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46 the System V Interface Definition (Issue 2).
61 * 2. Approximating expm1(r) by a special rational function on
64 * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
66 * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
68 * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
70 * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
74 * by 2**-61. In other words,
75 * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
76 * where Q1 = -1.6666666666666567384E-2,
84 * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
89 * 2 3
90 * r r [ 3 - (R1 + R1*r/2) ]
92 * 2 2 [ 6 - r*(3 - R1*r/2) ]
100 * ( 2 2 )
101 * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
103 * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
109 * expm1(x) = either 2^k*[expm1(r)+1] - 1
110 * = or 2^k*[expm1(r) + (1-2^-k)]
113 * to Qi*2^i, and replace z by (x^2)/2.
118 * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
120 * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
121 * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
122 * (vii) return 2^k(1-((E+2^-k)-r))
210 else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */ in _NAME_64()
231 if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ in _NAME_64()
241 SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */ in _NAME_64()
247 SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */ in _NAME_64()