drivers/staging/brcm80211/util/qmath.c

   1 /*
   2  * Copyright (c) 2010 Broadcom Corporation
   3  *
   4  * Permission to use, copy, modify, and/or distribute this software for any
   5  * purpose with or without fee is hereby granted, provided that the above
   6  * copyright notice and this permission notice appear in all copies.
   7  *
   8  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
   9  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
  10  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
  11  * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  12  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
  13  * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
  14  * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  15  */
  16
  17 #include <linux/types.h>
  18 #include "qmath.h"
  19
  20 /*
  21 Description: This function saturate input 32 bit number into a 16 bit number.
  22 If input number is greater than 0x7fff then output is saturated to 0x7fff.
  23 else if input number is less than 0xffff8000 then output is saturated to 0xffff8000
  24 else output is same as input.
  25 */
  26 s16 qm_sat32(s32 op)
  27 {
  28         s16 result;
  29         if (op > (s32) 0x7fff) {
  30                 result = 0x7fff;
  31         } else if (op < (s32) 0xffff8000) {
  32                 result = (s16) (0x8000);
  33         } else {
  34                 result = (s16) op;
  35         }
  36         return result;
  37 }
  38
  39 /*
  40 Description: This function multiply two input 16 bit numbers and return the 32 bit result.
  41 This multiplication is similar to compiler multiplication. This operation is defined if
  42 16 bit multiplication on the processor platform is cheaper than 32 bit multiplication (as
  43 the most of qmath functions can be replaced with processor intrinsic instructions).
  44 */
  45 s32 qm_mul321616(s16 op1, s16 op2)
  46 {
  47         return (s32) (op1) * (s32) (op2);
  48 }
  49
  50 /*
  51 Description: This function make 16 bit multiplication and return the result in 16 bits.
  52 To fit the result into 16 bits the 32 bit multiplication result is right
  53 shifted by 16 bits.
  54 */
  55 s16 qm_mul16(s16 op1, s16 op2)
  56 {
  57         s32 result;
  58         result = ((s32) (op1) * (s32) (op2));
  59         return (s16) (result >> 16);
  60 }
  61
  62 /*
  63 Description: This function multiply two 16 bit numbers and return the result in 32 bits.
  64 This function remove the extra sign bit created by the multiplication by leftshifting the
  65 32 bit multiplication result by 1 bit before returning the result. So the output is
  66 twice that of compiler multiplication. (i.e. qm_muls321616(2,3)=12).
  67 When both input 16 bit numbers are 0x8000, then the result is saturated to 0x7fffffff.
  68 */
  69 s32 qm_muls321616(s16 op1, s16 op2)
  70 {
  71         s32 result;
  72         if (op1 == (s16) (0x8000) && op2 == (s16) (0x8000)) {
  73                 result = 0x7fffffff;
  74         } else {
  75                 result = ((s32) (op1) * (s32) (op2));
  76                 result = result << 1;
  77         }
  78         return result;
  79 }
  80
  81 /*
  82 Description: This function make 16 bit unsigned multiplication. To fit the output into
  83 16 bits the 32 bit multiplication result is right shifted by 16 bits.
  84 */
  85 u16 qm_mulu16(u16 op1, u16 op2)
  86 {
  87         return (u16) (((u32) op1 * (u32) op2) >> 16);
  88 }
  89
  90 /*
  91 Description: This function make 16 bit multiplication and return the result in 16 bits.
  92 To fit the multiplication result into 16 bits the multiplication result is right shifted by
  93 15 bits. Right shifting 15 bits instead of 16 bits is done to remove the extra sign bit formed
  94 due to the multiplication.
  95 When both the 16bit inputs are 0x8000 then the output is saturated to 0x7fffffff.
  96 */
  97 s16 qm_muls16(s16 op1, s16 op2)
  98 {
  99         s32 result;
 100         if (op1 == (s16) 0x8000 && op2 == (s16) 0x8000) {
 101                 result = 0x7fffffff;
 102         } else {
 103                 result = ((s32) (op1) * (s32) (op2));
 104         }
 105         return (s16) (result >> 15);
 106 }
 107
 108 /*
 109 Description: This function add two 32 bit numbers and return the 32bit result.
 110 If the result overflow 32 bits, the output will be saturated to 32bits.
 111 */
 112 s32 qm_add32(s32 op1, s32 op2)
 113 {
 114         s32 result;
 115         result = op1 + op2;
 116         if (op1 < 0 && op2 < 0 && result > 0) {
 117                 result = 0x80000000;
 118         } else if (op1 > 0 && op2 > 0 && result < 0) {
 119                 result = 0x7fffffff;
 120         }
 121         return result;
 122 }
 123
 124 /*
 125 Description: This function add two 16 bit numbers and return the 16bit result.
 126 If the result overflow 16 bits, the output will be saturated to 16bits.
 127 */
 128 s16 qm_add16(s16 op1, s16 op2)
 129 {
 130         s16 result;
 131         s32 temp = (s32) op1 + (s32) op2;
 132         if (temp > (s32) 0x7fff) {
 133                 result = (s16) 0x7fff;
 134         } else if (temp < (s32) 0xffff8000) {
 135                 result = (s16) 0xffff8000;
 136         } else {
 137                 result = (s16) temp;
 138         }
 139         return result;
 140 }
 141
 142 /*
 143 Description: This function make 16 bit subtraction and return the 16bit result.
 144 If the result overflow 16 bits, the output will be saturated to 16bits.
 145 */
 146 s16 qm_sub16(s16 op1, s16 op2)
 147 {
 148         s16 result;
 149         s32 temp = (s32) op1 - (s32) op2;
 150         if (temp > (s32) 0x7fff) {
 151                 result = (s16) 0x7fff;
 152         } else if (temp < (s32) 0xffff8000) {
 153                 result = (s16) 0xffff8000;
 154         } else {
 155                 result = (s16) temp;
 156         }
 157         return result;
 158 }
 159
 160 /*
 161 Description: This function make 32 bit subtraction and return the 32bit result.
 162 If the result overflow 32 bits, the output will be saturated to 32bits.
 163 */
 164 s32 qm_sub32(s32 op1, s32 op2)
 165 {
 166         s32 result;
 167         result = op1 - op2;
 168         if (op1 >= 0 && op2 < 0 && result < 0) {
 169                 result = 0x7fffffff;
 170         } else if (op1 < 0 && op2 > 0 && result > 0) {
 171                 result = 0x80000000;
 172         }
 173         return result;
 174 }
 175
 176 /*
 177 Description: This function multiply input 16 bit numbers and accumulate the result
 178 into the input 32 bit number and return the 32 bit accumulated result.
 179 If the accumulation result in overflow, then the output will be saturated.
 180 */
 181 s32 qm_mac321616(s32 acc, s16 op1, s16 op2)
 182 {
 183         s32 result;
 184         result = qm_add32(acc, qm_mul321616(op1, op2));
 185         return result;
 186 }
 187
 188 /*
 189 Description: This function make a 32 bit saturated left shift when the specified shift
 190 is +ve. This function will make a 32 bit right shift when the specified shift is -ve.
 191 This function return the result after shifting operation.
 192 */
 193 s32 qm_shl32(s32 op, int shift)
 194 {
 195         int i;
 196         s32 result;
 197         result = op;
 198         if (shift > 31)
 199                 shift = 31;
 200         else if (shift < -31)
 201                 shift = -31;
 202         if (shift >= 0) {
 203                 for (i = 0; i < shift; i++) {
 204                         result = qm_add32(result, result);
 205                 }
 206         } else {
 207                 result = result >> (-shift);
 208         }
 209         return result;
 210 }
 211
 212 /*
 213 Description: This function make a 32 bit right shift when shift is +ve.
 214 This function make a 32 bit saturated left shift when shift is -ve. This function
 215 return the result of the shift operation.
 216 */
 217 s32 qm_shr32(s32 op, int shift)
 218 {
 219         return qm_shl32(op, -shift);
 220 }
 221
 222 /*
 223 Description: This function make a 16 bit saturated left shift when the specified shift
 224 is +ve. This function will make a 16 bit right shift when the specified shift is -ve.
 225 This function return the result after shifting operation.
 226 */
 227 s16 qm_shl16(s16 op, int shift)
 228 {
 229         int i;
 230         s16 result;
 231         result = op;
 232         if (shift > 15)
 233                 shift = 15;
 234         else if (shift < -15)
 235                 shift = -15;
 236         if (shift > 0) {
 237                 for (i = 0; i < shift; i++) {
 238                         result = qm_add16(result, result);
 239                 }
 240         } else {
 241                 result = result >> (-shift);
 242         }
 243         return result;
 244 }
 245
 246 /*
 247 Description: This function make a 16 bit right shift when shift is +ve.
 248 This function make a 16 bit saturated left shift when shift is -ve. This function
 249 return the result of the shift operation.
 250 */
 251 s16 qm_shr16(s16 op, int shift)
 252 {
 253         return qm_shl16(op, -shift);
 254 }
 255
 256 /*
 257 Description: This function return the number of redundant sign bits in a 16 bit number.
 258 Example: qm_norm16(0x0080) = 7.
 259 */
 260 s16 qm_norm16(s16 op)
 261 {
 262         u16 u16extraSignBits;
 263         if (op == 0) {
 264                 return 15;
 265         } else {
 266                 u16extraSignBits = 0;
 267                 while ((op >> 15) == (op >> 14)) {
 268                         u16extraSignBits++;
 269                         op = op << 1;
 270                 }
 271         }
 272         return u16extraSignBits;
 273 }
 274
 275 /*
 276 Description: This function return the number of redundant sign bits in a 32 bit number.
 277 Example: qm_norm32(0x00000080) = 23
 278 */
 279 s16 qm_norm32(s32 op)
 280 {
 281         u16 u16extraSignBits;
 282         if (op == 0) {
 283                 return 31;
 284         } else {
 285                 u16extraSignBits = 0;
 286                 while ((op >> 31) == (op >> 30)) {
 287                         u16extraSignBits++;
 288                         op = op << 1;
 289                 }
 290         }
 291         return u16extraSignBits;
 292 }
 293
 294 /*
 295 Description: This function divide two 16 bit unsigned numbers.
 296 The numerator should be less than denominator. So the quotient is always less than 1.
 297 This function return the quotient in q.15 format.
 298 */
 299 s16 qm_div_s(s16 num, s16 denom)
 300 {
 301         s16 var_out;
 302         s16 iteration;
 303         s32 L_num;
 304         s32 L_denom;
 305         L_num = (num) << 15;
 306         L_denom = (denom) << 15;
 307         for (iteration = 0; iteration < 15; iteration++) {
 308                 L_num <<= 1;
 309                 if (L_num >= L_denom) {
 310                         L_num = qm_sub32(L_num, L_denom);
 311                         L_num = qm_add32(L_num, 1);
 312                 }
 313         }
 314         var_out = (s16) (L_num & 0x7fff);
 315         return var_out;
 316 }
 317
 318 /*
 319 Description: This function compute the absolute value of a 16 bit number.
 320 */
 321 s16 qm_abs16(s16 op)
 322 {
 323         if (op < 0) {
 324                 if (op == (s16) 0xffff8000) {
 325                         return 0x7fff;
 326                 } else {
 327                         return -op;
 328                 }
 329         } else {
 330                 return op;
 331         }
 332 }
 333
 334 /*
 335 Description: This function divide two 16 bit numbers.
 336 The quotient is returned through return value.
 337 The qformat of the quotient is returned through the pointer (qQuotient) passed
 338 to this function. The qformat of quotient is adjusted appropriately such that
 339 the quotient occupies all 16 bits.
 340 */
 341 s16 qm_div16(s16 num, s16 denom, s16 *qQuotient)
 342 {
 343         s16 sign;
 344         s16 nNum, nDenom;
 345         sign = num ^ denom;
 346         num = qm_abs16(num);
 347         denom = qm_abs16(denom);
 348         nNum = qm_norm16(num);
 349         nDenom = qm_norm16(denom);
 350         num = qm_shl16(num, nNum - 1);
 351         denom = qm_shl16(denom, nDenom);
 352         *qQuotient = nNum - 1 - nDenom + 15;
 353         if (sign >= 0) {
 354                 return qm_div_s(num, denom);
 355         } else {
 356                 return -qm_div_s(num, denom);
 357         }
 358 }
 359
 360 /*
 361 Description: This function compute absolute value of a 32 bit number.
 362 */
 363 s32 qm_abs32(s32 op)
 364 {
 365         if (op < 0) {
 366                 if (op == (s32) 0x80000000) {
 367                         return 0x7fffffff;
 368                 } else {
 369                         return -op;
 370                 }
 371         } else {
 372                 return op;
 373         }
 374 }
 375
 376 /*
 377 Description: This function divide two 32 bit numbers. The division is performed
 378 by considering only important 16 bits in 32 bit numbers.
 379 The quotient is returned through return value.
 380 The qformat of the quotient is returned through the pointer (qquotient) passed
 381 to this function. The qformat of quotient is adjusted appropriately such that
 382 the quotient occupies all 16 bits.
 383 */
 384 s16 qm_div163232(s32 num, s32 denom, s16 *qquotient)
 385 {
 386         s32 sign;
 387         s16 nNum, nDenom;
 388         sign = num ^ denom;
 389         num = qm_abs32(num);
 390         denom = qm_abs32(denom);
 391         nNum = qm_norm32(num);
 392         nDenom = qm_norm32(denom);
 393         num = qm_shl32(num, nNum - 1);
 394         denom = qm_shl32(denom, nDenom);
 395         *qquotient = nNum - 1 - nDenom + 15;
 396         if (sign >= 0) {
 397                 return qm_div_s((s16) (num >> 16), (s16) (denom >> 16));
 398         } else {
 399                 return -qm_div_s((s16) (num >> 16), (s16) (denom >> 16));
 400         }
 401 }
 402
 403 /*
 404 Description: This function multiply a 32 bit number with a 16 bit number.
 405 The multiplicaton result is right shifted by 16 bits to fit the result
 406 into 32 bit output.
 407 */
 408 s32 qm_mul323216(s32 op1, s16 op2)
 409 {
 410         s16 hi;
 411         u16 lo;
 412         s32 result;
 413         hi = op1 >> 16;
 414         lo = (s16) (op1 & 0xffff);
 415         result = qm_mul321616(hi, op2);
 416         result = result + (qm_mulsu321616(op2, lo) >> 16);
 417         return result;
 418 }
 419
 420 /*
 421 Description: This function multiply signed 16 bit number with unsigned 16 bit number and return
 422 the result in 32 bits.
 423 */
 424 s32 qm_mulsu321616(s16 op1, u16 op2)
 425 {
 426         return (s32) (op1) * op2;
 427 }
 428
 429 /*
 430 Description: This function multiply 32 bit number with 16 bit number. The multiplication result is
 431 right shifted by 15 bits to fit the result into 32 bits. Right shifting by only 15 bits instead of
 432 16 bits is done to remove the extra sign bit formed by multiplication from the return value.
 433 When the input numbers are 0x80000000, 0x8000 the return value is saturated to 0x7fffffff.
 434 */
 435 s32 qm_muls323216(s32 op1, s16 op2)
 436 {
 437         s16 hi;
 438         u16 lo;
 439         s32 result;
 440         hi = op1 >> 16;
 441         lo = (s16) (op1 & 0xffff);
 442         result = qm_muls321616(hi, op2);
 443         result = qm_add32(result, (qm_mulsu321616(op2, lo) >> 15));
 444         return result;
 445 }
 446
 447 /*
 448 Description: This function multiply two 32 bit numbers. The multiplication result is right
 449 shifted by 32 bits to fit the multiplication result into 32 bits. The right shifted
 450 multiplication result is returned as output.
 451 */
 452 s32 qm_mul32(s32 a, s32 b)
 453 {
 454         s16 hi1, hi2;
 455         u16 lo1, lo2;
 456         s32 result;
 457         hi1 = a >> 16;
 458         hi2 = b >> 16;
 459         lo1 = (u16) (a & 0xffff);
 460         lo2 = (u16) (b & 0xffff);
 461         result = qm_mul321616(hi1, hi2);
 462         result = result + (qm_mulsu321616(hi1, lo2) >> 16);
 463         result = result + (qm_mulsu321616(hi2, lo1) >> 16);
 464         return result;
 465 }
 466
 467 /*
 468 Description: This function multiply two 32 bit numbers. The multiplication result is
 469 right shifted by 31 bits to fit the multiplication result into 32 bits. The right
 470 shifted multiplication result is returned as output. Right shifting by only 31 bits
 471 instead of 32 bits is done to remove the extra sign bit formed by multiplication.
 472 When the input numbers are 0x80000000, 0x80000000 the return value is saturated to
 473 0x7fffffff.
 474 */
 475 s32 qm_muls32(s32 a, s32 b)
 476 {
 477         s16 hi1, hi2;
 478         u16 lo1, lo2;
 479         s32 result;
 480         hi1 = a >> 16;
 481         hi2 = b >> 16;
 482         lo1 = (u16) (a & 0xffff);
 483         lo2 = (u16) (b & 0xffff);
 484         result = qm_muls321616(hi1, hi2);
 485         result = qm_add32(result, (qm_mulsu321616(hi1, lo2) >> 15));
 486         result = qm_add32(result, (qm_mulsu321616(hi2, lo1) >> 15));
 487         result = qm_add32(result, (qm_mulu16(lo1, lo2) >> 15));
 488         return result;
 489 }
 490
 491 /* This table is log2(1+(i/32)) where i=[0:1:31], in q.15 format */
 492 static const s16 log_table[] = {
 493         0,
 494         1455,
 495         2866,
 496         4236,
 497         5568,
 498         6863,
 499         8124,
 500         9352,
 501         10549,
 502         11716,
 503         12855,
 504         13968,
 505         15055,
 506         16117,
 507         17156,
 508         18173,
 509         19168,
 510         20143,
 511         21098,
 512         22034,
 513         22952,
 514         23852,
 515         24736,
 516         25604,
 517         26455,
 518         27292,
 519         28114,
 520         28922,
 521         29717,
 522         30498,
 523         31267,
 524         32024
 525 };
 526
 527 #define LOG_TABLE_SIZE 32       /* log_table size */
 528 #define LOG2_LOG_TABLE_SIZE 5   /* log2(log_table size) */
 529 #define Q_LOG_TABLE 15          /* qformat of log_table */
 530 #define LOG10_2         19728   /* log10(2) in q.16 */
 531
 532 /*
 533 Description:
 534 This routine takes the input number N and its q format qN and compute
 535 the log10(N). This routine first normalizes the input no N.     Then N is in mag*(2^x) format.
 536 mag is any number in the range 2^30-(2^31 - 1). Then log2(mag * 2^x) = log2(mag) + x is computed.
 537 From that log10(mag * 2^x) = log2(mag * 2^x) * log10(2) is computed.
 538 This routine looks the log2 value in the table considering LOG2_LOG_TABLE_SIZE+1 MSBs.
 539 As the MSB is always 1, only next LOG2_OF_LOG_TABLE_SIZE MSBs are used for table lookup.
 540 Next 16 MSBs are used for interpolation.
 541 Inputs:
 542 N - number to which log10 has to be found.
 543 qN - q format of N
 544 log10N - address where log10(N) will be written.
 545 qLog10N - address where log10N qformat will be written.
 546 Note/Problem:
 547 For accurate results input should be in normalized or near normalized form.
 548 */
 549 void qm_log10(s32 N, s16 qN, s16 *log10N, s16 *qLog10N)
 550 {
 551         s16 s16norm, s16tableIndex, s16errorApproximation;
 552         u16 u16offset;
 553         s32 s32log;
 554
 555         /* normalize the N. */
 556         s16norm = qm_norm32(N);
 557         N = N << s16norm;
 558
 559         /* The qformat of N after normalization.
 560          * -30 is added to treat the no as between 1.0 to 2.0
 561          * i.e. after adding the -30 to the qformat the decimal point will be
 562          * just rigtht of the MSB. (i.e. after sign bit and 1st MSB). i.e.
 563          * at the right side of 30th bit.
 564          */
 565         qN = qN + s16norm - 30;
 566
 567         /* take the table index as the LOG2_OF_LOG_TABLE_SIZE bits right of the MSB */
 568         s16tableIndex = (s16) (N >> (32 - (2 + LOG2_LOG_TABLE_SIZE)));
 569
 570         /* remove the MSB. the MSB is always 1 after normalization. */
 571         s16tableIndex =
 572             s16tableIndex & (s16) ((1 << LOG2_LOG_TABLE_SIZE) - 1);
 573
 574         /* remove the (1+LOG2_OF_LOG_TABLE_SIZE) MSBs in the N. */
 575         N = N & ((1 << (32 - (2 + LOG2_LOG_TABLE_SIZE))) - 1);
 576
 577         /* take the offset as the 16 MSBS after table index.
 578          */
 579         u16offset = (u16) (N >> (32 - (2 + LOG2_LOG_TABLE_SIZE + 16)));
 580
 581         /* look the log value in the table. */
 582         s32log = log_table[s16tableIndex];      /* q.15 format */
 583
 584         /* interpolate using the offset. */
 585         s16errorApproximation = (s16) qm_mulu16(u16offset, (u16) (log_table[s16tableIndex + 1] - log_table[s16tableIndex]));    /* q.15 */
 586
 587         s32log = qm_add16((s16) s32log, s16errorApproximation); /* q.15 format */
 588
 589         /* adjust for the qformat of the N as
 590          * log2(mag * 2^x) = log2(mag) + x
 591          */
 592         s32log = qm_add32(s32log, ((s32) -qN) << 15);   /* q.15 format */
 593
 594         /* normalize the result. */
 595         s16norm = qm_norm32(s32log);
 596
 597         /* bring all the important bits into lower 16 bits */
 598         s32log = qm_shl32(s32log, s16norm - 16);        /* q.15+s16norm-16 format */
 599
 600         /* compute the log10(N) by multiplying log2(N) with log10(2).
 601          * as log10(mag * 2^x) = log2(mag * 2^x) * log10(2)
 602          * log10N in q.15+s16norm-16+1 (LOG10_2 is in q.16)
 603          */
 604         *log10N = qm_muls16((s16) s32log, (s16) LOG10_2);
 605
 606         /* write the q format of the result. */
 607         *qLog10N = 15 + s16norm - 16 + 1;
 608
 609         return;
 610 }
 611
 612 /*
 613 Description:
 614 This routine compute 1/N.
 615 This routine reformates the given no N as N * 2^qN where N is in between 0.5 and 1.0
 616 in q.15 format in 16 bits. So the problem now boils down to finding the inverse of a
 617 q.15 no in 16 bits which is in the range of 0.5 to 1.0. The output is always between
 618 2.0 to 1. So the output is 2.0 to 1.0 in q.30 format. Once the final output format is found
 619 by taking the qN into account. Inverse is found with newton rapson method. Initially
 620 inverse (x) is guessed as 1/0.75 (with appropriate sign). The new guess is calculated
 621 using the formula x' = 2*x - N*x*x. After 4 or 5 iterations the inverse is very close to
 622 inverse of N.
 623 Inputs:
 624 N - number to which 1/N has to be found.
 625 qn - q format of N.
 626 sqrtN - address where 1/N has to be written.
 627 qsqrtN - address where q format of 1/N has to be written.
 628 */
 629 #define qx 29
 630 void qm_1byN(s32 N, s16 qN, s32 *result, s16 *qResult)
 631 {
 632         s16 normN;
 633         s32 s32firstTerm, s32secondTerm, x;
 634         int i;
 635
 636         normN = qm_norm32(N);
 637
 638         /* limit N to least significant 16 bits. 15th bit is the sign bit. */
 639         N = qm_shl32(N, normN - 16);
 640         qN = qN + normN - 16 - 15;
 641         /* -15 is added to treat N as 16 bit q.15 number in the range from 0.5 to 1 */
 642
 643         /* Take the initial guess as 1/0.75 in qx format with appropriate sign. */
 644         if (N >= 0) {
 645                 x = (s32) ((1 / 0.75) * (1 << qx));
 646                 /* input no is in the range 0.5 to 1. So 1/0.75 is taken as initial guess. */
 647         } else {
 648                 x = (s32) ((1 / -0.75) * (1 << qx));
 649                 /* input no is in the range -0.5 to -1. So 1/-0.75 is taken as initial guess. */
 650         }
 651
 652         /* iterate the equation x = 2*x - N*x*x for 4 times. */
 653         for (i = 0; i < 4; i++) {
 654                 s32firstTerm = qm_shl32(x, 1);  /* s32firstTerm = 2*x in q.29 */
 655                 s32secondTerm =
 656                     qm_muls321616((s16) (s32firstTerm >> 16),
 657                                   (s16) (s32firstTerm >> 16));
 658                 /* s32secondTerm = x*x in q.(29+1-16)*2+1 */
 659                 s32secondTerm =
 660                     qm_muls321616((s16) (s32secondTerm >> 16), (s16) N);
 661                 /* s32secondTerm = N*x*x in q.((29+1-16)*2+1)-16+15+1 i.e. in q.29 */
 662                 x = qm_sub32(s32firstTerm, s32secondTerm);
 663                 /* can be added directly as both are in q.29 */
 664         }
 665
 666         /* Bring the x to q.30 format. */
 667         *result = qm_shl32(x, 1);
 668         /* giving the output in q.30 format for q.15 input in 16 bits. */
 669
 670         /* compute the final q format of the result. */
 671         *qResult = -qN + 30;    /* adjusting the q format of actual output */
 672
 673         return;
 674 }
 675
 676 #undef qx