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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 combined asin/acos approximation including range reduction by
Joachim Wesner, <joachim.wesner@frankfurt.netsurf.de>, see also
mc 8/1991 p. 78-93. This version done in June/July 1998.
No special handling of illegal arguments or NANs, yet !!!
*/
/*
improved and modified by Kazushige Goto <goto@statabo.rim.or.jp>
*/
.set noreorder
.set noat
#ifdef __ELF__
.section .rodata
#else
.rdata
#endif
.align 5
K:
.t_floating 5.00000000000000000000e-1
.quad 0x3ff7ffffffc00000
.t_floating 1.00000000000000000000
.t_floating 1.50000000000000000000
.t_floating -2.38238591536702379869e1
.t_floating 1.50952708410306058795e2
.t_floating 4.17144302482604132365e2
.t_floating -6.96745734473506517226e-1
.t_floating -3.96888629975048772280e1
.t_floating -3.81863033617501514527e2
.t_floating -1.64210967144985602317e2
.t_floating 1.01525222338064633476e1
.t_floating 5.72082278778917299178e1
.t_floating -2.73684945241642552105e1
.t_floating 1.57079632679489655800e0
.t_floating 3.14159265358979311600e0
sqrtdata:
.long 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866
.long 0xf14a, 0x1091b, 0x11fcd, 0x13552, 0x14999, 0x15c98, 0x16e34, 0x17e5f
.long 0x18d03, 0x19a01, 0x1a545, 0x1ae8a, 0x1b5c4, 0x1bb01, 0x1bfde, 0x1c28d
.long 0x1c2de, 0x1c0db, 0x1ba73, 0x1b11c, 0x1a4b5, 0x1953d, 0x18266, 0x16be0
.long 0x1683e, 0x179d8, 0x18a4d, 0x19992, 0x1a789, 0x1b445, 0x1bf61, 0x1c989
.long 0x1d16d, 0x1d77b, 0x1dddf, 0x1e2ad, 0x1e5bf, 0x1e6e8, 0x1e654, 0x1e3cd
.long 0x1df2a, 0x1d635, 0x1cb16, 0x1be2c, 0x1ae4e, 0x19bde, 0x1868e, 0x16e2e
.long 0x1527f, 0x1334a, 0x11051, 0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd
.text
.align 5
.globl asin
.ent asin
asin:
fabs $f16, $f0 # x1 = fabs(x)
ldgp $29,.-asin($27)
mult $f16, $f16, $f11 # y1 = x * x
.frame $30,16,$26,0
#ifdef PROF
lda $28, _mcount
jsr $28, ($28), _mcount
unop
unop
#endif
.prologue 1
lda $28,K
br $17, $cont
.end asin
.align 5
.globl acos
.ent acos
acos:
fabs $f16, $f0 # x1 = fabs(x)
ldgp $29,.-acos($27)
mult $f16, $f16, $f11 # y1 = x * x
.frame $30,16,$26,0
#ifdef PROF
lda $28, _mcount
jsr $28, ($28), _mcount
unop
unop
#endif
.prologue 1
mov 1, $17
unop
lda $28,K
unop
.align 4
$cont:
ldt $f10, 0($28) # K[0]
ldt $f23, 64($28) # K[5]
ldt $f19, 32($28) # K[1]
ldt $f27, 96($28) # K[9]
cmptlt $f10, $f0, $f15 # flag = ( K[0] < x1)
mult $f0, $f10, $f1 # r1 = x1 * K[0]
lda $30, -16($30)
ldt $f20, 40($28) # K[2]
mult $f11, $f11, $f12 # y2 = y1 * y1
ldt $f21, 48($28) # K[3]
ldt $f22, 56($28) # K[4]
fbeq $f15, $L4
subt $f10, $f1, $f11 # y1 = K[0] - r1
bsr $27, inner_sqrt
mult $f11, $f11, $f12 # y2 = y1 * y1
addt $f0, $f0, $f0 # x1 = 2 * sqrt(y1)
.align 4
$L4:
mult $f20, $f11, $f20 # r2($f19) = K[2] * y1
ldt $f24, 72($28) # K[6]
addt $f11, $f19, $f19 # r1($f20) = y1 + K[1]
ldt $f25, 80($28) # K[7]
mult $f21, $f11, $f21 # r3($f21) = K[3] * y1
ldt $f26, 88($28) # K[8]
mult $f22, $f11, $f22 # t1($f22) = K[4] * y1
ldt $f28, 104($28) # K[10]
mult $f23, $f11, $f23 # t2($f23) = K[5] * y1
addt $f20, $f24, $f20 # r2 = r2 + K[6]
mult $f12, $f12, $f14 # y4($f13) = y2 * y2
addt $f21, $f25, $f21 # r3 = r3 + K[7]
mult $f12, $f11, $f13 # y3($f14) = y2 * y1
addt $f22, $f26, $f22 # t1 = t1 + K[8]
mult $f0, $f11, $f18 # t3($f18) = x1 * y1
addt $f23, $f27, $f23 # t2 = t2 + K[9]
mult $f20, $f12, $f20 # r2 = r2 * y2
mult $f19, $f14, $f19 # r1 = r1 * y4
mult $f22, $f13, $f22 # t1 = t1 * y3
mult $f23, $f11, $f23 # t2 = t2 * y1
addt $f19, $f20, $f19 # r1 = r1 + r2
addt $f22, $f23, $f22 # t1 = t1 + t2
addt $f19, $f21, $f19 # r1 = r1 + r3
addt $f22, $f28, $f22 # t1 = t1 + K[10]
mult $f22, $f18, $f22 # t1 = t1 * t3
divt $f22, $f19, $f19 # t1/r1
# Very very long wait, wait, wait, ....
ldt $f29, 112($28) # K[11]
ldt $f30, 120($28) # K[12]
addq $30, 16,$30
addt $f0, $f19, $f0 # y = x1 + t1/r1
blbs $17, $L5 # if (mode) goto $L5
fbeq $f15, $L10 # if (!$flag) goto $L10
fbge $f16, $L13 # if (x>=0) goto $L8
subt $f0, $f29, $f0 # y = K[11] - y
ret $31,($26),1
$L13:
subt $f29, $f0, $f0 # y = K[11] - y
ret $31,($26),1
$L10:
fbge $f16, $L8
fneg $f0, $f0 # y = -y
$L8:
ret $31,($26),1
.align 4
$L5:
fbeq $f15, $L9 # if (flag==0) goto $L9
fbge $f16, $L11 # if (x>0) goto $L8
subt $f30, $f0, $f0 # y = K[12] - y
$L11:
ret $31,($26),1
.align 4
$L9:
fble $f16, $L12
subt $f29, $f0, $f0 # r1 = K[11] - y
ret $31,($26),1
$L12:
addt $f29, $f0, $f0 # r2 = K[11] + y
ret $31,($26),1
.end acos
.align 5
.ent inner_sqrt
inner_sqrt:
.frame $30 , 0, $26
.prologue 1
stt $f11, 0($30)
mult $f11, $f10, $f24 # x*0.5
ldah $2 , 0x5fe8
nop
ldq $3 , 0($30)
srl $3 , 33, $1
subl $2 , $1 , $2
srl $2 , 12, $1
and $1 , 0xfc, $1
addq $1 , $28 , $1
ldl $1 , 128($1)
subl $2 , $1 , $2
sll $2 , 32, $2
stq $2 , 8($30)
ldt $f25, 8($28)
ldt $f30, 16($28)
ldt $f29, 24($28)
ldt $f0, 8($30)
mult $f24, $f0, $f1 # fm : $f10 = (x * 0.5) * y
mult $f1, $f0, $f1 # fm : $f10 = ((x * 0.5) * y) * y
subt $f29, $f1, $f1 # fa : $f1 = (1.5 - 0.5*x*y*y)
mult $f0, $f1, $f0 # fm : yp = y*(1.5 - 0.5*x*y*y)
mult $f24, $f0, $f1 # fm : $f24 = x * 0.5 * yp
mult $f1, $f0, $f24 # fm : $f24 = (x * 0.5 * yp) * yp
subt $f25, $f24, $f1 # fa : $f1= (1.5-2^-30) - 0.5*x*yp*yp
mult $f0, $f1, $f0 # fm : ypp = $f13 = yp*$f1
mult $f11, $f0, $f1 # fm : z = $f10 = x * ypp
mult $f1, $f0, $f0 # fm : $f24 = z*ypp
mult $f1, $f10, $f24 # fm : $f10 = z*0.5
subt $f30, $f0, $f0 # .. fa : $f1 = 1 - z*ypp
mult $f24, $f0, $f0 # fm : $f0 = z*0.5*(1 - z*ypp)
addt $f1, $f0, $f0 # fa : zp=res=$f0= z + z*0.5*(1 - z*ypp)
ret $31,($27),1
.end inner_sqrt
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