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authorDuncan Wilkie <antigravityd@gmail.com>2023-11-18 06:11:09 -0600
committerDuncan Wilkie <antigravityd@gmail.com>2023-11-18 06:11:09 -0600
commit11da511c784eca003deb90c23570f0873954e0de (patch)
treee14fdd3d5d6345956d67e79ae771d0633d28362b /gmp-6.3.0/mpn/generic/get_d.c
Initial commit.
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+/* mpn_get_d -- limbs to double conversion.
+
+ THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY. THEY'RE ALMOST
+ CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
+ FUTURE GNU MP RELEASES.
+
+Copyright 2003, 2004, 2007, 2009, 2010, 2012, 2018 Free Software
+Foundation, Inc.
+
+This file is part of the GNU MP Library.
+
+The GNU MP Library is free software; you can redistribute it and/or modify
+it under the terms of either:
+
+ * the GNU Lesser General Public License as published by the Free
+ Software Foundation; either version 3 of the License, or (at your
+ option) any later version.
+
+or
+
+ * the GNU General Public License as published by the Free Software
+ Foundation; either version 2 of the License, or (at your option) any
+ later version.
+
+or both in parallel, as here.
+
+The GNU MP Library is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
+for more details.
+
+You should have received copies of the GNU General Public License and the
+GNU Lesser General Public License along with the GNU MP Library. If not,
+see https://www.gnu.org/licenses/. */
+
+#include "config.h"
+
+#if HAVE_FLOAT_H
+#include <float.h> /* for DBL_MANT_DIG and FLT_RADIX */
+#endif
+
+#include "gmp-impl.h"
+#include "longlong.h"
+
+#ifndef _GMP_IEEE_FLOATS
+#define _GMP_IEEE_FLOATS 0
+#endif
+
+/* To force use of the generic C code for testing, put
+ "#define _GMP_IEEE_FLOATS 0" at this point. */
+
+
+/* In alpha gcc prior to 3.4, signed DI comparisons involving constants are
+ rearranged from "x < n" to "x+(-n) < 0", which is of course hopelessly
+ wrong if that addition overflows.
+
+ The workaround here avoids this bug by ensuring n is not a literal constant.
+ Note that this is alpha specific. The offending transformation is/was in
+ alpha.c alpha_emit_conditional_branch() under "We want to use cmpcc/bcc".
+
+ Bizarrely, this happens also with Cray cc on alphaev5-cray-unicosmk2.0.6.X,
+ and has the same solution. Don't know why or how. */
+
+#if HAVE_HOST_CPU_FAMILY_alpha \
+ && ((defined (__GNUC__) && ! __GMP_GNUC_PREREQ(3,4)) \
+ || defined (_CRAY))
+static volatile const long CONST_1024 = 1024;
+static volatile const long CONST_NEG_1023 = -1023;
+static volatile const long CONST_NEG_1022_SUB_53 = -1022 - 53;
+#else
+#define CONST_1024 (1024)
+#define CONST_NEG_1023 (-1023)
+#define CONST_NEG_1022_SUB_53 (-1022 - 53)
+#endif
+
+
+/* Return the value {ptr,size}*2^exp, and negative if sign<0. Must have
+ size>=1, and a non-zero high limb ptr[size-1].
+
+ When we know the fp format, the result is truncated towards zero. This is
+ consistent with other gmp conversions, like mpz_set_f or mpz_set_q, and is
+ easy to implement and test.
+
+ When we do not know the format, such truncation seems much harder. One
+ would need to defeat any rounding mode, including round-up.
+
+ It's felt that GMP is not primarily concerned with hardware floats, and
+ really isn't enhanced by getting involved with hardware rounding modes
+ (which could even be some weird unknown style), so something unambiguous and
+ straightforward is best.
+
+
+ The IEEE code below is the usual case, it knows either a 32-bit or 64-bit
+ limb and is done with shifts and masks. The 64-bit case in particular
+ should come out nice and compact.
+
+ The generic code used to work one bit at a time, which was not only slow,
+ but implicitly relied upon denorms for intermediates, since the lowest bits'
+ weight of a perfectly valid fp number underflows in non-denorm. Therefore,
+ the generic code now works limb-per-limb, initially creating a number x such
+ that 1 <= x <= BASE. (BASE is reached only as result of rounding.) Then
+ x's exponent is scaled with explicit code (not ldexp to avoid libm
+ dependency). It is a tap-dance to avoid underflow or overflow, beware!
+
+
+ Traps:
+
+ Hardware traps for overflow to infinity, underflow to zero, or unsupported
+ denorms may or may not be taken. The IEEE code works bitwise and so
+ probably won't trigger them, the generic code works by float operations and
+ so probably will. This difference might be thought less than ideal, but
+ again its felt straightforward code is better than trying to get intimate
+ with hardware exceptions (of perhaps unknown nature).
+
+
+ Not done:
+
+ mpz_get_d in the past handled size==1 with a cast limb->double. This might
+ still be worthwhile there (for up to the mantissa many bits), but for
+ mpn_get_d here, the cost of applying "exp" to the resulting exponent would
+ probably use up any benefit a cast may have over bit twiddling. Also, if
+ the exponent is pushed into denorm range then bit twiddling is the only
+ option, to ensure the desired truncation is obtained.
+
+
+ Other:
+
+ For reference, note that HPPA 8000, 8200, 8500 and 8600 trap FCNV,UDW,DBL
+ to the kernel for values >= 2^63. This makes it slow, and worse the kernel
+ Linux (what versions?) apparently uses untested code in its trap handling
+ routines, and gets the sign wrong. We don't use such a limb-to-double
+ cast, neither in the IEEE or generic code. */
+
+
+
+#undef FORMAT_RECOGNIZED
+
+double
+mpn_get_d (mp_srcptr up, mp_size_t size, mp_size_t sign, long exp)
+{
+ int lshift, nbits;
+ mp_limb_t x, mhi, mlo;
+
+ ASSERT (size >= 0);
+ ASSERT_MPN (up, size);
+ ASSERT (size == 0 || up[size-1] != 0);
+
+ if (size == 0)
+ return 0.0;
+
+ /* Adjust exp to a radix point just above {up,size}, guarding against
+ overflow. After this exp can of course be reduced to anywhere within
+ the {up,size} region without underflow. */
+ if (UNLIKELY ((unsigned long) (GMP_NUMB_BITS * size)
+ > ((unsigned long) LONG_MAX - exp)))
+ {
+#if _GMP_IEEE_FLOATS
+ goto ieee_infinity;
+#endif
+
+ /* generic */
+ exp = LONG_MAX;
+ }
+ else
+ {
+ exp += GMP_NUMB_BITS * size;
+ }
+
+#if _GMP_IEEE_FLOATS
+ {
+ union ieee_double_extract u;
+
+ up += size;
+
+#if GMP_LIMB_BITS == 64
+ mlo = up[-1];
+ count_leading_zeros (lshift, mlo);
+
+ exp -= (lshift - GMP_NAIL_BITS) + 1;
+ mlo <<= lshift;
+
+ nbits = GMP_LIMB_BITS - lshift;
+
+ if (nbits < 53 && size > 1)
+ {
+ x = up[-2];
+ x <<= GMP_NAIL_BITS;
+ x >>= nbits;
+ mlo |= x;
+ nbits += GMP_NUMB_BITS;
+
+ if (LIMBS_PER_DOUBLE >= 3 && nbits < 53 && size > 2)
+ {
+ x = up[-3];
+ x <<= GMP_NAIL_BITS;
+ x >>= nbits;
+ mlo |= x;
+ nbits += GMP_NUMB_BITS;
+ }
+ }
+ mhi = mlo >> (32 + 11);
+ mlo = mlo >> 11; /* later implicitly truncated to 32 bits */
+#endif
+#if GMP_LIMB_BITS == 32
+ x = *--up;
+ count_leading_zeros (lshift, x);
+
+ exp -= (lshift - GMP_NAIL_BITS) + 1;
+ x <<= lshift;
+ mhi = x >> 11;
+
+ if (lshift < 11) /* FIXME: never true if NUMB < 20 bits */
+ {
+ /* All 20 bits in mhi */
+ mlo = x << 21;
+ /* >= 1 bit in mlo */
+ nbits = GMP_LIMB_BITS - lshift - 21;
+ }
+ else
+ {
+ if (size > 1)
+ {
+ nbits = GMP_LIMB_BITS - lshift;
+
+ x = *--up, size--;
+ x <<= GMP_NAIL_BITS;
+ mhi |= x >> nbits >> 11;
+
+ mlo = x << (GMP_LIMB_BITS - nbits - 11);
+ nbits = nbits + 11 - GMP_NAIL_BITS;
+ }
+ else
+ {
+ mlo = 0;
+ goto done;
+ }
+ }
+
+ /* Now all needed bits in mhi have been accumulated. Add bits to mlo. */
+
+ if (LIMBS_PER_DOUBLE >= 2 && nbits < 32 && size > 1)
+ {
+ x = up[-1];
+ x <<= GMP_NAIL_BITS;
+ x >>= nbits;
+ mlo |= x;
+ nbits += GMP_NUMB_BITS;
+
+ if (LIMBS_PER_DOUBLE >= 3 && nbits < 32 && size > 2)
+ {
+ x = up[-2];
+ x <<= GMP_NAIL_BITS;
+ x >>= nbits;
+ mlo |= x;
+ nbits += GMP_NUMB_BITS;
+
+ if (LIMBS_PER_DOUBLE >= 4 && nbits < 32 && size > 3)
+ {
+ x = up[-3];
+ x <<= GMP_NAIL_BITS;
+ x >>= nbits;
+ mlo |= x;
+ nbits += GMP_NUMB_BITS;
+ }
+ }
+ }
+
+ done:;
+
+#endif
+ if (UNLIKELY (exp >= CONST_1024))
+ {
+ /* overflow, return infinity */
+ ieee_infinity:
+ mhi = 0;
+ mlo = 0;
+ exp = 1024;
+ }
+ else if (UNLIKELY (exp <= CONST_NEG_1023))
+ {
+ int rshift;
+
+ if (LIKELY (exp <= CONST_NEG_1022_SUB_53))
+ return 0.0; /* denorm underflows to zero */
+
+ rshift = -1022 - exp;
+ ASSERT (rshift > 0 && rshift < 53);
+#if GMP_LIMB_BITS > 53
+ mlo >>= rshift;
+ mhi = mlo >> 32;
+#else
+ if (rshift >= 32)
+ {
+ mlo = mhi;
+ mhi = 0;
+ rshift -= 32;
+ }
+ lshift = GMP_LIMB_BITS - rshift;
+ mlo = (mlo >> rshift) | (rshift == 0 ? 0 : mhi << lshift);
+ mhi >>= rshift;
+#endif
+ exp = -1023;
+ }
+ u.s.manh = mhi;
+ u.s.manl = mlo;
+ u.s.exp = exp + 1023;
+ u.s.sig = (sign < 0);
+ return u.d;
+ }
+#define FORMAT_RECOGNIZED 1
+#endif
+
+#if HAVE_DOUBLE_VAX_D
+ {
+ union double_extract u;
+
+ up += size;
+
+ mhi = up[-1];
+
+ count_leading_zeros (lshift, mhi);
+ exp -= lshift;
+ mhi <<= lshift;
+
+ mlo = 0;
+ if (size > 1)
+ {
+ mlo = up[-2];
+ if (lshift != 0)
+ mhi += mlo >> (GMP_LIMB_BITS - lshift);
+ mlo <<= lshift;
+
+ if (size > 2 && lshift > 8)
+ {
+ x = up[-3];
+ mlo += x >> (GMP_LIMB_BITS - lshift);
+ }
+ }
+
+ if (UNLIKELY (exp >= 128))
+ {
+ /* overflow, return maximum number */
+ mhi = 0xffffffff;
+ mlo = 0xffffffff;
+ exp = 127;
+ }
+ else if (UNLIKELY (exp < -128))
+ {
+ return 0.0; /* underflows to zero */
+ }
+
+ u.s.man3 = mhi >> 24; /* drop msb, since implicit */
+ u.s.man2 = mhi >> 8;
+ u.s.man1 = (mhi << 8) + (mlo >> 24);
+ u.s.man0 = mlo >> 8;
+ u.s.exp = exp + 128;
+ u.s.sig = sign < 0;
+ return u.d;
+ }
+#define FORMAT_RECOGNIZED 1
+#endif
+
+#if ! FORMAT_RECOGNIZED
+
+#if !defined(GMP_DBL_MANT_BITS)
+#if defined(DBL_MANT_DIG) && FLT_RADIX == 2
+#define GMP_DBL_MANT_BITS DBL_MANT_DIG
+#else
+/* FIXME: Chose a smarter default value. */
+#define GMP_DBL_MANT_BITS (16 * sizeof (double))
+#endif
+#endif
+
+ { /* Non-IEEE or strange limb size, generically convert
+ GMP_DBL_MANT_BITS bits. */
+ mp_limb_t l;
+ int m;
+ mp_size_t i;
+ double d, weight;
+ unsigned long uexp;
+
+ /* First generate an fp number disregarding exp, instead keeping things
+ within the numb base factor from 1, which should prevent overflow and
+ underflow even for the most exponent limited fp formats. */
+ i = size - 1;
+ l = up[i];
+ count_leading_zeros (m, l);
+ m = m + GMP_DBL_MANT_BITS - GMP_LIMB_BITS;
+ if (m < 0)
+ l &= GMP_NUMB_MAX << -m;
+ d = l;
+ for (weight = 1/MP_BASE_AS_DOUBLE; m > 0 && --i >= 0;)
+ {
+ l = up[i];
+ m -= GMP_NUMB_BITS;
+ if (m < 0)
+ l &= GMP_NUMB_MAX << -m;
+ d += l * weight;
+ weight /= MP_BASE_AS_DOUBLE;
+ if (weight == 0)
+ break;
+ }
+
+ /* Now apply exp. */
+ exp -= GMP_NUMB_BITS;
+ if (exp > 0)
+ {
+ weight = 2.0;
+ uexp = exp;
+ }
+ else
+ {
+ weight = 0.5;
+ uexp = NEG_CAST (unsigned long, exp);
+ }
+#if 1
+ /* Square-and-multiply exponentiation. */
+ if (uexp & 1)
+ d *= weight;
+ while (uexp >>= 1)
+ {
+ weight *= weight;
+ if (uexp & 1)
+ d *= weight;
+ }
+#else
+ /* Plain exponentiation. */
+ while (uexp > 0)
+ {
+ d *= weight;
+ uexp--;
+ }
+#endif
+
+ return sign >= 0 ? d : -d;
+ }
+#endif
+}