[PATCHv4] New generic sinf

diff --git a/sysdeps/ieee754/flt-32/s_sinf.c b/sysdeps/ieee754/flt-32/s_sinf.c
index 3ec98f811d..739723b267 100644
--- a/sysdeps/ieee754/flt-32/s_sinf.c
+++ b/sysdeps/ieee754/flt-32/s_sinf.c
@@ -1,21 +1,20 @@ 
-/* s_sinf.c -- float version of s_sin.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: s_sinf.c,v 1.4 1995/05/10 20:48:16 jtc Exp $";
-#endif
+/* Compute sine of argument.
+   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/>.  */
 
 #include <errno.h>
 #include <math.h>
@@ -28,35 +27,216 @@  static char rcsid[] = "$NetBSD: s_sinf.c,v 1.4 1995/05/10 20:48:16 jtc Exp $";
 # define SINF_FUNC SINF
 #endif
 
-float SINF_FUNC(float x)
-{
-	float y[2],z=0.0;
-	int32_t n, ix;
+/* 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;
 
-	GET_FLOAT_WORD(ix,x);
+/* 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;
 
-    /* |x| ~< pi/4 */
-	ix &= 0x7fffffff;
-	if(ix <= 0x3f490fd8) return __kernel_sinf(x,z,0);
+/* Chebyshev constants for sin, range 2^-27 - 2^-5.  */
+static const double SS0 = -0x1.555555543d49dp-3;
+static const double SS1 =  0x1.110f475cec8c5p-7;
 
-    /* sin(Inf or NaN) is NaN */
-	else if (ix>=0x7f800000) {
-	  if (ix == 0x7f800000)
-	    __set_errno (EDOM);
-	  return x-x;
-	}
+/* 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
+};
+
+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 int ones[] = { +1, -1 };
 
-    /* argument reduction needed */
-	else {
-	    n = __ieee754_rem_pio2f(x,y);
-	    switch(n&3) {
-		case 0: return  __kernel_sinf(y[0],y[1],1);
-		case 1: return  __kernel_cosf(y[0],y[1]);
-		case 2: return -__kernel_sinf(y[0],y[1],1);
-		default:
-			return -__kernel_cosf(y[0],y[1]);
+/* 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 long n,
+	 const unsigned long signbit)
+{
+  double sx;
+  const double theta2 = theta * theta;
+  /* We are operating on |x|, so we need to add back the original
+     signbit for sinf.  */
+  int 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)
+{
+  double cx;
+  double theta = x;
+  double abstheta = fabs (theta);
+  /*  if |x|< Pi/4.  */
+  if (abstheta < M_PI_4)
+    {
+      if (abstheta >= 0x1p-5) /* |x| >= 2^-5.  */
+	{
+	  const double theta2 = theta * theta;
+	  /* Chebyshev polynomial of the form for sin
+	   * 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;
+	  return 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).  */
+	  const double theta2 = theta * theta;
+	  cx = SS0 + theta2 * SS1;
+	  cx = theta + theta * theta2 * cx;
+	  return cx;
+	}
+      else
+	{
+	  /* Handle some special cases.  */
+	  if (theta)
+	    return theta - (theta * SMALL);
+	  else
+	    return theta;
+	}
+    }
+  else                          /* |x| >= Pi/4.  */
+    {
+      unsigned long signbit = (x < 0);
+      if (abstheta < 9 * M_PI_4)        /* |x| < 9*Pi/4.  */
+	{
+	  unsigned long n = (abstheta * inv_PI_4) + 1;
+	  theta = abstheta - pio2_table[n / 2];
+	  return reduced (theta, n, signbit);
+	}
+      else if (abstheta < INFINITY)
+	{
+	  if (abstheta < 0x1p+23)     /* |x| < 2^23.  */
+	    {
+	      unsigned long n = floor (abstheta * inv_PI_4) + 1.0;
+	      double x = floor (n / 2.0);
+	      theta = x * PI_2_lo + (x * PI_2_hi + abstheta);
+	      /* Argument reduction needed.  */
+	      return reduced (theta, n, signbit);
+	    }
+	  else                  /* |x| >= 2^23.  */
+	    {
+	      x = fabs (x);
+	      int exponent;
+	      GET_FLOAT_WORD (exponent, x);
+	      exponent =
+	        (exponent >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;
+	      exponent += 3;
+	      exponent = (exponent * (0x100000000 / 28 + 1)) >> 32;
+	      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;
+	      unsigned long 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;
+	          return reduced (e, l + 1, signbit);
+	        }
+	      else
+	        {
+	          e += b;
+	          e += c;
+	          e += d;
+	          if (e <= 1.0)
+	            {
+	              e *= M_PI_4;
+	              return reduced (e, l + 1, signbit);
+	            }
+	          else
+	            {
+	              l++;
+	              e -= 2.0;
+	              e *= M_PI_4;
+	              return reduced (e, l + 1, signbit);
+	            }
+	        }
 	    }
 	}
+      else
+	{
+	  int32_t ix;
+	  /* High word of x.  */
+	  GET_FLOAT_WORD (ix, abstheta);
+	  /* sin(Inf or NaN) is NaN.  */
+	  if (ix == 0x7f800000)
+	    __set_errno (EDOM);
+	  return x - x;
+	}
+    }
 }
 
 #ifndef SINF