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1.1 ! root 1: page ,132 ! 2: title manditer - compute next iteration of mandelbrot set ! 3: %out manditer ! 4: ! 5: ; Conditional assembly flags: ! 6: ; ! 7: ; TARGET_287 Defined if the target machine will be a 286 ! 8: ; with a 287. This allows the 287 specific ! 9: ; instruction FSTSW AX to be used. ! 10: ; ! 11: ; DO_SCAN Defined if an entire scan is to be processed. ! 12: ; If so, extra parameters are supplied consisting ! 13: ; of the increment for the real portion of the ! 14: ; seed, a word buffer where the results will be ! 15: ; stored, and the count of points to compute. ! 16: ! 17: TARGET_287 equ 0 ! 18: DO_SCAN equ 0 ! 19: ! 20: ifdef TARGET_287 ! 21: .286c ! 22: .287 ! 23: else ! 24: .8087 ! 25: endif ! 26: ! 27: ! 28: memS equ 1 ;Define small model program ! 29: ?PLM = 0 ;Define 'C' calling convention ! 30: ?WIN = 0 ;Define non-windows prologue ! 31: ! 32: .xlist ! 33: include cmacros.inc ! 34: .list ! 35: ! 36: ! 37: sBegin code ! 38: assumes cs,code ! 39: assumes ds,nothing ! 40: ! 41: four dq 4.0 ;Constant 4.0 ! 42: ! 43: ! 44: ; The Mandelbrot set is defined to be the set of all complex ! 45: ; numbers C for which the size of Z^2 + C is finite after an ! 46: ; indefinate number of iterations (Z is initially 0). ! 47: ; ! 48: ; The square of a complex number C = C_Real + C_imag is ! 49: ; ! 50: ; (C_Real^2) - (2*C_Real*C_Imag)i - (C_Imag^2) ! 51: ; ! 52: ; ! 53: ; The size of a complex number is just it's distance from ! 54: ; the complex number 0. The distance from complex 0 is ! 55: ; the hypotenuse of the right triangle whose sides are the ! 56: ; real and imaginary parts of the complex number. Thus the ! 57: ; size is SQRT(Z_real^2 + Z_imag). If the size ever becomes ! 58: ; >= 2, the number will grow to infinity. ! 59: ! 60: ! 61: ! 62: cProc manditer,<PUBLIC> ! 63: ! 64: parmq creal ;Real part of mandelbrot seed ! 65: parmq cimag ;Imaginary part of mandelbrot seed ! 66: parmw max_iteration ;Maximum loop counter ! 67: ! 68: ifdef DO_SCAN ;If to do an entire scan line ! 69: parmw point_count ;Number of points to calculate ! 70: parmw results_buffer ;Near pointer to where results go ! 71: parmq creal_step ;Increment to next point ! 72: endif ! 73: ! 74: ifndef TARGET_287 ;If not explicitly for a 287 ! 75: localw fstatus ;x87 status word ! 76: endif ! 77: ! 78: cBegin ! 79: ifdef DO_SCAN ;If to do an entire scan line ! 80: push si ;'C' requires SI to be saved ! 81: mov si,results_buffer ;DS:SI --> destination buffer ! 82: mov dx,point_count ;# of points to calculate ! 83: endif ! 84: ! 85: finit ;Initialize co-porcessor ! 86: ! 87: mov bx,max_iteration ;Max iteration counter ! 88: ! 89: fld four ;Load constant 4.0 for comparison ! 90: ; |-------------------------------| ! 91: ; | 4 | st(0) ! 92: ; |-------------------------------| ! 93: ! 94: ! 95: fld creal ;Load real part of seed ! 96: ; |-------------------------------| ! 97: ; | C real | st(1) ! 98: ; |-------------------------------| ! 99: ; | 4 | st(2) ! 100: ; |-------------------------------| ! 101: ! 102: ! 103: fld cimag ;Load imaginary part of seed ! 104: ; |-------------------------------| ! 105: ; | C imag | st(0) ! 106: ; |-------------------------------| ! 107: ; | C real | st(1) ! 108: ; |-------------------------------| ! 109: ; | 4 | st(2) ! 110: ; |-------------------------------| ! 111: ! 112: ! 113: ifdef DO_SCAN ;If to do an entire scan ! 114: fld creal_step ; load creal increment ! 115: else ;else ! 116: fdecstp ; Reserve location, tag as invalid ! 117: endif ! 118: ; |-------------------------------| ! 119: ; | Reserved or C real increment | st(0) ! 120: ; |-------------------------------| ! 121: ; | C imag | st(1) ! 122: ; |-------------------------------| ! 123: ; | C real | st(2) ! 124: ; |-------------------------------| ! 125: ; | 4 | st(3) ! 126: ; |-------------------------------| ! 127: ! 128: ! 129: scan_loop: ! 130: ! 131: ; Because this program optimizes the use of C real ^ 2 ! 132: ; and C imag ^ 2, the size test will terminate one iteration ! 133: ; late. The original Mandelzoom was: ! 134: ; ! 135: ; Z = 0 ! 136: ; Count = 0; ! 137: ; repeat ! 138: ; Z = Z^2 + C ! 139: ; count = count + 1 ! 140: ; size = size of Z ! 141: ; until (count > 1000 or size >= 4) ! 142: ; ! 143: ; This program uses the intermediate calculations used for ! 144: ; the squaring for the size test. However, the result of ! 145: ; the first complex square operation will simply be the ! 146: ; constant C (0^2+C). By setting the initial value of Z ! 147: ; to C instead of 0, this latency will be corrected. ! 148: ! 149: ! 150: ! 151: fld st(1) ;Initialize imaginary part of sum ! 152: ; |-------------------------------| ! 153: ; | Z imag = C imag | st(0) ! 154: ; |-------------------------------| ! 155: ; | Reserved or C real increment | st(1) ! 156: ; |-------------------------------| ! 157: ; | C imag | st(2) ! 158: ; |-------------------------------| ! 159: ; | C real | st(3) ! 160: ; |-------------------------------| ! 161: ; | 4 | st(4) ! 162: ; |-------------------------------| ! 163: ! 164: ! 165: fld st(3) ;Initialize real part of sum ! 166: ; |-------------------------------| ! 167: ; | Z real = C real | st(0) ! 168: ; |-------------------------------| ! 169: ; | Z imag = C image | st(1) ! 170: ; |-------------------------------| ! 171: ; | Reserved or C real increment | st(2) ! 172: ; |-------------------------------| ! 173: ; | C imag | st(3) ! 174: ; |-------------------------------| ! 175: ; | C real | st(4) ! 176: ; |-------------------------------| ! 177: ; | 4 | st(5) ! 178: ; |-------------------------------| ! 179: ! 180: ! 181: mov cx,bx ;max iteration counter ! 182: ! 183: iterate_loop: ! 184: ! 185: ! 186: fld st(0) ! 187: ; |-------------------------------| ! 188: ; | Z real | st(0) ! 189: ; |-------------------------------| ! 190: ; | Z real | st(1) ! 191: ; |-------------------------------| ! 192: ; | Z imag | st(2) ! 193: ; |-------------------------------| ! 194: ; | Reserved or C real increment | st(3) ! 195: ; |-------------------------------| ! 196: ; | C imag | st(4) ! 197: ; |-------------------------------| ! 198: ; | C real | st(5) ! 199: ; |-------------------------------| ! 200: ; | 4 | st(6) ! 201: ; |-------------------------------| ! 202: ! 203: ! 204: fmul st(1),st ! 205: ; |-------------------------------| ! 206: ; | Z real | st(0) ! 207: ; |-------------------------------| ! 208: ; | (Z real)^2 | st(1) ! 209: ; |-------------------------------| ! 210: ; | Z imag | st(2) ! 211: ; |-------------------------------| ! 212: ; | Reserved or C real increment | st(3) ! 213: ; |-------------------------------| ! 214: ; | C imag | st(4) ! 215: ; |-------------------------------| ! 216: ; | C real | st(5) ! 217: ; |-------------------------------| ! 218: ; | 4 | st(6) ! 219: ; |-------------------------------| ! 220: ! 221: ! 222: fmul st,st(2) ! 223: ; |-------------------------------| ! 224: ; | Z real * Z imag | st(0) ! 225: ; |-------------------------------| ! 226: ; | (Z real)^2 | st(1) ! 227: ; |-------------------------------| ! 228: ; | Z imag | st(2) ! 229: ; |-------------------------------| ! 230: ; | Reserved or C real increment | st(3) ! 231: ; |-------------------------------| ! 232: ; | C imag | st(4) ! 233: ; |-------------------------------| ! 234: ; | C real | st(5) ! 235: ; |-------------------------------| ! 236: ; | 4 | st(6) ! 237: ; |-------------------------------| ! 238: ! 239: ! 240: fadd st,st(0) ! 241: ; |-------------------------------| ! 242: ; | Z real * Z imag * 2 | st(0) ! 243: ; |-------------------------------| ! 244: ; | Z real ^ 2 | st(1) ! 245: ; |-------------------------------| ! 246: ; | Z imag | st(2) ! 247: ; |-------------------------------| ! 248: ; | Reserved or C real increment | st(3) ! 249: ; |-------------------------------| ! 250: ; | C imag | st(4) ! 251: ; |-------------------------------| ! 252: ; | C real | st(5) ! 253: ; |-------------------------------| ! 254: ; | 4 | st(6) ! 255: ; |-------------------------------| ! 256: ! 257: ! 258: fadd st,st(4) ! 259: ; |-------------------------------| ! 260: ; | Z real * Z imag * 2 + C imag | st(0) ! 261: ; |-------------------------------| ! 262: ; | Z real ^ 2 | st(1) ! 263: ; |-------------------------------| ! 264: ; | Z imag | st(2) ! 265: ; |-------------------------------| ! 266: ; | Reserved or C real increment | st(3) ! 267: ; |-------------------------------| ! 268: ; | C imag | st(4) ! 269: ; |-------------------------------| ! 270: ; | C real | st(5) ! 271: ; |-------------------------------| ! 272: ; | 4 | st(6) ! 273: ; |-------------------------------| ! 274: ! 275: ! 276: fxch st(2) ! 277: ; |-------------------------------| ! 278: ; | Z imag | st(0) ! 279: ; |-------------------------------| ! 280: ; | Z real ^ 2 | st(1) ! 281: ; |-------------------------------| ! 282: ; | Z real * Z imag * 2 + C imag | st(2) ! 283: ; |-------------------------------| ! 284: ; | Reserved or C real increment | st(3) ! 285: ; |-------------------------------| ! 286: ; | C imag | st(4) ! 287: ; |-------------------------------| ! 288: ; | C real | st(5) ! 289: ; |-------------------------------| ! 290: ; | 4 | st(6) ! 291: ; |-------------------------------| ! 292: ! 293: ! 294: fmul st,st(0) ! 295: ; |-------------------------------| ! 296: ; | Z imag ^ 2 | st(0) ! 297: ; |-------------------------------| ! 298: ; | Z real ^ 2 | st(1) ! 299: ; |-------------------------------| ! 300: ; | Z real * Z imag * 2 + C imag | st(2) ! 301: ; |-------------------------------| ! 302: ; | Reserved or C real increment | st(3) ! 303: ; |-------------------------------| ! 304: ; | C imag | st(4) ! 305: ; |-------------------------------| ! 306: ; | C real | st(5) ! 307: ; |-------------------------------| ! 308: ; | 4 | st(6) ! 309: ; |-------------------------------| ! 310: ! 311: ! 312: fld st(1) ! 313: ; |-------------------------------| ! 314: ; | Z real ^ 2 | st(0) ! 315: ; |-------------------------------| ! 316: ; | Z imag ^ 2 | st(1) ! 317: ; |-------------------------------| ! 318: ; | Z real ^ 2 | st(2) ! 319: ; |-------------------------------| ! 320: ; | Z real * Z imag * 2 + C imag | st(3) ! 321: ; |-------------------------------| ! 322: ; | Reserved or C real increment | st(4) ! 323: ; |-------------------------------| ! 324: ; | C imag | st(5) ! 325: ; |-------------------------------| ! 326: ; | C real | st(6) ! 327: ; |-------------------------------| ! 328: ; | 4 | st(7) ! 329: ; |-------------------------------| ! 330: ! 331: ! 332: fadd st,st(1) ! 333: ; |-------------------------------| ! 334: ; | Z real ^ 2 + Z imag ^ 2 | st(0) ! 335: ; |-------------------------------| ! 336: ; | Z imag ^ 2 | st(1) ! 337: ; |-------------------------------| ! 338: ; | Z real ^ 2 | st(2) ! 339: ; |-------------------------------| ! 340: ; | Z real * Z imag * 2 + C imag | st(3) ! 341: ; |-------------------------------| ! 342: ; | Reserved or C real increment | st(4) ! 343: ; |-------------------------------| ! 344: ; | C imag | st(5) ! 345: ; |-------------------------------| ! 346: ; | C real | st(6) ! 347: ; |-------------------------------| ! 348: ; | 4 | st(7) ! 349: ; |-------------------------------| ! 350: ! 351: ! 352: fcomp st(7) ! 353: ; |-------------------------------| ! 354: ; | Z imag ^ 2 | st(0) ! 355: ; |-------------------------------| ! 356: ; | Z real ^ 2 | st(1) ! 357: ; |-------------------------------| ! 358: ; | Z real * Z imag * 2 + C imag | st(2) ! 359: ; |-------------------------------| ! 360: ; | Reserved or C real increment | st(3) ! 361: ; |-------------------------------| ! 362: ; | C imag | st(4) ! 363: ; |-------------------------------| ! 364: ; | C real | st(5) ! 365: ; |-------------------------------| ! 366: ; | 4 | st(6) ! 367: ; |-------------------------------| ! 368: ! 369: ! 370: ifdef TARGET_287 ;If 287, then store status word ! 371: fwait ; straight to ax. Have to wait! ! 372: fstsw ax ; ! 373: else ;else ! 374: fstsw fstatus ; will have to store to memory ! 375: endif ! 376: ; |-------------------------------| ! 377: ; | Z imag ^ 2 | st(0) ! 378: ; |-------------------------------| ! 379: ; | Z real ^ 2 | st(1) ! 380: ; |-------------------------------| ! 381: ; | Z real * Z imag * 2 + C imag | st(2) ! 382: ; |-------------------------------| ! 383: ; | Reserved or C real increment | st(3) ! 384: ; |-------------------------------| ! 385: ; | C imag | st(4) ! 386: ; |-------------------------------| ! 387: ; | C real | st(5) ! 388: ; |-------------------------------| ! 389: ; | 4 | st(6) ! 390: ; |-------------------------------| ! 391: ! 392: ! 393: fsubp st(1),st ! 394: ; |-------------------------------| ! 395: ; | Z real ^ 2 - Z imag ^ 2 | st(0) ! 396: ; |-------------------------------| ! 397: ; | Z real * Z imag * 2 + C imag | st(1) ! 398: ; |-------------------------------| ! 399: ; | Reserved or C real increment | st(2) ! 400: ; |-------------------------------| ! 401: ; | C imag | st(3) ! 402: ; |-------------------------------| ! 403: ; | C real | st(4) ! 404: ; |-------------------------------| ! 405: ; | 4 | st(5) ! 406: ; |-------------------------------| ! 407: ! 408: ! 409: ! 410: ; Do a little work while the FSUBP executes ! 411: ! 412: ifndef TARGET_287 ;If not a 287 ! 413: mov ah,byte ptr (fstatus+1) ; load status word from memory ! 414: endif ! 415: ! 416: and ah,045h ;If size>= 4, outside of mandelbrot ! 417: xor ah,1 ; set. ! 418: jnz done_iterating ;Outside of set ! 419: ! 420: ! 421: fadd st,st(4) ! 422: ; |-------------------------------| ! 423: ; | Z real^2 - Z imag^2 + C real | st(0) ! 424: ; |-------------------------------| ! 425: ; | Z real * Z imag * 2 + C imag | st(1) ! 426: ; |-------------------------------| ! 427: ; | Reserved or C real increment | st(2) ! 428: ; |-------------------------------| ! 429: ; | C imag | st(3) ! 430: ; |-------------------------------| ! 431: ; | C real | st(4) ! 432: ; |-------------------------------| ! 433: ; | 4 | st(5) ! 434: ; |-------------------------------| ! 435: ! 436: ! 437: loop iterate_loop ;If loop expires, in mandelbrot set ! 438: ! 439: done_iterating: ! 440: mov ax,bx ;Max iteration count ! 441: sub ax,cx ;Compute number of iterations ! 442: ! 443: ifdef DO_SCAN ;If to do an entire scan ! 444: mov word ptr [si],ax ;Save result in result_buffer ! 445: add si,2 ;--> next slot of buffer ! 446: dec dx ;Any more points? ! 447: jz done_scan ;No, all done ! 448: ! 449: fstp st(0) ;Remove sum from stack ! 450: fstp st(0) ! 451: ; |-------------------------------| ! 452: ; | Reserved or C real increment | st(0) ! 453: ; |-------------------------------| ! 454: ; | C imag | st(1) ! 455: ; |-------------------------------| ! 456: ; | C real | st(2) ! 457: ; |-------------------------------| ! 458: ; | 4 | st(3) ! 459: ; |-------------------------------| ! 460: ! 461: ! 462: fadd st(2),st ;Update c real ! 463: ; |-------------------------------| ! 464: ; | Reserved or C real increment | st(0) ! 465: ; |-------------------------------| ! 466: ; | C imag | st(1) ! 467: ; |-------------------------------| ! 468: ; | C real + C real increment | st(2) ! 469: ; |-------------------------------| ! 470: ; | 4 | st(3) ! 471: ; |-------------------------------| ! 472: ! 473: jmp scan_loop ! 474: ! 475: done_scan: ! 476: pop si ;Return last result ! 477: endif ! 478: ! 479: ! 480: cEnd ! 481: ! 482: sEnd code ! 483: end
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