORD(i,y);
+		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */
+	   } else {
+	        int32_t i;
+		SET_FLOAT_WORD(t,((0x7f-k)<<23));	/* 2^-k */
+	       	y = x-(e+t);
+	       	y += one;
+		GET_FLOAT_WORD(i,y);
+		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */
+	    }
+	}
+	return y;
+}
+
+static const float shuge = 1.0e37;
+
+float rb_sinh(float x)
+{
+	float t,w,h;
+	int32_t ix,jx;
+
+	GET_FLOAT_WORD(jx,x);
+	ix = jx&0x7fffffff;
+
+    /* x is INF or NaN */
+	if(ix>=0x7f800000) return x+x;	
+
+	h = 0.5;
+	if (jx<0) h = -h;
+    /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
+	if (ix < 0x41b00000) {		/* |x|<22 */
+	    if (ix<0x31800000) 		/* |x|<2**-28 */
+		if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
+	    t = rb_expm1(rb_fabs(x));
+	    if(ix<0x3f800000) return h*((float)2.0*t-t*t/(t+one));
+	    return h*(t+t/(t+one));
+	}
+
+    /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
+	if (ix < 0x42b17180)  return h*rb_exp(rb_fabs(x));
+
+    /* |x| in [log(maxdouble), overflowthresold] */
+	if (ix<=0x42b2d4fc) {
+	    w = rb_exp((float)0.5*rb_fabs(x));
+	    t = h*w;
+	    return t*w;
+	}
+
+    /* |x| > overflowthresold, sinh(x) overflow */
+	return x*shuge;
+}
+
+
+/* Tangent,
+   taken from glibc-2.8 */
+
+static const float
+pio4  =  7.8539812565e-01, /* 0x3f490fda */
+pio4lo=  3.7748947079e-08, /* 0x33222168 */
+T[] =  {
+  3.3333334327e-01, /* 0x3eaaaaab */
+  1.3333334029e-01, /* 0x3e088889 */
+  5.3968254477e-02, /* 0x3d5d0dd1 */
+  2.1869488060e-02, /* 0x3cb327a4 */
+  8.8632395491e-03, /* 0x3c11371f */
+  3.5920790397e-03, /* 0x3b6b6916 */
+  1.4562094584e-03, /* 0x3abede48 */
+  5.8804126456e-04, /* 0x3a1a26c8 */
+  2.4646313977e-04, /* 0x398137b9 */
+  7.8179444245e-05, /* 0x38a3f445 */
+  7.1407252108e-05, /* 0x3895c07a */
+ -1.8558637748e-05, /* 0xb79bae5f */
+  2.5907305826e-05, /* 0x37d95384 */
+};
+
+float kernel_tan(float x, float y, int iy)
+{
+	float z,r,v,w,s;
+	int32_t ix,hx;
+	GET_FLOAT_WORD(hx,x);
+	ix = hx&0x7fffffff;	/* high word of |x| */
+	if(ix<0x31800000)			/* x < 2**-28 */
+	    {if((int)x==0) {			/* generate inexact */
+		if((ix|(iy+1))==0) return one/rb_fabs(x);
+		else return (iy==1)? x: -one/x;
+	    }
+	    }
+	if(ix>=0x3f2ca140) { 			/* |x|>=0.6744 */
+	    if(hx<0) {x = -x; y = -y;}
+	    z = pio4-x;
+	    w = pio4lo-y;
+	    x = z+w; y = 0.0;
+	}
+	z	=  x*x;
+	w 	=  z*z;
+    /* Break x^5*(T[1]+x^2*T[2]+...) into
+     *	  x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
+     *	  x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
+     */
+	r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
+	v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
+	s = z*x;
+	r = y + z*(s*(r+v)+y);
+	r += T[0]*s;
+	w = x+r;
+	if(ix>=0x3f2ca140) {
+	    v = (float)iy;
+	    return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
+	}
+	if(iy==1) return w;
+	else {		/* if allow error up to 2 ulp, 
+			   simply return -1.0/(x+r) here */
+     /*  compute -1.0/(x+r) accurately */
+	    float a,t;
+	    int32_t i;
+	    z  = w;
+	    GET_FLOAT_WORD(i,z);
+	    SET_FLOAT_WORD(z,i&0xfffff000);
+	    v  = r-(z - x); 	/* z+v = r+x */
+	    t = a  = -(float)1.0/w;	/* a = -1.0/w */
+	    GET_FLOAT_WORD(i,t);
+	    SET_FLOAT_WORD(t,i&0xfffff000);
+	    s  = (float)1.0+t*z;
+	    return t+a*(s+t*v);
+	}
+}
+
+
+
+static const int init_jk[] = {4,7,9}; /* initial value for jk */
+
+static const float PIo2[] = {
+  1.5703125000e+00, /* 0x3fc90000 */
+  4.5776367188e-04, /* 0x39f00000 */
+  2.5987625122e-05, /* 0x37da0000 */
+  7.5437128544e-08, /* 0x33a20000 */
+  6.0026650317e-11, /* 0x2e840000 */
+  7.3896444519e-13, /* 0x2b500000 */
+  5.3845816694e-15, /* 0x27c20000 */
+  5.6378512969e-18, /* 0x22d00000 */
+  8.3009228831e-20, /* 0x1fc40000 */
+  3.2756352257e-22, /* 0x1bc60000 */
+  6.3331015649e-25, /* 0x17440000 */
+};
+
+static const float			
+two8   =  2.5600000000e+02, /* 0x43800000 */
+twon8  =  3.9062500000e-03; /* 0x3b800000 */
+
+int kernel_rem_pio2(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)
+{
+	int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
+	float z,fw,f[20],fq[20],q[20];
+
+    /* initialize jk*/
+	jk = init_jk[prec];
+	jp = jk;
+
+    /* determine jx,jv,q0, note that 3>q0 */
+	jx =  nx-1;
+	jv = (e0-3)/8; if(jv<0) jv=0;
+	q0 =  e0-8*(jv+1);
+
+    /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
+	j = jv-jx; m = jx+jk;
+	for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
+
+    /* compute q[0],q[1],...q[jk] */
+	for (i=0;i<=jk;i++) {
+	    for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
+	}
+
+	jz = jk;
+recompute:
+    /* distill q[] into iq[] reversingly */
+	for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
+	    fw    =  (float)((int32_t)(twon8* z));
+	    iq[i] =  (int32_t)(z-two8*fw);
+	    z     =  q[j-1]+fw;
+	}
+
+    /* compute n */
+	z  = rb_scalbnf(z,q0);		/* actual value of z */
+	z -= (float)8.0*rb_floor(z*(float)0.125);	/* trim off integer >= 8 */
+	n  = (int32_t) z;
+	z -= (float)n;
+	ih = 0;
+	if(q0>0) {	/* need iq[jz-1] to determine n */
+	    i  = (iq[jz-1]>>(8-q0)); n += i;
+	    iq[jz-1] -= i<<(8-q0);
+	    ih = iq[jz-1]>>(7-q0);
+	} 
+	else if(q0==0) ih = iq[jz-1]>>8;
+	else if(z>=(float)0.5) ih=2;
+
+	if(ih>0) {	/* q > 0.5 */
+	    n += 1; carry = 0;
+	    for(i=0;i<jz ;i++) {	/* compute 1-q */
+		j = iq[i];
+		if(carry==0) {
+		    if(j!=0) {
+			carry = 1; iq[i] = 0x100- j;
+		    }
+		} else  iq[i] = 0xff - j;
+	    }
+	    if(q0>0) {		/* rare case: chance is 1 in 12 */
+	        switch(q0) {
+	        case 1:
+	    	   iq[jz-1] &= 0x7f; break;
+	    	case 2:
+	    	   iq[jz-1] &= 0x3f; break;
+	        }
+	    }
+	    if(ih==2) {
+		z = one - z;
+		if(carry!=0) z -= rb_scalbnf(one,q0);
+	    }
+	}
+
+    /* check if recomputation is needed */
+	if(z==zero) {
+	    j = 0;
+	    for (i=jz-1;i>=jk;i--) j |= iq[i];
+	    if(j==0) { /* need recomputation */
+		for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */
+
+		for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
+		    f[jx+i] = (float) ipio2[jv+i];
+		    for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
+		    q[i] = fw;
+		}
+		jz += k;
+		goto recompute;
+	    }
+	}
+
+    /* chop off zero terms */
+	if(z==(float)0.0) {
+	    jz -= 1; q0 -= 8;
+	    while(iq[jz]==0) { jz--; q0-=8;}
+	} else { /* break z into 8-bit if necessary */
+	    z = rb_scalbnf(z,-q0);
+	    if(z>=two8) { 
+		fw = (float)((int32_t)(twon8*z));
+		iq[jz] = (int32_t)(z-two8*fw);
+		jz += 1; q0 += 8;
+		iq[jz] = (int32_t) fw;
+	    } else iq[jz] = (int32_t) z ;
+	}
+
+    /* convert integer "bit" chunk to floating-point value */
+	fw = rb_scalbnf(one,q0);
+	for(i=jz;i>=0;i--) {
+	    q[i] = fw*(float)iq[i]; fw*=twon8;
+	}
+
+    /* compute PIo2[0,...,jp]*q[jz,...,0] */
+	for(i=jz;i>=0;i--) {
+	    for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
+	    fq[jz-i] = fw;
+	}
+
+    /* compress fq[] into y[] */
+	switch(prec) {
+	    case 0:
+		fw = 0.0;
+		for (i=jz;i>=0;i--) fw += fq[i];
+		y[0] = (ih==0)? fw: -fw; 
+		break;
+	    case 1:
+	    case 2:
+		fw = 0.0;
+		for (i=jz;i>=0;i--) fw += fq[i]; 
+		y[0] = (ih==0)? fw: -fw; 
+		fw = fq[0]-fw;
+		for (i=1;i<=jz;i++) fw += fq[i];
+		y[1] = (ih==0)? fw: -fw; 
+		break;
+	    case 3:	/* painful */
+		for (i=jz;i>0;i--) {
+		    fw      = fq[i-1]+fq[i]; 
+		    fq[i]  += fq[i-1]-fw;
+		    fq[i-1] = fw;
+		}
+		for (i=jz;i>1;i--) {
+		    fw      = fq[i-1]+fq[i]; 
+		    fq[i]  += fq[i-1]-fw;
+		    fq[i-1] = fw;
+		}
+		for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 
+		if(ih==0) {
+		    y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
+		} else {
+		    y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
+		}
+	}
+	return n&7;
+}
+
+
+static const int32_t two_over_pi[] = {
+0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
+0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,
+0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
+0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
+0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
+0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,
+0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
+0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
+0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
+0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,
+0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
+0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
+0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
+0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,
+0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
+0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
+0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
+0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,
+0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
+0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
+0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
+0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
+};
+
+static const int32_t npio2_hw[] = {
+0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
+0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
+0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
+0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
+0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
+0x4242c700, 0x42490f00
+};
+
+/*
+ * invpio2:  24 bits of 2/pi
+ * pio2_1:   first  17 bit of pi/2
+ * pio2_1t:  pi/2 - pio2_1
+ * pio2_2:   second 17 bit of pi/2
+ * pio2_2t:  pi/2 - (pio2_1+pio2_2)
+ * pio2_3:   third  17 bit of pi/2
+ * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
+ */
+
+static const float
+half =  5.0000000000e-01, /* 0x3f000000 */
+invpio2 =  6.3661980629e-01, /* 0x3f22f984 */
+pio2_1  =  1.5707855225e+00, /* 0x3fc90f80 */
+pio2_1t =  1.0804334124e-05, /* 0x37354443 */
+pio2_2  =  1.0804273188e-05, /* 0x37354400 */
+pio2_2t =  6.0770999344e-11, /* 0x2e85a308 */
+pio2_3  =  6.0770943833e-11, /* 0x2e85a300 */
+pio2_3t =  6.1232342629e-17; /* 0x248d3132 */
+
+int32_t rem_pio2(float x, float *y)
+{
+	float z,w,t,r,fn;
+	float tx[3];
+	int32_t e0,i,j,nx,n,ix,hx;
+
+	GET_FLOAT_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix<=0x3f490fd8)   /* |x| ~<= pi/4 , no need for reduction */
+	    {y[0] = x; y[1] = 0; return 0;}
+	if(ix<0x4016cbe4) {  /* |x| < 3pi/4, special case with n=+-1 */
+	    if(hx>0) {
+		z = x - pio2_1;
+		if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
+		    y[0] = z - pio2_1t;
+		    y[1] = (z-y[0])-pio2_1t;
+		} else {		/* near pi/2, use 24+24+24 bit pi */
+		    z -= pio2_2;
+		    y[0] = z - pio2_2t;
+		    y[1] = (z-y[0])-pio2_2t;
+		}
+		return 1;
+	    } else {	/* negative x */
+		z = x + pio2_1;
+		if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
+		    y[0] = z + pio2_1t;
+		    y[1] = (z-y[0])+pio2_1t;
+		} else {		/* near pi/2, use 24+24+24 bit pi */
+		    z += pio2_2;
+		    y[0] = z + pio2_2t;
+		    y[1] = (z-y[0])+pio2_2t;
+		}
+		return -1;
+	    }
+	}
+	if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
+	    t  = rb_fabs(x);
+	    n  = (int32_t) (t*invpio2+half);
+	    fn = (float)n;
+	    r  = t-fn*pio2_1;
+	    w  = fn*pio2_1t;	/* 1st round good to 40 bit */
+	    if(n<32&&(int32_t)(ix&0xffffff00)!=npio2_hw[n-1]) {
+		y[0] = r-w;	/* quick check no cancellation */
+	    } else {
+	        uint32_t high;
+	        j  = ix>>23;
+	        y[0] = r-w;
+		GET_FLOAT_WORD(high,y[0]);
+	        i = j-((high>>23)&0xff);
+	        if(i>8) {  /* 2nd iteration needed, good to 57 */
+		    t  = r;
+		    w  = fn*pio2_2;
+		    r  = t-w;
+		    w  = fn*pio2_2t-((t-r)-w);
+		    y[0] = r-w;
+		    GET_FLOAT_WORD(high,y[0]);
+		    i = j-((high>>23)&0xff);
+		    if(i>25)  {	/* 3rd iteration need, 74 bits acc */
+		    	t  = r;	/* will cover all possible cases */
+		    	w  = fn*pio2_3;
+		    	r  = t-w;
+		    	w  = fn*pio2_3t-((t-r)-w);
+		    	y[0] = r-w;
+		    }
+		}
+	    }
+	    y[1] = (r-y[0])-w;
+	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
+	    else	 return n;
+	}
+    /*
+     * all other (large) arguments
+     */
+	if(ix>=0x7f800000) {		/* x is inf or NaN */
+	    y[0]=y[1]=x-x; return 0;
+	}
+    /* set z = scalbn(|x|,ilogb(x)-7) */
+	e0 	= (ix>>23)-134;		/* e0 = ilogb(z)-7; */
+	SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));
+	for(i=0;i<2;i++) {
+		tx[i] = (float)((int32_t)(z));
+		z     = (z-tx[i])*two8;
+	}
+	tx[2] = z;
+	nx = 3;
+	while(tx[nx-1]==zero) nx--;	/* skip zero term */
+	n  =  kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
+	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
+	return n;
+}
+
+float rb_tan(float x)
+{
+	float y[2],z=0.0;
+	int32_t n, ix;
+
+	GET_FLOAT_WORD(ix,x);
+
+    /* |x| ~< pi/4 */
+	ix &= 0x7fffffff;
+	if(ix <= 0x3f490fda) return kernel_tan(x,z,1);
+
+    /* tan(Inf or NaN) is NaN */
+	else if (ix>=0x7f800000) return x-x;		/* NaN */
+
+    /* argument reduction needed */
+	else {
+	    n = rem_pio2(x,y);
+	    return kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
+							      -1 -- n odd */
+	}
+}
+
+
+
+/* Exponential function,
+   taken from glibc-2.8
+   As it uses double values and udefines some symbols,
+   it was moved to the end of the source code */
+
+#define W52 (2.22044605e-16)
+#define W55 (2.77555756e-17)
+#define W58 (3.46944695e-18)
+#define W59 (1.73472348e-18)
+#define W60 (8.67361738e-19)
+const float __exp_deltatable[178] = {
+         0*W60,  16558714*W60, -10672149*W59,   1441652*W60,
+ -15787963*W55,    462888*W60,   7291806*W60,   1698880*W60,
+ -14375103*W58,  -2021016*W60,    728829*W60,  -3759654*W60,
+   3202123*W60, -10916019*W58,   -251570*W60,  -1043086*W60,
+   8207536*W60,   -409964*W60,  -5993931*W60,   -475500*W60,
+   2237522*W60,    324170*W60,   -244117*W60,     32077*W60,
+    123907*W60,  -1019734*W60,      -143*W60,    813077*W60,
+    743345*W60,    462461*W60,    629794*W60,   2125066*W60,
+  -2339121*W60,   -337951*W60,   9922067*W60,   -648704*W60,
+    149407*W60,  -2687209*W60,   -631608*W60,   2128280*W60,
+  -4882082*W60,   2001360*W60,    175074*W60,   2923216*W60,
+   -538947*W60,  -1212193*W60,  -1920926*W60,  -1080577*W60,
+   3690196*W60,   2643367*W60,   2911937*W60,    671455*W60,
+  -1128674*W60,    593282*W60,  -5219347*W60,  -1941490*W60,
+  11007953*W60,    239609*W60,  -2969658*W60,  -1183650*W60,
+    942998*W60,    699063*W60,    450569*W60,   -329250*W60,
+  -7257875*W60,   -312436*W60,     51626*W60,    555877*W60,
+   -641761*W60,   1565666*W60,    884327*W60, -10960035*W60,
+  -2004679*W60,   -995793*W60,  -2229051*W60,   -146179*W60,
+   -510327*W60,   1453482*W60,  -3778852*W60,  -2238056*W60,
+  -4895983*W60,   3398883*W60,   -252738*W60,   1230155*W60,
+    346918*W60,   1109352*W60,    268941*W60,  -2930483*W60,
+  -1036263*W60,  -1159280*W60,   1328176*W60,   2937642*W60,
+  -9371420*W60,  -6902650*W60,  -1419134*W60,   1442904*W60,
+  -1319056*W60,    -16369*W60,    696555*W60,   -279987*W60,
+  -7919763*W60,    252741*W60,    459711*W60,  -1709645*W60,
+    354913*W60,   6025867*W60,   -421460*W60,   -853103*W60,
+   -338649*W60,    962151*W60,    955965*W60,    784419*W60,
+  -3633653*W60,   2277133*W60,  -8847927*W52,   1223028*W60,
+   5907079*W60,    623167*W60,   5142888*W60,   2599099*W60,
+   1214280*W60,   4870359*W60,    593349*W60,    -57705*W60,
+   7761209*W60,  -5564097*W60,   2051261*W60,   6216869*W60,
+   4692163*W60,    601691*W60,  -5264906*W60,   1077872*W60,
+  -3205949*W60,   1833082*W60,   2081746*W60,   -987363*W60,
+  -1049535*W60,   2015244*W60,    874230*W60,   2168259*W60,
+  -1740124*W60, -10068269*W60,    -18242*W60,  -3013583*W60,
+    580601*W60,  -2547161*W60,   -535689*W60,   2220815*W60,
+   1285067*W60,   2806933*W60,   -983086*W60,  -1729097*W60,
+  -1162985*W60,  -2561904*W60,    801988*W60,    244351*W60,
+   1441893*W60,  -7517981*W60,    271781*W60, -15021588*W60,
+  -2341588*W60,   -919198*W60,   1642232*W60,   4771771*W60,
+  -1220099*W60,  -3062372*W60,    628624*W60,   1278114*W60,
+  13083513*W60, -10521925*W60,   3180310*W60,  -1659307*W60,
+   3543773*W60,   2501203*W60,      4151*W60,   -340748*W60,
+  -2285625*W60,   2495202*W60
+};
+
+const double __exp_atable[355] /* __attribute__((mode(DF))) */ = {
+ 0.707722561055888932371, /* 0x0.b52d4e46605c27ffd */
+ 0.709106182438804188967, /* 0x0.b587fb96f75097ffb */
+ 0.710492508843861281234, /* 0x0.b5e2d649899167ffd */
+ 0.711881545564593931623, /* 0x0.b63dde74d36bdfffe */
+ 0.713273297897442870573, /* 0x0.b699142f945f87ffc */
+ 0.714667771153751463236, /* 0x0.b6f477909c4ea0001 */
+ 0.716064970655995725059, /* 0x0.b75008aec758f8004 */
+ 0.717464901723956938193, /* 0x0.b7abc7a0eea7e0002 */
+ 0.718867569715736398602, /* 0x0.b807b47e1586c7ff8 */
+ 0.720272979947266023271, /* 0x0.b863cf5d10e380003 */
+ 0.721681137825144314297, /* 0x0.b8c01855195c37ffb */
+ 0.723092048691992950199, /* 0x0.b91c8f7d213740004 */
+ 0.724505717938892290800, /* 0x0.b97934ec5002d0007 */
+ 0.725922150953176470431, /* 0x0.b9d608b9c92ea7ffc */
+ 0.727341353138962865022, /* 0x0.ba330afcc29e98003 */
+ 0.728763329918453162104, /* 0x0.ba903bcc8618b7ffc */
+ 0.730188086709957051568, /* 0x0.baed9b40591ba0000 */
+ 0.731615628948127705309, /* 0x0.bb4b296f931e30002 */
+ 0.733045962086486091436, /* 0x0.bba8e671a05617ff9 */
+ 0.734479091556371366251, /* 0x0.bc06d25dd49568001 */
+ 0.735915022857225542529, /* 0x0.bc64ed4bce8f6fff9 */
+ 0.737353761441304711410, /* 0x0.bcc33752f915d7ff9 */
+ 0.738795312814142124419, /* 0x0.bd21b08af98e78005 */
+ 0.740239682467211168593, /* 0x0.bd80590b65e9a8000 */
+ 0.741686875913991849885, /* 0x0.bddf30ebec4a10000 */
+ 0.743136898669507939299, /* 0x0.be3e38443c84e0007 */
+ 0.744589756269486091620, /* 0x0.be9d6f2c1d32a0002 */
+ 0.746045454254026796384, /* 0x0.befcd5bb59baf8004 */
+ 0.747503998175051087583, /* 0x0.bf5c6c09ca84c0003 */
+ 0.748965393601880857739, /* 0x0.bfbc322f5b18b7ff8 */
+ 0.750429646104262104698, /* 0x0.c01c2843f776fffff */
+ 0.751896761271877989160, /* 0x0.c07c4e5fa18b88002 */
+ 0.753366744698445112140, /* 0x0.c0dca49a5fb18fffd */
+ 0.754839601988627206827, /* 0x0.c13d2b0c444db0005 */
+ 0.756315338768691947122, /* 0x0.c19de1cd798578006 */
+ 0.757793960659406629066, /* 0x0.c1fec8f623723fffd */
+ 0.759275473314173443536, /* 0x0.c25fe09e8a0f47ff8 */
+ 0.760759882363831851927, /* 0x0.c2c128dedc88f8000 */
+ 0.762247193485956486805, /* 0x0.c322a1cf7d6e7fffa */
+ 0.763737412354726363781, /* 0x0.c3844b88cb9347ffc */
+ 0.765230544649828092739, /* 0x0.c3e626232bd8f7ffc */
+ 0.766726596071518051729, /* 0x0.c44831b719bf18002 */
+ 0.768225572321911687194, /* 0x0.c4aa6e5d12d078001 */
+ 0.769727479119219348810, /* 0x0.c50cdc2da64a37ffb */
+ 0.771232322196981678892, /* 0x0.c56f7b41744490001 */
+ 0.772740107296721268087, /* 0x0.c5d24bb1259e70004 */
+ 0.774250840160724651565, /* 0x0.c6354d95640dd0007 */
+ 0.775764526565368872643, /* 0x0.c6988106fec447fff */
+ 0.777281172269557396602, /* 0x0.c6fbe61eb1bd0ffff */
+ 0.778800783068235302750, /* 0x0.c75f7cf560942fffc */
+ 0.780323364758801041312, /* 0x0.c7c345a3f1983fffe */
+ 0.781848923151573727006, /* 0x0.c8274043594cb0002 */
+ 0.783377464064598849602, /* 0x0.c88b6cec94b3b7ff9 */
+ 0.784908993312207869935, /* 0x0.c8efcbb89cba27ffe */
+ 0.786443516765346961618, /* 0x0.c9545cc0a88c70003 */
+ 0.787981040257604625744, /* 0x0.c9b9201dc643bfffa */
+ 0.789521569657452682047, /* 0x0.ca1e15e92a5410007 */
+ 0.791065110849462849192, /* 0x0.ca833e3c1ae510005 */
+ 0.792611669712891875319, /* 0x0.cae8992fd84667ffd */
+ 0.794161252150049179450, /* 0x0.cb4e26ddbc207fff8 */
+ 0.795713864077794763584, /* 0x0.cbb3e75f301b60003 */
+ 0.797269511407239561694, /* 0x0.cc19dacd978cd8002 */
+ 0.798828200086368567220, /* 0x0.cc8001427e55d7ffb */
+ 0.800389937624300440456, /* 0x0.cce65ade24d360006 */
+ 0.801954725261124767840, /* 0x0.cd4ce7a5de839fffb */
+ 0.803522573691593189330, /* 0x0.cdb3a7c79a678fffd */
+ 0.805093487311204114563, /* 0x0.ce1a9b563965ffffc */
+ 0.806667472122675088819, /* 0x0.ce81c26b838db8000 */
+ 0.808244534127439906441, /* 0x0.cee91d213f8428002 */
+ 0.809824679342317166307, /* 0x0.cf50ab9144d92fff9 */
+ 0.811407913793616542005, /* 0x0.cfb86dd5758c2ffff */
+ 0.812994243520784198882, /* 0x0.d0206407c20e20005 */
+ 0.814583674571603966162, /* 0x0.d0888e4223facfff9 */
+ 0.816176213022088536960, /* 0x0.d0f0ec9eb3f7c8002 */
+ 0.817771864936188586101, /* 0x0.d1597f377d6768002 */
+ 0.819370636400374108252, /* 0x0.d1c24626a46eafff8 */
+ 0.820972533518165570298, /* 0x0.d22b41865ff1e7ff9 */
+ 0.822577562404315121269, /* 0x0.d2947170f32ec7ff9 */
+ 0.824185729164559344159, /* 0x0.d2fdd60097795fff8 */
+ 0.825797039949601741075, /* 0x0.d3676f4fb796d0001 */
+ 0.827411500902565544264, /* 0x0.d3d13d78b5f68fffb */
+ 0.829029118181348834154, /* 0x0.d43b40960546d8001 */
+ 0.830649897953322891022, /* 0x0.d4a578c222a058000 */
+ 0.832273846408250750368, /* 0x0.d50fe617a3ba78005 */
+ 0.833900969738858188772, /* 0x0.d57a88b1218e90002 */
+ 0.835531274148056613016, /* 0x0.d5e560a94048f8006 */
+ 0.837164765846411529371, /* 0x0.d6506e1aac8078003 */
+ 0.838801451086016225394, /* 0x0.d6bbb1204074e0001 */
+ 0.840441336100884561780, /* 0x0.d72729d4c28518004 */
+ 0.842084427144139224814, /* 0x0.d792d8530e12b0001 */
+ 0.843730730487052604790, /* 0x0.d7febcb61273e7fff */
+ 0.845380252404570153833, /* 0x0.d86ad718c308dfff9 */
+ 0.847032999194574087728, /* 0x0.d8d727962c69d7fff */
+ 0.848688977161248581090, /* 0x0.d943ae49621ce7ffb */
+ 0.850348192619261200615, /* 0x0.d9b06b4d832ef8005 */
+ 0.852010651900976245816, /* 0x0.da1d5ebdc22220005 */
+ 0.853676361342631029337, /* 0x0.da8a88b555baa0006 */
+ 0.855345327311054837175, /* 0x0.daf7e94f965f98004 */
+ 0.857017556155879489641, /* 0x0.db6580a7c98f7fff8 */
+ 0.858693054267390953857, /* 0x0.dbd34ed9617befff8 */
+ 0.860371828028939855647, /* 0x0.dc4153ffc8b65fff9 */
+ 0.862053883854957292436, /* 0x0.dcaf90368bfca8004 */
+ 0.863739228154875360306, /* 0x0.dd1e0399328d87ffe */
+ 0.865427867361348468455, /* 0x0.dd8cae435d303fff9 */
+ 0.867119807911702289458, /* 0x0.ddfb9050b1cee8006 */
+ 0.868815056264353846599, /* 0x0.de6aa9dced8448001 */
+ 0.870513618890481399881, /* 0x0.ded9fb03db7320006 */
+ 0.872215502247877139094, /* 0x0.df4983e1380657ff8 */
+ 0.873920712852848668986, /* 0x0.dfb94490ffff77ffd */
+ 0.875629257204025623884, /* 0x0.e0293d2f1cb01fff9 */
+ 0.877341141814212965880, /* 0x0.e0996dd786fff0007 */
+ 0.879056373217612985183, /* 0x0.e109d6a64f5d57ffc */
+ 0.880774957955916648615, /* 0x0.e17a77b78e72a7ffe */
+ 0.882496902590150900078, /* 0x0.e1eb5127722cc7ff8 */
+ 0.884222213673356738383, /* 0x0.e25c63121fb0c8006 */
+ 0.885950897802399772740, /* 0x0.e2cdad93ec5340003 */
+ 0.887682961567391237685, /* 0x0.e33f30c925fb97ffb */
+ 0.889418411575228162725, /* 0x0.e3b0ecce2d05ffff9 */
+ 0.891157254447957902797, /* 0x0.e422e1bf727718006 */
+ 0.892899496816652704641, /* 0x0.e4950fb9713fc7ffe */
+ 0.894645145323828439008, /* 0x0.e50776d8b0e60fff8 */
+ 0.896394206626591749641, /* 0x0.e57a1739c8fadfffc */
+ 0.898146687421414902124, /* 0x0.e5ecf0f97c5798007 */
+ 0.899902594367530173098, /* 0x0.e660043464e378005 */
+ 0.901661934163603406867, /* 0x0.e6d3510747e150006 */
+ 0.903424713533971135418, /* 0x0.e746d78f06cd97ffd */
+ 0.905190939194458810123, /* 0x0.e7ba97e879c91fffc */
+ 0.906960617885092856864, /* 0x0.e82e92309390b0007 */
+ 0.908733756358986566306, /* 0x0.e8a2c6845544afffa */
+ 0.910510361377119825629, /* 0x0.e9173500c8abc7ff8 */
+ 0.912290439722343249336, /* 0x0.e98bddc30f98b0002 */
+ 0.914073998177417412765, /* 0x0.ea00c0e84bc4c7fff */
+ 0.915861043547953501680, /* 0x0.ea75de8db8094fffe */
+ 0.917651582652244779397, /* 0x0.eaeb36d09d3137ffe */
+ 0.919445622318405764159, /* 0x0.eb60c9ce4ed3dffff */
+ 0.921243169397334638073, /* 0x0.ebd697a43995b0007 */
+ 0.923044230737526172328, /* 0x0.ec4ca06fc7768fffa */
+ 0.924848813220121135342, /* 0x0.ecc2e44e865b6fffb */
+ 0.926656923710931002014, /* 0x0.ed39635df34e70006 */
+ 0.928468569126343790092, /* 0x0.edb01dbbc2f5b7ffa */
+ 0.930283756368834757725, /* 0x0.ee2713859aab57ffa */
+ 0.932102492359406786818, /* 0x0.ee9e44d9342870004 */
+ 0.933924784042873379360, /* 0x0.ef15b1d4635438005 */
+ 0.935750638358567643520, /* 0x0.ef8d5a94f60f50007 */
+ 0.937580062297704630580, /* 0x0.f0053f38f345cffff */
+ 0.939413062815381727516, /* 0x0.f07d5fde3a2d98001 */
+ 0.941249646905368053689, /* 0x0.f0f5bca2d481a8004 */
+ 0.943089821583810716806, /* 0x0.f16e55a4e497d7ffe */
+ 0.944933593864477061592, /* 0x0.f1e72b028a2827ffb */
+ 0.946780970781518460559, /* 0x0.f2603cd9fb5430001 */
+ 0.948631959382661205081, /* 0x0.f2d98b497d2a87ff9 */
+ 0.950486566729423554277, /* 0x0.f353166f63e3dffff */
+ 0.952344799896018723290, /* 0x0.f3ccde6a11ae37ffe */
+ 0.954206665969085765512, /* 0x0.f446e357f66120000 */
+ 0.956072172053890279009, /* 0x0.f4c12557964f0fff9 */
+ 0.957941325265908139014, /* 0x0.f53ba48781046fffb */
+ 0.959814132734539637840, /* 0x0.f5b66106555d07ffa */
+ 0.961690601603558903308, /* 0x0.f6315af2c2027fffc */
+ 0.963570739036113010927, /* 0x0.f6ac926b8aeb80004 */
+ 0.965454552202857141381, /* 0x0.f728078f7c5008002 */
+ 0.967342048278315158608, /* 0x0.f7a3ba7d66a908001 */
+ 0.969233234469444204768, /* 0x0.f81fab543e1897ffb */
+ 0.971128118008140250896, /* 0x0.f89bda33122c78007 */
+ 0.973026706099345495256, /* 0x0.f9184738d4cf97ff8 */
+ 0.974929006031422851235, /* 0x0.f994f284d3a5c0008 */
+ 0.976835024947348973265, /* 0x0.fa11dc35bc7820002 */
+ 0.978744770239899142285, /* 0x0.fa8f046b4fb7f8007 */
+ 0.980658249138918636210, /* 0x0.fb0c6b449ab1cfff9 */
+ 0.982575468959622777535, /* 0x0.fb8a10e1088fb7ffa */
+ 0.984496437054508843888, /* 0x0.fc07f5602d79afffc */
+ 0.986421160608523028820, /* 0x0.fc8618e0e55e47ffb */
+ 0.988349647107594098099, /* 0x0.fd047b83571b1fffa */
+ 0.990281903873210800357, /* 0x0.fd831d66f4c018002 */
+ 0.992217938695037382475, /* 0x0.fe01fead3320bfff8 */
+ 0.994157757657894713987, /* 0x0.fe811f703491e8006 */
+ 0.996101369488558541238, /* 0x0.ff007fd5744490005 */
+ 0.998048781093141101932, /* 0x0.ff801ffa9b9280007 */
+ 1.000000000000000000000, /* 0x1.00000000000000000 */
+ 1.001955033605393285965, /* 0x1.0080200565d29ffff */
+ 1.003913889319761887310, /* 0x1.0100802aa0e80fff0 */
+ 1.005876574715736104818, /* 0x1.01812090377240007 */
+ 1.007843096764807100351, /* 0x1.020201541aad7fff6 */
+ 1.009813464316352327214, /* 0x1.0283229c4c9820007 */
+ 1.011787683565730677817, /* 0x1.030484836910a000e */
+ 1.013765762469146736174, /* 0x1.0386272b9c077fffe */
+ 1.015747708536026694351, /* 0x1.04080ab526304fff0 */
+ 1.017733529475172815584, /* 0x1.048a2f412375ffff0 */
+ 1.019723232714418781378, /* 0x1.050c94ef7ad5e000a */
+ 1.021716825883923762690, /* 0x1.058f3be0f1c2d0004 */
+ 1.023714316605201180057, /* 0x1.06122436442e2000e */
+ 1.025715712440059545995, /* 0x1.06954e0fec63afff2 */
+ 1.027721021151397406936, /* 0x1.0718b98f41c92fff6 */
+ 1.029730250269221158939, /* 0x1.079c66d49bb2ffff1 */
+ 1.031743407506447551857, /* 0x1.082056011a9230009 */
+ 1.033760500517691527387, /* 0x1.08a487359ebd50002 */
+ 1.035781537016238873464, /* 0x1.0928fa93490d4fff3 */
+ 1.037806524719013578963, /* 0x1.09adb03b3e5b3000d */
+ 1.039835471338248051878, /* 0x1.0a32a84e9e5760004 */
+ 1.041868384612101516848, /* 0x1.0ab7e2eea5340ffff */
+ 1.043905272300907460835, /* 0x1.0b3d603ca784f0009 */
+ 1.045946142174331239262, /* 0x1.0bc3205a042060000 */
+ 1.047991002016745332165, /* 0x1.0c4923682a086fffe */
+ 1.050039859627715177527, /* 0x1.0ccf698898f3a000d */
+ 1.052092722826109660856, /* 0x1.0d55f2dce5d1dfffb */
+ 1.054149599440827866881, /* 0x1.0ddcbf86b09a5fff6 */
+ 1.056210497317612961855, /* 0x1.0e63cfa7abc97fffd */
+ 1.058275424318780855142, /* 0x1.0eeb23619c146fffb */
+ 1.060344388322010722446, /* 0x1.0f72bad65714bffff */
+ 1.062417397220589476718, /* 0x1.0ffa9627c38d30004 */
+ 1.064494458915699715017, /* 0x1.1082b577d0eef0003 */
+ 1.066575581342167566880, /* 0x1.110b18e893a90000a */
+ 1.068660772440545025953, /* 0x1.1193c09c267610006 */
+ 1.070750040138235936705, /* 0x1.121cacb4959befff6 */
+ 1.072843392435016474095, /* 0x1.12a5dd543cf36ffff */
+ 1.074940837302467588937, /* 0x1.132f529d59552000b */
+ 1.077042382749654914030, /* 0x1.13b90cb250d08fff5 */
+ 1.079148036789447484528, /* 0x1.14430bb58da3dfff9 */
+ 1.081257807444460983297, /* 0x1.14cd4fc984c4a000e */
+ 1.083371702785017154417, /* 0x1.1557d910df9c7000e */
+ 1.085489730853784307038, /* 0x1.15e2a7ae292d30002 */
+ 1.087611899742884524772, /* 0x1.166dbbc422d8c0004 */
+ 1.089738217537583819804, /* 0x1.16f9157586772ffff */
+ 1.091868692357631731528, /* 0x1.1784b4e533cacfff0 */
+ 1.094003332327482702577, /* 0x1.18109a360fc23fff2 */
+ 1.096142145591650907149, /* 0x1.189cc58b155a70008 */
+ 1.098285140311341168136, /* 0x1.1929370751ea50002 */
+ 1.100432324652149906842, /* 0x1.19b5eecdd79cefff0 */
+ 1.102583706811727015711, /* 0x1.1a42ed01dbdba000e */
+ 1.104739294993289488947, /* 0x1.1ad031c69a2eafff0 */
+ 1.106899097422573863281, /* 0x1.1b5dbd3f66e120003 */
+ 1.109063122341542140286, /* 0x1.1beb8f8fa8150000b */
+ 1.111231377994659874592, /* 0x1.1c79a8dac6ad0fff4 */
+ 1.113403872669181282605, /* 0x1.1d0809445a97ffffc */
+ 1.115580614653132185460, /* 0x1.1d96b0effc9db000e */
+ 1.117761612217810673898, /* 0x1.1e25a001332190000 */
+ 1.119946873713312474002, /* 0x1.1eb4d69bdb2a9fff1 */
+ 1.122136407473298902480, /* 0x1.1f4454e3bfae00006 */
+ 1.124330221845670330058, /* 0x1.1fd41afcbb48bfff8 */
+ 1.126528325196519908506, /* 0x1.2064290abc98c0001 */
+ 1.128730725913251964394, /* 0x1.20f47f31c9aa7000f */
+ 1.130937432396844410880, /* 0x1.21851d95f776dfff0 */
+ 1.133148453059692917203, /* 0x1.2216045b6784efffa */
+ 1.135363796355857157764, /* 0x1.22a733a6692ae0004 */
+ 1.137583470716100553249, /* 0x1.2338ab9b3221a0004 */
+ 1.139807484614418608939, /* 0x1.23ca6c5e27aadfff7 */
+ 1.142035846532929888057, /* 0x1.245c7613b7f6c0004 */
+ 1.144268564977221958089, /* 0x1.24eec8e06b035000c */
+ 1.146505648458203463465, /* 0x1.258164e8cea85fff8 */
+ 1.148747105501412235671, /* 0x1.26144a5180d380009 */
+ 1.150992944689175123667, /* 0x1.26a7793f5de2efffa */
+ 1.153243174560058870217, /* 0x1.273af1d712179000d */
+ 1.155497803703682491111, /* 0x1.27ceb43d81d42fff1 */
+ 1.157756840726344771440, /* 0x1.2862c097a3d29000c */
+ 1.160020294239811677834, /* 0x1.28f7170a74cf4fff1 */
+ 1.162288172883275239058, /* 0x1.298bb7bb0faed0004 */
+ 1.164560485298402170388, /* 0x1.2a20a2ce920dffff4 */
+ 1.166837240167474476460, /* 0x1.2ab5d86a4631ffff6 */
+ 1.169118446164539637555, /* 0x1.2b4b58b36d5220009 */
+ 1.171404112007080167155, /* 0x1.2be123cf786790002 */
+ 1.173694246390975415341, /* 0x1.2c7739e3c0aac000d */
+ 1.175988858069749065617, /* 0x1.2d0d9b15deb58fff6 */
+ 1.178287955789017793514, /* 0x1.2da4478b627040002 */
+ 1.180591548323240091978, /* 0x1.2e3b3f69fb794fffc */
+ 1.182899644456603782686, /* 0x1.2ed282d76421d0004 */
+ 1.185212252993012693694, /* 0x1.2f6a11f96c685fff3 */
+ 1.187529382762033236513, /* 0x1.3001ecf60082ffffa */
+ 1.189851042595508889847, /* 0x1.309a13f30f28a0004 */
+ 1.192177241354644978669, /* 0x1.31328716a758cfff7 */
+ 1.194507987909589896687, /* 0x1.31cb4686e1e85fffb */
+ 1.196843291137896336843, /* 0x1.32645269dfd04000a */
+ 1.199183159977805113226, /* 0x1.32fdaae604c39000f */
+ 1.201527603343041317132, /* 0x1.339750219980dfff3 */
+ 1.203876630171082595692, /* 0x1.3431424300e480007 */
+ 1.206230249419600664189, /* 0x1.34cb8170b3fee000e */
+ 1.208588470077065268869, /* 0x1.35660dd14dbd4fffc */
+ 1.210951301134513435915, /* 0x1.3600e78b6bdfc0005 */
+ 1.213318751604272271958, /* 0x1.369c0ec5c38ebfff2 */
+ 1.215690830512196507537, /* 0x1.373783a718d29000f */
+ 1.218067546930756250870, /* 0x1.37d3465662f480007 */
+ 1.220448909901335365929, /* 0x1.386f56fa770fe0008 */
+ 1.222834928513994334780, /* 0x1.390bb5ba5fc540004 */
+ 1.225225611877684750397, /* 0x1.39a862bd3c7a8fff3 */
+ 1.227620969111500981433, /* 0x1.3a455e2a37bcafffd */
+ 1.230021009336254911271, /* 0x1.3ae2a8287dfbefff6 */
+ 1.232425741726685064472, /* 0x1.3b8040df76f39fffa */
+ 1.234835175450728295084, /* 0x1.3c1e287682e48fff1 */
+ 1.237249319699482263931, /* 0x1.3cbc5f151b86bfff8 */
+ 1.239668183679933477545, /* 0x1.3d5ae4e2cc0a8000f */
+ 1.242091776620540377629, /* 0x1.3df9ba07373bf0006 */
+ 1.244520107762172811399, /* 0x1.3e98deaa0d8cafffe */
+ 1.246953186383919165383, /* 0x1.3f3852f32973efff0 */
+ 1.249391019292643401078, /* 0x1.3fd816ffc72b90001 */
+ 1.251833623164381181797, /* 0x1.40782b17863250005 */
+ 1.254280999953110153911, /* 0x1.41188f42caf400000 */
+ 1.256733161434815393410, /* 0x1.41b943b42945bfffd */
+ 1.259190116985283935980, /* 0x1.425a4893e5f10000a */
+ 1.261651875958665236542, /* 0x1.42fb9e0a2df4c0009 */
+ 1.264118447754797758244, /* 0x1.439d443f608c4fff9 */
+ 1.266589841787181258708, /* 0x1.443f3b5bebf850008 */
+ 1.269066067469190262045, /* 0x1.44e183883e561fff7 */
+ 1.271547134259576328224, /* 0x1.45841cecf7a7a0001 */
+ 1.274033051628237434048, /* 0x1.462707b2c43020009 */
+ 1.276523829025464573684, /* 0x1.46ca44023aa410007 */
+ 1.279019475999373156531, /* 0x1.476dd2045d46ffff0 */
+ 1.281520002043128991825, /* 0x1.4811b1e1f1f19000b */
+ 1.284025416692967214122, /* 0x1.48b5e3c3edd74fff4 */
+ 1.286535729509738823464, /* 0x1.495a67d3613c8fff7 */
+ 1.289050950070396384145, /* 0x1.49ff3e396e19d000b */
+ 1.291571087985403654081, /* 0x1.4aa4671f5b401fff1 */
+ 1.294096152842774794011, /* 0x1.4b49e2ae56d19000d */
+ 1.296626154297237043484, /* 0x1.4befb10fd84a3fff4 */
+ 1.299161101984141142272, /* 0x1.4c95d26d41d84fff8 */
+ 1.301701005575179204100, /* 0x1.4d3c46f01d9f0fff3 */
+ 1.304245874766450485904, /* 0x1.4de30ec21097d0003 */
+ 1.306795719266019562007, /* 0x1.4e8a2a0ccce3d0002 */
+ 1.309350548792467483458, /* 0x1.4f3198fa10346fff5 */
+ 1.311910373099227200545, /* 0x1.4fd95bb3be8cffffd */
+ 1.314475201942565174546, /* 0x1.50817263bf0e5fffb */
+ 1.317045045107389400535, /* 0x1.5129dd3418575000e */
+ 1.319619912422941299109, /* 0x1.51d29c4f01c54ffff */
+ 1.322199813675649204855, /* 0x1.527bafde83a310009 */
+ 1.324784758729532718739, /* 0x1.5325180cfb8b3fffd */
+ 1.327374757430096474625, /* 0x1.53ced504b2bd0fff4 */
+ 1.329969819671041886272, /* 0x1.5478e6f02775e0001 */
+ 1.332569955346704748651, /* 0x1.55234df9d8a59fff8 */
+ 1.335175174370685002822, /* 0x1.55ce0a4c5a6a9fff6 */
+ 1.337785486688218616860, /* 0x1.56791c1263abefff7 */
+ 1.340400902247843806217, /* 0x1.57248376aef21fffa */
+ 1.343021431036279800211, /* 0x1.57d040a420c0bfff3 */
+ 1.345647083048053138662, /* 0x1.587c53c5a630f0002 */
+ 1.348277868295411074918, /* 0x1.5928bd063fd7bfff9 */
+ 1.350913796821875845231, /* 0x1.59d57c9110ad60006 */
+ 1.353554878672557082439, /* 0x1.5a8292913d68cfffc */
+ 1.356201123929036356254, /* 0x1.5b2fff3212db00007 */
+ 1.358852542671913132777, /* 0x1.5bddc29edcc06fff3 */
+ 1.361509145047255398051, /* 0x1.5c8bdd032ed16000f */
+ 1.364170941142184734180, /* 0x1.5d3a4e8a5bf61fff4 */
+ 1.366837941171020309735, /* 0x1.5de9176042f1effff */
+ 1.369510155261156381121, /* 0x1.5e9837b062f4e0005 */
+ 1.372187593620959988833, /* 0x1.5f47afa69436cfff1 */
+ 1.374870266463378287715, /* 0x1.5ff77f6eb3f8cfffd */
+ 1.377558184010425845733, /* 0x1.60a7a734a9742fff9 */
+ 1.380251356531521533853, /* 0x1.6158272490016000c */
+ 1.382949794301995272203, /* 0x1.6208ff6a8978a000f */
+ 1.385653507605306700170, /* 0x1.62ba3032c0a280004 */
+ 1.388362506772382154503, /* 0x1.636bb9a994784000f */
+ 1.391076802081129493127, /* 0x1.641d9bfb29a7bfff6 */
+ 1.393796403973427855412, /* 0x1.64cfd7545928b0002 */
+ 1.396521322756352656542, /* 0x1.65826be167badfff8 */
+ 1.399251568859207761660, /* 0x1.663559cf20826000c */
+ 1.401987152677323100733, /* 0x1.66e8a14a29486fffc */
+ 1.404728084651919228815, /* 0x1.679c427f5a4b6000b */
+ 1.407474375243217723560, /* 0x1.68503d9ba0add000f */
+ 1.410226034922914983815, /* 0x1.690492cbf6303fff9 */
+ 1.412983074197955213304, /* 0x1.69b9423d7b548fff6 */
+};
+
+/* All floating-point numbers can be put in one of these categories.  */
+enum
+  {
+    FP_NAN,
+# define FP_NAN FP_NAN
+    FP_INFINITE,
+# define FP_INFINITE FP_INFINITE
+    FP_ZERO,
+# define FP_ZERO FP_ZERO
+    FP_SUBNORMAL,
+# define FP_SUBNORMAL FP_SUBNORMAL
+    FP_NORMAL
+# define FP_NORMAL FP_NORMAL
+  };
+
+
+int
+__fpclassifyf (float x)
+{
+  uint32_t wx;
+  int retval = FP_NORMAL;
+
+  GET_FLOAT_WORD (wx, x);
+  wx &= 0x7fffffff;
+  if (wx == 0)
+    retval = FP_ZERO;
+  else if (wx < 0x800000)
+    retval = FP_SUBNORMAL;
+  else if (wx >= 0x7f800000)
+    retval = wx > 0x7f800000 ? FP_NAN : FP_INFINITE;
+
+  return retval;
+}
+
+
+int
+__isinff (float x)
+{
+	int32_t ix,t;
+	GET_FLOAT_WORD(ix,x);
+	t = ix & 0x7fffffff;
+	t ^= 0x7f800000;
+	t |= -t;
+	return ~(t >> 31) & (ix >> 30);
+}
+
+/* Return nonzero value if arguments are unordered.  */
+#  define fpclassify(x) \
+     (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassifyf (x))
+
+# ifndef isunordered
+#  define isunordered(u, v) \
+  (__extension__							      \
+   ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);			      \
+      fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
+# endif
+
+/* Return nonzero value if X is less than Y.  */
+# ifndef isless
+#  define isless(x, y) \
+  (__extension__							      \
+   ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);			      \
+      !isunordered (__x, __y) && __x < __y; }))
+# endif
+
+/* Return nonzero value if X is greater than Y.  */
+# ifndef isgreater
+#  define isgreater(x, y) \
+  (__extension__							      \
+   ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);			      \
+      !isunordered (__x, __y) && __x > __y; }))
+# endif
+
+union ieee754_double
+  {
+    double d;
+
+    /* This is the IEEE 754 double-precision format.  */
+    struct
+      {
+#if	defined(ROCKBOX_BIG_ENDIAN)
+	unsigned int negative:1;
+	unsigned int exponent:11;
+	/* Together these comprise the mantissa.  */
+	unsigned int mantissa0:20;
+	unsigned int mantissa1:32;
+#else
+# if	__FLOAT_WORD_ORDER == __BIG_ENDIAN
+	unsigned int mantissa0:20;
+	unsigned int exponent:11;
+	unsigned int negative:1;
+	unsigned int mantissa1:32;
+# else
+	/* Together these comprise the mantissa.  */
+	unsigned int mantissa1:32;
+	unsigned int mantissa0:20;
+	unsigned int exponent:11;
+	unsigned int negative:1;
+# endif
+#endif				/* Little endian.  */
+      } ieee;
+
+    /* This format makes it easier to see if a NaN is a signalling NaN.  */
+    struct
+      {
+#if	defined(ROCKBOX_BIG_ENDIAN)
+	unsigned int negative:1;
+	unsigned int exponent:11;
+	unsigned int quiet_nan:1;
+	/* Together these comprise the mantissa.  */
+	unsigned int mantissa0:19;
+	unsigned int mantissa1:32;
+#else
+# if	__FLOAT_WORD_ORDER == __BIG_ENDIAN
+	unsigned int mantissa0:19;
+	unsigned int quiet_nan:1;
+	unsigned int exponent:11;
+	unsigned int negative:1;
+	unsigned int mantissa1:32;
+# else
+	/* Together these comprise the mantissa.  */
+	unsigned int mantissa1:32;
+	unsigned int mantissa0:19;
+	unsigned int quiet_nan:1;
+	unsigned int exponent:11;
+	unsigned int negative:1;
+# endif
+#endif
+      } ieee_nan;
+  };
+
+
+static const volatile float TWOM100 = 7.88860905e-31;
+static const volatile float TWO127 = 1.7014118346e+38;
+
+float rb_exp(float x)
+{
+  static const float himark = 88.72283935546875;
+  static const float lomark = -103.972084045410;
+  /* Check for usual case.  */
+  if (isless (x, himark) && isgreater (x, lomark))
+    {
+      static const float THREEp42 = 13194139533312.0;
+      static const float THREEp22 = 12582912.0;
+      /* 1/ln(2).  */
+#undef M_1_LN2
+      static const float M_1_LN2 = 1.44269502163f;
+      /* ln(2) */
+#undef M_LN2
+      static const double M_LN2 = .6931471805599452862;
+
+      int tval;
+      double x22, t, result, dx;
+      float n, delta;
+      union ieee754_double ex2_u;
+#ifndef ROCKBOX
+      fenv_t oldenv;
+
+      feholdexcept (&oldenv);
+#endif
+
+#ifdef FE_TONEAREST
+      fesetround (FE_TONEAREST);
+#endif
+
+      /* Calculate n.  */
+      n = x * M_1_LN2 + THREEp22;
+      n -= THREEp22;
+      dx = x - n*M_LN2;
+
+      /* Calculate t/512.  */
+      t = dx + THREEp42;
+      t -= THREEp42;
+      dx -= t;
+
+      /* Compute tval = t.  */
+      tval = (int) (t * 512.0);
+
+      if (t >= 0)
+	delta = - __exp_deltatable[tval];
+      else
+	delta = __exp_deltatable[-tval];
+
+      /* Compute ex2 = 2^n e^(t/512+delta[t]).  */
+      ex2_u.d = __exp_atable[tval+177];
+      ex2_u.ieee.exponent += (int) n;
+
+      /* Approximate e^(dx+delta) - 1, using a second-degree polynomial,
+	 with maximum error in [-2^-10-2^-28,2^-10+2^-28]
+	 less than 5e-11.  */
+      x22 = (0.5000000496709180453 * dx + 1.0000001192102037084) * dx + delta;
+
+      /* Return result.  */
+#ifndef ROCKBOX
+      fesetenv (&oldenv);
+#endif
+
+      result = x22 * ex2_u.d + ex2_u.d;
+      return (float) result;
+    }
+  /* Exceptional cases:  */
+  else if (isless (x, himark))
+    {
+      if (__isinff (x))
+	/* e^-inf == 0, with no error.  */
+	return 0;
+      else
+	/* Underflow */
+	return TWOM100 * TWOM100;
+    }
+  else
+    /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
+    return TWO127*x;
+}
+
+
+/* Division with rest, original. */
+div_t div(int x, int y)
+{
+    div_t result;
+
+    result.quot = x / y;
+    result.rem = x % y;
+
+    /* Addition from glibc-2.8: */
+    if(x >= 0 && result.rem < 0)
+    {
+        result.quot += 1;
+        result.rem -= y;
+    }
+
+    return result;
+}
+
+
+/* Placeholder function. */
+/* Originally defined in s_midi.c */
+void sys_listmididevs(void)
+{
+}
+
+/* Placeholder function,
+   as we do sleep in the core thread
+   and not in the scheduler function. */
+/* Originally defined in s_inter.c */
+void sys_microsleep(int microsec)
+{
+    (void) microsec;
+}
+
+/* Get running time in milliseconds. */
+/* Originally defined in s_inter.c */
+extern uint64_t runningtime;
+t_time sys_getrealtime(void)
+{
+    return runningtime;
+}
+
+/* Place holder, as we do no IPC. */
+/* Originally defined in s_inter.c */
+void glob_ping(void* dummy)
+{
+    (void) dummy;
+}
+
+/* Call to quit. */
+/* Originally defined in s_inter.c */
+extern bool quit;
+void glob_quit(void* dummy)
+{
+    (void) dummy;
+
+    static bool reentered = false;
+
+    if(!reentered)
+    {
+        reentered = true;
+
+        /* Close audio subsystem. */
+        sys_close_audio();
+
+        /* Stop main loop. */
+        quit = true;
+    }
+}
+
+/* Open file. Originally in s_main.c */
+void glob_evalfile(t_pd *ignore, t_symbol *name, t_symbol *dir);
+void openit(const char *dirname, const char *filename)
+{
+    char dirbuf[MAXPDSTRING], *nameptr;
+
+    /* Workaround: If the file resides in the root directory,
+                   add a trailing slash to prevent directory part
+                   of the filename from being removed. */
+    char ffilename[MAXPDSTRING];
+    ffilename[0] = '/';
+    ffilename[1] = '\0';
+    strcat(ffilename, filename);
+
+    int fd = open_via_path(dirname, ffilename, "", dirbuf, &nameptr,
+    	MAXPDSTRING, 0);
+    if (fd)
+    {
+    	close (fd);
+    	glob_evalfile(0, gensym(nameptr), gensym(dirbuf));
+    }
+    else
+    	error("%s: can't open", filename);
+}
+
+
+/* Get current working directory. */
+extern char* filename;
+char* rb_getcwd(char* buf, ssize_t size)
+{
+    char* end_of_dir = strrchr(filename, '/');
+
+    /* Check whether buffer may hold enough data. */
+    if(size < end_of_dir - filename)
+        return NULL;
+
+    /* Copy current working directory to buffer. */
+    strncpy(buf, filename, end_of_dir - filename);
+    return buf;
+}
+
+
+/* Execute instructions supplied on command-line.
+   Basically a placeholder, because the only
+   command line argument we get is the name of the .pd file. */
+/* Originally defined in s_main.c */
+extern t_namelist* sys_openlist;
+void glob_initfromgui(void *dummy, t_symbol *s, int argc, t_atom *argv)
+{
+    (void) dummy;
+    (void) s;
+    (void) argc;
+    (void) argv;
+
+    t_namelist *nl;
+    char cwd[MAXPDSTRING];
+
+    /* Get current working directory. */
+    rb_getcwd(cwd, MAXPDSTRING);
+
+    /* open patches specifies with "-open" args */
+    for(nl = sys_openlist; nl; nl = nl->nl_next)
+        openit(cwd, nl->nl_string);
+    namelist_free(sys_openlist);
+    sys_openlist = 0;
+}
+
+/* Fake GUI start. Originally in s_inter.c */
+static int defaultfontshit[] = {
+    8, 5, 9, 10, 6, 10, 12, 7, 13, 14, 9, 17, 16, 10, 19, 24, 15, 28,
+    	24, 15, 28};
+extern t_binbuf* inbinbuf;
+int sys_startgui(const char *guidir)
+{
+    unsigned int i;
+    t_atom zz[23];
+    char cmdbuf[4*MAXPDSTRING];
+
+    (void) guidir;
+
+    inbinbuf = binbuf_new();
+
+    if(!rb_getcwd(cmdbuf, MAXPDSTRING))
+        strcpy(cmdbuf, ".");
+    SETSYMBOL(zz, gensym(cmdbuf));
+    for (i = 1; i < 22; i++)
+        SETFLOAT(zz + i, defaultfontshit[i-1]);
+    SETFLOAT(zz+22,0);
+
+    glob_initfromgui(0, 0, 23, zz);
+
+    return 0;
+}
+
+/* Return default DAC block size. */
+/* Originally defined in s_main.c */
+int sys_getblksize(void)
+{
+    return (DEFDACBLKSIZE);
+}
+
+/* Find library directory and set it. */
+void sys_findlibdir(const char* filename)
+{
+    char sbuf[MAXPDSTRING];
+
+    (void) filename;
+
+    /* Make current working directory the system library directory. */
+    rb_getcwd(sbuf, MAXPDSTRING);
+    sys_libdir = gensym(sbuf);
+}