# exp(x) = 2^hi + 2^hi (2^lo - 1)
# where hi+lo = log2e*x with 128bit precision
# exact log2e*x calculation depends on nearest rounding mode
+# using the exact multiplication method of Dekker and Veltkamp
.global expl
.type expl,@function
expl:
fldt 4(%esp)
- # special cases: 2*x is +-inf, nan or |x| < 0x1p-32
- # check (exponent|0x8000)+2 < 0xbfff+2-32
- movw 12(%esp), %ax
- movw %ax, %dx
- orw $0x8000, %dx
- addw $2, %dx
- cmpw $0xbfff-30, %dx
- jnb 3f
- cmpw $1, %dx
- jbe 1f
- # if |x|<0x1p-32 return 1+x
+ # interesting case: 0x1p-32 <= |x| < 16384
+ # check if (exponent|0x8000) is in [0xbfff-32, 0xbfff+13]
+ mov 12(%esp), %ax
+ or $0x8000, %ax
+ sub $0xbfdf, %ax
+ cmp $45, %ax
+ jbe 2f
+ test %ax, %ax
fld1
- jmp 2f
-1: testw %ax, %ax
- jns 1f
- # if 2*x == -inf,-nan return -0/x
- fldz
- fchs
- fdivp
+ js 1f
+ # if |x|>=0x1p14 or nan return 2^trunc(x)
+ fscale
+ fstp %st(1)
ret
- # if 2*x == inf,nan return 2*x
-1: fld %st(0)
-2: faddp
+ # if |x|<0x1p-32 return 1+x
+1: faddp
ret
- # should be 0x1.71547652b82fe178p0 == 0x3fff b8aa3b29 5c17f0bc
+ # should be 0x1.71547652b82fe178p0L == 0x3fff b8aa3b29 5c17f0bc
# it will be wrong on non-nearest rounding mode
-3: fldl2e
-# subl $32, %esp
+2: fldl2e
subl $44, %esp
# hi = log2e_hi*x
# 2^hi = exp2l(hi)
fstpt (%esp)
fstpt 16(%esp)
fstpt 32(%esp)
- call exp2l
+.hidden __exp2l
+ call __exp2l
# if 2^hi == inf return 2^hi
fld %st(0)
fstpt (%esp)
fldt 16(%esp)
# fpu stack: 2^hi x hi
# exact mult: x*log2e
- fld %st(1) # x
+ fld %st(1)
# c = 0x1p32+1
pushl $0x41f00000
pushl $0x00100000