Adding upstream version 115.7.0esr.upstream/115.7.0esrupstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 113 insertions, 0 deletions

diff --git a/modules/fdlibm/src/s_cbrt.cpp b/modules/fdlibm/src/s_cbrt.cpp
new file mode 100644
index 0000000000..d1946781d1
--- /dev/null
+++ b/modules/fdlibm/src/s_cbrt.cpp
@@ -0,0 +1,113 @@
+/* @(#)s_cbrt.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ *
+ * Optimized by Bruce D. Evans.
+ */
+
+//#include <sys/cdefs.h>
+//__FBSDID("$FreeBSD$");
+
+#include <float.h>
+#include "math_private.h"
+
+/* cbrt(x)
+ * Return cube root of x
+ */
+static const u_int32_t
+	B1 = 715094163, /* B1 = (1023-1023/3-0.03306235651)*2**20 */
+	B2 = 696219795; /* B2 = (1023-1023/3-54/3-0.03306235651)*2**20 */
+
+/* |1/cbrt(x) - p(x)| < 2**-23.5 (~[-7.93e-8, 7.929e-8]). */
+static const double
+P0 =  1.87595182427177009643,		/* 0x3ffe03e6, 0x0f61e692 */
+P1 = -1.88497979543377169875,		/* 0xbffe28e0, 0x92f02420 */
+P2 =  1.621429720105354466140,		/* 0x3ff9f160, 0x4a49d6c2 */
+P3 = -0.758397934778766047437,		/* 0xbfe844cb, 0xbee751d9 */
+P4 =  0.145996192886612446982;		/* 0x3fc2b000, 0xd4e4edd7 */
+
+double
+cbrt(double x)
+{
+	int32_t	hx;
+	union {
+	    double value;
+	    uint64_t bits;
+	} u;
+	double r,s,t=0.0,w;
+	u_int32_t sign;
+	u_int32_t high,low;
+
+	EXTRACT_WORDS(hx,low,x);
+	sign=hx&0x80000000; 		/* sign= sign(x) */
+	hx  ^=sign;
+	if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
+
+    /*
+     * Rough cbrt to 5 bits:
+     *    cbrt(2**e*(1+m) ~= 2**(e/3)*(1+(e%3+m)/3)
+     * where e is integral and >= 0, m is real and in [0, 1), and "/" and
+     * "%" are integer division and modulus with rounding towards minus
+     * infinity.  The RHS is always >= the LHS and has a maximum relative
+     * error of about 1 in 16.  Adding a bias of -0.03306235651 to the
+     * (e%3+m)/3 term reduces the error to about 1 in 32. With the IEEE
+     * floating point representation, for finite positive normal values,
+     * ordinary integer division of the value in bits magically gives
+     * almost exactly the RHS of the above provided we first subtract the
+     * exponent bias (1023 for doubles) and later add it back.  We do the
+     * subtraction virtually to keep e >= 0 so that ordinary integer
+     * division rounds towards minus infinity; this is also efficient.
+     */
+	if(hx<0x00100000) { 		/* zero or subnormal? */
+	    if((hx|low)==0)
+		return(x);		/* cbrt(0) is itself */
+	    SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
+	    t*=x;
+	    GET_HIGH_WORD(high,t);
+	    INSERT_WORDS(t,sign|((high&0x7fffffff)/3+B2),0);
+	} else
+	    INSERT_WORDS(t,sign|(hx/3+B1),0);
+
+    /*
+     * New cbrt to 23 bits:
+     *    cbrt(x) = t*cbrt(x/t**3) ~= t*P(t**3/x)
+     * where P(r) is a polynomial of degree 4 that approximates 1/cbrt(r)
+     * to within 2**-23.5 when |r - 1| < 1/10.  The rough approximation
+     * has produced t such than |t/cbrt(x) - 1| ~< 1/32, and cubing this
+     * gives us bounds for r = t**3/x.
+     *
+     * Try to optimize for parallel evaluation as in k_tanf.c.
+     */
+	r=(t*t)*(t/x);
+	t=t*((P0+r*(P1+r*P2))+((r*r)*r)*(P3+r*P4));
+
+    /*
+     * Round t away from zero to 23 bits (sloppily except for ensuring that
+     * the result is larger in magnitude than cbrt(x) but not much more than
+     * 2 23-bit ulps larger).  With rounding towards zero, the error bound
+     * would be ~5/6 instead of ~4/6.  With a maximum error of 2 23-bit ulps
+     * in the rounded t, the infinite-precision error in the Newton
+     * approximation barely affects third digit in the final error
+     * 0.667; the error in the rounded t can be up to about 3 23-bit ulps
+     * before the final error is larger than 0.667 ulps.
+     */
+	u.value=t;
+	u.bits=(u.bits+0x80000000)&0xffffffffc0000000ULL;
+	t=u.value;
+
+    /* one step Newton iteration to 53 bits with error < 0.667 ulps */
+	s=t*t;				/* t*t is exact */
+	r=x/s;				/* error <= 0.5 ulps; |r| < |t| */
+	w=t+t;				/* t+t is exact */
+	r=(r-t)/(w+r);			/* r-t is exact; w+r ~= 3*t */
+	t=t+t*r;			/* error <= (0.5 + 0.5/3) * ulp */
+
+	return(t);
+}