1/* 2 * Copyright (c) 1987 Regents of the University of California. 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms are permitted 6 * provided that the above copyright notice and this paragraph are 7 * duplicated in all such forms and that any documentation, 8 * advertising materials, and other materials related to such 9 * distribution and use acknowledge that the software was developed 10 * by the University of California, Berkeley. The name of the 11 * University may not be used to endorse or promote products derived 12 * from this software without specific prior written permission. 13 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR 14 * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED 15 * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE. 16 * 17 * All recipients should regard themselves as participants in an ongoing 18 * research project and hence should feel obligated to report their 19 * experiences (good or bad) with these elementary function codes, using 20 * the sendbug(8) program, to the authors. 21 */ 22 .data 23 .align 2 24_sccsid: 25 .asciz "@(#)support.s 5.4 (ucb.elefunt) 06/30/88" 26/* 27 * copysign(x,y), 28 * logb(x), 29 * scalb(x,N), 30 * finite(x), 31 * drem(x,y), 32 * Coded in vax assembly language by K. C. Ng 4/9/85. 33 * Re-coded in tahoe assembly language by Z. Alex Liu 7/13/87. 34 */ 35/* 36 * double copysign(x,y) 37 * double x,y; 38 */ 39 .globl _copysign 40 .text 41 .align 2 42_copysign: 43 .word 0x0004 # save r2 44 movl 8(fp),r1 45 movl 4(fp),r0 # r0:r1 = x 46 andl3 $0x7f800000,r0,r2 # r2 = biased exponent of x 47 beql 1f # if 0 or reserved op then return x 48 andl3 $0x80000000,12(fp),r2 # r2 = sign bit of y at bit-31 49 andl2 $0x7fffffff,r0 # replace x by |x| 50 orl2 r2,r0 # copy the sign bit of y to x 511: ret 52/* 53 * double logb(x) 54 * double x; 55 */ 56 .globl _logb 57 .text 58 .align 2 59_logb: 60 .word 0x0000 # save nothing 61 andl3 $0x7f800000,4(fp),r0 # r0[b23:b30] = biased exponent of x 62 beql 1f 63 shrl $23,r0,r0 # r0[b0:b7] = biased exponent of x 64 subl2 $129,r0 # r0 = unbiased exponent of x 65 cvld r0 # acc = unbiased exponent of x (double) 66 std r0 # r0 = unbiased exponent of x (double) 67 ret 681: movl 8(fp),r1 # 8(fp) must be moved first 69 movl 4(fp),r0 # r0:r1 = x (zero or reserved op) 70 blss 2f # simply return if reserved op 71 movl $0xfe000000,r1 72 movl $0xcfffffff,r0 # -2147483647.0 732: ret 74/* 75 * long finite(x) 76 * double x; 77 */ 78 .globl _finite 79 .text 80 .align 2 81_finite: 82 .word 0x0000 # save nothing 83 andl3 $0xff800000,4(fp),r0 # r0 = sign of x & its biased exponent 84 cmpl r0,$0x80000000 # is x a reserved op? 85 beql 1f # if so, return FALSE (0) 86 movl $1,r0 # else return TRUE (1) 87 ret 881: clrl r0 89 ret 90/* 91 * double scalb(x,N) 92 * double x; int N; 93 */ 94 .globl _scalb 95 .set ERANGE,34 96 .text 97 .align 2 98_scalb: 99 .word 0x000c # save r2-r3 100 movl 8(fp),r1 101 movl 4(fp),r0 # r0:r1 = x (-128 <= Ex <= 126) 102 andl3 $0x7f800000,r0,r3 # r3[b23:b30] = biased exponent of x 103 beql 1f # is x a 0 or a reserved operand? 104 movl 12(fp),r2 # r2 = N 105 cmpl r2,$0xff # if N >= 255 106 bgeq 2f # then the result must overflow 107 cmpl r2,$-0xff # if N <= -255 108 bleq 3f # then the result must underflow 109 shrl $23,r3,r3 # r3[b0:b7] = biased exponent of x 110 addl2 r2,r3 # r3 = biased exponent of the result 111 bleq 3f # if <= 0 then the result underflows 112 cmpl r3,$0x100 # if >= 256 then the result overflows 113 bgeq 2f 114 shll $23,r3,r3 # r3[b23:b30] = biased exponent of res. 115 andl2 $0x807fffff,r0 116 orl2 r3,r0 # r0:r1 = x*2^N 1171: ret 1182: pushl $ERANGE # if the result would overflow 119 callf $8,_infnan # and _infnan returns 120 andl3 $0x80000000,4(fp),r2 # get the sign of input arg 121 orl2 r2,r0 # re-attach the sign to r0:r1 122 ret 1233: clrl r1 # if the result would underflow 124 clrl r0 # then return 0 125 ret 126/* 127 * double drem(x,y) 128 * double x,y; 129 * Returns x-n*y where n=[x/y] rounded (to even in the half way case). 130 */ 131 .globl _drem 132 .set EDOM,33 133 .text 134 .align 2 135_drem: 136 .word 0x1ffc # save r2-r12 137 movl 16(fp),r3 138 movl 12(fp),r2 # r2:r3 = y 139 movl 8(fp),r1 140 movl 4(fp),r0 # r0:r1 = x 141 andl3 $0xff800000,r0,r4 142 cmpl r4,$0x80000000 # is x a reserved operand? 143 beql 1f # if yes then propagate x and return 144 andl3 $0xff800000,r2,r4 145 cmpl r4,$0x80000000 # is y a reserved operand? 146 bneq 2f 147 movl r3,r1 148 movl r2,r0 # if yes then propagate y and return 1491: ret 150 1512: tstl r4 # is y a 0? 152 bneq 3f 153 pushl $EDOM # if so then generate reserved op fault 154 callf $8,_infnan 155 ret 156 1573: andl2 $0x7fffffff,r2 # r2:r3 = y <- |y| 158 clrl r12 # r12 = nx := 0 159 cmpl r2,$0x1c800000 # Ey ? 57 160 bgtr 4f # if Ey > 57 goto 4 161 addl2 $0x1c800000,r2 # scale up y by 2**57 162 movl $0x1c800000,r12 # r12[b23:b30] = nx = 57 1634: pushl r12 # pushed onto stack: nf := nx 164 andl3 $0x80000000,r0,-(sp) # pushed onto stack: sign of x 165 andl2 $0x7fffffff,r0 # r0:r1 = x <- |x| 166 movl r3,r11 # r10:r11 = y1 = y w/ last 27 bits 0 167 andl3 $0xf8000000,r10,r11 # clear last 27 bits of y1 168 169Loop: cmpd2 r0,r2 # x ? y 170 bleq 6f # if x <= y goto 6 171 /* # begin argument reduction */ 172 movl r3,r5 173 movl r2,r4 # r4:r5 = t = y 174 movl r11,r7 175 movl r10,r6 # r6:r7 = t1 = y1 176 andl3 $0x7f800000,r0,r8 # r8[b23:b30] = Ex:biased exponent of x 177 andl3 $0x7f800000,r2,r9 # r9[b23:b30] = Ey:biased exponent of y 178 subl2 r9,r8 # r8[b23:b30] = Ex-Ey 179 subl2 $0x0c800000,r8 # r8[b23:b30] = k = Ex-Ey-25 180 blss 5f # if k < 0 goto 5 181 addl2 r8,r4 # t += k 182 addl2 r8,r6 # t1 += k, scale up t and t1 1835: ldd r0 # acc = x 184 divd r4 # acc = x/t 185 cvdl r8 # r8 = n = [x/t] truncated 186 cvld r8 # acc = dble(n) 187 std r8 # r8:r9 = dble(n) 188 ldd r4 # acc = t 189 subd r6 # acc = t-t1 190 muld r8 # acc = n*(t-t1) 191 std r4 # r4:r5 = n*(t-t1) 192 ldd r6 # acc = t1 193 muld r8 # acc = n*t1 194 subd r0 # acc = n*t1-x 195 negd # acc = x-n*t1 196 subd r4 # acc = (x-n*t1)-n*(t-t1) 197 std r0 # r0:r1 = (x-n*t1)-n*(t-t1) 198 brb Loop 199 2006: movl r12,r6 # r6 = nx 201 beql 7f # if nx == 0 goto 7 202 addl2 r6,r0 # x <- x*2**57:scale x up by nx 203 clrl r12 # clear nx 204 brb Loop 205 2067: movl r3,r5 207 movl r2,r4 # r4:r5 = y 208 subl2 $0x800000,r4 # r4:r5 = y/2 209 cmpd2 r0,r4 # x ? y/2 210 blss 9f # if x < y/2 goto 9 211 bgtr 8f # if x > y/2 goto 8 212 ldd r8 # acc = dble(n) 213 cvdl r8 # r8 = ifix(dble(n)) 214 bbc $0,r8,9f # if the last bit is zero, goto 9 2158: ldd r0 # acc = x 216 subd r2 # acc = x-y 217 std r0 # r0:r1 = x-y 2189: xorl2 (sp)+,r0 # x^sign (exclusive or) 219 movl (sp)+,r6 # r6 = nf 220 andl3 $0x7f800000,r0,r8 # r8 = biased exponent of x 221 andl2 $0x807fffff,r0 # r0 = x w/ exponent zapped 222 subl2 r6,r8 # r8 = Ex-nf 223 bgtr 0f # if Ex-nf > 0 goto 0 224 clrl r8 # clear r8 225 clrl r0 226 clrl r1 # x underflows to zero 2270: orl2 r8,r0 # put r8 into x's exponent field 228 ret 229