[1/3] New generic sincosf

diff --git a/sysdeps/ieee754/flt-32/s_cosf.c b/sysdeps/ieee754/flt-32/s_cosf.c
index ac6d044449..d19397faca 100644
--- a/sysdeps/ieee754/flt-32/s_cosf.c
+++ b/sysdeps/ieee754/flt-32/s_cosf.c
@@ -20,6 +20,7 @@ 
 #include <math.h>
 #include <math_private.h>
 #include <libm-alias-float.h>
+#include "s_sincos.h"
 
 #ifndef COSF
 # define COSF_FUNC __cosf
@@ -27,95 +28,6 @@ 
 # define COSF_FUNC COSF
 #endif
 
-/* Chebyshev constants for cos, range -PI/4 - PI/4.  */
-static const double C0 = -0x1.ffffffffe98aep-2;
-static const double C1 =  0x1.55555545c50c7p-5;
-static const double C2 = -0x1.6c16b348b6874p-10;
-static const double C3 =  0x1.a00eb9ac43ccp-16;
-static const double C4 = -0x1.23c97dd8844d7p-22;
-
-/* Chebyshev constants for sin, range -PI/4 - PI/4.  */
-static const double S0 = -0x1.5555555551cd9p-3;
-static const double S1 =  0x1.1111110c2688bp-7;
-static const double S2 = -0x1.a019f8b4bd1f9p-13;
-static const double S3 =  0x1.71d7264e6b5b4p-19;
-static const double S4 = -0x1.a947e1674b58ap-26;
-
-/* Chebyshev constants for cos, range 2^-27 - 2^-5.  */
-static const double CC0 = -0x1.fffffff5cc6fdp-2;
-static const double CC1 =  0x1.55514b178dac5p-5;
-
-/* PI/2 with 98 bits of accuracy.  */
-static const double PI_2_hi = 0x1.921fb544p+0;
-static const double PI_2_lo = 0x1.0b4611a626332p-34;
-
-static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI.  */
-
-#define FLOAT_EXPONENT_SHIFT 23
-#define FLOAT_EXPONENT_BIAS 127
-
-static const double pio2_table[] = {
-  0 * M_PI_2,
-  1 * M_PI_2,
-  2 * M_PI_2,
-  3 * M_PI_2,
-  4 * M_PI_2,
-  5 * M_PI_2
-};
-
-static const double invpio4_table[] = {
-  0x0p+0,
-  0x1.45f306cp+0,
-  0x1.c9c882ap-28,
-  0x1.4fe13a8p-58,
-  0x1.f47d4dp-85,
-  0x1.bb81b6cp-112,
-  0x1.4acc9ep-142,
-  0x1.0e4107cp-169
-};
-
-static const double ones[] = { 1.0, -1.0 };
-
-/* Compute the cosine value using Chebyshev polynomials where
-   THETA is the range reduced absolute value of the input
-   and it is less than Pi/4,
-   N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
-   whether a sine or cosine approximation is more accurate and
-   the sign of the result.  */
-static inline float
-reduced (double theta, unsigned int n)
-{
-  double sign, cx;
-  const double theta2 = theta * theta;
-
-  /* Determine positive or negative primary interval.  */
-  n += 2;
-  sign = ones[(n >> 2) & 1];
-
-  /* Are we in the primary interval of sin or cos?  */
-  if ((n & 2) == 0)
-    {
-      /* Here cosf() is calculated using sin Chebyshev polynomial:
-	x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).  */
-      cx = S3 + theta2 * S4;
-      cx = S2 + theta2 * cx;
-      cx = S1 + theta2 * cx;
-      cx = S0 + theta2 * cx;
-      cx = theta + theta * theta2 * cx;
-    }
-  else
-    {
-     /* Here cosf() is calculated using cos Chebyshev polynomial:
-	1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))).  */
-      cx = C3 + theta2 * C4;
-      cx = C2 + theta2 * cx;
-      cx = C1 + theta2 * cx;
-      cx = C0 + theta2 * cx;
-      cx = 1. + theta2 * cx;
-    }
-  return sign * cx;
-}
-
 float
 COSF_FUNC (float x)
 {
@@ -161,7 +73,7 @@  COSF_FUNC (float x)
 	     pio2_table must go to 5 (9 / 2 + 1).  */
 	  unsigned int n = (abstheta * inv_PI_4) + 1;
 	  theta = abstheta - pio2_table[n / 2];
-	  return reduced (theta, n);
+	  return reduced_cos (theta, n);
 	}
       else if (isless (abstheta, INFINITY))
 	{
@@ -171,7 +83,7 @@  COSF_FUNC (float x)
 	      double x = n / 2;
 	      theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
 	      /* Argument reduction needed.  */
-	      return reduced (theta, n);
+	      return reduced_cos (theta, n);
 	    }
 	  else /* |theta| >= 2^23.  */
 	    {
@@ -199,7 +111,7 @@  COSF_FUNC (float x)
 		  e += c;
 		  e += d;
 		  e *= M_PI_4;
-		  return reduced (e, l + 1);
+		  return reduced_cos (e, l + 1);
 		}
 	      else
 		{
@@ -209,14 +121,14 @@  COSF_FUNC (float x)
 		  if (e <= 1.0)
 		    {
 		      e *= M_PI_4;
-		      return reduced (e, l + 1);
+		      return reduced_cos (e, l + 1);
 		    }
 		  else
 		    {
 		      l++;
 		      e -= 2.0;
 		      e *= M_PI_4;
-		      return reduced (e, l + 1);
+		      return reduced_cos (e, l + 1);
 		    }
 		}
 	    }
diff --git a/sysdeps/ieee754/flt-32/s_sincos.h b/sysdeps/ieee754/flt-32/s_sincos.h
new file mode 100644
index 0000000000..b0110fc2af
--- /dev/null
+++ b/sysdeps/ieee754/flt-32/s_sincos.h
@@ -0,0 +1,155 @@ 
+/* Used by sinf, cosf and sincosf functions.
+   Copyright (C) 2017 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 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
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+/* Chebyshev constants for cos, range -PI/4 - PI/4.  */
+static const double C0 = -0x1.ffffffffe98aep-2;
+static const double C1 =  0x1.55555545c50c7p-5;
+static const double C2 = -0x1.6c16b348b6874p-10;
+static const double C3 =  0x1.a00eb9ac43ccp-16;
+static const double C4 = -0x1.23c97dd8844d7p-22;
+
+/* Chebyshev constants for sin, range -PI/4 - PI/4.  */
+static const double S0 = -0x1.5555555551cd9p-3;
+static const double S1 =  0x1.1111110c2688bp-7;
+static const double S2 = -0x1.a019f8b4bd1f9p-13;
+static const double S3 =  0x1.71d7264e6b5b4p-19;
+static const double S4 = -0x1.a947e1674b58ap-26;
+
+/* Chebyshev constants for sin, range 2^-27 - 2^-5.  */
+static const double SS0 = -0x1.555555543d49dp-3;
+static const double SS1 =  0x1.110f475cec8c5p-7;
+
+/* Chebyshev constants for cos, range 2^-27 - 2^-5.  */
+static const double CC0 = -0x1.fffffff5cc6fdp-2;
+static const double CC1 =  0x1.55514b178dac5p-5;
+
+/* PI/2 with 98 bits of accuracy.  */
+static const double PI_2_hi = 0x1.921fb544p+0;
+static const double PI_2_lo = 0x1.0b4611a626332p-34;
+
+static const double SMALL = 0x1p-50; /* 2^-50.  */
+static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI.  */
+
+#define FLOAT_EXPONENT_SHIFT 23
+#define FLOAT_EXPONENT_BIAS 127
+
+static const double pio2_table[] = {
+  0 * M_PI_2,
+  1 * M_PI_2,
+  2 * M_PI_2,
+  3 * M_PI_2,
+  4 * M_PI_2,
+  5 * M_PI_2
+};
+
+static const double invpio4_table[] = {
+  0x0p+0,
+  0x1.45f306cp+0,
+  0x1.c9c882ap-28,
+  0x1.4fe13a8p-58,
+  0x1.f47d4dp-85,
+  0x1.bb81b6cp-112,
+  0x1.4acc9ep-142,
+  0x1.0e4107cp-169
+};
+
+static const double ones[] = { 1.0, -1.0 };
+
+/* Compute the sine value using Chebyshev polynomials where
+   THETA is the range reduced absolute value of the input
+   and it is less than Pi/4,
+   N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
+   whether a sine or cosine approximation is more accurate and
+   SIGNBIT is used to add the correct sign after the Chebyshev
+   polynomial is computed.  */
+static inline float
+reduced_sin (const double theta, const unsigned int n,
+	 const unsigned int signbit)
+{
+  double sx;
+  const double theta2 = theta * theta;
+  /* We are operating on |x|, so we need to add back the original
+     signbit for sinf.  */
+  double sign;
+  /* Determine positive or negative primary interval.  */
+  sign = ones[((n >> 2) & 1) ^ signbit];
+  /* Are we in the primary interval of sin or cos?  */
+  if ((n & 2) == 0)
+    {
+      /* Here sinf() is calculated using sin Chebyshev polynomial:
+	x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).  */
+      sx = S3 + theta2 * S4;     /* S3+x^2*S4.  */
+      sx = S2 + theta2 * sx;     /* S2+x^2*(S3+x^2*S4).  */
+      sx = S1 + theta2 * sx;     /* S1+x^2*(S2+x^2*(S3+x^2*S4)).  */
+      sx = S0 + theta2 * sx;     /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))).  */
+      sx = theta + theta * theta2 * sx;
+    }
+  else
+    {
+     /* Here sinf() is calculated using cos Chebyshev polynomial:
+	1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))).  */
+      sx = C3 + theta2 * C4;     /* C3+x^2*C4.  */
+      sx = C2 + theta2 * sx;     /* C2+x^2*(C3+x^2*C4).  */
+      sx = C1 + theta2 * sx;     /* C1+x^2*(C2+x^2*(C3+x^2*C4)).  */
+      sx = C0 + theta2 * sx;     /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))).  */
+      sx = 1.0 + theta2 * sx;
+    }
+
+  /* Add in the signbit and assign the result.  */
+  return sign * sx;
+}
+
+/* Compute the cosine value using Chebyshev polynomials where
+   THETA is the range reduced absolute value of the input
+   and it is less than Pi/4,
+   N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
+   whether a sine or cosine approximation is more accurate and
+   the sign of the result.  */
+static inline float
+reduced_cos (double theta, unsigned int n)
+{
+  double sign, cx;
+  const double theta2 = theta * theta;
+
+  /* Determine positive or negative primary interval.  */
+  n += 2;
+  sign = ones[(n >> 2) & 1];
+
+  /* Are we in the primary interval of sin or cos?  */
+  if ((n & 2) == 0)
+    {
+      /* Here cosf() is calculated using sin Chebyshev polynomial:
+	x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).  */
+      cx = S3 + theta2 * S4;
+      cx = S2 + theta2 * cx;
+      cx = S1 + theta2 * cx;
+      cx = S0 + theta2 * cx;
+      cx = theta + theta * theta2 * cx;
+    }
+  else
+    {
+     /* Here cosf() is calculated using cos Chebyshev polynomial:
+	1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))).  */
+      cx = C3 + theta2 * C4;
+      cx = C2 + theta2 * cx;
+      cx = C1 + theta2 * cx;
+      cx = C0 + theta2 * cx;
+      cx = 1. + theta2 * cx;
+    }
+  return sign * cx;
+}
diff --git a/sysdeps/ieee754/flt-32/s_sincosf.c b/sysdeps/ieee754/flt-32/s_sincosf.c
index 4946a6eb54..b9f775d45b 100644
--- a/sysdeps/ieee754/flt-32/s_sincosf.c
+++ b/sysdeps/ieee754/flt-32/s_sincosf.c
@@ -1,7 +1,6 @@ 
 /* Compute sine and cosine of argument.
-   Copyright (C) 1997-2017 Free Software Foundation, Inc.
+   Copyright (C) 2017 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
-   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
 
    The GNU C Library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Lesser General Public
@@ -19,9 +18,9 @@ 
 
 #include <errno.h>
 #include <math.h>
-
 #include <math_private.h>
 #include <libm-alias-float.h>
+#include "s_sincos.h"
 
 #ifndef SINCOSF
 # define SINCOSF_FUNC __sincosf
@@ -32,50 +31,137 @@ 
 void
 SINCOSF_FUNC (float x, float *sinx, float *cosx)
 {
-  int32_t ix;
-
-  /* High word of x. */
-  GET_FLOAT_WORD (ix, x);
-
-  /* |x| ~< pi/4 */
-  ix &= 0x7fffffff;
-  if (ix <= 0x3f490fd8)
-    {
-      *sinx = __kernel_sinf (x, 0.0, 0);
-      *cosx = __kernel_cosf (x, 0.0);
-    }
-  else if (ix>=0x7f800000)
+  double cx;
+  double theta = x;
+  double abstheta = fabs (theta);
+  /* If |x|< Pi/4.  */
+  if (isless (abstheta, M_PI_4))
     {
-      /* sin(Inf or NaN) is NaN */
-      *sinx = *cosx = x - x;
-      if (ix == 0x7f800000)
-	__set_errno (EDOM);
+      if (abstheta >= 0x1p-5) /* |x| >= 2^-5.  */
+	{
+	  const double theta2 = theta * theta;
+	  /* Chebyshev polynomial of the form for sin and cos.  */
+	  cx = C3 + theta2 * C4;
+	  cx = C2 + theta2 * cx;
+	  cx = C1 + theta2 * cx;
+	  cx = C0 + theta2 * cx;
+	  cx = 1.0 + theta2 * cx;
+	  *cosx = cx;
+	  cx = S3 + theta2 * S4;
+	  cx = S2 + theta2 * cx;
+	  cx = S1 + theta2 * cx;
+	  cx = S0 + theta2 * cx;
+	  cx = theta + theta * theta2 * cx;
+	  *sinx = cx;
+	}
+      else if (abstheta >= 0x1p-27)     /* |x| >= 2^-27.  */
+	{
+	  /* A simpler Chebyshev approximation is close enough for this range:
+	     for sin: x+x^3*(SS0+x^2*SS1)
+	     for cos: 1.0+x^2*(CC0+x^3*CC1).  */
+	  const double theta2 = theta * theta;
+	  cx = CC0 + theta * theta2 * CC1;
+	  cx = 1.0 + theta2 * cx;
+	  *cosx = cx;
+	  cx = SS0 + theta2 * SS1;
+	  cx = theta + theta * theta2 * cx;
+	  *sinx = cx;
+	}
+      else
+	{
+	  /* Handle some special cases.  */
+	  if (theta)
+	    *sinx = theta - (theta * SMALL);
+	  else
+	    *sinx = theta;
+	  *cosx = 1.0 - abstheta;
+	}
     }
-  else
+  else                          /* |x| >= Pi/4.  */
     {
-      /* Argument reduction needed.  */
-      float y[2];
-      int n;
-
-      n = __ieee754_rem_pio2f (x, y);
-      switch (n & 3)
+      unsigned int signbit = isless (x, 0);
+      if (isless (abstheta, 9 * M_PI_4))        /* |x| < 9*Pi/4.  */
+	{
+	  /* There are cases where FE_UPWARD rounding mode can
+	     produce a result of abstheta * inv_PI_4 == 9,
+	     where abstheta < 9pi/4, so the domain for
+	     pio2_table must go to 5 (9 / 2 + 1).  */
+	  unsigned int n = (abstheta * inv_PI_4) + 1;
+	  theta = abstheta - pio2_table[n / 2];
+	  *sinx = reduced_sin (theta, n, signbit);
+	  *cosx = reduced_cos (theta, n);
+	}
+      else if (isless (abstheta, INFINITY))
+	{
+	  if (abstheta < 0x1p+23)     /* |x| < 2^23.  */
+	    {
+	      unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
+	      double x = n / 2;
+	      theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
+	      /* Argument reduction needed.  */
+	      *sinx = reduced_sin (theta, n, signbit);
+	      *cosx = reduced_cos (theta, n);
+	    }
+	  else                  /* |x| >= 2^23.  */
+	    {
+	      x = fabsf (x);
+	      int exponent;
+	      GET_FLOAT_WORD (exponent, x);
+	      exponent
+	        = (exponent >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;
+	      exponent += 3;
+	      exponent /= 28;
+	      double a = invpio4_table[exponent] * x;
+	      double b = invpio4_table[exponent + 1] * x;
+	      double c = invpio4_table[exponent + 2] * x;
+	      double d = invpio4_table[exponent + 3] * x;
+	      uint64_t l = a;
+	      l &= ~0x7;
+	      a -= l;
+	      double e = a + b;
+	      l = e;
+	      e = a - l;
+	      if (l & 1)
+	        {
+	          e -= 1.0;
+	          e += b;
+	          e += c;
+	          e += d;
+	          e *= M_PI_4;
+		  *sinx = reduced_sin (e, l + 1, signbit);
+		  *cosx = reduced_cos (e, l + 1);
+	        }
+	      else
+		{
+		  e += b;
+		  e += c;
+		  e += d;
+		  if (e <= 1.0)
+		    {
+		      e *= M_PI_4;
+		      *sinx = reduced_sin (e, l + 1, signbit);
+		      *cosx = reduced_cos (e, l + 1);
+		    }
+		  else
+		    {
+		      l++;
+		      e -= 2.0;
+		      e *= M_PI_4;
+		      *sinx = reduced_sin (e, l + 1, signbit);
+		      *cosx = reduced_cos (e, l + 1);
+		    }
+		}
+	    }
+	}
+      else
 	{
-	case 0:
-	  *sinx = __kernel_sinf (y[0], y[1], 1);
-	  *cosx = __kernel_cosf (y[0], y[1]);
-	  break;
-	case 1:
-	  *sinx = __kernel_cosf (y[0], y[1]);
-	  *cosx = -__kernel_sinf (y[0], y[1], 1);
-	  break;
-	case 2:
-	  *sinx = -__kernel_sinf (y[0], y[1], 1);
-	  *cosx = -__kernel_cosf (y[0], y[1]);
-	  break;
-	default:
-	  *sinx = -__kernel_cosf (y[0], y[1]);
-	  *cosx = __kernel_sinf (y[0], y[1], 1);
-	  break;
+	  int32_t ix;
+	  /* High word of x.  */
+	  GET_FLOAT_WORD (ix, abstheta);
+	  /* sin/cos(Inf or NaN) is NaN.  */
+	  *sinx = *cosx = x - x;
+	  if (ix == 0x7f800000)
+	    __set_errno (EDOM);
 	}
     }
 }
diff --git a/sysdeps/ieee754/flt-32/s_sinf.c b/sysdeps/ieee754/flt-32/s_sinf.c
index 418d4487c5..c682bc64fc 100644
--- a/sysdeps/ieee754/flt-32/s_sinf.c
+++ b/sysdeps/ieee754/flt-32/s_sinf.c
@@ -20,6 +20,7 @@ 
 #include <math.h>
 #include <math_private.h>
 #include <libm-alias-float.h>
+#include "s_sincos.h"
 
 #ifndef SINF
 # define SINF_FUNC __sinf
@@ -27,100 +28,6 @@ 
 # define SINF_FUNC SINF
 #endif
 
-/* Chebyshev constants for cos, range -PI/4 - PI/4.  */
-static const double C0 = -0x1.ffffffffe98aep-2;
-static const double C1 =  0x1.55555545c50c7p-5;
-static const double C2 = -0x1.6c16b348b6874p-10;
-static const double C3 =  0x1.a00eb9ac43ccp-16;
-static const double C4 = -0x1.23c97dd8844d7p-22;
-
-/* Chebyshev constants for sin, range -PI/4 - PI/4.  */
-static const double S0 = -0x1.5555555551cd9p-3;
-static const double S1 =  0x1.1111110c2688bp-7;
-static const double S2 = -0x1.a019f8b4bd1f9p-13;
-static const double S3 =  0x1.71d7264e6b5b4p-19;
-static const double S4 = -0x1.a947e1674b58ap-26;
-
-/* Chebyshev constants for sin, range 2^-27 - 2^-5.  */
-static const double SS0 = -0x1.555555543d49dp-3;
-static const double SS1 =  0x1.110f475cec8c5p-7;
-
-/* PI/2 with 98 bits of accuracy.  */
-static const double PI_2_hi = -0x1.921fb544p+0;
-static const double PI_2_lo = -0x1.0b4611a626332p-34;
-
-static const double SMALL = 0x1p-50; /* 2^-50.  */
-static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI.  */
-
-#define FLOAT_EXPONENT_SHIFT 23
-#define FLOAT_EXPONENT_BIAS 127
-
-static const double pio2_table[] = {
-  0 * M_PI_2,
-  1 * M_PI_2,
-  2 * M_PI_2,
-  3 * M_PI_2,
-  4 * M_PI_2,
-  5 * M_PI_2
-};
-
-static const double invpio4_table[] = {
-  0x0p+0,
-  0x1.45f306cp+0,
-  0x1.c9c882ap-28,
-  0x1.4fe13a8p-58,
-  0x1.f47d4dp-85,
-  0x1.bb81b6cp-112,
-  0x1.4acc9ep-142,
-  0x1.0e4107cp-169
-};
-
-static const double ones[] = { 1.0, -1.0 };
-
-/* Compute the sine value using Chebyshev polynomials where
-   THETA is the range reduced absolute value of the input
-   and it is less than Pi/4,
-   N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
-   whether a sine or cosine approximation is more accurate and
-   SIGNBIT is used to add the correct sign after the Chebyshev
-   polynomial is computed.  */
-static inline float
-reduced (const double theta, const unsigned int n,
-	 const unsigned int signbit)
-{
-  double sx;
-  const double theta2 = theta * theta;
-  /* We are operating on |x|, so we need to add back the original
-     signbit for sinf.  */
-  double sign;
-  /* Determine positive or negative primary interval.  */
-  sign = ones[((n >> 2) & 1) ^ signbit];
-  /* Are we in the primary interval of sin or cos?  */
-  if ((n & 2) == 0)
-    {
-      /* Here sinf() is calculated using sin Chebyshev polynomial:
-	x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).  */
-      sx = S3 + theta2 * S4;     /* S3+x^2*S4.  */
-      sx = S2 + theta2 * sx;     /* S2+x^2*(S3+x^2*S4).  */
-      sx = S1 + theta2 * sx;     /* S1+x^2*(S2+x^2*(S3+x^2*S4)).  */
-      sx = S0 + theta2 * sx;     /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))).  */
-      sx = theta + theta * theta2 * sx;
-    }
-  else
-    {
-     /* Here sinf() is calculated using cos Chebyshev polynomial:
-	1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))).  */
-      sx = C3 + theta2 * C4;     /* C3+x^2*C4.  */
-      sx = C2 + theta2 * sx;     /* C2+x^2*(C3+x^2*C4).  */
-      sx = C1 + theta2 * sx;     /* C1+x^2*(C2+x^2*(C3+x^2*C4)).  */
-      sx = C0 + theta2 * sx;     /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))).  */
-      sx = 1.0 + theta2 * sx;
-    }
-
-  /* Add in the signbit and assign the result.  */
-  return sign * sx;
-}
-
 float
 SINF_FUNC (float x)
 {
@@ -171,7 +78,7 @@  SINF_FUNC (float x)
 	     pio2_table must go to 5 (9 / 2 + 1).  */
 	  unsigned int n = (abstheta * inv_PI_4) + 1;
 	  theta = abstheta - pio2_table[n / 2];
-	  return reduced (theta, n, signbit);
+	  return reduced_sin (theta, n, signbit);
 	}
       else if (isless (abstheta, INFINITY))
 	{
@@ -179,9 +86,9 @@  SINF_FUNC (float x)
 	    {
 	      unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
 	      double x = n / 2;
-	      theta = x * PI_2_lo + (x * PI_2_hi + abstheta);
+	      theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
 	      /* Argument reduction needed.  */
-	      return reduced (theta, n, signbit);
+	      return reduced_sin (theta, n, signbit);
 	    }
 	  else                  /* |x| >= 2^23.  */
 	    {
@@ -209,7 +116,7 @@  SINF_FUNC (float x)
 	          e += c;
 	          e += d;
 	          e *= M_PI_4;
-	          return reduced (e, l + 1, signbit);
+	          return reduced_sin (e, l + 1, signbit);
 	        }
 	      else
 		{
@@ -219,14 +126,14 @@  SINF_FUNC (float x)
 		  if (e <= 1.0)
 		    {
 		      e *= M_PI_4;
-		      return reduced (e, l + 1, signbit);
+		      return reduced_sin (e, l + 1, signbit);
 		    }
 		  else
 		    {
 		      l++;
 		      e -= 2.0;
 		      e *= M_PI_4;
-		      return reduced (e, l + 1, signbit);
+		      return reduced_sin (e, l + 1, signbit);
 		    }
 		}
 	    }