Update.

2001-04-16  Stephen L Moshier  <moshier@mediaone.net>

	* sysdeps/ieee754/flt-32/e_asinf.c (pio2_hi, pio2_lo, pio4_hi):
	Correct the values. (pSx, qSx): Replace by shorter approximation.
	Use f suffix on float constants.

	* sysdeps/ieee754/ldbl-128/k_tanl.c: New file.
	Contributed by Stephen L Moshier <moshier@mediaone.net>.

2 files changed, 173 insertions, 25 deletions

diff --git a/sysdeps/ieee754/flt-32/e_asinf.c b/sysdeps/ieee754/flt-32/e_asinf.c
index 5270f31144..5c3f0d500f 100644
--- a/sysdeps/ieee754/flt-32/e_asinf.c
+++ b/sysdeps/ieee754/flt-32/e_asinf.c
@@ -13,6 +13,12 @@
  * ====================================================
  */
 
+/*
+  Single precision expansion contributed by
+  Stephen L. Moshier <moshier@na-net.ornl.gov>
+*/
+
+
 #if defined(LIBM_SCCS) && !defined(lint)
 static char rcsid[] = "$NetBSD: e_asinf.c,v 1.5 1995/05/12 04:57:25 jtc Exp $";
 #endif
@@ -27,20 +33,19 @@ static float
 #endif
 one =  1.0000000000e+00, /* 0x3F800000 */
 huge =  1.000e+30,
-pio2_hi =  1.5707962513e+00, /* 0x3fc90fda */
-pio2_lo =  7.5497894159e-08, /* 0x33a22168 */
-pio4_hi =  7.8539818525e-01, /* 0x3f490fdb */
-	/* coefficient for R(x^2) */
-pS0 =  1.6666667163e-01, /* 0x3e2aaaab */
-pS1 = -3.2556581497e-01, /* 0xbea6b090 */
-pS2 =  2.0121252537e-01, /* 0x3e4e0aa8 */
-pS3 = -4.0055535734e-02, /* 0xbd241146 */
-pS4 =  7.9153501429e-04, /* 0x3a4f7f04 */
-pS5 =  3.4793309169e-05, /* 0x3811ef08 */
-qS1 = -2.4033949375e+00, /* 0xc019d139 */
-qS2 =  2.0209457874e+00, /* 0x4001572d */
-qS3 = -6.8828397989e-01, /* 0xbf303361 */
-qS4 =  7.7038154006e-02; /* 0x3d9dc62e */
+
+pio2_hi = 1.57079637050628662109375f,
+pio2_lo = -4.37113900018624283e-8f,
+pio4_hi = 0.785398185253143310546875f,
+
+/* asin x = x + x^3 p(x^2)
+   -0.5 <= x <= 0.5;
+   Peak relative error 4.8e-9 */
+p0 = 1.666675248e-1f,
+p1 = 7.495297643e-2f,
+p2 = 4.547037598e-2f,
+p3 = 2.417951451e-2f,
+p4 = 4.216630880e-2f;
 
 #ifdef __STDC__
 	float __ieee754_asinf(float x)
@@ -63,30 +68,26 @@ qS4 =  7.7038154006e-02; /* 0x3d9dc62e */
 		if(huge+x>one) return x;/* return x with inexact if x!=0*/
 	    } else {
 		t = x*x;
-		p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
-		q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
-		w = p/q;
+		w = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4))));
 		return x+x*w;
 	    }
 	}
 	/* 1> |x|>= 0.5 */
 	w = one-fabsf(x);
-	t = w*(float)0.5;
-	p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
-	q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
+	t = w*0.5f;
+	p = t * (p0 + t * (p1 + t * (p2 + t * (p3 + t * p4))));
 	s = __ieee754_sqrtf(t);
 	if(ix>=0x3F79999A) { 	/* if |x| > 0.975 */
-	    w = p/q;
-	    t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo);
+	    t = pio2_hi-(2.0f*(s+s*p)-pio2_lo);
 	} else {
 	    int32_t iw;
 	    w  = s;
 	    GET_FLOAT_WORD(iw,w);
 	    SET_FLOAT_WORD(w,iw&0xfffff000);
 	    c  = (t-w*w)/(s+w);
-	    r  = p/q;
-	    p  = (float)2.0*s*r-(pio2_lo-(float)2.0*c);
-	    q  = pio4_hi-(float)2.0*w;
+	    r  = p;
+	    p  = 2.0f*s*r-(pio2_lo-2.0f*c);
+	    q  = pio4_hi-2.0f*w;
 	    t  = pio4_hi-(p-q);
 	}
 	if(hx>0) return t; else return -t;
diff --git a/sysdeps/ieee754/ldbl-128/k_tanl.c b/sysdeps/ieee754/ldbl-128/k_tanl.c
new file mode 100644
index 0000000000..3d8e0342e8
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128/k_tanl.c
@@ -0,0 +1,147 @@
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/*
+  Long double expansions contributed by
+  Stephen L. Moshier <moshier@na-net.ornl.gov>
+*/
+
+/* __kernel_tanl( x, y, k )
+ * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ * Input k indicates whether tan (if k=1) or
+ * -1/tan (if k= -1) is returned.
+ *
+ * Algorithm
+ *	1. Since tan(-x) = -tan(x), we need only to consider positive x.
+ *	2. if x < 2^-57, return x with inexact if x!=0.
+ *	3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)
+ *          on [0,0.67433].
+ *
+ *	   Note: tan(x+y) = tan(x) + tan'(x)*y
+ *		          ~ tan(x) + (1+x*x)*y
+ *	   Therefore, for better accuracy in computing tan(x+y), let
+ *		r = x^3 * R(x^2)
+ *	   then
+ *		tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))
+ *
+ *      4. For x in [0.67433,pi/4],  let y = pi/4 - x, then
+ *		tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
+ *		       = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
+ */
+
+#include "math.h"
+#include "math_private.h"
+#ifdef __STDC__
+static const long double
+#else
+static long double
+#endif
+  one = 1.0L,
+  pio4hi = 7.8539816339744830961566084581987569936977E-1L,
+  pio4lo = 2.1679525325309452561992610065108379921906E-35L,
+
+  /* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2)
+     0 <= x <= 0.6743316650390625
+     Peak relative error 8.0e-36  */
+ TH =  3.333333333333333333333333333333333333333E-1L,
+ T0 = -1.813014711743583437742363284336855889393E7L,
+ T1 =  1.320767960008972224312740075083259247618E6L,
+ T2 = -2.626775478255838182468651821863299023956E4L,
+ T3 =  1.764573356488504935415411383687150199315E2L,
+ T4 = -3.333267763822178690794678978979803526092E-1L,
+
+ U0 = -1.359761033807687578306772463253710042010E8L,
+ U1 =  6.494370630656893175666729313065113194784E7L,
+ U2 = -4.180787672237927475505536849168729386782E6L,
+ U3 =  8.031643765106170040139966622980914621521E4L,
+ U4 = -5.323131271912475695157127875560667378597E2L;
+  /* 1.000000000000000000000000000000000000000E0 */
+
+
+#ifdef __STDC__
+long double
+__kernel_tanl (long double x, long double y, int iy)
+#else
+long double
+__kernel_tanl (x, y, iy)
+     long double x, y;
+     int iy;
+#endif
+{
+  long double z, r, v, w, s;
+  int32_t ix, sign;
+  ieee854_long_double_shape_type u, u1;
+
+  u.value = x;
+  ix = u.parts32.w0 & 0x7fffffff;
+  if (ix < 0x3fc60000)		/* x < 2**-57 */
+    {
+      if ((int) x == 0)
+	{			/* generate inexact */
+	  if ((ix | u.parts32.w1 | u.parts32.w2 | u.parts32.w3
+	       | (iy + 1)) == 0)
+	    return one / fabs (x);
+	  else
+	    return (iy == 1) ? x : -one / x;
+	}
+    }
+  if (ix >= 0x3ffe5942) /* |x| >= 0.6743316650390625 */
+    {
+      if ((u.parts32.w0 & 0x80000000) != 0)
+	{
+	  x = -x;
+	  y = -y;
+	  sign = -1;
+	}
+      else
+	sign = 1;
+      z = pio4hi - x;
+      w = pio4lo - y;
+      x = z + w;
+      y = 0.0;
+    }
+  z = x * x;
+  r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));
+  v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));
+  r = r / v;
+
+  s = z * x;
+  r = y + z * (s * r + y);
+  r += TH * s;
+  w = x + r;
+  if (ix >= 0x3ffe5942)
+    {
+      v = (long double) iy;
+      w = (v - 2.0 * (x - (w * w / (w + v) - r)));
+      if (sign < 0)
+	w = -w;
+      return w;
+    }
+  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 */
+      u1.value = w;
+      u1.parts32.w2 = 0;
+      u1.parts32.w3 = 0;
+      v = r - (u1.value - x);		/* u1+v = r+x */
+      z = -1.0 / w;
+      u.value = z;
+      u.parts32.w2 = 0;
+      u.parts32.w3 = 0;
+      s = 1.0 + u.value * u1.value;
+      return u.value + z * (s + u.value * v);
+    }
+}