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Diffstat (limited to 'sysdeps/ieee754/dbl-64/k_rem_pio2.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/k_rem_pio2.c | 362 |
1 files changed, 0 insertions, 362 deletions
diff --git a/sysdeps/ieee754/dbl-64/k_rem_pio2.c b/sysdeps/ieee754/dbl-64/k_rem_pio2.c deleted file mode 100644 index 2b5add6976..0000000000 --- a/sysdeps/ieee754/dbl-64/k_rem_pio2.c +++ /dev/null @@ -1,362 +0,0 @@ -/* @(#)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[] ouput 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_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; - fv = math_narrow_eval (fq[0] - fv); - 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; -} |