| Index: fusl/src/math/x86_64/expl.s
|
| diff --git a/fusl/src/math/x86_64/expl.s b/fusl/src/math/x86_64/expl.s
|
| new file mode 100644
|
| index 0000000000000000000000000000000000000000..798261d2835346a9d219f1e45b276c09b6b795c2
|
| --- /dev/null
|
| +++ b/fusl/src/math/x86_64/expl.s
|
| @@ -0,0 +1,101 @@
|
| +# 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 8(%rsp)
|
| +
|
| + # interesting case: 0x1p-32 <= |x| < 16384
|
| + # check if (exponent|0x8000) is in [0xbfff-32, 0xbfff+13]
|
| + mov 16(%rsp), %ax
|
| + or $0x8000, %ax
|
| + sub $0xbfdf, %ax
|
| + cmp $45, %ax
|
| + jbe 2f
|
| + test %ax, %ax
|
| + fld1
|
| + js 1f
|
| + # if |x|>=0x1p14 or nan return 2^trunc(x)
|
| + fscale
|
| + fstp %st(1)
|
| + ret
|
| + # if |x|<0x1p-32 return 1+x
|
| +1: faddp
|
| + ret
|
| +
|
| + # should be 0x1.71547652b82fe178p0L == 0x3fff b8aa3b29 5c17f0bc
|
| + # it will be wrong on non-nearest rounding mode
|
| +2: fldl2e
|
| + subq $48, %rsp
|
| + # hi = log2e_hi*x
|
| + # 2^hi = exp2l(hi)
|
| + fmul %st(1),%st
|
| + fld %st(0)
|
| + fstpt (%rsp)
|
| + fstpt 16(%rsp)
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| + fstpt 32(%rsp)
|
| + call exp2l@PLT
|
| + # if 2^hi == inf return 2^hi
|
| + fld %st(0)
|
| + fstpt (%rsp)
|
| + cmpw $0x7fff, 8(%rsp)
|
| + je 1f
|
| + fldt 32(%rsp)
|
| + fldt 16(%rsp)
|
| + # fpu stack: 2^hi x hi
|
| + # exact mult: x*log2e
|
| + fld %st(1)
|
| + # c = 0x1p32+1
|
| + movq $0x41f0000000100000,%rax
|
| + pushq %rax
|
| + fldl (%rsp)
|
| + # xh = x - c*x + c*x
|
| + # xl = x - xh
|
| + fmulp
|
| + fld %st(2)
|
| + fsub %st(1), %st
|
| + faddp
|
| + fld %st(2)
|
| + fsub %st(1), %st
|
| + # yh = log2e_hi - c*log2e_hi + c*log2e_hi
|
| + movq $0x3ff7154765200000,%rax
|
| + pushq %rax
|
| + fldl (%rsp)
|
| + # fpu stack: 2^hi x hi xh xl yh
|
| + # lo = hi - xh*yh + xl*yh
|
| + fld %st(2)
|
| + fmul %st(1), %st
|
| + fsubp %st, %st(4)
|
| + fmul %st(1), %st
|
| + faddp %st, %st(3)
|
| + # yl = log2e_hi - yh
|
| + movq $0x3de705fc2f000000,%rax
|
| + pushq %rax
|
| + fldl (%rsp)
|
| + # fpu stack: 2^hi x lo xh xl yl
|
| + # lo += xh*yl + xl*yl
|
| + fmul %st, %st(2)
|
| + fmulp %st, %st(1)
|
| + fxch %st(2)
|
| + faddp
|
| + faddp
|
| + # log2e_lo
|
| + movq $0xbfbe,%rax
|
| + pushq %rax
|
| + movq $0x82f0025f2dc582ee,%rax
|
| + pushq %rax
|
| + fldt (%rsp)
|
| + addq $40,%rsp
|
| + # fpu stack: 2^hi x lo log2e_lo
|
| + # lo += log2e_lo*x
|
| + # return 2^hi + 2^hi (2^lo - 1)
|
| + fmulp %st, %st(2)
|
| + faddp
|
| + f2xm1
|
| + fmul %st(1), %st
|
| + faddp
|
| +1: addq $48, %rsp
|
| + ret
|
|
|