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authorSzabolcs Nagy <nsz@port70.net>2012-12-16 17:30:29 +0100
committerSzabolcs Nagy <nsz@port70.net>2012-12-16 17:30:29 +0100
commit58bba42d1bd14e1ab01f3249ffc98afdbf841a6a (patch)
tree8790505fc53cfcd7a3bd6ecd4b1f7877018e2e17 /src
parent525ad96e0ef6e46b6ac28438ef2ffa1d5317fb64 (diff)
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math: x86_64 version of expl, fixed some comments in the i386 version
Diffstat (limited to 'src')
-rw-r--r--src/math/i386/expl.s4
-rw-r--r--src/math/i386/expm1f.s2
-rw-r--r--src/math/i386/expm1l.s2
-rw-r--r--src/math/x86_64/expl.s108
4 files changed, 112 insertions, 4 deletions
diff --git a/src/math/i386/expl.s b/src/math/i386/expl.s
index 3f2f707d..8ceb40d2 100644
--- a/src/math/i386/expl.s
+++ b/src/math/i386/expl.s
@@ -1,6 +1,7 @@
# 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
@@ -35,7 +36,6 @@ expl:
# should be 0x1.71547652b82fe178p0 == 0x3fff b8aa3b29 5c17f0bc
# it will be wrong on non-nearest rounding mode
3: fldl2e
-# subl $32, %esp
subl $44, %esp
# hi = log2e_hi*x
# 2^hi = exp2l(hi)
@@ -54,7 +54,7 @@ expl:
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
diff --git a/src/math/i386/expm1f.s b/src/math/i386/expm1f.s
index 89c2d290..f335a3e5 100644
--- a/src/math/i386/expm1f.s
+++ b/src/math/i386/expm1f.s
@@ -1 +1 @@
-# see expm1.s
+# see exp.s
diff --git a/src/math/i386/expm1l.s b/src/math/i386/expm1l.s
index 89c2d290..f335a3e5 100644
--- a/src/math/i386/expm1l.s
+++ b/src/math/i386/expm1l.s
@@ -1 +1 @@
-# see expm1.s
+# see exp.s
diff --git a/src/math/x86_64/expl.s b/src/math/x86_64/expl.s
index e69de29b..6d5c1ceb 100644
--- a/src/math/x86_64/expl.s
+++ b/src/math/x86_64/expl.s
@@ -0,0 +1,108 @@
+# 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)
+
+ # special cases: 2*x is +-inf, nan or |x| < 0x1p-32
+ # check (exponent|0x8000)+2 < 0xbfff+2-32
+ movw 16(%rsp), %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
+ fld1
+ jmp 2f
+1: testw %ax, %ax
+ jns 1f
+ # if 2*x == -inf,-nan return -0/x
+ fldz
+ fchs
+ fdivp
+ ret
+ # if 2*x == inf,nan return 2*x
+1: fld %st(0)
+2: faddp
+ ret
+
+ # should be 0x1.71547652b82fe178p0 == 0x3fff b8aa3b29 5c17f0bc
+ # it will be wrong on non-nearest rounding mode
+3: 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
+ # 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