/*

 * 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 <libm-alias-ldouble.h>

#include <machine/asm.h>

#include <i386-math-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

	.type 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)

	.type 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

	.type 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)

	.type 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

	.type 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)

DEFINE_LDBL_MIN

#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	6f		/* 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

	/* Test for arguments that are small but not subnormal.  */

	movzwl	4+8(%esp), %eax

	andl	$0x7fff, %eax

	cmpl	$0x3fbf, %eax

	jge	3f

	/* Argument's exponent below -64; avoid spurious underflow if

	   normal.  */

	cmpl	$0x0001, %eax

	jge	2f

	/* Force underflow and return the argument, to avoid wrong signs

	   of zero results from the code below in some rounding modes.  */

	fld	%st

	fmul	%st

	fstp	%st

	jmp	2f

#else

	movzwl	4+8(%esp), %eax

	andl	$0x7fff, %eax

	cmpl	$0x400d, %eax

	jg	5f

	cmpl	$0x3fbc, %eax

	jge	3f

	/* Argument's exponent below -67, result rounds to 1.  */

	fld1

	faddp

	jmp	2f

5:	/* 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	6f		/* 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)    */

	/* Set round-to-nearest temporarily.  */

	subl	$8, %esp

	cfi_adjust_cfa_offset (8)

	fstcw	4(%esp)

	movl	$0xf3ff, %edx

	andl	4(%esp), %edx

	movl	%edx, (%esp)

	fldcw	(%esp)

	frndint			/* 1  i               */

	fld	%st(1)		/* 2  x               */

	frndint			/* 2  xi              */

	fldcw	4(%esp)

	addl	$8, %esp

	cfi_adjust_cfa_offset (-8)

	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  */

	LDBL_CHECK_FORCE_UFLOW_NONNEG

#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

6:	/* NaN argument.  */

	fadd	%st

	ret

END(IEEE754_EXPL)

#ifdef USE_AS_EXPM1L

libm_hidden_def (__expm1l)

libm_alias_ldouble (__expm1, expm1)

#else

strong_alias (IEEE754_EXPL, EXPL_FINITE)

#endif