build: move package sources from src/pkg to src

Preparation was in CL 134570043.
This CL contains only the effect of 'hg mv src/pkg/* src'.
For more about the move, see golang.org/s/go14nopkg.

1 files changed, 191 insertions, 0 deletions

diff --git a/src/math/exp.go b/src/math/exp.go
new file mode 100644
index 000000000..f31585fa7
--- /dev/null
+++ b/src/math/exp.go
@@ -0,0 +1,191 @@
+// 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
+
+// Exp returns e**x, the base-e exponential of x.
+//
+// Special cases are:
+//	Exp(+Inf) = +Inf
+//	Exp(NaN) = NaN
+// Very large values overflow to 0 or +Inf.
+// Very small values underflow to 1.
+func Exp(x float64) float64
+
+// The original C code, the long comment, and the constants
+// below are from FreeBSD's /usr/src/lib/msun/src/e_exp.c
+// and came with this notice.  The go code is a simplified
+// version of the original C.
+//
+// ====================================================
+// Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
+//
+// Permission to use, copy, modify, and distribute this
+// software is freely granted, provided that this notice
+// is preserved.
+// ====================================================
+//
+//
+// exp(x)
+// Returns the exponential of x.
+//
+// Method
+//   1. Argument reduction:
+//      Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
+//      Given x, find r and integer k such that
+//
+//               x = k*ln2 + r,  |r| <= 0.5*ln2.
+//
+//      Here r will be represented as r = hi-lo for better
+//      accuracy.
+//
+//   2. Approximation of exp(r) by a special rational function on
+//      the interval [0,0.34658]:
+//      Write
+//          R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
+//      We use a special Remes algorithm on [0,0.34658] to generate
+//      a polynomial of degree 5 to approximate R. The maximum error
+//      of this polynomial approximation is bounded by 2**-59. In
+//      other words,
+//          R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
+//      (where z=r*r, and the values of P1 to P5 are listed below)
+//      and
+//          |                  5          |     -59
+//          | 2.0+P1*z+...+P5*z   -  R(z) | <= 2
+//          |                             |
+//      The computation of exp(r) thus becomes
+//                             2*r
+//              exp(r) = 1 + -------
+//                            R - r
+//                                 r*R1(r)
+//                     = 1 + r + ----------- (for better accuracy)
+//                                2 - R1(r)
+//      where
+//                               2       4             10
+//              R1(r) = r - (P1*r  + P2*r  + ... + P5*r   ).
+//
+//   3. Scale back to obtain exp(x):
+//      From step 1, we have
+//         exp(x) = 2**k * exp(r)
+//
+// Special cases:
+//      exp(INF) is INF, exp(NaN) is NaN;
+//      exp(-INF) is 0, and
+//      for finite argument, only exp(0)=1 is exact.
+//
+// Accuracy:
+//      according to an error analysis, the error is always less than
+//      1 ulp (unit in the last place).
+//
+// Misc. info.
+//      For IEEE double
+//          if x >  7.09782712893383973096e+02 then exp(x) overflow
+//          if x < -7.45133219101941108420e+02 then exp(x) underflow
+//
+// Constants:
+// The hexadecimal values are the intended ones for the following
+// constants. The decimal values may be used, provided that the
+// compiler will convert from decimal to binary accurately enough
+// to produce the hexadecimal values shown.
+
+func exp(x float64) float64 {
+	const (
+		Ln2Hi = 6.93147180369123816490e-01
+		Ln2Lo = 1.90821492927058770002e-10
+		Log2e = 1.44269504088896338700e+00
+
+		Overflow  = 7.09782712893383973096e+02
+		Underflow = -7.45133219101941108420e+02
+		NearZero  = 1.0 / (1 << 28) // 2**-28
+	)
+
+	// special cases
+	switch {
+	case IsNaN(x) || IsInf(x, 1):
+		return x
+	case IsInf(x, -1):
+		return 0
+	case x > Overflow:
+		return Inf(1)
+	case x < Underflow:
+		return 0
+	case -NearZero < x && x < NearZero:
+		return 1 + x
+	}
+
+	// reduce; computed as r = hi - lo for extra precision.
+	var k int
+	switch {
+	case x < 0:
+		k = int(Log2e*x - 0.5)
+	case x > 0:
+		k = int(Log2e*x + 0.5)
+	}
+	hi := x - float64(k)*Ln2Hi
+	lo := float64(k) * Ln2Lo
+
+	// compute
+	return expmulti(hi, lo, k)
+}
+
+// Exp2 returns 2**x, the base-2 exponential of x.
+//
+// Special cases are the same as Exp.
+func Exp2(x float64) float64
+
+func exp2(x float64) float64 {
+	const (
+		Ln2Hi = 6.93147180369123816490e-01
+		Ln2Lo = 1.90821492927058770002e-10
+
+		Overflow  = 1.0239999999999999e+03
+		Underflow = -1.0740e+03
+	)
+
+	// special cases
+	switch {
+	case IsNaN(x) || IsInf(x, 1):
+		return x
+	case IsInf(x, -1):
+		return 0
+	case x > Overflow:
+		return Inf(1)
+	case x < Underflow:
+		return 0
+	}
+
+	// argument reduction; x = r×lg(e) + k with |r| ≤ ln(2)/2.
+	// computed as r = hi - lo for extra precision.
+	var k int
+	switch {
+	case x > 0:
+		k = int(x + 0.5)
+	case x < 0:
+		k = int(x - 0.5)
+	}
+	t := x - float64(k)
+	hi := t * Ln2Hi
+	lo := -t * Ln2Lo
+
+	// compute
+	return expmulti(hi, lo, k)
+}
+
+// exp1 returns e**r × 2**k where r = hi - lo and |r| ≤ ln(2)/2.
+func expmulti(hi, lo float64, k int) float64 {
+	const (
+		P1 = 1.66666666666666019037e-01  /* 0x3FC55555; 0x5555553E */
+		P2 = -2.77777777770155933842e-03 /* 0xBF66C16C; 0x16BEBD93 */
+		P3 = 6.61375632143793436117e-05  /* 0x3F11566A; 0xAF25DE2C */
+		P4 = -1.65339022054652515390e-06 /* 0xBEBBBD41; 0xC5D26BF1 */
+		P5 = 4.13813679705723846039e-08  /* 0x3E663769; 0x72BEA4D0 */
+	)
+
+	r := hi - lo
+	t := r * r
+	c := r - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))))
+	y := 1 - ((lo - (r*c)/(2-c)) - hi)
+	// TODO(rsc): make sure Ldexp can handle boundary k
+	return Ldexp(y, k)
+}