# Comparison simplifications
(('inot', ('flt', a, b)), ('fge', a, b)),
(('inot', ('fge', a, b)), ('flt', a, b)),
+ (('inot', ('feq', a, b)), ('fne', a, b)),
+ (('inot', ('fne', a, b)), ('feq', a, b)),
(('inot', ('ilt', a, b)), ('ige', a, b)),
(('inot', ('ige', a, b)), ('ilt', a, b)),
+ (('inot', ('ieq', a, b)), ('ine', a, b)),
+ (('inot', ('ine', a, b)), ('ieq', a, b)),
(('fge', ('fneg', ('fabs', a)), 0.0), ('feq', a, 0.0)),
(('bcsel', ('flt', a, b), a, b), ('fmin', a, b)),
(('bcsel', ('flt', a, b), b, a), ('fmax', a, b)),
(('bcsel', ('inot', 'a@bool'), b, c), ('bcsel', a, c, b)),
(('bcsel', a, ('bcsel', a, b, c), d), ('bcsel', a, b, d)),
+ (('fmin', a, a), a),
+ (('fmax', a, a), a),
+ (('imin', a, a), a),
+ (('imax', a, a), a),
+ (('umin', a, a), a),
+ (('umax', a, a), a),
(('fmin', ('fmax', a, 0.0), 1.0), ('fsat', a), '!options->lower_fsat'),
+ (('fmax', ('fmin', a, 1.0), 0.0), ('fsat', a), '!options->lower_fsat'),
(('fsat', a), ('fmin', ('fmax', a, 0.0), 1.0), 'options->lower_fsat'),
(('fsat', ('fsat', a)), ('fsat', a)),
(('fmin', ('fmax', ('fmin', ('fmax', a, 0.0), 1.0), 0.0), 1.0), ('fmin', ('fmax', a, 0.0), 1.0)),
(('ior', ('flt', a, b), ('flt', a, c)), ('flt', a, ('fmax', b, c))),
+ (('ior', ('flt', a, c), ('flt', b, c)), ('flt', ('fmin', a, b), c)),
(('ior', ('fge', a, b), ('fge', a, c)), ('fge', a, ('fmin', b, c))),
+ (('ior', ('fge', a, c), ('fge', b, c)), ('fge', ('fmax', a, b), c)),
(('slt', a, b), ('b2f', ('flt', a, b)), 'options->lower_scmp'),
(('sge', a, b), ('b2f', ('fge', a, b)), 'options->lower_scmp'),
(('seq', a, b), ('b2f', ('feq', a, b)), 'options->lower_scmp'),
(('ushr', a, 0), a),
# Exponential/logarithmic identities
(('fexp2', ('flog2', a)), a), # 2^lg2(a) = a
- (('fexp', ('flog', a)), a), # e^ln(a) = a
(('flog2', ('fexp2', a)), a), # lg2(2^a) = a
- (('flog', ('fexp', a)), a), # ln(e^a) = a
(('fpow', a, b), ('fexp2', ('fmul', ('flog2', a), b)), 'options->lower_fpow'), # a^b = 2^(lg2(a)*b)
(('fexp2', ('fmul', ('flog2', a), b)), ('fpow', a, b), '!options->lower_fpow'), # 2^(lg2(a)*b) = a^b
- (('fexp', ('fmul', ('flog', a), b)), ('fpow', a, b), '!options->lower_fpow'), # e^(ln(a)*b) = a^b
(('fpow', a, 1.0), a),
(('fpow', a, 2.0), ('fmul', a, a)),
(('fpow', a, 4.0), ('fmul', ('fmul', a, a), ('fmul', a, a))),
(('fpow', 2.0, a), ('fexp2', a)),
+ (('fpow', ('fpow', a, 2.2), 0.454545), a),
+ (('fpow', ('fabs', ('fpow', a, 2.2)), 0.454545), ('fabs', a)),
(('fsqrt', ('fexp2', a)), ('fexp2', ('fmul', 0.5, a))),
- (('fsqrt', ('fexp', a)), ('fexp', ('fmul', 0.5, a))),
(('frcp', ('fexp2', a)), ('fexp2', ('fneg', a))),
- (('frcp', ('fexp', a)), ('fexp', ('fneg', a))),
(('frsq', ('fexp2', a)), ('fexp2', ('fmul', -0.5, a))),
- (('frsq', ('fexp', a)), ('fexp', ('fmul', -0.5, a))),
(('flog2', ('fsqrt', a)), ('fmul', 0.5, ('flog2', a))),
- (('flog', ('fsqrt', a)), ('fmul', 0.5, ('flog', a))),
(('flog2', ('frcp', a)), ('fneg', ('flog2', a))),
- (('flog', ('frcp', a)), ('fneg', ('flog', a))),
(('flog2', ('frsq', a)), ('fmul', -0.5, ('flog2', a))),
- (('flog', ('frsq', a)), ('fmul', -0.5, ('flog', a))),
(('flog2', ('fpow', a, b)), ('fmul', b, ('flog2', a))),
- (('flog', ('fpow', a, b)), ('fmul', b, ('flog', a))),
(('fadd', ('flog2', a), ('flog2', b)), ('flog2', ('fmul', a, b))),
- (('fadd', ('flog', a), ('flog', b)), ('flog', ('fmul', a, b))),
(('fadd', ('flog2', a), ('fneg', ('flog2', b))), ('flog2', ('fdiv', a, b))),
- (('fadd', ('flog', a), ('fneg', ('flog', b))), ('flog', ('fdiv', a, b))),
(('fmul', ('fexp2', a), ('fexp2', b)), ('fexp2', ('fadd', a, b))),
- (('fmul', ('fexp', a), ('fexp', b)), ('fexp', ('fadd', a, b))),
# Division and reciprocal
(('fdiv', 1.0, a), ('frcp', a)),
(('frcp', ('frcp', a)), a),