J.T. Conklin's latest version of the Sun math library.

-- Begin comments from J.T. Conklin:
The most significant improvement is the addition of "float" versions
of the math functions that take float arguments, return floats, and do
all operations in floating point.  This doesn't help (performance)
much on the i386, but they are still nice to have.

The float versions were orginally done by Cygnus' Ian Taylor when
fdlibm was integrated into the libm we support for embedded systems.
I gave Ian a copy of my libm as a starting point since I had already
fixed a lot of bugs & problems in Sun's original code.  After he was
done, I cleaned it up a bit and integrated the changes back into my
libm.
-- End comments

Reviewed by:	jkh
Submitted by:	jtc

1 files changed, 213 insertions, 0 deletions

diff --git a/lib/msun/src/k_rem_pio2f.c b/lib/msun/src/k_rem_pio2f.c
new file mode 100644
index 0000000..c243a56
--- /dev/null
+++ b/lib/msun/src/k_rem_pio2f.c
@@ -0,0 +1,213 @@
+/* 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.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: k_rem_pio2f.c,v 1.2 1994/08/18 23:06:12 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+/* In the float version, the input parameter x contains 8 bit
+   integers, not 24 bit integers.  113 bit precision is not supported.  */
+
+#ifdef __STDC__
+static const int init_jk[] = {4,7,9}; /* initial value for jk */
+#else
+static int init_jk[] = {4,7,9}; 
+#endif
+
+#ifdef __STDC__
+static const float PIo2[] = {
+#else
+static float PIo2[] = {
+#endif
+  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 */
+};
+
+#ifdef __STDC__
+static const float			
+#else
+static float			
+#endif
+zero   = 0.0,
+one    = 1.0,
+two8   =  2.5600000000e+02, /* 0x43800000 */
+twon8  =  3.9062500000e-03; /* 0x3b800000 */
+
+#ifdef __STDC__
+	int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2) 
+#else
+	int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2) 	
+	float x[], y[]; int e0,nx,prec; int32_t ipio2[];
+#endif
+{
+	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]>>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 -= 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 = 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:
+		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;
+}