25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * CDDL HEADER START
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
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25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
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25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Use is subject to license terms.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis .file "expm1.s"
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#include "libm.h"
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr JasiukajtisLIBM_ANSI_PRAGMA_WEAK(expm1,function)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis .data
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis .align 4
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis.mhundred: .float -100.0
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ENTRY(expm1)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis movl 8(%esp),%ecx / ecx <-- hi_32(x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis andl $0x7fffffff,%ecx / ecx <-- hi_32(|x|)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis cmpl $0x3fe62e42,%ecx / Is |x| < ln(2)?
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis jb .shortcut / If so, take a shortcut.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis je .check_tail / |x| may be only slightly < ln(2)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis cmpl $0x7ff00000,%ecx / hi_32(|x|) >= hi_32(INF)?
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis jae .not_finite / if so, x is not finite
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis.finite_non_special: / Here, ln(2) < |x| < INF
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldl 4(%esp) / push x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis subl $8,%esp / save RP and set round-to-64-bits
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fstcw (%esp)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis movw (%esp),%ax
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis movw %ax,4(%esp)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis orw $0x0300,%ax
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis movw %ax,(%esp)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldcw (%esp)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldl2e / push log2e }not for xtndd_dbl
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fmulp %st,%st(1) / z = x*log2e }not for xtndd_dbl
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fld %st(0) / duplicate stack top
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis frndint / [z],z
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis / [z] != 0, compute exp(x) and then subtract one to get expm1(x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fxch / z,[z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fsub %st(1),%st / z-[z],[z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis f2xm1 / 2**(z-[z])-1,[z]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis / avoid spurious underflow when scaling to compute exp(x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis PIC_SETUP(1)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis flds PIC_L(.mhundred)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis PIC_WRAPUP
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fucom %st(2) / if -100 !< [z], then use -100
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fstsw %ax
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis sahf
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis jb .got_int_part
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fxch %st(2)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis.got_int_part:
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fstp %st(0) / 2**(z-[z])-1,max([z],-100)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fld1 / 1,2**(z-[z])-1,max([z],-100)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis faddp %st,%st(1) / 2**(z-[z]) ,max([z],-100)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fscale / exp(x) ,max([z],-100)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fld1 / 1,exp(x) ,max([z],-100)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fxch / exp(x),1 ,max([z],-100)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fsubp %st,%st(1) / exp(x)-1 ,max([z],-100)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fstp %st(1)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fstcw (%esp) / restore old RP
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis movw (%esp),%dx
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis andw $0xfcff,%dx
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis movw 4(%esp),%cx
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis andw $0x0300,%cx
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis orw %dx,%cx
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis movw %cx,(%esp)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldcw (%esp)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis add $8,%esp
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ret
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis.check_tail:
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis movl 4(%esp),%edx / edx <-- lo_32(x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis cmpl $0xfefa39ef,%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*log2(e)| < 1,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis / whence z is in f2xm1's domain.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldl 4(%esp) / push x
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fldl2e / push log2e }not for xtndd_dbl
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fmulp %st,%st(1) / z = x*log2e }not for xtndd_dbl
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis f2xm1 / 2**(x*log2(e))-1 = e**x - 1
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ret
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis.not_finite:
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis / Here, flags still have settings from execution of
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis / cmpl $0x7ff00000,%ecx / hi_32(|x|) > hi_32(INF)?
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ja .NaN_or_pinf / if not, x may be +/- INF
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 8(%esp),%eax / eax <-- hi_32(x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis andl $0x80000000,%eax / here, x is infinite, but +/-?
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis jz .NaN_or_pinf / branch if x = +INF
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fld1 / Here, x = -inf, so return -1
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fchs
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 fldl 4(%esp)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis fwait
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ret
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis .align 4
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis SET_SIZE(expm1)