poly1305_ieee754.c

/*
 * Copyright 2016-2018 The OpenSSL Project Authors. All Rights Reserved.
 *
 * Licensed under the OpenSSL license (the "License").  You may not use
 * this file except in compliance with the License.  You can obtain a copy
 * in the file LICENSE in the source distribution or at
 * https://www.openssl.org/source/license.html
 */

/*
 * This module is meant to be used as template for non-x87 floating-
 * point assembly modules. The template itself is x86_64-specific
 * though, as it was debugged on x86_64. So that implementor would
 * have to recognize platform-specific parts, UxTOy and inline asm,
 * and act accordingly.
 *
 * Huh? x86_64-specific code as template for non-x87? Note seven, which
 * is not a typo, but reference to 80-bit precision. This module on the
 * other hand relies on 64-bit precision operations, which are default
 * for x86_64 code. And since we are at it, just for sense of it,
 * large-block performance in cycles per processed byte for *this* code
 * is:
 *                      gcc-4.8         icc-15.0        clang-3.4(*)
 *
 * Westmere             4.96            5.09            4.37
 * Sandy Bridge         4.95            4.90            4.17
 * Haswell              4.92            4.87            3.78
 * Bulldozer            4.67            4.49            4.68
 * VIA Nano             7.07            7.05            5.98
 * Silvermont           10.6            9.61            12.6
 *
 * (*)  clang managed to discover parallelism and deployed SIMD;
 *
 * And for range of other platforms with unspecified gcc versions:
 *
 * Freescale e300       12.5
 * PPC74x0              10.8
 * POWER6               4.92
 * POWER7               4.50
 * POWER8               4.10
 *
 * z10                  11.2
 * z196+                7.30
 *
 * UltraSPARC III       16.0
 * SPARC T4             16.1
 */

#if !(defined(__GNUC__) && __GNUC__>=2)
# error "this is gcc-specific template"
#endif

#include <stdlib.h>

typedef unsigned char u8;
typedef unsigned int u32;
typedef unsigned long long u64;
typedef union { double d; u64 u; } elem64;

#define TWO(p)          ((double)(1ULL<<(p)))
#define TWO0            TWO(0)
#define TWO32           TWO(32)
#define TWO64           (TWO32*TWO(32))
#define TWO96           (TWO64*TWO(32))
#define TWO130          (TWO96*TWO(34))

#define EXP(p)          ((1023ULL+(p))<<52)

#if defined(__x86_64__) || (defined(__PPC__) && defined(__LITTLE_ENDIAN__))
# define U8TOU32(p)     (*(const u32 *)(p))
# define U32TO8(p,v)    (*(u32 *)(p) = (v))
#elif defined(__PPC__)
# define U8TOU32(p)     ({u32 ret; asm ("lwbrx	%0,0,%1":"=r"(ret):"b"(p)); ret; })
# define U32TO8(p,v)    asm ("stwbrx %0,0,%1"::"r"(v),"b"(p):"memory")
#elif defined(__s390x__)
# define U8TOU32(p)     ({u32 ret; asm ("lrv	%0,%1":"=d"(ret):"m"(*(u32 *)(p))); ret; })
# define U32TO8(p,v)    asm ("strv	%1,%0":"=m"(*(u32 *)(p)):"d"(v))
#endif

#ifndef U8TOU32
# define U8TOU32(p)     ((u32)(p)[0]     | (u32)(p)[1]<<8 |     \
                         (u32)(p)[2]<<16 | (u32)(p)[3]<<24  )
#endif
#ifndef U32TO8
# define U32TO8(p,v)    ((p)[0] = (u8)(v),       (p)[1] = (u8)((v)>>8), \
                         (p)[2] = (u8)((v)>>16), (p)[3] = (u8)((v)>>24) )
#endif

typedef struct {
    elem64 h[4];
    double r[8];
    double s[6];
} poly1305_internal;

/* "round toward zero (truncate), mask all exceptions" */
#if defined(__x86_64__)
static const u32 mxcsr = 0x7f80;
#elif defined(__PPC__)
static const u64 one = 1;
#elif defined(__s390x__)
static const u32 fpc = 1;
#elif defined(__sparc__)
static const u64 fsr = 1ULL<<30;
#elif defined(__mips__)
static const u32 fcsr = 1;
#else
#error "unrecognized platform"
#endif

int poly1305_init(void *ctx, const unsigned char key[16])
{
    poly1305_internal *st = (poly1305_internal *) ctx;
    elem64 r0, r1, r2, r3;

    /* h = 0, biased */
#if 0
    st->h[0].d = TWO(52)*TWO0;
    st->h[1].d = TWO(52)*TWO32;
    st->h[2].d = TWO(52)*TWO64;
    st->h[3].d = TWO(52)*TWO96;
#else
    st->h[0].u = EXP(52+0);
    st->h[1].u = EXP(52+32);
    st->h[2].u = EXP(52+64);
    st->h[3].u = EXP(52+96);
#endif

    if (key) {
        /*
         * set "truncate" rounding mode
         */
#if defined(__x86_64__)
        u32 mxcsr_orig;

        asm volatile ("stmxcsr	%0":"=m"(mxcsr_orig));
        asm volatile ("ldmxcsr	%0"::"m"(mxcsr));
#elif defined(__PPC__)
        double fpscr_orig, fpscr = *(double *)&one;

        asm volatile ("mffs	%0":"=f"(fpscr_orig));
        asm volatile ("mtfsf	255,%0"::"f"(fpscr));
#elif defined(__s390x__)
        u32 fpc_orig;

        asm volatile ("stfpc	%0":"=m"(fpc_orig));
        asm volatile ("lfpc	%0"::"m"(fpc));
#elif defined(__sparc__)
        u64 fsr_orig;

        asm volatile ("stx	%%fsr,%0":"=m"(fsr_orig));
        asm volatile ("ldx	%0,%%fsr"::"m"(fsr));
#elif defined(__mips__)
        u32 fcsr_orig;

        asm volatile ("cfc1	%0,$31":"=r"(fcsr_orig));
        asm volatile ("ctc1	%0,$31"::"r"(fcsr));
#endif

        /* r &= 0xffffffc0ffffffc0ffffffc0fffffff */
        r0.u = EXP(52+0)  | (U8TOU32(&key[0])  & 0x0fffffff);
        r1.u = EXP(52+32) | (U8TOU32(&key[4])  & 0x0ffffffc);
        r2.u = EXP(52+64) | (U8TOU32(&key[8])  & 0x0ffffffc);
        r3.u = EXP(52+96) | (U8TOU32(&key[12]) & 0x0ffffffc);

        st->r[0] = r0.d - TWO(52)*TWO0;
        st->r[2] = r1.d - TWO(52)*TWO32;
        st->r[4] = r2.d - TWO(52)*TWO64;
        st->r[6] = r3.d - TWO(52)*TWO96;

        st->s[0] = st->r[2] * (5.0/TWO130);
        st->s[2] = st->r[4] * (5.0/TWO130);
        st->s[4] = st->r[6] * (5.0/TWO130);

        /*
         * base 2^32 -> base 2^16
         */
        st->r[1] = (st->r[0] + TWO(52)*TWO(16)*TWO0) -
                               TWO(52)*TWO(16)*TWO0;
        st->r[0] -= st->r[1];

        st->r[3] = (st->r[2] + TWO(52)*TWO(16)*TWO32) -
                               TWO(52)*TWO(16)*TWO32;
        st->r[2] -= st->r[3];

        st->r[5] = (st->r[4] + TWO(52)*TWO(16)*TWO64) -
                               TWO(52)*TWO(16)*TWO64;
        st->r[4] -= st->r[5];

        st->r[7] = (st->r[6] + TWO(52)*TWO(16)*TWO96) -
                               TWO(52)*TWO(16)*TWO96;
        st->r[6] -= st->r[7];

        st->s[1] = (st->s[0] + TWO(52)*TWO(16)*TWO0/TWO96) -
                               TWO(52)*TWO(16)*TWO0/TWO96;
        st->s[0] -= st->s[1];

        st->s[3] = (st->s[2] + TWO(52)*TWO(16)*TWO32/TWO96) -
                               TWO(52)*TWO(16)*TWO32/TWO96;
        st->s[2] -= st->s[3];

        st->s[5] = (st->s[4] + TWO(52)*TWO(16)*TWO64/TWO96) -
                               TWO(52)*TWO(16)*TWO64/TWO96;
        st->s[4] -= st->s[5];

        /*
         * restore original FPU control register
         */
#if defined(__x86_64__)
        asm volatile ("ldmxcsr	%0"::"m"(mxcsr_orig));
#elif defined(__PPC__)
        asm volatile ("mtfsf	255,%0"::"f"(fpscr_orig));
#elif defined(__s390x__)
        asm volatile ("lfpc	%0"::"m"(fpc_orig));
#elif defined(__sparc__)
        asm volatile ("ldx	%0,%%fsr"::"m"(fsr_orig));
#elif defined(__mips__)
        asm volatile ("ctc1	%0,$31"::"r"(fcsr_orig));
#endif
    }

    return 0;
}

void poly1305_blocks(void *ctx, const unsigned char *inp, size_t len,
                     int padbit)
{
    poly1305_internal *st = (poly1305_internal *)ctx;
    elem64 in0, in1, in2, in3;
    u64 pad = (u64)padbit<<32;

    double x0, x1, x2, x3;
    double h0lo, h0hi, h1lo, h1hi, h2lo, h2hi, h3lo, h3hi;
    double c0lo, c0hi, c1lo, c1hi, c2lo, c2hi, c3lo, c3hi;

    const double r0lo = st->r[0];
    const double r0hi = st->r[1];
    const double r1lo = st->r[2];
    const double r1hi = st->r[3];
    const double r2lo = st->r[4];
    const double r2hi = st->r[5];
    const double r3lo = st->r[6];
    const double r3hi = st->r[7];

    const double s1lo = st->s[0];
    const double s1hi = st->s[1];
    const double s2lo = st->s[2];
    const double s2hi = st->s[3];
    const double s3lo = st->s[4];
    const double s3hi = st->s[5];

    /*
     * set "truncate" rounding mode
     */
#if defined(__x86_64__)
    u32 mxcsr_orig;

    asm volatile ("stmxcsr	%0":"=m"(mxcsr_orig));
    asm volatile ("ldmxcsr	%0"::"m"(mxcsr));
#elif defined(__PPC__)
    double fpscr_orig, fpscr = *(double *)&one;

    asm volatile ("mffs		%0":"=f"(fpscr_orig));
    asm volatile ("mtfsf	255,%0"::"f"(fpscr));
#elif defined(__s390x__)
    u32 fpc_orig;

    asm volatile ("stfpc	%0":"=m"(fpc_orig));
    asm volatile ("lfpc		%0"::"m"(fpc));
#elif defined(__sparc__)
    u64 fsr_orig;

    asm volatile ("stx		%%fsr,%0":"=m"(fsr_orig));
    asm volatile ("ldx		%0,%%fsr"::"m"(fsr));
#elif defined(__mips__)
    u32 fcsr_orig;

    asm volatile ("cfc1		%0,$31":"=r"(fcsr_orig));
    asm volatile ("ctc1		%0,$31"::"r"(fcsr));
#endif

    /*
     * load base 2^32 and de-bias
     */
    h0lo = st->h[0].d - TWO(52)*TWO0;
    h1lo = st->h[1].d - TWO(52)*TWO32;
    h2lo = st->h[2].d - TWO(52)*TWO64;
    h3lo = st->h[3].d - TWO(52)*TWO96;

#ifdef __clang__
    h0hi = 0;
    h1hi = 0;
    h2hi = 0;
    h3hi = 0;
#else
    in0.u = EXP(52+0)  | U8TOU32(&inp[0]);
    in1.u = EXP(52+32) | U8TOU32(&inp[4]);
    in2.u = EXP(52+64) | U8TOU32(&inp[8]);
    in3.u = EXP(52+96) | U8TOU32(&inp[12]) | pad;

    x0 = in0.d - TWO(52)*TWO0;
    x1 = in1.d - TWO(52)*TWO32;
    x2 = in2.d - TWO(52)*TWO64;
    x3 = in3.d - TWO(52)*TWO96;

    x0 += h0lo;
    x1 += h1lo;
    x2 += h2lo;
    x3 += h3lo;

    goto fast_entry;
#endif

    do {
        in0.u = EXP(52+0)  | U8TOU32(&inp[0]);
        in1.u = EXP(52+32) | U8TOU32(&inp[4]);
        in2.u = EXP(52+64) | U8TOU32(&inp[8]);
        in3.u = EXP(52+96) | U8TOU32(&inp[12]) | pad;

        x0 = in0.d - TWO(52)*TWO0;
        x1 = in1.d - TWO(52)*TWO32;
        x2 = in2.d - TWO(52)*TWO64;
        x3 = in3.d - TWO(52)*TWO96;

        /*
         * note that there are multiple ways to accumulate input, e.g.
         * one can as well accumulate to h0lo-h1lo-h1hi-h2hi...
         */
        h0lo += x0;
        h0hi += x1;
        h2lo += x2;
        h2hi += x3;

        /*
         * carries that cross 32n-bit (and 130-bit) boundaries
         */
        c0lo = (h0lo + TWO(52)*TWO32)  - TWO(52)*TWO32;
        c1lo = (h1lo + TWO(52)*TWO64)  - TWO(52)*TWO64;
        c2lo = (h2lo + TWO(52)*TWO96)  - TWO(52)*TWO96;
        c3lo = (h3lo + TWO(52)*TWO130) - TWO(52)*TWO130;

        c0hi = (h0hi + TWO(52)*TWO32)  - TWO(52)*TWO32;
        c1hi = (h1hi + TWO(52)*TWO64)  - TWO(52)*TWO64;
        c2hi = (h2hi + TWO(52)*TWO96)  - TWO(52)*TWO96;
        c3hi = (h3hi + TWO(52)*TWO130) - TWO(52)*TWO130;

        /*
         * base 2^48 -> base 2^32 with last reduction step
         */
        x1 =  (h1lo - c1lo) + c0lo;
        x2 =  (h2lo - c2lo) + c1lo;
        x3 =  (h3lo - c3lo) + c2lo;
        x0 =  (h0lo - c0lo) + c3lo * (5.0/TWO130);

        x1 += (h1hi - c1hi) + c0hi;
        x2 += (h2hi - c2hi) + c1hi;
        x3 += (h3hi - c3hi) + c2hi;
        x0 += (h0hi - c0hi) + c3hi * (5.0/TWO130);

#ifndef __clang__
    fast_entry:
#endif
        /*
         * base 2^32 * base 2^16 = base 2^48
         */
        h0lo = s3lo * x1 + s2lo * x2 + s1lo * x3 + r0lo * x0;
        h1lo = r0lo * x1 + s3lo * x2 + s2lo * x3 + r1lo * x0;
        h2lo = r1lo * x1 + r0lo * x2 + s3lo * x3 + r2lo * x0;
        h3lo = r2lo * x1 + r1lo * x2 + r0lo * x3 + r3lo * x0;

        h0hi = s3hi * x1 + s2hi * x2 + s1hi * x3 + r0hi * x0;
        h1hi = r0hi * x1 + s3hi * x2 + s2hi * x3 + r1hi * x0;
        h2hi = r1hi * x1 + r0hi * x2 + s3hi * x3 + r2hi * x0;
        h3hi = r2hi * x1 + r1hi * x2 + r0hi * x3 + r3hi * x0;

        inp += 16;
        len -= 16;

    } while (len >= 16);

    /*
     * carries that cross 32n-bit (and 130-bit) boundaries
     */
    c0lo = (h0lo + TWO(52)*TWO32)  - TWO(52)*TWO32;
    c1lo = (h1lo + TWO(52)*TWO64)  - TWO(52)*TWO64;
    c2lo = (h2lo + TWO(52)*TWO96)  - TWO(52)*TWO96;
    c3lo = (h3lo + TWO(52)*TWO130) - TWO(52)*TWO130;

    c0hi = (h0hi + TWO(52)*TWO32)  - TWO(52)*TWO32;
    c1hi = (h1hi + TWO(52)*TWO64)  - TWO(52)*TWO64;
    c2hi = (h2hi + TWO(52)*TWO96)  - TWO(52)*TWO96;
    c3hi = (h3hi + TWO(52)*TWO130) - TWO(52)*TWO130;

    /*
     * base 2^48 -> base 2^32 with last reduction step
     */
    x1 =  (h1lo - c1lo) + c0lo;
    x2 =  (h2lo - c2lo) + c1lo;
    x3 =  (h3lo - c3lo) + c2lo;
    x0 =  (h0lo - c0lo) + c3lo * (5.0/TWO130);

    x1 += (h1hi - c1hi) + c0hi;
    x2 += (h2hi - c2hi) + c1hi;
    x3 += (h3hi - c3hi) + c2hi;
    x0 += (h0hi - c0hi) + c3hi * (5.0/TWO130);

    /*
     * store base 2^32, with bias
     */
    st->h[1].d = x1 + TWO(52)*TWO32;
    st->h[2].d = x2 + TWO(52)*TWO64;
    st->h[3].d = x3 + TWO(52)*TWO96;
    st->h[0].d = x0 + TWO(52)*TWO0;

    /*
     * restore original FPU control register
     */
#if defined(__x86_64__)
    asm volatile ("ldmxcsr	%0"::"m"(mxcsr_orig));
#elif defined(__PPC__)
    asm volatile ("mtfsf	255,%0"::"f"(fpscr_orig));
#elif defined(__s390x__)
    asm volatile ("lfpc		%0"::"m"(fpc_orig));
#elif defined(__sparc__)
    asm volatile ("ldx		%0,%%fsr"::"m"(fsr_orig));
#elif defined(__mips__)
    asm volatile ("ctc1		%0,$31"::"r"(fcsr_orig));
#endif
}

void poly1305_emit(void *ctx, unsigned char mac[16], const u32 nonce[4])
{
    poly1305_internal *st = (poly1305_internal *) ctx;
    u64 h0, h1, h2, h3, h4;
    u32 g0, g1, g2, g3, g4;
    u64 t;
    u32 mask;

    /*
     * thanks to bias masking exponent gives integer result
     */
    h0 = st->h[0].u & 0x000fffffffffffffULL;
    h1 = st->h[1].u & 0x000fffffffffffffULL;
    h2 = st->h[2].u & 0x000fffffffffffffULL;
    h3 = st->h[3].u & 0x000fffffffffffffULL;

    /*
     * can be partially reduced, so reduce...
     */
    h4 = h3>>32; h3 &= 0xffffffffU;
    g4 = h4&-4;
    h4 &= 3;
    g4 += g4>>2;

    h0 += g4;
    h1 += h0>>32; h0 &= 0xffffffffU;
    h2 += h1>>32; h1 &= 0xffffffffU;
    h3 += h2>>32; h2 &= 0xffffffffU;

    /* compute h + -p */
    g0 = (u32)(t = h0 + 5);
    g1 = (u32)(t = h1 + (t >> 32));
    g2 = (u32)(t = h2 + (t >> 32));
    g3 = (u32)(t = h3 + (t >> 32));
    g4 = h4 + (u32)(t >> 32);

    /* if there was carry, select g0-g3 */
    mask = 0 - (g4 >> 2);
    g0 &= mask;
    g1 &= mask;
    g2 &= mask;
    g3 &= mask;
    mask = ~mask;
    g0 |= (h0 & mask);
    g1 |= (h1 & mask);
    g2 |= (h2 & mask);
    g3 |= (h3 & mask);

    /* mac = (h + nonce) % (2^128) */
    g0 = (u32)(t = (u64)g0 + nonce[0]);
    g1 = (u32)(t = (u64)g1 + (t >> 32) + nonce[1]);
    g2 = (u32)(t = (u64)g2 + (t >> 32) + nonce[2]);
    g3 = (u32)(t = (u64)g3 + (t >> 32) + nonce[3]);

    U32TO8(mac + 0, g0);
    U32TO8(mac + 4, g1);
    U32TO8(mac + 8, g2);
    U32TO8(mac + 12, g3);
}