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) |
+ 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 |