Patchwork Remove unused math files

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Submitter Wilco Dijkstra
Date Aug. 23, 2018, 11:06 a.m.
Message ID <DB5PR08MB1030F9A26572A5A40BDBA00083370@DB5PR08MB1030.eurprd08.prod.outlook.com>
Download mbox | patch
Permalink /patch/29025/
State New
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Comments

Wilco Dijkstra - Aug. 23, 2018, 11:06 a.m.
Joseph Myers wrote:

> This doesn't look like a complete set of such files to remove.  I'd expect 
> the m68k and ia64 versions of e_rem_pio2.c, e_rem_pio2f.c, k_rem_pio2f.c 
> to be removed at the same time.

Indeed, using find rather than grep shows up some more empty files, including 
a one in i386. Here is the updated version:


Remove empty files due to the sin/cos improvements: k_sinf.c, k_cosf.c,
k_cos.c, k_sin.c.  After the tanf change s_rem_pio2f.c and k_rem_pio2f.c
(and the ia64, m68k and powerpc equivalents) are no longer used, 
so remove them.  All e_rem_pio2.c files were already empty or commented
out, so remove them too.

Passes buildmanyglibcs (only i686 compiler fails to build).

OK for commit?

ChangeLog:
2018-08-23  Wilco Dijkstra  <wdijkstr@arm.com>

	* math/Makefile: Remove empty files k_sin(f).c, k_cos(f).c. 
	Remove unused files e_rem_pio2(f).c, k_rem_pio2f.c.
	* sysdeps/i386/fpu/e_rem_pio2.c: Delete file.
	* sysdeps/ia64/fpu/e_rem_pio2.c: Likewise.
	* sysdeps/ia64/fpu/e_rem_pio2f.c: Likewise.
	* sysdeps/ia64/fpu/k_rem_pio2f.c: Likewise.
	* sysdeps/ieee754/dbl-64/e_rem_pio2.c: Likewise.
	* sysdeps/ieee754/dbl-64/k_cos.c: Likewise.
	* sysdeps/ieee754/dbl-64/k_sin.c: Likewise.
	* sysdeps/ieee754/flt-32/e_rem_pio2f.c: Likewise.
	* sysdeps/ieee754/flt-32/k_cosf.c: Likewise.
	* sysdeps/ieee754/flt-32/k_rem_pio2f.c: Likewise.
	* sysdeps/ieee754/flt-32/k_sinf.c: Likewise.
	* sysdeps/m68k/m680x0/fpu/e_rem_pio2.c: Likewise
	* sysdeps/m68k/m680x0/fpu/e_rem_pio2f.c: Likewise
	* sysdeps/m68k/m680x0/fpu/k_rem_pio2f.c: Likewise
	* sysdeps/powerpc/fpu/e_rem_pio2f.c: Likewise.
	* sysdeps/powerpc/fpu/k_rem_pio2f.c: Likewise.

--
Joseph Myers - Aug. 23, 2018, 7:53 p.m.
On Thu, 23 Aug 2018, Wilco Dijkstra wrote:

> Joseph Myers wrote:
> 
> > This doesn't look like a complete set of such files to remove.  I'd expect 
> > the m68k and ia64 versions of e_rem_pio2.c, e_rem_pio2f.c, k_rem_pio2f.c 
> > to be removed at the same time.
> 
> Indeed, using find rather than grep shows up some more empty files, including 
> a one in i386. Here is the updated version:

This version is OK.

Patch

diff --git a/math/Makefile b/math/Makefile
index 5210430e81d21776b6de37dc12c475fc5841371e..bff726fe81415f3d81227dd843a8221cb0792c1d 100644
--- a/math/Makefile
+++ b/math/Makefile
@@ -64,9 +64,9 @@  gen-libm-calls = cargF conjF cimagF crealF cabsF s_cacosF		  \
 libm-calls =								  \
 	e_acosF e_acoshF e_asinF e_atan2F e_atanhF e_coshF e_expF e_fmodF \
 	e_hypotF e_j0F e_j1F e_jnF e_lgammaF_r e_logF e_log10F e_powF	  \
-	e_rem_pio2F e_remainderF e_scalbF e_sinhF e_sqrtF e_gammaF_r	  \
+	e_remainderF e_scalbF e_sinhF e_sqrtF e_gammaF_r	  \
 	e_ilogbF							  \
-	k_cosF k_sinF k_tanF s_asinhF s_atanF s_cbrtF			  \
+	k_tanF s_asinhF s_atanF s_cbrtF					  \
 	s_ceilF s_cosF s_erfF s_expm1F s_fabsF				  \
 	s_floorF s_log1pF s_logbF				  \
 	s_nextafterF s_nexttowardF s_rintF s_scalblnF			  \
@@ -119,23 +119,25 @@  test-types-basic = ldouble double float
 
 # long double support
 type-ldouble-suffix := l
-type-ldouble-routines := t_sincosl k_sincosl s_iscanonicall
+type-ldouble-routines := t_sincosl k_sinl k_cosl k_sincosl s_iscanonicall \
+			 e_rem_pio2l
 type-ldouble-yes := ldouble
 
 # double support
 type-double-suffix :=
 type-double-routines := branred doasin dosincos mpa mpatan2	\
-		       mpatan mpsqrt mptan sincos32	\
-		       sincostab k_rem_pio2
+		       k_rem_pio2 mpatan mpsqrt mptan sincos32	\
+		       sincostab
 
 # float support
 type-float-suffix := f
-type-float-routines := k_rem_pio2f math_errf e_exp2f_data e_logf_data	\
+type-float-routines := math_errf e_exp2f_data e_logf_data	\
 		       e_log2f_data e_powf_log2_data s_sincosf_data
 
 # _Float128 support
 type-float128-suffix := f128
-type-float128-routines := t_sincosf128 k_sincosf128
+type-float128-routines := t_sincosf128 k_sinf128 k_cosf128 k_sincosf128 \
+			  e_rem_pio2f128
 type-float128-yes := float128
 
 # _Float64x may be supported, only as an alias type.
diff --git a/sysdeps/i386/fpu/e_rem_pio2.c b/sysdeps/i386/fpu/e_rem_pio2.c
deleted file mode 100644
index 1347b0468c925e6ea21d530b61dfce4b05d4822c..0000000000000000000000000000000000000000
--- a/sysdeps/i386/fpu/e_rem_pio2.c
+++ /dev/null
@@ -1,3 +0,0 @@ 
-/* Empty.  This file is only meant to avoid compiling the file with the
-   same name in the libm-ieee754 directory.  The code is not used since
-   there is an assembler version for all users of this file.  */
diff --git a/sysdeps/ia64/fpu/e_rem_pio2.c b/sysdeps/ia64/fpu/e_rem_pio2.c
deleted file mode 100644
index 41254ae60a03a2e76edd28d3adcc68e182966cb2..0000000000000000000000000000000000000000
--- a/sysdeps/ia64/fpu/e_rem_pio2.c
+++ /dev/null
@@ -1 +0,0 @@ 
-/* Not needed. */
diff --git a/sysdeps/ia64/fpu/e_rem_pio2f.c b/sysdeps/ia64/fpu/e_rem_pio2f.c
deleted file mode 100644
index 41254ae60a03a2e76edd28d3adcc68e182966cb2..0000000000000000000000000000000000000000
--- a/sysdeps/ia64/fpu/e_rem_pio2f.c
+++ /dev/null
@@ -1 +0,0 @@ 
-/* Not needed. */
diff --git a/sysdeps/ia64/fpu/k_rem_pio2f.c b/sysdeps/ia64/fpu/k_rem_pio2f.c
deleted file mode 100644
index 41254ae60a03a2e76edd28d3adcc68e182966cb2..0000000000000000000000000000000000000000
--- a/sysdeps/ia64/fpu/k_rem_pio2f.c
+++ /dev/null
@@ -1 +0,0 @@ 
-/* Not needed. */
diff --git a/sysdeps/ieee754/dbl-64/e_rem_pio2.c b/sysdeps/ieee754/dbl-64/e_rem_pio2.c
deleted file mode 100644
index 81a3d073d4142f943b9b09c5ee97e8d51e1d75cf..0000000000000000000000000000000000000000
--- a/sysdeps/ieee754/dbl-64/e_rem_pio2.c
+++ /dev/null
@@ -1,193 +0,0 @@ 
-#ifdef NOT_NEEDED_ANYMORE
-
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-
-/* __ieee754_rem_pio2(x,y)
- *
- * return the remainder of x rem pi/2 in y[0]+y[1]
- * use __kernel_rem_pio2()
- */
-
-#include <math.h>
-#include <math_private.h>
-
-/*
- * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
- */
-static const int32_t two_over_pi[] = {
-0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
-0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
-0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
-0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
-0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
-0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
-0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
-0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
-0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
-0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
-0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
-};
-
-static const int32_t npio2_hw[] = {
-0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
-0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
-0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
-0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
-0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
-0x404858EB, 0x404921FB,
-};
-
-/*
- * invpio2:  53 bits of 2/pi
- * pio2_1:   first  33 bit of pi/2
- * pio2_1t:  pi/2 - pio2_1
- * pio2_2:   second 33 bit of pi/2
- * pio2_2t:  pi/2 - (pio2_1+pio2_2)
- * pio2_3:   third  33 bit of pi/2
- * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
- */
-
-static const double
-  zero    = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
-  half    = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
-  two24   = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
-  invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
-  pio2_1  = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
-  pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
-  pio2_2  = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
-  pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
-  pio2_3  = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
-  pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
-
-int32_t
-__ieee754_rem_pio2 (double x, double *y)
-{
-  double z, w, t, r, fn;
-  double tx[3];
-  int32_t e0, i, j, nx, n, ix, hx;
-  uint32_t low;
-
-  GET_HIGH_WORD (hx, x);                /* high word of x */
-  ix = hx & 0x7fffffff;
-  if (ix <= 0x3fe921fb)      /* |x| ~<= pi/4 , no need for reduction */
-    {
-      y[0] = x; y[1] = 0; return 0;
-    }
-  if (ix < 0x4002d97c)       /* |x| < 3pi/4, special case with n=+-1 */
-    {
-      if (hx > 0)
-	{
-	  z = x - pio2_1;
-	  if (ix != 0x3ff921fb)         /* 33+53 bit pi is good enough */
-	    {
-	      y[0] = z - pio2_1t;
-	      y[1] = (z - y[0]) - pio2_1t;
-	    }
-	  else                          /* near pi/2, use 33+33+53 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 != 0x3ff921fb)         /* 33+53 bit pi is good enough */
-	    {
-	      y[0] = z + pio2_1t;
-	      y[1] = (z - y[0]) + pio2_1t;
-	    }
-	  else                          /* near pi/2, use 33+33+53 bit pi */
-	    {
-	      z += pio2_2;
-	      y[0] = z + pio2_2t;
-	      y[1] = (z - y[0]) + pio2_2t;
-	    }
-	  return -1;
-	}
-    }
-  if (ix <= 0x413921fb)      /* |x| ~<= 2^19*(pi/2), medium size */
-    {
-      t = fabs (x);
-      n = (int32_t) (t * invpio2 + half);
-      fn = (double) n;
-      r = t - fn * pio2_1;
-      w = fn * pio2_1t;         /* 1st round good to 85 bit */
-      if (n < 32 && ix != npio2_hw[n - 1])
-	{
-	  y[0] = r - w;         /* quick check no cancellation */
-	}
-      else
-	{
-	  uint32_t high;
-	  j = ix >> 20;
-	  y[0] = r - w;
-	  GET_HIGH_WORD (high, y[0]);
-	  i = j - ((high >> 20) & 0x7ff);
-	  if (i > 16)       /* 2nd iteration needed, good to 118 */
-	    {
-	      t = r;
-	      w = fn * pio2_2;
-	      r = t - w;
-	      w = fn * pio2_2t - ((t - r) - w);
-	      y[0] = r - w;
-	      GET_HIGH_WORD (high, y[0]);
-	      i = j - ((high >> 20) & 0x7ff);
-	      if (i > 49)       /* 3rd iteration need, 151 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 >= 0x7ff00000)                 /* x is inf or NaN */
-    {
-      y[0] = y[1] = x - x; return 0;
-    }
-  /* set z = scalbn(|x|,ilogb(x)-23) */
-  GET_LOW_WORD (low, x);
-  SET_LOW_WORD (z, low);
-  e0 = (ix >> 20) - 1046;               /* e0 = ilogb(z)-23; */
-  SET_HIGH_WORD (z, ix - ((int32_t) (e0 << 20)));
-  for (i = 0; i < 2; i++)
-    {
-      tx[i] = (double) ((int32_t) (z));
-      z = (z - tx[i]) * two24;
-    }
-  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;
-}
-#endif
diff --git a/sysdeps/ieee754/dbl-64/k_cos.c b/sysdeps/ieee754/dbl-64/k_cos.c
deleted file mode 100644
index cc5c205a5fc4d7d2a5e9d09961e8710976211e6e..0000000000000000000000000000000000000000
--- a/sysdeps/ieee754/dbl-64/k_cos.c
+++ /dev/null
@@ -1 +0,0 @@ 
-/* Not needed anymore.  */
diff --git a/sysdeps/ieee754/dbl-64/k_sin.c b/sysdeps/ieee754/dbl-64/k_sin.c
deleted file mode 100644
index cc5c205a5fc4d7d2a5e9d09961e8710976211e6e..0000000000000000000000000000000000000000
--- a/sysdeps/ieee754/dbl-64/k_sin.c
+++ /dev/null
@@ -1 +0,0 @@ 
-/* Not needed anymore.  */
diff --git a/sysdeps/ieee754/flt-32/e_rem_pio2f.c b/sysdeps/ieee754/flt-32/e_rem_pio2f.c
deleted file mode 100644
index bd871a26c2e0bfdb59b937c1151c73bb167988b6..0000000000000000000000000000000000000000
--- a/sysdeps/ieee754/flt-32/e_rem_pio2f.c
+++ /dev/null
@@ -1,179 +0,0 @@ 
-/* e_rem_pio2f.c -- float version of e_rem_pio2.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.
- * ====================================================
- */
-
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: e_rem_pio2f.c,v 1.5 1995/05/10 20:46:03 jtc Exp $";
-#endif
-
-/* __ieee754_rem_pio2f(x,y)
- *
- * return the remainder of x rem pi/2 in y[0]+y[1]
- * use __kernel_rem_pio2f()
- */
-
-#include <math.h>
-#include <math_private.h>
-
-/*
- * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
- */
-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,
-};
-
-/* This array is like the one in e_rem_pio2.c, but the numbers are
-   single precision and the last 8 bits are forced to 0.  */
-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
-zero =  0.0000000000e+00, /* 0x00000000 */
-half =  5.0000000000e-01, /* 0x3f000000 */
-two8 =  2.5600000000e+02, /* 0x43800000 */
-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 __ieee754_rem_pio2f(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&0xffffffc0)!=0x3fc90fc0) { /* 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&0xffffffc0)!=0x3fc90fc0) { /* 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  = fabsf(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_pio2f(tx,y,e0,nx,2,two_over_pi);
-	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
-	return n;
-}
diff --git a/sysdeps/ieee754/flt-32/k_cosf.c b/sysdeps/ieee754/flt-32/k_cosf.c
deleted file mode 100644
index 1cc8931700702e65d29a6e2af287175d23c6b182..0000000000000000000000000000000000000000
--- a/sysdeps/ieee754/flt-32/k_cosf.c
+++ /dev/null
@@ -1 +0,0 @@ 
-/* Not needed.  */
diff --git a/sysdeps/ieee754/flt-32/k_rem_pio2f.c b/sysdeps/ieee754/flt-32/k_rem_pio2f.c
deleted file mode 100644
index ea4915b765b3e19d7c3a6e40e75fb3d8a93d1700..0000000000000000000000000000000000000000
--- a/sysdeps/ieee754/flt-32/k_rem_pio2f.c
+++ /dev/null
@@ -1,219 +0,0 @@ 
-/* k_rem_pio2f.c -- float version of k_rem_pio2.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.
- * ====================================================
- */
-
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: k_rem_pio2f.c,v 1.4 1995/05/10 20:46:28 jtc Exp $";
-#endif
-
-#include <math.h>
-#include <math-narrow-eval.h>
-#include <math_private.h>
-#include <libc-diag.h>
-
-/* In the float version, the input parameter x contains 8 bit
-   integers, not 24 bit integers.  113 bit precision is not supported.  */
-
-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
-zero   = 0.0,
-one    = 1.0,
-two8   =  2.5600000000e+02, /* 0x43800000 */
-twon8  =  3.9062500000e-03; /* 0x3b800000 */
-
-int __kernel_rem_pio2f(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  = __scalbnf(z,q0);		/* actual value of z */
-	z -= (float)8.0*__floorf(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]>>7;
-	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 -= __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 */
-		/* On s390x gcc 6.1 -O3 produces the warning "array subscript is
-		   below array bounds [-Werror=array-bounds]".  Only
-		   __ieee754_rem_pio2f calls __kernel_rem_pio2f for normal
-		   numbers and |x| ~> 2^7*(pi/2).  Thus x can't be zero and
-		   ipio2 is not zero, too.  Thus not all iq[] values can't be
-		   zero.  */
-		DIAG_PUSH_NEEDS_COMMENT;
-		DIAG_IGNORE_NEEDS_COMMENT (6.1, "-Warray-bounds");
-		for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */
-		DIAG_POP_NEEDS_COMMENT;
-
-		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 = __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 = __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:;
-		float fv = 0.0;
-		for (i=jz;i>=0;i--) fv = math_narrow_eval (fv + fq[i]);
-		y[0] = (ih==0)? fv: -fv;
-		/* GCC mainline (to be GCC 9), as of 2018-05-22 on
-		   i686, warns that fq[0] may be used uninitialized.
-		   This is not possible because jz is always
-		   nonnegative when the above loop initializing fq is
-		   executed, because the result is never zero to full
-		   precision (this function is not called for zero
-		   arguments).  */
-		DIAG_PUSH_NEEDS_COMMENT;
-		DIAG_IGNORE_NEEDS_COMMENT (9, "-Wmaybe-uninitialized");
-		fv = math_narrow_eval (fq[0]-fv);
-		DIAG_POP_NEEDS_COMMENT;
-		for (i=1;i<=jz;i++) fv = math_narrow_eval (fv + fq[i]);
-		y[1] = (ih==0)? fv: -fv;
-		break;
-	    case 3:	/* painful */
-		for (i=jz;i>0;i--) {
-		    float fv = math_narrow_eval (fq[i-1]+fq[i]);
-		    fq[i]  += fq[i-1]-fv;
-		    fq[i-1] = fv;
-		}
-		for (i=jz;i>1;i--) {
-		    float fv = math_narrow_eval (fq[i-1]+fq[i]);
-		    fq[i]  += fq[i-1]-fv;
-		    fq[i-1] = fv;
-		}
-		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;
-}
diff --git a/sysdeps/ieee754/flt-32/k_sinf.c b/sysdeps/ieee754/flt-32/k_sinf.c
deleted file mode 100644
index 1cc8931700702e65d29a6e2af287175d23c6b182..0000000000000000000000000000000000000000
--- a/sysdeps/ieee754/flt-32/k_sinf.c
+++ /dev/null
@@ -1 +0,0 @@ 
-/* Not needed.  */
diff --git a/sysdeps/m68k/m680x0/fpu/e_rem_pio2.c b/sysdeps/m68k/m680x0/fpu/e_rem_pio2.c
deleted file mode 100644
index 1347b0468c925e6ea21d530b61dfce4b05d4822c..0000000000000000000000000000000000000000
--- a/sysdeps/m68k/m680x0/fpu/e_rem_pio2.c
+++ /dev/null
@@ -1,3 +0,0 @@ 
-/* Empty.  This file is only meant to avoid compiling the file with the
-   same name in the libm-ieee754 directory.  The code is not used since
-   there is an assembler version for all users of this file.  */
diff --git a/sysdeps/m68k/m680x0/fpu/e_rem_pio2f.c b/sysdeps/m68k/m680x0/fpu/e_rem_pio2f.c
deleted file mode 100644
index 1347b0468c925e6ea21d530b61dfce4b05d4822c..0000000000000000000000000000000000000000
--- a/sysdeps/m68k/m680x0/fpu/e_rem_pio2f.c
+++ /dev/null
@@ -1,3 +0,0 @@ 
-/* Empty.  This file is only meant to avoid compiling the file with the
-   same name in the libm-ieee754 directory.  The code is not used since
-   there is an assembler version for all users of this file.  */
diff --git a/sysdeps/m68k/m680x0/fpu/k_rem_pio2f.c b/sysdeps/m68k/m680x0/fpu/k_rem_pio2f.c
deleted file mode 100644
index 1347b0468c925e6ea21d530b61dfce4b05d4822c..0000000000000000000000000000000000000000
--- a/sysdeps/m68k/m680x0/fpu/k_rem_pio2f.c
+++ /dev/null
@@ -1,3 +0,0 @@ 
-/* Empty.  This file is only meant to avoid compiling the file with the
-   same name in the libm-ieee754 directory.  The code is not used since
-   there is an assembler version for all users of this file.  */
diff --git a/sysdeps/powerpc/fpu/e_rem_pio2f.c b/sysdeps/powerpc/fpu/e_rem_pio2f.c
deleted file mode 100644
index 30fd53ee2c4288fdd4fb5923d668d097ecfcb290..0000000000000000000000000000000000000000
--- a/sysdeps/powerpc/fpu/e_rem_pio2f.c
+++ /dev/null
@@ -1,188 +0,0 @@ 
-/* e_rem_pio2f.c -- float version of e_rem_pio2.c
-   Copyright (C) 2011-2018 Free Software Foundation, Inc.
-   This file is part of the GNU C Library.
-   Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
-
-   The GNU C Library is free software; you can redistribute it and/or
-   modify it under the terms of the GNU Library General Public License as
-   published by the Free Software Foundation; either version 2 of the
-   License, or (at your option) any later version.
-
-   The GNU C Library is distributed in the hope that it will be useful,
-   but WITHOUT ANY WARRANTY; without even the implied warranty of
-   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
-   Library General Public License for more details.
-
-   You should have received a copy of the GNU Library General Public
-   License along with the GNU C Library; see the file COPYING.LIB.  If
-   not, see <http://www.gnu.org/licenses/>.  */
-
-#include <math.h>
-
-#include <math_private.h>
-#include "s_float_bitwise.h"
-
-/* defined in sysdeps/powerpc/fpu/k_rem_pio2f.c */
-int __fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx);
-
-/* __ieee754_rem_pio2f(x,y)
- *
- * return the remainder of x rem pi/2 in y[0]+y[1]
- */
-
-static const float npio2_hw[] = {
-  1.57077026e+00, 3.14154053e+00, 4.71228027e+00, 6.28308105e+00,
-  7.85388184e+00, 9.42456055e+00, 1.09953613e+01, 1.25661621e+01,
-  1.41369629e+01, 1.57077637e+01, 1.72783203e+01, 1.88491211e+01,
-  2.04199219e+01, 2.19907227e+01, 2.35615234e+01, 2.51323242e+01,
-  2.67031250e+01, 2.82739258e+01, 2.98447266e+01, 3.14155273e+01,
-  3.29863281e+01, 3.45566406e+01, 3.61279297e+01, 3.76982422e+01,
-  3.92695312e+01, 4.08398438e+01, 4.24111328e+01, 4.39814453e+01,
-  4.55527344e+01, 4.71230469e+01, 4.86943359e+01, 5.02646484e+01
-};
-
-
-static const float zero  = 0.0000000000e+00;
-static const float two8  = 2.5600000000e+02;
-
-static const float half    = 5.0000000000e-01;
-static const float invpio2 = 6.3661980629e-01;
-static const float pio2_1  = 1.5707855225e+00;
-static const float pio2_1t = 1.0804334124e-05;
-static const float pio2_2  = 1.0804273188e-05;
-static const float pio2_2t = 6.0770999344e-11;
-static const float pio2_3  = 6.0770943833e-11;
-static const float pio2_3t = 6.1232342629e-17;
-
-static const float pio4     = 7.8539801e-01;
-static const float pio3_4   = 2.3561945e+00;
-static const float pio2_24b = 1.5707951e+00;
-static const float pio2_2e7 = 2.0106054e+02;
-
-
-int32_t
-__ieee754_rem_pio2f (float x, float *y)
-{
-  float ax, z, n, r, w, t, e0;
-  float tx[3];
-  int32_t i, nx;
-
-  ax = __builtin_fabsf (x);
-  if (ax <= pio4)
-    {
-      y[0] = x;
-      y[1] = 0;
-      return 0;
-    }
-  if (ax < pio3_4)
-    {
-      if (x > 0)
-	{
-	  z = x - pio2_1;
-	  if (!__float_and_test28 (ax, pio2_24b))
-	    {
-	      y[0] = z - pio2_1t;
-	      y[1] = (z - y[0]) - pio2_1t;
-	    }
-	  else
-	    {
-	      z -= pio2_2;
-	      y[0] = z - pio2_2t;
-	      y[1] = (z - y[0]) - pio2_2t;
-	    }
-	  return 1;
-	}
-      else
-	{
-	  z = x + pio2_1;
-	  if (!__float_and_test28 (ax, pio2_24b))
-	    {
-	      y[0] = z + pio2_1t;
-	      y[1] = (z - y[0]) + pio2_1t;
-	    }
-	  else
-	    {
-	      z += pio2_2;
-	      y[0] = z + pio2_2t;
-	      y[1] = (z - y[0]) + pio2_2t;
-	    }
-	  return -1;
-	}
-    }
-  if (ax <= pio2_2e7)
-    {
-      n = __floorf (ax * invpio2 + half);
-      i = (int32_t) n;
-      r = ax - n * pio2_1;
-      w = n * pio2_1t;		/* 1st round good to 40 bit */
-      if (i < 32 && !__float_and_test24 (ax, npio2_hw[i - 1]))
-	{
-	  y[0] = r - w;
-	}
-      else
-	{
-	  float i, j;
-	  j = __float_and8 (ax);
-	  y[0] = r - w;
-	  i = __float_and8 (y[0]);
-	  if (j / i > 256.0 || j / i < 3.9062500e-3)
-	    {			/* 2nd iterations needed, good to 57 */
-	      t = r;
-	      w = n * pio2_2;
-	      r = t - w;
-	      w = n * pio2_2t - ((t - r) - w);
-	      y[0] = r - w;
-	      i = __float_and8 (y[0]);
-	      if (j / i > 33554432 || j / i < 2.9802322e-8)
-		{		/* 3rd iteration needed, 74 bits acc */
-		  t = r;
-		  w = n * pio2_3;
-		  r = t - w;
-		  w = n * pio2_3t - ((t - r) - w);
-		  y[0] = r - w;
-		}
-	    }
-	}
-      y[1] = (r - y[0]) - w;
-      if (x < 0)
-	{
-	  y[0] = -y[0];
-	  y[1] = -y[1];
-	  return -i;
-	}
-      else
-	{
-	  return i;
-	}
-    }
-
-  /* all other (large) arguments */
-  if (isnanf (x) || isinff (x))
-    {
-      y[0] = y[1] = x - x;
-      return 0;
-    }
-
-  /* set z = scalbn(|x|,ilogb(x)-7) */
-  e0 = __float_and8 (ax / 128.0);
-  z = ax / e0;
-
-  tx[0] = __floorf (z);
-  z = (z - tx[0]) * two8;
-  tx[1] = __floorf (z);
-  z = (z - tx[1]) * two8;
-  tx[2] = __floorf (z);
-
-  nx = 3;
-  while (tx[nx - 1] == zero)
-    nx--;
-
-  i = __fp_kernel_rem_pio2f (tx, y, e0, nx);
-  if (x < 0)
-    {
-      y[0] = -y[0];
-      y[1] = -y[1];
-      return -i;
-    }
-  return i;
-}
diff --git a/sysdeps/powerpc/fpu/k_rem_pio2f.c b/sysdeps/powerpc/fpu/k_rem_pio2f.c
deleted file mode 100644
index 7e5a08ba5a5f0d535266467f806cc91162d7f886..0000000000000000000000000000000000000000
--- a/sysdeps/powerpc/fpu/k_rem_pio2f.c
+++ /dev/null
@@ -1,273 +0,0 @@ 
-/* k_rem_pio2f.c -- float version of e_rem_pio2.c
-   Copyright (C) 2011-2018 Free Software Foundation, Inc.
-   This file is part of the GNU C Library.
-   Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
-
-   The GNU C Library is free software; you can redistribute it and/or
-   modify it under the terms of the GNU Library General Public License as
-   published by the Free Software Foundation; either version 2 of the
-   License, or (at your option) any later version.
-
-   The GNU C Library is distributed in the hope that it will be useful,
-   but WITHOUT ANY WARRANTY; without even the implied warranty of
-   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
-   Library General Public License for more details.
-
-   You should have received a copy of the GNU Library General Public
-   License along with the GNU C Library; see the file COPYING.LIB.  If
-   not, see <http://www.gnu.org/licenses/>.  */
-
-#include <math.h>
-
-#include <math_private.h>
-#include "s_float_bitwise.h"
-
-
-static const float two_over_pi[] = {
-  1.62000000e+02, 2.49000000e+02, 1.31000000e+02, 1.10000000e+02,
-  7.80000000e+01, 6.80000000e+01, 2.10000000e+01, 4.10000000e+01,
-  2.52000000e+02, 3.90000000e+01, 8.70000000e+01, 2.09000000e+02,
-  2.45000000e+02, 5.20000000e+01, 2.21000000e+02, 1.92000000e+02,
-  2.19000000e+02, 9.80000000e+01, 1.49000000e+02, 1.53000000e+02,
-  6.00000000e+01, 6.70000000e+01, 1.44000000e+02, 6.50000000e+01,
-  2.54000000e+02, 8.10000000e+01, 9.90000000e+01, 1.71000000e+02,
-  2.22000000e+02, 1.87000000e+02, 1.97000000e+02, 9.70000000e+01,
-  1.83000000e+02, 3.60000000e+01, 1.10000000e+02, 5.80000000e+01,
-  6.60000000e+01, 7.70000000e+01, 2.10000000e+02, 2.24000000e+02,
-  6.00000000e+00, 7.30000000e+01, 4.60000000e+01, 2.34000000e+02,
-  9.00000000e+00, 2.09000000e+02, 1.46000000e+02, 2.80000000e+01,
-  2.54000000e+02, 2.90000000e+01, 2.35000000e+02, 2.80000000e+01,
-  1.77000000e+02, 4.10000000e+01, 1.67000000e+02, 6.20000000e+01,
-  2.32000000e+02, 1.30000000e+02, 5.30000000e+01, 2.45000000e+02,
-  4.60000000e+01, 1.87000000e+02, 6.80000000e+01, 1.32000000e+02,
-  2.33000000e+02, 1.56000000e+02, 1.12000000e+02, 3.80000000e+01,
-  1.80000000e+02, 9.50000000e+01, 1.26000000e+02, 6.50000000e+01,
-  5.70000000e+01, 1.45000000e+02, 2.14000000e+02, 5.70000000e+01,
-  1.31000000e+02, 8.30000000e+01, 5.70000000e+01, 2.44000000e+02,
-  1.56000000e+02, 1.32000000e+02, 9.50000000e+01, 1.39000000e+02,
-  1.89000000e+02, 2.49000000e+02, 4.00000000e+01, 5.90000000e+01,
-  3.10000000e+01, 2.48000000e+02, 1.51000000e+02, 2.55000000e+02,
-  2.22000000e+02, 5.00000000e+00, 1.52000000e+02, 1.50000000e+01,
-  2.39000000e+02, 4.70000000e+01, 1.70000000e+01, 1.39000000e+02,
-  9.00000000e+01, 1.00000000e+01, 1.09000000e+02, 3.10000000e+01,
-  1.09000000e+02, 5.40000000e+01, 1.26000000e+02, 2.07000000e+02,
-  3.90000000e+01, 2.03000000e+02, 9.00000000e+00, 1.83000000e+02,
-  7.90000000e+01, 7.00000000e+01, 6.30000000e+01, 1.02000000e+02,
-  1.58000000e+02, 9.50000000e+01, 2.34000000e+02, 4.50000000e+01,
-  1.17000000e+02, 3.90000000e+01, 1.86000000e+02, 1.99000000e+02,
-  2.35000000e+02, 2.29000000e+02, 2.41000000e+02, 1.23000000e+02,
-  6.10000000e+01, 7.00000000e+00, 5.70000000e+01, 2.47000000e+02,
-  1.38000000e+02, 8.20000000e+01, 1.46000000e+02, 2.34000000e+02,
-  1.07000000e+02, 2.51000000e+02, 9.50000000e+01, 1.77000000e+02,
-  3.10000000e+01, 1.41000000e+02, 9.30000000e+01, 8.00000000e+00,
-  8.60000000e+01, 3.00000000e+00, 4.80000000e+01, 7.00000000e+01,
-  2.52000000e+02, 1.23000000e+02, 1.07000000e+02, 1.71000000e+02,
-  2.40000000e+02, 2.07000000e+02, 1.88000000e+02, 3.20000000e+01,
-  1.54000000e+02, 2.44000000e+02, 5.40000000e+01, 2.90000000e+01,
-  1.69000000e+02, 2.27000000e+02, 1.45000000e+02, 9.70000000e+01,
-  9.40000000e+01, 2.30000000e+02, 2.70000000e+01, 8.00000000e+00,
-  1.01000000e+02, 1.53000000e+02, 1.33000000e+02, 9.50000000e+01,
-  2.00000000e+01, 1.60000000e+02, 1.04000000e+02, 6.40000000e+01,
-  1.41000000e+02, 2.55000000e+02, 2.16000000e+02, 1.28000000e+02,
-  7.70000000e+01, 1.15000000e+02, 3.90000000e+01, 4.90000000e+01,
-  6.00000000e+00, 6.00000000e+00, 2.10000000e+01, 8.60000000e+01,
-  2.02000000e+02, 1.15000000e+02, 1.68000000e+02, 2.01000000e+02,
-  9.60000000e+01, 2.26000000e+02, 1.23000000e+02, 1.92000000e+02,
-  1.40000000e+02, 1.07000000e+02
-};
-
-
-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 zero  = 0.0000000000e+00;
-static const float one   = 1.0000000000;
-static const float twon8 = 3.9062500000e-03;
-static const float two8  = 2.5600000000e+02;
-
-
-int32_t
-__fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx)
-{
-  int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih, exp;
-  float z, fw, f[20], fq[20], q[20];
-
-  /* initialize jk */
-  jp = jk = 9;
-
-  /* determine jx,jv,q0, note that 3>q0 */
-  jx = nx - 1;
-  exp = __float_get_exp (e0) - 127;
-  jv = (exp - 3) / 8;
-  if (jv < 0)
-    jv = 0;
-  q0 = exp - 8 * (jv + 1);
-
-  /* set up f[0] to f[jx+jk] where f[jx+jk] = two_over_pi[jv+jk] */
-  j = jv - jx;
-  m = jx + jk;
-  for (i = 0; i <= m; i++, j++)
-    f[i] = (j < 0) ? zero : two_over_pi[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 = __truncf (twon8 * z);
-      iq[i] = (int32_t) (z - two8 * fw);
-      z = q[j - 1] + fw;
-    }
-
-  /* compute n */
-  z = __scalbnf (z, q0);	/* actual value of z */
-  z -= 8.0 * __floorf (z * 0.125);	/* trim off integer >= 8 */
-  n = (int32_t) z;
-  z -= __truncf (z);
-  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] >> 7;
-  else if (z >= 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 -= __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] = two_over_pi[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 == 0.0)
-    {
-      jz -= 1;
-      q0 -= 8;
-      while (iq[jz] == 0)
-	{
-	  jz--;
-	  q0 -= 8;
-	}
-    }
-  else
-    {				/* break z into 8-bit if necessary */
-      z = __scalbnf (z, -q0);
-      if (z >= two8)
-	{
-	  fw = __truncf (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 = __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[] */
-  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;
-
-  return n & 7;
-}