[thirdparty/glibc.git] / sysdeps / i386 / fpu / e_expl.S

/*
 * Written by J.T. Conklin <jtc@netbsd.org>.
 * Public domain.
 *
 * Adapted for `long double' by Ulrich Drepper <drepper@cygnus.com>.
 */

/*
 * The 8087 method for the exponential function is to calculate
 *   exp(x) = 2^(x log2(e))
 * after separating integer and fractional parts
 *   x log2(e) = i + f, |f| <= .5
 * 2^i is immediate but f needs to be precise for long double accuracy.
 * Suppress range reduction error in computing f by the following.
 * Separate x into integer and fractional parts
 *   x = xi + xf, |xf| <= .5
 * Separate log2(e) into the sum of an exact number c0 and small part c1.
 *   c0 + c1 = log2(e) to extra precision
 * Then
 *   f = (c0 xi - i) + c0 xf + c1 x
 * where c0 xi is exact and so also is (c0 xi - i).
 * -- moshier@na-net.ornl.gov
 */

#include <machine/asm.h>

#ifdef USE_AS_EXP10L
# define IEEE754_EXPL __ieee754_exp10l
# define EXPL_FINITE __exp10l_finite
# define FLDLOG fldl2t
#elif defined USE_AS_EXPM1L
# define IEEE754_EXPL __expm1l
# undef EXPL_FINITE
# define FLDLOG fldl2e
#else
# define IEEE754_EXPL __ieee754_expl
# define EXPL_FINITE __expl_finite
# define FLDLOG fldl2e
#endif

	.section .rodata.cst16,"aM",@progbits,16

	.p2align 4
#ifdef USE_AS_EXP10L
	ASM_TYPE_DIRECTIVE(c0,@object)
c0:	.byte 0, 0, 0, 0, 0, 0, 0x9a, 0xd4, 0x00, 0x40
	.byte 0, 0, 0, 0, 0, 0
	ASM_SIZE_DIRECTIVE(c0)
	ASM_TYPE_DIRECTIVE(c1,@object)
c1:	.byte 0x58, 0x92, 0xfc, 0x15, 0x37, 0x9a, 0x97, 0xf0, 0xef, 0x3f
	.byte 0, 0, 0, 0, 0, 0
	ASM_SIZE_DIRECTIVE(c1)
#else
	ASM_TYPE_DIRECTIVE(c0,@object)
c0:	.byte 0, 0, 0, 0, 0, 0, 0xaa, 0xb8, 0xff, 0x3f
	.byte 0, 0, 0, 0, 0, 0
	ASM_SIZE_DIRECTIVE(c0)
	ASM_TYPE_DIRECTIVE(c1,@object)
c1:	.byte 0x20, 0xfa, 0xee, 0xc2, 0x5f, 0x70, 0xa5, 0xec, 0xed, 0x3f
	.byte 0, 0, 0, 0, 0, 0
	ASM_SIZE_DIRECTIVE(c1)
#endif
#ifndef USE_AS_EXPM1L
	ASM_TYPE_DIRECTIVE(csat,@object)
csat:	.byte 0, 0, 0, 0, 0, 0, 0, 0x80, 0x0e, 0x40
	.byte 0, 0, 0, 0, 0, 0
	ASM_SIZE_DIRECTIVE(csat)
#endif

#ifdef PIC
# define MO(op) op##@GOTOFF(%ecx)
#else
# define MO(op) op
#endif

	.text
ENTRY(IEEE754_EXPL)
#ifdef USE_AS_EXPM1L
	movzwl	4+8(%esp), %eax
	xorb	$0x80, %ah	// invert sign bit (now 1 is "positive")
	cmpl	$0xc006, %eax	// is num positive and exp >= 6 (number is >= 128.0)?
	jae	HIDDEN_JUMPTARGET (__expl) // (if num is denormal, it is at least >= 64.0)
#endif
	fldt	4(%esp)
/* I added the following ugly construct because expl(+-Inf) resulted
   in NaN.  The ugliness results from the bright minds at Intel.
   For the i686 the code can be written better.
   -- drepper@cygnus.com.  */
	fxam			/* Is NaN or +-Inf?  */
#ifdef PIC
	LOAD_PIC_REG (cx)
#endif
#ifdef USE_AS_EXPM1L
	xorb	$0x80, %ah
	cmpl	$0xc006, %eax
	fstsw	%ax
	movb	$0x45, %dh
	jb	4f

	/* Below -64.0 (may be -NaN or -Inf). */
	andb	%ah, %dh
	cmpb	$0x01, %dh
	je	2f		/* Is +-NaN, jump.  */
	jmp	1f		/* -large, possibly -Inf.  */

4:	/* In range -64.0 to 64.0 (may be +-0 but not NaN or +-Inf).  */
	/* Test for +-0 as argument.  */
	andb	%ah, %dh
	cmpb	$0x40, %dh
	je	2f
#else
	movzwl	4+8(%esp), %eax
	andl	$0x7fff, %eax
	cmpl	$0x400d, %eax
	jle	3f
	/* Overflow, underflow or infinity or NaN as argument.  */
	fstsw	%ax
	movb	$0x45, %dh
	andb	%ah, %dh
	cmpb	$0x05, %dh
	je	1f		/* Is +-Inf, jump.    */
	cmpb	$0x01, %dh
	je	2f		/* Is +-NaN, jump.    */
	/* Overflow or underflow; saturate.  */
	fstp	%st
	fldt	MO(csat)
	andb	$2, %ah
	jz	3f
	fchs
#endif
3:	FLDLOG			/* 1  log2(base)      */
	fmul	%st(1), %st	/* 1  x log2(base)    */
	frndint			/* 1  i               */
	fld	%st(1)		/* 2  x               */
	frndint			/* 2  xi              */
	fld	%st(1)		/* 3  i               */
	fldt	MO(c0)		/* 4  c0              */
	fld	%st(2)		/* 5  xi              */
	fmul	%st(1), %st	/* 5  c0 xi           */
	fsubp	%st, %st(2)	/* 4  f = c0 xi  - i  */
	fld	%st(4)		/* 5  x               */
	fsub	%st(3), %st	/* 5  xf = x - xi     */
	fmulp	%st, %st(1)	/* 4  c0 xf           */
	faddp	%st, %st(1)	/* 3  f = f + c0 xf   */
	fldt	MO(c1)		/* 4                  */
	fmul	%st(4), %st	/* 4  c1 * x          */
	faddp	%st, %st(1)	/* 3  f = f + c1 * x  */
	f2xm1			/* 3 2^(fract(x * log2(base))) - 1 */
#ifdef USE_AS_EXPM1L
	fstp	%st(1)		/* 2                  */
	fscale			/* 2 scale factor is st(1); base^x - 2^i */
	fxch			/* 2 i                */
	fld1			/* 3 1.0              */
	fscale			/* 3 2^i              */
	fld1			/* 4 1.0              */
	fsubrp	%st, %st(1)	/* 3 2^i - 1.0        */
	fstp	%st(1)		/* 2                  */
	faddp	%st, %st(1)	/* 1 base^x - 1.0     */
#else
	fld1			/* 4 1.0              */
	faddp			/* 3 2^(fract(x * log2(base))) */
	fstp	%st(1)		/* 2  */
	fscale			/* 2 scale factor is st(1); base^x */
	fstp	%st(1)		/* 1  */
#endif
	fstp	%st(1)		/* 0  */
	jmp	2f
1:
#ifdef USE_AS_EXPM1L
	/* For expm1l, only negative sign gets here.  */
	fstp	%st
	fld1
	fchs
#else
	testl	$0x200, %eax	/* Test sign.  */
	jz	2f		/* If positive, jump.  */
	fstp	%st
	fldz			/* Set result to 0.  */
#endif
2:	ret
END(IEEE754_EXPL)
#ifdef USE_AS_EXPM1L
libm_hidden_def (__expm1l)
weak_alias (__expm1l, expm1l)
#else
strong_alias (IEEE754_EXPL, EXPL_FINITE)
#endif
Commit	Line	Data
6698b8bf JM	1	/*
	2	* Written by J.T. Conklin <jtc@netbsd.org>.
	3	* Public domain.
	4	*
	5	* Adapted for `long double' by Ulrich Drepper <drepper@cygnus.com>.
	6	*/
	7
	8	/*
	9	* The 8087 method for the exponential function is to calculate
	10	* exp(x) = 2^(x log2(e))
	11	* after separating integer and fractional parts
	12	* x log2(e) = i + f, \|f\| <= .5
	13	* 2^i is immediate but f needs to be precise for long double accuracy.
	14	* Suppress range reduction error in computing f by the following.
	15	* Separate x into integer and fractional parts
	16	* x = xi + xf, \|xf\| <= .5
	17	* Separate log2(e) into the sum of an exact number c0 and small part c1.
	18	* c0 + c1 = log2(e) to extra precision
	19	* Then
	20	* f = (c0 xi - i) + c0 xf + c1 x
	21	* where c0 xi is exact and so also is (c0 xi - i).
	22	* -- moshier@na-net.ornl.gov
	23	*/
	24
	25	#include <machine/asm.h>
	26
d8b82cad JM	27	#ifdef USE_AS_EXP10L
	28	# define IEEE754_EXPL __ieee754_exp10l
	29	# define EXPL_FINITE __exp10l_finite
	30	# define FLDLOG fldl2t
495fd99f JM	31	#elif defined USE_AS_EXPM1L
	32	# define IEEE754_EXPL __expm1l
	33	# undef EXPL_FINITE
	34	# define FLDLOG fldl2e
d8b82cad JM	35	#else
	36	# define IEEE754_EXPL __ieee754_expl
	37	# define EXPL_FINITE __expl_finite
	38	# define FLDLOG fldl2e
	39	#endif
	40
6698b8bf JM	41	.section .rodata.cst16,"aM",@progbits,16
	42
	43	.p2align 4
d8b82cad JM	44	#ifdef USE_AS_EXP10L
	45	ASM_TYPE_DIRECTIVE(c0,@object)
	46	c0: .byte 0, 0, 0, 0, 0, 0, 0x9a, 0xd4, 0x00, 0x40
	47	.byte 0, 0, 0, 0, 0, 0
	48	ASM_SIZE_DIRECTIVE(c0)
	49	ASM_TYPE_DIRECTIVE(c1,@object)
	50	c1: .byte 0x58, 0x92, 0xfc, 0x15, 0x37, 0x9a, 0x97, 0xf0, 0xef, 0x3f
	51	.byte 0, 0, 0, 0, 0, 0
	52	ASM_SIZE_DIRECTIVE(c1)
	53	#else
6698b8bf JM	54	ASM_TYPE_DIRECTIVE(c0,@object)
	55	c0: .byte 0, 0, 0, 0, 0, 0, 0xaa, 0xb8, 0xff, 0x3f
	56	.byte 0, 0, 0, 0, 0, 0
	57	ASM_SIZE_DIRECTIVE(c0)
	58	ASM_TYPE_DIRECTIVE(c1,@object)
	59	c1: .byte 0x20, 0xfa, 0xee, 0xc2, 0x5f, 0x70, 0xa5, 0xec, 0xed, 0x3f
	60	.byte 0, 0, 0, 0, 0, 0
	61	ASM_SIZE_DIRECTIVE(c1)
d8b82cad	62	#endif
f17ac40d	63	#ifndef USE_AS_EXPM1L
41498f4d JM	64	ASM_TYPE_DIRECTIVE(csat,@object)
	65	csat: .byte 0, 0, 0, 0, 0, 0, 0, 0x80, 0x0e, 0x40
	66	.byte 0, 0, 0, 0, 0, 0
	67	ASM_SIZE_DIRECTIVE(csat)
f17ac40d	68	#endif
6698b8bf JM	69
	70	#ifdef PIC
	71	# define MO(op) op##@GOTOFF(%ecx)
	72	#else
	73	# define MO(op) op
	74	#endif
	75
	76	.text
d8b82cad	77	ENTRY(IEEE754_EXPL)
495fd99f JM	78	#ifdef USE_AS_EXPM1L
	79	movzwl 4+8(%esp), %eax
	80	xorb $0x80, %ah // invert sign bit (now 1 is "positive")
	81	cmpl $0xc006, %eax // is num positive and exp >= 6 (number is >= 128.0)?
	82	jae HIDDEN_JUMPTARGET (__expl) // (if num is denormal, it is at least >= 64.0)
	83	#endif
6698b8bf JM	84	fldt 4(%esp)
	85	/* I added the following ugly construct because expl(+-Inf) resulted
	86	in NaN. The ugliness results from the bright minds at Intel.
	87	For the i686 the code can be written better.
	88	-- drepper@cygnus.com. */
	89	fxam /* Is NaN or +-Inf? */
	90	#ifdef PIC
	91	LOAD_PIC_REG (cx)
	92	#endif
f17ac40d JM	93	#ifdef USE_AS_EXPM1L
	94	xorb $0x80, %ah
	95	cmpl $0xc006, %eax
	96	fstsw %ax
	97	movb $0x45, %dh
	98	jb 4f
	99
	100	/* Below -64.0 (may be -NaN or -Inf). */
	101	andb %ah, %dh
	102	cmpb $0x01, %dh
	103	je 2f /* Is +-NaN, jump. */
	104	jmp 1f /* -large, possibly -Inf. */
	105
	106	4: /* In range -64.0 to 64.0 (may be +-0 but not NaN or +-Inf). */
	107	/* Test for +-0 as argument. */
	108	andb %ah, %dh
	109	cmpb $0x40, %dh
	110	je 2f
	111	#else
41498f4d JM	112	movzwl 4+8(%esp), %eax
	113	andl $0x7fff, %eax
	114	cmpl $0x400d, %eax
	115	jle 3f
	116	/* Overflow, underflow or infinity or NaN as argument. */
6698b8bf JM	117	fstsw %ax
	118	movb $0x45, %dh
	119	andb %ah, %dh
	120	cmpb $0x05, %dh
	121	je 1f /* Is +-Inf, jump. */
41498f4d JM	122	cmpb $0x01, %dh
	123	je 2f /* Is +-NaN, jump. */
	124	/* Overflow or underflow; saturate. */
	125	fstp %st
	126	fldt MO(csat)
	127	andb $2, %ah
	128	jz 3f
	129	fchs
495fd99f	130	#endif
f17ac40d	131	3: FLDLOG /* 1 log2(base) */
d8b82cad	132	fmul %st(1), %st /* 1 x log2(base) */
6698b8bf JM	133	frndint /* 1 i */
	134	fld %st(1) /* 2 x */
	135	frndint /* 2 xi */
	136	fld %st(1) /* 3 i */
	137	fldt MO(c0) /* 4 c0 */
	138	fld %st(2) /* 5 xi */
	139	fmul %st(1), %st /* 5 c0 xi */
	140	fsubp %st, %st(2) /* 4 f = c0 xi - i */
	141	fld %st(4) /* 5 x */
	142	fsub %st(3), %st /* 5 xf = x - xi */
	143	fmulp %st, %st(1) /* 4 c0 xf */
	144	faddp %st, %st(1) /* 3 f = f + c0 xf */
	145	fldt MO(c1) /* 4 */
	146	fmul %st(4), %st /* 4 c1 * x */
	147	faddp %st, %st(1) /* 3 f = f + c1 * x */
d8b82cad	148	f2xm1 /* 3 2^(fract(x * log2(base))) - 1 */
495fd99f JM	149	#ifdef USE_AS_EXPM1L
	150	fstp %st(1) /* 2 */
	151	fscale /* 2 scale factor is st(1); base^x - 2^i */
	152	fxch /* 2 i */
	153	fld1 /* 3 1.0 */
	154	fscale /* 3 2^i */
	155	fld1 /* 4 1.0 */
	156	fsubrp %st, %st(1) /* 3 2^i - 1.0 */
	157	fstp %st(1) /* 2 */
	158	faddp %st, %st(1) /* 1 base^x - 1.0 */
	159	#else
6698b8bf	160	fld1 /* 4 1.0 */
d8b82cad	161	faddp /* 3 2^(fract(x * log2(base))) */
6698b8bf	162	fstp %st(1) /* 2 */
d8b82cad	163	fscale /* 2 scale factor is st(1); base^x */
6698b8bf	164	fstp %st(1) /* 1 */
495fd99f	165	#endif
6698b8bf JM	166	fstp %st(1) /* 0 */
6698b8bf JM	167	jmp 2f
f17ac40d	168	1:
495fd99f	169	#ifdef USE_AS_EXPM1L
f17ac40d JM	170	/* For expm1l, only negative sign gets here. */
f17ac40d JM	171	fstp %st
495fd99f JM	172	fld1
	173	fchs
	174	#else
f17ac40d JM	175	testl $0x200, %eax /* Test sign. */
	176	jz 2f /* If positive, jump. */
	177	fstp %st
6698b8bf	178	fldz /* Set result to 0. */
495fd99f	179	#endif
6698b8bf	180	2: ret
d8b82cad	181	END(IEEE754_EXPL)
495fd99f JM	182	#ifdef USE_AS_EXPM1L
	183	libm_hidden_def (__expm1l)
	184	weak_alias (__expm1l, expm1l)
	185	#else
d8b82cad	186	strong_alias (IEEE754_EXPL, EXPL_FINITE)
495fd99f	187	#endif