1# exp(x) = 2^hi + 2^hi (2^lo - 1)
2# where hi+lo = log2e*x with 128bit precision
3# exact log2e*x calculation depends on nearest rounding mode
4# using the exact multiplication method of Dekker and Veltkamp
5
6.global expl
7.type expl,@function
8expl:
9	fldt 4(%esp)
10
11		# interesting case: 0x1p-32 <= |x| < 16384
12		# check if (exponent|0x8000) is in [0xbfff-32, 0xbfff+13]
13	mov 12(%esp), %ax
14	or $0x8000, %ax
15	sub $0xbfdf, %ax
16	cmp $45, %ax
17	jbe 2f
18	test %ax, %ax
19	fld1
20	js 1f
21		# if |x|>=0x1p14 or nan return 2^trunc(x)
22	fscale
23	fstp %st(1)
24	ret
25		# if |x|<0x1p-32 return 1+x
261:	faddp
27	ret
28
29		# should be 0x1.71547652b82fe178p0L == 0x3fff b8aa3b29 5c17f0bc
30		# it will be wrong on non-nearest rounding mode
312:	fldl2e
32	subl $44, %esp
33		# hi = log2e_hi*x
34		# 2^hi = exp2l(hi)
35	fmul %st(1),%st
36	fld %st(0)
37	fstpt (%esp)
38	fstpt 16(%esp)
39	fstpt 32(%esp)
40.hidden __exp2l
41	call __exp2l
42		# if 2^hi == inf return 2^hi
43	fld %st(0)
44	fstpt (%esp)
45	cmpw $0x7fff, 8(%esp)
46	je 1f
47	fldt 32(%esp)
48	fldt 16(%esp)
49		# fpu stack: 2^hi x hi
50		# exact mult: x*log2e
51	fld %st(1)
52		# c = 0x1p32+1
53	pushl $0x41f00000
54	pushl $0x00100000
55	fldl (%esp)
56		# xh = x - c*x + c*x
57		# xl = x - xh
58	fmulp
59	fld %st(2)
60	fsub %st(1), %st
61	faddp
62	fld %st(2)
63	fsub %st(1), %st
64		# yh = log2e_hi - c*log2e_hi + c*log2e_hi
65	pushl $0x3ff71547
66	pushl $0x65200000
67	fldl (%esp)
68		# fpu stack: 2^hi x hi xh xl yh
69		# lo = hi - xh*yh + xl*yh
70	fld %st(2)
71	fmul %st(1), %st
72	fsubp %st, %st(4)
73	fmul %st(1), %st
74	faddp %st, %st(3)
75		# yl = log2e_hi - yh
76	pushl $0x3de705fc
77	pushl $0x2f000000
78	fldl (%esp)
79		# fpu stack: 2^hi x lo xh xl yl
80		# lo += xh*yl + xl*yl
81	fmul %st, %st(2)
82	fmulp %st, %st(1)
83	fxch %st(2)
84	faddp
85	faddp
86		# log2e_lo
87	pushl $0xbfbe
88	pushl $0x82f0025f
89	pushl $0x2dc582ee
90	fldt (%esp)
91	addl $36,%esp
92		# fpu stack: 2^hi x lo log2e_lo
93		# lo += log2e_lo*x
94		# return 2^hi + 2^hi (2^lo - 1)
95	fmulp %st, %st(2)
96	faddp
97	f2xm1
98	fmul %st(1), %st
99	faddp
1001:	addl $44, %esp
101	ret
102