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1.1 ! root 1: //////// ! 2: / ! 3: / Intel 8086 floating point. ! 4: / Double divide. ! 5: / SMALL model. ! 6: / ! 7: //////// ! 8: ! 9: .globl drdiv ! 10: .globl dldiv ! 11: .globl _fpac_ ! 12: .globl dzero ! 13: ! 14: oerror_: ret ! 15: ! 16: //////// ! 17: / ! 18: / drdiv - double divide (rvalue) ! 19: / dldiv - double divide (lvalue) ! 20: / ! 21: / compiler calling sequences: ! 22: / push <right double argument> ! 23: / push <left double argument> ! 24: / call drdiv ! 25: / add sp,16 ! 26: / ! 27: / mov ax,offset <right double argument> ! 28: / push ax ! 29: / push <left double argument> ! 30: / call dldiv ! 31: / add sp,10 ! 32: / ! 33: / outputs: ! 34: / _fpac_ = result. ! 35: / ! 36: / see Knuth "Art of Computer Programming" vol 2 for explanation of ! 37: / multiprecision divide. ! 38: / ! 39: //////// ! 40: ! 41: l = 8 / left argument ! 42: r = 16 / right argument (rvalue) ! 43: rp = 16 / right argument (lvalue) ! 44: ! 45: sign = -2 ! 46: exp = -4 ! 47: q0 = -6 ! 48: q1 = -8 ! 49: q2 = -10 ! 50: q3 = -12 ! 51: ! 52: claim = -q3 / stack claim size ! 53: ! 54: drdiv: ! 55: push si ! 56: push di ! 57: push bp ! 58: mov bp, sp ! 59: ! 60: lea si, r(bp) / si = pointer to right op. ! 61: jmp 0f ! 62: ! 63: dldiv: ! 64: push si ! 65: push di ! 66: push bp ! 67: mov bp, sp ! 68: ! 69: mov si, rp(bp) / si = pointer to right op. ! 70: 0: ! 71: sub sp, $claim ! 72: ! 73: mov ax, l+6(bp) ! 74: shl ax, $1 / l exp in ah ! 75: jne 0f ! 76: retz: ! 77: call dzero ! 78: jmp done ! 79: 0: ! 80: rclb dl, $1 / form sign ! 81: mov bx, 6(si) ! 82: shl bx, $1 / r exp in bh ! 83: adcb dl, $0 ! 84: movb sign(bp), dl ! 85: orb bh, bh ! 86: je retinf ! 87: ! 88: movb al, ah ! 89: movb bl, bh ! 90: subb ah, ah ! 91: movb bh, ah ! 92: sub ax, bx ! 93: add ax, $129 ! 94: js retz / exp will only get smaller ! 95: ! 96: cmp ax, $257 / by at most 2 ! 97: ja retinf ! 98: ! 99: mov exp(bp), ax ! 100: mov bx, l+5(bp) / set up l fraction (u) for divide loop ! 101: orb bh, $128 / implicit bit of hi order word ! 102: mov cx, l+3(bp) ! 103: mov di, l+1(bp) ! 104: movb ah, l(bp) ! 105: subb al, al ! 106: shr bx, $1 / shift r to guarantee valid divide ! 107: rcr cx, $1 ! 108: rcr di, $1 ! 109: rcr ax, $1 ! 110: add bp, $q0 + 2 / quotient pushed from here to top ! 111: jmp 0f ! 112: overf: ! 113: mov (bp), $-1 / q^ = word size - 1 ! 114: sub dx, cx / do multiply and subtract using adds ! 115: mov bx, ax / u1 ! 116: sub ax, ax ! 117: add bx, cx ! 118: adcb dl, al / must keep track of u0 for a while ! 119: ! 120: sub bx, 3(si) / u1 u2 -= q^ * v2 ! 121: sbbb dl, al ! 122: add di, 3(si) ! 123: adc bx, ax ! 124: adcb dl, al ! 125: js 2f / adjust q^ and fall in ! 126: ! 127: mov cx, di / u2 ! 128: mov di, 1(si) / v3 ! 129: sub cx, di / u2 u3 -= q^ * v3 ! 130: sbb bx, ax ! 131: sbbb dl, al ! 132: add di, _fpac_ / pick up u3 ! 133: adc cx, ax ! 134: adc bx, ax ! 135: adcb dl, al ! 136: ! 137: movb ah, (si) / u3 u4 -= q^ * v4 ! 138: sub di, ax ! 139: jmp 3f / fall in ! 140: ! 141: 0: ! 142: sub bp, $2 ! 143: mov _fpac_, ax / u3 ! 144: ! 145: mov dx, bx / u0 ! 146: mov ax, cx / u1 ! 147: mov cx, 5(si) ! 148: orb ch, $128 / v1 ! 149: cmp dx, cx ! 150: je overf ! 151: jb 9f ! 152: call oerror_ ! 153: 9: ! 154: ! 155: div cx ! 156: mov (bp), ax / q+2 >= a = q^ >= q ! 157: mov bx, dx / bx = dx = remainder = new u1 <= v1 ! 158: ! 159: mul 3(si) / dx ax = q^ * v2 ! 160: sub di, ax / subtract from new u1 new u2 ! 161: sbb bx, dx / = new u1 old u3 ! 162: jnc 1f / ok - no prelim q^ adjust ! 163: 2: ! 164: dec (bp) / q^ too big ! 165: add di, 3(si) / adjust u1 u2 ! 166: adc bx, cx ! 167: jnc 2b / until positive ( at most twice) ! 168: 1: / now q+1 >= q^ >= q ! 169: mov cx, di / shift new u2 = old u3 ! 170: mov di, _fpac_ / shift new u3 = old u4 ! 171: / ( new u4 = 0) ! 172: mov ax, 1(si) ! 173: mul (bp) / dx ax = v3 * q^ ! 174: sub di, ax / subtract from u2 u3 ! 175: sbb cx, dx ! 176: mov ax, $0 ! 177: sbb bx, ax ! 178: sbbb ah, ah ! 179: movb _fpac_+2, ah / save carry into u0 ! 180: ! 181: movb ah, (si) / last word is short 8 bits ! 182: mul (bp) / dx ax = v4 * q^ ! 183: neg ax / ax := u4 - ax = 0 - ax ! 184: sbb di, dx ! 185: movb dl, _fpac_+2 ! 186: 3: ! 187: sbb cx, $0 ! 188: sbb bx, $0 ! 189: sbbb dl, $0 ! 190: je 1f / q = q^ ok ( this is usually the case) ! 191: ! 192: dec (bp) / else q = q^ - 1 ! 193: addb ah, (si) / add v1 v2 v3 v4 to u1 u2 u3 u4 ! 194: adc di, 1(si) ! 195: adc cx, 3(si) ! 196: adc bx, $0 ! 197: mov dx, 5(si) ! 198: orb dh, $128 ! 199: add bx, dx ! 200: 1: ! 201: cmp bp, sp ! 202: jne 0b ! 203: ! 204: add bp, $claim ! 205: mov ax, exp(bp) ! 206: mov dx, q3(bp) ! 207: mov di, q2(bp) ! 208: mov cx, q1(bp) ! 209: mov bx, q0(bp) ! 210: orb bh, bh ! 211: js 0f / normalized ! 212: ! 213: dec ax / only need to shift once ! 214: shl dx, $1 ! 215: rcl di, $1 ! 216: rcl cx, $1 ! 217: rcl bx, $1 ! 218: 0: ! 219: shlb dl, $1 / round ! 220: adcb dh, $0 ! 221: adc di, $0 ! 222: adc cx, $0 ! 223: adc bx, $0 ! 224: jnc 0f ! 225: ! 226: rcr bx, $1 / exactly 1/2 ! 227: dec ax ! 228: 0: ! 229: orb ah, ah / check exp ! 230: js retz / too small ! 231: jne retinf / too big ! 232: ! 233: movb _fpac_, dh / ok store it ! 234: mov _fpac_+1, di ! 235: mov _fpac_+3, cx ! 236: shlb bh, $1 ! 237: movb ah, sign(bp) ! 238: shr ax, $1 ! 239: rcrb bh, $1 ! 240: mov _fpac_+5, bx ! 241: movb _fpac_+7, al ! 242: done: ! 243: mov sp, bp ! 244: pop bp ! 245: pop di ! 246: pop si ! 247: ret ! 248: retinf: ! 249: mov ax, $-1 ! 250: mov _fpac_, ax ! 251: mov _fpac_+2, ax ! 252: mov _fpac_+4, ax ! 253: movb dl, sign(bp) ! 254: shrb dl, $1 ! 255: rcrb ah, $1 ! 256: mov _fpac_+6, ax ! 257: jmp done
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