350 lines
11 KiB
C
350 lines
11 KiB
C
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#ifndef PQCLEAN_FALCON512_AVX2_FPR_H
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#define PQCLEAN_FALCON512_AVX2_FPR_H
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/*
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* Floating-point operations.
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*
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* ==========================(LICENSE BEGIN)============================
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*
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* Copyright (c) 2017-2019 Falcon Project
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*
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* Permission is hereby granted, free of charge, to any person obtaining
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* a copy of this software and associated documentation files (the
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* "Software"), to deal in the Software without restriction, including
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* without limitation the rights to use, copy, modify, merge, publish,
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* distribute, sublicense, and/or sell copies of the Software, and to
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* permit persons to whom the Software is furnished to do so, subject to
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* the following conditions:
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*
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* The above copyright notice and this permission notice shall be
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* included in all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
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* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
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* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
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* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
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* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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*
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* ===========================(LICENSE END)=============================
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*
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* @author Thomas Pornin <thomas.pornin@nccgroup.com>
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*/
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/* ====================================================================== */
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#include <immintrin.h>
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#include <math.h>
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#define FMADD(a, b, c) _mm256_add_pd(_mm256_mul_pd(a, b), c)
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#define FMSUB(a, b, c) _mm256_sub_pd(_mm256_mul_pd(a, b), c)
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/*
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* We wrap the native 'double' type into a structure so that the C compiler
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* complains if we inadvertently use raw arithmetic operators on the 'fpr'
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* type instead of using the inline functions below. This should have no
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* extra runtime cost, since all the functions below are 'inline'.
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*/
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typedef struct {
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double v;
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} fpr;
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static inline fpr
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FPR(double v) {
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fpr x;
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x.v = v;
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return x;
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}
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static inline fpr
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fpr_of(int64_t i) {
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return FPR((double)i);
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}
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static const fpr fpr_q = { 12289.0 };
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static const fpr fpr_inverse_of_q = { 1.0 / 12289.0 };
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static const fpr fpr_inv_2sqrsigma0 = { .150865048875372721532312163019 };
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static const fpr fpr_inv_sigma = { .005819826392951607426919370871 };
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static const fpr fpr_sigma_min_9 = { 1.291500756233514568549480827642 };
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static const fpr fpr_sigma_min_10 = { 1.311734375905083682667395805765 };
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static const fpr fpr_log2 = { 0.69314718055994530941723212146 };
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static const fpr fpr_inv_log2 = { 1.4426950408889634073599246810 };
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static const fpr fpr_bnorm_max = { 16822.4121 };
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static const fpr fpr_zero = { 0.0 };
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static const fpr fpr_one = { 1.0 };
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static const fpr fpr_two = { 2.0 };
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static const fpr fpr_onehalf = { 0.5 };
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static const fpr fpr_invsqrt2 = { 0.707106781186547524400844362105 };
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static const fpr fpr_invsqrt8 = { 0.353553390593273762200422181052 };
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static const fpr fpr_ptwo31 = { 2147483648.0 };
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static const fpr fpr_ptwo31m1 = { 2147483647.0 };
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static const fpr fpr_mtwo31m1 = { -2147483647.0 };
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static const fpr fpr_ptwo63m1 = { 9223372036854775807.0 };
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static const fpr fpr_mtwo63m1 = { -9223372036854775807.0 };
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static const fpr fpr_ptwo63 = { 9223372036854775808.0 };
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static inline int64_t
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fpr_rint(fpr x) {
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/*
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* We do not want to use llrint() since it might be not
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* constant-time.
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*
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* Suppose that x >= 0. If x >= 2^52, then it is already an
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* integer. Otherwise, if x < 2^52, then computing x+2^52 will
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* yield a value that will be rounded to the nearest integer
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* with exactly the right rules (round-to-nearest-even).
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*
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* In order to have constant-time processing, we must do the
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* computation for both x >= 0 and x < 0 cases, and use a
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* cast to an integer to access the sign and select the proper
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* value. Such casts also allow us to find out if |x| < 2^52.
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*/
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int64_t sx, tx, rp, rn, m;
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uint32_t ub;
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sx = (int64_t)(x.v - 1.0);
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tx = (int64_t)x.v;
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rp = (int64_t)(x.v + 4503599627370496.0) - 4503599627370496;
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rn = (int64_t)(x.v - 4503599627370496.0) + 4503599627370496;
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/*
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* If tx >= 2^52 or tx < -2^52, then result is tx.
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* Otherwise, if sx >= 0, then result is rp.
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* Otherwise, result is rn. We use the fact that when x is
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* close to 0 (|x| <= 0.25) then both rp and rn are correct;
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* and if x is not close to 0, then trunc(x-1.0) yields the
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* appropriate sign.
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*/
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/*
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* Clamp rp to zero if tx < 0.
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* Clamp rn to zero if tx >= 0.
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*/
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m = sx >> 63;
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rn &= m;
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rp &= ~m;
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/*
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* Get the 12 upper bits of tx; if they are not all zeros or
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* all ones, then tx >= 2^52 or tx < -2^52, and we clamp both
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* rp and rn to zero. Otherwise, we clamp tx to zero.
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*/
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ub = (uint32_t)((uint64_t)tx >> 52);
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m = -(int64_t)((((ub + 1) & 0xFFF) - 2) >> 31);
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rp &= m;
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rn &= m;
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tx &= ~m;
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/*
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* Only one of tx, rn or rp (at most) can be non-zero at this
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* point.
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*/
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return tx | rn | rp;
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}
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static inline int64_t
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fpr_floor(fpr x) {
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int64_t r;
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/*
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* The cast performs a trunc() (rounding toward 0) and thus is
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* wrong by 1 for most negative values. The correction below is
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* constant-time as long as the compiler turns the
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* floating-point conversion result into a 0/1 integer without a
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* conditional branch or another non-constant-time construction.
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* This should hold on all modern architectures with an FPU (and
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* if it is false on a given arch, then chances are that the FPU
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* itself is not constant-time, making the point moot).
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*/
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r = (int64_t)x.v;
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return r - (x.v < (double)r);
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}
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static inline int64_t
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fpr_trunc(fpr x) {
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return (int64_t)x.v;
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}
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static inline fpr
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fpr_add(fpr x, fpr y) {
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return FPR(x.v + y.v);
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}
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static inline fpr
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fpr_sub(fpr x, fpr y) {
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return FPR(x.v - y.v);
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}
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static inline fpr
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fpr_neg(fpr x) {
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return FPR(-x.v);
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}
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static inline fpr
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fpr_half(fpr x) {
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return FPR(x.v * 0.5);
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}
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static inline fpr
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fpr_double(fpr x) {
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return FPR(x.v + x.v);
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}
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static inline fpr
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fpr_mul(fpr x, fpr y) {
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return FPR(x.v * y.v);
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}
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static inline fpr
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fpr_sqr(fpr x) {
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return FPR(x.v * x.v);
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}
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static inline fpr
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fpr_inv(fpr x) {
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return FPR(1.0 / x.v);
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}
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static inline fpr
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fpr_div(fpr x, fpr y) {
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return FPR(x.v / y.v);
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}
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static inline void
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fpr_sqrt_avx2(double *t) {
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__m128d x;
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x = _mm_load1_pd(t);
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x = _mm_sqrt_pd(x);
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_mm_storel_pd(t, x);
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}
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static inline fpr
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fpr_sqrt(fpr x) {
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/*
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* We prefer not to have a dependency on libm when it can be
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* avoided. On x86, calling the sqrt() libm function inlines
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* the relevant opcode (fsqrt or sqrtsd, depending on whether
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* the 387 FPU or SSE2 is used for floating-point operations)
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* but then makes an optional call to the library function
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* for proper error handling, in case the operand is negative.
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*
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* To avoid this dependency, we use intrinsics or inline assembly
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* on recognized platforms:
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*
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* - If AVX2 is explicitly enabled, then we use SSE2 intrinsics.
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*
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* - On GCC/Clang with SSE maths, we use SSE2 intrinsics.
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*
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* - On GCC/Clang on i386, or MSVC on i386, we use inline assembly
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* to call the 387 FPU fsqrt opcode.
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*
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* - On GCC/Clang/XLC on PowerPC, we use inline assembly to call
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* the fsqrt opcode (Clang needs a special hack).
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*
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* - On GCC/Clang on ARM with hardware floating-point, we use
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* inline assembly to call the vqsrt.f64 opcode. Due to a
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* complex ecosystem of compilers and assembly syntaxes, we
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* have to call it "fsqrt" or "fsqrtd", depending on case.
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*
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* If the platform is not recognized, a call to the system
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* library function sqrt() is performed. On some compilers, this
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* may actually inline the relevant opcode, and call the library
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* function only when the input is invalid (e.g. negative);
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* Falcon never actually calls sqrt() on a negative value, but
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* the dependency to libm will still be there.
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*/
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fpr_sqrt_avx2(&x.v);
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return x;
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}
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static inline int
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fpr_lt(fpr x, fpr y) {
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return x.v < y.v;
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}
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static inline uint64_t
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fpr_expm_p63(fpr x, fpr ccs) {
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/*
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* Polynomial approximation of exp(-x) is taken from FACCT:
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* https://eprint.iacr.org/2018/1234
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* Specifically, values are extracted from the implementation
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* referenced from the FACCT article, and available at:
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* https://github.com/raykzhao/gaussian
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* Tests over more than 24 billions of random inputs in the
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* 0..log(2) range have never shown a deviation larger than
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* 2^(-50) from the true mathematical value.
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*/
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/*
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* AVX2 implementation uses more operations than Horner's method,
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* but with a lower expression tree depth. This helps because
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* additions and multiplications have a latency of 4 cycles on
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* a Skylake, but the CPU can issue two of them per cycle.
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*/
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static const union {
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double d[12];
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__m256d v[3];
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} c = {
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{
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0.999999999999994892974086724280,
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0.500000000000019206858326015208,
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0.166666666666984014666397229121,
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0.041666666666110491190622155955,
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0.008333333327800835146903501993,
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0.001388888894063186997887560103,
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0.000198412739277311890541063977,
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0.000024801566833585381209939524,
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0.000002755586350219122514855659,
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0.000000275607356160477811864927,
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0.000000025299506379442070029551,
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0.000000002073772366009083061987
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}
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};
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double d1, d2, d4, d8, y;
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__m256d d14, d58, d9c;
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d1 = -x.v;
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d2 = d1 * d1;
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d4 = d2 * d2;
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d8 = d4 * d4;
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d14 = _mm256_set_pd(d4, d2 * d1, d2, d1);
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d58 = _mm256_mul_pd(d14, _mm256_set1_pd(d4));
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d9c = _mm256_mul_pd(d14, _mm256_set1_pd(d8));
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d14 = _mm256_mul_pd(d14, _mm256_loadu_pd(&c.d[0]));
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d58 = FMADD(d58, _mm256_loadu_pd(&c.d[4]), d14);
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d9c = FMADD(d9c, _mm256_loadu_pd(&c.d[8]), d58);
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d9c = _mm256_hadd_pd(d9c, d9c);
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y = 1.0 + _mm_cvtsd_f64(_mm256_castpd256_pd128(d9c)) // _mm256_cvtsd_f64(d9c)
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+ _mm_cvtsd_f64(_mm256_extractf128_pd(d9c, 1));
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y *= ccs.v;
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/*
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* Final conversion goes through int64_t first, because that's what
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* the underlying opcode (vcvttsd2si) will do, and we know that the
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* result will fit, since x >= 0 and ccs < 1. If we did the
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* conversion directly to uint64_t, then the compiler would add some
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* extra code to cover the case of a source value of 2^63 or more,
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* and though the alternate path would never be exercised, the
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* extra comparison would cost us some cycles.
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*/
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return (uint64_t)(int64_t)(y * fpr_ptwo63.v);
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}
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#define fpr_gm_tab PQCLEAN_FALCON512_AVX2_fpr_gm_tab
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extern const fpr fpr_gm_tab[];
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#define fpr_p2_tab PQCLEAN_FALCON512_AVX2_fpr_p2_tab
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extern const fpr fpr_p2_tab[];
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/* ====================================================================== */
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#endif
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