25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * CDDL HEADER START
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
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25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
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25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * CDDL HEADER END
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Use is subject to license terms.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis .file "expl.s"
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#include "libm.h"
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr JasiukajtisLIBM_ANSI_PRAGMA_WEAK(expl,function)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis .data
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis .align 4
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisln2_hi: .long 0xd1d00000, 0xb17217f7, 0x00003ffe
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisln2_lo: .long 0x4c67fc0d, 0x8654361c, 0x0000bfce
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ENTRY(expl)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis movl 12(%esp),%ecx / cx <--sign&bexp(x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis andl $0x7fff,%ecx / ecx <-- zero_xtnd(bexp(x))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis cmpl $0x3ffe,%ecx / Is |x| < 0.5?
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis jb 2f / If so, see which shortcut to take
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis je .check_tail / More checking if 0.5 <= |x| < 1
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis cmpl $0x00007fff,%ecx / bexp(|x|) = bexp(INF)?
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis je .not_finite / if so, x is not finite
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis cmpl $0x0000400e,%ecx / |x| < 32768 = 2^15?
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis jb .finite_non_special / if so, proceed with argument reduction
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldt 4(%esp) / x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fld1 / 1, x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis jmp 1f
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis.finite_non_special: / Here, ln(2) < |x| < 2^15
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldt 4(%esp) / x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fld %st(0) / x, x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldl2e / log2(e), x, x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fmulp / z := x*log2(e), x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis frndint / [z], x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fst %st(2) / [z], x, [z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis PIC_SETUP(1)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldt PIC_L(ln2_hi) / ln2_hi, [z], x, [z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fmulp / [z]*ln2_hi, x, [z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fsubrp %st,%st(1) / x-[z]*ln2_hi, [z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldt PIC_L(ln2_lo) / ln2_lo, x-[z]*ln2_hi, [z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis PIC_WRAPUP
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fmul %st(2),%st / [z]*ln2_lo, x-[z]*ln2_hi, [z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fsubrp %st,%st(1) / r := x-[z]*ln(2), [z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldl2e / log2(e), r, [z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fmulp / f := r*log2(e), [z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis f2xm1 / 2^f-1,[z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fld1 / 1, 2^f-1, [z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis faddp %st,%st(1) / 2^f, [z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis1:
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fscale / e^x, [z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fstp %st(1)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ret
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis2: / Here, |x| < 0.5
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis cmpl $0x3fbe,%ecx / Is |x| >= 2^-65?
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis jae .shortcut / If so, take a shortcut
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldt 4(%esp) / x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fld1 / 1, x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis faddp %st,%st(1) / 1+x (for inexact & directed rounding)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ret
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis.check_tail:
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis movl 8(%esp),%ecx / ecx <-- hi_32(sgnfcnd(x))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis cmpl $0xb17217f7,%ecx / Is |x| < ln(2)?
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ja .finite_non_special
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis jb .shortcut
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis movl 4(%esp),%edx / edx <-- lo_32(x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis cmpl $0xd1cf79ab,%edx / Is |x| slightly < ln(2)?
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ja .finite_non_special / branch if |x| slightly > ln(2)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis.shortcut:
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis / Here, |x| < ln(2), so |z| = |x/ln(2)| < 1,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis / whence z is in f2xm1's domain.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldt 4(%esp) / x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldl2e / log2(e), x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fmulp / x*log2(e)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis f2xm1 / 2^(x*log2(e))-1 = e^x-1
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fld1 / 1, e^x-1
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis faddp %st,%st(1) / e^x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ret
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis.not_finite:
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis movl 8(%esp),%ecx / ecx <-- hi_32(sgnfcnd(x))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis cmpl $0x80000000,%ecx / hi_32(|x|) = hi_32(INF)?
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis jne .NaN_or_pinf / if not, x is NaN
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis movl 4(%esp),%edx / edx <-- lo_32(x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis cmpl $0,%edx / lo_32(x) = 0?
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis jne .NaN_or_pinf / if not, x is NaN
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis movl 12(%esp),%eax / ax <-- sign&bexp((x))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis andl $0x00008000,%eax / here, x is infinite, but +/-?
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis jz .NaN_or_pinf / branch if x = +INF
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldz / Here, x = -inf, so return 0
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ret
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis.NaN_or_pinf:
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis / Here, x = NaN or +inf, so load x and return immediately.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldt 4(%esp)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fadd %st(0),%st / quiet SNaN
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ret
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis .align 4
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis SET_SIZE(expl)