diff --git a/math/s_ccoshf.c b/math/s_ccoshf.c
index d6f8110..9ca57b2 100644
--- a/math/s_ccoshf.c
+++ b/math/s_ccoshf.c
@@ -39,7 +39,15 @@ __ccoshf (__complex__ float x)
const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2);
float sinix, cosix;
- __sincosf (__imag__ x, &sinix, &cosix);
+ if (__builtin_expect (icls != FP_SUBNORMAL, 1))
+ {
+ __sincosf (__imag__ x, &sinix, &cosix);
+ }
+ else
+ {
+ sinix = __imag__ x;
+ cosix = 1.0f;
+ }
if (fabsf (__real__ x) > t)
{
@@ -92,7 +100,15 @@ __ccoshf (__complex__ float x)
/* Imaginary part is finite. */
float sinix, cosix;
- __sincosf (__imag__ x, &sinix, &cosix);
+ if (__builtin_expect (icls != FP_SUBNORMAL, 1))
+ {
+ __sincosf (__imag__ x, &sinix, &cosix);
+ }
+ else
+ {
+ sinix = __imag__ x;
+ cosix = 1.0f;
+ }
__real__ retval = __copysignf (HUGE_VALF, cosix);
__imag__ retval = (__copysignf (HUGE_VALF, sinix)
diff --git a/math/s_cexpf.c b/math/s_cexpf.c
index 4aa9765..41fcea5 100644
--- a/math/s_cexpf.c
+++ b/math/s_cexpf.c
@@ -39,7 +39,15 @@ __cexpf (__complex__ float x)
const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2);
float sinix, cosix;
- __sincosf (__imag__ x, &sinix, &cosix);
+ if (__builtin_expect (icls != FP_SUBNORMAL, 1))
+ {
+ __sincosf (__imag__ x, &sinix, &cosix);
+ }
+ else
+ {
+ sinix = __imag__ x;
+ cosix = 1.0f;
+ }
if (__real__ x > t)
{
@@ -95,7 +103,15 @@ __cexpf (__complex__ float x)
{
float sinix, cosix;
- __sincosf (__imag__ x, &sinix, &cosix);
+ if (__builtin_expect (icls != FP_SUBNORMAL, 1))
+ {
+ __sincosf (__imag__ x, &sinix, &cosix);
+ }
+ else
+ {
+ sinix = __imag__ x;
+ cosix = 1.0f;
+ }
__real__ retval = __copysignf (value, cosix);
__imag__ retval = __copysignf (value, sinix);
diff --git a/math/s_csinf.c b/math/s_csinf.c
index c1d6a4f..d53f943 100644
--- a/math/s_csinf.c
+++ b/math/s_csinf.c
@@ -42,7 +42,15 @@ __csinf (__complex__ float x)
const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2);
float sinix, cosix;
- __sincosf (__real__ x, &sinix, &cosix);
+ if (__builtin_expect (rcls != FP_SUBNORMAL, 1))
+ {
+ __sincosf (__real__ x, &sinix, &cosix);
+ }
+ else
+ {
+ sinix = __real__ x;
+ cosix = 1.0f;
+ }
if (fabsf (__imag__ x) > t)
{
@@ -115,7 +123,15 @@ __csinf (__complex__ float x)
/* Real part is finite. */
float sinix, cosix;
- __sincosf (__real__ x, &sinix, &cosix);
+ if (__builtin_expect (rcls != FP_SUBNORMAL, 1))
+ {
+ __sincosf (__real__ x, &sinix, &cosix);
+ }
+ else
+ {
+ sinix = __real__ x;
+ cosix = 1.0f;
+ }
__real__ retval = __copysignf (HUGE_VALF, sinix);
__imag__ retval = __copysignf (HUGE_VALF, cosix);
diff --git a/math/s_csinhf.c b/math/s_csinhf.c
index ba85e79..4b019a0 100644
--- a/math/s_csinhf.c
+++ b/math/s_csinhf.c
@@ -42,7 +42,15 @@ __csinhf (__complex__ float x)
const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2);
float sinix, cosix;
- __sincosf (__imag__ x, &sinix, &cosix);
+ if (__builtin_expect (icls != FP_SUBNORMAL, 1))
+ {
+ __sincosf (__imag__ x, &sinix, &cosix);
+ }
+ else
+ {
+ sinix = __imag__ x;
+ cosix = 1.0f;
+ }
if (fabsf (__real__ x) > t)
{
@@ -109,7 +117,15 @@ __csinhf (__complex__ float x)
/* Imaginary part is finite. */
float sinix, cosix;
- __sincosf (__imag__ x, &sinix, &cosix);
+ if (__builtin_expect (icls != FP_SUBNORMAL, 1))
+ {
+ __sincosf (__imag__ x, &sinix, &cosix);
+ }
+ else
+ {
+ sinix = __imag__ x;
+ cosix = 1.0f;
+ }
__real__ retval = __copysignf (HUGE_VALF, cosix);
__imag__ retval = __copysignf (HUGE_VALF, sinix);
diff --git a/math/s_ctanf.c b/math/s_ctanf.c
index 2559f83..fd2b797 100644
--- a/math/s_ctanf.c
+++ b/math/s_ctanf.c
@@ -57,7 +57,15 @@ __ctanf (__complex__ float x)
/* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
= (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
- __sincosf (__real__ x, &sinrx, &cosrx);
+ if (__builtin_expect (fpclassify(__real__ x) != FP_SUBNORMAL, 1))
+ {
+ __sincosf (__real__ x, &sinrx, &cosrx);
+ }
+ else
+ {
+ sinrx = __real__ x;
+ cosrx = 1.0f;
+ }
if (fabsf (__imag__ x) > t)
{
diff --git a/math/s_ctanhf.c b/math/s_ctanhf.c
index ca36a83..862845f 100644
--- a/math/s_ctanhf.c
+++ b/math/s_ctanhf.c
@@ -57,7 +57,15 @@ __ctanhf (__complex__ float x)
/* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
= (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
- __sincosf (__imag__ x, &sinix, &cosix);
+ if (__builtin_expect (fpclassify(__imag__ x) != FP_SUBNORMAL, 1))
+ {
+ __sincosf (__imag__ x, &sinix, &cosix);
+ }
+ else
+ {
+ sinix = __imag__ x;
+ cosix = 1.0f;
+ }
if (fabsf (__real__ x) > t)
{
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index f0701ef..80c14d0 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1490,9 +1490,9 @@ float: 1
ifloat: 1
Test "Real part of: cpow (0.75 + 1.25 i, 1.0 + 1.0 i) == 0.0846958290317209430433805274189191353 + 0.513285749182902449043287190519090481 i":
double: 2
-float: 3
+float: 4
idouble: 2
-ifloat: 3
+ifloat: 4
ildouble: 3
ldouble: 3
Test "Imaginary part of: cpow (0.75 + 1.25 i, 1.0 + 1.0 i) == 0.0846958290317209430433805274189191353 + 0.513285749182902449043287190519090481 i":
@@ -1704,6 +1704,8 @@ ldouble: 1
# ctan
Test "Real part of: ctan (-2 - 3 i) == 0.376402564150424829275122113032269084e-2 - 1.00323862735360980144635859782192726 i":
+float: 1
+ifloat: 1
double: 1
idouble: 1
ildouble: 1
@@ -1797,6 +1799,8 @@ Test "Imaginary part of: ctan_towardzero (0x1.921fb54442d18p+0 + 0x1p-1074 i) ==
ildouble: 1
ldouble: 1
Test "Real part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
ildouble: 1
ldouble: 1
Test "Imaginary part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
@@ -1827,9 +1831,9 @@ ildouble: 2
ldouble: 2
Test "Imaginary part of: ctan_upward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
double: 1
-float: 1
+float: 2
idouble: 1
-ifloat: 1
+ifloat: 2
ildouble: 1
ldouble: 1
@@ -1940,6 +1944,8 @@ ifloat: 3
ildouble: 4
ldouble: 4
Test "Imaginary part of: ctanh_towardzero (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
ildouble: 1
ldouble: 1
@@ -1954,9 +1960,9 @@ ildouble: 1
ldouble: 1
Test "Real part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
double: 1
-float: 1
+float: 2
idouble: 1
-ifloat: 1
+ifloat: 2
ildouble: 1
ldouble: 1
Test "Imaginary part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
@@ -2556,9 +2562,6 @@ ifloat: 1
Test "sincos (-0x1p65, &sin_res, &cos_res) puts 0.047183876212354673805106149805700013943218 in sin_res":
float: 1
ifloat: 1
-Test "sincos (0x1p+50, &sin_res, &cos_res) puts 8.68095904660550604334592502063501320395739e-01 in cos_res":
-float: 1
-ifloat: 1
Test "sincos (0x1p65, &sin_res, &cos_res) puts -0.047183876212354673805106149805700013943218 in sin_res":
float: 1
ifloat: 1
@@ -3434,6 +3437,8 @@ ildouble: 1
ldouble: 1
Function: Real part of "ctan_towardzero":
+float: 1
+ifloat: 1
double: 1
idouble: 1
ildouble: 1
@@ -3453,9 +3458,9 @@ ldouble: 2
Function: Imaginary part of "ctan_upward":
double: 1
-float: 1
+float: 2
idouble: 1
-ifloat: 1
+ifloat: 2
ildouble: 4
ldouble: 4
@@ -3506,6 +3511,8 @@ ildouble: 4
ldouble: 4
Function: Imaginary part of "ctanh_towardzero":
+float: 1
+ifloat: 1
double: 1
idouble: 1
ildouble: 1
@@ -3513,9 +3520,9 @@ ldouble: 1
Function: Real part of "ctanh_upward":
double: 1
-float: 1
+float: 2
idouble: 1
-ifloat: 1
+ifloat: 2
ildouble: 4
ldouble: 4
diff --git a/sysdeps/i386/i686/fpu/multiarch/Makefile b/sysdeps/i386/i686/fpu/multiarch/Makefile
index aa28f72..7d90892 100644
--- a/sysdeps/i386/i686/fpu/multiarch/Makefile
+++ b/sysdeps/i386/i686/fpu/multiarch/Makefile
@@ -1,3 +1,4 @@
ifeq ($(subdir),math)
-libm-sysdep_routines += e_expf-sse2 e_expf-ia32 s_sinf-sse2 s_cosf-sse2
+libm-sysdep_routines += e_expf-sse2 e_expf-ia32 s_sinf-sse2 s_cosf-sse2 \
+ s_sincosf-sse2
endif
diff --git a/sysdeps/i386/i686/fpu/multiarch/s_cosf-sse2.S b/sysdeps/i386/i686/fpu/multiarch/s_cosf-sse2.S
index 2b5a2a5..405c6ea 100644
--- a/sysdeps/i386/i686/fpu/multiarch/s_cosf-sse2.S
+++ b/sysdeps/i386/i686/fpu/multiarch/s_cosf-sse2.S
@@ -50,25 +50,29 @@
* 9) if x is NaN, return x-x.
*
* Special cases:
- * cos(+-0)==+-0 not raising inexact/underflow,
- * cos(subnormal) raises inexact/underflow
- * cos(min_normalized) raises inexact/underflow
- * cos(normalized) raises inexact
- * cos(Inf) = NaN, raises invalid, sets errno to EDOM
- * cos(NaN) = NaN
+ * cos(+-0) = 1 not raising inexact,
+ * cos(subnormal) raises inexact,
+ * cos(min_normalized) raises inexact,
+ * cos(normalized) raises inexact,
+ * cos(Inf) = NaN, raises invalid, sets errno to EDOM,
+ * cos(NaN) = NaN.
*/
#ifdef PIC
# define MO1(symbol) L(symbol)##@GOTOFF(%ebx)
# define MO2(symbol,reg2,_scale) L(symbol)##@GOTOFF(%ebx,reg2,_scale)
-# define SAVE_BX pushl %ebx
-# define RESTORE_BX popl %ebx
+# define CFI_PUSH(REG) cfi_adjust_cfa_offset(4); cfi_rel_offset(REG,0)
+# define CFI_POP(REG) cfi_adjust_cfa_offset(-4); cfi_restore(REG)
+# define PUSH(REG) pushl REG; CFI_PUSH(REG)
+# define POP(REG) popl REG; CFI_POP(REG)
+# define ENTRANCE PUSH(%ebx); LOAD_PIC_REG(bx)
+# define RETURN POP(%ebx); ret; CFI_PUSH(%ebx)
# define ARG_X 8(%esp)
#else
# define MO1(symbol) L(symbol)
# define MO2(symbol,reg2,_scale) L(symbol)(,reg2,_scale)
-# define SAVE_BX
-# define RESTORE_BX
+# define ENTRANCE
+# define RETURN ret
# define ARG_X 4(%esp)
#endif
@@ -76,11 +80,7 @@
ENTRY(__cosf_sse2)
/* Input: single precision x on stack at address ARG_X */
-#ifdef PIC
- SAVE_BX
- LOAD_PIC_REG(bx)
-#endif
-
+ ENTRANCE
movl ARG_X, %eax /* Bits of x */
cvtss2sd ARG_X, %xmm0 /* DP x */
andl $0x7fffffff, %eax /* |x| */
@@ -143,8 +143,7 @@ L(reconstruction):
fldl 0(%esp) /* ...to FPU. */
/* Return back 4 bytes of stack frame */
lea 8(%esp), %esp
- RESTORE_BX
- ret
+ RETURN
.p2align 4
L(sin_poly):
@@ -183,9 +182,7 @@ L(sin_poly):
fldl 0(%esp) /* ...to FPU. */
/* Return back 4 bytes of stack frame */
lea 8(%esp), %esp
- RESTORE_BX
- ret
-
+ RETURN
.p2align 4
L(large_args):
@@ -275,7 +272,6 @@ L(very_large_skip2):
jmp L(reconstruction) /* end of very_large_args peth */
-
.p2align 4
L(arg_less_pio4):
/* Here if |x|. */
+
+#include
+#define __need_Emath
+#include
+
+/* Short algorithm description:
+ *
+ * 1) if |x|==0: sin(x)=x,
+ * cos(x)=1.
+ * 2) if |x|<2^-27: sin(x)=x-x*DP_SMALL, raising underflow only when needed,
+ * cos(x)=1-|x|.
+ * 3) if |x|<2^-5 : sin(x)=x+x*x^2*DP_SIN2_0+x^5*DP_SIN2_1,
+ * cos(x)=1+1*x^2*DP_COS2_0+x^5*DP_COS2_1
+ * 4) if |x|< Pi/4: sin(x)=x+x*x^2*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))),
+ * cos(x)=1+1*x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))).
+ * 5) if |x| < 9*Pi/4:
+ * 5.1) Range reduction:
+ * k=trunc(|x|/(Pi/4)), j=(k+1)&0x0e, n=k+1, t=|x|-j*Pi/4.
+ * 5.2) Reconstruction:
+ * sign_sin = sign(x) * (-1.0)^(( n >>2)&1)
+ * sign_cos = (-1.0)^(((n+2)>>2)&1)
+ * poly_sin = ((((S4*t^2 + S3)*t^2 + S2)*t^2 + S1)*t^2 + S0)*t^2*t+t
+ * poly_cos = ((((C4*t^2 + C3)*t^2 + C2)*t^2 + C1)*t^2 + C0)*t^2*s+s
+ * if(n&2 != 0) {
+ * using cos(t) and sin(t) polynomials for |t|= 2^23, very large args:
+ * 7.1) Range reduction:
+ * k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+1, t=|x|-j*Pi/4.
+ * 7.2) Reconstruction same as (5.2).
+ * 8) if x is Inf, return x-x, and set errno=EDOM.
+ * 9) if x is NaN, return x-x.
+ *
+ * Special cases:
+ * sin/cos(+-0) = +-0/1 not raising inexact/underflow,
+ * sin/cos(subnormal) raises inexact/underflow,
+ * sin/cos(min_normalized) raises inexact/underflow,
+ * sin/cos(normalized) raises inexact,
+ * sin/cos(Inf) = NaN, raises invalid, sets errno to EDOM,
+ * sin/cos(NaN) = NaN.
+ */
+
+#ifdef PIC
+# define MO1(symbol) L(symbol)##@GOTOFF(%ebx)
+# define MO2(symbol,reg2,_scale) L(symbol)##@GOTOFF(%ebx,reg2,_scale)
+# define CFI_PUSH(REG) cfi_adjust_cfa_offset(4); cfi_rel_offset(REG,0)
+# define CFI_POP(REG) cfi_adjust_cfa_offset(-4); cfi_restore(REG)
+# define PUSH(REG) pushl REG; CFI_PUSH(REG)
+# define POP(REG) popl REG; CFI_POP(REG)
+# define ENTRANCE PUSH(%ebx); LOAD_PIC_REG(bx)
+# define RETURN POP(%ebx); ret; CFI_PUSH(%ebx)
+# define ARG_X 8(%esp)
+# define ARG_SIN_PTR 12(%esp)
+# define ARG_COS_PTR 16(%esp)
+#else
+# define MO1(symbol) L(symbol)
+# define MO2(symbol,reg2,_scale) L(symbol)(,reg2,_scale)
+# define ENTRANCE
+# define RETURN ret
+# define ARG_X 4(%esp)
+# define ARG_SIN_PTR 8(%esp)
+# define ARG_COS_PTR 12(%esp)
+#endif
+
+ .text
+ENTRY(__sincosf_sse2)
+ /* Input: single precision x on stack at address ARG_X */
+ /* pointer to sin result on stack at address ARG_SIN_PTR */
+ /* pointer to cos result on stack at address ARG_COS_PTR */
+
+ ENTRANCE
+ movl ARG_X, %eax /* Bits of x */
+ cvtss2sd ARG_X, %xmm0 /* DP x */
+ andl $0x7fffffff, %eax /* |x| */
+
+ cmpl $0x3f490fdb, %eax /* |x|=Pi/4 */
+ movd %eax, %xmm3 /* SP |x| */
+ andpd MO1(DP_ABS_MASK),%xmm0 /* DP |x| */
+ movss MO1(SP_INVPIO4), %xmm2 /* SP 1/(Pi/4) */
+
+ cmpl $0x40e231d6, %eax /* |x|<9*Pi/4 ? */
+ jae L(large_args)
+
+ /* Here if Pi/4<=|x|<9*Pi/4 */
+ mulss %xmm3, %xmm2 /* SP |x|/(Pi/4) */
+ movl ARG_X, %ecx /* Load x */
+ cvttss2si %xmm2, %eax /* k, number of Pi/4 in x */
+ shrl $29, %ecx /* (sign of x) << 2 */
+ addl $1, %eax /* k+1 */
+ movl $0x0e, %edx
+ andl %eax, %edx /* j = (k+1)&0x0e */
+ subsd MO2(PIO4J,%edx,8), %xmm0/* t = |x| - j * Pi/4 */
+
+L(reconstruction):
+ /* Input: %eax=n, %xmm0=t, %ecx=sign(x) */
+
+ movaps %xmm0, %xmm4 /* t */
+ movhpd MO1(DP_ONES), %xmm4 /* 1|t */
+ mulsd %xmm0, %xmm0 /* y=t^2 */
+ movl $2, %edx
+ unpcklpd %xmm0, %xmm0 /* y|y */
+ addl %eax, %edx /* k+2 */
+ movaps %xmm0, %xmm1 /* y|y */
+ mulpd %xmm0, %xmm0 /* z=t^4|z=t^4 */
+
+ movaps MO1(DP_SC4), %xmm2 /* S4 */
+ mulpd %xmm0, %xmm2 /* z*S4 */
+ movaps MO1(DP_SC3), %xmm3 /* S3 */
+ mulpd %xmm0, %xmm3 /* z*S3 */
+ xorl %eax, %ecx /* (sign_x ^ (k>>2))<<2 */
+ addpd MO1(DP_SC2), %xmm2 /* S2+z*S4 */
+ mulpd %xmm0, %xmm2 /* z*(S2+z*S4) */
+ shrl $2, %edx /* (k+2)>>2 */
+ addpd MO1(DP_SC1), %xmm3 /* S1+z*S3 */
+ mulpd %xmm0, %xmm3 /* z*(S1+z*S3) */
+ shrl $2, %ecx /* sign_x ^ k>>2 */
+ addpd MO1(DP_SC0), %xmm2 /* S0+z*(S2+z*S4) */
+ andl $1, %edx /* sign_cos = ((k+2)>>2)&1 */
+ mulpd %xmm1, %xmm2 /* y*(S0+z*(S2+z*S4)) */
+ andl $1, %ecx /* sign_sin = sign_x ^ ((k>>2)&1) */
+ addpd %xmm2, %xmm3 /* y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */
+ mulpd %xmm4, %xmm3 /*t*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))))*/
+ testl $2, %eax /* n&2 != 0 ? */
+ addpd %xmm4, %xmm3 /*t+t*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))*/
+ jnz L(sin_result_sin_poly)
+
+/*L(sin_result_cos_poly):*/
+ /*
+ * Here if
+ * cos(x) = poly_sin * sign_cos
+ * sin(x) = poly_cos * sign_sin
+ */
+ movsd MO2(DP_ONES,%ecx,8), %xmm4/* 0|sign_sin */
+ movhpd MO2(DP_ONES,%edx,8), %xmm4/* sign_cos|sign_sin */
+ mulpd %xmm4, %xmm3 /* result_cos|result_sin */
+ movl ARG_SIN_PTR, %eax
+ cvtpd2ps %xmm3, %xmm0 /* SP results */
+ movl ARG_COS_PTR, %ecx
+ movss %xmm0, (%eax) /* store sin(x) from xmm0[0] */
+ shufps $1, %xmm0, %xmm0 /* move cos(x) to xmm0[0] */
+ movss %xmm0, (%ecx) /* store cos(x) */
+ RETURN
+
+ .p2align 4
+L(sin_result_sin_poly):
+ /*
+ * Here if
+ * sin(x) = poly_sin * sign_sin
+ * cos(x) = poly_cos * sign_cos
+ */
+ movsd MO2(DP_ONES,%edx,8), %xmm4/* 0|sign_cos */
+ movhpd MO2(DP_ONES,%ecx,8), %xmm4/* sign_sin|sign_cos */
+ mulpd %xmm4, %xmm3 /* result_sin|result_cos */
+ movl ARG_SIN_PTR, %eax
+ cvtpd2ps %xmm3, %xmm0 /* SP results */
+ movl ARG_COS_PTR, %ecx
+ movss %xmm0, (%ecx) /* store cos(x) from xmm0[0] */
+ shufps $1, %xmm0, %xmm0 /* move sin(x) to xmm0[0] */
+ movss %xmm0, (%eax) /* store sin(x) */
+ RETURN
+
+ .p2align 4
+L(large_args):
+ /* Here if |x|>=9*Pi/4 */
+ cmpl $0x7f800000, %eax /* x is Inf or NaN ? */
+ jae L(arg_inf_or_nan)
+
+ /* Here if finite |x|>=9*Pi/4 */
+ cmpl $0x4b000000, %eax /* |x|<2^23 ? */
+ jae L(very_large_args)
+
+ /* Here if 9*Pi/4<=|x|<2^23 */
+ movsd MO1(DP_INVPIO4), %xmm1 /* 1/(Pi/4) */
+ mulsd %xmm0, %xmm1 /* |x|/(Pi/4) */
+ cvttsd2si %xmm1, %eax /* k=trunc(|x|/(Pi/4)) */
+ addl $1, %eax /* k+1 */
+ movl %eax, %edx
+ andl $0xfffffffe, %edx /* j=(k+1)&0xfffffffe */
+ cvtsi2sdl %edx, %xmm4 /* DP j */
+ movl ARG_X, %ecx /* Load x */
+ movsd MO1(DP_PIO4HI), %xmm2 /* -PIO4HI = high part of -Pi/4 */
+ shrl $29, %ecx /* (sign of x) << 2 */
+ mulsd %xmm4, %xmm2 /* -j*PIO4HI */
+ movsd MO1(DP_PIO4LO), %xmm3 /* -PIO4LO = low part of -Pi/4 */
+ addsd %xmm2, %xmm0 /* |x| - j*PIO4HI */
+ mulsd %xmm3, %xmm4 /* j*PIO4LO */
+ addsd %xmm4, %xmm0 /* t = |x| - j*PIO4HI - j*PIO4LO */
+ jmp L(reconstruction)
+
+ .p2align 4
+L(very_large_args):
+ /* Here if finite |x|>=2^23 */
+
+ /* bitpos = (ix>>23) - BIAS_32 + 59; */
+ shrl $23, %eax /* eb = biased exponent of x */
+ subl $68, %eax /* bitpos=eb-0x7f+59, where 0x7f */
+ /*is exponent bias */
+ movl $28, %ecx /* %cl=28 */
+ movl %eax, %edx /* bitpos copy */
+
+ /* j = bitpos/28; */
+ div %cl /* j in register %al=%ax/%cl */
+ movapd %xmm0, %xmm3 /* |x| */
+ andl $0xff, %eax /* clear unneeded remainder from %ah*/
+
+ imull $28, %eax, %ecx /* j*28 */
+ movsd MO1(DP_HI_MASK), %xmm4 /* DP_HI_MASK */
+ movapd %xmm0, %xmm5 /* |x| */
+ mulsd -2*8+MO2(_FPI,%eax,8), %xmm3/* tmp3 = FPI[j-2]*|x| */
+ movapd %xmm0, %xmm1 /* |x| */
+ mulsd -1*8+MO2(_FPI,%eax,8), %xmm5/* tmp2 = FPI[j-1]*|x| */
+ mulsd 0*8+MO2(_FPI,%eax,8), %xmm0/* tmp0 = FPI[j]*|x| */
+ addl $19, %ecx /* j*28+19 */
+ mulsd 1*8+MO2(_FPI,%eax,8), %xmm1/* tmp1 = FPI[j+1]*|x| */
+ cmpl %ecx, %edx /* bitpos>=j*28+19 ? */
+ jl L(very_large_skip1)
+
+ /* Here if bitpos>=j*28+19 */
+ andpd %xmm3, %xmm4 /* HI(tmp3) */
+ subsd %xmm4, %xmm3 /* tmp3 = tmp3 - HI(tmp3) */
+L(very_large_skip1):
+
+ movsd MO1(DP_2POW52), %xmm6
+ movapd %xmm5, %xmm2 /* tmp2 copy */
+ addsd %xmm3, %xmm5 /* tmp5 = tmp3 + tmp2 */
+ movl $1, %edx
+ addsd %xmm5, %xmm6 /* tmp6 = tmp5 + 2^52 */
+ movsd 8+MO1(DP_2POW52), %xmm4
+ movd %xmm6, %eax /* k = I64_LO(tmp6); */
+ addsd %xmm6, %xmm4 /* tmp4 = tmp6 - 2^52 */
+ movl ARG_X, %ecx /* Load x */
+ comisd %xmm5, %xmm4 /* tmp4 > tmp5 ? */
+ jbe L(very_large_skip2)
+
+ /* Here if tmp4 > tmp5 */
+ subl $1, %eax /* k-- */
+ addsd 8+MO1(DP_ONES), %xmm4 /* tmp4 -= 1.0 */
+L(very_large_skip2):
+
+ andl %eax, %edx /* k&1 */
+ subsd %xmm4, %xmm3 /* tmp3 -= tmp4 */
+ addsd MO2(DP_ZERONE,%edx,8), %xmm3/* t = DP_ZERONE[k&1] + tmp3 */
+ addsd %xmm2, %xmm3 /* t += tmp2 */
+ shrl $29, %ecx /* (sign of x) << 2 */
+ addsd %xmm3, %xmm0 /* t += tmp0 */
+ addl $1, %eax /* n=k+1 */
+ addsd %xmm1, %xmm0 /* t += tmp1 */
+ mulsd MO1(DP_PIO4), %xmm0 /* t *= PI04 */
+
+ jmp L(reconstruction) /* end of very_large_args peth */
+
+ .p2align 4
+L(arg_less_pio4):
+ /* Here if |x|. */
+
+#include
+
+extern void __sincosf_sse2 (float, float *, float *);
+extern void __sincosf_ia32 (float, float *, float *);
+void __sincosf (float, float *, float *);
+
+libm_ifunc (__sincosf, HAS_SSE2 ? __sincosf_sse2 : __sincosf_ia32);
+weak_alias (__sincosf, sincosf);
+
+#define SINCOSF __sincosf_ia32
+#include
diff --git a/sysdeps/i386/i686/fpu/multiarch/s_sinf-sse2.S b/sysdeps/i386/i686/fpu/multiarch/s_sinf-sse2.S
index cda1750..49d59b5 100644
--- a/sysdeps/i386/i686/fpu/multiarch/s_sinf-sse2.S
+++ b/sysdeps/i386/i686/fpu/multiarch/s_sinf-sse2.S
@@ -50,25 +50,29 @@
* 9) if x is NaN, return x-x.
*
* Special cases:
- * sin(+-0)==+-0 not raising inexact/underflow,
- * sin(subnormal) raises inexact/underflow
- * sin(min_normalized) raises inexact/underflow
- * sin(normalized) raises inexact
- * sin(Inf) = NaN, raises invalid, sets errno to EDOM
- * sin(NaN) = NaN
+ * sin(+-0) = +-0 not raising inexact/underflow,
+ * sin(subnormal) raises inexact/underflow,
+ * sin(min_normalized) raises inexact/underflow,
+ * sin(normalized) raises inexact,
+ * sin(Inf) = NaN, raises invalid, sets errno to EDOM,
+ * sin(NaN) = NaN.
*/
#ifdef PIC
# define MO1(symbol) L(symbol)##@GOTOFF(%ebx)
# define MO2(symbol,reg2,_scale) L(symbol)##@GOTOFF(%ebx,reg2,_scale)
-# define SAVE_BX pushl %ebx
-# define RESTORE_BX popl %ebx
+# define CFI_PUSH(REG) cfi_adjust_cfa_offset(4); cfi_rel_offset(REG,0)
+# define CFI_POP(REG) cfi_adjust_cfa_offset(-4); cfi_restore(REG)
+# define PUSH(REG) pushl REG; CFI_PUSH(REG)
+# define POP(REG) popl REG; CFI_POP(REG)
+# define ENTRANCE PUSH(%ebx); LOAD_PIC_REG(bx)
+# define RETURN POP(%ebx); ret; CFI_PUSH(%ebx)
# define ARG_X 8(%esp)
#else
# define MO1(symbol) L(symbol)
# define MO2(symbol,reg2,_scale) L(symbol)(,reg2,_scale)
-# define SAVE_BX
-# define RESTORE_BX
+# define ENTRANCE
+# define RETURN ret
# define ARG_X 4(%esp)
#endif
@@ -76,11 +80,7 @@
ENTRY(__sinf_sse2)
/* Input: single precision x on stack at address ARG_X */
-#ifdef PIC
- SAVE_BX
- LOAD_PIC_REG(bx)
-#endif
-
+ ENTRANCE
movl ARG_X, %eax /* Bits of x */
cvtss2sd ARG_X, %xmm0 /* DP x */
andl $0x7fffffff, %eax /* |x| */
@@ -145,8 +145,7 @@ L(reconstruction):
fldl 0(%esp) /* ...to FPU. */
/* Return back 4 bytes of stack frame */
lea 8(%esp), %esp
- RESTORE_BX
- ret
+ RETURN
.p2align 4
L(sin_poly):
@@ -186,9 +185,7 @@ L(sin_poly):
fldl 0(%esp) /* ...to FPU. */
/* Return back 4 bytes of stack frame */
lea 8(%esp), %esp
- RESTORE_BX
- ret
-
+ RETURN
.p2align 4
L(large_args):
@@ -281,10 +278,6 @@ L(very_large_skip2):
jmp L(reconstruction) /* end of very_large_args peth */
-
-
-
-
.p2align 4
L(arg_less_pio4):
/* Here if |x|
+#ifndef SINCOSF
+# define SINCOSF_FUNC __sincosf
+#else
+# define SINCOSF_FUNC SINCOSF
+#endif
void
-__sincosf (float x, float *sinx, float *cosx)
+SINCOSF_FUNC (float x, float *sinx, float *cosx)
{
int32_t ix;
@@ -70,4 +75,7 @@ __sincosf (float x, float *sinx, float *cosx)
}
}
}
+
+#ifndef SINCOSF
weak_alias (__sincosf, sincosf)
+#endif
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index b02b9e6..d79578c 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1579,6 +1579,9 @@ ildouble: 1
ldouble: 1
# ctan
+Test "Real part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i":
+float: 1
+ifloat: 1
Test "Real part of: ctan (-2 - 3 i) == 0.376402564150424829275122113032269084e-2 - 1.00323862735360980144635859782192726 i":
double: 1
float: 1
@@ -1612,6 +1615,8 @@ Test "Imaginary part of: ctan (0x1p1023 + 1 i) == -0.225462792499754505792678258
ildouble: 1
ldouble: 1
Test "Imaginary part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i":
+float: 2
+ifloat: 2
double: 1
idouble: 1
Test "Real part of: ctan (0x3.243f6cp-1 + 0 i) == -2.287733242885645987394874673945769518150e7 + 0.0 i":
@@ -1757,6 +1762,8 @@ idouble: 1
ildouble: 1
ldouble: 1
Test "Real part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i":
+float: 2
+ifloat: 2
double: 1
idouble: 1
Test "Imaginary part of: ctanh (45 + 1 i) == 1.000000000000000000000000000000000000001 + 1.490158918874345552942703234806348520895e-39 i":
@@ -1765,6 +1772,9 @@ ldouble: 1
Test "Imaginary part of: ctanh (47 + 1 i) == 1.0 + 2.729321264492904590777293425576722354636e-41 i":
ildouble: 2
ldouble: 2
+Test "Imaginary part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i":
+float: 1
+ifloat: 1
# ctanh_downward
Test "Real part of: ctanh_downward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
@@ -2399,8 +2409,8 @@ ifloat: 2
ildouble: 1
ldouble: 1
Test "sin_upward (3) == 0.1411200080598672221007448028081102798469":
-float: 1
-ifloat: 1
+float: 2
+ifloat: 2
ildouble: 1
ldouble: 1
Test "sin_upward (4) == -0.7568024953079282513726390945118290941359":
@@ -2430,12 +2440,6 @@ ifloat: 1
Test "sincos (0.80190127184058835, &sin_res, &cos_res) puts 0.69534156199418473 in cos_res":
double: 1
idouble: 1
-Test "sincos (0x1p+120, &sin_res, &cos_res) puts -9.25879022854837867303861764107414946730833e-01 in cos_res":
-float: 1
-ifloat: 1
-Test "sincos (0x1p+127, &sin_res, &cos_res) puts 7.81914638714960072263910298466369236613162e-01 in cos_res":
-float: 1
-ifloat: 1
Test "sincos (M_PI_6l*2.0, &sin_res, &cos_res) puts 0.5 in cos_res":
double: 1
float: 1
@@ -2705,6 +2709,8 @@ Test "y1 (0x1.001000001p+593) == 3.927269966354206207832593635798954916263e-90":
ildouble: 2
ldouble: 2
Test "y1 (0x1.27e204p+99) == -8.881610148467797208469612080785210013461e-16":
+float: 1
+ifloat: 1
double: 1
idouble: 1
ildouble: 1
@@ -3085,8 +3091,8 @@ ildouble: 1
ldouble: 1
Function: "cos_upward":
-float: 1
-ifloat: 1
+float: 2
+ifloat: 2
ildouble: 1
ldouble: 1
@@ -3174,17 +3180,17 @@ ldouble: 1
Function: Real part of "ctan":
double: 1
-float: 1
+float: 2
idouble: 1
-ifloat: 1
+ifloat: 2
ildouble: 2
ldouble: 2
Function: Imaginary part of "ctan":
double: 1
-float: 1
+float: 2
idouble: 1
-ifloat: 1
+ifloat: 2
ildouble: 1
ldouble: 1
@@ -3242,9 +3248,9 @@ ldouble: 4
Function: Real part of "ctanh":
double: 1
-float: 1
+float: 2
idouble: 1
-ifloat: 1
+ifloat: 2
ildouble: 1
ldouble: 1
@@ -3445,8 +3451,8 @@ ildouble: 1
ldouble: 1
Function: "sin_upward":
-float: 1
-ifloat: 1
+float: 2
+ifloat: 2
ildouble: 1
ldouble: 1
diff --git a/sysdeps/x86_64/fpu/s_cosf.S b/sysdeps/x86_64/fpu/s_cosf.S
index 7eeefe8..dc8c76a 100644
--- a/sysdeps/x86_64/fpu/s_cosf.S
+++ b/sysdeps/x86_64/fpu/s_cosf.S
@@ -50,12 +50,12 @@
* 9) if x is NaN, return x-x.
*
* Special cases:
- * cos(+-0)==+-0 not raising inexact/underflow,
- * cos(subnormal) raises inexact/underflow
- * cos(min_normalized) raises inexact/underflow
- * cos(normalized) raises inexact
- * cos(Inf) = NaN, raises invalid, sets errno to EDOM
- * cos(NaN) = NaN
+ * cos(+-0) = 1 not raising inexact,
+ * cos(subnormal) raises inexact,
+ * cos(min_normalized) raises inexact,
+ * cos(normalized) raises inexact,
+ * cos(Inf) = NaN, raises invalid, sets errno to EDOM,
+ * cos(NaN) = NaN.
*/
.text
@@ -163,10 +163,6 @@ L(sin_poly):
cvtsd2ss %xmm3, %xmm0 /* SP result */
ret
-
-
-
-
.p2align 4
L(large_args):
/* Here if |x|>=9*Pi/4 */
@@ -257,7 +253,6 @@ L(very_large_skip2):
jmp L(reconstruction) /* end of very_large_args peth */
-
.p2align 4
L(arg_less_pio4):
/* Here if |x|. */
+
+#include
+#define __need_Emath
+#include
+
+/* Short algorithm description:
+ *
+ * 1) if |x|==0: sin(x)=x,
+ * cos(x)=1.
+ * 2) if |x|<2^-27: sin(x)=x-x*DP_SMALL, raising underflow only when needed,
+ * cos(x)=1-|x|.
+ * 3) if |x|<2^-5 : sin(x)=x+x*x^2*DP_SIN2_0+x^5*DP_SIN2_1,
+ * cos(x)=1+1*x^2*DP_COS2_0+x^5*DP_COS2_1
+ * 4) if |x|< Pi/4: sin(x)=x+x*x^2*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))),
+ * cos(x)=1+1*x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))).
+ * 5) if |x| < 9*Pi/4:
+ * 5.1) Range reduction:
+ * k=trunc(|x|/(Pi/4)), j=(k+1)&0x0e, n=k+1, t=|x|-j*Pi/4.
+ * 5.2) Reconstruction:
+ * sign_sin = sign(x) * (-1.0)^(( n >>2)&1)
+ * sign_cos = (-1.0)^(((n+2)>>2)&1)
+ * poly_sin = ((((S4*t^2 + S3)*t^2 + S2)*t^2 + S1)*t^2 + S0)*t^2*t+t
+ * poly_cos = ((((C4*t^2 + C3)*t^2 + C2)*t^2 + C1)*t^2 + C0)*t^2*s+s
+ * if(n&2 != 0) {
+ * using cos(t) and sin(t) polynomials for |t|= 2^23, very large args:
+ * 7.1) Range reduction:
+ * k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+1, t=|x|-j*Pi/4.
+ * 7.2) Reconstruction same as (5.2).
+ * 8) if x is Inf, return x-x, and set errno=EDOM.
+ * 9) if x is NaN, return x-x.
+ *
+ * Special cases:
+ * sin/cos(+-0) = +-0/1 not raising inexact/underflow,
+ * sin/cos(subnormal) raises inexact/underflow,
+ * sin/cos(min_normalized) raises inexact/underflow,
+ * sin/cos(normalized) raises inexact,
+ * sin/cos(Inf) = NaN, raises invalid, sets errno to EDOM,
+ * sin/cos(NaN) = NaN.
+ */
+
+# define ARG_SIN_PTR %rdi
+# define ARG_COS_PTR %rsi
+
+ .text
+ENTRY(__sincosf)
+ /* Input: %xmm0 contains single precision argument x */
+ /* %rdi points to sin result */
+ /* %rsi points to cos result */
+
+ movd %xmm0, %eax /* Bits of x */
+ movaps %xmm0, %xmm7 /* Copy of x */
+ cvtss2sd %xmm0, %xmm0 /* DP x */
+ movss L(SP_ABS_MASK)(%rip), %xmm3
+ movl %eax, %r8d /* Copy of x bits */
+ andl $0x7fffffff, %eax /* |x| */
+
+ cmpl $0x3f490fdb, %eax /* |x|=Pi/4 */
+ andps %xmm7, %xmm3 /* SP |x| */
+ andpd L(DP_ABS_MASK)(%rip),%xmm0 /* DP |x| */
+ movss L(SP_INVPIO4)(%rip), %xmm2 /* SP 1/(Pi/4) */
+
+ cmpl $0x40e231d6, %eax /* |x|<9*Pi/4 ? */
+ jae L(large_args)
+
+ /* Here if Pi/4<=|x|<9*Pi/4 */
+ mulss %xmm3, %xmm2 /* SP |x|/(Pi/4) */
+ movl %r8d, %ecx /* Load x */
+ cvttss2si %xmm2, %eax /* k, number of Pi/4 in x */
+ lea L(PIO4J)(%rip), %r9
+ shrl $29, %ecx /* (sign of x) << 2 */
+ addl $1, %eax /* k+1 */
+ movl $0x0e, %edx
+ andl %eax, %edx /* j = (k+1)&0x0e */
+ subsd (%r9,%rdx,8), %xmm0 /* t = |x| - j * Pi/4 */
+
+L(reconstruction):
+ /* Input: %eax=n, %xmm0=t, %ecx=sign(x) */
+
+ movaps %xmm0, %xmm4 /* t */
+ movhpd L(DP_ONES)(%rip), %xmm4 /* 1|t */
+ mulsd %xmm0, %xmm0 /* y=t^2 */
+ movl $2, %edx
+ unpcklpd %xmm0, %xmm0 /* y|y */
+ addl %eax, %edx /* k+2 */
+ movaps %xmm0, %xmm1 /* y|y */
+ mulpd %xmm0, %xmm0 /* z=t^4|z=t^4 */
+
+ movaps L(DP_SC4)(%rip), %xmm2 /* S4 */
+ mulpd %xmm0, %xmm2 /* z*S4 */
+ movaps L(DP_SC3)(%rip), %xmm3 /* S3 */
+ mulpd %xmm0, %xmm3 /* z*S3 */
+ xorl %eax, %ecx /* (sign_x ^ (k>>2))<<2 */
+ addpd L(DP_SC2)(%rip), %xmm2 /* S2+z*S4 */
+ mulpd %xmm0, %xmm2 /* z*(S2+z*S4) */
+ shrl $2, %edx /* (k+2)>>2 */
+ addpd L(DP_SC1)(%rip), %xmm3 /* S1+z*S3 */
+ mulpd %xmm0, %xmm3 /* z*(S1+z*S3) */
+ shrl $2, %ecx /* sign_x ^ k>>2 */
+ addpd L(DP_SC0)(%rip), %xmm2 /* S0+z*(S2+z*S4) */
+ andl $1, %edx /* sign_cos = ((k+2)>>2)&1 */
+ mulpd %xmm1, %xmm2 /* y*(S0+z*(S2+z*S4)) */
+ andl $1, %ecx /* sign_sin = sign_x ^ ((k>>2)&1) */
+ addpd %xmm2, %xmm3 /* y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */
+ lea L(DP_ONES)(%rip), %r9
+ mulpd %xmm4, %xmm3 /*t*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))))*/
+ testl $2, %eax /* n&2 != 0 ? */
+ addpd %xmm4, %xmm3 /*t+t*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))*/
+ jnz L(sin_result_sin_poly)
+
+/*L(sin_result_cos_poly):*/
+ /*
+ * Here if
+ * cos(x) = poly_sin * sign_cos
+ * sin(x) = poly_cos * sign_sin
+ */
+ movsd (%r9,%rcx,8), %xmm4 /* 0|sign_sin */
+ movhpd (%r9,%rdx,8), %xmm4 /* sign_cos|sign_sin */
+ mulpd %xmm4, %xmm3 /* result_cos|result_sin */
+ cvtpd2ps %xmm3, %xmm0 /* SP results */
+ movss %xmm0, (ARG_SIN_PTR) /* store sin(x) from xmm0[0] */
+ shufps $1, %xmm0, %xmm0 /* move cos(x) to xmm0[0] */
+ movss %xmm0, (ARG_COS_PTR) /* store cos(x) */
+ ret
+
+ .p2align 4
+L(sin_result_sin_poly):
+ /*
+ * Here if
+ * sin(x) = poly_sin * sign_sin
+ * cos(x) = poly_cos * sign_cos
+ */
+ movsd (%r9,%rdx,8), %xmm4 /* 0|sign_cos */
+ movhpd (%r9,%rcx,8), %xmm4 /* sign_sin|sign_cos */
+ mulpd %xmm4, %xmm3 /* result_sin|result_cos */
+ cvtpd2ps %xmm3, %xmm0 /* SP results */
+ movss %xmm0, (ARG_COS_PTR) /* store cos(x) from xmm0[0] */
+ shufps $1, %xmm0, %xmm0 /* move sin(x) to xmm0[0] */
+ movss %xmm0, (ARG_SIN_PTR) /* store sin(x) */
+ ret
+
+ .p2align 4
+L(large_args):
+ /* Here if |x|>=9*Pi/4 */
+ cmpl $0x7f800000, %eax /* x is Inf or NaN ? */
+ jae L(arg_inf_or_nan)
+
+ /* Here if finite |x|>=9*Pi/4 */
+ cmpl $0x4b000000, %eax /* |x|<2^23 ? */
+ jae L(very_large_args)
+
+ /* Here if 9*Pi/4<=|x|<2^23 */
+ movsd L(DP_INVPIO4)(%rip), %xmm1 /* 1/(Pi/4) */
+ mulsd %xmm0, %xmm1 /* |x|/(Pi/4) */
+ cvttsd2si %xmm1, %eax /* k=trunc(|x|/(Pi/4)) */
+ addl $1, %eax /* k+1 */
+ movl %eax, %edx
+ andl $0xfffffffe, %edx /* j=(k+1)&0xfffffffe */
+ cvtsi2sdl %edx, %xmm4 /* DP j */
+ movl %r8d, %ecx /* Load x */
+ movsd L(DP_PIO4HI)(%rip), %xmm2 /* -PIO4HI = high part of -Pi/4 */
+ shrl $29, %ecx /* (sign of x) << 2 */
+ mulsd %xmm4, %xmm2 /* -j*PIO4HI */
+ movsd L(DP_PIO4LO)(%rip), %xmm3 /* -PIO4LO = low part of -Pi/4 */
+ addsd %xmm2, %xmm0 /* |x| - j*PIO4HI */
+ mulsd %xmm3, %xmm4 /* j*PIO4LO */
+ addsd %xmm4, %xmm0 /* t = |x| - j*PIO4HI - j*PIO4LO */
+ jmp L(reconstruction)
+
+ .p2align 4
+L(very_large_args):
+ /* Here if finite |x|>=2^23 */
+
+ /* bitpos = (ix>>23) - BIAS_32 + 59; */
+ shrl $23, %eax /* eb = biased exponent of x */
+ subl $68, %eax /* bitpos=eb-0x7f+59, where 0x7f */
+ /*is exponent bias */
+ movl $28, %ecx /* %cl=28 */
+ movl %eax, %edx /* bitpos copy */
+
+ /* j = bitpos/28; */
+ div %cl /* j in register %al=%ax/%cl */
+ movapd %xmm0, %xmm3 /* |x| */
+ andl $0xff, %eax /* clear unneeded remainder from %ah*/
+
+ imull $28, %eax, %ecx /* j*28 */
+ lea L(_FPI)(%rip), %r9
+ movsd L(DP_HI_MASK)(%rip), %xmm4 /* DP_HI_MASK */
+ movapd %xmm0, %xmm5 /* |x| */
+ mulsd -16(%r9,%rax,8), %xmm3 /* tmp3 = FPI[j-2]*|x| */
+ movapd %xmm0, %xmm1 /* |x| */
+ mulsd -8(%r9,%rax,8), %xmm5 /* tmp2 = FPI[j-1]*|x| */
+ mulsd (%r9,%rax,8), %xmm0 /* tmp0 = FPI[j]*|x| */
+ addl $19, %ecx /* j*28+19 */
+ mulsd 8(%r9,%rax,8), %xmm1 /* tmp1 = FPI[j+1]*|x| */
+ cmpl %ecx, %edx /* bitpos>=j*28+19 ? */
+ jl L(very_large_skip1)
+
+ /* Here if bitpos>=j*28+19 */
+ andpd %xmm3, %xmm4 /* HI(tmp3) */
+ subsd %xmm4, %xmm3 /* tmp3 = tmp3 - HI(tmp3) */
+L(very_large_skip1):
+
+ movsd L(DP_2POW52)(%rip), %xmm6
+ movapd %xmm5, %xmm2 /* tmp2 copy */
+ addsd %xmm3, %xmm5 /* tmp5 = tmp3 + tmp2 */
+ movl $1, %edx
+ addsd %xmm5, %xmm6 /* tmp6 = tmp5 + 2^52 */
+ movsd 8+L(DP_2POW52)(%rip), %xmm4
+ movd %xmm6, %eax /* k = I64_LO(tmp6); */
+ addsd %xmm6, %xmm4 /* tmp4 = tmp6 - 2^52 */
+ movl %r8d, %ecx /* Load x */
+ comisd %xmm5, %xmm4 /* tmp4 > tmp5 ? */
+ jbe L(very_large_skip2)
+
+ /* Here if tmp4 > tmp5 */
+ subl $1, %eax /* k-- */
+ addsd 8+L(DP_ONES)(%rip), %xmm4 /* tmp4 -= 1.0 */
+L(very_large_skip2):
+
+ andl %eax, %edx /* k&1 */
+ lea L(DP_ZERONE)(%rip), %r9
+ subsd %xmm4, %xmm3 /* tmp3 -= tmp4 */
+ addsd (%r9,%rdx,8), %xmm3 /* t = DP_ZERONE[k&1] + tmp3 */
+ addsd %xmm2, %xmm3 /* t += tmp2 */
+ shrl $29, %ecx /* (sign of x) << 2 */
+ addsd %xmm3, %xmm0 /* t += tmp0 */
+ addl $1, %eax /* n=k+1 */
+ addsd %xmm1, %xmm0 /* t += tmp1 */
+ mulsd L(DP_PIO4)(%rip), %xmm0 /* t *= PI04 */
+
+ jmp L(reconstruction) /* end of very_large_args peth */
+
+ .p2align 4
+L(arg_less_pio4):
+ /* Here if |x|=9*Pi/4 */
@@ -262,7 +261,6 @@ L(very_large_skip2):
jmp L(reconstruction) /* end of very_large_args peth */
-
.p2align 4
L(arg_less_pio4):
/* Here if |x|