Adding upstream version 1.16.10.upstream/1.16.10upstream

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

1 files changed, 144 insertions, 0 deletions

diff --git a/src/math/sqrt.go b/src/math/sqrt.go
new file mode 100644
index 0000000..1077a62
--- /dev/null
+++ b/src/math/sqrt.go
@@ -0,0 +1,144 @@
+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package math
+
+// The original C code and the long comment below are
+// from FreeBSD's /usr/src/lib/msun/src/e_sqrt.c and
+// came with this notice. The go code is a simplified
+// version of the original C.
+//
+// ====================================================
+// 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.
+// ====================================================
+//
+// __ieee754_sqrt(x)
+// Return correctly rounded sqrt.
+//           -----------------------------------------
+//           | Use the hardware sqrt if you have one |
+//           -----------------------------------------
+// Method:
+//   Bit by bit method using integer arithmetic. (Slow, but portable)
+//   1. Normalization
+//      Scale x to y in [1,4) with even powers of 2:
+//      find an integer k such that  1 <= (y=x*2**(2k)) < 4, then
+//              sqrt(x) = 2**k * sqrt(y)
+//   2. Bit by bit computation
+//      Let q  = sqrt(y) truncated to i bit after binary point (q = 1),
+//           i                                                   0
+//                                     i+1         2
+//          s  = 2*q , and      y  =  2   * ( y - q  ).          (1)
+//           i      i            i                 i
+//
+//      To compute q    from q , one checks whether
+//                  i+1       i
+//
+//                            -(i+1) 2
+//                      (q + 2      )  <= y.                     (2)
+//                        i
+//                                                            -(i+1)
+//      If (2) is false, then q   = q ; otherwise q   = q  + 2      .
+//                             i+1   i             i+1   i
+//
+//      With some algebraic manipulation, it is not difficult to see
+//      that (2) is equivalent to
+//                             -(i+1)
+//                      s  +  2       <= y                       (3)
+//                       i                i
+//
+//      The advantage of (3) is that s  and y  can be computed by
+//                                    i      i
+//      the following recurrence formula:
+//          if (3) is false
+//
+//          s     =  s  ,       y    = y   ;                     (4)
+//           i+1      i          i+1    i
+//
+//      otherwise,
+//                         -i                      -(i+1)
+//          s     =  s  + 2  ,  y    = y  -  s  - 2              (5)
+//           i+1      i          i+1    i     i
+//
+//      One may easily use induction to prove (4) and (5).
+//      Note. Since the left hand side of (3) contain only i+2 bits,
+//            it is not necessary to do a full (53-bit) comparison
+//            in (3).
+//   3. Final rounding
+//      After generating the 53 bits result, we compute one more bit.
+//      Together with the remainder, we can decide whether the
+//      result is exact, bigger than 1/2ulp, or less than 1/2ulp
+//      (it will never equal to 1/2ulp).
+//      The rounding mode can be detected by checking whether
+//      huge + tiny is equal to huge, and whether huge - tiny is
+//      equal to huge for some floating point number "huge" and "tiny".
+//
+//
+// Notes:  Rounding mode detection omitted. The constants "mask", "shift",
+// and "bias" are found in src/math/bits.go
+
+// Sqrt returns the square root of x.
+//
+// Special cases are:
+//	Sqrt(+Inf) = +Inf
+//	Sqrt(±0) = ±0
+//	Sqrt(x < 0) = NaN
+//	Sqrt(NaN) = NaN
+func Sqrt(x float64) float64
+
+// Note: Sqrt is implemented in assembly on some systems.
+// Others have assembly stubs that jump to func sqrt below.
+// On systems where Sqrt is a single instruction, the compiler
+// may turn a direct call into a direct use of that instruction instead.
+
+func sqrt(x float64) float64 {
+	// special cases
+	switch {
+	case x == 0 || IsNaN(x) || IsInf(x, 1):
+		return x
+	case x < 0:
+		return NaN()
+	}
+	ix := Float64bits(x)
+	// normalize x
+	exp := int((ix >> shift) & mask)
+	if exp == 0 { // subnormal x
+		for ix&(1<<shift) == 0 {
+			ix <<= 1
+			exp--
+		}
+		exp++
+	}
+	exp -= bias // unbias exponent
+	ix &^= mask << shift
+	ix |= 1 << shift
+	if exp&1 == 1 { // odd exp, double x to make it even
+		ix <<= 1
+	}
+	exp >>= 1 // exp = exp/2, exponent of square root
+	// generate sqrt(x) bit by bit
+	ix <<= 1
+	var q, s uint64               // q = sqrt(x)
+	r := uint64(1 << (shift + 1)) // r = moving bit from MSB to LSB
+	for r != 0 {
+		t := s + r
+		if t <= ix {
+			s = t + r
+			ix -= t
+			q += r
+		}
+		ix <<= 1
+		r >>= 1
+	}
+	// final rounding
+	if ix != 0 { // remainder, result not exact
+		q += q & 1 // round according to extra bit
+	}
+	ix = q>>1 + uint64(exp-1+bias)<<shift // significand + biased exponent
+	return Float64frombits(ix)
+}