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/**************************************************************** |
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The author of this software is David M. Gay. |
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Copyright (C) 1998, 1999 by Lucent Technologies |
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All Rights Reserved |
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Permission to use, copy, modify, and distribute this software and |
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its documentation for any purpose and without fee is hereby |
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granted, provided that the above copyright notice appear in all |
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copies and that both that the copyright notice and this |
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permission notice and warranty disclaimer appear in supporting |
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documentation, and that the name of Lucent or any of its entities |
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not be used in advertising or publicity pertaining to |
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distribution of the software without specific, written prior |
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permission. |
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LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, |
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INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. |
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IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY |
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SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
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WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER |
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IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, |
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ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF |
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THIS SOFTWARE. |
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****************************************************************/ |
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/* Please send bug reports to David M. Gay (dmg at acm dot org, |
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* with " at " changed at "@" and " dot " changed to "."). */ |
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#include "gdtoaimp.h" |
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/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. |
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* |
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* Inspired by "How to Print Floating-Point Numbers Accurately" by |
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* Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126]. |
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* |
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* Modifications: |
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* 1. Rather than iterating, we use a simple numeric overestimate |
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* to determine k = floor(log10(d)). We scale relevant |
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* quantities using O(log2(k)) rather than O(k) multiplications. |
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* 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't |
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* try to generate digits strictly left to right. Instead, we |
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* compute with fewer bits and propagate the carry if necessary |
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* when rounding the final digit up. This is often faster. |
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* 3. Under the assumption that input will be rounded nearest, |
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* mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. |
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* That is, we allow equality in stopping tests when the |
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* round-nearest rule will give the same floating-point value |
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* as would satisfaction of the stopping test with strict |
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* inequality. |
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* 4. We remove common factors of powers of 2 from relevant |
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* quantities. |
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* 5. When converting floating-point integers less than 1e16, |
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* we use floating-point arithmetic rather than resorting |
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* to multiple-precision integers. |
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* 6. When asked to produce fewer than 15 digits, we first try |
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* to get by with floating-point arithmetic; we resort to |
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* multiple-precision integer arithmetic only if we cannot |
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* guarantee that the floating-point calculation has given |
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* the correctly rounded result. For k requested digits and |
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* "uniformly" distributed input, the probability is |
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* something like 10^(k-15) that we must resort to the Long |
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* calculation. |
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*/ |
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#ifdef Honor_FLT_ROUNDS |
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#undef Check_FLT_ROUNDS |
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#define Check_FLT_ROUNDS |
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#else |
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#define Rounding Flt_Rounds |
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#endif |
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char * |
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dtoa |
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#ifdef KR_headers |
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(d0, mode, ndigits, decpt, sign, rve) |
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double d0; int mode, ndigits, *decpt, *sign; char **rve; |
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#else |
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(double d0, int mode, int ndigits, int *decpt, int *sign, char **rve) |
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#endif |
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{ |
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/* Arguments ndigits, decpt, sign are similar to those |
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of ecvt and fcvt; trailing zeros are suppressed from |
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the returned string. If not null, *rve is set to point |
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to the end of the return value. If d is +-Infinity or NaN, |
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then *decpt is set to 9999. |
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mode: |
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0 ==> shortest string that yields d when read in |
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and rounded to nearest. |
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1 ==> like 0, but with Steele & White stopping rule; |
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e.g. with IEEE P754 arithmetic , mode 0 gives |
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1e23 whereas mode 1 gives 9.999999999999999e22. |
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2 ==> max(1,ndigits) significant digits. This gives a |
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return value similar to that of ecvt, except |
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that trailing zeros are suppressed. |
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3 ==> through ndigits past the decimal point. This |
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gives a return value similar to that from fcvt, |
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except that trailing zeros are suppressed, and |
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ndigits can be negative. |
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4,5 ==> similar to 2 and 3, respectively, but (in |
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round-nearest mode) with the tests of mode 0 to |
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possibly return a shorter string that rounds to d. |
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With IEEE arithmetic and compilation with |
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-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same |
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as modes 2 and 3 when FLT_ROUNDS != 1. |
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6-9 ==> Debugging modes similar to mode - 4: don't try |
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fast floating-point estimate (if applicable). |
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Values of mode other than 0-9 are treated as mode 0. |
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Sufficient space is allocated to the return value |
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to hold the suppressed trailing zeros. |
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*/ |
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int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, |
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j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, |
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spec_case, try_quick; |
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Long L; |
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#ifndef Sudden_Underflow |
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int denorm; |
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ULong x; |
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#endif |
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Bigint *b, *b1, *delta, *mlo, *mhi, *S; |
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U d, d2, eps; |
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double ds; |
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char *s, *s0; |
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#ifdef SET_INEXACT |
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int inexact, oldinexact; |
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#endif |
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#ifdef Honor_FLT_ROUNDS /*{*/ |
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int Rounding; |
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#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */ |
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Rounding = Flt_Rounds; |
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#else /*}{*/ |
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Rounding = 1; |
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switch(fegetround()) { |
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case FE_TOWARDZERO: Rounding = 0; break; |
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case FE_UPWARD: Rounding = 2; break; |
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case FE_DOWNWARD: Rounding = 3; |
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} |
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#endif /*}}*/ |
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#endif /*}*/ |
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#ifndef MULTIPLE_THREADS |
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if (dtoa_result) { |
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freedtoa(dtoa_result); |
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dtoa_result = 0; |
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} |
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#endif |
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d.d = d0; |
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✗✓ |
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if (word0(&d) & Sign_bit) { |
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/* set sign for everything, including 0's and NaNs */ |
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*sign = 1; |
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word0(&d) &= ~Sign_bit; /* clear sign bit */ |
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} |
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else |
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*sign = 0; |
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#if defined(IEEE_Arith) + defined(VAX) |
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#ifdef IEEE_Arith |
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✗✓ |
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if ((word0(&d) & Exp_mask) == Exp_mask) |
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#else |
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if (word0(&d) == 0x8000) |
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#endif |
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{ |
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/* Infinity or NaN */ |
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*decpt = 9999; |
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#ifdef IEEE_Arith |
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if (!word1(&d) && !(word0(&d) & 0xfffff)) |
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return nrv_alloc("Infinity", rve, 8); |
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#endif |
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return nrv_alloc("NaN", rve, 3); |
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} |
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#endif |
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#ifdef IBM |
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dval(&d) += 0; /* normalize */ |
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#endif |
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✓✓ |
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if (!dval(&d)) { |
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*decpt = 1; |
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return nrv_alloc("0", rve, 1); |
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} |
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#ifdef SET_INEXACT |
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try_quick = oldinexact = get_inexact(); |
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inexact = 1; |
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#endif |
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#ifdef Honor_FLT_ROUNDS |
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if (Rounding >= 2) { |
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if (*sign) |
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Rounding = Rounding == 2 ? 0 : 2; |
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else |
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if (Rounding != 2) |
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Rounding = 0; |
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} |
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#endif |
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b = d2b(dval(&d), &be, &bbits); |
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✗✓ |
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if (b == NULL) |
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return (NULL); |
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#ifdef Sudden_Underflow |
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i = (int)(word0(&d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); |
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#else |
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✓✗ |
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if (( i = (int)(word0(&d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)) )!=0) { |
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#endif |
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dval(&d2) = dval(&d); |
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word0(&d2) &= Frac_mask1; |
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word0(&d2) |= Exp_11; |
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#ifdef IBM |
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if (( j = 11 - hi0bits(word0(&d2) & Frac_mask) )!=0) |
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dval(&d2) /= 1 << j; |
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#endif |
215 |
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216 |
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/* log(x) ~=~ log(1.5) + (x-1.5)/1.5 |
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* log10(x) = log(x) / log(10) |
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* ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) |
219 |
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* log10(&d) = (i-Bias)*log(2)/log(10) + log10(&d2) |
220 |
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* |
221 |
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* This suggests computing an approximation k to log10(&d) by |
222 |
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* |
223 |
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* k = (i - Bias)*0.301029995663981 |
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* + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); |
225 |
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* |
226 |
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* We want k to be too large rather than too small. |
227 |
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* The error in the first-order Taylor series approximation |
228 |
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* is in our favor, so we just round up the constant enough |
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* to compensate for any error in the multiplication of |
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* (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, |
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* and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, |
232 |
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* adding 1e-13 to the constant term more than suffices. |
233 |
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* Hence we adjust the constant term to 0.1760912590558. |
234 |
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* (We could get a more accurate k by invoking log10, |
235 |
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* but this is probably not worthwhile.) |
236 |
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*/ |
237 |
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|
238 |
|
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i -= Bias; |
239 |
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#ifdef IBM |
240 |
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i <<= 2; |
241 |
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i += j; |
242 |
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#endif |
243 |
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#ifndef Sudden_Underflow |
244 |
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denorm = 0; |
245 |
|
222 |
} |
246 |
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else { |
247 |
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/* d is denormalized */ |
248 |
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|
249 |
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i = bbits + be + (Bias + (P-1) - 1); |
250 |
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x = i > 32 ? word0(&d) << (64 - i) | word1(&d) >> (i - 32) |
251 |
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: word1(&d) << (32 - i); |
252 |
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dval(&d2) = x; |
253 |
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word0(&d2) -= 31*Exp_msk1; /* adjust exponent */ |
254 |
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i -= (Bias + (P-1) - 1) + 1; |
255 |
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denorm = 1; |
256 |
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} |
257 |
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#endif |
258 |
|
222 |
ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981; |
259 |
|
222 |
k = (int)ds; |
260 |
✓✓✓✗
|
412 |
if (ds < 0. && ds != k) |
261 |
|
190 |
k--; /* want k = floor(ds) */ |
262 |
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k_check = 1; |
263 |
✓✓ |
222 |
if (k >= 0 && k <= Ten_pmax) { |
264 |
✗✓ |
32 |
if (dval(&d) < tens[k]) |
265 |
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k--; |
266 |
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k_check = 0; |
267 |
|
32 |
} |
268 |
|
222 |
j = bbits - i - 1; |
269 |
✓✗ |
222 |
if (j >= 0) { |
270 |
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b2 = 0; |
271 |
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s2 = j; |
272 |
|
222 |
} |
273 |
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else { |
274 |
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b2 = -j; |
275 |
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s2 = 0; |
276 |
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} |
277 |
✓✓ |
222 |
if (k >= 0) { |
278 |
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b5 = 0; |
279 |
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s5 = k; |
280 |
|
32 |
s2 += k; |
281 |
|
32 |
} |
282 |
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else { |
283 |
|
190 |
b2 -= k; |
284 |
|
190 |
b5 = -k; |
285 |
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|
s5 = 0; |
286 |
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} |
287 |
✗✓ |
222 |
if (mode < 0 || mode > 9) |
288 |
|
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mode = 0; |
289 |
|
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|
290 |
|
|
#ifndef SET_INEXACT |
291 |
|
|
#ifdef Check_FLT_ROUNDS |
292 |
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try_quick = Rounding == 1; |
293 |
|
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#else |
294 |
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|
try_quick = 1; |
295 |
|
|
#endif |
296 |
|
|
#endif /*SET_INEXACT*/ |
297 |
|
|
|
298 |
✗✓ |
222 |
if (mode > 5) { |
299 |
|
|
mode -= 4; |
300 |
|
|
try_quick = 0; |
301 |
|
|
} |
302 |
|
|
leftright = 1; |
303 |
|
|
ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */ |
304 |
|
|
/* silence erroneous "gcc -Wall" warning. */ |
305 |
✗✗✗✗
✓✓✓ |
666 |
switch(mode) { |
306 |
|
|
case 0: |
307 |
|
|
case 1: |
308 |
|
|
i = 18; |
309 |
|
|
ndigits = 0; |
310 |
|
|
break; |
311 |
|
|
case 2: |
312 |
|
|
leftright = 0; |
313 |
|
|
/* no break */ |
314 |
|
|
case 4: |
315 |
|
|
if (ndigits <= 0) |
316 |
|
|
ndigits = 1; |
317 |
|
|
ilim = ilim1 = i = ndigits; |
318 |
|
|
break; |
319 |
|
|
case 3: |
320 |
|
222 |
leftright = 0; |
321 |
|
|
/* no break */ |
322 |
|
|
case 5: |
323 |
|
222 |
i = ndigits + k + 1; |
324 |
|
|
ilim = i; |
325 |
|
|
ilim1 = i - 1; |
326 |
✓✓ |
222 |
if (i <= 0) |
327 |
|
38 |
i = 1; |
328 |
|
|
} |
329 |
|
222 |
s = s0 = rv_alloc(i); |
330 |
✗✓ |
222 |
if (s == NULL) |
331 |
|
|
return (NULL); |
332 |
|
|
|
333 |
|
|
#ifdef Honor_FLT_ROUNDS |
334 |
|
|
if (mode > 1 && Rounding != 1) |
335 |
|
|
leftright = 0; |
336 |
|
|
#endif |
337 |
|
|
|
338 |
✓✓ |
222 |
if (ilim >= 0 && ilim <= Quick_max && try_quick) { |
339 |
|
|
|
340 |
|
|
/* Try to get by with floating-point arithmetic. */ |
341 |
|
|
|
342 |
|
|
i = 0; |
343 |
|
|
dval(&d2) = dval(&d); |
344 |
|
|
k0 = k; |
345 |
|
|
ilim0 = ilim; |
346 |
|
|
ieps = 2; /* conservative */ |
347 |
✓✓ |
204 |
if (k > 0) { |
348 |
|
12 |
ds = tens[k&0xf]; |
349 |
|
12 |
j = k >> 4; |
350 |
✗✓ |
12 |
if (j & Bletch) { |
351 |
|
|
/* prevent overflows */ |
352 |
|
|
j &= Bletch - 1; |
353 |
|
|
dval(&d) /= bigtens[n_bigtens-1]; |
354 |
|
|
ieps++; |
355 |
|
|
} |
356 |
✗✓ |
12 |
for(; j; j >>= 1, i++) |
357 |
|
|
if (j & 1) { |
358 |
|
|
ieps++; |
359 |
|
|
ds *= bigtens[i]; |
360 |
|
|
} |
361 |
|
12 |
dval(&d) /= ds; |
362 |
|
12 |
} |
363 |
✓✓ |
192 |
else if (( j1 = -k )!=0) { |
364 |
|
172 |
dval(&d) *= tens[j1 & 0xf]; |
365 |
✗✓ |
344 |
for(j = j1 >> 4; j; j >>= 1, i++) |
366 |
|
|
if (j & 1) { |
367 |
|
|
ieps++; |
368 |
|
|
dval(&d) *= bigtens[i]; |
369 |
|
|
} |
370 |
|
|
} |
371 |
✓✓✗✓
|
376 |
if (k_check && dval(&d) < 1. && ilim > 0) { |
372 |
|
|
if (ilim1 <= 0) |
373 |
|
|
goto fast_failed; |
374 |
|
|
ilim = ilim1; |
375 |
|
|
k--; |
376 |
|
|
dval(&d) *= 10.; |
377 |
|
|
ieps++; |
378 |
|
|
} |
379 |
|
204 |
dval(&eps) = ieps*dval(&d) + 7.; |
380 |
|
204 |
word0(&eps) -= (P-1)*Exp_msk1; |
381 |
✓✓ |
204 |
if (ilim == 0) { |
382 |
|
|
S = mhi = 0; |
383 |
|
20 |
dval(&d) -= 5.; |
384 |
✗✓ |
20 |
if (dval(&d) > dval(&eps)) |
385 |
|
|
goto one_digit; |
386 |
|
|
if (dval(&d) < -dval(&eps)) |
387 |
|
|
goto no_digits; |
388 |
|
|
goto fast_failed; |
389 |
|
|
} |
390 |
|
|
#ifndef No_leftright |
391 |
✗✓ |
184 |
if (leftright) { |
392 |
|
|
/* Use Steele & White method of only |
393 |
|
|
* generating digits needed. |
394 |
|
|
*/ |
395 |
|
|
dval(&eps) = 0.5/tens[ilim-1] - dval(&eps); |
396 |
|
|
for(i = 0;;) { |
397 |
|
|
L = dval(&d); |
398 |
|
|
dval(&d) -= L; |
399 |
|
|
*s++ = '0' + (int)L; |
400 |
|
|
if (dval(&d) < dval(&eps)) |
401 |
|
|
goto ret1; |
402 |
|
|
if (1. - dval(&d) < dval(&eps)) |
403 |
|
|
goto bump_up; |
404 |
|
|
if (++i >= ilim) |
405 |
|
|
break; |
406 |
|
|
dval(&eps) *= 10.; |
407 |
|
|
dval(&d) *= 10.; |
408 |
|
|
} |
409 |
|
|
} |
410 |
|
|
else { |
411 |
|
|
#endif |
412 |
|
|
/* Generate ilim digits, then fix them up. */ |
413 |
|
184 |
dval(&eps) *= tens[ilim-1]; |
414 |
|
262 |
for(i = 1;; i++, dval(&d) *= 10.) { |
415 |
|
262 |
L = (Long)(dval(&d)); |
416 |
✗✓ |
262 |
if (!(dval(&d) -= L)) |
417 |
|
|
ilim = i; |
418 |
|
262 |
*s++ = '0' + (int)L; |
419 |
✓✓ |
262 |
if (i == ilim) { |
420 |
✓✓ |
184 |
if (dval(&d) > 0.5 + dval(&eps)) |
421 |
|
|
goto bump_up; |
422 |
✓✗ |
147 |
else if (dval(&d) < 0.5 - dval(&eps)) { |
423 |
✓✓ |
153 |
while(*--s == '0'); |
424 |
|
147 |
s++; |
425 |
|
147 |
goto ret1; |
426 |
|
|
} |
427 |
|
|
break; |
428 |
|
|
} |
429 |
|
|
} |
430 |
|
|
#ifndef No_leftright |
431 |
|
|
} |
432 |
|
|
#endif |
433 |
|
|
fast_failed: |
434 |
|
|
s = s0; |
435 |
|
|
dval(&d) = dval(&d2); |
436 |
|
|
k = k0; |
437 |
|
|
ilim = ilim0; |
438 |
|
|
} |
439 |
|
|
|
440 |
|
|
/* Do we have a "small" integer? */ |
441 |
|
|
|
442 |
✗✓ |
18 |
if (be >= 0 && k <= Int_max) { |
443 |
|
|
/* Yes. */ |
444 |
|
|
ds = tens[k]; |
445 |
|
|
if (ndigits < 0 && ilim <= 0) { |
446 |
|
|
S = mhi = 0; |
447 |
|
|
if (ilim < 0 || dval(&d) <= 5*ds) |
448 |
|
|
goto no_digits; |
449 |
|
|
goto one_digit; |
450 |
|
|
} |
451 |
|
|
for(i = 1;; i++, dval(&d) *= 10.) { |
452 |
|
|
L = (Long)(dval(&d) / ds); |
453 |
|
|
dval(&d) -= L*ds; |
454 |
|
|
#ifdef Check_FLT_ROUNDS |
455 |
|
|
/* If FLT_ROUNDS == 2, L will usually be high by 1 */ |
456 |
|
|
if (dval(&d) < 0) { |
457 |
|
|
L--; |
458 |
|
|
dval(&d) += ds; |
459 |
|
|
} |
460 |
|
|
#endif |
461 |
|
|
*s++ = '0' + (int)L; |
462 |
|
|
if (!dval(&d)) { |
463 |
|
|
#ifdef SET_INEXACT |
464 |
|
|
inexact = 0; |
465 |
|
|
#endif |
466 |
|
|
break; |
467 |
|
|
} |
468 |
|
|
if (i == ilim) { |
469 |
|
|
#ifdef Honor_FLT_ROUNDS |
470 |
|
|
if (mode > 1) |
471 |
|
|
switch(Rounding) { |
472 |
|
|
case 0: goto ret1; |
473 |
|
|
case 2: goto bump_up; |
474 |
|
|
} |
475 |
|
|
#endif |
476 |
|
|
dval(&d) += dval(&d); |
477 |
|
|
#ifdef ROUND_BIASED |
478 |
|
|
if (dval(&d) >= ds) |
479 |
|
|
#else |
480 |
|
|
if (dval(&d) > ds || (dval(&d) == ds && L & 1)) |
481 |
|
|
#endif |
482 |
|
|
{ |
483 |
|
|
bump_up: |
484 |
✓✓ |
38 |
while(*--s == '9') |
485 |
✓✗ |
1 |
if (s == s0) { |
486 |
|
|
k++; |
487 |
|
|
*s = '0'; |
488 |
|
|
break; |
489 |
|
|
} |
490 |
|
37 |
++*s++; |
491 |
|
37 |
} |
492 |
|
|
break; |
493 |
|
|
} |
494 |
|
|
} |
495 |
|
|
goto ret1; |
496 |
|
|
} |
497 |
|
|
|
498 |
|
|
m2 = b2; |
499 |
|
|
m5 = b5; |
500 |
|
|
mhi = mlo = 0; |
501 |
✗✓ |
18 |
if (leftright) { |
502 |
|
|
i = |
503 |
|
|
#ifndef Sudden_Underflow |
504 |
|
|
denorm ? be + (Bias + (P-1) - 1 + 1) : |
505 |
|
|
#endif |
506 |
|
|
#ifdef IBM |
507 |
|
|
1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3); |
508 |
|
|
#else |
509 |
|
|
1 + P - bbits; |
510 |
|
|
#endif |
511 |
|
|
b2 += i; |
512 |
|
|
s2 += i; |
513 |
|
|
mhi = i2b(1); |
514 |
|
|
if (mhi == NULL) |
515 |
|
|
return (NULL); |
516 |
|
|
} |
517 |
✓✗ |
18 |
if (m2 > 0 && s2 > 0) { |
518 |
|
18 |
i = m2 < s2 ? m2 : s2; |
519 |
|
18 |
b2 -= i; |
520 |
|
18 |
m2 -= i; |
521 |
|
18 |
s2 -= i; |
522 |
|
18 |
} |
523 |
✓✗ |
18 |
if (b5 > 0) { |
524 |
✗✓ |
18 |
if (leftright) { |
525 |
|
|
if (m5 > 0) { |
526 |
|
|
mhi = pow5mult(mhi, m5); |
527 |
|
|
if (mhi == NULL) |
528 |
|
|
return (NULL); |
529 |
|
|
b1 = mult(mhi, b); |
530 |
|
|
if (b1 == NULL) |
531 |
|
|
return (NULL); |
532 |
|
|
Bfree(b); |
533 |
|
|
b = b1; |
534 |
|
|
} |
535 |
|
|
if (( j = b5 - m5 )!=0) { |
536 |
|
|
b = pow5mult(b, j); |
537 |
|
|
if (b == NULL) |
538 |
|
|
return (NULL); |
539 |
|
|
} |
540 |
|
|
} |
541 |
|
|
else { |
542 |
|
18 |
b = pow5mult(b, b5); |
543 |
✗✓ |
18 |
if (b == NULL) |
544 |
|
|
return (NULL); |
545 |
|
|
} |
546 |
|
|
} |
547 |
|
18 |
S = i2b(1); |
548 |
✗✓ |
18 |
if (S == NULL) |
549 |
|
|
return (NULL); |
550 |
✗✓ |
18 |
if (s5 > 0) { |
551 |
|
|
S = pow5mult(S, s5); |
552 |
|
|
if (S == NULL) |
553 |
|
|
return (NULL); |
554 |
|
|
} |
555 |
|
|
|
556 |
|
|
/* Check for special case that d is a normalized power of 2. */ |
557 |
|
|
|
558 |
|
|
spec_case = 0; |
559 |
✗✓ |
18 |
if ((mode < 2 || leftright) |
560 |
|
|
#ifdef Honor_FLT_ROUNDS |
561 |
|
|
&& Rounding == 1 |
562 |
|
|
#endif |
563 |
|
|
) { |
564 |
|
|
if (!word1(&d) && !(word0(&d) & Bndry_mask) |
565 |
|
|
#ifndef Sudden_Underflow |
566 |
|
|
&& word0(&d) & (Exp_mask & ~Exp_msk1) |
567 |
|
|
#endif |
568 |
|
|
) { |
569 |
|
|
/* The special case */ |
570 |
|
|
b2 += Log2P; |
571 |
|
|
s2 += Log2P; |
572 |
|
|
spec_case = 1; |
573 |
|
|
} |
574 |
|
|
} |
575 |
|
|
|
576 |
|
|
/* Arrange for convenient computation of quotients: |
577 |
|
|
* shift left if necessary so divisor has 4 leading 0 bits. |
578 |
|
|
* |
579 |
|
|
* Perhaps we should just compute leading 28 bits of S once |
580 |
|
|
* and for all and pass them and a shift to quorem, so it |
581 |
|
|
* can do shifts and ors to compute the numerator for q. |
582 |
|
|
*/ |
583 |
|
|
#ifdef Pack_32 |
584 |
✗✓✓✗
|
36 |
if (( i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f )!=0) |
585 |
|
18 |
i = 32 - i; |
586 |
|
|
#else |
587 |
|
|
if (( i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf )!=0) |
588 |
|
|
i = 16 - i; |
589 |
|
|
#endif |
590 |
✓✓ |
18 |
if (i > 4) { |
591 |
|
15 |
i -= 4; |
592 |
|
15 |
b2 += i; |
593 |
|
15 |
m2 += i; |
594 |
|
15 |
s2 += i; |
595 |
|
15 |
} |
596 |
✓✓ |
3 |
else if (i < 4) { |
597 |
|
1 |
i += 28; |
598 |
|
1 |
b2 += i; |
599 |
|
1 |
m2 += i; |
600 |
|
1 |
s2 += i; |
601 |
|
1 |
} |
602 |
✓✓ |
18 |
if (b2 > 0) { |
603 |
|
16 |
b = lshift(b, b2); |
604 |
✗✓ |
16 |
if (b == NULL) |
605 |
|
|
return (NULL); |
606 |
|
|
} |
607 |
✓✗ |
18 |
if (s2 > 0) { |
608 |
|
18 |
S = lshift(S, s2); |
609 |
✗✓ |
18 |
if (S == NULL) |
610 |
|
|
return (NULL); |
611 |
|
|
} |
612 |
✓✗ |
18 |
if (k_check) { |
613 |
✗✓ |
18 |
if (cmp(b,S) < 0) { |
614 |
|
|
k--; |
615 |
|
|
b = multadd(b, 10, 0); /* we botched the k estimate */ |
616 |
|
|
if (b == NULL) |
617 |
|
|
return (NULL); |
618 |
|
|
if (leftright) { |
619 |
|
|
mhi = multadd(mhi, 10, 0); |
620 |
|
|
if (mhi == NULL) |
621 |
|
|
return (NULL); |
622 |
|
|
} |
623 |
|
|
ilim = ilim1; |
624 |
|
|
} |
625 |
|
|
} |
626 |
✓✗✓✗
|
36 |
if (ilim <= 0 && (mode == 3 || mode == 5)) { |
627 |
|
18 |
S = multadd(S,5,0); |
628 |
✗✓ |
18 |
if (S == NULL) |
629 |
|
|
return (NULL); |
630 |
✗✓✗✗
|
18 |
if (ilim < 0 || cmp(b,S) <= 0) { |
631 |
|
|
/* no digits, fcvt style */ |
632 |
|
|
no_digits: |
633 |
|
18 |
k = -1 - ndigits; |
634 |
|
18 |
goto ret; |
635 |
|
|
} |
636 |
|
|
one_digit: |
637 |
|
20 |
*s++ = '1'; |
638 |
|
20 |
k++; |
639 |
|
20 |
goto ret; |
640 |
|
|
} |
641 |
|
|
if (leftright) { |
642 |
|
|
if (m2 > 0) { |
643 |
|
|
mhi = lshift(mhi, m2); |
644 |
|
|
if (mhi == NULL) |
645 |
|
|
return (NULL); |
646 |
|
|
} |
647 |
|
|
|
648 |
|
|
/* Compute mlo -- check for special case |
649 |
|
|
* that d is a normalized power of 2. |
650 |
|
|
*/ |
651 |
|
|
|
652 |
|
|
mlo = mhi; |
653 |
|
|
if (spec_case) { |
654 |
|
|
mhi = Balloc(mhi->k); |
655 |
|
|
if (mhi == NULL) |
656 |
|
|
return (NULL); |
657 |
|
|
Bcopy(mhi, mlo); |
658 |
|
|
mhi = lshift(mhi, Log2P); |
659 |
|
|
if (mhi == NULL) |
660 |
|
|
return (NULL); |
661 |
|
|
} |
662 |
|
|
|
663 |
|
|
for(i = 1;;i++) { |
664 |
|
|
dig = quorem(b,S) + '0'; |
665 |
|
|
/* Do we yet have the shortest decimal string |
666 |
|
|
* that will round to d? |
667 |
|
|
*/ |
668 |
|
|
j = cmp(b, mlo); |
669 |
|
|
delta = diff(S, mhi); |
670 |
|
|
if (delta == NULL) |
671 |
|
|
return (NULL); |
672 |
|
|
j1 = delta->sign ? 1 : cmp(b, delta); |
673 |
|
|
Bfree(delta); |
674 |
|
|
#ifndef ROUND_BIASED |
675 |
|
|
if (j1 == 0 && mode != 1 && !(word1(&d) & 1) |
676 |
|
|
#ifdef Honor_FLT_ROUNDS |
677 |
|
|
&& Rounding >= 1 |
678 |
|
|
#endif |
679 |
|
|
) { |
680 |
|
|
if (dig == '9') |
681 |
|
|
goto round_9_up; |
682 |
|
|
if (j > 0) |
683 |
|
|
dig++; |
684 |
|
|
#ifdef SET_INEXACT |
685 |
|
|
else if (!b->x[0] && b->wds <= 1) |
686 |
|
|
inexact = 0; |
687 |
|
|
#endif |
688 |
|
|
*s++ = dig; |
689 |
|
|
goto ret; |
690 |
|
|
} |
691 |
|
|
#endif |
692 |
|
|
if (j < 0 || (j == 0 && mode != 1 |
693 |
|
|
#ifndef ROUND_BIASED |
694 |
|
|
&& !(word1(&d) & 1) |
695 |
|
|
#endif |
696 |
|
|
)) { |
697 |
|
|
if (!b->x[0] && b->wds <= 1) { |
698 |
|
|
#ifdef SET_INEXACT |
699 |
|
|
inexact = 0; |
700 |
|
|
#endif |
701 |
|
|
goto accept_dig; |
702 |
|
|
} |
703 |
|
|
#ifdef Honor_FLT_ROUNDS |
704 |
|
|
if (mode > 1) |
705 |
|
|
switch(Rounding) { |
706 |
|
|
case 0: goto accept_dig; |
707 |
|
|
case 2: goto keep_dig; |
708 |
|
|
} |
709 |
|
|
#endif /*Honor_FLT_ROUNDS*/ |
710 |
|
|
if (j1 > 0) { |
711 |
|
|
b = lshift(b, 1); |
712 |
|
|
if (b == NULL) |
713 |
|
|
return (NULL); |
714 |
|
|
j1 = cmp(b, S); |
715 |
|
|
#ifdef ROUND_BIASED |
716 |
|
|
if (j1 >= 0 /*)*/ |
717 |
|
|
#else |
718 |
|
|
if ((j1 > 0 || (j1 == 0 && dig & 1)) |
719 |
|
|
#endif |
720 |
|
|
&& dig++ == '9') |
721 |
|
|
goto round_9_up; |
722 |
|
|
} |
723 |
|
|
accept_dig: |
724 |
|
|
*s++ = dig; |
725 |
|
|
goto ret; |
726 |
|
|
} |
727 |
|
|
if (j1 > 0) { |
728 |
|
|
#ifdef Honor_FLT_ROUNDS |
729 |
|
|
if (!Rounding) |
730 |
|
|
goto accept_dig; |
731 |
|
|
#endif |
732 |
|
|
if (dig == '9') { /* possible if i == 1 */ |
733 |
|
|
round_9_up: |
734 |
|
|
*s++ = '9'; |
735 |
|
|
goto roundoff; |
736 |
|
|
} |
737 |
|
|
*s++ = dig + 1; |
738 |
|
|
goto ret; |
739 |
|
|
} |
740 |
|
|
#ifdef Honor_FLT_ROUNDS |
741 |
|
|
keep_dig: |
742 |
|
|
#endif |
743 |
|
|
*s++ = dig; |
744 |
|
|
if (i == ilim) |
745 |
|
|
break; |
746 |
|
|
b = multadd(b, 10, 0); |
747 |
|
|
if (b == NULL) |
748 |
|
|
return (NULL); |
749 |
|
|
if (mlo == mhi) { |
750 |
|
|
mlo = mhi = multadd(mhi, 10, 0); |
751 |
|
|
if (mlo == NULL) |
752 |
|
|
return (NULL); |
753 |
|
|
} |
754 |
|
|
else { |
755 |
|
|
mlo = multadd(mlo, 10, 0); |
756 |
|
|
if (mlo == NULL) |
757 |
|
|
return (NULL); |
758 |
|
|
mhi = multadd(mhi, 10, 0); |
759 |
|
|
if (mhi == NULL) |
760 |
|
|
return (NULL); |
761 |
|
|
} |
762 |
|
|
} |
763 |
|
|
} |
764 |
|
|
else |
765 |
|
|
for(i = 1;; i++) { |
766 |
|
|
*s++ = dig = quorem(b,S) + '0'; |
767 |
|
|
if (!b->x[0] && b->wds <= 1) { |
768 |
|
|
#ifdef SET_INEXACT |
769 |
|
|
inexact = 0; |
770 |
|
|
#endif |
771 |
|
|
goto ret; |
772 |
|
|
} |
773 |
|
|
if (i >= ilim) |
774 |
|
|
break; |
775 |
|
|
b = multadd(b, 10, 0); |
776 |
|
|
if (b == NULL) |
777 |
|
|
return (NULL); |
778 |
|
|
} |
779 |
|
|
|
780 |
|
|
/* Round off last digit */ |
781 |
|
|
|
782 |
|
|
#ifdef Honor_FLT_ROUNDS |
783 |
|
|
switch(Rounding) { |
784 |
|
|
case 0: goto trimzeros; |
785 |
|
|
case 2: goto roundoff; |
786 |
|
|
} |
787 |
|
|
#endif |
788 |
|
|
b = lshift(b, 1); |
789 |
|
|
if (b == NULL) |
790 |
|
|
return (NULL); |
791 |
|
|
j = cmp(b, S); |
792 |
|
|
#ifdef ROUND_BIASED |
793 |
|
|
if (j >= 0) |
794 |
|
|
#else |
795 |
|
|
if (j > 0 || (j == 0 && dig & 1)) |
796 |
|
|
#endif |
797 |
|
|
{ |
798 |
|
|
roundoff: |
799 |
|
|
while(*--s == '9') |
800 |
|
|
if (s == s0) { |
801 |
|
|
k++; |
802 |
|
|
*s++ = '1'; |
803 |
|
|
goto ret; |
804 |
|
|
} |
805 |
|
|
++*s++; |
806 |
|
|
} |
807 |
|
|
else { |
808 |
|
|
#ifdef Honor_FLT_ROUNDS |
809 |
|
|
trimzeros: |
810 |
|
|
#endif |
811 |
|
|
while(*--s == '0'); |
812 |
|
|
s++; |
813 |
|
|
} |
814 |
|
|
ret: |
815 |
|
38 |
Bfree(S); |
816 |
✗✓ |
38 |
if (mhi) { |
817 |
|
|
if (mlo && mlo != mhi) |
818 |
|
|
Bfree(mlo); |
819 |
|
|
Bfree(mhi); |
820 |
|
|
} |
821 |
|
|
ret1: |
822 |
|
|
#ifdef SET_INEXACT |
823 |
|
|
if (inexact) { |
824 |
|
|
if (!oldinexact) { |
825 |
|
|
word0(&d) = Exp_1 + (70 << Exp_shift); |
826 |
|
|
word1(&d) = 0; |
827 |
|
|
dval(&d) += 1.; |
828 |
|
|
} |
829 |
|
|
} |
830 |
|
|
else if (!oldinexact) |
831 |
|
|
clear_inexact(); |
832 |
|
|
#endif |
833 |
|
222 |
Bfree(b); |
834 |
|
222 |
*s = 0; |
835 |
|
222 |
*decpt = k + 1; |
836 |
✓✗ |
222 |
if (rve) |
837 |
|
222 |
*rve = s; |
838 |
|
222 |
return s0; |
839 |
|
422 |
} |
840 |
|
|
DEF_STRONG(dtoa); |