math: x86_64 version of expl, fixed some comments in the i386 version

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