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diff --git a/plugins/supereq/nsfft-1.00/ooura/pi_fft.c b/plugins/supereq/nsfft-1.00/ooura/pi_fft.c
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+++ b/plugins/supereq/nsfft-1.00/ooura/pi_fft.c
@@ -0,0 +1,1616 @@
+/*
+---- calculation of PI(= 3.14159...) using FFT ----
+ by T.Ooura, ver. LG1.1.2-MP1.5a Sep. 2001.
+
+This is a test program to estimate the performance of
+the FFT routines: fft*g.c.
+
+Example compilation:
+ GNU : gcc -O6 -ffast-math pi_fft.c fftsg.c -lm -o pi_fftsg
+ SUN : cc -fast -xO5 pi_fft.c fft8g.c -lm -o pi_fft8g
+ Microsoft: cl /O2 /G6 pi_fft.c fft4g.c /Fepi_fft4g.exe
+ ...
+ etc.
+*/
+
+/* Please check the following macros before compiling */
+#ifndef DBL_ERROR_MARGIN
+#define DBL_ERROR_MARGIN 0.3 /* must be < 0.5 */
+#endif
+
+
+#include <math.h>
+#include <limits.h>
+#include <float.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <time.h>
+
+
+void mp_load_0(int n, int radix, int out[]);
+void mp_load_1(int n, int radix, int out[]);
+void mp_copy(int n, int radix, int in[], int out[]);
+void mp_round(int n, int radix, int m, int inout[]);
+int mp_cmp(int n, int radix, int in1[], int in2[]);
+void mp_add(int n, int radix, int in1[], int in2[], int out[]);
+void mp_sub(int n, int radix, int in1[], int in2[], int out[]);
+void mp_imul(int n, int radix, int in1[], int in2, int out[]);
+int mp_idiv(int n, int radix, int in1[], int in2, int out[]);
+void mp_idiv_2(int n, int radix, int in[], int out[]);
+double mp_mul_radix_test(int n, int radix, int nfft,
+ double tmpfft[], int ip[], double w[]);
+void mp_mul(int n, int radix, int in1[], int in2[], int out[],
+ int tmp[], int nfft, double tmp1fft[], double tmp2fft[],
+ double tmp3fft[], int ip[], double w[]);
+void mp_squ(int n, int radix, int in[], int out[], int tmp[],
+ int nfft, double tmp1fft[], double tmp2fft[],
+ int ip[], double w[]);
+void mp_mulh(int n, int radix, int in1[], int in2[], int out[],
+ int nfft, double in1fft[], double outfft[],
+ int ip[], double w[]);
+void mp_squh(int n, int radix, int in[], int out[],
+ int nfft, double inoutfft[], int ip[], double w[]);
+int mp_inv(int n, int radix, int in[], int out[],
+ int tmp1[], int tmp2[], int nfft,
+ double tmp1fft[], double tmp2fft[], int ip[], double w[]);
+int mp_sqrt(int n, int radix, int in[], int out[],
+ int tmp1[], int tmp2[], int nfft,
+ double tmp1fft[], double tmp2fft[], int ip[], double w[]);
+void mp_sprintf(int n, int log10_radix, int in[], char out[]);
+void mp_sscanf(int n, int log10_radix, char in[], int out[]);
+void mp_fprintf(int n, int log10_radix, int in[], FILE *fout);
+
+
+int main()
+{
+ int nfft, log2_nfft, radix, log10_radix, n, npow, nprc;
+ double err, d_time, n_op;
+ int *a, *b, *c, *e, *i1, *i2, *ip;
+ double *d1, *d2, *d3, *w;
+ time_t t_1, t_2;
+ FILE *f_log, *f_out;
+
+ f_log = fopen("pi.log", "w");
+ printf("PI calculation to estimate the FFT benchmarks\n");
+ fprintf(f_log, "PI calculation to estimate the FFT benchmarks\n");
+ printf("length of FFT =?\n");
+ scanf("%d", &nfft);
+
+ printf("initializing...\n");
+ for (log2_nfft = 1; (1 << log2_nfft) < nfft; log2_nfft++);
+ nfft = 1 << log2_nfft;
+ n = nfft + 2;
+ ip = (int *) malloc((3 + (int) sqrt(0.5 * nfft)) * sizeof(int));
+ w = (double *) malloc(nfft / 2 * sizeof(double));
+ a = (int *) malloc((n + 2) * sizeof(int));
+ b = (int *) malloc((n + 2) * sizeof(int));
+ c = (int *) malloc((n + 2) * sizeof(int));
+ e = (int *) malloc((n + 2) * sizeof(int));
+ i1 = (int *) malloc((n + 2) * sizeof(int));
+ i2 = (int *) malloc((n + 2) * sizeof(int));
+ d1 = (double *) malloc((nfft + 2) * sizeof(double));
+ d2 = (double *) malloc((nfft + 2) * sizeof(double));
+ d3 = (double *) malloc((nfft + 2) * sizeof(double));
+ if (d3 == NULL) {
+ printf("Allocation Failure!\n");
+ exit(1);
+ }
+ ip[0] = 0;
+ /* ---- radix test ---- */
+ log10_radix = 1;
+ radix = 10;
+ err = mp_mul_radix_test(n, radix, nfft, d1, ip, w);
+ err += DBL_EPSILON * (n * radix * radix / 4);
+ while (100 * err < DBL_ERROR_MARGIN && radix <= INT_MAX / 20) {
+ err *= 100;
+ log10_radix++;
+ radix *= 10;
+ }
+ printf("nfft= %d\nradix= %d\nerror_margin= %g\n", nfft, radix, err);
+ fprintf(f_log, "nfft= %d\nradix= %d\nerror_margin= %g\n", nfft, radix, err);
+ printf("calculating %d digits of PI...\n", log10_radix * (n - 2));
+ fprintf(f_log, "calculating %d digits of PI...\n", log10_radix * (n - 2));
+ /* ---- time check ---- */
+ time(&t_1);
+ /*
+ * ---- a formula based on the AGM (Arithmetic-Geometric Mean) ----
+ * c = sqrt(0.125);
+ * a = 1 + 3 * c;
+ * b = sqrt(a);
+ * e = b - 0.625;
+ * b = 2 * b;
+ * c = e - c;
+ * a = a + e;
+ * npow = 4;
+ * do {
+ * npow = 2 * npow;
+ * e = (a + b) / 2;
+ * b = sqrt(a * b);
+ * e = e - b;
+ * b = 2 * b;
+ * c = c - e;
+ * a = e + b;
+ * } while (e > SQRT_SQRT_EPSILON);
+ * e = e * e / 4;
+ * a = a + b;
+ * pi = (a * a - e - e / 2) / (a * c - e) / npow;
+ * ---- modification ----
+ * This is a modified version of Gauss-Legendre formula
+ * (by T.Ooura). It is faster than original version.
+ * ---- reference ----
+ * 1. E.Salamin,
+ * Computation of PI Using Arithmetic-Geometric Mean,
+ * Mathematics of Computation, Vol.30 1976.
+ * 2. R.P.Brent,
+ * Fast Multiple-Precision Evaluation of Elementary Functions,
+ * J. ACM 23 1976.
+ * 3. D.Takahasi, Y.Kanada,
+ * Calculation of PI to 51.5 Billion Decimal Digits on
+ * Distributed Memoriy Parallel Processors,
+ * Transactions of Information Processing Society of Japan,
+ * Vol.39 No.7 1998.
+ * 4. T.Ooura,
+ * Improvement of the PI Calculation Algorithm and
+ * Implementation of Fast Multiple-Precision Computation,
+ * Information Processing Society of Japan SIG Notes,
+ * 98-HPC-74, 1998.
+ */
+ /* ---- c = sqrt(0.125) ---- */
+ mp_sscanf(n, log10_radix, "0.125", a);
+ mp_sqrt(n, radix, a, c, i1, i2, nfft, d1, d2, ip, w);
+ /* ---- a = 1 + 3 * c ---- */
+ mp_imul(n, radix, c, 3, e);
+ mp_sscanf(n, log10_radix, "1", a);
+ mp_add(n, radix, a, e, a);
+ /* ---- b = sqrt(a) ---- */
+ mp_sqrt(n, radix, a, b, i1, i2, nfft, d1, d2, ip, w);
+ /* ---- e = b - 0.625 ---- */
+ mp_sscanf(n, log10_radix, "0.625", e);
+ mp_sub(n, radix, b, e, e);
+ /* ---- b = 2 * b ---- */
+ mp_add(n, radix, b, b, b);
+ /* ---- c = e - c ---- */
+ mp_sub(n, radix, e, c, c);
+ /* ---- a = a + e ---- */
+ mp_add(n, radix, a, e, a);
+ printf("AGM iteration\n");
+ fprintf(f_log, "AGM iteration\n");
+ npow = 4;
+ do {
+ npow *= 2;
+ /* ---- e = (a + b) / 2 ---- */
+ mp_add(n, radix, a, b, e);
+ mp_idiv_2(n, radix, e, e);
+ /* ---- b = sqrt(a * b) ---- */
+ mp_mul(n, radix, a, b, a, i1, nfft, d1, d2, d3, ip, w);
+ mp_sqrt(n, radix, a, b, i1, i2, nfft, d1, d2, ip, w);
+ /* ---- e = e - b ---- */
+ mp_sub(n, radix, e, b, e);
+ /* ---- b = 2 * b ---- */
+ mp_add(n, radix, b, b, b);
+ /* ---- c = c - e ---- */
+ mp_sub(n, radix, c, e, c);
+ /* ---- a = e + b ---- */
+ mp_add(n, radix, e, b, a);
+ /* ---- convergence check ---- */
+ nprc = -e[1];
+ if (e[0] == 0) {
+ nprc = n;
+ }
+ printf("precision= %d\n", 4 * nprc * log10_radix);
+ fprintf(f_log, "precision= %d\n", 4 * nprc * log10_radix);
+ } while (4 * nprc <= n);
+ /* ---- e = e * e / 4 (half precision) ---- */
+ mp_idiv_2(n, radix, e, e);
+ mp_squh(n, radix, e, e, nfft, d1, ip, w);
+ /* ---- a = a + b ---- */
+ mp_add(n, radix, a, b, a);
+ /* ---- a = (a * a - e - e / 2) / (a * c - e) / npow ---- */
+ mp_mul(n, radix, a, c, c, i1, nfft, d1, d2, d3, ip, w);
+ mp_sub(n, radix, c, e, c);
+ mp_inv(n, radix, c, b, i1, i2, nfft, d1, d2, ip, w);
+ mp_squ(n, radix, a, a, i1, nfft, d1, d2, ip, w);
+ mp_sub(n, radix, a, e, a);
+ mp_idiv_2(n, radix, e, e);
+ mp_sub(n, radix, a, e, a);
+ mp_mul(n, radix, a, b, a, i1, nfft, d1, d2, d3, ip, w);
+ mp_idiv(n, radix, a, npow, a);
+ /* ---- time check ---- */
+ time(&t_2);
+ /* ---- output ---- */
+ f_out = fopen("pi.dat", "w");
+ printf("writing pi.dat...\n");
+ mp_fprintf(n - 1, log10_radix, a, f_out);
+ fclose(f_out);
+ free(d3);
+ free(d2);
+ free(d1);
+ free(i2);
+ free(i1);
+ free(e);
+ free(c);
+ free(b);
+ free(a);
+ free(w);
+ free(ip);
+ /* ---- benchmark ---- */
+ n_op = 50.0 * nfft * log2_nfft * log2_nfft;
+ printf("floating point operation: %g op.\n", n_op);
+ fprintf(f_log, "floating point operation: %g op.\n", n_op);
+ /* ---- difftime ---- */
+ d_time = difftime(t_2, t_1);
+ printf("execution time: %g sec. (real time)\n", d_time);
+ fprintf(f_log, "execution time: %g sec. (real time)\n", d_time);
+ fclose(f_log);
+ return 0;
+}
+
+
+/* -------- multiple precision routines -------- */
+
+
+#include <math.h>
+#include <float.h>
+#include <stdio.h>
+
+/* ---- floating point format ----
+ data := data[0] * pow(radix, data[1]) *
+ (data[2] + data[3]/radix + data[4]/radix/radix + ...),
+ data[0] : sign (1;data>0, -1;data<0, 0;data==0)
+ data[1] : exponent (0;data==0)
+ data[2...n+1] : digits
+ ---- function prototypes ----
+ void mp_load_0(int n, int radix, int out[]);
+ void mp_load_1(int n, int radix, int out[]);
+ void mp_copy(int n, int radix, int in[], int out[]);
+ void mp_round(int n, int radix, int m, int inout[]);
+ int mp_cmp(int n, int radix, int in1[], int in2[]);
+ void mp_add(int n, int radix, int in1[], int in2[], int out[]);
+ void mp_sub(int n, int radix, int in1[], int in2[], int out[]);
+ void mp_imul(int n, int radix, int in1[], int in2, int out[]);
+ int mp_idiv(int n, int radix, int in1[], int in2, int out[]);
+ void mp_idiv_2(int n, int radix, int in[], int out[]);
+ double mp_mul_radix_test(int n, int radix, int nfft,
+ double tmpfft[], int ip[], double w[]);
+ void mp_mul(int n, int radix, int in1[], int in2[], int out[],
+ int tmp[], int nfft, double tmp1fft[], double tmp2fft[],
+ double tmp3fft[], int ip[], double w[]);
+ void mp_squ(int n, int radix, int in[], int out[], int tmp[],
+ int nfft, double tmp1fft[], double tmp2fft[],
+ int ip[], double w[]);
+ void mp_mulh(int n, int radix, int in1[], int in2[], int out[],
+ int nfft, double in1fft[], double outfft[],
+ int ip[], double w[]);
+ void mp_squh(int n, int radix, int in[], int out[],
+ int nfft, double inoutfft[], int ip[], double w[]);
+ int mp_inv(int n, int radix, int in[], int out[],
+ int tmp1[], int tmp2[], int nfft,
+ double tmp1fft[], double tmp2fft[], int ip[], double w[]);
+ int mp_sqrt(int n, int radix, int in[], int out[],
+ int tmp1[], int tmp2[], int nfft,
+ double tmp1fft[], double tmp2fft[], int ip[], double w[]);
+ void mp_sprintf(int n, int log10_radix, int in[], char out[]);
+ void mp_sscanf(int n, int log10_radix, char in[], int out[]);
+ void mp_fprintf(int n, int log10_radix, int in[], FILE *fout);
+ ----
+*/
+
+
+/* -------- mp_load routines -------- */
+
+
+void mp_load_0(int n, int radix, int out[])
+{
+ int j;
+
+ for (j = 0; j <= n + 1; j++) {
+ out[j] = 0;
+ }
+}
+
+
+void mp_load_1(int n, int radix, int out[])
+{
+ int j;
+
+ out[0] = 1;
+ out[1] = 0;
+ out[2] = 1;
+ for (j = 3; j <= n + 1; j++) {
+ out[j] = 0;
+ }
+}
+
+
+void mp_copy(int n, int radix, int in[], int out[])
+{
+ int j;
+
+ for (j = 0; j <= n + 1; j++) {
+ out[j] = in[j];
+ }
+}
+
+
+void mp_round(int n, int radix, int m, int inout[])
+{
+ int j, x;
+
+ if (m < n) {
+ for (j = n + 1; j > m + 2; j--) {
+ inout[j] = 0;
+ }
+ x = 2 * inout[m + 2];
+ inout[m + 2] = 0;
+ if (x >= radix) {
+ for (j = m + 1; j >= 2; j--) {
+ x = inout[j] + 1;
+ if (x < radix) {
+ inout[j] = x;
+ break;
+ }
+ inout[j] = 0;
+ }
+ if (x >= radix) {
+ inout[2] = 1;
+ inout[1]++;
+ }
+ }
+ }
+}
+
+
+/* -------- mp_add routines -------- */
+
+
+int mp_cmp(int n, int radix, int in1[], int in2[])
+{
+ int mp_unsgn_cmp(int n, int in1[], int in2[]);
+
+ if (in1[0] > in2[0]) {
+ return 1;
+ } else if (in1[0] < in2[0]) {
+ return -1;
+ }
+ return in1[0] * mp_unsgn_cmp(n, &in1[1], &in2[1]);
+}
+
+
+void mp_add(int n, int radix, int in1[], int in2[], int out[])
+{
+ int mp_unsgn_cmp(int n, int in1[], int in2[]);
+ int mp_unexp_add(int n, int radix, int expdif,
+ int in1[], int in2[], int out[]);
+ int mp_unexp_sub(int n, int radix, int expdif,
+ int in1[], int in2[], int out[]);
+ int outsgn, outexp, expdif;
+
+ expdif = in1[1] - in2[1];
+ outexp = in1[1];
+ if (expdif < 0) {
+ outexp = in2[1];
+ }
+ outsgn = in1[0] * in2[0];
+ if (outsgn >= 0) {
+ if (outsgn > 0) {
+ outsgn = in1[0];
+ } else {
+ outsgn = in1[0] + in2[0];
+ outexp = in1[1] + in2[1];
+ expdif = 0;
+ }
+ if (expdif >= 0) {
+ outexp += mp_unexp_add(n, radix, expdif,
+ &in1[2], &in2[2], &out[2]);
+ } else {
+ outexp += mp_unexp_add(n, radix, -expdif,
+ &in2[2], &in1[2], &out[2]);
+ }
+ } else {
+ outsgn = mp_unsgn_cmp(n, &in1[1], &in2[1]);
+ if (outsgn >= 0) {
+ expdif = mp_unexp_sub(n, radix, expdif,
+ &in1[2], &in2[2], &out[2]);
+ } else {
+ expdif = mp_unexp_sub(n, radix, -expdif,
+ &in2[2], &in1[2], &out[2]);
+ }
+ outexp -= expdif;
+ outsgn *= in1[0];
+ if (expdif == n) {
+ outsgn = 0;
+ }
+ }
+ if (outsgn == 0) {
+ outexp = 0;
+ }
+ out[0] = outsgn;
+ out[1] = outexp;
+}
+
+
+void mp_sub(int n, int radix, int in1[], int in2[], int out[])
+{
+ int mp_unsgn_cmp(int n, int in1[], int in2[]);
+ int mp_unexp_add(int n, int radix, int expdif,
+ int in1[], int in2[], int out[]);
+ int mp_unexp_sub(int n, int radix, int expdif,
+ int in1[], int in2[], int out[]);
+ int outsgn, outexp, expdif;
+
+ expdif = in1[1] - in2[1];
+ outexp = in1[1];
+ if (expdif < 0) {
+ outexp = in2[1];
+ }
+ outsgn = in1[0] * in2[0];
+ if (outsgn <= 0) {
+ if (outsgn < 0) {
+ outsgn = in1[0];
+ } else {
+ outsgn = in1[0] - in2[0];
+ outexp = in1[1] + in2[1];
+ expdif = 0;
+ }
+ if (expdif >= 0) {
+ outexp += mp_unexp_add(n, radix, expdif,
+ &in1[2], &in2[2], &out[2]);
+ } else {
+ outexp += mp_unexp_add(n, radix, -expdif,
+ &in2[2], &in1[2], &out[2]);
+ }
+ } else {
+ outsgn = mp_unsgn_cmp(n, &in1[1], &in2[1]);
+ if (outsgn >= 0) {
+ expdif = mp_unexp_sub(n, radix, expdif,
+ &in1[2], &in2[2], &out[2]);
+ } else {
+ expdif = mp_unexp_sub(n, radix, -expdif,
+ &in2[2], &in1[2], &out[2]);
+ }
+ outexp -= expdif;
+ outsgn *= in1[0];
+ if (expdif == n) {
+ outsgn = 0;
+ }
+ }
+ if (outsgn == 0) {
+ outexp = 0;
+ }
+ out[0] = outsgn;
+ out[1] = outexp;
+}
+
+
+/* -------- mp_add child routines -------- */
+
+
+int mp_unsgn_cmp(int n, int in1[], int in2[])
+{
+ int j, cmp;
+
+ cmp = 0;
+ for (j = 0; j <= n && cmp == 0; j++) {
+ cmp = in1[j] - in2[j];
+ }
+ if (cmp > 0) {
+ cmp = 1;
+ } else if (cmp < 0) {
+ cmp = -1;
+ }
+ return cmp;
+}
+
+
+int mp_unexp_add(int n, int radix, int expdif,
+ int in1[], int in2[], int out[])
+{
+ int j, x, carry;
+
+ carry = 0;
+ if (expdif == 0 && in1[0] + in2[0] >= radix) {
+ x = in1[n - 1] + in2[n - 1];
+ carry = x >= radix ? -1 : 0;
+ for (j = n - 1; j > 0; j--) {
+ x = in1[j - 1] + in2[j - 1] - carry;
+ carry = x >= radix ? -1 : 0;
+ out[j] = x - (radix & carry);
+ }
+ out[0] = -carry;
+ } else {
+ if (expdif > n) {
+ expdif = n;
+ }
+ for (j = n - 1; j >= expdif; j--) {
+ x = in1[j] + in2[j - expdif] - carry;
+ carry = x >= radix ? -1 : 0;
+ out[j] = x - (radix & carry);
+ }
+ for (j = expdif - 1; j >= 0; j--) {
+ x = in1[j] - carry;
+ carry = x >= radix ? -1 : 0;
+ out[j] = x - (radix & carry);
+ }
+ if (carry != 0) {
+ for (j = n - 1; j > 0; j--) {
+ out[j] = out[j - 1];
+ }
+ out[0] = -carry;
+ }
+ }
+ return -carry;
+}
+
+
+int mp_unexp_sub(int n, int radix, int expdif,
+ int in1[], int in2[], int out[])
+{
+ int j, x, borrow, ncancel;
+
+ if (expdif > n) {
+ expdif = n;
+ }
+ borrow = 0;
+ for (j = n - 1; j >= expdif; j--) {
+ x = in1[j] - in2[j - expdif] + borrow;
+ borrow = x < 0 ? -1 : 0;
+ out[j] = x + (radix & borrow);
+ }
+ for (j = expdif - 1; j >= 0; j--) {
+ x = in1[j] + borrow;
+ borrow = x < 0 ? -1 : 0;
+ out[j] = x + (radix & borrow);
+ }
+ ncancel = 0;
+ for (j = 0; j < n && out[j] == 0; j++) {
+ ncancel = j + 1;
+ }
+ if (ncancel > 0 && ncancel < n) {
+ for (j = 0; j < n - ncancel; j++) {
+ out[j] = out[j + ncancel];
+ }
+ for (j = n - ncancel; j < n; j++) {
+ out[j] = 0;
+ }
+ }
+ return ncancel;
+}
+
+
+/* -------- mp_imul routines -------- */
+
+
+void mp_imul(int n, int radix, int in1[], int in2, int out[])
+{
+ void mp_unsgn_imul(int n, double dradix, int in1[], double din2,
+ int out[]);
+
+ if (in2 > 0) {
+ out[0] = in1[0];
+ } else if (in2 < 0) {
+ out[0] = -in1[0];
+ in2 = -in2;
+ } else {
+ out[0] = 0;
+ }
+ mp_unsgn_imul(n, radix, &in1[1], in2, &out[1]);
+ if (out[0] == 0) {
+ out[1] = 0;
+ }
+}
+
+
+int mp_idiv(int n, int radix, int in1[], int in2, int out[])
+{
+ void mp_load_0(int n, int radix, int out[]);
+ void mp_unsgn_idiv(int n, double dradix, int in1[], double din2,
+ int out[]);
+
+ if (in2 == 0) {
+ return -1;
+ }
+ if (in2 > 0) {
+ out[0] = in1[0];
+ } else {
+ out[0] = -in1[0];
+ in2 = -in2;
+ }
+ if (in1[0] == 0) {
+ mp_load_0(n, radix, out);
+ return 0;
+ }
+ mp_unsgn_idiv(n, radix, &in1[1], in2, &out[1]);
+ return 0;
+}
+
+
+void mp_idiv_2(int n, int radix, int in[], int out[])
+{
+ int j, ix, carry, shift;
+
+ out[0] = in[0];
+ shift = 0;
+ if (in[2] == 1) {
+ shift = 1;
+ }
+ out[1] = in[1] - shift;
+ carry = -shift;
+ for (j = 2; j <= n + 1 - shift; j++) {
+ ix = in[j + shift] + (radix & carry);
+ carry = -(ix & 1);
+ out[j] = ix >> 1;
+ }
+ if (shift > 0) {
+ out[n + 1] = (radix & carry) >> 1;
+ }
+}
+
+
+/* -------- mp_imul child routines -------- */
+
+
+void mp_unsgn_imul(int n, double dradix, int in1[], double din2,
+ int out[])
+{
+ int j, carry, shift;
+ double x, d1_radix;
+
+ d1_radix = 1.0 / dradix;
+ carry = 0;
+ for (j = n; j >= 1; j--) {
+ x = din2 * in1[j] + carry + 0.5;
+ carry = (int) (d1_radix * x);
+ out[j] = (int) (x - dradix * carry);
+ }
+ shift = 0;
+ x = carry + 0.5;
+ while (x > 1) {
+ x *= d1_radix;
+ shift++;
+ }
+ out[0] = in1[0] + shift;
+ if (shift > 0) {
+ while (shift > n) {
+ carry = (int) (d1_radix * carry + 0.5);
+ shift--;
+ }
+ for (j = n; j >= shift + 1; j--) {
+ out[j] = out[j - shift];
+ }
+ for (j = shift; j >= 1; j--) {
+ x = carry + 0.5;
+ carry = (int) (d1_radix * x);
+ out[j] = (int) (x - dradix * carry);
+ }
+ }
+}
+
+
+void mp_unsgn_idiv(int n, double dradix, int in1[], double din2,
+ int out[])
+{
+ int j, ix, carry, shift;
+ double x, d1_in2;
+
+ d1_in2 = 1.0 / din2;
+ shift = 0;
+ x = 0;
+ do {
+ shift++;
+ x *= dradix;
+ if (shift <= n) {
+ x += in1[shift];
+ }
+ } while (x < din2 - 0.5);
+ x += 0.5;
+ ix = (int) (d1_in2 * x);
+ carry = (int) (x - din2 * ix);
+ out[1] = ix;
+ shift--;
+ out[0] = in1[0] - shift;
+ if (shift >= n) {
+ shift = n - 1;
+ }
+ for (j = 2; j <= n - shift; j++) {
+ x = in1[j + shift] + dradix * carry + 0.5;
+ ix = (int) (d1_in2 * x);
+ carry = (int) (x - din2 * ix);
+ out[j] = ix;
+ }
+ for (j = n - shift + 1; j <= n; j++) {
+ x = dradix * carry + 0.5;
+ ix = (int) (d1_in2 * x);
+ carry = (int) (x - din2 * ix);
+ out[j] = ix;
+ }
+}
+
+
+/* -------- mp_mul routines -------- */
+
+
+double mp_mul_radix_test(int n, int radix, int nfft,
+ double tmpfft[], int ip[], double w[])
+{
+ void rdft(int n, int isgn, double *a, int *ip, double *w);
+ void mp_mul_csqu(int nfft, double dinout[]);
+ double mp_mul_d2i_test(int radix, int nfft, double din[]);
+ int j, ndata, radix_2;
+
+ ndata = (nfft >> 1) + 1;
+ if (ndata > n) {
+ ndata = n;
+ }
+ tmpfft[nfft + 1] = radix - 1;
+ for (j = nfft; j > ndata; j--) {
+ tmpfft[j] = 0;
+ }
+ radix_2 = (radix + 1) / 2;
+ for (j = ndata; j > 2; j--) {
+ tmpfft[j] = radix_2;
+ }
+ tmpfft[2] = radix;
+ tmpfft[1] = radix - 1;
+ tmpfft[0] = 0;
+ rdft(nfft, 1, &tmpfft[1], ip, w);
+ mp_mul_csqu(nfft, tmpfft);
+ rdft(nfft, -1, &tmpfft[1], ip, w);
+ return 2 * mp_mul_d2i_test(radix, nfft, tmpfft);
+}
+
+
+void mp_mul(int n, int radix, int in1[], int in2[], int out[],
+ int tmp[], int nfft, double tmp1fft[], double tmp2fft[],
+ double tmp3fft[], int ip[], double w[])
+{
+ void mp_copy(int n, int radix, int in[], int out[]);
+ void mp_add(int n, int radix, int in1[], int in2[], int out[]);
+ void rdft(int n, int isgn, double *a, int *ip, double *w);
+ void mp_mul_i2d(int n, int radix, int nfft, int shift,
+ int in[], double dout[]);
+ void mp_mul_cmul(int nfft, double din[], double dinout[]);
+ void mp_mul_cmuladd(int nfft, double din1[], double din2[],
+ double dinout[]);
+ void mp_mul_d2i(int n, int radix, int nfft, double din[], int out[]);
+ int n_h, shift;
+
+ shift = (nfft >> 1) + 1;
+ while (n > shift) {
+ if (in1[shift + 2] + in2[shift + 2] != 0) {
+ break;
+ }
+ shift++;
+ }
+ n_h = n / 2 + 1;
+ if (n_h < n - shift) {
+ n_h = n - shift;
+ }
+ /* ---- tmp3fft = (upper) in1 * (lower) in2 ---- */
+ mp_mul_i2d(n, radix, nfft, 0, in1, tmp1fft);
+ rdft(nfft, 1, &tmp1fft[1], ip, w);
+ mp_mul_i2d(n, radix, nfft, shift, in2, tmp3fft);
+ rdft(nfft, 1, &tmp3fft[1], ip, w);
+ mp_mul_cmul(nfft, tmp1fft, tmp3fft);
+ /* ---- tmp = (upper) in1 * (upper) in2 ---- */
+ mp_mul_i2d(n, radix, nfft, 0, in2, tmp2fft);
+ rdft(nfft, 1, &tmp2fft[1], ip, w);
+ mp_mul_cmul(nfft, tmp2fft, tmp1fft);
+ rdft(nfft, -1, &tmp1fft[1], ip, w);
+ mp_mul_d2i(n, radix, nfft, tmp1fft, tmp);
+ /* ---- tmp3fft += (upper) in2 * (lower) in1 ---- */
+ mp_mul_i2d(n, radix, nfft, shift, in1, tmp1fft);
+ rdft(nfft, 1, &tmp1fft[1], ip, w);
+ mp_mul_cmuladd(nfft, tmp1fft, tmp2fft, tmp3fft);
+ /* ---- out = tmp + tmp3fft ---- */
+ rdft(nfft, -1, &tmp3fft[1], ip, w);
+ mp_mul_d2i(n_h, radix, nfft, tmp3fft, out);
+ if (out[0] != 0) {
+ mp_add(n, radix, out, tmp, out);
+ } else {
+ mp_copy(n, radix, tmp, out);
+ }
+}
+
+
+void mp_squ(int n, int radix, int in[], int out[], int tmp[],
+ int nfft, double tmp1fft[], double tmp2fft[],
+ int ip[], double w[])
+{
+ void mp_add(int n, int radix, int in1[], int in2[], int out[]);
+ void rdft(int n, int isgn, double *a, int *ip, double *w);
+ void mp_mul_i2d(int n, int radix, int nfft, int shift,
+ int in[], double dout[]);
+ void mp_mul_cmul(int nfft, double din[], double dinout[]);
+ void mp_mul_csqu(int nfft, double dinout[]);
+ void mp_mul_d2i(int n, int radix, int nfft, double din[], int out[]);
+ int n_h, shift;
+
+ shift = (nfft >> 1) + 1;
+ while (n > shift) {
+ if (in[shift + 2] != 0) {
+ break;
+ }
+ shift++;
+ }
+ n_h = n / 2 + 1;
+ if (n_h < n - shift) {
+ n_h = n - shift;
+ }
+ /* ---- tmp = (upper) in * (lower) in ---- */
+ mp_mul_i2d(n, radix, nfft, 0, in, tmp1fft);
+ rdft(nfft, 1, &tmp1fft[1], ip, w);
+ mp_mul_i2d(n, radix, nfft, shift, in, tmp2fft);
+ rdft(nfft, 1, &tmp2fft[1], ip, w);
+ mp_mul_cmul(nfft, tmp1fft, tmp2fft);
+ rdft(nfft, -1, &tmp2fft[1], ip, w);
+ mp_mul_d2i(n_h, radix, nfft, tmp2fft, tmp);
+ /* ---- out = 2 * tmp + ((upper) in)^2 ---- */
+ mp_mul_csqu(nfft, tmp1fft);
+ rdft(nfft, -1, &tmp1fft[1], ip, w);
+ mp_mul_d2i(n, radix, nfft, tmp1fft, out);
+ if (tmp[0] != 0) {
+ mp_add(n_h, radix, tmp, tmp, tmp);
+ mp_add(n, radix, out, tmp, out);
+ }
+}
+
+
+void mp_mulh(int n, int radix, int in1[], int in2[], int out[],
+ int nfft, double in1fft[], double outfft[], int ip[], double w[])
+{
+ void rdft(int n, int isgn, double *a, int *ip, double *w);
+ void mp_mul_i2d(int n, int radix, int nfft, int shift,
+ int in[], double dout[]);
+ void mp_mul_cmul(int nfft, double din[], double dinout[]);
+ void mp_mul_d2i(int n, int radix, int nfft, double din[], int out[]);
+
+ mp_mul_i2d(n, radix, nfft, 0, in1, in1fft);
+ rdft(nfft, 1, &in1fft[1], ip, w);
+ mp_mul_i2d(n, radix, nfft, 0, in2, outfft);
+ rdft(nfft, 1, &outfft[1], ip, w);
+ mp_mul_cmul(nfft, in1fft, outfft);
+ rdft(nfft, -1, &outfft[1], ip, w);
+ mp_mul_d2i(n, radix, nfft, outfft, out);
+}
+
+
+void mp_mulh_use_in1fft(int n, int radix, double in1fft[],
+ int shift, int in2[], int out[], int nfft, double outfft[],
+ int ip[], double w[])
+{
+ void rdft(int n, int isgn, double *a, int *ip, double *w);
+ void mp_mul_i2d(int n, int radix, int nfft, int shift,
+ int in[], double dout[]);
+ void mp_mul_cmul(int nfft, double din[], double dinout[]);
+ void mp_mul_d2i(int n, int radix, int nfft, double din[], int out[]);
+ int n_h;
+
+ while (n > shift) {
+ if (in2[shift + 2] != 0) {
+ break;
+ }
+ shift++;
+ }
+ n_h = n / 2 + 1;
+ if (n_h < n - shift) {
+ n_h = n - shift;
+ }
+ mp_mul_i2d(n, radix, nfft, shift, in2, outfft);
+ rdft(nfft, 1, &outfft[1], ip, w);
+ mp_mul_cmul(nfft, in1fft, outfft);
+ rdft(nfft, -1, &outfft[1], ip, w);
+ mp_mul_d2i(n_h, radix, nfft, outfft, out);
+}
+
+
+void mp_squh(int n, int radix, int in[], int out[],
+ int nfft, double inoutfft[], int ip[], double w[])
+{
+ void rdft(int n, int isgn, double *a, int *ip, double *w);
+ void mp_mul_i2d(int n, int radix, int nfft, int shift,
+ int in[], double dout[]);
+ void mp_mul_csqu(int nfft, double dinout[]);
+ void mp_mul_d2i(int n, int radix, int nfft, double din[], int out[]);
+
+ mp_mul_i2d(n, radix, nfft, 0, in, inoutfft);
+ rdft(nfft, 1, &inoutfft[1], ip, w);
+ mp_mul_csqu(nfft, inoutfft);
+ rdft(nfft, -1, &inoutfft[1], ip, w);
+ mp_mul_d2i(n, radix, nfft, inoutfft, out);
+}
+
+
+void mp_squh_use_in1fft(int n, int radix, double inoutfft[], int out[],
+ int nfft, int ip[], double w[])
+{
+ void rdft(int n, int isgn, double *a, int *ip, double *w);
+ void mp_mul_csqu(int nfft, double dinout[]);
+ void mp_mul_d2i(int n, int radix, int nfft, double din[], int out[]);
+
+ mp_mul_csqu(nfft, inoutfft);
+ rdft(nfft, -1, &inoutfft[1], ip, w);
+ mp_mul_d2i(n, radix, nfft, inoutfft, out);
+}
+
+
+/* -------- mp_mul child routines -------- */
+
+
+void mp_mul_i2d(int n, int radix, int nfft, int shift,
+ int in[], double dout[])
+{
+ int j, x, carry, ndata, radix_2, topdgt;
+
+ ndata = 0;
+ topdgt = 0;
+ if (n > shift) {
+ topdgt = in[shift + 2];
+ ndata = (nfft >> 1) + 1;
+ if (ndata > n - shift) {
+ ndata = n - shift;
+ }
+ }
+ dout[nfft + 1] = in[0] * topdgt;
+ for (j = nfft; j > ndata; j--) {
+ dout[j] = 0;
+ }
+ /* ---- abs(dout[j]) <= radix/2 (to keep FFT precision) ---- */
+ if (ndata > 1) {
+ radix_2 = radix / 2;
+ carry = 0;
+ for (j = ndata + 1; j > 3; j--) {
+ x = in[j + shift] - carry;
+ carry = x >= radix_2 ? -1 : 0;
+ dout[j - 1] = x - (radix & carry);
+ }
+ dout[2] = in[shift + 3] - carry;
+ }
+ dout[1] = topdgt;
+ dout[0] = in[1] - shift;
+}
+
+
+void mp_mul_cmul(int nfft, double din[], double dinout[])
+{
+ int j;
+ double xr, xi, yr, yi;
+
+ dinout[0] += din[0];
+ dinout[1] *= din[1];
+ dinout[2] *= din[2];
+ for (j = 3; j < nfft; j += 2) {
+ xr = din[j];
+ xi = din[j + 1];
+ yr = dinout[j];
+ yi = dinout[j + 1];
+ dinout[j] = xr * yr - xi * yi;
+ dinout[j + 1] = xr * yi + xi * yr;
+ }
+ dinout[nfft + 1] *= din[nfft + 1];
+}
+
+
+void mp_mul_cmuladd(int nfft, double din1[], double din2[],
+ double dinout[])
+{
+ int j;
+ double xr, xi, yr, yi;
+
+ dinout[1] += din1[1] * din2[1];
+ dinout[2] += din1[2] * din2[2];
+ for (j = 3; j < nfft; j += 2) {
+ xr = din1[j];
+ xi = din1[j + 1];
+ yr = din2[j];
+ yi = din2[j + 1];
+ dinout[j] += xr * yr - xi * yi;
+ dinout[j + 1] += xr * yi + xi * yr;
+ }
+ dinout[nfft + 1] += din1[nfft + 1] * din2[nfft + 1];
+}
+
+
+void mp_mul_csqu(int nfft, double dinout[])
+{
+ int j;
+ double xr, xi;
+
+ dinout[0] *= 2;
+ dinout[1] *= dinout[1];
+ dinout[2] *= dinout[2];
+ for (j = 3; j < nfft; j += 2) {
+ xr = dinout[j];
+ xi = dinout[j + 1];
+ dinout[j] = xr * xr - xi * xi;
+ dinout[j + 1] = 2 * xr * xi;
+ }
+ dinout[nfft + 1] *= dinout[nfft + 1];
+}
+
+
+void mp_mul_d2i(int n, int radix, int nfft, double din[], int out[])
+{
+ int j, carry, carry1, carry2, shift, ndata;
+ double x, scale, d1_radix, d1_radix2, pow_radix, topdgt;
+
+ scale = 2.0 / nfft;
+ d1_radix = 1.0 / radix;
+ d1_radix2 = d1_radix * d1_radix;
+ topdgt = din[nfft + 1];
+ x = topdgt < 0 ? -topdgt : topdgt;
+ shift = x + 0.5 >= radix ? 1 : 0;
+ /* ---- correction of cyclic convolution of din[1] ---- */
+ x *= nfft * 0.5;
+ din[nfft + 1] = din[1] - x;
+ din[1] = x;
+ /* ---- output of digits ---- */
+ ndata = n;
+ if (n > nfft + 1 + shift) {
+ ndata = nfft + 1 + shift;
+ for (j = n + 1; j > ndata + 1; j--) {
+ out[j] = 0;
+ }
+ }
+ x = 0;
+ pow_radix = 1;
+ for (j = ndata + 1 - shift; j <= nfft + 1; j++) {
+ x += pow_radix * din[j];
+ pow_radix *= d1_radix;
+ if (pow_radix < DBL_EPSILON) {
+ break;
+ }
+ }
+ x = d1_radix2 * (scale * x + 0.5);
+ carry2 = ((int) x) - 1;
+ carry = (int) (radix * (x - carry2) + 0.5);
+ for (j = ndata; j > 1; j--) {
+ x = d1_radix2 * (scale * din[j - shift] + carry + 0.5);
+ carry = carry2;
+ carry2 = ((int) x) - 1;
+ x = radix * (x - carry2);
+ carry1 = (int) x;
+ out[j + 1] = (int) (radix * (x - carry1));
+ carry += carry1;
+ }
+ x = carry + ((double) radix) * carry2 + 0.5;
+ if (shift == 0) {
+ x += scale * din[1];
+ }
+ carry = (int) (d1_radix * x);
+ out[2] = (int) (x - ((double) radix) * carry);
+ if (carry > 0) {
+ for (j = n + 1; j > 2; j--) {
+ out[j] = out[j - 1];
+ }
+ out[2] = carry;
+ shift++;
+ }
+ /* ---- output of exp, sgn ---- */
+ x = din[0] + shift + 0.5;
+ shift = ((int) x) - 1;
+ out[1] = shift + ((int) (x - shift));
+ out[0] = topdgt > 0.5 ? 1 : -1;
+ if (out[2] == 0) {
+ out[0] = 0;
+ out[1] = 0;
+ }
+}
+
+
+double mp_mul_d2i_test(int radix, int nfft, double din[])
+{
+ int j, carry, carry1, carry2;
+ double x, scale, d1_radix, d1_radix2, err;
+
+ scale = 2.0 / nfft;
+ d1_radix = 1.0 / radix;
+ d1_radix2 = d1_radix * d1_radix;
+ /* ---- correction of cyclic convolution of din[1] ---- */
+ x = din[nfft + 1] * nfft * 0.5;
+ if (x < 0) {
+ x = -x;
+ }
+ din[nfft + 1] = din[1] - x;
+ /* ---- check of digits ---- */
+ err = 0;
+ carry = 0;
+ carry2 = 0;
+ for (j = nfft + 1; j > 1; j--) {
+ x = d1_radix2 * (scale * din[j] + carry + 0.5);
+ carry = carry2;
+ carry2 = ((int) x) - 1;
+ x = radix * (x - carry2);
+ carry1 = (int) x;
+ x = radix * (x - carry1);
+ carry += carry1;
+ x = x - 0.5 - ((int) x);
+ if (x > err) {
+ err = x;
+ } else if (-x > err) {
+ err = -x;
+ }
+ }
+ return err;
+}
+
+
+/* -------- mp_inv routines -------- */
+
+
+int mp_inv(int n, int radix, int in[], int out[],
+ int tmp1[], int tmp2[], int nfft,
+ double tmp1fft[], double tmp2fft[], int ip[], double w[])
+{
+ int mp_get_nfft_init(int radix, int nfft_max);
+ void mp_inv_init(int n, int radix, int in[], int out[]);
+ int mp_inv_newton(int n, int radix, int in[], int inout[],
+ int tmp1[], int tmp2[], int nfft, double tmp1fft[],
+ double tmp2fft[], int ip[], double w[]);
+ int n_nwt, nfft_nwt, thr, prc;
+
+ if (in[0] == 0) {
+ return -1;
+ }
+ nfft_nwt = mp_get_nfft_init(radix, nfft);
+ n_nwt = nfft_nwt + 2;
+ if (n_nwt > n) {
+ n_nwt = n;
+ }
+ mp_inv_init(n_nwt, radix, in, out);
+ thr = 8;
+ do {
+ n_nwt = nfft_nwt + 2;
+ if (n_nwt > n) {
+ n_nwt = n;
+ }
+ prc = mp_inv_newton(n_nwt, radix, in, out,
+ tmp1, tmp2, nfft_nwt, tmp1fft, tmp2fft, ip, w);
+ if (thr * nfft_nwt >= nfft) {
+ thr = 0;
+ if (2 * prc <= n_nwt - 2) {
+ nfft_nwt >>= 1;
+ }
+ } else {
+ if (3 * prc < n_nwt - 2) {
+ nfft_nwt >>= 1;
+ }
+ }
+ nfft_nwt <<= 1;
+ } while (nfft_nwt <= nfft);
+ return 0;
+}
+
+
+int mp_sqrt(int n, int radix, int in[], int out[],
+ int tmp1[], int tmp2[], int nfft,
+ double tmp1fft[], double tmp2fft[], int ip[], double w[])
+{
+ void mp_load_0(int n, int radix, int out[]);
+ int mp_get_nfft_init(int radix, int nfft_max);
+ void mp_sqrt_init(int n, int radix, int in[], int out[], int out_rev[]);
+ int mp_sqrt_newton(int n, int radix, int in[], int inout[],
+ int inout_rev[], int tmp[], int nfft, double tmp1fft[],
+ double tmp2fft[], int ip[], double w[], int *n_tmp1fft);
+ int n_nwt, nfft_nwt, thr, prc, n_tmp1fft;
+
+ if (in[0] < 0) {
+ return -1;
+ } else if (in[0] == 0) {
+ mp_load_0(n, radix, out);
+ return 0;
+ }
+ nfft_nwt = mp_get_nfft_init(radix, nfft);
+ n_nwt = nfft_nwt + 2;
+ if (n_nwt > n) {
+ n_nwt = n;
+ }
+ mp_sqrt_init(n_nwt, radix, in, out, tmp1);
+ n_tmp1fft = 0;
+ thr = 8;
+ do {
+ n_nwt = nfft_nwt + 2;
+ if (n_nwt > n) {
+ n_nwt = n;
+ }
+ prc = mp_sqrt_newton(n_nwt, radix, in, out,
+ tmp1, tmp2, nfft_nwt, tmp1fft, tmp2fft,
+ ip, w, &n_tmp1fft);
+ if (thr * nfft_nwt >= nfft) {
+ thr = 0;
+ if (2 * prc <= n_nwt - 2) {
+ nfft_nwt >>= 1;
+ }
+ } else {
+ if (3 * prc < n_nwt - 2) {
+ nfft_nwt >>= 1;
+ }
+ }
+ nfft_nwt <<= 1;
+ } while (nfft_nwt <= nfft);
+ return 0;
+}
+
+
+/* -------- mp_inv child routines -------- */
+
+
+int mp_get_nfft_init(int radix, int nfft_max)
+{
+ int nfft_init;
+ double r;
+
+ r = radix;
+ nfft_init = 1;
+ do {
+ r *= r;
+ nfft_init <<= 1;
+ } while (DBL_EPSILON * r < 1 && nfft_init < nfft_max);
+ return nfft_init;
+}
+
+
+void mp_inv_init(int n, int radix, int in[], int out[])
+{
+ void mp_unexp_d2mp(int n, int radix, double din, int out[]);
+ double mp_unexp_mp2d(int n, int radix, int in[]);
+ int outexp;
+ double din;
+
+ out[0] = in[0];
+ outexp = -in[1];
+ din = 1.0 / mp_unexp_mp2d(n, radix, &in[2]);
+ while (din < 1) {
+ din *= radix;
+ outexp--;
+ }
+ out[1] = outexp;
+ mp_unexp_d2mp(n, radix, din, &out[2]);
+}
+
+
+void mp_sqrt_init(int n, int radix, int in[], int out[], int out_rev[])
+{
+ void mp_unexp_d2mp(int n, int radix, double din, int out[]);
+ double mp_unexp_mp2d(int n, int radix, int in[]);
+ int outexp;
+ double din;
+
+ out[0] = 1;
+ out_rev[0] = 1;
+ outexp = in[1];
+ din = mp_unexp_mp2d(n, radix, &in[2]);
+ if (outexp % 2 != 0) {
+ din *= radix;
+ outexp--;
+ }
+ outexp /= 2;
+ din = sqrt(din);
+ if (din < 1) {
+ din *= radix;
+ outexp--;
+ }
+ out[1] = outexp;
+ mp_unexp_d2mp(n, radix, din, &out[2]);
+ outexp = -outexp;
+ din = 1.0 / din;
+ while (din < 1) {
+ din *= radix;
+ outexp--;
+ }
+ out_rev[1] = outexp;
+ mp_unexp_d2mp(n, radix, din, &out_rev[2]);
+}
+
+
+void mp_unexp_d2mp(int n, int radix, double din, int out[])
+{
+ int j, x;
+
+ for (j = 0; j < n; j++) {
+ x = (int) din;
+ if (x >= radix) {
+ x = radix - 1;
+ din = radix;
+ }
+ din = radix * (din - x);
+ out[j] = x;
+ }
+}
+
+
+double mp_unexp_mp2d(int n, int radix, int in[])
+{
+ int j;
+ double d1_radix, dout;
+
+ d1_radix = 1.0 / radix;
+ dout = 0;
+ for (j = n - 1; j >= 0; j--) {
+ dout = d1_radix * dout + in[j];
+ }
+ return dout;
+}
+
+
+int mp_inv_newton(int n, int radix, int in[], int inout[],
+ int tmp1[], int tmp2[], int nfft, double tmp1fft[],
+ double tmp2fft[], int ip[], double w[])
+{
+ void mp_load_1(int n, int radix, int out[]);
+ void mp_round(int n, int radix, int m, int inout[]);
+ void mp_add(int n, int radix, int in1[], int in2[], int out[]);
+ void mp_sub(int n, int radix, int in1[], int in2[], int out[]);
+ void mp_mulh(int n, int radix, int in1[], int in2[], int out[],
+ int nfft, double in1fft[], double outfft[],
+ int ip[], double w[]);
+ void mp_mulh_use_in1fft(int n, int radix, double in1fft[],
+ int shift, int in2[], int out[], int nfft, double outfft[],
+ int ip[], double w[]);
+ int n_h, shift, prc;
+
+ shift = (nfft >> 1) + 1;
+ n_h = n / 2 + 1;
+ if (n_h < n - shift) {
+ n_h = n - shift;
+ }
+ /* ---- tmp1 = inout * (upper) in (half to normal precision) ---- */
+ mp_round(n, radix, shift, inout);
+ mp_mulh(n, radix, inout, in, tmp1,
+ nfft, tmp1fft, tmp2fft, ip, w);
+ /* ---- tmp2 = 1 - tmp1 ---- */
+ mp_load_1(n, radix, tmp2);
+ mp_sub(n, radix, tmp2, tmp1, tmp2);
+ /* ---- tmp2 -= inout * (lower) in (half precision) ---- */
+ mp_mulh_use_in1fft(n, radix, tmp1fft, shift, in, tmp1,
+ nfft, tmp2fft, ip, w);
+ mp_sub(n_h, radix, tmp2, tmp1, tmp2);
+ /* ---- get precision ---- */
+ prc = -tmp2[1];
+ if (tmp2[0] == 0) {
+ prc = nfft + 1;
+ }
+ /* ---- tmp2 *= inout (half precision) ---- */
+ mp_mulh_use_in1fft(n_h, radix, tmp1fft, 0, tmp2, tmp2,
+ nfft, tmp2fft, ip, w);
+ /* ---- inout += tmp2 ---- */
+ if (tmp2[0] != 0) {
+ mp_add(n, radix, inout, tmp2, inout);
+ }
+ return prc;
+}
+
+
+int mp_sqrt_newton(int n, int radix, int in[], int inout[],
+ int inout_rev[], int tmp[], int nfft, double tmp1fft[],
+ double tmp2fft[], int ip[], double w[], int *n_tmp1fft)
+{
+ void mp_round(int n, int radix, int m, int inout[]);
+ void mp_add(int n, int radix, int in1[], int in2[], int out[]);
+ void mp_sub(int n, int radix, int in1[], int in2[], int out[]);
+ void mp_idiv_2(int n, int radix, int in[], int out[]);
+ void mp_mulh(int n, int radix, int in1[], int in2[], int out[],
+ int nfft, double in1fft[], double outfft[],
+ int ip[], double w[]);
+ void mp_squh(int n, int radix, int in[], int out[],
+ int nfft, double inoutfft[], int ip[], double w[]);
+ void mp_squh_use_in1fft(int n, int radix, double inoutfft[], int out[],
+ int nfft, int ip[], double w[]);
+ int n_h, nfft_h, shift, prc;
+
+ nfft_h = nfft >> 1;
+ shift = nfft_h + 1;
+ if (nfft_h < 2) {
+ nfft_h = 2;
+ }
+ n_h = n / 2 + 1;
+ if (n_h < n - shift) {
+ n_h = n - shift;
+ }
+ /* ---- tmp = inout_rev^2 (1/4 to half precision) ---- */
+ mp_round(n_h, radix, (nfft_h >> 1) + 1, inout_rev);
+ if (*n_tmp1fft != nfft_h) {
+ mp_squh(n_h, radix, inout_rev, tmp,
+ nfft_h, tmp1fft, ip, w);
+ } else {
+ mp_squh_use_in1fft(n_h, radix, tmp1fft, tmp,
+ nfft_h, ip, w);
+ }
+ /* ---- tmp = inout_rev - inout * tmp (half precision) ---- */
+ mp_round(n, radix, shift, inout);
+ mp_mulh(n_h, radix, inout, tmp, tmp,
+ nfft, tmp1fft, tmp2fft, ip, w);
+ mp_sub(n_h, radix, inout_rev, tmp, tmp);
+ /* ---- inout_rev += tmp ---- */
+ mp_add(n_h, radix, inout_rev, tmp, inout_rev);
+ /* ---- tmp = in - inout^2 (half to normal precision) ---- */
+ mp_squh_use_in1fft(n, radix, tmp1fft, tmp,
+ nfft, ip, w);
+ mp_sub(n, radix, in, tmp, tmp);
+ /* ---- get precision ---- */
+ prc = in[1] - tmp[1];
+ if (in[2] > tmp[2]) {
+ prc++;
+ }
+ if (tmp[0] == 0) {
+ prc = nfft + 1;
+ }
+ /* ---- tmp = tmp * inout_rev / 2 (half precision) ---- */
+ mp_round(n_h, radix, shift, inout_rev);
+ mp_mulh(n_h, radix, inout_rev, tmp, tmp,
+ nfft, tmp1fft, tmp2fft, ip, w);
+ *n_tmp1fft = nfft;
+ mp_idiv_2(n_h, radix, tmp, tmp);
+ /* ---- inout += tmp ---- */
+ if (tmp[0] != 0) {
+ mp_add(n, radix, inout, tmp, inout);
+ }
+ return prc;
+}
+
+
+/* -------- mp_io routines -------- */
+
+
+void mp_sprintf(int n, int log10_radix, int in[], char out[])
+{
+ int j, k, x, y, outexp, shift;
+
+ if (in[0] < 0) {
+ *out++ = '-';
+ }
+ x = in[2];
+ shift = log10_radix;
+ for (k = log10_radix; k > 0; k--) {
+ y = x % 10;
+ x /= 10;
+ out[k] = '0' + y;
+ if (y != 0) {
+ shift = k;
+ }
+ }
+ out[0] = out[shift];
+ out[1] = '.';
+ for (k = 1; k <= log10_radix - shift; k++) {
+ out[k + 1] = out[k + shift];
+ }
+ outexp = log10_radix - shift;
+ out += outexp + 2;
+ for (j = 3; j <= n + 1; j++) {
+ x = in[j];
+ for (k = log10_radix - 1; k >= 0; k--) {
+ y = x % 10;
+ x /= 10;
+ out[k] = '0' + y;
+ }
+ out += log10_radix;
+ }
+ *out++ = 'e';
+ outexp += log10_radix * in[1];
+ sprintf(out, "%d", outexp);
+}
+
+
+void mp_sscanf(int n, int log10_radix, char in[], int out[])
+{
+ char *s;
+ int j, x, outexp, outexp_mod;
+
+ while (*in == ' ') {
+ in++;
+ }
+ out[0] = 1;
+ if (*in == '-') {
+ out[0] = -1;
+ in++;
+ } else if (*in == '+') {
+ in++;
+ }
+ while (*in == ' ' || *in == '0') {
+ in++;
+ }
+ outexp = 0;
+ for (s = in; *s != '\0'; s++) {
+ if (*s == 'e' || *s == 'E' || *s == 'd' || *s == 'D') {
+ if (sscanf(++s, "%d", &outexp) != 1) {
+ outexp = 0;
+ }
+ break;
+ }
+ }
+ if (*in == '.') {
+ do {
+ outexp--;
+ while (*++in == ' ');
+ } while (*in == '0' && *in != '\0');
+ } else if (*in != '\0') {
+ s = in;
+ while (*++s == ' ');
+ while (*s >= '0' && *s <= '9' && *s != '\0') {
+ outexp++;
+ while (*++s == ' ');
+ }
+ }
+ x = outexp / log10_radix;
+ outexp_mod = outexp - log10_radix * x;
+ if (outexp_mod < 0) {
+ x--;
+ outexp_mod += log10_radix;
+ }
+ out[1] = x;
+ x = 0;
+ j = 2;
+ for (s = in; *s != '\0'; s++) {
+ if (*s == '.' || *s == ' ') {
+ continue;
+ }
+ if (*s < '0' || *s > '9') {
+ break;
+ }
+ x = 10 * x + (*s - '0');
+ if (--outexp_mod < 0) {
+ if (j > n + 1) {
+ break;
+ }
+ out[j++] = x;
+ x = 0;
+ outexp_mod = log10_radix - 1;
+ }
+ }
+ while (outexp_mod-- >= 0) {
+ x *= 10;
+ }
+ while (j <= n + 1) {
+ out[j++] = x;
+ x = 0;
+ }
+ if (out[2] == 0) {
+ out[0] = 0;
+ out[1] = 0;
+ }
+}
+
+
+void mp_fprintf(int n, int log10_radix, int in[], FILE *fout)
+{
+ int j, k, x, y, outexp, shift;
+ char out[256];
+
+ if (in[0] < 0) {
+ putc('-', fout);
+ }
+ x = in[2];
+ shift = log10_radix;
+ for (k = log10_radix; k > 0; k--) {
+ y = x % 10;
+ x /= 10;
+ out[k] = '0' + y;
+ if (y != 0) {
+ shift = k;
+ }
+ }
+ putc(out[shift], fout);
+ putc('.', fout);
+ for (k = 1; k <= log10_radix - shift; k++) {
+ putc(out[k + shift], fout);
+ }
+ outexp = log10_radix - shift;
+ for (j = 3; j <= n + 1; j++) {
+ x = in[j];
+ for (k = log10_radix - 1; k >= 0; k--) {
+ y = x % 10;
+ x /= 10;
+ out[k] = '0' + y;
+ }
+ for (k = 0; k < log10_radix; k++) {
+ putc(out[k], fout);
+ }
+ }
+ putc('e', fout);
+ outexp += log10_radix * in[1];
+ sprintf(out, "%d", outexp);
+ for (k = 0; out[k] != '\0'; k++) {
+ putc(out[k], fout);
+ }
+}
+
+
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