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-rw-r--r--sysdeps/libm-i387/e_rem_pio2.c3
-rw-r--r--sysdeps/libm-i387/e_rem_pio2f.c3
-rw-r--r--sysdeps/libm-i387/e_rem_pio2l.c3
-rw-r--r--sysdeps/libm-i387/k_rem_pio2.c3
-rw-r--r--sysdeps/libm-i387/k_rem_pio2f.c3
-rw-r--r--sysdeps/libm-i387/k_rem_pio2l.c3
-rw-r--r--sysdeps/libm-i387/s_cbrt.S78
-rw-r--r--sysdeps/libm-i387/s_cbrtf.S50
-rw-r--r--sysdeps/libm-i387/s_cbrtl.S143
9 files changed, 188 insertions, 101 deletions
diff --git a/sysdeps/libm-i387/e_rem_pio2.c b/sysdeps/libm-i387/e_rem_pio2.c
new file mode 100644
index 0000000000..1347b0468c
--- /dev/null
+++ b/sysdeps/libm-i387/e_rem_pio2.c
@@ -0,0 +1,3 @@
+/* Empty. This file is only meant to avoid compiling the file with the
+ same name in the libm-ieee754 directory. The code is not used since
+ there is an assembler version for all users of this file. */
diff --git a/sysdeps/libm-i387/e_rem_pio2f.c b/sysdeps/libm-i387/e_rem_pio2f.c
new file mode 100644
index 0000000000..1347b0468c
--- /dev/null
+++ b/sysdeps/libm-i387/e_rem_pio2f.c
@@ -0,0 +1,3 @@
+/* Empty. This file is only meant to avoid compiling the file with the
+ same name in the libm-ieee754 directory. The code is not used since
+ there is an assembler version for all users of this file. */
diff --git a/sysdeps/libm-i387/e_rem_pio2l.c b/sysdeps/libm-i387/e_rem_pio2l.c
new file mode 100644
index 0000000000..1347b0468c
--- /dev/null
+++ b/sysdeps/libm-i387/e_rem_pio2l.c
@@ -0,0 +1,3 @@
+/* Empty. This file is only meant to avoid compiling the file with the
+ same name in the libm-ieee754 directory. The code is not used since
+ there is an assembler version for all users of this file. */
diff --git a/sysdeps/libm-i387/k_rem_pio2.c b/sysdeps/libm-i387/k_rem_pio2.c
new file mode 100644
index 0000000000..1347b0468c
--- /dev/null
+++ b/sysdeps/libm-i387/k_rem_pio2.c
@@ -0,0 +1,3 @@
+/* Empty. This file is only meant to avoid compiling the file with the
+ same name in the libm-ieee754 directory. The code is not used since
+ there is an assembler version for all users of this file. */
diff --git a/sysdeps/libm-i387/k_rem_pio2f.c b/sysdeps/libm-i387/k_rem_pio2f.c
new file mode 100644
index 0000000000..1347b0468c
--- /dev/null
+++ b/sysdeps/libm-i387/k_rem_pio2f.c
@@ -0,0 +1,3 @@
+/* Empty. This file is only meant to avoid compiling the file with the
+ same name in the libm-ieee754 directory. The code is not used since
+ there is an assembler version for all users of this file. */
diff --git a/sysdeps/libm-i387/k_rem_pio2l.c b/sysdeps/libm-i387/k_rem_pio2l.c
new file mode 100644
index 0000000000..1347b0468c
--- /dev/null
+++ b/sysdeps/libm-i387/k_rem_pio2l.c
@@ -0,0 +1,3 @@
+/* Empty. This file is only meant to avoid compiling the file with the
+ same name in the libm-ieee754 directory. The code is not used since
+ there is an assembler version for all users of this file. */
diff --git a/sysdeps/libm-i387/s_cbrt.S b/sysdeps/libm-i387/s_cbrt.S
index 4b9a2b11c6..3f6a0174f2 100644
--- a/sysdeps/libm-i387/s_cbrt.S
+++ b/sysdeps/libm-i387/s_cbrt.S
@@ -28,34 +28,36 @@
#endif
.align ALIGNARG(4)
- ASM_TYPE_DIRECTIVE(f1,@object)
-f1: .double 0.354895765043919860
- ASM_SIZE_DIRECTIVE(f1)
- ASM_TYPE_DIRECTIVE(f2,@object)
-f2: .double 1.50819193781584896
- ASM_SIZE_DIRECTIVE(f2)
- ASM_TYPE_DIRECTIVE(f3,@object)
-f3: .double -2.11499494167371287
- ASM_SIZE_DIRECTIVE(f3)
- ASM_TYPE_DIRECTIVE(f4,@object)
-f4: .double 2.44693122563534430
- ASM_SIZE_DIRECTIVE(f4)
- ASM_TYPE_DIRECTIVE(f5,@object)
-f5: .double -1.83469277483613086
- ASM_SIZE_DIRECTIVE(f5)
- ASM_TYPE_DIRECTIVE(f6,@object)
-f6: .double 0.784932344976639262
- ASM_SIZE_DIRECTIVE(f6)
ASM_TYPE_DIRECTIVE(f7,@object)
f7: .double -0.145263899385486377
ASM_SIZE_DIRECTIVE(f7)
+ ASM_TYPE_DIRECTIVE(f6,@object)
+f6: .double 0.784932344976639262
+ ASM_SIZE_DIRECTIVE(f6)
+ ASM_TYPE_DIRECTIVE(f5,@object)
+f5: .double -1.83469277483613086
+ ASM_SIZE_DIRECTIVE(f5)
+ ASM_TYPE_DIRECTIVE(f4,@object)
+f4: .double 2.44693122563534430
+ ASM_SIZE_DIRECTIVE(f4)
+ ASM_TYPE_DIRECTIVE(f3,@object)
+f3: .double -2.11499494167371287
+ ASM_SIZE_DIRECTIVE(f3)
+ ASM_TYPE_DIRECTIVE(f2,@object)
+f2: .double 1.50819193781584896
+ ASM_SIZE_DIRECTIVE(f2)
+ ASM_TYPE_DIRECTIVE(f1,@object)
+f1: .double 0.354895765043919860
+ ASM_SIZE_DIRECTIVE(f1)
-#define CBRT2 1.2599210498948731648
-#define SQR_CBRT2 1.5874010519681994748
+#define CBRT2 1.2599210498948731648
+#define ONE_CBRT2 0.793700525984099737355196796584
+#define SQR_CBRT2 1.5874010519681994748
+#define ONE_SQR_CBRT2 0.629960524947436582364439673883
ASM_TYPE_DIRECTIVE(factor,@object)
-factor: .double 1.0 / SQR_CBRT2
- .double 1.0 / CBRT2
+factor: .double ONE_SQR_CBRT2
+ .double ONE_CBRT2
.double 1.0
.double CBRT2
.double SQR_CBRT2
@@ -67,10 +69,10 @@ two54: .byte 0, 0, 0, 0, 0, 0, 0x50, 0x43
#ifdef PIC
#define MO(op) op##@GOTOFF(%ebx)
-#define MOX(op,x,f) op##@GOTOFF(%ebx,x,f)
+#define MOX(op,x) op##@GOTOFF(%ebx,x,1)
#else
#define MO(op) op
-#define MOX(op,x,f) op(,x,f)
+#define MOX(op,x) op(x)
#endif
.text
@@ -102,8 +104,13 @@ ENTRY(__cbrt)
#endif
fmull MO(two54)
movl $-54, %ecx
+#ifdef PIC
+ fstpl 8(%esp)
+ movl 12(%esp), %eax
+#else
fstpl 4(%esp)
movl 8(%esp), %eax
+#endif
movl %eax, %edx
andl $0x7fffffff, %eax
@@ -123,11 +130,16 @@ ENTRY(__cbrt)
#endif
fabs
- /* The following code has two track:
+ /* The following code has two tracks:
a) compute the normalized cbrt value
b) compute xe/3 and xe%3
The right track computes the value for b) and this is done
- in an optimized way by avoiding division. */
+ in an optimized way by avoiding division.
+
+ But why two tracks at all? Very easy: efficiency. Some FP
+ instruction can overlap with a certain amount of integer (and
+ FP) instructions. So we get (except for the imull) all
+ instructions for free. */
fld %st(0) /* xm : xm */
@@ -161,20 +173,24 @@ ENTRY(__cbrt)
fadd %st(0) /* 2*t2 : t2+2*xm : u : xm */
subl %edx, %ecx
faddp %st, %st(3) /* t2+2*xm : u : 2*t2+xm */
+ shll $3, %ecx
fmulp /* u*(t2+2*xm) : 2*t2+xm */
fdivp %st, %st(1) /* u*(t2+2*xm)/(2*t2+xm) */
- fmull MOX(16+factor,%ecx,8) /* u*(t2+2*xm)/(2*t2+xm)*FACT */
+ fmull MOX(16+factor,%ecx) /* u*(t2+2*xm)/(2*t2+xm)*FACT */
pushl %eax
fildl (%esp) /* xe/3 : u*(t2+2*xm)/(2*t2+xm)*FACT */
fxch /* u*(t2+2*xm)/(2*t2+xm)*FACT : xe/3 */
- popl %eax
fscale /* u*(t2+2*xm)/(2*t2+xm)*FACT*2^xe/3 */
- fstp %st(1)
+ popl %edx
#ifdef PIC
+ movl 12(%esp), %eax
popl %ebx
+#else
+ movl 8(%esp), %eax
#endif
- testl $0x80000000, 8(%esp)
- jz 4f
+ testl %eax, %eax
+ fstp %st(1)
+ jns 4f
fchs
4: ret
diff --git a/sysdeps/libm-i387/s_cbrtf.S b/sysdeps/libm-i387/s_cbrtf.S
index 6978da2d40..a14e04ed2f 100644
--- a/sysdeps/libm-i387/s_cbrtf.S
+++ b/sysdeps/libm-i387/s_cbrtf.S
@@ -28,22 +28,25 @@
#endif
.align ALIGNARG(4)
- ASM_TYPE_DIRECTIVE(f1,@object)
-f1: .double 0.492659620528969547
- ASM_SIZE_DIRECTIVE(f1)
- ASM_TYPE_DIRECTIVE(f2,@object)
-f2: .double 0.697570460207922770
- ASM_SIZE_DIRECTIVE(f2)
ASM_TYPE_DIRECTIVE(f3,@object)
f3: .double 0.191502161678719066
ASM_SIZE_DIRECTIVE(f3)
+ ASM_TYPE_DIRECTIVE(f2,@object)
+f2: .double 0.697570460207922770
+ ASM_SIZE_DIRECTIVE(f2)
+ ASM_TYPE_DIRECTIVE(f1,@object)
+f1: .double 0.492659620528969547
+ ASM_SIZE_DIRECTIVE(f1)
-#define CBRT2 1.2599210498948731648
-#define SQR_CBRT2 1.5874010519681994748
+#define CBRT2 1.2599210498948731648
+#define ONE_CBRT2 0.793700525984099737355196796584
+#define SQR_CBRT2 1.5874010519681994748
+#define ONE_SQR_CBRT2 0.629960524947436582364439673883
ASM_TYPE_DIRECTIVE(factor,@object)
-factor: .double 1.0 / SQR_CBRT2
- .double 1.0 / CBRT2
+ .align ALIGNARG(4)
+factor: .double ONE_SQR_CBRT2
+ .double ONE_CBRT2
.double 1.0
.double CBRT2
.double SQR_CBRT2
@@ -55,10 +58,10 @@ two25: .byte 0, 0, 0, 0x4c
#ifdef PIC
#define MO(op) op##@GOTOFF(%ebx)
-#define MOX(op,x,f) op##@GOTOFF(%ebx,x,f)
+#define MOX(op,x) op##@GOTOFF(%ebx,x,1)
#else
#define MO(op) op
-#define MOX(op,x,f) op(,x,f)
+#define MOX(op,x) op(x)
#endif
.text
@@ -114,11 +117,16 @@ ENTRY(__cbrtf)
#endif
fabs
- /* The following code has two track:
+ /* The following code has two tracks:
a) compute the normalized cbrt value
b) compute xe/3 and xe%3
The right track computes the value for b) and this is done
- in an optimized way by avoiding division. */
+ in an optimized way by avoiding division.
+
+ But why two tracks at all? Very easy: efficiency. Some FP
+ instruction can overlap with a certain amount of integer (and
+ FP) instructions. So we get (except for the imull) all
+ instructions for free. */
fld %st(0) /* xm : xm */
fmull MO(f3) /* f3*xm : xm */
@@ -142,20 +150,24 @@ ENTRY(__cbrtf)
fadd %st(0) /* 2*t2 : t2+2*xm : u : xm */
subl %edx, %ecx
faddp %st, %st(3) /* t2+2*xm : u : 2*t2+xm */
+ shll $3, %ecx
fmulp /* u*(t2+2*xm) : 2*t2+xm */
fdivp %st, %st(1) /* u*(t2+2*xm)/(2*t2+xm) */
- fmull MOX(16+factor,%ecx,8) /* u*(t2+2*xm)/(2*t2+xm)*FACT */
+ fmull MOX(16+factor,%ecx) /* u*(t2+2*xm)/(2*t2+xm)*FACT */
pushl %eax
fildl (%esp) /* xe/3 : u*(t2+2*xm)/(2*t2+xm)*FACT */
fxch /* u*(t2+2*xm)/(2*t2+xm)*FACT : xe/3 */
- popl %eax
fscale /* u*(t2+2*xm)/(2*t2+xm)*FACT*2^xe/3 */
- fstp %st(1)
+ popl %edx
#ifdef PIC
+ movl 8(%esp), %eax
popl %ebx
+#else
+ movl 4(%esp), %eax
#endif
- testl $0x80000000, 4(%esp)
- jz 4f
+ testl %eax, %eax
+ fstp %st(1)
+ jns 4f
fchs
4: ret
diff --git a/sysdeps/libm-i387/s_cbrtl.S b/sysdeps/libm-i387/s_cbrtl.S
index b2023d1991..6a3b9a8dc5 100644
--- a/sysdeps/libm-i387/s_cbrtl.S
+++ b/sysdeps/libm-i387/s_cbrtl.S
@@ -28,52 +28,69 @@
#endif
.align ALIGNARG(4)
- ASM_TYPE_DIRECTIVE(f1,@object)
-f1: .double 0.338058687610520237
- ASM_SIZE_DIRECTIVE(f1)
- ASM_TYPE_DIRECTIVE(f2,@object)
-f2: .double 1.67595307700780102
- ASM_SIZE_DIRECTIVE(f2)
- ASM_TYPE_DIRECTIVE(f3,@object)
-f3: .double -2.82414939754975962
- ASM_SIZE_DIRECTIVE(f3)
- ASM_TYPE_DIRECTIVE(f4,@object)
-f4: .double 4.09559907378707839
- ASM_SIZE_DIRECTIVE(f4)
- ASM_TYPE_DIRECTIVE(f5,@object)
-f5: .double -4.11151425200350531
- ASM_SIZE_DIRECTIVE(f5)
- ASM_TYPE_DIRECTIVE(f6,@object)
-f6: .double 2.65298938441952296
- ASM_SIZE_DIRECTIVE(f6)
- ASM_TYPE_DIRECTIVE(f7,@object)
-f7: .double -0.988553671195413709
- ASM_SIZE_DIRECTIVE(f7)
ASM_TYPE_DIRECTIVE(f8,@object)
-f8: .double 0.161617097923756032
+f8: .tfloat 0.161617097923756032
ASM_SIZE_DIRECTIVE(f8)
+ .align ALIGNARG(4)
+ ASM_TYPE_DIRECTIVE(f7,@object)
+f7: .tfloat -0.988553671195413709
+ ASM_SIZE_DIRECTIVE(f7)
+ .align ALIGNARG(4)
+ ASM_TYPE_DIRECTIVE(f6,@object)
+f6: .tfloat 2.65298938441952296
+ ASM_SIZE_DIRECTIVE(f6)
+ .align ALIGNARG(4)
+ ASM_TYPE_DIRECTIVE(f5,@object)
+f5: .tfloat -4.11151425200350531
+ ASM_SIZE_DIRECTIVE(f5)
+ .align ALIGNARG(4)
+ ASM_TYPE_DIRECTIVE(f4,@object)
+f4: .tfloat 4.09559907378707839
+ ASM_SIZE_DIRECTIVE(f4)
+ .align ALIGNARG(4)
+ ASM_TYPE_DIRECTIVE(f3,@object)
+f3: .tfloat -2.82414939754975962
+ ASM_SIZE_DIRECTIVE(f3)
+ .align ALIGNARG(4)
+ ASM_TYPE_DIRECTIVE(f2,@object)
+f2: .tfloat 1.67595307700780102
+ ASM_SIZE_DIRECTIVE(f2)
+ .align ALIGNARG(4)
+ ASM_TYPE_DIRECTIVE(f1,@object)
+f1: .tfloat 0.338058687610520237
+ ASM_SIZE_DIRECTIVE(f1)
-#define CBRT2 1.2599210498948731648
-#define SQR_CBRT2 1.5874010519681994748
+#define CBRT2 1.2599210498948731648
+#define ONE_CBRT2 0.793700525984099737355196796584
+#define SQR_CBRT2 1.5874010519681994748
+#define ONE_SQR_CBRT2 0.629960524947436582364439673883
+ /* We make the entries in the following table all 16 bytes
+ wide to avoid having to implement a multiplication by 10. */
ASM_TYPE_DIRECTIVE(factor,@object)
-factor: .double 1.0 / SQR_CBRT2
- .double 1.0 / CBRT2
- .double 1.0
- .double CBRT2
- .double SQR_CBRT2
+ .align ALIGNARG(4)
+factor: .tfloat ONE_SQR_CBRT2
+ .byte 0, 0, 0, 0, 0, 0
+ .tfloat ONE_CBRT2
+ .byte 0, 0, 0, 0, 0, 0
+ .tfloat 1.0
+ .byte 0, 0, 0, 0, 0, 0
+ .tfloat CBRT2
+ .byte 0, 0, 0, 0, 0, 0
+ .tfloat SQR_CBRT2
ASM_SIZE_DIRECTIVE(factor)
ASM_TYPE_DIRECTIVE(two64,@object)
+ .align ALIGNARG(4)
two64: .byte 0, 0, 0, 0, 0, 0, 0xf0, 0x43
ASM_SIZE_DIRECTIVE(two64)
#ifdef PIC
#define MO(op) op##@GOTOFF(%ebx)
-#define MOX(op,x,f) op##@GOTOFF(%ebx,x,f)
+#define MOX(op,x) op##@GOTOFF(%ebx,x,1)
#else
#define MO(op) op
-#define MOX(op,x,f) op(,x,f)
+#define MOX(op,x) op(x)
#endif
.text
@@ -97,7 +114,7 @@ ENTRY(__cbrtl)
#endif
cmpl $0, %eax
- je 2f
+ jne 2f
#ifdef PIC
fldt 8(%esp)
@@ -106,8 +123,13 @@ ENTRY(__cbrtl)
#endif
fmull MO(two64)
movl $-64, %ecx
+#ifdef PIC
+ fstpt 8(%esp)
+ movl 16(%esp), %eax
+#else
fstpt 4(%esp)
movl 12(%esp), %eax
+#endif
movl %eax, %edx
andl $0x7fff, %eax
@@ -126,31 +148,45 @@ ENTRY(__cbrtl)
#endif
fabs
- /* The following code has two track:
+ /* The following code has two tracks:
a) compute the normalized cbrt value
b) compute xe/3 and xe%3
The right track computes the value for b) and this is done
- in an optimized way by avoiding division. */
+ in an optimized way by avoiding division.
- fld %st(0) /* xm : xm */
+ But why two tracks at all? Very easy: efficiency. Some FP
+ instruction can overlap with a certain amount of integer (and
+ FP) instructions. So we get (except for the imull) all
+ instructions for free. */
- fmull MO(f7) /* f7*xm : xm */
+ fldt MO(f8) /* f8 : xm */
+ fmul %st(1) /* f8*xm : xm */
+
+ fldt MO(f7)
+ faddp /* f7+f8*xm : xm */
+ fmul %st(1) /* (f7+f8*xm)*xm : xm */
movl $1431655766, %eax
- faddl MO(f6) /* f6+f7*xm : xm */
+ fldt MO(f6)
+ faddp /* f6+(f7+f8*xm)*xm : xm */
imull %ecx
- fmul %st(1) /* (f6+f7*xm)*xm : xm */
+ fmul %st(1) /* (f6+(f7+f8*xm)*xm)*xm : xm */
movl %ecx, %eax
- faddl MO(f5) /* f5+(f6+f7*xm)*xm : xm */
+ fldt MO(f5)
+ faddp /* f5+(f6+(f7+f8*xm)*xm)*xm : xm */
sarl $31, %eax
- fmul %st(1) /* (f5+(f6+f7*xm)*xm)*xm : xm */
+ fmul %st(1) /* (f5+(f6+(f7+f8*xm)*xm)*xm)*xm : xm */
subl %eax, %edx
- faddl MO(f4) /* f4+(f5+(f6+f7*xm)*xm)*xm : xm */
- fmul %st(1) /* (f4+(f5+(f6+f7*xm)*xm)*xm)*xm : xm */
- faddl MO(f3) /* f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm : xm */
- fmul %st(1) /* (f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm)*xm : xm */
- faddl MO(f2) /* f2+(f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm)*xm : xm */
- fmul %st(1) /* (f2+(f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm)*xm)*xm : xm */
- faddl MO(f1) /* u:=f1+(f2+(f3+(f4+(f5+(f6+f7*xm)*xm)*xm)*xm)*xm)*xm : xm */
+ fldt MO(f4)
+ faddp /* f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm : xm */
+ fmul %st(1) /* (f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm : xm */
+ fldt MO(f3)
+ faddp /* f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm : xm */
+ fmul %st(1) /* (f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm : xm */
+ fldt MO(f2)
+ faddp /* f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm : xm */
+ fmul %st(1) /* (f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm)*xm : xm */
+ fldt MO(f1)
+ faddp /* u:=f1+(f2+(f3+(f4+(f5+(f6+(f7+f8*xm)*xm)*xm)*xm)*xm)*xm)*xm : xm */
fld %st /* u : u : xm */
fmul %st(1) /* u*u : u : xm */
@@ -164,19 +200,24 @@ ENTRY(__cbrtl)
fadd %st(0) /* 2*t2 : t2+2*xm : u : xm */
subl %edx, %ecx
faddp %st, %st(3) /* t2+2*xm : u : 2*t2+xm */
+ shll $4, %ecx
fmulp /* u*(t2+2*xm) : 2*t2+xm */
fdivp %st, %st(1) /* u*(t2+2*xm)/(2*t2+xm) */
- fmull MOX(16+factor,%ecx,8) /* u*(t2+2*xm)/(2*t2+xm)*FACT */
+ fldt MOX(32+factor,%ecx)
+ fmulp /* u*(t2+2*xm)/(2*t2+xm)*FACT */
pushl %eax
fildl (%esp) /* xe/3 : u*(t2+2*xm)/(2*t2+xm)*FACT */
fxch /* u*(t2+2*xm)/(2*t2+xm)*FACT : xe/3 */
- popl %eax
fscale /* u*(t2+2*xm)/(2*t2+xm)*FACT*2^xe/3 */
- fstp %st(1)
+ popl %edx
#ifdef PIC
+ movl 16(%esp), %eax
popl %ebx
+#else
+ movl 12(%esp), %eax
#endif
- testl $0x8000, 12(%esp)
+ testl $0x8000, %eax
+ fstp %st(1)
jz 4f
fchs
4: ret
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