mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-15 17:40:06 +00:00
a1b02ae763
Apply the following spelling fixes: $ git grep -F -l 'relevent' | xargs sed -i 's/relevent/relevant/g' $ git grep -F -l 'checked fot' | xargs sed -i 's/checked fot/checked for/g' $ git grep -F -l "could't" | xargs sed -i "s/could't/couldn't/g" $ git grep -F -l 'wheter' | grep -Fv ChangeLog.old | xargs sed -i 's/wheter/whether/g' $ git grep -F -l 'neccessary' | grep -Fv ChangeLog.old | xargs sed -i 's/neccessary/necessary/g' $ git grep -F -l 'ouput' | xargs sed -i 's/ouput/output/g' $ git grep -F -w -l 'iput' | xargs sed -i 's/iput/input/g' This is inspired by a gnulib bug report at https://lists.gnu.org/archive/html/bug-gnulib/2019-01/msg00081.html * argp/argp-help.c: Fix typo in comment. * misc/sys/cdefs.h: Likewise. * posix/regexec.c (sift_states_iter_mb): Likewise. * socket/sockatmark.c: Likewise. * socket/sys/socket.h: Likewise. * sysdeps/ia64/fpu/libm_sincos_large.S: Likewise. * sysdeps/ia64/fpu/libm_sincosl.S: Likewise. * sysdeps/ia64/fpu/s_cosl.S: Likewise. * sysdeps/ieee754/dbl-64/k_rem_pio2.c: Likewise. * sysdeps/unix/sockatmark.c: Likewise. * time/strptime_l.c: Likewise.
373 lines
9.9 KiB
C
373 lines
9.9 KiB
C
/* @(#)k_rem_pio2.c 5.1 93/09/24 */
|
|
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*/
|
|
|
|
#if defined(LIBM_SCCS) && !defined(lint)
|
|
static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $";
|
|
#endif
|
|
|
|
/*
|
|
* __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
|
|
* double x[],y[]; int e0,nx,prec; int ipio2[];
|
|
*
|
|
* __kernel_rem_pio2 return the last three digits of N with
|
|
* y = x - N*pi/2
|
|
* so that |y| < pi/2.
|
|
*
|
|
* The method is to compute the integer (mod 8) and fraction parts of
|
|
* (2/pi)*x without doing the full multiplication. In general we
|
|
* skip the part of the product that are known to be a huge integer (
|
|
* more accurately, = 0 mod 8 ). Thus the number of operations are
|
|
* independent of the exponent of the input.
|
|
*
|
|
* (2/pi) is represented by an array of 24-bit integers in ipio2[].
|
|
*
|
|
* Input parameters:
|
|
* x[] The input value (must be positive) is broken into nx
|
|
* pieces of 24-bit integers in double precision format.
|
|
* x[i] will be the i-th 24 bit of x. The scaled exponent
|
|
* of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
|
|
* match x's up to 24 bits.
|
|
*
|
|
* Example of breaking a double positive z into x[0]+x[1]+x[2]:
|
|
* e0 = ilogb(z)-23
|
|
* z = scalbn(z,-e0)
|
|
* for i = 0,1,2
|
|
* x[i] = floor(z)
|
|
* z = (z-x[i])*2**24
|
|
*
|
|
*
|
|
* y[] output result in an array of double precision numbers.
|
|
* The dimension of y[] is:
|
|
* 24-bit precision 1
|
|
* 53-bit precision 2
|
|
* 64-bit precision 2
|
|
* 113-bit precision 3
|
|
* The actual value is the sum of them. Thus for 113-bit
|
|
* precision, one may have to do something like:
|
|
*
|
|
* long double t,w,r_head, r_tail;
|
|
* t = (long double)y[2] + (long double)y[1];
|
|
* w = (long double)y[0];
|
|
* r_head = t+w;
|
|
* r_tail = w - (r_head - t);
|
|
*
|
|
* e0 The exponent of x[0]
|
|
*
|
|
* nx dimension of x[]
|
|
*
|
|
* prec an integer indicating the precision:
|
|
* 0 24 bits (single)
|
|
* 1 53 bits (double)
|
|
* 2 64 bits (extended)
|
|
* 3 113 bits (quad)
|
|
*
|
|
* ipio2[]
|
|
* integer array, contains the (24*i)-th to (24*i+23)-th
|
|
* bit of 2/pi after binary point. The corresponding
|
|
* floating value is
|
|
*
|
|
* ipio2[i] * 2^(-24(i+1)).
|
|
*
|
|
* External function:
|
|
* double scalbn(), floor();
|
|
*
|
|
*
|
|
* Here is the description of some local variables:
|
|
*
|
|
* jk jk+1 is the initial number of terms of ipio2[] needed
|
|
* in the computation. The recommended value is 2,3,4,
|
|
* 6 for single, double, extended,and quad.
|
|
*
|
|
* jz local integer variable indicating the number of
|
|
* terms of ipio2[] used.
|
|
*
|
|
* jx nx - 1
|
|
*
|
|
* jv index for pointing to the suitable ipio2[] for the
|
|
* computation. In general, we want
|
|
* ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
|
|
* is an integer. Thus
|
|
* e0-3-24*jv >= 0 or (e0-3)/24 >= jv
|
|
* Hence jv = max(0,(e0-3)/24).
|
|
*
|
|
* jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
|
|
*
|
|
* q[] double array with integral value, representing the
|
|
* 24-bits chunk of the product of x and 2/pi.
|
|
*
|
|
* q0 the corresponding exponent of q[0]. Note that the
|
|
* exponent for q[i] would be q0-24*i.
|
|
*
|
|
* PIo2[] double precision array, obtained by cutting pi/2
|
|
* into 24 bits chunks.
|
|
*
|
|
* f[] ipio2[] in floating point
|
|
*
|
|
* iq[] integer array by breaking up q[] in 24-bits chunk.
|
|
*
|
|
* fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
|
|
*
|
|
* ih integer. If >0 it indicates q[] is >= 0.5, hence
|
|
* it also indicates the *sign* of the result.
|
|
*
|
|
*/
|
|
|
|
|
|
/*
|
|
* Constants:
|
|
* The hexadecimal values are the intended ones for the following
|
|
* constants. The decimal values may be used, provided that the
|
|
* compiler will convert from decimal to binary accurately enough
|
|
* to produce the hexadecimal values shown.
|
|
*/
|
|
|
|
#include <math.h>
|
|
#include <math-narrow-eval.h>
|
|
#include <math_private.h>
|
|
#include <libc-diag.h>
|
|
|
|
static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
|
|
|
|
static const double PIo2[] = {
|
|
1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
|
|
7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
|
|
5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
|
|
3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
|
|
1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
|
|
1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
|
|
2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
|
|
2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
|
|
};
|
|
|
|
static const double
|
|
zero = 0.0,
|
|
one = 1.0,
|
|
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
|
|
twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
|
|
|
|
int
|
|
__kernel_rem_pio2 (double *x, double *y, int e0, int nx, int prec,
|
|
const int32_t *ipio2)
|
|
{
|
|
int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih;
|
|
double z, fw, f[20], fq[20], q[20];
|
|
|
|
/* initialize jk*/
|
|
jk = init_jk[prec];
|
|
jp = jk;
|
|
|
|
/* determine jx,jv,q0, note that 3>q0 */
|
|
jx = nx - 1;
|
|
jv = (e0 - 3) / 24; if (jv < 0)
|
|
jv = 0;
|
|
q0 = e0 - 24 * (jv + 1);
|
|
|
|
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
|
|
j = jv - jx; m = jx + jk;
|
|
for (i = 0; i <= m; i++, j++)
|
|
f[i] = (j < 0) ? zero : (double) ipio2[j];
|
|
|
|
/* compute q[0],q[1],...q[jk] */
|
|
for (i = 0; i <= jk; i++)
|
|
{
|
|
for (j = 0, fw = 0.0; j <= jx; j++)
|
|
fw += x[j] * f[jx + i - j];
|
|
q[i] = fw;
|
|
}
|
|
|
|
jz = jk;
|
|
recompute:
|
|
/* distill q[] into iq[] reversingly */
|
|
for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--)
|
|
{
|
|
fw = (double) ((int32_t) (twon24 * z));
|
|
iq[i] = (int32_t) (z - two24 * fw);
|
|
z = q[j - 1] + fw;
|
|
}
|
|
|
|
/* compute n */
|
|
z = __scalbn (z, q0); /* actual value of z */
|
|
z -= 8.0 * floor (z * 0.125); /* trim off integer >= 8 */
|
|
n = (int32_t) z;
|
|
z -= (double) n;
|
|
ih = 0;
|
|
if (q0 > 0) /* need iq[jz-1] to determine n */
|
|
{
|
|
i = (iq[jz - 1] >> (24 - q0)); n += i;
|
|
iq[jz - 1] -= i << (24 - q0);
|
|
ih = iq[jz - 1] >> (23 - q0);
|
|
}
|
|
else if (q0 == 0)
|
|
ih = iq[jz - 1] >> 23;
|
|
else if (z >= 0.5)
|
|
ih = 2;
|
|
|
|
if (ih > 0) /* q > 0.5 */
|
|
{
|
|
n += 1; carry = 0;
|
|
for (i = 0; i < jz; i++) /* compute 1-q */
|
|
{
|
|
j = iq[i];
|
|
if (carry == 0)
|
|
{
|
|
if (j != 0)
|
|
{
|
|
carry = 1; iq[i] = 0x1000000 - j;
|
|
}
|
|
}
|
|
else
|
|
iq[i] = 0xffffff - j;
|
|
}
|
|
if (q0 > 0) /* rare case: chance is 1 in 12 */
|
|
{
|
|
switch (q0)
|
|
{
|
|
case 1:
|
|
iq[jz - 1] &= 0x7fffff; break;
|
|
case 2:
|
|
iq[jz - 1] &= 0x3fffff; break;
|
|
}
|
|
}
|
|
if (ih == 2)
|
|
{
|
|
z = one - z;
|
|
if (carry != 0)
|
|
z -= __scalbn (one, q0);
|
|
}
|
|
}
|
|
|
|
/* check if recomputation is needed */
|
|
if (z == zero)
|
|
{
|
|
j = 0;
|
|
for (i = jz - 1; i >= jk; i--)
|
|
j |= iq[i];
|
|
if (j == 0) /* need recomputation */
|
|
{
|
|
/* On s390x gcc 6.1 -O3 produces the warning "array subscript is below
|
|
array bounds [-Werror=array-bounds]". Only __ieee754_rem_pio2l
|
|
calls __kernel_rem_pio2 for normal numbers and |x| > pi/4 in case
|
|
of ldbl-96 and |x| > 3pi/4 in case of ldbl-128[ibm].
|
|
Thus x can't be zero and ipio2 is not zero, too. Thus not all iq[]
|
|
values can't be zero. */
|
|
DIAG_PUSH_NEEDS_COMMENT;
|
|
DIAG_IGNORE_NEEDS_COMMENT (6.1, "-Warray-bounds");
|
|
for (k = 1; iq[jk - k] == 0; k++)
|
|
; /* k = no. of terms needed */
|
|
DIAG_POP_NEEDS_COMMENT;
|
|
|
|
for (i = jz + 1; i <= jz + k; i++) /* add q[jz+1] to q[jz+k] */
|
|
{
|
|
f[jx + i] = (double) ipio2[jv + i];
|
|
for (j = 0, fw = 0.0; j <= jx; j++)
|
|
fw += x[j] * f[jx + i - j];
|
|
q[i] = fw;
|
|
}
|
|
jz += k;
|
|
goto recompute;
|
|
}
|
|
}
|
|
|
|
/* chop off zero terms */
|
|
if (z == 0.0)
|
|
{
|
|
jz -= 1; q0 -= 24;
|
|
while (iq[jz] == 0)
|
|
{
|
|
jz--; q0 -= 24;
|
|
}
|
|
}
|
|
else /* break z into 24-bit if necessary */
|
|
{
|
|
z = __scalbn (z, -q0);
|
|
if (z >= two24)
|
|
{
|
|
fw = (double) ((int32_t) (twon24 * z));
|
|
iq[jz] = (int32_t) (z - two24 * fw);
|
|
jz += 1; q0 += 24;
|
|
iq[jz] = (int32_t) fw;
|
|
}
|
|
else
|
|
iq[jz] = (int32_t) z;
|
|
}
|
|
|
|
/* convert integer "bit" chunk to floating-point value */
|
|
fw = __scalbn (one, q0);
|
|
for (i = jz; i >= 0; i--)
|
|
{
|
|
q[i] = fw * (double) iq[i]; fw *= twon24;
|
|
}
|
|
|
|
/* compute PIo2[0,...,jp]*q[jz,...,0] */
|
|
for (i = jz; i >= 0; i--)
|
|
{
|
|
for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++)
|
|
fw += PIo2[k] * q[i + k];
|
|
fq[jz - i] = fw;
|
|
}
|
|
|
|
/* compress fq[] into y[] */
|
|
switch (prec)
|
|
{
|
|
case 0:
|
|
fw = 0.0;
|
|
for (i = jz; i >= 0; i--)
|
|
fw += fq[i];
|
|
y[0] = (ih == 0) ? fw : -fw;
|
|
break;
|
|
case 1:
|
|
case 2:;
|
|
double fv = 0.0;
|
|
for (i = jz; i >= 0; i--)
|
|
fv = math_narrow_eval (fv + fq[i]);
|
|
y[0] = (ih == 0) ? fv : -fv;
|
|
/* GCC mainline (to be GCC 9), as of 2018-05-22 on i686, warns
|
|
that fq[0] may be used uninitialized. This is not possible
|
|
because jz is always nonnegative when the above loop
|
|
initializing fq is executed, because the result is never zero
|
|
to full precision (this function is not called for zero
|
|
arguments). */
|
|
DIAG_PUSH_NEEDS_COMMENT;
|
|
DIAG_IGNORE_NEEDS_COMMENT (9, "-Wmaybe-uninitialized");
|
|
fv = math_narrow_eval (fq[0] - fv);
|
|
DIAG_POP_NEEDS_COMMENT;
|
|
for (i = 1; i <= jz; i++)
|
|
fv = math_narrow_eval (fv + fq[i]);
|
|
y[1] = (ih == 0) ? fv : -fv;
|
|
break;
|
|
case 3: /* painful */
|
|
for (i = jz; i > 0; i--)
|
|
{
|
|
double fv = math_narrow_eval (fq[i - 1] + fq[i]);
|
|
fq[i] += fq[i - 1] - fv;
|
|
fq[i - 1] = fv;
|
|
}
|
|
for (i = jz; i > 1; i--)
|
|
{
|
|
double fv = math_narrow_eval (fq[i - 1] + fq[i]);
|
|
fq[i] += fq[i - 1] - fv;
|
|
fq[i - 1] = fv;
|
|
}
|
|
for (fw = 0.0, i = jz; i >= 2; i--)
|
|
fw += fq[i];
|
|
if (ih == 0)
|
|
{
|
|
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
|
|
}
|
|
else
|
|
{
|
|
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
|
|
}
|
|
}
|
|
return n & 7;
|
|
}
|