math: use ** for exponentiation in comments
R=rsc
CC=golang-dev
https://golang.org/cl/908041
diff --git a/src/pkg/math/expm1.go b/src/pkg/math/expm1.go
index 9e8ae3f..35100ca 100644
--- a/src/pkg/math/expm1.go
+++ b/src/pkg/math/expm1.go
@@ -34,13 +34,13 @@
// 2. Approximating expm1(r) by a special rational function on
// the interval [0,0.34658]:
// Since
-// r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
+// r*(exp(r)+1)/(exp(r)-1) = 2+ r**2/6 - r**4/360 + ...
// we define R1(r*r) by
-// r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
+// r*(exp(r)+1)/(exp(r)-1) = 2+ r**2/6 * R1(r*r)
// That is,
// R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
// = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
-// = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
+// = 1 - r**2/60 + r**4/2520 - r**6/100800 + ...
// We use a special Reme algorithm on [0,0.347] to generate
// a polynomial of degree 5 in r*r to approximate R1. The
// maximum error of this polynomial approximation is bounded
@@ -79,20 +79,20 @@
// = r - E
// 3. Scale back to obtain expm1(x):
// From step 1, we have
-// expm1(x) = either 2^k*[expm1(r)+1] - 1
-// = or 2^k*[expm1(r) + (1-2^-k)]
+// expm1(x) = either 2**k*[expm1(r)+1] - 1
+// = or 2**k*[expm1(r) + (1-2**-k)]
// 4. Implementation notes:
// (A). To save one multiplication, we scale the coefficient Qi
-// to Qi*2^i, and replace z by (x^2)/2.
+// to Qi*2**i, and replace z by (x**2)/2.
// (B). To achieve maximum accuracy, we compute expm1(x) by
// (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
// (ii) if k=0, return r-E
// (iii) if k=-1, return 0.5*(r-E)-0.5
// (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
// else return 1.0+2.0*(r-E);
-// (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
-// (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
-// (vii) return 2^k(1-((E+2^-k)-r))
+// (v) if (k<-2||k>56) return 2**k(1-(E-r)) - 1 (or exp(x)-1)
+// (vi) if k <= 20, return 2**k((1-2**-k)-(E-r)), else
+// (vii) return 2**k(1-((E+2**-k)-r))
//
// Special cases:
// expm1(INF) is INF, expm1(NaN) is NaN;
@@ -114,7 +114,7 @@
// to produce the hexadecimal values shown.
//
-// Expm1 returns e^x - 1, the base-e exponential of x minus 1.
+// Expm1 returns e**x - 1, the base-e exponential of x minus 1.
// It is more accurate than Exp(x) - 1 when x is near zero.
//
// Special cases are:
@@ -131,7 +131,7 @@
Ln2Hi = 6.93147180369123816490e-01 // 0x3fe62e42fee00000
Ln2Lo = 1.90821492927058770002e-10 // 0x3dea39ef35793c76
InvLn2 = 1.44269504088896338700e+00 // 0x3ff71547652b82fe
- Tiny = 1.0 / (1 << 54) // 2^-54 = 0x3c90000000000000
+ Tiny = 1.0 / (1 << 54) // 2**-54 = 0x3c90000000000000
// scaled coefficients related to expm1
Q1 = -3.33333333333331316428e-02 // 0xBFA11111111110F4
Q2 = 1.58730158725481460165e-03 // 0x3F5A01A019FE5585
@@ -194,7 +194,7 @@
}
x = hi - lo
c = (hi - x) - lo
- } else if absx < Tiny { // when |x| < 2^-54, return x
+ } else if absx < Tiny { // when |x| < 2**-54, return x
return x
} else {
k = 0
@@ -223,12 +223,12 @@
return y - 1
}
if k < 20 {
- t := Float64frombits(0x3ff0000000000000 - (0x20000000000000 >> uint(k))) // t=1-2^-k
+ t := Float64frombits(0x3ff0000000000000 - (0x20000000000000 >> uint(k))) // t=1-2**-k
y := t - (e - x)
y = Float64frombits(Float64bits(y) + uint64(k)<<52) // add k to y's exponent
return y
}
- t := Float64frombits(uint64((0x3ff - k) << 52)) // 2^-k
+ t := Float64frombits(uint64((0x3ff - k) << 52)) // 2**-k
y := x - (e + t)
y += 1
y = Float64frombits(Float64bits(y) + uint64(k)<<52) // add k to y's exponent
