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/*
libffm - Free, pretty fast replacement for some math (libm) routines
on Linux/AXP, optimized for the 21164
Copyright (C) 1998 Joachim Wesner <joachim.wesner@frankfurt.netsurf.de>
and Kazushige Goto <goto@statabo.rim.or.jp>
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public
License as published by the Free Software Foundation; either
version 2 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with this library (see file COPYING.LIB); if not, write
to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge,
MA 02139, USA.
*/
/*
Fast 2^x, exp(x), 10^x approximations including range reduction
by Joachim Wesner, <joachim.wesner@frankfurt.netsurf.de>,
see also mc 8/1991 p. 78-93. Done in July 1998.
This version uses a "longer" 11th order polynomial approximation,
but requires a somewhat simpler range reduction.
*/
/* improved and rescheduled by Kazushige Goto<goto@statabo.rim.or.jp> */
/*
now including illegal argument handling by Kazushige Goto / Joachim Wesner
*/
.set noat
.set noreorder
#ifdef __ELF__
.section .rodata
#else
.rdata
#endif
.align 5
R:
.quad 0x40862E42FEFA39EE
.quad 0xC086232BDD7ABCD1
.quad 0x408FFFFFFFFFFFFF
.quad 0xc08FEFFFFFFFFFFF
.t_floating 1.00000000000000000000e0
.t_floating 1.442695040888963407e0 # LDE
.t_floating 6.93359375e-1 # K1
.t_floating -2.1219444005469060e-4 # K2
.quad 0x40734413509F79FE
.quad 0xC0733A7146f72A41
.quad 0x7e37e43c8800759c # 1.0e300(dummy)
.quad 0
.t_floating 1.00000000000000000000e0
.t_floating 3.321928094887362347 # LD10
.t_floating 3.0103000998497010e-001 # J1
.t_floating -1.4320988897547790e-008 # J2
/*
2^x (0..1)
Derived from Chebyshev Approx.
rel. error 4e-18
*/
.t_floating 6.29768236459390291646e-10
.t_floating 1.02577755722569533985e-7
.t_floating 1.52532278639779265219e-5
.t_floating 1.33335587324213489593e-3
.t_floating 5.55041086659065138753e-2
.t_floating 6.93147180559946507472e-1
.t_floating 6.54053877719848751881e-9
.t_floating 1.32077456410841510838e-6
.t_floating 1.54035094120123436379e-4
.t_floating 9.61812909725173574571e-3
.t_floating 2.40226506959042129807e-1
.t_floating 9.99999999999999996e-01
.text
.align 5
.globl exp2
.ent exp2
exp2:
lda $30, -16($30)
ldgp $29,.-exp2($27)
stt $f16, 0($30)
.frame $30,16,$26,0
#ifdef PROF
lda $28, _mcount
jsr $28, ($28), _mcount
unop
unop
#endif
.prologue 1
lda $1, R
ldq $3, 16($1)
ldq $2, 0($30)
ldq $4, 24($1)
sll $2, 1, $0
blt $2, $Negative2
cmplt $3, $2, $5
bne $5, $exception # Value is too Large
srl $0, 53, $0
br $Calc2
$Negative2:
cmplt $4, $2, $5
srl $0, 53, $0
bne $5, $exception # Value is too Small
$Calc2:
ldt $f19, 128($1)
unop
beq $0, $SubNormal
.align 4
cvttq/c $f16, $f10 # double -> int
ldt $f1, 32($1)
ldt $f19, 128($1)
ldt $f20, 136($1)
ldt $f21, 144($1)
ldt $f22, 152($1)
ldt $f23, 160($1)
ldt $f24, 168($1)
cvtqt $f10, $f10 # int -> double
ldt $f25, 176($1)
ldt $f26, 184($1)
ldt $f27, 192($1)
ldt $f28, 200($1)
fbge $f16,$L2
subt $f10, $f1, $f10 # iexp -= R[0]
.align 4
$L2:
subt $f16, $f10, $f16 # x -= iexp
ldt $f29, 208($1)
cvttqc $f10,$f10 # double -> int
ldt $f30, 216($1)
br $31, $exp_continue
.end exp2
.align 5
.globl exp10
.ent exp10
exp10:
lda $30, -16($30)
ldgp $29,.-exp10($27)
stt $f16, 0($30)
.frame $30,16,$26,0
#ifdef PROF
lda $28, _mcount
jsr $28, ($28), _mcount
unop
unop
#endif
.prologue 1
lda $1, R
ldq $3, 64($1)
ldq $4, 72($1)
ldt $f1, 96($1)
ldq $2, 0($30)
ldt $f0, 104($1) # LDE
ldt $f29,112($1) # K1
ldt $f30,120($1) # K2
br $31, $continue
.end exp10
.align 5
.globl exp
.ent exp
exp:
lda $30, -16($30)
ldgp $29,.-exp($27)
stt $f16, 0($30)
.frame $30,16,$26,0
#ifdef PROF
lda $28, _mcount
jsr $28, ($28), _mcount
unop
unop
#endif
.prologue 1
lda $1, R
ldq $3, 0($1)
ldq $4, 8($1)
ldt $f1, 32($1)
ldq $2, 0($30)
ldt $f0, 40($1) # LDE
ldt $f29, 48($1) # K1
ldt $f30, 56($1) # K2
.align 4
$continue:
sll $2, 1, $0
blt $2, $Negative
cmplt $3, $2, $5
bne $5, $exception # Value is too Large
srl $0, 53, $6
br $Calc
$Negative:
cmplt $4, $2, $7
srl $0, 53, $6
bne $7, $exception # Value is too Small
$Calc:
ldt $f19, 128($1)
unop
beq $6, $SubNormal
.align 4
mult $f16, $f0, $f10 # iexp = x*LDE
ldt $f20, 136($1)
ldt $f21, 144($1)
ldt $f22, 152($1)
ldt $f23, 160($1)
ldt $f24, 168($1)
ldt $f25, 176($1)
ldt $f26, 184($1)
cvttq/c $f10, $f11 # double -> int
ldt $f27, 192($1)
ldt $f28, 200($1)
cvtqt $f11, $f10 # int -> double
fbge $f16, $L4 # if x>=0 goto $L4
subt $f10, $f1, $f10 # iexp -= R[0]
$L4:
fbeq $f10, $L5
mult $f10, $f29, $f29 # iexp*K1
mult $f10, $f30, $f30 # iexp*K2
subt $f16, $f29, $f17 # x - iexp*K1
subt $f17, $f30, $f16 # x - iexp*K2
.align 4
$L5:
mult $f16, $f0, $f16 # x *= LDE
ldt $f29, 208($1)
ldt $f30, 216($1)
cvttqc $f10, $f10 # double -> int
.align 4
$exp_continue:
mult $f16, $f16, $f11 # x2 = x * x
mult $f19, $f16, $f19 # y1 = R[4] * x
mult $f20, $f16, $f20 # y2 = R[5] * x
mult $f21, $f16, $f21 # y3 = R[6] * x
mult $f11, $f11, $f12 # x4 = x2 * x2
mult $f22, $f16, $f22 # y4 = R[8] * x
stt $f10, 0($30)
addt $f19, $f25, $f19 # y1 += R[10]
mult $f23, $f16, $f23 # y5 = R[9] * x
addt $f20, $f26, $f20 # y2 += R[11]
mult $f24, $f16, $f24 # y6 = R[10] * x
addt $f21, $f27, $f21 # y3 += R[12]
mult $f12, $f11, $f13 # x6 = x4 * x2
mult $f12, $f12, $f14 # x8 = x4 * x4
addt $f22, $f28, $f22 # y4 += R[13]
addt $f23, $f29, $f23 # y5 += R[14]
ldq $1, 0($30)
addt $f24, $f30, $f24 # y6 += R[15]
mult $f13, $f12, $f15 # x10 = x6 * x4
mult $f20, $f14, $f20 # y2 *= x8
mult $f21, $f13, $f21 # y3 *= x6
lda $1,1023($1)
mult $f22, $f12, $f22 # y4 *= x4
sll $1, 52, $1
mult $f19, $f15, $f17 # y1 *= x10
stq $1, 8($30)
mult $f23, $f11, $f23 # y5 *= x2
addt $f17, $f20, $f19 # y1 += y2
addt $f19, $f21, $f17 # y1 += y3
addt $f17, $f22, $f19 # y1 += y4
ldt $f25, 8($30)
addt $f19, $f23, $f17 # y1 += y5
addt $f17, $f24, $f19 # y1 += y6
addq $30, 16, $30
mult $f19, $f25, $f0
ret $31
.align 4
$SubNormal:
ldt $f0, 32($1) # return 1.0
addq $30, 16, $30
ret
.align 4
$exception: /* exp(INF) = INF, exp(NaN) = NaN, exp(-INF) = 0 */
sll $2, 1, $0
lda $3, 0x7ff
srl $0, 53, $0
cmpeq $0, $3, $4
bne $4, $Inf_or_NaN
bne $5, $TooLarge # Argument is too large
br $Zero
.align 4
$Inf_or_NaN:
sll $2, 12, $0
bne $0, $NaN
.align 4
$Infinity:
blt $2, $Zero
sll $3, 52, $0
stq $0, 0($30)
ldt $f0, 0($30)
addq $30, 16, $30
ret
.align 4
$TooLarge:
blt $2,$Zero # too small/negative
sll $3, 52, $0
stq $0, 0($30)
ldt $f0, 0($30)
addq $30, 16, $30
ret
.align 4
$NaN:
lda $0, -1
stq $0, 0($30)
ldt $f0, 0($30)
addq $30, 16, $30
ret
.align 4
$Zero:
fclr $f0
addq $30, 16, $30
ret
.end exp
|
