/**************************************************************************** * libs/libc/stdio/legacy_dtoa.c * * This file was ported to NuttX by Yolande Cates. * * Copyright (c) 1990, 1993 * The Regents of the University of California. All rights reserved. * * This code is derived from software contributed to Berkeley by * Chris Torek. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. All advertising materials mentioning features or use of this software * must display the following acknowledgement: * This product includes software developed by the University of * California, Berkeley and its contributors. * 4. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * ****************************************************************************/ /**************************************************************************** * Included Files ****************************************************************************/ #include #include #include #include #include "libc.h" /**************************************************************************** * Pre-processor Definitions ****************************************************************************/ #ifdef CONFIG_DTOA_UNSIGNED_SHIFTS # define SIGN_EXTEND(a,b) if (b < 0) a |= 0xffff0000; #else # define SIGN_EXTEND(a,b) /* no-op */ #endif #ifdef CONFIG_ENDIAN_BIG # define WORD0(x) ((uint32_t *)&x)[0] # define WORD1(x) ((uint32_t *)&x)[1] #else # define WORD0(x) ((uint32_t *)&x)[1] # define WORD1(x) ((uint32_t *)&x)[0] #endif #ifdef CONFIG_ENDIAN_BIG # define STOREINC(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \ ((unsigned short *)a)[1] = (unsigned short)c, a++) #else # define STOREINC(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \ ((unsigned short *)a)[0] = (unsigned short)c, a++) #endif #define EXP_SHIFT 20 #define EXP_SHIFT1 20 #define EXP_MSK1 0x100000 #define EXP_MSK11 0x100000 #define EXP_MASK 0x7ff00000 #define P 53 #define BIAS 1023 #define IEEE_ARITH #define EMIN (-1022) #define EXP_1 0x3ff00000 #define EXP_11 0x3ff00000 #define EBITS 11 #define FRAC_MASK 0xfffff #define FRAC_MASK1 0xfffff #define TEN_PMAX 22 #define BLETCH 0x10 #define BNDRY_MASK 0xfffff #define BNDRY_MASK1 0xfffff #define LSB 1 #define SIGN_BIT 0x80000000 #define LOG2P 1 #define TINY0 0 #define TINY1 1 #define QUICK_MAX 14 #define SMALL_MAX 14 #define INFINITE(x) (WORD0(x) == 0x7ff00000) /* sufficient test for here */ #define KMAX 15 #define BCOPY(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ y->wds*sizeof(long) + 2*sizeof(int)) /**************************************************************************** * Private Type Definitions ****************************************************************************/ struct bigint_s { FAR struct bigint_s *next; int k; int maxwds; int sign; int wds; unsigned long x[1]; }; typedef struct bigint_s bigint_t; /**************************************************************************** * Private Data ****************************************************************************/ /* REVISIT: __dtoa is not thread safe due to these two global variables. * Options: * * 1. Allocate on stack. g_freelist is rather large, however.. around 275 * bytes (it could be shrunk a little by using stdint types instead of * int. * 2. Semaphore protect the global variables and handle interrupt level * calls as a special case (perhaps refusing them? Or having a duplicate * set of variables, one for tasks and one for interrupt usage) */ static FAR bigint_t *g_freelist[KMAX + 1]; static FAR bigint_t *g_p5s; #ifdef IEEE_ARITH static const double g_bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; # define n_bigtens 5 #else static const double g_bigtens[] = { 1e16, 1e32 }; # define n_bigtens 2 #endif /**************************************************************************** * Private Functions ****************************************************************************/ static FAR bigint_t *balloc(int k) { FAR bigint_t *rv; int x; if ((rv = g_freelist[k])) { g_freelist[k] = rv->next; } else { x = 1 << k; rv = (FAR bigint_t *) lib_malloc(sizeof(bigint_t) + (x - 1) * sizeof(long)); rv->k = k; rv->maxwds = x; } rv->sign = 0; rv->wds = 0; return rv; } static void bfree(FAR bigint_t *v) { if (v != NULL) { v->next = g_freelist[v->k]; g_freelist[v->k] = v; } } /* Multiply by m and add a */ static FAR bigint_t *multadd(FAR bigint_t *b, int m, int a) { FAR bigint_t *b1; FAR unsigned long *x; unsigned long y; #ifdef CONFIG_DTOA_PACK32 unsigned long xi; unsigned long z; #endif int wds; int i; wds = b->wds; x = b->x; i = 0; do { #ifdef CONFIG_DTOA_PACK32 xi = *x; y = (xi & 0xffff) * m + a; z = (xi >> 16) * m + (y >> 16); a = (int)(z >> 16); *x++ = (z << 16) + (y & 0xffff); #else y = *x * m + a; a = (int)(y >> 16); *x++ = y & 0xffff; #endif } while (++i < wds); if (a != 0) { if (wds >= b->maxwds) { b1 = balloc(b->k + 1); BCOPY(b1, b); bfree(b); b = b1; } b->x[wds++] = a; b->wds = wds; } return b; } static int hi0bits(unsigned long x) { int k = 0; if ((x & 0xffff0000) == 0) { k = 16; x <<= 16; } if ((x & 0xff000000) == 0) { k += 8; x <<= 8; } if ((x & 0xf0000000) == 0) { k += 4; x <<= 4; } if ((x & 0xc0000000) == 0) { k += 2; x <<= 2; } if ((x & 0x80000000) == 0) { k++; if ((x & 0x40000000) == 0) { return 32; } } return k; } static int lo0bits(FAR unsigned long *y) { unsigned long x = *y; int k; if ((x & 7) != 0) { if (x & 1) { return 0; } if ((x & 2) != 0) { *y = x >> 1; return 1; } *y = x >> 2; return 2; } k = 0; if ((x & 0xffff) == 0) { k = 16; x >>= 16; } if ((x & 0xff) == 0) { k += 8; x >>= 8; } if ((x & 0xf) == 0) { k += 4; x >>= 4; } if ((x & 0x3) == 0) { k += 2; x >>= 2; } if ((x & 1) == 0) { k++; x >>= 1; if ((!x & 1) != 0) { return 32; } } *y = x; return k; } static FAR bigint_t *i2b(int i) { FAR bigint_t *b; b = balloc(1); b->x[0] = i; b->wds = 1; return b; } static FAR bigint_t *mult(FAR bigint_t *a, FAR bigint_t *b) { FAR bigint_t *c; FAR unsigned long *x; FAR unsigned long *xa; FAR unsigned long *xae; FAR unsigned long *xb; FAR unsigned long *xbe; FAR unsigned long *xc; FAR unsigned long *xc0; unsigned long carry; unsigned long y; unsigned long z; #ifdef CONFIG_DTOA_PACK32 uint32_t z2; #endif int k; int wa; int wb; int wc; if (a->wds < b->wds) { c = a; a = b; b = c; } k = a->k; wa = a->wds; wb = b->wds; wc = wa + wb; if (wc > a->maxwds) { k++; } c = balloc(k); for (x = c->x, xa = x + wc; x < xa; x++) { *x = 0; } xa = a->x; xae = xa + wa; xb = b->x; xbe = xb + wb; xc0 = c->x; #ifdef CONFIG_DTOA_PACK32 for (; xb < xbe; xb++, xc0++) { if ((y = *xb & 0xffff) != 0) { x = xa; xc = xc0; carry = 0; do { z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; carry = z >> 16; z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; carry = z2 >> 16; STOREINC(xc, z2, z); } while (x < xae); *xc = carry; } if ((y = *xb >> 16)) { x = xa; xc = xc0; carry = 0; z2 = *xc; do { z = (*x & 0xffff) * y + (*xc >> 16) + carry; carry = z >> 16; STOREINC(xc, z, z2); z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; carry = z2 >> 16; } while (x < xae); *xc = z2; } } #else for (; xb < xbe; xc0++) { if ((y = *xb++)) { x = xa; xc = xc0; carry = 0; do { z = *x++ * y + *xc + carry; carry = z >> 16; *xc++ = z & 0xffff; } while (x < xae); *xc = carry; } } #endif for (xc0 = c->x, xc = xc0 + wc; wc > 0 && *--xc == 0; --wc); c->wds = wc; return c; } static FAR bigint_t *pow5mult(FAR bigint_t *b, int k) { FAR bigint_t *b1; FAR bigint_t *p5; FAR bigint_t *p51; int i; static int p05[3] = { 5, 25, 125 }; if ((i = k & 3) != 0) { b = multadd(b, p05[i - 1], 0); } if ((k >>= 2) == 0) { return b; } if ((p5 = g_p5s) == 0) { /* First time */ g_p5s = i2b(625); p5 = g_p5s; p5->next = 0; } for (; ; ) { if ((k & 1) != 0) { b1 = mult(b, p5); bfree(b); b = b1; } if ((k >>= 1) == 0) { break; } if ((p51 = p5->next) == 0) { p5->next = mult(p5, p5); p51 = p5->next; p51->next = 0; } p5 = p51; } return b; } static FAR bigint_t *lshift(FAR bigint_t *b, int k) { FAR bigint_t *b1; FAR unsigned long *x; FAR unsigned long *x1; FAR unsigned long *xe; unsigned long z; int i; int k1; int n; int n1; #ifdef CONFIG_DTOA_PACK32 n = k >> 5; #else n = k >> 4; #endif k1 = b->k; n1 = n + b->wds + 1; for (i = b->maxwds; n1 > i; i <<= 1) { k1++; } b1 = balloc(k1); x1 = b1->x; for (i = 0; i < n; i++) { *x1++ = 0; } x = b->x; xe = x + b->wds; #ifdef CONFIG_DTOA_PACK32 if ((k &= 0x1f) != 0) { k1 = 32 - k; z = 0; do { *x1++ = *x << k | z; z = *x++ >> k1; } while (x < xe); if ((*x1 = z) != 0) { ++n1; } } #else if ((k &= 0xf) != 0) { k1 = 16 - k; z = 0; do { *x1++ = ((*x << k) & 0xffff) | z; z = *x++ >> k1; } while (x < xe); if ((*x1 = z) != 0) { ++n1; } } #endif else { do { *x1++ = *x++; } while (x < xe); } b1->wds = n1 - 1; bfree(b); return b1; } static int cmp(FAR bigint_t *a, FAR bigint_t *b) { FAR unsigned long *xa; FAR unsigned long *xa0; FAR unsigned long *xb; FAR unsigned long *xb0; int i; int j; i = a->wds; j = b->wds; #ifdef CONFIG_DEBUG_LIB if (i > 1 && a->x[i - 1] == 0) { lerr("ERROR: cmp called with a->x[a->wds-1] == 0\n"); } if (j > 1 && b->x[j - 1] == 0) { lerr("ERROR: cmp called with b->x[b->wds-1] == 0\n"); } #endif if (i -= j) { return i; } xa0 = a->x; xa = xa0 + j; xb0 = b->x; xb = xb0 + j; for (; ; ) { if (*--xa != *--xb) { return *xa < *xb ? -1 : 1; } if (xa <= xa0) { break; } } return 0; } static FAR bigint_t *diff(FAR bigint_t *a, FAR bigint_t *b) { FAR bigint_t *c; FAR unsigned long *xa; FAR unsigned long *xae; FAR unsigned long *xb; FAR unsigned long *xbe; FAR unsigned long *xc; long borrow; /* We need signed shifts here. */ long y; #ifdef CONFIG_DTOA_PACK32 int32_t z; #endif int i; int wa; int wb; i = cmp(a, b); if (i == 0) { c = balloc(0); c->wds = 1; c->x[0] = 0; return c; } if (i < 0) { c = a; a = b; b = c; i = 1; } else { i = 0; } c = balloc(a->k); c->sign = i; wa = a->wds; xa = a->x; xae = xa + wa; wb = b->wds; xb = b->x; xbe = xb + wb; xc = c->x; borrow = 0; #ifdef CONFIG_DTOA_PACK32 do { y = (*xa & 0xffff) - (*xb & 0xffff) + borrow; borrow = y >> 16; SIGN_EXTEND(borrow, y); z = (*xa++ >> 16) - (*xb++ >> 16) + borrow; borrow = z >> 16; SIGN_EXTEND(borrow, z); STOREINC(xc, z, y); } while (xb < xbe); while (xa < xae) { y = (*xa & 0xffff) + borrow; borrow = y >> 16; SIGN_EXTEND(borrow, y); z = (*xa++ >> 16) + borrow; borrow = z >> 16; SIGN_EXTEND(borrow, z); STOREINC(xc, z, y); } #else do { y = *xa++ - *xb++ + borrow; borrow = y >> 16; SIGN_EXTEND(borrow, y); *xc++ = y & 0xffff; } while (xb < xbe); while (xa < xae) { y = *xa++ + borrow; borrow = y >> 16; SIGN_EXTEND(borrow, y); *xc++ = y & 0xffff; } #endif while (*--xc == 0) { wa--; } c->wds = wa; return c; } static FAR bigint_t *d2b(double d, int *e, int *bits) { FAR bigint_t *b; FAR unsigned long *x; unsigned long y; unsigned long z; int de; int i; int k; #ifdef CONFIG_DTOA_PACK32 b = balloc(1); #else b = balloc(2); #endif x = b->x; z = WORD0(d) & FRAC_MASK; WORD0(d) &= 0x7fffffff; /* Clear sign bit, which we ignore */ de = (int)(WORD0(d) >> EXP_SHIFT); if (de != 0) { z |= EXP_MSK1; } #ifdef CONFIG_DTOA_PACK32 if ((y = WORD1(d)) != 0) { if ((k = lo0bits(&y)) != 0) { x[0] = y | z << (32 - k); z >>= k; } else { x[0] = y; } b->wds = (x[1] = z) ? 2 : 1; i = b->wds; } else { #ifdef CONFIG_DEBUG_LIB if (z == 0) { lerr("ERROR: Zero passed to d2b\n"); } #endif k = lo0bits(&z); x[0] = z; i = b->wds = 1; k += 32; } #else if ((y = WORD1(d)) != 0) { if ((k = lo0bits(&y)) != 0) { if (k >= 16) { x[0] = y | ((z << (32 - k)) & 0xffff); x[1] = z >> (k - 16) & 0xffff; x[2] = z >> k; i = 2; } else { x[0] = y & 0xffff; x[1] = (y >> 16) | ((z << (16 - k)) & 0xffff); x[2] = z >> k & 0xffff; x[3] = z >> (k + 16); i = 3; } } else { x[0] = y & 0xffff; x[1] = y >> 16; x[2] = z & 0xffff; x[3] = z >> 16; i = 3; } } else { #ifdef CONFIG_DEBUG_LIB if (z == 0) { lerr("ERROR: Zero passed to d2b\n"); } #endif k = lo0bits(&z); if (k >= 16) { x[0] = z; i = 0; } else { x[0] = z & 0xffff; x[1] = z >> 16; i = 1; } k += 32; } while (!x[i]) { --i; } b->wds = i + 1; #endif if (de != 0) { *e = de - BIAS - (P - 1) + k; *bits = P - k; } else { *e = de - BIAS - (P - 1) + 1 + k; #ifdef CONFIG_DTOA_PACK32 *bits = 32 * i - hi0bits(x[i - 1]); #else *bits = (i + 2) * 16 - hi0bits(x[i]); #endif } return b; } static const double tens[] = { 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22 }; static int quorem(FAR bigint_t *b, FAR bigint_t *s) { long borrow; long y; unsigned long carry; unsigned long q; unsigned long ys; FAR unsigned long *bx; FAR unsigned long *bxe; FAR unsigned long *sx; FAR unsigned long *sxe; #ifdef CONFIG_DTOA_PACK32 int32_t z; uint32_t si; uint32_t zs; #endif int n; n = s->wds; #ifdef CONFIG_DEBUG_LIB if (b->wds > n) { lerr("ERROR: oversize b in quorem\n"); } #endif if (b->wds < n) { return 0; } sx = s->x; sxe = sx + --n; bx = b->x; bxe = bx + n; q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ #ifdef CONFIG_DEBUG_LIB if (q > 9) { lerr("ERROR: oversized quotient in quorem\n"); } #endif if (q != 0) { borrow = 0; carry = 0; do { #ifdef CONFIG_DTOA_PACK32 si = *sx++; ys = (si & 0xffff) * q + carry; zs = (si >> 16) * q + (ys >> 16); carry = zs >> 16; y = (*bx & 0xffff) - (ys & 0xffff) + borrow; borrow = y >> 16; SIGN_EXTEND(borrow, y); z = (*bx >> 16) - (zs & 0xffff) + borrow; borrow = z >> 16; SIGN_EXTEND(borrow, z); STOREINC(bx, z, y); #else ys = *sx++ * q + carry; carry = ys >> 16; y = *bx - (ys & 0xffff) + borrow; borrow = y >> 16; SIGN_EXTEND(borrow, y); *bx++ = y & 0xffff; #endif } while (sx <= sxe); if (*bxe == 0) { bx = b->x; while (--bxe > bx && *bxe == 0) { --n; } b->wds = n; } } if (cmp(b, s) >= 0) { q++; borrow = 0; carry = 0; bx = b->x; sx = s->x; do { #ifdef CONFIG_DTOA_PACK32 si = *sx++; ys = (si & 0xffff) + carry; zs = (si >> 16) + (ys >> 16); carry = zs >> 16; y = (*bx & 0xffff) - (ys & 0xffff) + borrow; borrow = y >> 16; SIGN_EXTEND(borrow, y); z = (*bx >> 16) - (zs & 0xffff) + borrow; borrow = z >> 16; SIGN_EXTEND(borrow, z); STOREINC(bx, z, y); #else ys = *sx++ + carry; carry = ys >> 16; y = *bx - (ys & 0xffff) + borrow; borrow = y >> 16; SIGN_EXTEND(borrow, y); *bx++ = y & 0xffff; #endif } while (sx <= sxe); bx = b->x; bxe = bx + n; if (*bxe == 0) { while (--bxe > bx && *bxe == 0) { --n; } b->wds = n; } } return q; } /**************************************************************************** * Public Functions ****************************************************************************/ /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. * * Inspired by "How to Print Floating-Point Numbers Accurately" by * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101]. * * Modifications: * 1. Rather than iterating, we use a simple numeric overestimate * to determine k = floor(log10(d)). We scale relevant * quantities using O(log2(k)) rather than O(k) multiplications. * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't * try to generate digits strictly left to right. Instead, we * compute with fewer bits and propagate the carry if necessary * when rounding the final digit up. This is often faster. * 3. Under the assumption that input will be rounded nearest, * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. * That is, we allow equality in stopping tests when the * round-nearest rule will give the same floating-point value * as would satisfaction of the stopping test with strict * inequality. * 4. We remove common factors of powers of 2 from relevant * quantities. * 5. When converting floating-point integers less than 1e16, * we use floating-point arithmetic rather than resorting * to multiple-precision integers. * 6. When asked to produce fewer than 15 digits, we first try * to get by with floating-point arithmetic; we resort to * multiple-precision integer arithmetic only if we cannot * guarantee that the floating-point calculation has given * the correctly rounded result. For k requested digits and * "uniformly" distributed input, the probability is * something like 10^(k-15) that we must resort to the int32_t * calculation. */ FAR char *__dtoa(double d, int mode, int ndigits, FAR int *decpt, FAR int *sign, FAR char **rve) { /* Arguments ndigits, decpt, sign are similar to those of ecvt and fcvt; * trailing zeros are suppressed from the returned string. If not null, * *rve is set to point to the end of the return value. If d is +-Infinity * or NaN, then *decpt is set to 9999. * * mode: 0 ==> shortest string that yields d when read in and rounded to * nearest. 1 ==> like 0, but with Steele & White stopping rule; e.g. with * IEEE P754 arithmetic , mode 0 gives 1e23 whereas mode 1 gives * 9.999999999999999e22. 2 ==> max(1,ndigits) significant digits. This * gives a return value similar to that of ecvt, except that trailing zeros * are suppressed. 3 ==> through ndigits past the decimal point. This * gives a return value similar to that from fcvt, except that trailing * zeros are suppressed, and ndigits can be negative. 4-9 should give the * same return values as 2-3, i.e., 4 <= mode <= 9 ==> same return as mode * 2 + (mode & 1). These modes are mainly for debugging; often they run * slower but sometimes faster than modes 2-3. 4,5,8,9 ==> left-to-right * digit generation. 6-9 ==> don't try fast floating-point estimate (if * applicable). * * Values of mode other than 0-9 are treated as mode 0. * * Sufficient space is allocated to the return value to hold the suppressed * trailing zeros. */ static FAR bigint_t *result; static int result_k; FAR bigint_t *b; FAR bigint_t *b1; FAR bigint_t *delta; FAR bigint_t *mlo = NULL; FAR bigint_t *mhi; FAR bigint_t *s; FAR char *st; FAR char *st0; double d2; double ds; double eps; long l; unsigned long x; int denorm; int bbits; int b2; int b5; int be; int dig; int i; int ieps; int ilim = 0; int ilim0; int ilim1 = 0; int j; int j_1; int k; int k0; int k_check; int leftright; int m2; int m5; int s2; int s5; int spec_case = 0; int try_quick; if (result != 0) { result->k = result_k; result->maxwds = 1 << result_k; bfree(result); result = 0; } if ((WORD0(d) & SIGN_BIT) != 0) { /* Set sign for everything, including 0's and NaNs */ *sign = 1; WORD0(d) &= ~SIGN_BIT; /* clear sign bit */ } else { *sign = 0; } #if defined(IEEE_ARITH) # ifdef IEEE_ARITH if ((WORD0(d) & EXP_MASK) == EXP_MASK) #else if (WORD0(d) == 0x8000) #endif { /* Infinity or NaN */ *decpt = 9999; st = #ifdef IEEE_ARITH !WORD1(d) && !(WORD0(d) & 0xfffff) ? "Infinity" : #endif "NaN"; if (rve != NULL) { *rve = #ifdef IEEE_ARITH st[3] ? st + 8 : #endif st + 3; } return st; } #endif if (d == 0) { *decpt = 1; st = "0"; if (rve != NULL) { *rve = st + 1; } return st; } b = d2b(d, &be, &bbits); i = (int)(WORD0(d) >> EXP_SHIFT1 & (EXP_MASK >> EXP_SHIFT1)); if (i != 0) { d2 = d; WORD0(d2) &= FRAC_MASK1; WORD0(d2) |= EXP_11; /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 log10(x) = log(x) / log(10) ~=~ * log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) log10(d) = * (i-BIAS)*log(2)/log(10) + log10(d2) This suggests computing an * approximation k to log10(d) by k = (i - BIAS)*0.301029995663981 + ( * (d2-1.5)*0.289529654602168 + 0.176091259055681 ); We want k to be * too large rather than too small. The error in the first-order Taylor * series approximation is in our favor, so we just round up the * constant enough to compensate for any error in the multiplication of * (i - BIAS) by 0.301029995663981; since |i - BIAS| <= 1077, and * 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, adding 1e-13 to the constant * term more than suffices. Hence we adjust the constant term to * 0.1760912590558. (We could get a more accurate k by invoking log10, * but this is probably not worthwhile.) */ i -= BIAS; denorm = 0; } else { /* d is denormalized */ i = bbits + be + (BIAS + (P - 1) - 1); x = i > 32 ? WORD0(d) << (64 - i) | WORD1(d) >> (i - 32) : WORD1(d) << (32 - i); d2 = x; WORD0(d2) -= 31 * EXP_MSK1; /* Adjust exponent */ i -= (BIAS + (P - 1) - 1) + 1; denorm = 1; } ds = (d2 - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981; k = (int)ds; if (ds < 0. && ds != k) { k--; /* Want k = floor(ds) */ } k_check = 1; if (k >= 0 && k <= TEN_PMAX) { if (d < tens[k]) { k--; } k_check = 0; } j = bbits - i - 1; if (j >= 0) { b2 = 0; s2 = j; } else { b2 = -j; s2 = 0; } if (k >= 0) { b5 = 0; s5 = k; s2 += k; } else { b2 -= k; b5 = -k; s5 = 0; } if (mode < 0 || mode > 9) { mode = 0; } try_quick = 1; if (mode > 5) { mode -= 4; try_quick = 0; } leftright = 1; switch (mode) { case 0: case 1: ilim = ilim1 = -1; i = 18; ndigits = 0; break; case 2: leftright = 0; /* FALLTHROUGH */ case 4: if (ndigits <= 0) { ndigits = 1; } i = ndigits; ilim1 = i; ilim = i; break; case 3: leftright = 0; /* FALLTHROUGH */ case 5: i = ndigits + k + 1; ilim = i; ilim1 = i - 1; if (i <= 0) { i = 1; } } j = sizeof(unsigned long); for (result_k = 0; (signed)(sizeof(bigint_t) - sizeof(unsigned long) + j) <= i; j <<= 1) { result_k++; } result = balloc(result_k); st0 = (FAR char *)result; st = st0; if (ilim >= 0 && ilim <= QUICK_MAX && try_quick) { /* Try to get by with floating-point arithmetic. */ i = 0; d2 = d; k0 = k; ilim0 = ilim; ieps = 2; /* Conservative */ if (k > 0) { ds = tens[k & 0xf]; j = k >> 4; if ((j & BLETCH) != 0) { /* Prevent overflows */ j &= BLETCH - 1; d /= g_bigtens[n_bigtens - 1]; ieps++; } for (; j; j >>= 1, i++) { if (j & 1) { ieps++; ds *= g_bigtens[i]; } } d /= ds; } else if ((j_1 = -k)) { d *= tens[j_1 & 0xf]; for (j = j_1 >> 4; j; j >>= 1, i++) { if ((j & 1) != 0) { ieps++; d *= g_bigtens[i]; } } } if (k_check && d < 1. && ilim > 0) { if (ilim1 <= 0) { goto fast_failed; } ilim = ilim1; k--; d *= 10.; ieps++; } eps = ieps * d + 7.; WORD0(eps) -= (P - 1) * EXP_MSK1; if (ilim == 0) { mhi = 0; s = 0; d -= 5.; if (d > eps) { goto one_digit; } if (d < -eps) { goto no_digits; } goto fast_failed; } #ifndef CONFIG_DTOA_NO_LEFTRIGHT if (leftright) { /* Use Steele & White method of only generating digits needed. */ eps = 0.5 / tens[ilim - 1] - eps; for (i = 0; ; ) { l = (int)d; d -= l; *st++ = '0' + (int)l; if (d < eps) { goto ret1; } if (1. - d < eps) { goto bump_up; } if (++i >= ilim) { break; } eps *= 10.; d *= 10.; } } else { #endif /* Generate ilim digits, then fix them up. */ eps *= tens[ilim - 1]; for (i = 1; ; i++, d *= 10.) { l = (int)d; d -= l; *st++ = '0' + (int)l; if (i == ilim) { if (d > 0.5 + eps) { goto bump_up; } else if (d < 0.5 - eps) { while (*--st == '0') { } st++; goto ret1; } break; } } #ifndef CONFIG_DTOA_NO_LEFTRIGHT } #endif fast_failed: st = st0; d = d2; k = k0; ilim = ilim0; } /* Do we have a "small" integer? */ if (be >= 0 && k <= SMALL_MAX) { /* Yes. */ ds = tens[k]; if (ndigits < 0 && ilim <= 0) { s = mhi = 0; if (ilim < 0 || d <= 5 * ds) { goto no_digits; } goto one_digit; } for (i = 1; ; i++) { l = (int)(d / ds); d -= l * ds; #ifdef Check_FLT_ROUNDS /* If FLT_ROUNDS == 2, l will usually be high by 1 */ if (d < 0) { l--; d += ds; } #endif *st++ = '0' + (int)l; if (i == ilim) { d += d; if (d > ds || (d == ds && (l & 1))) { bump_up: while (*--st == '9') { if (st == st0) { k++; *st = '0'; break; } } ++*st++; } break; } if ((d *= 10.) == 0) { break; } } goto ret1; } m2 = b2; m5 = b5; mhi = mlo = 0; if (leftright) { if (mode < 2) { i = denorm ? be + (BIAS + (P - 1) - 1 + 1) : 1 + P - bbits; } else { j = ilim - 1; if (m5 >= j) { m5 -= j; } else { s5 += j -= m5; b5 += j; m5 = 0; } if ((i = ilim) < 0) { m2 -= i; i = 0; } } b2 += i; s2 += i; mhi = i2b(1); } if (m2 > 0 && s2 > 0) { i = m2 < s2 ? m2 : s2; b2 -= i; m2 -= i; s2 -= i; } if (b5 > 0) { if (leftright) { if (m5 > 0) { mhi = pow5mult(mhi, m5); b1 = mult(mhi, b); bfree(b); b = b1; } if ((j = b5 - m5) != 0) { b = pow5mult(b, j); } } else { b = pow5mult(b, b5); } } s = i2b(1); if (s5 > 0) { s = pow5mult(s, s5); } /* Check for special case that d is a normalized power of 2. */ if (mode < 2) { if (WORD1(d) == 0 && (WORD0(d) & BNDRY_MASK) == 0 && (WORD0(d) & EXP_MASK) != 0) { /* The special case */ b2 += LOG2P; s2 += LOG2P; spec_case = 1; } else { spec_case = 0; } } /* Arrange for convenient computation of quotients: shift left if * necessary so divisor has 4 leading 0 bits. * * Perhaps we should just compute leading 28 bits of s once and for all * and pass them and a shift to quorem, so it can do shifts and ors * to compute the numerator for q. */ #ifdef CONFIG_DTOA_PACK32 i = ((s5 ? 32 - hi0bits(s->x[s->wds - 1]) : 1) + s2) & 0x1f; if (i != 0) { i = 32 - i; } #else i = ((s5 ? 32 - hi0bits(s->x[s->wds - 1]) : 1) + s2) & 0xf; if (i != 0) { i = 16 - i; } #endif if (i > 4) { i -= 4; b2 += i; m2 += i; s2 += i; } else if (i < 4) { i += 28; b2 += i; m2 += i; s2 += i; } if (b2 > 0) { b = lshift(b, b2); } if (s2 > 0) { s = lshift(s, s2); } if (k_check) { if (cmp(b, s) < 0) { k--; b = multadd(b, 10, 0); /* we botched the k estimate */ if (leftright) { mhi = multadd(mhi, 10, 0); } ilim = ilim1; } } if (ilim <= 0 && mode > 2) { if (ilim < 0 || cmp(b, s = multadd(s, 5, 0)) <= 0) { /* no digits, fcvt style */ no_digits: k = -1 - ndigits; goto ret; } one_digit: *st++ = '1'; k++; goto ret; } if (leftright) { if (m2 > 0) { mhi = lshift(mhi, m2); } /* Compute mlo -- check for special case that d is a normalized power * of 2. */ mlo = mhi; if (spec_case) { mhi = balloc(mhi->k); BCOPY(mhi, mlo); mhi = lshift(mhi, LOG2P); } for (i = 1; ; i++) { dig = quorem(b, s) + '0'; /* Have we yet the shortest decimal string that will round to d? */ j = cmp(b, mlo); delta = diff(s, mhi); j_1 = delta->sign ? 1 : cmp(b, delta); bfree(delta); #ifndef CONFIG_DTOA_ROUND_BIASED if (j_1 == 0 && !mode && !(WORD1(d) & 1)) { if (dig == '9') { goto round_9_up; } if (j > 0) { dig++; } *st++ = dig; goto ret; } #endif if (j < 0 || (j == 0 && !mode #ifndef CONFIG_DTOA_ROUND_BIASED && ((WORD1(d) & 1) == 0) #endif )) { if ((j_1 > 0)) { b = lshift(b, 1); j_1 = cmp(b, s); if ((j_1 > 0 || (j_1 == 0 && (dig & 1))) && dig++ == '9') { goto round_9_up; } } *st++ = dig; goto ret; } if (j_1 > 0) { if (dig == '9') { /* Possible if i == 1 */ round_9_up: *st++ = '9'; goto roundoff; } *st++ = dig + 1; goto ret; } *st++ = dig; if (i == ilim) { break; } b = multadd(b, 10, 0); if (mlo == mhi) { mhi = multadd(mhi, 10, 0); mlo = mhi; } else { mlo = multadd(mlo, 10, 0); mhi = multadd(mhi, 10, 0); } } } else { for (i = 1; ; i++) { *st++ = dig = quorem(b, s) + '0'; if (i >= ilim) { break; } b = multadd(b, 10, 0); } } /* Round off last digit */ b = lshift(b, 1); j = cmp(b, s); if (j > 0 || (j == 0 && (dig & 1))) { roundoff: while (*--st == '9') { if (st == st0) { k++; *st++ = '1'; goto ret; } } ++*st++; } else { while (*--st == '0') { } st++; } ret: bfree(s); if (mhi) { if (mlo && mlo != mhi) { bfree(mlo); } bfree(mhi); } ret1: bfree(b); if (st == st0) { /* Don't return empty string */ *st++ = '0'; k = 0; } *st = 0; *decpt = k + 1; if (rve != NULL) { *rve = st; } return st0; }