450 lines
11 KiB
ArmAsm
450 lines
11 KiB
ArmAsm
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; Copyright (c) 1985 Regents of the University of California.
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; All rights reserved.
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;
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; Redistribution and use in source and binary forms, with or without
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; modification, are permitted provided that the following conditions
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; are met:
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; 1. Redistributions of source code must retain the above copyright
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; notice, this list of conditions and the following disclaimer.
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; 2. Redistributions in binary form must reproduce the above copyright
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; notice, this list of conditions and the following disclaimer in the
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; documentation and/or other materials provided with the distribution.
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; 3. All advertising materials mentioning features or use of this software
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; must display the following acknowledgement:
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; This product includes software developed by the University of
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; California, Berkeley and its contributors.
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; 4. Neither the name of the University nor the names of its contributors
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; may be used to endorse or promote products derived from this software
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; without specific prior written permission.
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;
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; THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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; ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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; ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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; FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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; DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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; OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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; HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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; LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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; OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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; SUCH DAMAGE.
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;
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; @(#)support.s 5.4 (Berkeley) 10/9/90
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;
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; IEEE recommended functions
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;
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; double copysign(x,y)
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; double x,y;
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; IEEE 754 recommended function, return x*sign(y)
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; Coded by K.C. Ng in National 32k assembler, 11/9/85.
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;
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.vers 2
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.text
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.align 2
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.globl _copysign
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_copysign:
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movl 4(sp),f0
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movd 8(sp),r0
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movd 16(sp),r1
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xord r0,r1
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andd 0x80000000,r1
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cmpqd 0,r1
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beq end
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negl f0,f0
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end: ret 0
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;
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; double logb(x)
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; double x;
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; IEEE p854 recommended function, return the exponent of x (return float(N)
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; such that 1 <= x*2**-N < 2, even for subnormal number.
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; Coded by K.C. Ng in National 32k assembler, 11/9/85.
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; Note: subnormal number (if implemented) will be taken care of.
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;
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.vers 2
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.text
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.align 2
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.globl _logb
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_logb:
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;
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; extract the exponent of x
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; glossaries: r0 = high part of x
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; r1 = unbias exponent of x
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; r2 = 20 (first exponent bit position)
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;
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movd 8(sp),r0
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movd 20,r2
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extd r2,r0,r1,11 ; extract the exponent of x
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cmpqd 0,r1 ; if exponent bits = 0, goto L3
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beq L3
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cmpd 0x7ff,r1
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beq L2 ; if exponent bits = 0x7ff, goto L2
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L1: subd 1023,r1 ; unbias the exponent
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movdl r1,f0 ; convert the exponent to floating value
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ret 0
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;
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; x is INF or NaN, simply return x
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;
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L2:
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movl 4(sp),f0 ; logb(+inf)=+inf, logb(NaN)=NaN
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ret 0
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;
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; x is 0 or subnormal
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;
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L3:
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movl 4(sp),f0
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cmpl 0f0,f0
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beq L5 ; x is 0 , goto L5 (return -inf)
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;
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; Now x is subnormal
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;
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mull L64,f0 ; scale up f0 with 2**64
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movl f0,tos
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movd tos,r0
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movd tos,r0 ; now r0 = new high part of x
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extd r2,r0,r1,11 ; extract the exponent of x to r1
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subd 1087,r1 ; unbias the exponent with correction
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movdl r1,f0 ; convert the exponent to floating value
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ret 0
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;
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; x is 0, return logb(0)= -INF
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;
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L5:
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movl 0f1.0e300,f0
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mull 0f-1.0e300,f0 ; multiply two big numbers to get -INF
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ret 0
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;
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; double rint(x)
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; double x;
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; ... delivers integer nearest x in direction of prevailing rounding
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; ... mode
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; Coded by K.C. Ng in National 32k assembler, 11/9/85.
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; Note: subnormal number (if implemented) will be taken care of.
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;
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.vers 2
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.text
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.align 2
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.globl _rint
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_rint:
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;
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movd 8(sp),r0
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movd 20,r2
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extd r2,r0,r1,11 ; extract the exponent of x
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cmpd 0x433,r1
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ble itself
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movl L52,f2 ; f2 = L = 2**52
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cmpqd 0,r0
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ble L1
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negl f2,f2 ; f2 = s = copysign(L,x)
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L1: addl f2,f0 ; f0 = x + s
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subl f2,f0 ; f0 = f0 - s
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ret 0
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itself: movl 4(sp),f0
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ret 0
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L52: .double 0x0,0x43300000 ; L52=2**52
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;
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; int finite(x)
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; double x;
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; IEEE 754 recommended function, return 0 if x is NaN or INF, else 0
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; Coded by K.C. Ng in National 32k assembler, 11/9/85.
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;
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.vers 2
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.text
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.align 2
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.globl _finite
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_finite:
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movd 4(sp),r1
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andd 0x800fffff,r1
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cmpd 0x7ff00000,r1
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sned r0 ; r0=0 if exponent(x) = 0x7ff
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ret 0
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;
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; double scalb(x,N)
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; double x; int N;
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; IEEE 754 recommended function, return x*2**N by adjusting
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; exponent of x.
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; Coded by K.C. Ng in National 32k assembler, 11/9/85.
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; Note: subnormal number (if implemented) will be taken care of
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;
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.vers 2
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.text
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.align 2
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.globl _scalb
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_scalb:
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;
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; if x=0 return 0
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;
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movl 4(sp),f0
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cmpl 0f0,f0
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beq end ; scalb(0,N) is x itself
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;
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; extract the exponent of x
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; glossaries: r0 = high part of x,
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; r1 = unbias exponent of x,
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; r2 = 20 (first exponent bit position).
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;
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movd 8(sp),r0 ; r0 = high part of x
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movd 20,r2 ; r2 = 20
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extd r2,r0,r1,11 ; extract the exponent of x in r1
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cmpd 0x7ff,r1
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;
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; if exponent of x is 0x7ff, then x is NaN or INF; simply return x
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;
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beq end
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cmpqd 0,r1
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;
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; if exponent of x is zero, then x is subnormal; goto L19
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;
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beq L19
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addd 12(sp),r1 ; r1 = (exponent of x) + N
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bfs inof ; if integer overflows, goto inof
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cmpqd 0,r1 ; if new exponent <= 0, goto underflow
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bge underflow
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cmpd 2047,r1 ; if new exponent >= 2047 goto overflow
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ble overflow
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insd r2,r1,r0,11 ; insert the new exponent
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movd r0,tos
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movd 8(sp),tos
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movl tos,f0 ; return x*2**N
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end: ret 0
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inof: bcs underflow ; negative int overflow if Carry bit is set
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overflow:
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andd 0x80000000,r0 ; keep the sign of x
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ord 0x7fe00000,r0 ; set x to a huge number
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movd r0,tos
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movqd 0,tos
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movl tos,f0
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mull 0f1.0e300,f0 ; multiply two huge number to get overflow
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ret 0
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underflow:
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addd 64,r1 ; add 64 to exonent to see if it is subnormal
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cmpqd 0,r1
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bge zero ; underflow to zero
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insd r2,r1,r0,11 ; insert the new exponent
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movd r0,tos
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movd 8(sp),tos
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movl tos,f0
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mull L30,f0 ; readjust x by multiply it with 2**-64
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ret 0
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zero: andd 0x80000000,r0 ; keep the sign of x
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ord 0x00100000,r0 ; set x to a tiny number
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movd r0,tos
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movqd 0,tos
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movl tos,f0
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mull 0f1.0e-300,f0 ; underflow to 0 by multipling two tiny nos.
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ret 0
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L19: ; subnormal number
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mull L32,f0 ; scale up x by 2**64
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movl f0,tos
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movd tos,r0
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movd tos,r0 ; get the high part of new x
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extd r2,r0,r1,11 ; extract the exponent of x in r1
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addd 12(sp),r1 ; exponent of x + N
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subd 64,r1 ; adjust it by subtracting 64
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cmpqd 0,r1
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bge underflow
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cmpd 2047,r1
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ble overflow
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insd r2,r1,r0,11 ; insert back the incremented exponent
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movd r0,tos
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movd 8(sp),tos
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movl tos,f0
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end: ret 0
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L30: .double 0x0,0x3bf00000 ; floating point 2**-64
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L32: .double 0x0,0x43f00000 ; floating point 2**64
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;
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; double drem(x,y)
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; double x,y;
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; IEEE double remainder function, return x-n*y, where n=x/y rounded to
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; nearest integer (half way case goes to even). Result exact.
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; Coded by K.C. Ng in National 32k assembly, 11/19/85.
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;
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.vers 2
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.text
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.align 2
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.globl _drem
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_drem:
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;
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; glossaries:
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; r2 = high part of x
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; r3 = exponent of x
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; r4 = high part of y
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; r5 = exponent of y
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; r6 = sign of x
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; r7 = constant 0x7ff00000
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;
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; 16(fp) : y
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; 8(fp) : x
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; -12(fp) : adjustment on y when y is subnormal
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; -16(fp) : fsr
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; -20(fp) : nx
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; -28(fp) : t
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; -36(fp) : t1
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; -40(fp) : nf
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;
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;
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enter [r3,r4,r5,r6,r7],40
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movl f6,tos
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movl f4,tos
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movl 0f0,-12(fp)
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movd 0,-20(fp)
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movd 0,-40(fp)
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movd 0x7ff00000,r7 ; initialize r7=0x7ff00000
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movd 12(fp),r2 ; r2 = high(x)
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movd r2,r3
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andd r7,r3 ; r3 = xexp
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cmpd r7,r3
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; if x is NaN or INF goto L1
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beq L1
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movd 20(fp),r4
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bicd [31],r4 ; r4 = high part of |y|
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movd r4,20(fp) ; y = |y|
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movd r4,r5
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andd r7,r5 ; r5 = yexp
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cmpd r7,r5
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beq L2 ; if y is NaN or INF goto L2
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cmpd 0x04000000,r5 ;
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bgt L3 ; if y is tiny goto L3
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;
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; now y != 0 , x is finite
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;
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L10:
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movd r2,r6
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andd 0x80000000,r6 ; r6 = sign(x)
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bicd [31],r2 ; x <- |x|
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sfsr r1
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movd r1,-16(fp) ; save fsr in -16(fp)
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bicd [5],r1
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lfsr r1 ; disable inexact interupt
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movd 16(fp),r0 ; r0 = low part of y
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movd r0,r1 ; r1 = r0 = low part of y
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andd 0xf8000000,r1 ; mask off the lsb 27 bits of y
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movd r2,12(fp) ; update x to |x|
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movd r0,-28(fp) ;
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movd r4,-24(fp) ; t = y
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movd r4,-32(fp) ;
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movd r1,-36(fp) ; t1 = y with trialing 27 zeros
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movd 0x01900000,r1 ; r1 = 25 in exponent field
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LOOP:
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movl 8(fp),f0 ; f0 = x
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movl 16(fp),f2 ; f2 = y
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cmpl f0,f2
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ble fnad ; goto fnad (final adjustment) if x <= y
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movd r4,-32(fp)
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movd r3,r0
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subd r5,r0 ; xexp - yexp
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subd r1,r0 ; r0 = xexp - yexp - m25
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cmpqd 0,r0 ; r0 > 0 ?
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bge 1f
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addd r4,r0 ; scale up (high) y
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movd r0,-24(fp) ; scale up t
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movl -28(fp),f2 ; t
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movd r0,-32(fp) ; scale up t1
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1:
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movl -36(fp),f4 ; t1
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movl f0,f6
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divl f2,f6 ; f6 = x/t
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floorld f6,r0 ; r0 = [x/t]
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movdl r0,f6 ; f6 = n
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subl f4,f2 ; t = t - t1 (tail of t1)
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mull f6,f4 ; f4 = n*t1 ...exact
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subl f4,f0 ; x = x - n*t1
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|
mull f6,f2 ; n*(t-t1) ...exact
|
||
|
|
subl f2,f0 ; x = x - n*(t-t1)
|
||
|
|
; update xexp
|
||
|
|
movl f0,8(fp)
|
||
|
|
movd 12(fp),r3
|
||
|
|
andd r7,r3
|
||
|
|
jump LOOP
|
||
|
|
fnad:
|
||
|
|
cmpqd 0,-20(fp) ; 0 = nx?
|
||
|
|
beq final
|
||
|
|
mull -12(fp),8(fp) ; scale up x the same amount as y
|
||
|
|
movd 0,-20(fp)
|
||
|
|
movd 12(fp),r2
|
||
|
|
movd r2,r3
|
||
|
|
andd r7,r3 ; update exponent of x
|
||
|
|
jump LOOP
|
||
|
|
|
||
|
|
final:
|
||
|
|
movl 16(fp),f2 ; f2 = y (f0=x, r0=n)
|
||
|
|
subd 0x100000,r4 ; high y /2
|
||
|
|
movd r4,-24(fp)
|
||
|
|
movl -28(fp),f4 ; f4 = y/2
|
||
|
|
cmpl f0,f4 ; x > y/2 ?
|
||
|
|
bgt 1f
|
||
|
|
bne 2f
|
||
|
|
andd 1,r0 ; n is odd or even
|
||
|
|
cmpqd 0,r0
|
||
|
|
beq 2f
|
||
|
|
1:
|
||
|
|
subl f2,f0 ; x = x - y
|
||
|
|
2:
|
||
|
|
cmpqd 0,-40(fp)
|
||
|
|
beq 3f
|
||
|
|
divl -12(fp),f0 ; scale down the answer
|
||
|
|
3:
|
||
|
|
movl f0,tos
|
||
|
|
xord r6,tos
|
||
|
|
movl tos,f0
|
||
|
|
movd -16(fp),r0
|
||
|
|
lfsr r0 ; restore the fsr
|
||
|
|
|
||
|
|
end: movl tos,f4
|
||
|
|
movl tos,f6
|
||
|
|
exit [r3,r4,r5,r6,r7]
|
||
|
|
ret 0
|
||
|
|
;
|
||
|
|
; y is NaN or INF
|
||
|
|
;
|
||
|
|
L2:
|
||
|
|
movd 16(fp),r0 ; r0 = low part of y
|
||
|
|
andd 0xfffff,r4 ; r4 = high part of y & 0x000fffff
|
||
|
|
ord r4,r0
|
||
|
|
cmpqd 0,r0
|
||
|
|
beq L4
|
||
|
|
movl 16(fp),f0 ; y is NaN, return y
|
||
|
|
jump end
|
||
|
|
L4: movl 8(fp),f0 ; y is inf, return x
|
||
|
|
jump end
|
||
|
|
;
|
||
|
|
; exponent of y is less than 64, y may be zero or subnormal
|
||
|
|
;
|
||
|
|
L3:
|
||
|
|
movl 16(fp),f0
|
||
|
|
cmpl 0f0,f0
|
||
|
|
bne L5
|
||
|
|
divl f0,f0 ; y is 0, return NaN by doing 0/0
|
||
|
|
jump end
|
||
|
|
;
|
||
|
|
; subnormal y or tiny y
|
||
|
|
;
|
||
|
|
L5:
|
||
|
|
movd 0x04000000,-20(fp) ; nx = 64 in exponent field
|
||
|
|
movl L64,f2
|
||
|
|
movl f2,-12(fp)
|
||
|
|
mull f2,f0
|
||
|
|
cmpl f0,LTINY
|
||
|
|
bgt L6
|
||
|
|
mull f2,f0
|
||
|
|
addd 0x04000000,-20(fp) ; nx = nx + 64 in exponent field
|
||
|
|
mull f2,-12(fp)
|
||
|
|
L6:
|
||
|
|
movd -20(fp),-40(fp)
|
||
|
|
movl f0,16(fp)
|
||
|
|
movd 20(fp),r4
|
||
|
|
movd r4,r5
|
||
|
|
andd r7,r5 ; exponent of new y
|
||
|
|
jump L10
|
||
|
|
;
|
||
|
|
; x is NaN or INF, return x-x
|
||
|
|
;
|
||
|
|
L1:
|
||
|
|
movl 8(fp),f0
|
||
|
|
subl f0,f0 ; if x is INF, then INF-INF is NaN
|
||
|
|
ret 0
|
||
|
|
L64: .double 0x0,0x43f00000 ; L64 = 2**64
|
||
|
|
LTINY: .double 0x0,0x04000000 ; LTINY = 2**-959
|